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Minimum watershed model structure for representation of runoff processes Micovic, Zoran 2005

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M I N I M U M WATERSHED M O D E L STRUCTURE FOR REPRESENTATION OF RUNOFF PROCESSES by ZORAN MICOV1C B.Sc, The University of Novi Sad, 1994 M.A.Sc, The University of British Columbia, 1998 A THESIS SUBMITED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES CIVIL ENGINEERING THE UNIVERSITY OF BRITISH COLUMBIA April 2005 © Zoran Micovic, 2005 ABSTRACT The aim of this study is to examine what degree of complexity in watershed model structure is required to obtain realistic representation of the runoff processes. Spatial and temporal distribution of hydrological processes are investigated, especially linear and non-linear algorithms and the sub-division of runoff time response according to the soil moisture status of the watershed. To carry out this investigation, hydrologic models, with structures of increasing complexity, were constructed and their capability to simulate runoff from a watershed was evaluated. The initial evaluation, with the point input meteorological data, was performed on a large (1150 km2) snow-dominated watershed and the findings were then verified on a smaller (188 km2) rain-dominated watershed. The continuous long term runoff simulations were performed for both watersheds using daily time steps. The results indicated that, for both types of watersheds, the modelling capability increased significantly if the following elements were introduced: at least two altitude zones; fast and slow runoff components, determined by soil moisture control of watershed impermeable fraction; routing of each component through a linear reservoir system; and two land cover representations, namely treed and open areas, which influenced snowmelt process. Further increase in model complexity gave negligible improvement in Nash-Sutcliffe efficiency. The nature of the Nash-Sutcliffe coefficient of efficiency was tested with both real and synthetic data and it was shown theoretically and from model results that the efficiency would always be higher when calculated for a longer time period. The investigation of meteorological point input data focused on the influence of the location and number of stations. In terms of location, it was shown that a low elevation station was inferior to a high elevation station because it was less representative of the average watershed climate and ii required greater complexity in model structure to compensate for the unrepresentative climate input at low altitude. In terms of the number of meteorological stations, it was shown that using two stations, each representing an adequate portion of the watershed, improved runoff simulation. Further investigation of the role of non-linearity in model design was performed by modelling several of the largest historical storms on record using an hourly time step. It was discovered that certain parameters that appeared unimportant during the long term simulation had significant effect on the short-term extreme event model simulation. In addition, the simpler model structure that was proven satisfactory for the long term simulation was, in some cases, inferior to the slightly more complex model structure when focus was on extreme event simulation. Therefore, the results of this work indicated that, in the most cases, a reasonably simple watershed model structure would provide satisfactory representation of watershed behaviour. Such cases comprise long term runoff simulation from large and small, snow-dominated and rain-dominated watersheds as well as some extreme flood simulations. However there are occasions when this simple model structure is inadequate and extra model structure is required to model the effects of intense precipitation events. The overall conclusion is that relatively simple model structures are capable of giving good estimation of runoff from complex mountain watersheds, and there is no measurable gain from further increase of model complexity. iii TABLE OF CONTENTS ABSTRACT ii LIST OF TABLES ix LIST OF FIGURES xii LIST OF SYMBOLS xvii ACKNOWLEDGEMENTS xix 1. INTRODUCTION 1 1.1 General Introduction 1 1.2 Study Outline 8 2. LITERATURE REVIEW 10 2.1 Terminology and Types of Watershed Models 10 2.2 Constraints of the Distributed Watershed Models 12 2.3 Modelling Natural Watersheds - Practical Applications 17 2.4 Structure of Conceptual Watershed Models 19 2.5 Summary 27 iv 3 WATERSHED MODEL STRUCTURE 29 3.1 General Discussion 29 3.2 Proposed Model Structures 32 3.2.1 Model Structure #1 32 3.2.2 Model Structure #2 32 3.2.3 Model Structure #3 33 3.2.4 Model Structure #4 34 3.2.5 Model Structure #5 , 34 3.2.6 Model Structure #6 35 4 EVALUATION OF WATERSHED MODEL STRUCTURES ON A SNOW- 42 DOMINATED WATERSHED 4.1 Illecillewaet Watershed 42 4.1.1 General Information 42 4.1.2 Degree of Detail in Watershed Description 44 4.1.3 Input Data - Meteorological and Streamflow 46 4.2 Statistical Measures of Model Efficiency 48 4.2.1 Effects of Different Time Scales on the Coefficient of Efficiency 50 4.3 Single High-Altitude Meteorological Station as Input 54 4.3.1 Watershed Represented with Single Elevation Band 55 4.3.1.1 Test#l 56 4.3.1.2 Test #2 58 4.3.1.3 Test #3 59 v 4.3.1.4 Test #4 61 4.3.1.5 Test #5 64 4.3.1.6 Test #6 67 4.3.1.7 Test #7 69 4.3.1.8 Test #8 71 4.3.1.9 Test #9 71 4.3.1.10 Test #10 75 4.3.2 Watershed Represented with Two and Eight Elevation Bands 79 4.3.3 Comparison of Calculated Statistics 98 4.3.4 General Comments on Presented Results for Uncalibrated Model 99 4.3.4.1 Effects of Model Structure 99 4.3.4.2 Effects of the Number of Elevation Band 101 4.3.4.3 Concluding Remarks for Uncalibrated Model 107 4.3.5 Sensitivity Analysis 107 4.3.6 Model Calibration Results with a Single High-Altitude Station 125 4.3.6.1 Comments on Results of Model Calibration 141 4.4 Single Low-Altitude Meteorological Station as Input 142 4.4.1 Sensitivity Analysis 145 4.4.2 Model Calibration Results with a Single Low-Altitude Station 152 4.4.2.1 Comments on Results of Model Calibration 167 4.5 Two Meteorological Stations as Input 168 4.5.1 General Discussion 168 4.5.2 Model Calibration Results 171 vi 4.5.2.1 Comments on Results of Model Calibration 173 5 EVALUATION OF WATERSHED MODEL STRUCTURES ON A RAIN- 175 DOMINATED WATERSHED 5.1 Runoff Generating Mechanism 175 5.2 Coquitlam Watershed 177 5.2.1 General Information 177 5.2.2 Degree of Detail in Watershed Description 179 5.2.3 Input Data - Meteorological and Streamflow 181 5.3 Model Calibration Results 183 5.3.1 Comments on Results of Model Calibration 190 6. THE ROLE OF NON-LINEARITY IN WATERSHED MODELLING 192 6.1 Types of Non-Linearity in Watershed Behaviour 192 6.2 Modelling Extreme Events 194 6.2.1 Illecillewaet Results 196 6.2.2 Coquitlam Results 202 6.2.3 General Comments on Modelling of Extreme Events 209 6.3 Variable Source Area as Non-Linearity Concept 210 7. CONCLUSIONS AND RECOMMENDATIONS 215 7.1 Conclusions 215 7.1.1 Long-Term Simulation 216 vii 7.1.2 Extreme Event Simulation 221 7.1.3 Final Discussion 223 7.2 Recommendations 225 REFERENCES 227 APPENDIX A - Theoretical Investigation of Watershed Response and 234 Statistical Measures of Model Efficiency APPENDIX B - Detailed Statistics From Chapter 4 249 vin LIST OF TABLES 4-1 Illecillewaet watershed description (8 elevation bands) 45 4-2 Illecillewaet watershed description (2 elevation bands) 45 4-3 Illecillewaet watershed description (1 elevation band) 45 4-4 Observed flow at the watershed outlet (Illecillewaet River at Greely) 47 4-5 Calculated statistics of Test #4 without calibration (Mt. Fidelity; 1 elevation band). 62 4-6 Annual statistics of Test #5 without calibration (Mt. Fidelity; 1 elevation band) 65 4-7 Annual statistics of Test #6 without calibration (Mt. Fidelity; 1 elevation band) 67 4-8 Annual statistics of Test #7 without calibration (Mt. Fidelity; 1 elevation band) 69 4-9 Annual statistics of Test #8 without calibration (Mt. Fidelity; 1 elevation band) 71 4-10 Annual statistics of Test #9 without calibration (Mt. Fidelity; 1 elevation band) 75 4-11 Annual statistics of Test #10 without calibration (Mt. Fidelity; 1 elevation band).... 76 4-12 List of parameters used in the tests (one meteorological station, one elevation band) 78 4-13 Comparison of model statistics achieved without calibration (Mt. Fidelity) 98 4-14 Parameter values before and after calibration in Test #1 (Mt. Fidelity) 126 4-15 Parameter values before and after calibration in Test #2 (Mt. Fidelity) 126 4-16 Parameter values before and after calibration in Test #3 (Mt. Fidelity) 126 4-17 Parameter values before and after calibration in Test #4 (Mt. Fidelity) 127 4-18 Parameter values before and after calibration in Test #5 (Mt. Fidelity) 127 4-19 Parameter values before and after calibration in Test #6 (Mt. Fidelity) 127 ix 4-20 Parameter values before and after calibration in Test #7 (Mt. Fidelity) 128 4-21 Parameter values before and after calibration in Test #8 (Mt. Fidelity) 128 4-22 Parameter values before and after calibration in Test #9 (Mt. Fidelity) 129 4-23 Parameter values before and after calibration in Test #10 (Mt. Fidelity) 129 4-24 Comparison of model statistics before and after calibration (Mt. Fidelity) 140 4-25 Parameter values before and after calibration in Test #1 (Revelstoke) 152 4-26 Parameter values before and after calibration in Test #2 (Revelstoke) 152 4-27 Parameter values before and after calibration in Test #3 (Revelstoke) 153 4-28 Parameter values before and after calibration in Test #4 (Revelstoke) 153 4-29 Parameter values before and after calibration in Test #5 (Revelstoke) 153 4-30 Parameter values before and after calibration in Test #6 (Revelstoke) 154 4-31 Parameter values before and after calibration in Test #7 (Revelstoke) 154 4-32 Parameter values before and after calibration in Test #8 (Revelstoke) 154 4-33 Parameter values before and after calibration in Test #9 (Revelstoke) 155 4-34 Parameter values before and after calibration in Test #10 (Revelstoke) 155 4-35 Comparison of model statistics before and after calibration (Revelstoke) 166 4-36 Coefficient of efficiency (27-year average) before and after calibration 168 4-37 Parameter values for one and two input stations in Test #9 (2 elevation bands) 171 4-38 Parameter values for one and two input stations in Test #9 (8 elevation bands) 171 4- 39 Model statistics for single and multiple input stations (Test #9) 172 5- 1 Coquitlam Lake Reservoir daily inflows (1954-1998) 179 5-2 Coquitlam watershed description (11 elevation bands) 180 x 5-3 Coquitlam watershed description (2 elevation bands) 180 5-4 Coquitlam watershed description (1 elevation band) 180 5-5 Parameter values before and after calibration in Test #6 (Coquitlam) 184 5-6 Parameter values before and after calibration in Test #9 (Coquitlam) 184 5-7 Model statistics before and after calibration for Test #6 (Coquitlam) 189 5- 8 Model statistics before and after calibration for Test #9 (Coquitlam) 189 6- 1 Historical floods at Coquitlam and Illecillewaet watersheds 195 6-2 Parameter values before and after calibration in Test #6 196 6-3 Parameter values before and after calibration in Test #9 196 6-4 IMPA modifications in the model without VSA concept - Coquitlam watershed .... 211 A - l Inflow and Outflow from Rainfall #1 239 A-2 Inflow and Outflow from Rainfall #2 239 A-3 Inflow and Outflow from Rainfall #1 and Rainfall #2 244 A-4 Coefficients of efficiency El, and correlation p, for the routing time constant K=l .. 246 A-5 Coefficients of efficiency El, and correlation p, for the routing time constant K=2 .. 248 xi LIST OF FIGURES 3-1 Diagram of model structure # 1 36 3-2 Diagram of model structure #2 37 3-3 Diagram of model structure #3 38 3-4 Diagram of model structure #4 39 3-5 Diagram of model structure #5 40 3- 6 Diagram of model structure #6 41 4- 1 Illecillewaet watershed 43 4-2 Different scenarios for a two-day rainfall event 51 4-3 Outflow hydrographs for rainfalls #1 and #2 52 4-4 Meteorological data recorded at Mt. Fidelity station (1875m) 55 4-5 Modelling Results of Test #1 (Mt. Fidelity; 1 elevation band) 57 4-5(a) Test #1 calibration results (Mt. Fidelity; 1 elevation band) 57 4-6 Modelling Results of Test #2 (Mt. Fidelity; 1 elevation band) 58 4-7 Modelling Results of Test #3 (Mt. Fidelity; 1 elevation band) 60 4-8 Modelling Results of Test #4 (Mt. Fidelity; 1 elevation band) 63 4-9 Modelling Results of Test #5 (Mt. Fidelity; 1 elevation band) 66 4-10 Modelling Results of Test #6 (Mt. Fidelity; 1 elevation band) 68 4-11 Modelling Results of Test #7 (Mt. Fidelity; 1 elevation band) 70 xii 4-12 Modelling Results of Test #8 (Mt. Fidelity; 1 elevation band) 72 4-13 Modelling Results of Test #9 (Mt. Fidelity; 1 elevation band) 74 4-14 Modelling Results of Test #10 (Mt. Fidelity; 1 elevation band) 77 4-15 Test #1 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 80 4-16 Test #2 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 81 4-17 Test #3 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 82 4-18 Test #4 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 84 4-19 Test #5 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 85 4-20 Test #6 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 88 4-21 Test #7 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 90 4-22 Test #8 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 92 4-23 Test #9 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 94 4-24 Test #10 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 95 4-25 Differences in simulated flow between 2-bands and 8-bands approaches 102 4-26 Sensitivity analysis for Test #6 with 1 elevation band 110 4-27 Sensitivity analysis for Test #6 with 2 elevation bands I l l 4-28 Sensitivity analysis for Test #6 with 8 elevation bands 112 4-29 Sensitivity analysis for Test #8 with 1 elevation band 113 4-30 Sensitivity analysis for Test #8 with 2 elevation bands 114 4-31 Sensitivity analysis for Test #8 with 8 elevation bands 115 4-32 Sensitivity analysis for Test #9 with 1 elevation band 116 4-33 Sensitivity analysis for Test #9 with 2 elevation bands 117 4-34 Sensitivity analysis for Test #9 with 8 elevation bands 118 xiii 4-35 4-36 4-37 4-38 4-39 4-40 4-41 4-42 4-43 4-44 4-45 4-46 4-47 4-48 4-49 4-50 4-51 4-52 4-53 4-54 4-55 4-56 4-57 Sensitivity analysis for Test #10 with 1 elevation band 119 Sensitivity analysis for Test #10 with 2 elevation bands 120 Sensitivity analysis for Test #10 with 8 elevation bands 121 Sensitivity of the fast runoff time constant (FTK) (Test #9 with 2 elevation bands) 124 band, 2 bands, I I bands) (Mt. Fidelity) 130 band, 2 bands, I I bands) (Mt. Fidelity) 131 band, 2 bands, I i bands) (Mt. Fidelity) 132 band, 2 bands, I I bands) (Mt. Fidelity) 133 band, 2 bands, I I bands) (Mt. Fidelity) 134 band, 2 bands, I I bands) (Mt. Fidelity) 135 band, 2 bands, I I bands) (Mt. Fidelity) 136 band, 2 bands, \ I bands) (Mt. Fidelity) 137 band, 2 bands, \ ? bands) (Mt. Fidelity) 138 band, 2 bands, i I bands) (Mt. Fidelity) 139 Meteorological data recorded at Revelstoke station (443m) 144 Sensitivity analysis for Test #6 with 1 elevation band 145 Sensitivity analysis for Test #6 with 2 elevation bands 146 Sensitivity analysis for Test #6 with 8 elevation bands 147 Sensitivity analysis for Test #9 with 1 elevation band 148 Sensitivity analysis for Test #9 with 2 elevation bands 149 Sensitivity analysis for Test #9 with 8 elevation bands 150 Test #1 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 156 Test #2 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 157 xiv 4-58 Test #3 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 158 4-59 Test #4 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 159 4-60 Test #5 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 160 4-61 Test #6 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 161 4-62 Test #7 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 162 4-63 Test #8 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 163 4-64 Test #9 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 164 4- 65 Test #10 calibration results (top to bottom: 1 band, 2 bands, 8 bands)(Revelstoke) 165 5- 1 Coquitlam watershed 178 5-2 Averaged meteorological data used for Coquitlam watershed 182 5-3 Test #6 calibration results (top to bottom: 1 band, 2 bands, 11 bands) (Coquitlam) 185 5-4 Test #6 hydrographs before and after calibration (top to bottom: 1, 2 and 11 bands) 186 5-5 Test #9 calibration results (top to bottom: 1 band, 2 bands, 11 bands) (Coquitlam) 187 5- 6 Test #9 hydrographs before and after calibration (top to bottom: 1, 2 and 11 bands) 188 6- 1 Illecillewaet flood simulation using Tests #6 and #9 - before calibration 197 6-2 Illecillewaet flood simulation using Tests #6 and #9 - after calibration 197 6-3 Illecillewaet flood event simulation using 2 and 8 elevation bands 198 6-4 Illecillewaet flood simulation using Tests #6 (total runoff components) 201 6-5 Illecillewaet flood simulation using Tests #9 (total runoff components) 201 6-6 Coquitlam flood simulation using Tests #6 and #9 - Storm 1 (before calibration) .. 203 6-7 Coquitlam flood simulation using Tests #6 and #9 - Storm 1 (after calibration).... 203 xv 6-8 Coquitlam flood simulation using Tests #6 and #9 - Storm 2 (before calibration).. 204 6-9 Coquitlam flood simulation using Tests #6 and #9 - Storm 2 (after calibration).... 204 6-10 Coquitlam flood simulation using Tests #6 and #9 - Storm 3 (before calibration).. 205 6-11 Coquitlam flood simulation using Tests #6 and #9 - Storm 3 (after calibration).... 205 6-12 Coquitlam flood simulation using Tests #6 and #9 - Storm 4 (before calibration).. 206 6-13 Coquitlam flood simulation using Tests #6 and #9 - Storm 4 (after calibration).... 206 6-14 Coquitlam flood simulation using Tests #6 (total runoff components) 208 6-15 Coquitlam flood simulation using Tests #9 (total runoff components) 208 6-16 Coquitlam flood simulation using Test #9 without VSA concept - Storm 1 212 6-17 Coquitlam flood simulation using Test #9 without VSA concept - Storm 2 212 6-18 Coquitlam flood simulation using Test #9 without VSA concept - Storm 3... . . . . . . 213 6-19 Coquitlam flood simulation using Test #9 without VSA concept - Storm 4 213 A - l Different scenarios for a two-day rainfall event 235 A-2 Outflow hydrographs for rainfalls #1 and #2 240 A-3 Differences between coefficients of correlation and efficiency 243 A-4 Hydrographs resulting from Rainfall #1 (Q0bs) and Rainfall #2 (Qcai) for K=l 246 A-5 Hydrographs resulting from Rainfall #1 (Q0bs) and Rainfall #2 (Qcai) for K=l 247 xvi LIST OF SYMBOLS a = coefficient in Eq. 4.6 b = coefficient in Eq. 4.6 DZSH = deep zone share of total groundwater DZTK = deep-zone groundwater time constant D! = coefficient of determination El = coefficient of efficiency FTK = fast flow (surface runoff) routing time constant GTK = total groundwater time constant GWFR = groundwater fraction of water available for groundwater and interflow I = inflow into the reservoir IMPA = impermeable fraction of the watershed area ITK = interflow time constant K = storage time constant n = number of days for daily runs or hours for hourly runs O = outflow from the reservoir PERC = maximum percolation to groundwater Qobs = observed discharge Qcai = calculated discharge RREP = Precipitation adjustment factor for rain xvii s = variance S = storage SREP = Precipitation adjustment factor for snow / = time TREE = Forested fraction of the watershed area UGTK = Upper groundwater time constant SV = volume error p = coefficient of correlation xviii ACKNOWLEDGEMENTS I would like to express my sincere appreciation and gratitude to my research supervisor, Dr. Michael Quick, who had a very positive impact on my academic as well as personal attitude. I appreciate the assistance I have received from Mr. Edmond Yu in the computer works. 1 am also thankful to Dr. Barbara Lence, Dr. Rob Millar and Dr. Dan Moore for their comments and suggestions which improved the quality of this thesis. This research has been partly funded by the Natural Sciences and Engineering Research Council (NSERC) Graduate Scholarship. Financial assistance received from BC Hydro is much appreciated as well. Finally, I would like to thank my ladies, Mila, Natasa, Sandra and Kova for putting up with me all these years and Don Pigone for being my role model. xix CHAPTER 1 INTRODUCTION 1.1 General Introduction Watershed models, rainfall-runoff models, or computer models of watershed hydrology are some of the names used for the models that have been constructed to simulate the transformation of precipitation into runoff from a given watershed. These models have proved to be extremely useful and, thus, are widely used tools in hydrology. The watershed models range in their complexity from the simple, empirical models to the very complex models with extensive data requirements. The reasonable approach to watershed modelling seems to be some kind of a conceptual approach, where certain approximations are used to explain otherwise very complex hydrological behaviour of natural watersheds. This view is reinforced by the simple fact that watershed hydrographs appear to exhibit much less variety than watershed topography, land cover and soils, indicating that averaging and suppression of local detail is taking place at the watershed scale. Input data such as precipitation, temperature, snowpack, radiation, etc. is usually available only on a sparse network, and in mountainous areas can be very limited. Therefore, it is necessary to limit the demands on input data and to make the model parameterisation as scale independent as possible. This requires use of a number of model parameters that, despite having some physical basis and being effective on the watershed scale, are not measurable in the field. Because of this, the watershed models must be calibrated. Ideally, calibration would result in one unique set of 1 model parameters for a given watershed that would later be used for runoff simulation outside a calibration period. However, what if the calibration process results in several different parameter sets that yield equally good simulation? And what if these different parameter sets produce significantly different simulation results outside a calibration period, for example during Probable Maximum Flood (PMF) simulation? In this case, parameter uncertainty is contributing to the uncertainty of predicted PMF. The same argument can be used for other types of extreme conditions such as low flow simulation. The number of model parameters is dictated by model structure, so that more complex models have more parameters. One of the main goals of this study is to examine how various levels of complexity in model structure affect a model's ability to accurately simulate hydrological behaviour of a given watershed. The analysis will focus on the main processes to be represented by a watershed model, as well as on the significance of linear and non-linear approaches in representing these processes. The various degrees of watershed model complexity, reflected through the required number of model parameters and the extent of watershed physical description, will be investigated. Special attention will be paid to the dependence of the model complexity on the temporal resolution by experimenting with different computational time steps. The study will also examine the ways in which location and density of meteorological input data affect both the model structure and its ability to successfully simulate runoff process. In addition, the statistical measures of success such as coefficients of correlation and efficiency will be analysed to determine how good and sensitive they are, especially when applied to different time scales. To accomplish these goals, six model structures, with gradual increase in complexity from 1 to 6, will be introduced and their performance will be tested and compared on both snowmelt-dominated and rainfall-dominated watersheds. These tests will include experiments with 2 different degrees of detail in watershed physical description, different locations and densities of meteorological input data and different durations of continuous model simulations. The UBC Watershed Model (UBCWM) will be used as an experimental tool in this study. It is important to note that this is not intended to be a test/validation of UBC Watershed Model, but more of an exploration of different modelling assumptions. However, certain limitations of the UBCWM should be considered. First, its soil moisture sub-model is intended for the areas in which soil moisture deficits sufficient to cause transpiration restriction and heavy droughts are unlikely to occur, meaning that actual evapotranspiration is computed using a simple relationship with empirically determined potential evapotranspiration. This means that application of UBCWM in arid regions with significant evapotranspiration effects may not be too successful. Also, as input, the UBCWM uses point measurements of temperature and precipitation, which are spatially distributed in an attempt to match true precipitation distribution over the watershed. Generally, there are two types of distribution that could be applied in watershed modelling, spatial and temporal. Spatial distribution refers to the physical structure of the watershed, i.e., the degree of detail in watershed description. The degree of detail in watershed description can be quite limited, or it can be quite complex. For example, a more detailed division of a watershed could require a large number of small grid cells with extensive input data requirements for each cell such as slope, length of flow plane, Manning number, depression storage, plant root depth, total porosity, average suction, etc. This approach has limited applicability in practice due to lack of data available on such a fine resolution. In this study, the only spatial sub-division of a watershed will be into elevation zones, referred to as bands. Each band will be assumed to have uniform hydrologic characteristics. One has to decide on the number of elevation bands that a watershed will be divided into, land cover representation for each band etc. A pure spatially lumped 3 approach would assume the watershed to be a single area of constant elevation and land cover. This approach implies no spatial variation within the watershed of precipitation, vegetative cover, soils or topography. The extent to which this representation will be successful may depend on the runoff generating mechanism. For example, we may simulate rain-dominated watersheds with only a single zone, representing the total watershed area. This is referred to as a one elevation band model, whereas a watershed with a significant snow component will likely require division in more than one elevation band to properly simulate snowpack accumulation/depletion processes. In the latter case, a question is whether only two bands are sufficient or more elevation bands would assure better simulation, and if so, how much better? Regarding land cover representation, it is known that snow melts differently under different land cover conditions. Thus, hydrological common sense implies division according to land cover, which increases the number of model parameters. However, it is interesting to test how much this increase in complexity contributes to overall increase in model efficiency. Temporal distribution refers to the timing of components of total watershed runoff. After the initial precipitation input has been subjected to interception and evapotranspiration losses, the remaining water in the system is available to contribute to streamfiow at the watershed outlet. Whether it does so within minutes or days or years depends on many factors. For example, in the case of high-intensity rainfall exceeding the infiltration capacity of the soil, a significant amount of water will move directly over the surface to the channel network and hence to the watershed outlet in a very short time. On the other hand, low-intensity rainfall or snowmelt on gently sloping permeable soil will drain down through the soil strata and, after several months, emerge as base flow at the watershed outlet. Also, in the case of watersheds with shallow soils, there is a potential for development of saturated source areas. These different components of total watershed runoff can be recognised in the outflow hydrograph because of their characteristically 4 different time delay signatures, which can vary by an order of magnitude. The UBCWM, for example, allows for four runoff components, namely fast, medium, slow and very slow. It is debatable how many flow components should be modelled. One can argue that there are more than four runoff components, each of them with slightly different time delays, or perhaps that four components are too many. Other debatable issues are the priorities or rules which decide in what order the water is allocated to these different runoff components. Fast runoff from impermeable surfaces, or from infiltration limitation is clearly a first priority. However, there can be differences in priority when it comes to allocating water to the runoff component with medium time delay, usually called interflow. One option is to let infiltrated water percolate to the groundwater up to specified maximum percolation value. If there is still an excess of water input, the residual is assumed to become a medium speed runoff, or interflow. In this approach, the percolation of infiltrated water to groundwater is given priority over interflow. Another option is to first satisfy interflow demand and then let the remaining water percolate to the groundwater, or to satisfy both of these demands at the same time. Obviously, the second approach will result in much higher peak flows due to interflow time delay of several days as opposed to several months for the groundwater. In this study both options and their effects will be tested by modifying model structure and response mechanisms. Natural watersheds are believed to have non-linear behaviour and this assumption appears to be true for arid watersheds and for high runoff events in most watersheds. Therefore, there must be concepts implemented to account for watershed non-linearity such as the previously mentioned concept of limiting percolation to groundwater and allocating a portion of the runoff to interflow. The concept of limiting the infiltration rate to permeable soils may be important for modelling runoff from high-intensity rainfall, and this also accounts for watershed non-linearity. Another non-linearity representation is the so-called "variable source area" concept, where 5 permeable areas become essentially impermeable in the case of a large precipitation event. This i means that a fraction of the permeable area in the watershed is not a constant value, but changes as a function of soil moisture deficit, or precipitation intensity. Next, the concept of soil moisture accounting where an actual evapotranspiration rate is also computed as a function of soil moisture deficit, represents watershed non-linearity. Finally, the routing of the runoff components could be non-linear, further increasing model complexity. Al l non-linearity representations may contribute to more realistic runoff modelling, but not to an equal extent. Some non-linearities may be absolutely necessary while some may cause only minor improvements. To summarise, it is not possible to accurately model a complete hydrological system of a natural watershed. Simplifications have to be made. For example, the first and probably the most obvious simplification would be the concept of 100% surface runoff from the watershed with instantaneous response. This unrealistic concept represents a totally impermeable watershed in which precipitation input reaches the watershed outlet without any delay. We can move closer to reality by modelling some delay in watershed response. However, that implies introduction of additional parameters and an increase in model complexity. This increase in model complexity is obviously necessary, since we know that in reality much of the flow goes to long-term delay components such as groundwater. Clearly, we can keep adding complexity to the model through the introduction of additional processes and parameters, and keep improving representation of the watershed hydrological behaviour. At some point, this improvement becomes so small that it does not justify increase in model complexity and additional effort and input requirements associated with it. 6 Therefore, the fundamental question in watershed modelling, which will be investigated in this study, is what degree of distribution and complexity is required to obtain realistic representation of the runoff processes? Finally, it should be noted that input data, usually precipitation and temperatures, have at least an equal effect on model output as does the model structure. Generally, more distributed meteorological input should provide better model efficiency, all other factors being equal, because using more meteorological stations, yields a better estimate of the true precipitation over a given area. However, station density by itself does not guarantee good modelling results. Density in certain areas can be achieved by having many valley stations and no high altitude stations. Valley stations can be located in "micro-climate" areas and be somewhat unrepresentative of overall precipitation patterns of the watershed. For example, if two out of three meteorological stations available for modelling are not representative of the watershed climate, using all three stations for simulation may result in lower model efficiency than using one single but representative station. The runoff-generating mechanism also has an effect on the required density of meteorological input data. Snowpacks are likely to be more uniform over large areas, especially as they result from many storms during the winter period. Also, snowmelt is influenced by air temperature, which may be reasonably constant and uniform at a given altitude on a daily basis. This implies that watersheds that are dominated by snow generated runoff may require a lower density of meteorological data network than watersheds dominated by rainfall, which is less uniform. 7 1.2 Study Outline This thesis is divided into seven chapters. > Chapter 1 is an introduction and rationale for the study. > Chapter 2 offers a literature review on the types of watershed models and the advantages and shortcomings of each type. It also discusses practical applications of conceptual watershed models and their structure. > Proposed model structures with increasing complexity are described in Chapter 3. > In Chapter 4, these model structures are tested on a snow-dominated watershed. The following is the ordered 'step-by-step' sequence of the tests presented in Chapter 4: 1. Al l the model structures introduced in Chapter 3 are tested using daily computational time steps and input data from a single high-altitude meteorological station, without any model calibration. The continuous long-term (28 year) simulation is performed as follows: • the watershed is first represented as a single elevation band, i.e., spatially lumped approach. • after that, the watershed is represented with two and eight elevation bands respectively to examine whether there are any potential improvements in the simulation results, compared to the spatially lumped approach. 2. A sensitivity analysis of the model parameters is performed. 8 3. After the sensitivity analysis all the tests from Step 1 are repeated but this time the model is calibrated. The goal is to examine how different model structures respond to model calibration. 4. Steps 1 through 3 are repeated, but instead of using the high-altitude data, the input data from a single low-altitude meteorological station is used. 5. Finally, both high-altitude and low-altitude meteorological stations are used simultaneously in order to investigate the added value of the extra information when using more than one station for input. > Chapter 5 validates the findings from Chapter 4 on a rain-dominated watershed. This time only the two key model structures are tested using the identical approach to that used in Chapter 4. > Chapter 6 deals with the watershed non-linear behaviour and explores the ways to capture watershed non-linearity in modelling. The two key model structures are used to simulate several of the largest historical floods using an hourly computational time step. The simulations are performed for both study watersheds. The goal is to re-evaluate the findings - about different model structures, which were defined previously from long-term daily simulation, and to test these structures on the individual extreme events that are likely to be more non-linear in their nature. This chapter also features the experiments that explore the ways in which watershed non-linearity concepts can be removed from the model structure and compensated for by model parameter manipulation. > The concluding remarks and recommendations are given in Chapter 7. 9 CHAPTER 2 LITERATURE REVIEW 2.1 Terminology and Types of Watershed Models Traditionally, hydrological models are classified as physically based or conceptual, depending on the degree of complexity and physical completeness in the formulation of the structure. Hydrological watershed models are further classified as lumped or distributed depending on the degree of discretization in watershed description. However, most of the models today, conceptual or physically based, are distributed to some degree, because there is always some splitting of the larger areas into the sub-areas based on various criteria (e.g. in the case of the UBC Watershed Model it is based on altitude). One of the commonly used classifications of hydrological models is "the colour code": Black box models - are constructed without any consideration of the physical processes that are otherwise associated with the watershed. These models are based on analyses of concurrent 1 input and output time series. Black box models may be empirical hydrological methods (e.g. the unit hydrograph), methods based on statistical correlation and/or regression (e.g. the Antecedent Precipitation Index model) or hydroinformatics methods (e.g. artificial neural networks and evolutionary algorithms). Grey box models - are conceptual where physical forms and equations are used together with empirical ones. They are usually lumped either over the whole watershed or to some extent and operate with different water storages (or reservoirs) representing the physical elements of a 10 watershed. Hydrologic systems are known to involve water storage, which delays runoff and changes its time distribution. These simple water storage models have proved to be an effective way of characterising the main aspects of the runoff process. Operation of this type of models, thus consists of a continuous accounting of the moisture content in the reservoirs. Due to the lumped nature, where parameters are averaged over the larger area, the description of the hydrological processes cannot be based on the equations that are supposed to be valid for the individual soil columns. Therefore the equations have some physical basis but are still empirical, which implies that the model parameters have to be obtained through the calibration process. White box models - are physically based and have to be fully distributed because the equations by which they are defined generally involve one or more space coordinates. They are also called causal models. These models attempt to describe a watershed as the natural system using continuum mechanics, i.e., the flows of water and energy are directly calculated from the governing partial differential equations, such as for instance the Saint Venant equations for overland and channel flow, Richards' equation for unsaturated zone flow and Boussinesq's equation for groundwater flow. Ideally, the parameters of a fully distributed, physically based model can be assessed directly from the field measurements, so that a calibration is not necessary. It is clear from these definitions that, in theory, the distributed physically based hydrologic models should have significant advantages over the lumped conceptual models. In theory, these models have the capability of predicting not only the watershed outflows but also the spatial pattern of various hydrological factors within a watershed. Additionally, these models would not, in principle, need calibration, because of physically meaningful and thus measurable parameters. However, these are only theoretical advantages. It is rather difficult to use these models for practical purposes, because the necessary parameters cannot be obtained in the 11 required spatial and temporal resolution. In practice, distributed physically based model algorithms are applied at scales for which the parameter values cannot be directly assessed, and will have to be determined through some kind of trial-and-error procedure. The following is a brief discussion on constraints of distributed physically based model algorithms. 2.2 Constraints of the Distributed Watershed Models Al l of the currently existing distributed physically based models are constructed using process descriptions which assume that the reality defined in well controlled experimental situations simply extends to other situations. It can be proven that this assumption may not be valid because the conditions under which the relationships are derived differ from those in the field. For example, Beven (2001) listed the limits/problems of distributed hydrological modelling as nonlinearity, scale, uniqueness, equifinality and uncertainty problems. In this review, the problems associated with physically based distributed models are summarised in three main types - process description, heterogeneity and scale. Problems of process description: Consider, as a first example, surface flow which all distributed watershed models available today model as sheet flow. From observation of real watershed behaviour it is clear that this is not an adequate description of surface flows on rough vegetated surfaces such as those of a natural watershed. Hence, Grayson et al. (1992), the authors of the Australian distributed model THALES (which also describes surface overland flow as sheet flow) admitted the inappropriateness of this description and concluded that the underlying assumptions relating to representation of the surface flow have as large an effect on the flow characteristics as do the parameter values. They found that the variation in simulated flow characteristics due to 12 parameter choice and representation of the flow itself is so great that argument over the complexity of the flow equations is futile. Similarly, Dunne (1982) concluded, after numerous field investigations, that there was no "physical basis" for the representation of surface flow on natural surfaces by broad sheet flow. This means, practically, that there is no "physical basis" for the calculated overland flows. Another example of the inadequate process description is the fact that the most advanced currently available distributed models base their description of subsurface flow on Darcy's law and the one-dimensional Richards' equation for unsaturated flow. This is known to be a good description of flow in laboratory soil columns, where the soil has been well mixed and homogenised. However, in an undisturbed heterogeneous soil column, especially with the presence of macropores (preferential flow paths), this concept is not realistic. Jones (1971) was among the first to describe the existence of the preferential flow paths or "pipeflow mechanism". Additionally, the true values of the parameters needed to solve Richards' equation cannot be measured for the particular field because current measurement techniques are destructive. Thus, measurement would obtain parameter values from a destroyed soil column. Because of this, these parameters have to be calibrated. Al l this applies for a stationary system. Changes over time such as soil shrinkage on drying will further exacerbate the problem. Thus, it can be concluded that the Darcy-Richards description of subsurface flow is far from being truly physically based for watershed scale applications. Problems of heterogeneity: A distributed hydrological model consists of a number of grid elements which are assumed to reflect heterogeneity (e.g. in topography, soil characteristics and precipitation distribution) of the watershed in question. It is therefore necessary to use the concept of effective parameter values, 13 where the parameters are assumed uniform over an individual grid element, which ranges in scale from tens of meters to tens of kilometres. The main problem then is that of defining the grid element effective parameters given sub-grid variability of the parameters. There is a large number of studies that have dealt with the problem of heterogeneity or spatial variability. Freeze (1980) used a stochastic-conceptual mathematical model of hillslope processes to study the influence of the spatial stochastic properties of the hillslope parameters on the statistical properties of the runoff events. He found that the representation of a heterogeneous hillslope by an "equivalent" homogeneous hillslope might lead to large errors in the statistical properties of the runoff. Western and Bloschl (1999) noted that the spatial scale of soil measurement is often inconsistent with the scale at which soil moisture predictions are needed. Consequently a change of scale (upscaling or downscaling) from the measurements to the prediction or model values is needed. They analysed high-resolution soil moisture data from the 10.5 ha watershed and concluded that the statistical properties that appear in the data were as a rule different from their true values because of bias introduced by the measurement scale. Vachaud and Chen (2002) stated that the amount of information available to run a spatially distributed model is often very much less than the ideal. They examined the impact of inaccuracy of information about the spatial distribution of input parameters, and impact of the scale at which this information is obtained. More recently, Skoien et al. (2003) after analysing soil moisture data from a comprehensive Australian data set reported that, in space, soil moisture was nonstationary and close to fractal over the sampling extent. This implies that the concept of effective parameter values that are uniform over an individual grid element is likely to yield errors even in the case of very small grid elements. 14 Problems of scale: These problems are closely related to the problems of data availability, because the finer the grid scale, the more realistic the watershed representation, but also the higher the data requirements. Since in practice these higher data requirements often cannot be met, the distributed models with fine grid scale are applied at scales for which the parameter values cannot be directly assessed. The scaling problem regarding spatial variability of soils, topography and precipitation input has been extensively researched (Wood et al. 1988, 1990; Obled et al. 1994; Becker and Braun 1999; Koren et al. 1999; Booij 2002). Indeed, the scale problem in hydrology depends largely on the operational viewpoint. From the perspective of a small lysimeter study, a watershed of the size of 1 km 2 may be considered large and highly heterogeneous, whereas a 10,000 km2 basin may be considered homogeneous by a hydrological forecaster. For example, the Fraser River Forecasting Model uses the UBC Watershed Model and subdivides the 250,000 km2 watershed into 13 sub-watersheds. One can ask whether it is even possible to model such large basins with reasonable efficiency, considering their variability and all of the complexities introduced by changing land use or developing infrastructure. In summary, it does not seem that distributed models are based on the correct equations to describe hydrological reality at the grid element scale. Dooge (1982) wrote "It has been found in practice that the models based on continuum mechanics (i.e., internal descriptions) are too complex to allow for the spatially variable nature of hydrologic systems and they have been simplified to such an extent that they become in effect simple conceptual models with unknown parameters." Similarly, Beven (1989) stated that in the case of physically based distributed models the parameters must be estimated or calibrated, just as in any other conceptual hydrologic model. This led him to further conclude that the available physically based 15 distributed models are, in fact, lumped conceptual models, although they work at the grid scale rather than at the catchment scale of more traditional lumped conceptual models. The recently completed "Distributed Model Intercomparison Project (DMIP)" (Reed et al., 2004) compared simulations from twelve different distributed models with both observed streamfiow and lumped model simulation. The DMIP results showed that distributed models had to be calibrated in order to improve the calibration results. The DMIP results also indicated that for the majority of basin-distributed model combination, the lumped models showed better overall performance than distributed models. Loague and VanderKwaak (2004), accept the existence of previously mentioned problems associated with physically based models as well as the inability to assess and verify their boundary conditions, and then point out that the structure of physically based models is an iterative process. This means that if the certain process representation is shown to be incorrect (the authors offer an example of using Richards' equation to describe flow in macropores), then it should be replaced, once the correct physics is known. Loague and VanderKwaak also admit that the data requirements for physically based models are extensive and unlikely to be routinely met in most situations, but that should not be reason to give up. The authors go on to offer an argument against giving up: "we have been to the Moon and back and landed on Mars". They do not mention the associated budget! An uncritical acceptance of the predictions obtained by physically based distributed models is likely driven by comprehensiveness of their theoretical basis. For practical applications, it would be useful to consider previously mentioned constraints of these models and exercise caution. Hence, future research should investigate how to make most efficient use of field information in applying distributed models, and at what point the acquisition of further information becomes unnecessary. The reasonable approach seems to be to shift focus from the smallest detail to a 16 somewhat larger scale. It remains to be determined what scale is appropriate. The answer is likely not universal, but rather depends on a particular application. To paraphrase Dooge (1982), it appears that the most useful and applicable watershed models should have a simplified structure which includes some basic principles of watershed physics but not the detail of distributed models based on continuum mechanics, and a limited number of parameters which, preferably, could be determined on the basis of field measurements. 2.3 Modelling Natural Watersheds - Practical Applications For a hydrologist with a distributed watershed model and an interest in detailed micro-scale modelling of processes, the shift to a natural basin is a very difficult, if not impossible, task, considering the tremendous amount of input data needed, as well as the variability in such a basin. Therefore, the only reasonable approach, apart from laboratory based micro-scale hydrological modelling, seems to be some kind of a conceptual approach. Conceptual watershed models have been and are still being widely applied in the design, planning and management of water resources projects all over the world. Evidently, in the case of conceptual watershed models, it is necessary to limit the demands on input data and to achieve a design which utilises model parameters which at least relate to the observed behaviour of storage, soil moisture and time distribution of runoff. Whether these parameters are scale independent is a matter for investigation, but experience with some conceptual models is that reasonably stable parameters can be defined. One example of this pragmatic approach is the forecasting of the Fraser River flow using the UBC Watershed Model, which provides satisfactory streamflow estimates despite very limited 17 amounts of input data due to the lack of meteorological stations, especially reliable, high altitude stations. The characteristic examples of this are two Fraser River sub-watersheds, namely the Upper Fraser (32,400 km2) and the North Thompson (19,600 km2) watersheds. Both of these watersheds are modelled with only two meteorological stations. This means that any two points at the same altitude in the watershed are assumed to have identical temperatures and precipitation even though they could be, in the case of Upper Fraser watershed, 380 km apart. Another example of successful hydrological modelling with sparse meteorological input is the Columbia River watershed above Mica Dam (Micovic, 1999), where the 21,287 km2 watershed was modelled using only three meteorological stations as an input (Golden, Rogers Pass and Blue River). This represents station density of one per 7000 km2, which is far below WMO standards (1981) of one station per 100-250 km2 as a minimum network density of precipitation stations in mountainous regions. However, long-term modelling efficiency is extremely high and above all standards. Mean Nash-Sutcliffe efficiency for the continuous simulation run from 1966 to 1997 on annual basis is 0.92 with a standard deviation of 0.02. The minimum efficiency value is 0.91 and the maximum is 0.98. Nash-Sutcliffe efficiency can range from -co to 1. Efficiency of 1 represents a perfect match between observed and simulated hydrograph, whereas negative efficiency means that the observed mean flows are closer to observed flows than the flows calculated by the model. Internationally, Bergstrom and Graham (1998) applied the standard version of the Swedish HBV watershed model to the continental scale catchment of the Baltic Sea. This "watershed" had drainage area of 1.6 million km2 and was fairly successfully modelled with this conceptual watershed model. 18 2.4 Structure of Conceptual Watershed Models Nash & Sutcliffe (1970) published a pioneering study on the topic of development and testing of conceptual watershed models. The main message of the study was a plea for realistic model structure complexity. Nash & Sutcliffe suggested that three basic requirements in a model development should be simplicity, lack of duplication and versatility. They argued that simplification of the operation of a watershed is necessary, but, at the same time, the model should reflect physical reality as close as possible. They recognised that if the model parameters are to be determined by comparison of computed and observed outputs, the more complex model the more difficult it becomes to establish the parameter values, particularly if the parameters are independent. In their "lack of duplication" requirement, Nash and Sutcliffe argued that there should be no unnecessary proliferation of parameters to be optimised and model parts with similar effects should not be combined. The versatility requirement implied that we should be prepared to accept additional parts and hence greater difficulty in determining parameter values only if the increased versatility of the model makes it much more likely to obtain a good fit between observed and computed output. Finally, Nash & Sutcliffe proposed a systematic procedure for determination of realistic model complexity. The procedure starts with a simple model, but one which can be elaborated further. This model is then calibrated, its parameters are analysed and the model efficiency is computed. After that the model is modified by the introduction of a new part. This new, more complex model is then evaluated using the principles established in the previous steps, and the modification is accepted or rejected. 19 The approach and principles put forward by Nash & Sutcliffe are in close agreement with the present work. A comprehensive comparative study of seven different conceptual watershed models by Franchini and Pacciani (1991) concluded that two distinct components may be identified in all of the models examined. The first component represents the soil-level water balance and the second represents the transfer to the watershed outlet. The part representing the soil-level water balance is the most important, and this part characterises a model. It expresses the balance between the moisture content of the soil, generally divided into several zones (upper, lower and deep) and the incoming (precipitation) and outgoing (evapotranspiration and runoff) water quantities. Franchini and Pacciani concluded that the transfer component in a majority of conceptual watershed models was made up of two distinct parts: the first represents the runoff transfer to the drainage net along the hillslopes and the second represents the runoff transfer along the drainage net to the watershed outlet. According to Franchini and Pacciani the transfer component, or routing as it is more commonly referred to in North America, unlike the water balance component, does not characterise a watershed model and is much less important than the water balance component. Franchini and Pacciani tested seven watershed models (STANFORD IV, SACRAMENTO, TANK, APIC, SSARR, XINANJIANG AND ARNO) on the 823 km 2 Sieve River watershed in Italy. The models were run from December 01, 1959 to March 31, 1960 and their simulation results were compared. The results revealed that, with the sole exception of the APIC model, all of the watershed models produced similar and equally valid results, despite the wide range of structural complexity among them. The degree of complexity, however, played a significant role in the calibration process. Therefore, significantly different models produced basically equivalent results, with calibration times generally proportional to the complexity of their 20 structure. On the other hand, too much simplification such as that in the TANK model structure caused loss of the link with the physics of the watershed and made it difficult to logically estimate parameter values. The TANK model was the easiest to calibrate due to the minimal number of parameters, but their physical meaning was hard to establish. The calibration of the STANFORD IV and SACRAMENTO models required the most effort due to the fact that their structure attempts to grasp different interactions of the various phases of the rainfall-runoff transformation within the soil. This results in a useless increase in the number of parameters according to Franchini and Pacciani. It is interesting to note that in the end the TANK model performed slightly better than both the STANFORD IV and SACRAMENTO models. Analysis further concluded that, for all models, when an appropriate description of the water balance is ensured, the type of the transfer component (i.e. routing mechanism) has little effect on the final result and may be either linear or non-linear. This conclusion agrees with the statement by Cordova and Rodriguez-Iturbe (1983) who said that "the problem is more what to route than how to route". In addition, Michaud and Sorooshian (1994) used two different watershed models to simulate runoff from a 150 km2 watershed in Arizona. The simple model was the Soil Conservation Service (SCS) model (SCS, 1964), which uses a linear, unit hydrograph routing method. The complex model was the physically based, distributed model KINEROS (Woolhiser et al., 1990), which uses non-linear kinematic routing. The simulation results indicated that both models have roughly similar abilities in predicting hydrograph shape and timing. The authors admitted being somewhat surprised when, after calibration, the linear-routing SCS model simulated hydrograph shape and timing more accurately than KINEROS. However, these results can be explained by reviewing the research of Loukas and Quick (1993). They showed that with "pipeflow" which 21 can develop on mountain slopes, the flow velocity can be reasonably constant, which implies a linear kinematic wave response. An interesting experiment was done by Naef (1981) who compared various modelling approaches on three small watersheds (2 km2, 11 km2 and 120 km2). The modelling concepts ranged from the simplest possible where "computed discharge = measured precipitation" to the application of a conceptual watershed model (i.e., a modified version of the Sacramento model). Naef concluded that even a very simple model could explain a large part of the variance of streamflow; that there were cases when the simple models were as accurate as the more complex ones; and that there were cases when none of the models could accurately simulate the watershed hydrograph. The application of a conceptual watershed model implies use of number of model parameters that, despite having some physical basis and being effective on the watershed scale, are not measurable in the field and have to be determined through calibration. This inability to determine parameter values through measurement raises the question of parameter uncertainty. Uhlenbrook et al. (1999) investigated the uncertainties in determining the parameter values of a conceptual watershed model. The previously mentioned Swedish HBV watershed model was applied to the mountainous Brugga Watershed (drainage area 40 km2) in southwestern Germany. Instead of calibrating the individual parameters, they randomly generated 400,000 different parameter sets, where each set contained 13 different parameters. This approach takes interdependecies between parameters implicitly into account as parameter sets instead of individual parameters are varied. For a ten-year calibration period, different parameter sets resulted in an equally good agreement between observed and simulated runoff and for the majority of parameters, good simulations were produced with values varying over wide ranges. This finding raises some interesting questions concerning the use of any given watershed model 22 for runoff forecasting. If different parameter sets are equally suitable to simulate runoff during the calibration period, then which set should be used for runoff prediction outside the calibration period where they might produce different outcomes? A possible solution may be that model forecasts be presented as ranges rather than as single values. Uhlenbrook et al. also defined insensitive and uncertain model parameters. In the first case, model output is not sensitive to different values of parameter, implying that the parameter is unnecessary. For an uncertain parameter, on the other hand, model output may be sensitive to changes of the parameter value, but these changes can be compensated for by other parameters. The Brugga Watershed exercise showed, for instance that the simulations were sensitive to changes in the maximum soil moisture storage parameter (FC) when it was changed independently; however, good simulations could be achieved over a wide range of FC values when other parameters were varied simultaneously. Evidently, many of the parameters in the model proved to be either insensitive or uncertain, which implies that their number should be reduced. The issue of parameter uncertainty has been and continues to be extensively investigated. Dawdy and Bergmann (1969) were among the first to investigate the effects of model parameter and input data uncertainty on simulated streamflow. More recent approaches to reducing the uncertainty of model parameters and predictions range from statistical approach (Beven and Freer, 2001) to the coupling of a conceptual watershed model with an Artificial Neural Network model (Abebe and Price, 2003). Jakeman and Homberger (1993) applied time series techniques for estimating transfer functions to determine how many parameters are appropriate to describe the relationship between precipitation and streamflow in the case where data on only precipitation, air temperature, and streamflow are available. They developed time series models for seven watersheds with widely varying physical characteristics in different temperate climatic regimes to demonstrate the method. Using this approach the authors found that for watersheds in temperate climates but over a wide range of scales, only a handful of parameters can be reliably estimated from rainfall-runoff data. They also found that after transforming the measured rainfall using a nonlinear loss function, the rainfall-runoff response of all watersheds is well represented using a linear model. Their findings, similarly to some of the previously mentioned articles, indicate that "nonlinearities can be described by the transformation of rainfall to excess rainfall", i.e. by appropriately determining the water quantities which can then be routed using linear method. Even the smallest watershed they analysed could be satisfactorily represented by linear storage routing, a somewhat surprising finding on such a small scale with an area of only 0.00049 km . Atkinson et al. (2003) investigated different integral components of a simple conceptual model and their relative importance in overall model efficiency. They used a simple storage model for sub-watersheds and the runoff generated from each sub-watershed was routed to the watershed outlet using a constant velocity (0.5 m/s) channel network routing model. Atkinson et al. used different timescales to test several modifications in simple storage model complexity such as uniform versus spatially variable rainfall input, uniform versus spatially variable catchment parameters and single versus multiple storages (or buckets). The results indicated that accounting for spatial variability in rainfall input and in catchment parameters brought negligible improvement over a lumped approach. Therefore the most crucial improvement was caused when hillslope representation by a single storage was replaced with hillslope representation via multiple buckets. The advantage of the multiple buckets approach is that small buckets representing the riparian zone allow immediate response to rainfall, rather than delaying the discharge for a longer time by storing the water in a single deep bucket. Evidently, the work by Atkinson et al. implies that hillslope process representation is the most important component of conceptual watershed models, which confirms earlier conclusions by Micovic and Quick (1999) 24 that land phase is the main control of the watershed runoff process and the channel phase may be neglected in modelling. Sivapalan (2003) pointed out the apparent lack of useful connection between the complexity observed at the hillslope scale and the apparent simplicity inferred at the watershed scale. The terms "upward" and "downward" modelling are introduced, where "upward" indicates physically based, and "downward" indicates a more conceptual approach. He described physically based modelling as an "upward" approach where detailed field measurements at hillslope scale are used to form models of hydrologic response. A major difficulty in generalising such a model to a larger scale is the considerable heterogeneity of hillslope properties both within and between watersheds. Sivapalan described an alternative "downward" approach to inferring model structure at the watershed scale, which involves systematic analysis of rainfall-runoff data at that scale, with or without the benefit of detailed internal process information that is only available in field experiments. This "downward" approach is further discussed in Littlewood et al. (2003) as the only feasible tool for the Prediction in Ungauged Basins (PUB) initiative. Littlewood et al. wrote that the "upward" approach attempts to represent all relevant processes and could have dozens of parameters which might be related statistically to others due to parameter identifiability problems. That is why, the authors explain, "upward approach" models tend to perform more poorly than "downward approach" models in simulation-mode, i.e. on periods of record not used for model calibration. Sivapalan (2003) concluded that any generalisation of the model structure would require a reconciliation of the structures and conceptualisations obtained by the two alternative (i.e. upward and downward) approaches. One way to achieve this reconciliation, Sivapalan suggests, is to focus on common concepts, features or patterns that have physical meaning that transcend 25 the range of scales in question, and which are easily scalable, and might over time, assist us in the development of a new theory of hydrology at the watershed scale by shifting the focus away from small scale theories at the hillslope (or lower) scales towards new hydrologic concepts that transcend spatial scales. It could be argued that this process has already occurred in many operational models. Wagener et al. (2001) attempted to establish a framework required to balance the level of model complexity supported by the available data with the level of performance suitable for the desired application. They define the level of structural complexity which can be actually supported by the information contained within the observations, as the number of parameters that can be identified. They do not consider other aspects of complexity, such as the number of model states, interactions between the state variables and the role of non-linearity in model structure. Wagener et al., based on previous research suggest that, in the case of rainfall-runoff modelling, up to five or six parameters only can be identified from time-series of external system variables measurements, i.e. streamflow and rainfall. This uncertainty in model parameters due to a lack of identifiability is usually overcome by less complicated model structures that represent only those response modes that are identifiable from the available data. Wagener et al. proposed two other approaches to reducing parameter uncertainty, besides widely applied model simplification. The first approach is to increase the amount of information available to identify the model parameters through the use of additional output variables (e.g. stream salinity and groundwater measurements). The second approach they suggest is the improved use of the information already available such as the use of different data periods to identify different parameters. 26 2.5. Summary It can be concluded that the most useful and applicable watershed models should have a simplified structure which includes some basic principles of watershed physics but not the detail of distributed models based on continuum mechanics, and have a limited number of parameters which, preferably, could be determined on the basis of field measurements. Generally such models are conceptual in nature and must balance two contrasting demands: firstly to be structurally simple and secondly to simulate physical processes fairly well thereby making it possible to use prior knowledge of the physical nature of the watershed to assist in calibrating parameters. It appears that watershed models with very simple structure and few parameters do as good a job in simulating watershed hydrographs as more complex models with a large number of parameters. The possible explanation may be that watershed hydrographs appear to exhibit much less variety than watershed topography, land cover and soils, indicating that averaging and suppression of local detail is taking place at the watershed scale. At the same time, since the natural watersheds exhibit a non-linear response, there must be concepts implemented to account for watershed non-linearity in order to have a successful model. Theoretically, these non-linearity concepts used in watershed modelling can be classified as follows: 1. Non-linearity incorporated in soil moisture accounting (e.g., evapotranspiration, variable source area concept, and limited infiltration for high-intensity rainfall) 2. Non-linearity incorporated in time distribution of runoff, i.e. splitting total runoff from a watershed into components with different time delay signatures or with non-linear routing 3. Degree of distribution in watershed physical description (i.e., division in many sub-areas or altitude bands and different land cover representation) 27 Clearly, item 1 from above influences the determination of the water budget and its allocation in different vertical zones of a watershed, whereas item 2 influences only the time distribution of already determined water quantities. Item 3 could influence both water quantity and its time distribution. It appears from this literature review that when an appropriate description of the water balance is ensured, the method of routing that water has little effect on the final result and may be either linear or non-linear. This means that linear routing will work well in a watershed model structure as long as the non-linear watershed response is handled either by soil moisture accounting or time distribution of runoff, or both. Therefore, we can keep adding complexity to the model structure by trying to represent more physical processes and consequently introducing additional parameters. At some point, this improvement becomes so small that it does not justify the increase in model complexity and additional effort and input requirements associated with it, and finding that point can be a rather challenging task. This study will attempt to examine these model complexity requirements by experimenting with different model structures, inputs and watersheds. 28 CHAPTER 3 WATERSHED MODEL STRUCTURE 3.1 General Discussion Different components of total watershed runoff can be recognised in the outflow hydrograph because of their characteristically different time delay signatures, which can vary by an order of magnitude. It is debatable how many flow components should be implemented in the watershed model structure, as well as what are the priorities or rules which decide the order in which the water is allocated to these different runoff components. In this study, several different model structures will be tested, starting from an extremely simplified concept and progressively increasing in complexity. It was mentioned previously that the UBC Watershed Model (UBCWM) will be used as an experimental tool for exploration of different modelling assumptions. This means that some of the UBCWM algorithms and routines (Quick, 1995) will be kept unchanged and used as a common part of all model structures tested in this study. They are as follows: • Al l snowmelt, temperature distribution, evapotranspiration and interception parameters. It should be mentioned that user input is generally not required in these routines because the parameters used in them are pre-calibrated and kept constant. The snowmelt algorithm uses an energy balance approach, which is discussed in detail in Quick (1995) and can account for forested and open areas, aspect and latitude. Glacier melt is also computed using this same method and parameters. 29 The meteorological sub-model, which distributes the point values of precipitation and temperatures to all elevation zones of a watershed. The variation of temperature with elevation controls whether precipitation falls as rain or snow and also controls the melting of the snowpacks and glaciers. The precipitation data used are point measurements and thus, have to be distributed over the watershed. Particularly important parameters are the snowfall (SREP) and rainfall (RREP) adjustment factors. They are used to adjust precipitation at each meteorological station. If the data from the meteorological stations are representative for the watershed, SREP and RREP are equal to zero. If this is not the case, precipitation amounts are increased or decreased by certain percentages compared to those recorded at the meteorological station, until the best possible efficiency (i.e., agreement with the observed flow) is achieved. For example, a SREP value of -0.15 means that snowfall is reduced by 15%. In mountain regions precipitation increases as a moist air mass is driven by wind across mountain barriers. This orographic enhancement of precipitation is modelled by the precipitation gradients. On the weather side, these gradients are generally the highest on lower mountain slopes, and get smaller close to the top of the mountain. On the lee side, however, an inverse situation may occur; high precipitation on the weather side of the range extends over to the lee side, but then decreases very sharply. This applies for both rain and snow, but snow shows greater spill-over effect because of its lower fall velocity. This meteorological sub-model has a capability of using three different precipitation gradients in a single watershed, namely the lower (GRADL), middle (GRADM) and upper (GRADU) gradient. Obviously, two more parameters are needed to determine precipitation gradient boundaries. They are EOLMID and EOLHI. EOLMID is an elevation below which precipitation gradient GRADL applies and above which the GRADM applies. EOLHI is an elevation above which precipitation gradient GRADU applies. Therefore, if all three 30 precipitation gradients are used, the number of parameters that has to be adjusted is five. However, it is often the case that satisfactory precipitation distribution by altitude is achieved using a single precipitation gradient and there is no need to use all five parameters. The starting values of the precipitation gradients may be judged from snowcourse measurements to some extent. Alternatively, in a given sub-region precipitation gradients may have to be assessed from the nearest similar watershed. If no such information exists, the values for the orographic gradients of precipitation have to be obtained by a trial-and-error optimisation procedure. Once determined, the estimated or calibrated values of the precipitation parameters are kept constant for a given watershed. To summarise, the UBCWM meteorological sub-model has two parameters for adjusting precipitation at the point of measurement and one, three or five parameters for distributing precipitation by altitude. It should be mentioned that in the case of a lumped approach when the watershed is represented by a single elevation band, there is no need for precipitation gradients, which considerably simplifies the modelling process. The routing sub-model uses linear routing, which leads to great simplifications of model structure. It guarantees conservation of mass and a simple and accurate water budget balance. Soil moisture control of runoff is introduced in Model structure #3 and higher. An important aspect of this structure is the so-called "impermeable area" that is used to describe three aspects of fast response watershed runoff behaviour. Part of the watershed may be rocky, and therefore impermeable, producing overland flow. Part of the watershed soils will become saturated, and will then become "impermeable", so fast runoff will occur; this region is usually riparian and the runoff usually occurs as "pipe-flow" within the soil matrix. Lastly, during high intensity rain, infiltration will be limited, and runoff will go directly to the fast 31 runoff system. Within the soil moisture sub-model, these three types of fast runoff are controlled by the "impermeable fraction", by the soil moisture deficit, and by the flash runoff threshold for the extreme rain, infdtration limiting runoff. The preceding was a brief explanation of UBCWM algorithms and routines that will be used as a common part of all model structures tested in this study. The following is a detailed description of each of six different modelling structures that will be examined in this work. 3.2 Proposed Model Structures 3.2.1 Model structure #1 This is a concept of 100% surface runoff from the watershed with instantaneous response. This unrealistic concept represents a totally impermeable watershed in which precipitation input reaches the watershed outlet without any delay. However, the model is very simple and has a minimal number of parameters. A diagram of the model structure is shown in Figure 3-1. 3.2.2 Model structure #2 This model structure also assumes a 100% impermeable watershed, which means that only surface runoff is modelled. The difference relative to the previous model structure is that the watershed response is not instantaneous. Precipitation input is routed through the watershed storage using a linear concept of reservoirs in series. This is the way to introduce some delay in 32 watershed response to precipitation input. However, watershed behaviour remains linear. A diagram of the model structure is shown in Figure 3-2. 3.2.3 Model structure #3: In this concept, which is clearly more realistic than previous two, soil moisture accounting is introduced in an attempt to model non-linear behaviour that watersheds are known to exhibit. Routing through watershed storage can remain linear because non-linearity in watershed behaviour is concentrated in the soil moisture sub-model. It is obvious that in this model structure two different components of total watershed runoff can be recognised since their time delays vary by an order of magnitude. Therefore this model structure allows for a faster surface runoff component and a much slower, groundwater runoff component. There are also set priorities which decide in what order the incoming rainfall and snowmelt input is allocated to these two runoff components. First priority is the impermeable area, which is the fast responding region of a watershed and is assumed to be adjacent to a well developed stream channel system. This area changes as a function of soil moisture deficit (variable source area). In addition, in the case of high-intensity rainfall exceeding infiltration capacity of the soil, excess water will move directly over the surface to the channel network and skip the soil moisture accounting algorithm. Second priority is the concept of soil moisture accounting where an actual evapotranspiration rate is computed as a function of soil moisture deficit. Remaining water is then allocated to the third and last priority by letting it percolate to groundwater storage. Evidently, both soil moisture accounting and runoff allocation priorities help represent watershed non-linear behaviour in this example of watershed model structure shown in Figure 3-3. 33 3.2.4 Model structure #4: This is the same as the previous model structure except that the groundwater runoff component is divided into two components, namely the upper-zone and the lower-zone groundwater, as shown in Figure 3-4. Model complexity increases compared to Model structure #3, because of separate routing of two groundwater components and the additional parameters associated with that. This division of groundwater component adds flexibility to the model. Instead of all groundwater having the same time delay, it is now possible to specify two fractions of groundwater going into slow and very slow components with considerably different time delays. 3.2.5 Model structure #5: This is the current UBC Watershed Model structure. Besides fast, slow and very slow runoff components, this structure allows for an additional, medium runoff component also known as interflow. In terms of runoff allocation priorities, interflow is assumed to be the fourth and last priority. This means that interflow will occur only if there is excess water remaining after soil moisture and groundwater abstraction have been satisfied. Transition from third to fourth priority is achieved through introduction of an additional parameter which determines the maximum amount of water that is allowed to percolate to groundwater. Therefore this model structure divides total watershed runoff into four components, each with a different time delay. Usual values for the time delays are 10 to 50 hours for the fast runoff component, 3 to 10 days for the interflow, 10 to 30 days for the upper zone groundwater and 1.5 to 6 months for the deep zone groundwater. Obviously, this model structure, as shown in Figure 3-5, is more complex than any of the previous ones. 34 3.2.6 Model structure #6: In this model structure, shown in Figure 3-6, interflow is given the same priority in the runoff allocation scheme as groundwater. This means that groundwater abstraction and interflow demand are satisfied at the same time. The incoming water input is divided into two specifiable fractions, which go to the interflow and total groundwater. Total groundwater is further divided into upper and lower zone components. Compared to previous model structures, this approach has the potential to result in higher peak flows because less water ends up in groundwater and more goes to the faster responding interflow component, depending on the specified interflow fraction. This model structure is introduced because some modelling concepts do not consider interflow to be last priority. For example, WATFLOOD model (Kouwen et al. 1993) recognises that infiltrated water within the upper zone of soil storage percolates downward to groundwater zone or is exfiltrated to nearby water courses and called interflow. However, the WATFLOOD concept ignores percolation downward and determines base flow from a measured hydrograph. 35 Meteorological data input and distribution by the altitude zone(s) PRECIPITATION TEMPERATURE Rainfall Snowfall Melt Computation Snowmelt and glacier melt Soil moisture control Impermeable fraction (700% of the watershed) Only one flow component Modifications by watershed storages Reservoir routing control (instantaneous response - no delay) Evaluation with recorded streamflow Generated streamflow Figure 3-1. Diagram of model structure #1 Meteorological data input and distribution by the altitude zone(s) PRECIPITATION TEMPERATURE Rainfall Snowfall Melt Computation Snowmelt and glacier melt 1 Soil moisture control Impermeable fraction (100% of the watershed) Only one flow component Modifications by watershed storages Reservoir routing control Time distribution of runoff Evaluation with recorded streamflow Surface runoff / V -Generated streamflow Figure 3-2. Diagram of model structure #2 Meteorological data input and distribution by the altitude zone(s) PRECIPITATION s | s o I s 3 as TEMPERATURE I Rainfall Snowfall Infiltration control Melt Computation Flash behaviour from high intensity rainfall Snowmelt and glacier melt Soil moisture control Impermeable fraction (has fixed minimum value, beyond that increases as a function of soil moisture ) I Fast runoff <D - r -00 Q_ Modifications by watershed storages Time distribution of runoff Evaluation with recorded streamflow Evapotranspiration losses M Permeable fraction (in each time step, equal to total watershed area minus the impermeable fraction) Percolation to groundwater Slow runoff Reservoir routing control 1 Surface runoff Groundwater Generated streamflow Figure 3-3. Diagram of model structure #3 38 Meteorological data input and distribution by the altitude zone(s) PRECIPITATION e s s 3 c -a a a I "S« c a as TEMPERATURE Rainfall Snowfall Infiltration control Melt Computation Flash behaviour from high intensity rainfall Snowmelt and glacier melt Soil moisture control Impermeable fraction (has fixed minimum value, beyond that increases as a function of soil moisture) Fast runoff T 3 O J= O H P Modifications by watershed storages Time distribution of runoff Evaluation with recorded streamflow Evapotranspiration losses M Permeable fraction (in each time step, equal to total watershed area minus the impermeable fraction) Percolation to groundwater Slow runoff | | Very slow runoff 7=i Reservoir routing control Upper zone Deep zone groundwater groundwater Generated streamflow Figure 3-4. Diagram of model structure #4 39 Meteorological data input and distribution by the altitude zone(s) PRECIPITATION Rainfall Infiltration control a -a Flash behaviour from high intensity rainfall s s & as • - o 0. Soil moisture control Impermeable fraction (has fixed minimum value, beyond that increases as a function of soil moisture) Fast runoff Modifications by watershed storages Time distribution of runoff Evaluation with recorded streamflow Evapotranspiration losses M Permeable fraction (in each time step, equal to total watershed area minus the impermeable fraction) Percolation to groundwater (up to specified constant value) I Slow runoff Excess water Very slow runoff M edium runoff -•<^^~Reservoir routing controi~^^>^-' 1 r •* Surface runoff Interflow Upper zone groundwater Deep zone groundwater Generated streamflow Figure 3-5. Diagram of model structure #5 40 Meteorological data input and distribution by the altitude zone(s) I § •a S s I s a 05 •C ' C o. Impermeable fraction (has fixed minimum value, beyond that increases as a function of soil moisture) I Fast runoff Modifications by watershed storages Time distribution of runoff Evapotranspiration losses Im-permeable fraction (in each time step, equal to total watershed area minus the impermeable fraction ) Interflow Percolation to groundwater M edium runoff Slow runoff Very slow runoff - " • ^ ^ ^ R e s e r v o i r routing controT^^^-1 r 1 r i r Surface runoff Interflow Upper zone groundwater Deep zone groundwater Evaluation with recorded streamflow Generated streamflow Figure 3-6. Diagram of model structure #6 41 CHAPTER 4 EVALUATION OF WATERSHED M O D E L STRUCTURES ON A SNOW-DOMINATED WATERSHED 4.1 Illecillewaet Watershed 4.1.1 General Information Location, size and topography: The Illecillewaet River (Figure 4-1) is an eastern tributary to the Columbia River with confluence at Revelstoke. The upper part of the Illecillewaet River watershed is located in Selkirk Mountains, while the lower part slopes down to Columbia River valley. The watershed is bounded by high glaciers and icefields, the most significant being Albert Glacier on the south, Illecillewaet Glacier on the east and Dismal and Durrand Glaciers on the northwest. Trans-Canada highway intersects the watershed into two almost equal halves. This is a rugged mountainous watershed with drainage area of 1150 km 2, 74% of which is covered with Interior Western Hemlock, Subalpine Engelmann Spruce and Subalpine Fir forest and 7% with glaciers. It has southwestern orientation and an average slope of 37% with an elevation range from 509 to 3271 m and a mean elevation of 1684 m. Geology: Most of the watershed is underlain by stratified Paleozoic rocks. A small part in the southwestern part of the watershed consists of metamorphic rocks of an undetermined age. Soils: The soils are predominantly Podzolic of Humo-Ferric type. 42 10 0 10 33 30 40 5 0 Kilometers Figure 4-1: Illecillewaet watershed Climate: This watershed belongs to the Southeast Interior climatic region of British Columbia usually referred to as the Interior Wet Belt because it receives more precipitation than the Central or Southwest Interior. Mean annual precipitation is 1715 mm. In an average year more than 66% of the annual precipitation falls as snow. Temperatures range from an average of-5.6 °C in January to 18.2 °C in July at lower elevations and from -10 °C in January to 12 °C in July 43 at higher elevations. There are two climate stations, Mt. Fidelity and Rogers Pass, located within the watershed and one station, Revelstoke, located just outside of the watershed. Location and altitude of each of these three stations is shown in Figure 4-1. Hydrologic regime: The snowmelt season continues from early April to late July, followed by a glacier melt season, once glaciers become snow-free. The annual floods are generated almost exclusively from seasonal snowmelt and occur in the mid May - early July period. The mean annual flood is 0.23 m3/s/km2, and the coefficient of variation of annual floods is 0.20. 4.1.2 Degree of Detail in Watershed Description During the initial modelling phase, we try to define the physical structure of the watershed by determining its measurable characteristics such as area, elevation and land cover. At the same time we have to decide on the extent of spatial distribution, i.e. degree of detail in watershed description. The pure spatially lumped approach would assume the watershed to be one area of constant elevation and land cover. This approach considerably simplifies the modelling process by implying no spatial variation within the watershed of precipitation, vegetative cover, soils or topography. Another approach is to spatially divide the watershed into many smaller areas that may or may not be correlated with elevation, and describe each of these areas individually. This approach increases the number of model parameters and model complexity. The question is how much this increase in complexity contributes to more realistic representation of runoff processes. Using the lllecillewaet watershed as an example, it is possible to test what effects different degrees of spatial distribution have on overall model efficiency. Tables 4-1, 4-2 and 4-3 show the physical structure of the lllecillewaet watershed divided into eight smaller areas, two small areas and described as one area, respectively. These sub-areas are commonly known as "elevation bands", because each of them occupies a different elevation range. 44 Table 4-1. Illecillewaet watershed description (8 elevation bands) Elevation Band 1 2 3 4 5 6 7 8 Mean elevation (m) 1000 1360 1540 1650 1790 1915 2085 2250 Area (km2) 230 115 115 115 115 115 115 230 Forested fraction 0.9 0.9 0.9 0.9 0.9 0.5 0.5 0.5 Glaciated area (km2) 0 0 0 0 0 0 0 76 Orientation (0=North; l=South) 1 1 1 1 1 1 1 1 Impermeable fraction* 0.1 0.1 0.1 0.1 0.1 0.5 0.5 0.5 Table 4-2. Illecillewaet watershed descri] ption (2 e evation bands) Elevation Band 1 2 Mean elevation (m) 1310 2058 Area (km2) 575 575 Forested fraction 0.9 0.58 Glaciated area (km ) 0 76 Orientation (0=North; l=South) 1 1 Impermeable fraction* 0.1 0.42 Table 4-3. Illecillewaet watershed description (1 elevation band) Elevation Band 1 Mean elevation (m) 1684 Area (km ) 1150 Forested fraction 0.74 Glaciated area (km ) 76 Orientation (0=North; l=South) 1 Impermeable fraction* 0.26 * Impermeable fraction is difficult to measure accurately and, as a starting value, is assumed to be equal to unforestedfraction of each band. This can be modified later during calibration procedure, if necessary. 45 4.1.3 Input Data - Meteorological and Streamflow It was already mentioned that the main question in watershed modelling, as well as in this study, is, given point input data, what degree of distribution is required to obtain realistic representation of the runoff processes? Point input data are measurements of temperature and precipitation, and discharge measurements at the watershed outlet. A discharge measurement at the watershed outlet is used to evaluate model efficiency. If the discharge simulated by model closely matches the observed discharge for an extended period of time, we can say that realistic representation of runoff processes is achieved. As shown in Figure 4-1, there are three climate stations available to provide input data for the modelling of the lllecillewaet watershed. The stations are Revelstoke at 443 m; Rogers Pass at 1323 m; and Mt. Fidelity at 1875 m. Each of these three stations may be used individually to model the entire watershed; all three together may be used at their corresponding elevation zones of the watershed; or any combination of two stations may be applied. Also, one may try to derive basin-average meteorological data using some average of these three stations. A logical first step is to start with the simplest option, that is modelling the entire watershed area as one elevation band and one land cover using point input data from a single meteorological station. The next steps are to observe what effects gradually increasing degree of distribution has on watershed modelling results. In the lllecillewaet watershed example, we will start by using input data from Mt. Fidelity only and representing the watershed as one elevation band. In terms of land cover, two options will be used alternatively - the entire watershed is assumed to be an open area without any vegetative cover; and part of the watershed is covered by forest. These starting assumptions about input data will be used to test the six previously mentioned model structures. Evaluation of model performance will be done by comparing flow simulated by the model with the observed flow shown in Table 4-4. 46 Table 4-4. Observed flow at the watershed outlet (lllecillewaet River at Greely) Observed Discharge (m3/s) Ranked by Daily maximum Ranked by Total Annual Water year Total Daily max. Rank Daily max. Water year Rank Total Water year 1969-1970 16878 242 1 436 1982-1983 1 23979 1975-1976 1970-1971 18965 254 2 360 1971-1972 2 23163 1996-1997 1971-1972 23098 360 3 341 1985-1986 3 23098 1971-1972 1972-1973 15682 241 4 328 1973-1974 4 22318 1990-1991 1973-1974 21769 328 5 316 1996-1997 5 21769 1973-1974 1974-1975 17327 246 6 309 1983-1984 6 20959 1995-1996 1975-1976 23979 275 7 284 1986-1987 7 20788 1981-1982 1976-1977 16304 246 8 277 1984-1985 8 20252 1980-1981 1977-1978 18353 205 9 275 1975-1976 9 20199 1989-1990 1978-1979 18219 225 10 272 1981-1982 10 19806 1985-1986 1979-1980 18365 225 11 271 1988-1989 11 19376 1983-1984 1980-1981 20252 234 12 266 1995-1996 12 19084 1982-1983 1981-1982 20788 272 13 263 1989-1990 13 18965 1970-1971 1982-1983 19084 436 14 263 1990-1991 14 18935 1986-1987 1983-1984 19376 309 15 254 1970-1971 15 18365 1979-1980 1984-1985 18047 277 16 246 1974-1975 16 18353 1977-1978 1985-1986 19806 341 . 17 246 1976-1977 17 18219 1978-1979 1986-1987 18935 284 18 242 1969-1970 18 18066 1987-1988 1987-1988 18066 214 19 241 1972-1973 19 18047 1984-1985 1988-1989 17256 271 20 234 1980-1981 20 18007 1993-1994 1989-1990 20199 263 21 225 1978-1979 21 17388 1991-1992 1990-1991 22318 263 22 225 1979-1980 22 17327 1974-1975 1991-1992 17388 224 23 225 1994-1995 23 17256 1988-1989 1992-1993 14961 212 24 224 1991-1992 24 17200 1994-1995 1993-1994 18007 219 25 219 1993-1994 25 16878 1969-1970 1994-1995 17200 225 26 214 1987-1988 26 16304 1976-1977 1995-1996 20959 266 27 212 1992-1993 .,27 15682 1972-1973 1996-1997 23163 316 28 205 1977-1978 28 14961 1992-1993 Average 19098 267 St. Dev. 2302 52 It should be mentioned that a water year shown in Table 4-4 runs from Oct. 1 to Sept. 30. In terms of the period chosen for the model calibration, an obvious good choice would be 47 01/10/1970 to 30/09/1976 period, because it contains three below-average years and three above-average years in terms of both total annual flow and annual maximum daily flood. It also contains years with the largest (1975-1976) and second lowest (1972-1973) annual flow. Therefore, this six-year continuous period is used for parameter sensitivity analysis and model calibration when required. 4.2 Statistical Measures of Model Efficiency Both the volumes and patterns of runoff simulated by the model have to show good agreement with those from the historical record. A model performance is measured visually and statistically. The visual criterion involves plotting the calculated hydrograph on top of the historical one and comparing goodness of fit. The most commonly accepted statistical criterion used in watershed modelling is the model efficiency suggested by Nash and Sutcliffe (1970), and based on the difference between variances of observed and calculated flow. The variances of calculated flow [s2(Qcai)] and observed flow [s2(Q0u-J\ can be expressed as follows: s 2 ( Q c a l ) n-\ (4.1) ^ ^ ( Qobs Q-obs ) (4.2) where, obs Qobs ~ ;=1 (4.3) n 48 and, n = the number of days for daily runs or hours for hourly runs Q'obs - the observed flow on day (hour) i Q'cal = the calculated flow on day (hour) i The model efficiency is then given as: Combining Equation (4.4) with Equations (4.1) and (4.2), tiQL-QL)2 E\ = l-^ — — (4.5) 2J ( Qobs ~ Qobs ) El relates how well the calculated hydrograph compares in volume and shape to the observed one. A negative value of El means that the observed mean flows are closer to observed flows than the flows calculated by model. The statistical module of the UBCWM uses additional statistics, namely the coefficient of determination (D!) which relates how well the calculated hydrograph compares in shape to the observed one. Therefore, it depends only on timing but not on volume; in fact, unlike the El, the DI can be high even when the volumes are quite different. The coefficient of determination is calculated as follows: D \ = l - ^ — n • — (4.6) 5J ( Qobs ~ Qobs ) where, 49 a n Q o b s ^^ll Qct • a  J (4.7) b n | n n 2a Q o b s ' Q c a l 2a Q o b s 2a Q < 1T\ ITT (4.8) The volume error is given as: SV = Q o b s Q < c a i (4.9) For a successfully calibrated model, the values of El, Dl, and (7 - SV) should be close to 1. In addition to visual evaluation of simulation efficiency, this study will use the statistical measures from Equations 4.5 through 4.9. Most of the time focus will be on coefficient of efficiency and volume error. During sensitivity analyses all three statistics will be displayed. The difference between coefficients of efficiency and determination is a useful indicator of the possibility of improvement during model calibration. The coefficient of determination is always higher than the coefficient of efficiency and the closer their values are to each other, the lesser the possibility for improvement. Consequently, a larger difference between El and Dl indicates that the model calibration can still be further improved. 4.2.1 Effects of Different Time Scales on the Coefficient of Efficiency Watershed hydrographs appear to exhibit much less variety than watershed topography, land cover and soils, indicating that averaging of local detail is taking place at the watershed scale. Also, similarly to the snow case, different rainfall inputs tend to produce outflows that are less different then the original inputs when applied to a watershed. This can be explained by the watershed response mechanism, i.e., its storage capability. From the Unit Hydrograph concept, it 50 is known that the instantaneous effective rainfall input in a given time step will not appear at the watershed outlet in its entirety within the same time step, but will rather be distributed over several time steps depending on the time delay in watershed response. This implies that because of the nature of runoff process (storage effects), watershed outputs are always better correlated than the meteorological inputs that caused them. It is relatively easy to show that two uncorrelated rainfall events shown in Figure 4-2 will produce instantaneous unit hydrographs (Figure 4-3) having certain mutual correlation. The detailed calculation and analysis of correlation between these two rainfall events and between the hydrographs caused by them is given in Appendix A. Rainfall #1 Rainfall #2 S a b 0 day 1 day 2 time day 1 day 2 time Figure 4-2. Different scenarios for a two-day rainfall event 51 — Outflow from rain #1 Outflow from rain #2 ( 2 3 4 5 6 7 8 9 10 Days Figure 4-3. Outflow hydrographs for rainfalls #1 and #2 It is obvious from Figures 4-2 and 4-3 that the two outflow hydrographs have better correlation than the rainfall events that caused them. Furthermore, if the comparison started on day 2 in Figure 4-3, the two hydrographs would be perfectly correlated, i.e., the correlation coefficient would be equal to 1. As the watershed storage increases, the outflow hydrographs resulting from totally uncorrelated rainfall events become even more correlated, as shown in Appendix A. This has important implications in understanding and subsequently modelling natural watershed behaviour. Flashy, fast-responding watersheds may require better, more representative precipitation data for successful modelling. On the other hand, slower responding watersheds may be less dependent on quality and representativness of meteorological input data. The hydrographs from Figure 4-3 are used to illustrate the behaviour of the Nash-Sutcliffe coefficient of efficiency ( £ 7 ) , especially its sensitivity to the time scale for which it is calculated. 52 For the purpose of calculating El, the hydrograph caused by Rainfall #1 is assumed to be the observed flow and the hydrograph caused by Rainfall #2 is assumed to be the calculated flow. The detailed analysis presented in Appendix A shows that: a) The high coefficient of correlation between the observed and calculated hydrographs does not necessarily imply high El; b) El is always higher when measured on longer periods of model run, regardless of the watershed storage capability. Clearly, since the measure of the model efficiency is dependent on duration of the calculated period, it is very important not to rush to the conclusion that a model is successful because it has a high annual coefficient of efficiency. This also could lead to the conclusion that certain model parameters are insensitive, while the truth may be that they are effective only for short periods of time and their sensitivity is dampened when analysed on a longer time window. It is fairly common to show the coefficient of model efficiency measured on an annual scale and that is often an acceptable measure of model validity. However to investigate less frequent phenomena, such as, for example, extreme floods during which non-linearity of the watershed is increased, one should focus on time windows much shorter than one year. Two watershed models may have similar efficiencies on an annual basis, and yet very different efficiencies during storms of weekly duration. Evidently, the better model is the one that has the higher efficiency during weeklong storms, because it captures less frequent non-linear behaviour that a watershed exhibits only during those unusual events. At that time, parameters that previously appeared unimportant could prove to make a difference between successful and unsuccessful model simulation. Because of this, it is important to also investigate the statistical model efficiency measures by modelling extreme historical events of relatively short duration. This short duration, 53 in most cases a few days, usually requires the decrease in computational time step within a model. 4.3 Single High-Altitude Meteorological Station as Input Mt. Fidelity meteorological station located at an elevation of 1875 m will be used as input into the previously described six model structures. Initially, the models will be run without calibration, i.e. all parameters in the model will have default values based on physical common sense (their values are shown in Table 4-12, page 78). In addition, meteorological input will not be modified and precipitation and temperature data will be used as measured at Mt. Fidelity station. This means that previously mentioned (Chapter 3.1) snowfall (SREP) and rainfall (RREP) adjustment factors that are used to adjust measured precipitation at the station will be equal to zero. The lllecillewaet watershed will first be modelled using a spatially lumped approach, i.e. the watershed will be represented with the single elevation band (Chapter 4.3.1). After that, a varying degree of spatial distribution will be examined by representing the watershed with two and then eight elevation bands (Chapter 4.3.2). The parameters will then be subjected to sensitivity analysis (Chapter 4.3.5), which will determine the sensitivity and acceptable range of value for each parameter. The information about sensitive ranges of the parameters will be used as input to calibration of the model (Chapter 4.3.6). For plotting purposes it was decided to show modelling results in the form of the hydrographs for a maximum of two consecutive years, because visual clarity of the charts is reduced under longer time period. However, where applicable, the statistics for the entire 28-year simulation periods are shown in corresponding tables. These tables, therefore, show the statistics for the 6-year calibration period (1970-1976) and the 22-year validation period (year 1969 and 1977-54 1997). The plotting period was chosen to be 01/10/1972 to 30/09/1974, because it shows second lowest water year followed by fifth highest water year. Meteorological input data from Mt. Fidelity station for this period is shown in Figure 4-4. Ol-Oct-72 31-Dec-72 01-Apr-73 01-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Tmax Tmiii Precipitation Figure 4-4. Meteorological data recorded at Mt. Fidelity station (1875 m) 4.3.1 Watershed Represented with Single Elevation Band As already mentioned, the following are the results achieved without calibration of the model. Default parameters will be described and explained as they are introduced in each of the following successive tests. The absence of calibration, i.e., uniformity of parameters, enables us to analyse the effects caused only by differences in model structure. Model calibration will be performed later and will, without doubt, improve these results. It will then be possible to check 55 if findings about differences among presented model structures for non-calibrated models hold true after model calibration. The first series of tests, Tests #1, #2 and #3, are very simplistic and would not be expected to yield good results. They are carried out for comparison with later tests, so that the role of increasing model complexity can be evaluated. 4.3.1.1 Test HI: This test uses Model structure #1 that is described in Chapter 3, Figure 3-1. The watershed is modelled as a single elevation band without any vegetative cover, i.e., 0% of forest cover. Results for two consecutive years are shown in Figure 4-5. As expected, this unrealistic concept results in very poor simulation results. After seeing such a mismatch between simulated and observed hydrographs in Figure 4-5, there is no need to perform statistical evaluation. Remember, Figure 4-5 shows the result achieved without model calibration. To illustrate what will happen later, the calibration results are shown in Figure 4-5(a) for this test only. For all other tests the calibration results are shown in Chapter 4.3.6, after sensitivity analysis is completed. The model calibration in Test #1 is comprised of modifying only two parameters as follows: the precipitation adjustment factor for snow (SREP) is changed from the default value of 0.0 to -0.4, and the precipitation adjustment factor for rain (RREP) was changed from the default value of 0.0 to -0.2. This calibration somewhat improved simulation as seen in Figure 4-5(a). However, it is clear that this unrealistic concept of surface runoff only, and instantaneous watershed response to rainfall and snowmelt input, produces a poor runoff simulation, even after the calibration. 56 Ol-Oct-72 31-Dec-72 OI-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Observed flow Calculated flow Figure 4-5. Modelling Results of Test #1 (Mt. Fidelity; 1 elevation band) Ol-Oct-72 3l-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 | Qobs Qcai (before calibration) Qcai (after calibration) Figure 4-5(a). Test #1 calibration results (Mt. Fidelity; 1 elevation band) 4.3.1.2 Test #2: This test also uses Model structure #1 and represents the watershed as a single elevation band. The only difference is in the land cover representation, because Test #2 uses two land cover types, forested and unforested (open) areas. It is known that snow melts differently under forest canopy than under open sky. Therefore, it is expected that use of two land cover representations would improve modelling results for the snowmelt-dominated Illecillewaet watershed. The measured value of 74% forested area is taken from Table 4-3. It can be seen in Figure 4-6 that the results improve slightly, due to the snowmelt process under forest canopy being somewhat delayed. However the results are still well below acceptable levels. This test, along with Test #1, indicates that the concept of instantaneous watershed response to rainfall and snowmelt input is a significant shortcoming that cannot be overcome in practical applications. 900 r 800 700 600 500 Ol-Oct-72 31-Dec-72 01-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Figure 4-6. Modelling Results of Test #2 (Mt. Fidelity; 1 elevation band) a Obs flow Cai flow 58 In both Test #1 and Test #2 precipitation data from Mt. Fidelity was not adjusted, i . e., precipitation adjustment factors SREP and RREP were not used. In addition, there was no need for precipitation gradient parameters since the watershed was represented by a single elevation band. 4.3.1.3 Test #3: This test uses Model structure #2 that is described in Chapter 3, Figure 3-2. The watershed is represented as a single elevation band without any vegetative cover, i.e., 0% of forest cover. As seen in Model structure #2 diagram, the watershed is still assumed to be 100% impermeable, which means that only the surface runoff component exists. However, some delay in watershed response is modelled, which requires introduction of a routing algorithm. Surface runoff is routed through the watershed storage using a linear routing concept of two reservoirs in series. This means that in this test, watershed non-linear behaviour is still not captured by the modelling concept. The incorporation of a routing algorithm in the model structure results in an additional parameter that is required to determine the routing time delay for fast surface runoff. This parameter is referred to as routing time constant. The fast surface runoff may be generated by three runoff-generating mechanisms, namely rainfall, snowmelt and glacier melt. Therefore one may decide to assign a different routing time constant values for each of the three fast runoff components. However in the modelling concept applied in this test, it was decided to have only one fast flow routing time constant (FTK) that would be the same for rainfall, glacier and snowmelt fast flow. Its value is assigned to be one day. The results of Test #3 are shown in Figure 4-7. Obviously, the introduction of a delay in watershed response improved simulation results compared to previous tests. 59 700 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 -Obs flow - Cal flow Figure 4-7(a). Comparison of Observed and Calculated flow: Test #3 (Mt. Fidelity; 1 elev. band) 700 600 500 400 300 200 100 0 Ol-Oct-72 31-Dec-72 01-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Gla. outflow - Snowmelt fastflow - Rainfall fastflow Figure 4-7(b). Calculated flow components: Test #3 (Mt. Fidelity; 1 elevation band) 60 It is interesting to note changes in simulated hydrographs from Test #1 (Figure 4-5) to Test #3 (Figure 4-7). Recall that the only difference between these two tests is delay in watershed response. The annual flood of 1973 simulated using an instantaneous response in Test #1 is 834 m3/s, whereas the same flood simulated using a routing time delay constant of 1 day in Test #3 is 598 m3/s. This represents a 28% decrease due to delay in watershed response. However, the 1974 annual flood simulated in Test #1 is 752 m3/s, and the same flood simulated in Test #3 is 699 m3/s, which represents a decrease of only 7%. An obvious question is why there is such a big difference in the peak flows decreases. This can be explained by the ways in which these two floods are built up. The simulated flood of 1973 is a result of a high-temperature spell that lasted only three days causing high snowmelt rate. After that three-day period, the temperature dropped and snow melting ceased. The result is a sharp, short-duration peak flow. If the snowmelt input causing this peak flow is routed through linear storage, the decrease in peak magnitude will be proportional to the duration of snowmelt causing the peak, i.e. the shorter the snowmelt event, the greater the decrease in simulated peak flow. This is why the simulated flood of 1973 decreased by 28% when a model structure with routing algorithm was used. On the other hand, the simulated flood of 1974 resulted from a longer high-temperature spell that lasted 14 days causing significant snowmelt. This explains the decrease in peak flow of only 7%. 4.3.1.4 Test #4: Model structure #2, is also used for Test #4. The only difference between this test and Test #3 is in land cover representation. While Test #3 assumed that entire watershed is open area, in this test two land covers were used. The measured value of 74% of forested area is taken from Table 4-3. In addition to the delay caused by the routing algorithm, simulated flow in this test is further delayed by slower snowmelt process under forest canopy. All this resulted in a significant 61 improvement compared to previous tests, even though watershed behaviour remains linear. Simulated and observed hydrographs are shown in Figure 4-8. The detailed calculated statistics are shown in Table 4-5. From this point on, for the remainder of the tests, only the summary statistics will be displayed in the main body of the text. The detailed calculated statistics for all performed tests can be seen in the Appendix B. Table 4-5. Calculated statistics of Test #4 without calibration (Mt. Fidelity; 1 elevation band) Water Year Coeff. of Eff. El Coeff. of Det. Dl Volume Error (%) 1969-1970 0.15 0.83 24.84 1970-1971 0.28 0.82 28.07 1971-1972 0.56 0.92 27.46 1972-1973 0.11 0.82 33.10 1973-1974 0.62 0.88 19.84 1974-1975 0.12 0.85 43.95 1975-1976 0.31 0.83 29.03 1976-1977 -0.13 0.84 39.14 1977-1978 0.11 0.77 30.24 1978-1979 -0.26 0.82 38.29 1979-1980 -0.01 0.80 32.94 1980-1981 -0.01 0.74 22.25 1981-1982 0.30 0.89 35.50 1982-1983 0.21 0.76 27.20 1983-1984 0.17 0.80 22.26 1984-1985 0.18 0.90 39.79 1985-1986 0.40 0.89 28.21 1986-1987 -0.04 0.82 40.13 1987-1988 -0.31 0.79 51.40 1988-1989 -0.77 0.82 51.37 1989-1990 0.09 0.86 36.80 1990-1991 0.06 0.87 36.90 1991-1992 -0.03 0.71 34.19 1992-1993 -0.13 0.79 33.37 1993-1994 0.00 0.72 27.53 1994-1995 0.07 0.78 31.69 1995-1996 0.49 0.85 15.65 1996-1997 0.68 0.91 13.13 Maximum 0.68 0.92 51.40 Minimum -0.77 0.71 13.13 Average 0.12 0.82 31.94 62 700 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 -Obsflow - Ca! flow Figure 4-8(a). Comparison of Observed and Calculated flow: Test #4 (Mt. Fidelity; 1 elev. band) Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 - Glacier outflow - Snowmelt fastflow - Rainfall fastflow Figure 4-8(b). Calculated flow components: Test #4 (Mt. Fidelity; 1 elevation band) 63 4.3.1.5 Test #5: This test uses Model structure #3 described in Chapter 3, Figure 3-3. The watershed is represented as a single elevation band without any vegetative cover, i.e., 0% of forest cover. In this modelling concept, part of the watershed is permeable, which means that infiltration is allowed to occur. Infiltrated water is subject to soil moisture accounting and evapotranspiration losses. Routing through watershed storage remains linear but non-linearity in watershed behaviour is captured by the soil moisture module (see Figure 3-3). In this test, two different components of total watershed runoff are recognised. They are the fast, surface runoff component and the much slower, groundwater component. This modelling concept is more complex than the one used in Tests #3 and #4, and thus requires two additional parameters. They are the fraction of impermeable area (IMPA) and the groundwater routing time constant (GTK). The fraction of impermeable area is assumed to correspond to the lack of forested area. Since the fraction of forested area is measured to be 0.74, the IMPA is assumed to be 0.26. Evidently, the "lack of forest" rule for impermeable fraction is not always accurate but in most cases is a good first assumption. If necessary, this parameter could be determined by a trial-and-error optimisation procedure. The groundwater time constant is assigned a value of 60 days. List of all parameters used in this and all the other tests is shown in Table 4-12 at the end of this chapter on page 78. Table 4-12 clearly shows how the number of required parameters increases with increases in model complexity. The significant advantage of the modelling concept implemented in Test #5, compared to previous tests, is the existence of a slower sub-surface runoff component. That is why Test #5 results in a more realistic representation of the watershed runoff process. The results are shown statistically in Table 4-6. More detailed statistics for this and the other tests, as mentioned previously, can be seen in the Appendix B. Hydrograph plots shown in Figure 4-9 reveal that much of the runoff oversimulation from previous tests is reduced, because 64 some water infiltrated to groundwater and was subjected to considerable delay. However, modelling of the entire watershed as a non-forested, open area caused some oversimulation due to unrealistically quick melting of snow throughout the watershed. Table 4-6. Annual statistics of Test #5 without calibration (Mt. Fidelity; 1 elevation band) 1969-1997 Coeff. of Eff. El Coeff. of Det. DI Volume Error (%) Maximum 0.85 0.86 44.72 Minimum 0.22 0.61. 6.65 Average 0.53 0.76 25.21 *Detailed annual statistics are shown in the Appendix B Note that maximum and minimum values of Volume Error from the Summary Table 4-6 do not correspond to the maximum and minimum values of El and DI (see the detailed statistics in Appendix B). For example, maximum Volume Error of 44.72% from Table 4-6 was from the water year 1988/89, whereas maximum El of 0.85 was from the water year 1996/97. 65 500 Ol-Oct-72 31-Dec-72 01-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Obs flow Cal flow Figure 4-9(a). Comparison of Observed and Calculated flow: Test #5 (Mt. Fidelity; 1 elev. band) 500 450 400 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glacier outflow Groundwater Snowmelt fastflow Rainfall fastflow Figure 4-9(b). Calculated flow components: Test #5 (Mt. Fidelity; 1 elevation band) 66 4.3.1.6 Test #6: In this test, everything was the same as in Test #5 except for the land cover characterisation. The forested fraction is 0.74. Part of the oversimulation from Test #5 was further reduced by the delay caused by the slower snowmelt process under the forest canopy. The results improved dramatically as shown in Table 4-7 and Figure 4-10. The detailed annual statistics can be seen in the Appendix B. Table 4-7. Annual statistics of Test #6 without calibration (Mt. Fidelity; 1 elevation band) 1969-1997 Coeff. of Eff. E! Coeff. of Det. DI Volume Error (%) Maximum 0.92 0.93 31.51 Minimum 0.71 0.79 -7.17 Average 0.84 0.88 13.37 ^Detailed annual statistics are shown in the Appendix B 67 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Obs flow Cai flow j Figure 4-10(a). Comparison of Observed and Calculated flow: Test #6 (Mt. Fidelity; 1 el. band) 350 T 1 300 250 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 | Glacier outflow Groundwater Snowmelt fastflow Rainfall fastflow Figure 4-10(b). Calculated flow components: Test #6 (Mt. Fidelity; 1 elevation band) 68 4.3.1.7 Test #7: This test uses Model structure #4 described in Chapter 3, Figure 3-4. The entire watershed is assumed to be an open, unforested area. Model structure #4 applied in this test is very similar to Model structure #3 used in the previous two tests. The only difference is that the groundwater runoff component is split in two components with different routing time delays. This is done by introducing three more parameters. First, the deep zone share (DZSH) divides total groundwater into a faster upper groundwater and a slower deep-zone groundwater. DZSH is a fraction of total groundwater that is allocated to the deep-zone groundwater. The second and third additional parameters are routing time constants for upper (UGTK) and deep-zone groundwater (DZTK). The UGTK and DZTK were assigned values of 30 and 210 days, respectively. The results of Test #7 are shown in Table 4-8 and Figure 4-11. It is interesting to compare these results with the results of Test #5, i.e., groundwater split in two components with different time delays versus total groundwater with uniform time delay. One would expect that the results of Test #7 would be at least equal to those of Test #5, if not better. However as shown in Table 4-8 versus Table 4-6, they are consistently worse. This means that in the case of an open (unforested) watershed, better results were achieved by representing groundwater as one component with a routing time constant of 60 days than by splitting it into faster (30 days) and slower responding components (210 days). Table 4-8. Annual statistics of Test #7 without calibration (Mt. Fidelity; 1 elevation band) 1969-1997 Coeff. of Eff. El Coeff. of Det. Dl Volume Error (%) Maximum 0.82 0.84 45.15 Minimum 0.20 0.55 0.73 Average 0.50 0.72 24.92 * Detailed annual statistics are shown in the Appendix B 69 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 -Obs flow Cal flow Figure 4-11(a). Comparison of Observed and Calculated flow: Test #7 (Mt. Fidelity; 1 el. band) 500 450 400 350 300 250 | 200 150 100 50 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow Upper groundwater Lower groundwater Snowmelt fastflow Rainfall fastflow Figure 4-11(b). Calculated flow components: Test #7 (Mt. Fidelity; 1 elevation band) 70 4.3.1.8 Test US: This test is the same as Test #7 except for land cover. The forested fraction is 0.74. The results of Test #8 are shown in Table 4-9 and Figure 4-12. Comparison between the results of this test and those of Test #6 shows that the concept of groundwater division into two components with different time delays brought only marginal improvement in simulation results. It is obvious from the performed tests that in the case of a snowmelt-dominated watershed such as the lllecillewaet, two land cover representations are essential for realistic representation of runoff processes. Therefore, the option of 0% of forest cover is not used in testing the remaining model structures. Table 4-9. Annual statistics of Test #8 without calibration (Mt. Fidelity; 1 elevation band) 1969-1997 Coeff. of Eff. El Coeff. of Det. DI Volume Error (%) Maximum 0.92 0.94 31.86 Minimum 0.74 0.79 -11.74 Average 0.85 0.88 13.55 * Detailed annual statistics are shown in the Appendix B 4.3.1.9 Test #9: In this test, Model structure #5, described in Chapter 3, Figure 3-5, is applied. One elevation band and two land covers are used. This is the current UBC Watershed Model structure. As shown in Figure 3-5, this concept allows for the additional component of total watershed runoff that is faster in response than groundwater but slower than fast surface runoff. This runoff 71 350 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 -Obs flow - Cai flow Figure 4-12(a). Comparison of Observed and Calculated flow: Test #8 (Mt. Fidelity; 1 el. band) 350 250 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow Upper groundwater Lower groundwater Snowmelt fastflow Rainfall fastflow Figure 4-12(b). Calculated flow components: Test #8 (Mt. Fidelity; 1 elevation band) 72 component is called interflow and is given last priority in moisture allocation within the soil moisture control routine. Increased complexity is reflected through introduction of two additional parameters. First, the groundwater percolation (PERC) parameter that determines the maximum amount of water that is allowed to percolate to groundwater. Any excess water becomes interflow. Therefore a second additional parameter that has to be introduced in this model structure is a routing time constant for interflow (ITK). Values assigned to these two parameters, along with the parameter values used in all other tests are shown in Table 4-12. The results of Test #9 are shown in Table 4-10 and Figure 4-13. Comparisons between the results of this test and tests #8 and even #6 show that significant improvement in model efficiency is achieved only by dividing total runoff into a faster surface component and a slower sub-surface component. Further divisions of sub-surface runoff into components with different time delay signatures resulted in rather small improvements. For example, modelling of interflow in Test #9 helped improve Tests #8 and #6 simulation of the 1974 flood (Figure 4-13), but worsened the simulation of the 1989 hydrograph. Generally, having the ability to model interflow helps in simulation of certain peak flows. It should be noted that no model calibration was performed in the tests and the watershed was represented by a single elevation band. Table 4-10. Annual statistics of Test #9 without calibration (Mt. Fidelity; 1 elevation band) 1969-1997 Coeff. of Eff. El Coeff. of Det. Dl Volume Error (%) Maximum 0.94 0.95 30.82 Minimum 0.70 0.80 -7.17 Average 0.85 0.89 13.51 Detailed annual statistics are shown in the Appendix B 73 350 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Obs flow Cai flow Figure 4-13(a). Comparison of Observed and Calculated flow: Test #9 (Mt. Fidelity; 1 el. band) 350 T 1 300 250 200 , i 'E 150 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow — Upper GW Lower GW Snow interflow Rain interflow Snow fastflow Rain fastflow Figure 4-13(b). Calculated flow components: Test #9 (Mt. Fidelity; 1 elevation band) 74 4.3.1.10 Test #10: This test uses Model structure #6 shown in Chapter 3, Figure 3-6. The watershed is represented by a single elevation band and two land covers are used. The model structure is similar to the previous one in terms of having the same number of runoff components. The difference is that interflow is given the same priority in the runoff allocation scheme as groundwater, assuming that groundwater abstraction and interflow demands are satisfied at the same time. One implication of this approach is that interflow occurs much more frequently than in the previous model structure. It can be seen in Table 4-12 that the number of required parameters is the same as in Test #9. The groundwater percolation (PERC) parameter that determines the maximum amount of water that is allowed to percolate to groundwater is not needed in this concept and is replaced by the parameter (GWFR) that determines the fraction of infiltrated water assigned to the groundwater. The rest of the infiltrated water is assigned to the interflow. In this test the GWFR was assigned value of 0.90. The results of Test #10 are shown in Table 4-11 and Figure 4-14. Comparison of the results of tests #10 and #9 indicates that giving priority to groundwater over the interflow yields very similar results as having them both occur at the same time. Calculated statistics in Table 4-11 indicate that Test #10 consistently oversimulated annual volume. This was the case in other tests as well. The reason for the volume oversimulation is the bias in input data. It was already mentioned and also shown in Table 4-12 that precipitation data from Mt. Fidelity is used without any modification, i.e. precipitation adjustment factors SREP and RREP are set to zero in each test. This precipitation data obviously has positive bias, indicating that original precipitation data should be reduced before being input into the model. Using a trial-and-error calibration 75 procedure, it is possible to find optimum values for the SRJEP and RREP parameters, as well as other sensitive parameters. A parameter is sensitive if a small change in parameter value causes a significant change in model simulation efficiency. Consequently, insensitive parameters do not require calibration as long as their value is within some reasonable range. Table 4-11. Annual statistics of Test #10 without calibration (Mt. Fidelity; 1 elev. band) 1969-1997 Coeff. of Eff. El Coeff. of Det. DI Volume Error (%) Maximum 0.93 0.94 37.36 Minimum 0.67 0.82 -4.00 Average 0.85 0.90 17.44 * Detailed annual statistics are shown in the Appendix B 76 Ol-Oct-72 31-Dec-72 Ol-Apr-73 01-Ju]-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 -Obs flow - Cal flow Figure 4-14(a). Comparison of Observed and Calculated flow: Test #10 (Mt. Fidelity; 1 el. band) 01-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow Upper GW Lower GW Snow interflow Rain interflow — Snow fastflow Rain fastflow Figure 4-14(b). Calculated flow components: Test #10 (Mt. Fidelity; 1 elevation band) 7 7 Table 4-12. List of parameters used in the tests (one meteorological station, one elevation band) Test# 1 2 3 4 5 6 7 8 9 10 SREP 0 0 0 0 0 0 0 0 0 0 RREP 0 0 0 0 0 0 0 0 0 0 TREE 0 0.74 0 0.74 0 0.74 0 0.74 0.74 0.74 +•» FTK 1 1 1 1 1 1 1 1 a> E IMPA 0.26 0.26 0.26 0.26 0.26 0.26 I Para GTK 60 60 I Para DZSH 0.53 0.53 0.53 0.53 •a UGTK 30 30 30 30 © DZTK 210 210 210 210 PERC 18 ITK 7 7 GWFR 0.90 Legend: SREP - Precipitation adjustment factor for snow RREP - Precipitation adjustment factor for rain TREE - Forested fraction of the watershed area FTK - Fast flow (surface runoff) routing time constant [days] IMPA - Impermeable fraction of the watershed area GTK - Total groundwater time constant [days] DZSH - Deep zone share of total groundwater UGTK - Upper groundwater time constant [days] DZTK - Deep-zone groundwater time constant [days] PERC - Maximum percolation to groundwater [mm/day] ITK - Interflow time constant [days] GWFR - Groundwater fraction of water available for groundwater and interflow 78 4.3.2 Watershed Represented with Two and Eight Elevation Bands In all ten presented tests, the Illecillewaet watershed was represented with a single elevation band. The identical tests are also performed for the cases where the watershed is divided into two and eight elevation bands. Again remember that these results are achieved without model calibration. The calibrated results will be presented later in Chapter 4.3.6. The watershed description parameters are shown in Tables 4-2 and 4-1. The goal is to see how much this increase in degree of detail in watershed description improves simulation results. Use of more than one elevation band allows the modeller to utilise previously mentioned precipitation gradients that model orographic enhancement of precipitation. It is mentioned before that these gradients are generally the highest on lower mountain slopes, and get smaller close to the top of the mountain. This hypothesis is followed in this study and therefore in all performed tests, precipitation gradient of 8% is used for elevations of up to 1940 m. Above this elevation a precipitation gradient of 3% is applied. Having in mind that precipitation is entered at Mt. Fidelity at an elevation of 1875 m, this means that precipitation is modelled to decrease by 8% per every 100 m below Mt. Fidelity and to increase for the same amount between Mt. Fidelity and an elevation of 1940 m. Above 1940 m, precipitation is assumed to increase by 3% per every 100 m. It should be noted that these gradients also existed in previous experiments with only one elevation band, but would have no effect, because the watershed was assumed to be a flat plane of constant elevation. The following are the results of tests #1 through #10 with two and eight elevation bands. They are then statistically compared with the previously shown results obtained using a single elevation band representation. 79 900 800 Figure 4-15. Test #1 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 900 800 Figure 4-16. Test #2 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) Figure 4-17. Test #3 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Gla. outflow Snowmelt fastflow Rainfall fastflow Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Gla. outflow Snowmelt fastflow Rainfall fastflow Figure 4-17 (contin.). Test #3: Cal. flow components; 2 bands (above) and 8 bands (below) Figure 4-18. Test #4 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) Figure 4-18 (contin.). Test #4: Cai. flow components; 2 bands (above) and 8 bands (below) 350 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Obs flow Cal flow 350 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Obs flow Cal flow Figure 4-19. Test #5 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 350 300 250 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glacier outflow Groundwater Snowmelt fastflow Rainfall fastflow _ . 350 300 E Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glacier outflow Groundwater Snowmelt fastflow Rainfall fastflow Figure 4-19 (contin.). Test #5: Cai. flow components; 2 bands (above) and 8 bands (below) 8 7 350 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Obs flow Cal flow 350 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Obs flow Cal flow Figure 4-20. Test #6 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 88 350 300 250 200 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 | Glacier outflow Groundwater Snowmelt fastflow Rainfall fastflow | 350 r 300 250 200 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 | Glacier outflow Groundwater Snowmelt fastflow Rainfall fastflow Figure 4-20 (contin.). Test #6: Cai. flow components; 2 bands (above) and 8 bands (below) 89 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Obs flow Cai flow Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Obs flow Cai flow Figure 4-21. Test #7 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 350 3(Kl 250 200 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 [ Glac. outflow — Upper groundwater Lower groundwater Snowmelt fastflow — Rainfall fastflow ] 350 300 200 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow — Upper groundwater Lower groundwater ^—Snowmelt fastflow Rainfall fastflow Figure 4-21 (contin.). Test #7: Cal. flow components; 2 bands (above) and 8 bands (below) 91 Figure 4-22. Test #8 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 350 300 250 200 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow Upper groundwater Lower groundwater Snowmelt fastflow Rainfall fastflow 350 300 250 200 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow Upper groundwater Lower groundwater Snowmelt fastflow -—Rainfall fastflow Figure 4-22 (contin.). Test #8: Cal. flow components; 2 bands (above) and 8 bands (below) 93 Figure 4-23. Test #9 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 350 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow ^—UpperGW LowerGW Snow interflow Rain interflow Snow fastflow — Rain fastflow 350 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow ~— Upper GW LowerGW Snow interflow Rain interflow Snow fastflow Rain fastflow Figure 4-23 (contin.). Test #9: Cal. flow components; 2 bands (above) and 8 bands (below) 95 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 -Obs flow Cai flow Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 -Obs flow - Cai flow Figure 4-24. Test #10 results with 2 bands (above) and 8 bands (below) (Mt. Fidelity) 96 300 250 200 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow Upper GW LowerGW Snow interflow Rain interflow Snow fastflow Rain fastflow 350 300 250 200 = Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Glac. outflow ^— Upper GW LowerGW Snow interflow Rain interflow — Snow fastflow Rain fastflow Figure 4-24 (contin.). Test #10: Cal. flow components; 2 bands (above) and 8 bands (below) 4.3.3 Comparison of Calculated Statistics Model statistics for each test with the watershed represented by one, two or eight elevation bands are calculated and compared in Table 4-13. The presented statistics are annual summaries only; detailed statistics for each individual test can be seen in the Appendix B. The results were achieved without model calibration. Also note that the Volume Errors do not correspond to the El values. Table 4-13. Comparison of model statistics achieved without calibration (Mt. Fidelity) 1969-1997 Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands Maximum 0.68 0.85 0.89 51.40 48.17 44.71 Vi <u Minimum -0.77 -0.14 -0.03 13.13 10.09 7.93 H Average 0.12 0.53 0.56 31.94 27.52 25.33 ICi Maximum 0.85 0.93 0.97 44.72 35.77 32.85 +j Vi <D Minimum 0.22 0.56 0.66 6.65 1.50 -1.45 H Average 0.53 0.80 0.86 25.21 19.26 15.53 Maximum 0.92 0.97 0.96 31.51 24.60 20.82 Vi <u Minimum 0.71 0.79 0.75 -7.17 -8.89 -10.62 H Average 0.84 0.88 0.87 13.37 9.30 7.94 r~ Maximum 0.82 0.93 0.97 45.15 38.38 33.16 Vi Minimum 0.20 0.59 0.70 0.73 -1.43 -2.96 H Average 0.50 0.81 0.87 24.92 19.14 15.61 00 Maximum 0.92 0.96 0.96 31.86 24.93 21.15 VI at Minimum 0.74 0.81 0.78 -11.74 -12.43 -13.81 H Average 0.85 0.89 0.89 13.55 9.45 8.23 o\ Maximum 0.94 0.97 0.96 30.82 24.06 20.49 VI <u Minimum 0.70 0.81 0.78 -7.17 -8.61 -10.95 H Average 0.85 0.89 0.89 13.51 9.40 8.03 o Maximum 0.93 0.97 0.97 37.36 28.39 23.37 +j Vi Minimum 0.67 0.80 0.79 -4.00 -7.01 -9.63 H Average 0.85 0.89 0.89 17.44 . 11.57 9.06 * Detailed annual statistics for each test are shown in the Appendix B 98 4.3.4 General Comments on Presented Results for Uncalibrated Model The results presented thus far are achieved without model calibration. Therefore, the following comments address the results of different non-calibrated model structures using average default parameter values. Calibration of a model will, without a doubt, improve these results. 4.3.4.1 Effects of Model Structure: Results from the ten tests representing six different watershed model structures were presented for the lllecillewaet watershed using point-input data from the Mt. Fidelity meteorological station. In addition, for each of the ten tests, three sub-tests were performed representing the watershed as one, two or eight elevation bands. Model structures 1 through 6 (Figures 3-1 through 3-6) were used as follows: • Model structure 1 was used in Test #1 (one land cover) and Test #2 (two land covers) • Model structure 2 was used in Test #3 (one land cover) and Test #4 (two land covers) • Model structure 3 was used in Test #5 (one land cover) and Test #6 (two land covers) • Model structure 4 was used in Test #7 (one land cover) and Test #8 (two land covers) • Model structure 5 was used in Test #9 (two land covers) • Model structure 6 was used in Test #10 (two land covers) The first and most obvious finding is the significance of land cover representation in modelling of snow-dominated watershed such as lllecillewaet. The reason for this is the significant difference between snowmelt rates in open area and those under forest canopy. This was especially noticeable in simpler model structures (Tests #1, #2, #3 and #4) because slower snowmelt process under canopy acts as a necessary delay. In more complex model structures 99 (Tests #5, #6, #7 and #8), the importance of land cover representation, although still rather high, decreased slightly. This is probably because the snowmelt process under canopy is not the only source of the delay in the watershed response. The model structures in these tests have soil moisture sub-model providing enough non-linearity and delay to somewhat dampen effects of different snowmelt processes under different land covers. Another important finding is that Model structures 1 and 2, which are fully linear, do not model any infiltration, and assume that all runoff from a watershed occurs as surface runoff, could not model streamflow from the lllecillewaet watershed realistically. Introduction of some delay in surface runoff response in Model structure 2 did improve results over instantaneous concept used in Model structure 1, but simulation results remained well below an acceptable level. Introduction of a soil moisture sub-model in Model structures 3 through 6, i.e., accounting for a surface as well as sub-surface runoff component, caused "order of magnitude" improvement in model efficiency as shown in the results of Tests #5 through #10. It is important to note that most of this improvement in efficiency occurred when Model structure 3 was applied (Tests #5 and #6). Remember, in Model structure 3 (Figure 3-3), total runoff is divided into faster surface component and slower sub-surface component. Further divisions of sub-surface runoff into components with different time delay signatures resulted in rather small improvements (Tests #7 through #10). This can be proven by comparing statistics shown in Table 4-13. For example, average annual model efficiency over a simulation period of 28 years for Test #6 (two runoff component - fast, surface runoff and slow, groundwater runoff) is 0.84, 0.88 and 0.87, for the one, two and eight elevation band cases, respectively. The same statistics for Test #8 (three runoff components - fast runoff and upper and lower groundwater) and for Test #9 (current UBCWM structure with four runoff components - fast runoff, interflow and upper and lower groundwater), are 0.85, 0.89 and 0.89. The Model structure 6 (Test #10), in which water 100 allocation priorities were modified so that groundwater percolation was not given priority over the interflow, yielded very similar results (Table 4-13). 4.3.4.2 Effects of the Number of Elevation Bands: In the case of one land cover representation, when the entire watershed is assumed to be unforested, open area (Tests #1, #3, #5 and #7), representing the watershed with a greater number of elevation bands results in better simulation. This was the case in each of the 28 simulated years, without a single exception. The reason, again, is in the snowmelt process. Melting from an open area is much faster than from a forested area and if the entire watershed is assumed to be an open area, snow will melt unrealistically fast from a single elevation band that has uniform temperature. Introduction of more elevation bands decreases temperature in higher bands and therefore delays snowmelt and improves the simulation results. That is why the approach with more elevation bands produces better results in the case of only one land cover. In the case of two land covers (Tests #2, #4, #6, #8, #9 and #10), representing the watershed with two or eight elevation bands produces better results than using a single elevation band approach, though improvement is rather modest (Table 4-13). However, it is very interesting to observe from these results that the two-elevation bands approach produces essentially the same results as an eight-elevation bands approach. Differences in simulated flow between the two-bands and eight-bands approaches are extremely small, essentially negligible and are shown in Figure 4-25. This agrees with the finding reported by Uhlenbrook et al. (1999) while testing the Swedish HBV watershed model with 1, 2, 5, 11 and 20 elevation bands. They reported that dividing the watershed into two elevation bands resulted in a significant increase in the model efficiency, whereas further divisions had negligible effect. 101 Test #1 700 600 Figure 4-25. Differences in simulated flow between 2-bands and 8-bands approaches 102 Test #3 600 t 500 Ol-Oct-72 31-Dcc-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Qcal(2bands) Qcal(8bands) Test #4 400 -• 350 I Ol-Oct-72 31-Dcc-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Qcal (2 bands) Qcal (8 bands) Figure 4-25 (continued). Differences in simulated flow between 2-bands and 8-bands approaches 103 Test #5 350 300 250 200 Ol-Oct-72 31-Dcc-72 Ol-Apr-73 Ol-Jul-73 30-Scp-73 30-Dcc-73 31-Mar-74 30-Jun-74 29-Scp-74 Qcai (2 bands) - Qcai (8 bands) Test #6 250 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Scp-73 30-Dcc-73 31-Mar-74 30-Jun-74 29-Scp-74 Qcai (2 bands) — Qcai (8 bands) Figure 4-25 (continued). Differences in simulated flow between 2-bands and 8-bands approaches 104 Test #7 350 (I I 1 > Ol-Oct-72 31-Dcc-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 Qcal (2 bands) Qcal (8 bands) Test #8 250 -i Figure 4-25 (continued). Differences in simulated flow between 2-bands and 8-bands approaches 105 Test #9 300 Ol-Oct-72 31-Dcc-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dcc-73 31-Mar-74 30-Jun-74 29-Scp-74 Qcai (2 bands) - Qcai (8 bands) Test #10 250 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Scp-74 Qcai (2 bands) - Qcai (8 bands) Figure 4-25 (continued). Differences in simulated flow between 2-bands and 8-bands approaches 106 4.3.4.3 Concluding Remarks forUncalibrated Model: From the results presented thus far, it can be concluded that in the case of the Illecillewaet Watershed and point input data, the minimum degree of distribution required to obtain realistic representation of runoff processes is achieved by Test #6 with two elevation bands. This test uses two land cover representations and Model structure 3 (Figure 3-3), where total runoff is divided into a faster surface component and a slower sub-surface component or groundwater with routing time constants of 1 and 60 days, respectively (Table 4-12). Running this model structure continuously for 28 years produces an average annual Nash-Sutcliffe efficiency of 0.88 with minimum and maximum values of 0.79 and 0.97, respectively (Table 4-13 and Appendix B). These statistics are rather satisfactory, especially knowing that no model calibration or input data adjustment is undertaken. More complex model structures and division in more than two elevation bands did not bring significant improvement in runoff simulation. However if model calibration was performed in the tests, the more complex model structures and greater number of elevation bands could prove to have a greater advantage over simpler concepts. For now, the relatively simple concept used in Test #6 appears to be quite satisfactory. 4.3.5 Sensitivity Analysis The following are the results of the analysis of the sensitivity of model parameters. More precisely, it is the sensitivity of the model output to a given change in each model parameter. It is common and convenient to refer to "parameter sensitivity" even though it is the model output which is the real sensitivity issue. 107 As previously mentioned Tests #1 through #4 could not produce realistic representation of watershed runoff process and are not explored further. Also, Tests #5 and #7 that had one land cover representation produced inferior results to the equivalent tests in which two land covers were used. Therefore, it is sufficient to perform sensitivity analysis and subsequent calibration only on Tests #6, #8, #9 and #10, in which two land covers were applied. For each of these tests, sensitivity analysis was performed for the versions with one, two and eight elevation bands. This was done in attempt to see what effect, if any, number of elevation bands has on parameter sensitivity. As previously mentioned the 1970-1976 period was chosen for sensitivity analysis and model calibration. Sensitivity analysis for an individual model parameter is performed by letting the analysed parameter change its value while all other parameters remain unchanged and recording the changes in model efficiency. It is known from curve-fitting techniques that better fit is achieved with a greater number of parameters. However, in order to avoid watershed modelling becoming a curve-fitting exercise, special attention should be paid to the parameters with low sensitivity, because of their negligible effect on model simulation results. An important implication of this is that before model calibration one should always perform a sensitivity analysis of the parameters that are about to be calibrated. It should be noted that parameter sensitivity is always tied to a statistical measure of model efficiency and its time window. It was shown (Appendix A) that Nash-Sutcliffe efficiency increases with the length of time window of the model run, i.e. due to seasonal shape of a hydrograph the efficiency is always higher when calculated on an annual than on monthly basis. Consequently, certain model parameters that come to play only during certain times of the year may show low sensitivity when the analysis is performed on an annual basis. For example, if we were to check sensitivity of a certain snowmelt parameter on an annual basis, it would show much lower sensitivity than if it were checked during the snowmelt season 108 only, because that parameter comes to play only about 50% of the time annually. This fact is even more important for the model parameters that come into effect only a few times within a year, for example during a big flood. Analysed annually they may be labelled insensitive or uncertain, but the reality is that they may be extremely important during certain times of year. Al l this implies that after the sensitivity analysis is performed on six-year runs in this study, we should be able to identify parameters that are sensitive when checked on time intervals equal to or greater than six years. The parameters that are not sensitive in this time frame may still be found relevant/sensitive when examined on a shorter time scale. Initial, non-calibrated values and descriptions for each parameter used in the tests with a single elevation band are shown in Table 4-12. In the case of two and eight elevation bands three additional parameters are added, namely the lower precipitation gradient (GRADL) of 8% per 100 m that is applied below the elevation barrier (EOLMID) of 1940 m and the upper precipitation gradient of 3% per 100 m that is applied above EOLMID. Sensitivity analysis comprises only parameters that are calibrated, i.e. parameters whose values are not determined by measurement. Therefore the forested fraction (parameter TREE from Table 4-12) is not included in this sensitivity analysis, because its value is already known. However, results presented thus far clearly indicate high sensitivity of this parameter. The following are the results of the sensitivity analysis. 109 Figure 4-26. Sensitivity analysis for Test #6 with 1 elevation band Note: The description of the parameters analysed in Figures 4-26 through 4-37 is given in Table 4-12 on page 78, as well as in Chapter 3.1. 110 SREP GRADM I E! ~ D! 0.3 -0.2 -- • I — B -1-Voi.Bror I I - Vol Brer ~ | Figure 4-27. Sensitivity analysis for Test #6 with 2 elevation bands I - VoL Error 0:9 0.8 --0.6 0.5 -1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 -1 - VoL Error 0.6 \ 0.5 -0.3 • 0.2 Figure 4-28. Sensitivity analysis for Test #6 with 8 elevation bands Figure 4-29. Sensitivity analysis for Test #8 with 1 elevation band E D! — 1 - VoL Error El D! 1 - VoL Error Figure 4-30. Sensitivity analysis for Test #8 with 2 elevation bands 1000 1100 1200 1300 1400 1500 1600 1700 IK00 1900 2000 2100 2200 2300 El 0.7 - -0.6 -0,5 0.6 0.7 0.8 0.9 I — E ! 0.6 0.5 -Figure 4-31. Sensitivity analysis for Test #8 with 8 elevation bands E D' — I - VoL. Error 0.3 0.2 0.S 0.4 -0.3 • 0.2 0.1 -lit Figure 4-32. Sensitivity analysis for Test #9 with 1 elevation band 116 Lll spireq uoi+BAsp i miA\ 6# jsa x JOi sisXrmre XJIAUISUSS '££-p S-inSij 09S fitt 00£ OLZ OtZ Oil 0R1 OS I on a oi t* o* it oc il o; i i oi 60 B'O fO 90 (hi i ; iioo; OOtl 0091 oost OOM co ro ro ro ro o rt>- ro- to- to- so--O.S -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 O.J 0.4 O.S 7 K 9 10 1000 1100 1200 IJ(H) 1400 1500 I (.00 170(1 I MOO I'MM) 2000 21UO 2300 2100 -0.5 -0.4 -O.J -0.2 -0.1 0 0.1 0.2 O.J 0.4 O.S — P - I - Vol. Error ~j 0.6 I 2 J 6 7 H 9 10 2.2 2.6 3 M 0.2 0.3 04 0.5 0.6 0.7 0.8 0.9 1 I — B 0.7 • - -0.6 0.5 15 20 25 JO 35 45 50 55 210 240 270 100 130 360 0 10 20 30 40 50 60 70 HO 90 100 16 IH 20 22 Figure 4-34. Sensitivity analysis for Test #9 with 8 elevation bands 118 Figure 4-35. Sensitivity analysis for Test #10 with 1 elevation band -O.S -0.4 -0.3 -0.2 -0.1 0 0,1 0.2 0.3 0.4 0.5 -0.3 -0.2 -0.1 0 0.1 0.: 0.1 04 05 I - Vol h w r 0.7 1- • 7 X 9 10 I — E l - l -Va lKnor ' — H Oj4- -1300 1400 1500 1600 1700 IH00 1900 2000 2100 2.2 2.6 3 3.4 0*4- -0.2 r - • 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 5 10 15 20 25 30 35 45 50 55 60 90 120 ISO 1 MO 210 240 270 J00 330 .160 0.3 4-0 01 OJ 03 OA 0.5 0.6 0.7 O.H U.I 10 12 14 16 - I - VoL Eiror I Figure 4-36. Sensitivity analysis for Test #10 with 2 elevation bands 120 1 S R E P 1 RREP 0.9 II s 0.7 0.9 0.8 0.7 (i i. 03 0.6 II 5 0J * 0.4 0.3 i).: i) i 0J 0.1 9 -.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0 5 0 A .$ -0.4 -0.3 -0.2 -0.1 0 0 1 0.2 0.3 0.4 0.5 E tit 1 - Vol Error 1 b' D> 1 - VoL Error | G R A D L , G R A D M 0.7 (IH 0.7 0.6 '.1.5 0.6 05 0.4 0.3 0.4 0.3 u: 0.1 0.2 0.1 0 Q I 2 J 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 10 -—— E! D! — 1 - Vol. Error | E IV 1-Vol. Error 1 I bhjhd 1 IMPA 0.8 0.7 0.9 0.8 0.7 ee*rr T T r r r ^ ^ J 0.6 0.J 0.6 0.5 0.4 0.3 0.4 0.3 II : ii i 0.2 0.1 0 IC (H) 11 Oil 1200 1300 1400 15(H) 1600 17(1(1 IHOO 1900 2000 2100 2200 23 Ml 0 0.1 0.2 0.3 0,4 0,5 0.6 0.7 0.H 0.9 1 E! D! 1-Vol. Error | E! D! I -Vol . Error 1 F I X 1 D Z S H 0.8 0.7 0.9 0.8 0.7 0.6 0.5 0.6 O.S (14 0.3 0.4 0.3 0.2 0.2 0.1 0 0 2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 0 1 1 1 1 1 , 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 E! D! — 1 - Vol. Error 1 1 E D! 1 - VoL Error ! 1 UGTK l D Z T K 0.9 0.8 0.7 0.9 0.8 0,7 0.6 0.5 0.6 0.5 0.4 0.3 0.4 0,3 0.2 0.2 0.1 0 J . , . . — — . — • . , . 5 10 IS 30 2) 30 35 40 41 50 5 0 & S 90 120 150 ISO 210 240 270 300 330 360 B D! 1-VoLError 1 E! Dl 1 - VoL Error | G W F R mc 0.9 0.9 0.7 0.7 0,6 0.3 0.6 0.5 0.4 0.3 (1 •! 0.1 0.2 0.1 0.2 0.1 • 0 J 1 1 , . 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 09 E! D>. 1 - VoL Error ! 0 • 2 4 6 8 10 12 14 16 18 20 22 E! D! 1 - VoL Error [ Figure 4-37. Sensitivity analysis for Test #10 with 8 elevation bands 121 The sensitivity analysis results presented in Figures 4-26 through 4-37 show that the most sensitive parameters, regardless of model structure, are the snowfall adjustment factor (SREP) and the fraction of impermeable area (IMPA). In order that model efficiency be high, simulated hydrograph volumes and their timing have to match those of observed hydrographs. Generally, the correct simulated volume is achieved by adjusting the precipitation input, and the correct timing is achieved through adjusting the delay in watershed response. As seen in the case of Illecillewaet watershed, the delay in watershed response could be adjusted by introducing more forest cover, more elevation bands, more permeable area, and by slowing down routing of runoff components. Watershed response time also, indirectly, affects the simulated volume because some of runoff that is delayed will not appear in the time window for which the simulated volume is being compared with the observed volume. Several conclusions can be drawn from Figures 4-26 through 4-37. First, precipitation adjustment parameters control the simulated volume and have to be very sensitive. Illecillewaet watershed runoff is mainly snowmelt-generated and this explains why rainfall adjustment factor (RREP) was not as sensitive as its snowfall counterpart (SSREP). Second, the fraction of impermeable area (IMPA) controls how much water becomes slow sub-surface runoff. IMPA exhibited high sensitivity, but the parameters that further divide sub-surface runoff into multiple components were not sensitive. This explains why model structure used in Test #6 (only two runoff components: fast, surface runoff and slower, groundwater) produced similar results to those produced by more complicated model structures used in Tests #8, #9 and #10. It is also an indication that sufficient accuracy in modelling of watershed response is achieved by just two runoff components with different time delay signatures. 122 Third and rather surprising finding from this sensitivity analysis was extremely low sensitivity of precipitation distribution parameters (GRADL, GRADM and EOLMID). As previously explained, these parameters model orographic enhancement of precipitation and thus affect the amount of simulated runoff volume in a manner similar to the precipitation adjustment parameters SREP and RREP. It can therefore be expected that these parameters exhibit similar, rather high sensitivity. However, in the presented tests this did not happen. A probable explanation is due to the elevation of the meteorological station used in the models. The elevation of the Mt. Fidelity meteorological station is 1875 m and the elevation range of the Illecillewaet watershed is from 509 to 3271 m. This means that precipitation data is entered in the model approximately in the middle of the watershed elevation range. Therefore precipitation gradients used in the model reduce precipitation in the lower half of the watershed (below the Mt. Fidelity elevation of 1875 m) and increase precipitation in the upper half of the watershed. This situation dampens the effects that precipitation gradients have on the amount of simulated runoff volume, resulting in their low sensitivity. An important implication of this finding may be that when using point-input data from high elevations that are well within the watershed elevation range, one can reasonably well represent runoff processes with relatively simple modelling concepts, because most of the parameters have low sensitivity and thus can be avoided. However, in most practical applications, input data available come from the valley stations that are often either in the bottom or below watershed elevation range. In these cases it is reasonable to assume that precipitation gradients will be rather sensitive and thus necessary. This assumption will later be tested in Chapter 4.4 by replacing the Mt. Fidelity station with the lower station that is located below the watershed, and repeating all 10 tests. It is also obvious from Figures 4-26 through 4-37 that the fast flow routing time constant (FTK) exhibits very low sensitivity. This parameter is a typical example of previously mentioned 123 parameters that come into play only during certain times of the year and show low sensitivity when the analysis is performed on an annual basis. Sensitivity results for FTK shown in Figures 4-26 through 4-37 are obtained by running the model for the six-year calibration period, and they indicate that the Nash-Sutcliffe efficiency is over 0.8 for any value of FTK between 0.2 and 3.5 days. However, when the sensitivity analysis for the FTK is conducted by running the model for the two-weeks period in July 1983 when the largest flood on record occurred in the lllecillewaet watershed, the FTK proved to be extremely sensitive, as shown in Figure 4-38. This shows that certain parameters that are very important during certain times of year may be labelled insensitive and deemed unnecessary when their sensitivity is analysed over the longer time periods. F T K (calibration period 01/10/1970 - 30/09/1976) FTK (calibrationperiod 05/07/1983 -19/07/1983) 0.9 0.9 0.8 0.7 0.8 0.6 0.5 -0.2 0.1 • 0 • 0 0.1 0 0 / 2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 E! D! 1-VoLError E! D! — 1-Vol. Eiror Figure 4-38. Sensitivity of the fast runoff time constant (FTK) (Test #9 with 2 elevation bands) Figure 4-38 also illustrates the correlation between Nash-Sutcliffe efficiency and time period for which the efficiency is calculated. The same model structure that produces a Nash-Sutcliffe efficiency of over 0.9 for the six-year period, does not even reach efficiency values of 0.8 for the 14-day period. 124 4.3.6 Model Calibration Results with a Single High-Altitude Station The sensitivity analysis is used as a tool for determining parameter ranges in model calibration that is performed for each of the ten tests. Many of the parameters in the presented modelling structures are mutually correlated. This implies that changes in one parameter value may be compensated for by changes in one or more of other parameters, resulting in equally good model efficiencies in the end. That is why the presented sensitivity analysis of individual parameters is only a tool to aid in the process of finding an optimal set of parameters. Because of this inter-correlation among the parameters, calibrated values of each individual parameter in a final "optimal" parameter set may not be the same as the optimal values indicated by the sensitivity analysis of the individual parameters. That is why the calibration procedure in this study was performed by letting all the parameters simultaneously change their values within the specified range. A semi-automatic approach was used where the value of each calibrated parameter was chosen randomly from the previously set range, thus creating an unique parameter set in each iteration. Simulation results produced by each of these randomly created parameter sets were statistically evaluated in comparison with the observed flow not only for the calibration period but also for the remainder of 28 years of continuous simulation and the best parameter set was finally chosen by the modeller. The following is the presentation of the calibration results for each of 10 tests and their comparison with the results previously obtained without calibration. Model parameter values before and after calibration are shown in Tables 4-14 through 4-23. The statistics for the calibrated models are calculated and compared with the previously calculated statistics for the non-calibrated models in Table 4-24. Note that the statistics presented in Table 4-24 are annual 125 summaries only; detailed statistics for each individual test can be seen in the Appendix B. Hydrographs of observed and calculated flow before and after calibration for the 1973 and 1974 water years are shown in Figures 4-39 through 4-48. As explained earlier, calibration is performed for the continuous period from 01/10/1970 to 30/09/1976. Table 4-14. Parameter values before and after calibration in Test #1 (Mt. Fidelity) 1 elevation band 2 bands 8 bands before after before after before after u SREP 0.0 -0.4 0.0 0.0 0.0 0.0 a O l RREP 0.0 -0.2 0.0 -0.7 0.0 -0.7 E GRADL 8 8 8 8 u 0 3 GRADM 3 3 3 3 CH EOLMID (m) 1940 1940 1940 1940 Table 4-15. Parameter values before and after calibration in Test #2 (Mt. Fidelity) 1 elevation band 2 bands 8 bands before after before after before after u SREP 0.0 -0.1 0.0 0.0 0.0 0.0 i i -*-» a RREP 0.0 -0.7 0.0 -0.7 0.0 -0.7 E C 3 GRADL 8 8 8 8 s. « GRADM 3 3 3 3 CH EOLMID (m) 1940 1940 1940 1940 Table 4-16. Parameter values before and after calibration in Test #3 (Mt. Fidelity) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 -0.51 0.0 -0.36 0.0 -0.25 u i i RREP 0.0 0.16 0.0 -0.27 0.0 -0.30 i i S GRADL 8 6 8 8 « s- GRADM 3 3 3 3 ca CH EOLMID (m) 1940 1500 1940 1940 FTK (days) 1 17 1 15 1 13 126 Table 4-17. Parameter values before and after calibration in Test #4 (Mt. Fidelity) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 -0.20 0.0 -0.14 0.0 -0.12 s- RREP 0.0 -0.35 0.0 -0.49 0.0 -0.42 <u g GRADL 8 9 8 8 ca•— GRADM 3 8 3 3 C8 CM EOLMID (m) 1940 1825 1940 1940 FTK (days) 1 9 1 4 1 2 Table 4-18. Parameter values before and after calibration in Test #5 (Mt. Fidelity) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 -0.07 0.0 -0.08 0.0 -0.14 0> RREP 0.0 -0.38 0.0 -0.40 0.0 -0.19 £ GRADL 8 6 8 9 ca s-ca GRADM 3 7 3 9 CH EOLMID (m) 1940 1985 1940 1325 <u •o FTK (days) 1 2.0 1 1.0 1 1.0 o IMPA 0.26 0.06 0.26 0.10 0.26 0.22 GTK (days) 60 60 60 45 60 47 Table 4-19. Parameter values before and after calibration in Test #6 (Mt. Fidelity) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 0.11 0.0 -0.10 0.0 -0.14 0> +^  RREP 0.0 -0.63 0.0 -0.40 0.0 -0.32 = GRADL 8 4 8 7 ca i> ca GRADM 3 9 3 1 CH EOLMID (m) 1940 1645 1940 1030 FTK (days) 1 1.0 1 1.3 1 1.1 © IMPA 0.26 0.43 0.26 0.60 0.26 0.49 GTK (days) 60 58 60 60 60 77 127 Table 4-20. Parameter values before and after calibration in Test #7 (Mt. Fidelity) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 0.0 0.0 -0.09 0.0 0.0 RREP 0.0 -0.41 0.0 -0.43 0.0 -0.38 GRADL 8 3 8 9 O E GRADM 3 6 3 6 93 U C3 EOLMID (m) 1940 1615 1940 1850 C H FTK (days) 1 1.6 1 1.3 1 1.0 Ol TJ IMPA 0.26 0.04 0.26 0.055 0.26 0.21 O DZSH 0.53 0.33 0.53 0.34 0.53 0.48 UGTK (days) 30 48 30 30 30 42 DZTK (days) 210 161 210 168 210 219 Table 4-21. Parameter values before and after calibration in Test #8 (Mt. Fidelity) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 0.10 0.0 -0.05 0.0 -0.12 RREP 0.0 -0.57 0.0 -0.28 0.0 -0.24 s-OJ GRADL 8 8 8 4 0) s GRADM 3 3 3 4 es u C3 EOLMID (m) 1940 1995 1940 1678 C H FTK (days) 1 1.2 1 1.0 1 1.1 Cd IMPA 0.26 0.40 0.26 0.54 0.26 0.54 © DZSH 0.53 0.38 0.53 0.57 0.53 0.50 UGTK (days) 30 37 30 35 30 49 DZTK (days) 210 175 210 231 210 235 128 Table 4-22. Parameter values before and after calibration in Test #9 (Mt. Fidelity) 1 elevation band 2 bands 8 bands before after before after before after 0.0 0.17 0.0 -0.09 0.0 -0.12 RREP 0.0 -0.62 0.0 -0.34 0.0 -0.25 GRADL 8 1 8 2 u <u GRADM 3 4 3 2 u E EOLMID (m) 1940 1345 1940 1180 IPara FTK (days) 1 1.3 1 1.0 1 1.1 IPara IMPA 0.26 0.32 0.26 0.41 0.26 0.41 •o DZSH 0.53 0.51 0.53 0.27 0.53 0.38 o s UGTK (days) 30 28 30 39 30 25 DZTK (days) 210 198 210 261 210 243 PERC (mm/day) 18 31 18 30 18 24 ITK(days) 7 6 7 9 7 3 Table 4-23. Parameter values before and after calibration in Test #10 (Mt. Fidelity) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 0.07 0.0 -0.06 0.0 -0.12 RREP 0.0 -0.35 0.0 -0.42 0.0 -0.25 GRADL 8 4 8 2 •— GRADM 3 4 3 0 <u s EOLMID (m) 1940 1400 1940 1200 sa i - FTK (days) 1 1.0 1 1.0 1 1.0 CM IMPA 0.26 0.30 0.26 0.34 0.26 0.26 <u DZSH 0.53 0.37 0.53 0.40 0.53 0.40 © UGTK (days) 30 50 30 35 30 30 DZTK (days) 210 270 210 250 210 210 GWFR 0.90 0.85 0.90 0.90 0.90 0.84 ITK(days) 7 4 7 5 7 3 129 130 600 0 I -0 c i -7 2 3 l - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D c c - 7 3 3 I - M ar -74 3 0 - J u n - 7 4 2 9 - S c p - 7 4 — — Q o b s Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (after c a i ib rai io n 1 J 6 0 0 500 O l - O c t - 7 2 3 l - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D c c - 7 3 3 1 - M ar -74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q o b s Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (a Tier c ul ih ratio n )~ | 600 500 O l - O c t - 7 2 3 1 - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D c c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p ~ 7 4 Q o b s — ~ ~ Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (after c a l i b r a t i o n ) | Figure 4-40. Test #2 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Mt. Fidelity) 131 600 500 4(H) O l - O c t - 7 2 3 1 - D e c - 7 2 01 A p r 7 3 O l - J u l - 7 3 3 0 - S e p 73 3 0 - D c c - 7 3 3 l - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 | 1 Q o b s Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a i (after c a l i b r a t i o n ) j 500 450 40 0 O l - O c t - 7 2 3 l - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 | Q o b s Q c a i ( b e f o r e c a l i b r a t i o n ) — — Q c a i (after c a l i b rat io n ) , Figure 4-41. Test #3 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Mt. Fidelity) 132 O l - O c t - 7 2 3 l - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 30 - S e p - 7 3 30 - D e c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S c p - 7 4 Q c a i ( b e f o r e c a l i b r a t i o n 1 Q c a i ( a f t e r c a l i b r a t i o n ) O l - O c t - 7 2 3 1 - D e c - 7 2 O I - A p r - 7 1 O l - J u l - 7 3 3 0 - S e p - 7 3 30 D e c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 - Q c a i ( b e f o r e c a l i b r a t i o n ) Q ca l i ii ft er c a I i b rat ion ) O l - O c t - 7 2 3 1 - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 l - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 - Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a i ( a f t e r c a l i b r a t i o n I Figure 4-42. Test #4 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Mt. Fidelity) 133 o -i 0 I 0 t-72 3 l - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 30 - S e p - 7 3 30 - O e e - 7 3 H - M ar -74 3 0 - J u n - 7 4 2 9 - S c p - 7 4 Q c a l ( b e fo re c a I ib ra t ion > - Q c a l (after c a l i b r a t i o n ) O l - O c t - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 30 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M a r - 7 4 30 - J u n - 7 4 2 9 - S e p - 7 4 - Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (af 'er c a l i b r a t i o n ) j O l - O c t - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 I - M ar-7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (after c a l i b r a t i o n ) Figure 4-43. Test #5 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Mt. Fidelity) 134 3 S 0 O l - O c t - 7 2 3 l - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M ar-7 4 3 0 - J u n - 7 4 2 9 - S c p - 7 4 Q o b s — Q c a l ( b e f o r e c a l ib r a i j o n ) Q c a l (after c a l i b r a t i o n ) i 350 O l - O c t - 7 2 3 l - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D c c - 7 3 31 - M ar-74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q o b s Q c a l (be fore c a l ib rat io n ) Q c a i (after c a l i b r a t i o n ) | O l - O c t - 7 2 3 I - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M ar-7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 | Q o b s Q c a l ( b e f o r e c a l i b r a t i o n ) — Q c a l (after c a l i b r a t i o n ) | Figure 4-44. Test #6 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Mt. Fidelity) 0 1 - O c i -7 2 3 I - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 I - M ar -74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 | Q o b s Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a l (after ca lib ratio n) | 350 O l - O c i - 7 2 3 1 -D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0- S e p - 7 3 3 0 - D e c - 7 3 3 1 - M a r - 7 4 30 - J u n - 7 4 2 9 - S c p - 7 4 i Q o b s Q c a i (be fore c a l i b ra t ion ) Q c a i (after c a l i b r a t i o n ) 3 5 0 01 O c t - 7 2 3 l - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 j Q ob s Q c a i ( b e f o r e c a l i b r a t i o n ? Q c a i (after c a l i b r a t i o n ) | Figure 4-45. Test #7 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Mt. Fidelity) 136 350 0J - O c i - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D e c - 7 3 3 1 - M ar-74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q o b s Q c a l [ b e f o r e c a l i b r a t i o n ) Q c a l (after c a l i b r a t i o n ) | 350 0 1 - O c i - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M ar-7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q o b s Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (after c a l i b r a t i o n ) | 350 O l - O c t - 7 2 3 1 - D ec-7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D ec-7 3 3 I - M ar-7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q o b s — y c J I (be I'o re c a l i b r a t i o n ) Q c a l (after c a l i b r a t i o n ) Figure 4-46. Test #8 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Mt. Fidelity) 137 350 O l - O c t - 7 2 3 i - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 30 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M a r - 7 4 30 - J u n - 7 4 2 9 - S e p - 7 4 | — • Q o b s Q c a i ( b e f o r e c a l i b r a t i o n ) — Q c a i (after c a l i b r a t i o n ) j 350 O l - O c t - 7 2 3 l - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D e c - 7 3 3 I - M ar -74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 [ Q o b s Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a i (after c a l i b r a t i o n ) 350 O l - O c t - 7 2 3 1 - D ec-7 2 O l - A p r - 7 3 0 I - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M ar-7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 : Q o b s Q c a i ( b e f o r e c a l i b r a t i o n ) — Q c a l j a f t e r c a l i b r a t i o n) | Figure 4-47. Test #9 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Mt. Fidelity) 138 3 50 O l - O c t - 7 2 3 1 - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 30 - S e p - 7 3 3 0 - D c c - 7 3 3 1 - M ar -74 3 0 - J u n - 7 4 2 9 - S c p - 7 4 [ Q o b s Q c a I (b c f o re c a l i b r a t i o n > Q c a i (a ftcr ca lib ratio n) | 350 O l - O c t - 7 2 3 1 - D ec-7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D c c - 7 3 3 1 - M ar-74 30 - J u n - 7 4 2 9 - S e p - 7 4 | Q o b s Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (after c a l i b r a t i o n ) | 350 O l - O c t - 7 2 3 1 - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D c c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 | Q o b s Q c a l (be fore c a l i b r a t i o n) Q c a l (after c a l i b r a t i o n ) | Figure 4-48. Test #10 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Mt. Fidelity) 139 Table 4-24. Comparison of model statistics before and after calibration (Mt. Fidelity) Coefficient of Efficiency (E!) Volume Error (%) 1969-1997 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after <n Max. -0.05 0.81 0.58 0.86 0.72 0.89 61.94 28.69 59.06 20.69 55.00 18.37 fx ii M i n . -2.58 0.44 -0.97 0.63 -0.68 0.63 21.52 -14.43 17.74 -12.78 15.18 -14.28 H Average -1.31 0.68 0.02 0.78 0.20 0.79 41.41 10.14 37.20 6.86 34.24 6.33 T Max. 0.68 0.86 0.85 0.91 0.89 0.96 51.40 18.77 48.17 13.57 44.71 13.82 -«-» ce ii M i n . -0.77 0.52 -0.14 0.67 -0.03 0.61 13.13 -14.16 10.09 -17.11 7.93 -16.13 H Average 0.12 0.76 0.53 0.84 0.56 0.84 31.94 6.26 27.52 6.20 25.33 6.13 in Max. 0.85 0.89 0.93 0.94 0.97 0.97 44.72 14.37 38.17 14.29 32.85 15.68 ii M i n . 0.22 0.66 0.56 0.81 0.66 0.86 6.65 -15.37 1.50 -15.79 -1.45 -14.18 H Average 0.53 0.78 0.80 0.89 0.86 0.93 25.21 7.24 19.26 7.40 15.53 6.71 Max. 0.92 0.95 0.97 0.96 0.96 0.97 31.51 12.12 24.60 15.87 20.82 13.97 ii, M i n . 0.71 0.75 0.79 0.80 0.75 0.83 -7.17 -17.24 -8.89 -14.93 -10.62 -16.30 H Average 0.84 0.87 0.88 0.91 0.87 0.91 13.37 7.32 9.30 6.61 7.94 6.84 Max. 0.82 0.89 0.93 0.94 0.97 0.96 45.15 18.71 38.38 14.16 33.16 14.68 ii M i n . 0.20 0.66 0.59 0.77 0.70 0.82 0.73 -13.27 -1.43 -16.16 -2.96 -15.82 H Average 0.50 0.78 0.81 0.89 0.87 0.91 24.92 8.14 19.14 7.69 15.61 7.69 00 Max. 0.92 0.95 0.96 0.95 0.96 0.97 31.86 13.66 24.93 17.14 21.15 17.01 eo M i n . 0.74 0.76 0.81 0.82 0.78 0.81 -11.74 -16.53 -12.43 -14.56 -13.81 -14.11 H Average 0.85 0.88 0.89 0.91 0.89 0.91 13.55 7.15 9.45 6.65 8.23 6.59 e> Max. 0.94 0.94 0.97 0.95 0.96 0.97 30.82 15.52 24.06 13.83 20.49 16.11 CU M i n . 0.70 0.78 0.81 0.84 0.78 0.81 -7.17 -16.27 -8.61 -16.54 -10.95 -14.56 H Average 0.85 0.89 0.89 0.92 0.89 0.91 13.51 7.61 9.40 6.73 8.03 6.57 o Max. 0.93 0.95 0.97 0.96 0.97 0.95 37.36 24.03 28.39 12.35 23.37 16.43 M i n . 0.67 0.79 0.80 0.85 0.79 0.86 -4.00 -9.24 -7.01 -18.50 -9.63 -14.69 H Average 0.85 0.89 0.89 0.92 0.89 0.92 17.44 9.88 11.57 7.53 9.06 6.94 *Detailed annual statistics for each test are shown in the Appendix B **The maximum Volume Error values and the maximum efficiency values are not from the same year 140 4.3.6. J Comments on Results of Model Calibration: Presented calibration results (Table 4-24 and Figures 4-39 through 4-48) lead to similar conclusions as those drawn from the tests with non-calibrated models. Model structures 3 through 6, i.e. accounting for surface as well as the sub-surface runoff component, caused "order of magnitude" improvements in model efficiency as shown in the results of Tests #5 through #10. It is important to note that most of this improvement in efficiency occurred when Model structure 3 was applied (Tests #5 and #6). In Model structure 3 (Figure 3-3) total runoff is divided into a faster surface component and a slower sub-surface component. Further divisions of sub-surface runoff into components with different time delay signatures resulted in rather small improvements (Tests #7 through #10). It should also be mentioned that after calibration, even Test #4 produced rather good results as shown in Figure 4-42 and Table 4-24. Recall that in this test Model structure 2 was applied. As seen in the Model structure #2 diagram (Figure 3-2), the watershed is assumed to be 100% impermeable, which means that only surface runoff component exists. However, some delay in watershed response is modelled by routing surface runoff through the watershed storage using the linear routing concept of two reservoirs in series. This means that in this test, watershed non-linear behaviour is not captured by the modelling concept. However, despite all this, the calibrated model in Test #4 produced an average annual model efficiency over simulation period of 28 years of 0.76, 0.84 and 0.84, for one, two and eight elevation bands, respectively (see Table 4-24). Representing the watershed with two or eight elevation bands produced better results than using a single elevation band approach, similar to the non-calibrated runs. Also the two-elevation bands approach produced essentially the same, sometimes even better (Table 4-24), results as the eight-elevation bands approach. In terms of land cover, representing the watershed with a greater number of elevation bands improves simulation results much more in case of only one 141 land cover class than in case of two land covers. This is especially apparent in Tests #5 and #6 that use the same model structure, except that Test #5 assumes entire watershed as an open area and Test #6 accounts for open and forested areas. Table 4-24 shows that improvement when using eight-band approach is greater in Test #5 than in Test #6. Generally, the presented results indicate that model calibration has a greater effect when performed on simpler modelling concepts. It can be summarised that even after calibration, the general conclusion drawn from the non-calibrated tests still holds true. That is, in the case of the Illecillewaet watershed with point input data, the minimum degree of distribution required to obtain realistic representation of runoff processes is achieved by Test #6 with two elevation bands. This test uses two land cover representations and Model structure 3 (Figure 3-3), where total runoff is divided into a faster surface component and a slower sub-surface component. Running this model structure continuously for 28 years produced rather high annual Nash-Sutcliffe efficiencies as shown in Table 4-24 (also see detailed statistics in Appendix B). More complex model structures and division in more than two elevation bands did not significantly improve runoff simulation. 4.4 Single Low-Altitude Meteorological Station as Input In the previously performed simulations, precipitation distribution parameters (GRADL, GRADM and EOLMID - all described in Chapter 3) exhibited surprisingly low sensitivity. As previously explained these parameters model orographic enhancement of precipitation and thus affect the amount of simulated runoff volume in a manner similar to precipitation adjustment parameters SREP and RREP. It is therefore expected that these parameters exhibit similar, rather 142 high sensitivity. However, in the previous tests this did not happen. One probable explanation for this is in elevation of the meteorological station used in the models. The elevation of the Mt. Fidelity meteorological station is 1875 m and the elevation range of lllecillewaet watershed is from 509 to 3271 m. This means that precipitation data is entered in the model approximately in the middle of the watershed elevation range. Therefore precipitation gradients used in the model reduce precipitation in the lower half of the watershed (below Mt. Fidelity elevation of 1875 m) and increase precipitation in the upper half of the watershed. This situation dampens the effects that precipitation gradients have on the amount of simulated runoff volume, resulting in their low sensitivity. An important implication of this finding may be that when using point input data from high elevations that are well within the watershed elevation range, one can reasonably well represent runoff processes with relatively simple modelling concepts, because most of the parameters have low sensitivity and thus can be avoided. However, in most practical applications, input data available come from the valley stations that are often either in the bottom of or below the watershed elevation range. In these cases it is reasonable to assume that the precipitation gradients will be rather sensitive and thus necessary. This assumption will be tested here by replacing the Mt. Fidelity station with a lower station, Revelstoke, that is located below the watershed at 443 m, and repeating all ten tests. Meteorological input data from the Revelstoke station for the 01/10/1972 to 30/09/1974 period is shown in Figure 4-49. Comparison with the data from Mt. Fidelity shown in Figure 4-4 shows that besides lower precipitation, Revelstoke has a noticeably greater diurnal temperature range than Mt. Fidelity. 143 Ol-Oct-72 31-Dec-72 Ol-Apr-73 Ol-Jul-73 30-Sep-73 30-Dec-73 31-Mar-74 30-Jun-74 29-Sep-74 ! Tmax —- Tmin Precipitation | Figure 4-49. Meteorological data recorded at Revelstoke station (443m) Following the Mt. Fidelity example, the results of Tests #1 through #10 with one, two and eight elevation bands were first obtained without calibration. The same starting parameter values used in the tests with Mt. Fidelity data and shown in Table 4-12 are applied in these tests as well, and the sensitivity analysis is performed. Since the sensitivity analysis with the data from Mt. Fidelity performed on Tests 6, 8, 9 and 10 shows that individual parameters exhibit very similar sensitivity trends for each test, it was decided that the sensitivity analysis with the data from Revelstoke be conducted for the Tests 6 and 9 only. After the sensitivity analysis, the models are calibrated and the results are compared with those obtained without the calibration. The following are the results of the sensitivity analysis for Tests 6 and 9. 144 4.4.1 Sensitivity Analysis Figure 4-50. Sensitivity analysis for Test #6 with 1 elevation band Note: The description of the parameters analysed in Figures 4-50 through 4-55 is given in Table 4-12 on page 78, as well as in Chapter 3.1. 145 Figure 4-51. Sensitivity analysis for Test #6 with 2 elevation bands Figure 4-52. Sensitivity analysis for Test #6 with 8 elevation bands 2.2 2.6 3 3.4 90 120 150 240 270 300 330 360 10 20 30 40 SO 60 70 80 90 100 10 12 14 16 IN 20 22 Figure 4-53. Sensitivity analysis for Test #9 with 1 elevation band 148 Figure 4-54. Sensitivity analysis for Test #9 with 2 elevation bands Figure 4-55. Sensitivity analysis for Test #9 with 8 elevation bands 150 The sensitivity analysis results obtained using the low elevation meteorological station (Revelstoke 443 m) presented in Figures 4-50 through 4-55 offer some interesting conclusions when compared with the results previously obtained with high elevation meteorological station (Mt. Fidelity 1875 m). First, as expected, precipitation distribution parameters (GRADL, GRADM and EOLMID) proved to be quite sensitive when the low elevation station was used. This is because these parameters distribute precipitation from the station elevation of 443 m to the top of the watershed, which lies between 509 and 3271 m. This means that these precipitation gradients increase precipitation throughout whole watershed, unlike in the case of the Mt. Fidelity station where the same gradients reduced precipitation below the Mt. Fidelity elevation and increased precipitation above the Mt. Fidelity elevation, thereby minimising their importance. A second important observation was that all parameters exhibited significantly higher sensitivity when low elevation station was used. Indeed this observed difference in parameter sensitivity is an important finding in terms of watershed modelling. It suggests that when using point-input data from high elevations that are well within watershed elevation range, one can reasonably well represent runoff processes with relatively simple modelling concepts, because most of the parameters have low sensitivity and thus can be avoided. Consequently, when using data from a low elevation station below or close to the watershed outlet, one is forced to use complicated modelling concepts to compensate for the unrepresentative climate input data, hence the need for more model parameters and their increased sensitivity. Unfortunately, in most practical applications, input data available come from the valley stations that are often either in the bottom or below watershed elevation range. 151 4.4.2 Model Calibration Results with a Single Low-Altitude Station The following is presentation of the calibration results for each of the ten tests and their comparison with the previously obtained results without calibration. Model parameter values before and after calibration are shown in Tables 4-25 through 4-34. The summary statistics before and after calibration are shown in Table 4-35; detailed statistics for each individual test can be seen in the Appendix B. Hydrographs of observed and calculated flows before and after calibration for the 1973 and 1974 water years are shown in Figures 4-56 through 4-65. As explained earlier, calibration is performed for the continuous period from 01/10/1970 to 30/09/1976. Table 4-25. Parameter values before and after calibration in Test #1 (Revelstoke) 1 elevation band 2 bands 8 bands before after before after before after 1- SREP 0.0 -0.7 0.0 -0.5 0.0 -0.6 -*H cu RREP 0.0 -0.5 0.0 -0.6 0.0 -0.5 £ C3 GRADL 8 7 8 6 8 2 U C3 GRADM 3 7 3 3 3 12 PH EOLMID (m) 1940 1940 2000 1940 1400 Table 4-26. Parameter values before and after calibration in Test #2 (Revelstoke) 1 elevation band 2 bands 8 bands before after before after before after u SREP 0.0 -0.3 0.0 -0.3 0.0 -0.3 cu cu RREP 0.0 -0.8 0.0 -0.7 0.0 -0.7 £ C3 GRADL 8 8 8 8 8 8 u C3 GRADM 3 3 3 4 3 5 C H EOLMID (m) 1940 1940 1940 1900 1940 1800 152 Table 4-27. Parameter values before and after calibration in Test #3 (Revelstoke) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 -0.56 0.0 -0.70 0.0 -0.65 s-i> RREP 0.0 -0.33 0.0 -0.47 0.0 -0.50 o g GRADL 8 7 8 10 8 9 « La GRADM 3 10 3 11 3 11 M CH EOLMID (m) 1940 1264 1940 1780 1940 1900 FTK (days) 1 20 1 13 1 11 Table 4-28. Parameter values before and after calibration in Test #4 (Revelstoke) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 -0.37 0.0 -0.46 0.0 -0.65 u <u RREP 0.0 -0.35 0.0 -0.02 0.0 -0.27 tu s GRADL 8 11 8 4 8 6 « u GRADM 3 3 3 9 3 11 es CH EOLMID (m) 1940 762 1940 1334 1940 1265 FTK (days) 1 10 1 7 1 7 Table 4-29. Parameter values before and after calibration in Test #5 (Revelstoke) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 -0.14 0.0 -0.28 0.0 -0.30 l a <U - * a RREP 0.0 -0.15 0.0 -0.30 0.0 -0.55 ii a GRADL 8 4 8 5 8 7 u GRADM 3 8 3 14 3 12 CH EOLMID (m) 1940 1200 1940 1550 1940 1570 13 FTK (days) 1 1.7 1 1.4 1 1.6 O IMPA 0.26 0.00 0.26 0.02 0.26 0.04 GTK(days) 60 68 60 62 60 63 153 Table 4-30. Parameter values before and after calibration in Test #6 (Revelstoke) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 0.51 0.0 0.30 0.0 -0.17 a> RREP 0.0 -0.57 0.0 -0.05 0.0 -0.37 E GRADL 8 5 8 4 8 6 cs u ca GRADM 3 3 3 3 3 11 CH EOLMID (m) 1940 950 1940 1700 1940 1670 •c FTK (days) 1 1.2 1 1.1 1 1.2 o IMPA 0.26 0.25 0.26 0.22 0.26 0.24 GTK (days) 60 81 60 88 60 120 Table 4-31. Parameter values before and after calibration in Test #7 (Revelstoke) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 -0.39 0.0 0.04 0.0 -0.30 RREP 0.0 -0.35 0.0 -0.12 0.0 -0.55 a> •*-» GRADL 8 8 8 3 8 6 o E GRADM 3 9 3 9 3 12 « s-es EOLMID (m) 1940 1055 1940 1560 1940 1250 CH FTK (days) 1 1.7 1 1.1 1 1.9 o •o IMPA 0.26 0.00 0.26 0.03 0.26 0.05 o DZSH 0.53 0.31 0.53 0.48 0.53 0.41 UGTK (days) 30 46 30 48 30 65 DZTK (days) 210 97 210 76 210 238 Table 4-32. Parameter values before and after calibration in Test #8 (Revelstoke) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 0.54 0.0 0.36 0.0 -0.17 RREP 0.0 -0.48 0.0 -0.07 0.0 -0.44 4> -*w GRADL 8 4 8 5 8 7 E GRADM 3 4 3 1 3 9 03 u C3 EOLMID (m) 1940 1940 1385 1940 1643 CH FTK (days) 1 0.9 1 0.9 1 1.6 <u IMPA 0.26 0.14 0.26 0.12 0.26 0.54 o DZSH 0.53 0.51 0.53 0.41 0.53 0.25 UGTK (days) 30 36 30 35 30 70 DZTK (days) 210 212 210 273 210 196 154 Table 4-33. Parameter values before and after calibration in Test #9 (Revelstoke) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 0.13 0.0 0.20 0.0 0.40 RREP 0.0 -0.43 0.0 0.10 0.0 0.00 GRADL 8 8 8 2 8 0 1-GRADM 3 4 3 9 3 12 S EOLMID (m) 1940 1080 1940 1590 1940 1500 S3 U 03 FTK (days) 1 1.2 1 1.1 1 1.3 CH IMPA 0.26 0.16 0.26 0.235 0.26 0.23 Ot •a DZSH 0.53 0.49 0.53 0.40 0.53 0.40 o UGTK (days) 30 31 30 50 30 71 DZTK (days) 210 251 210 208 210 160 PERC (mm/day) 18 35 18 30 18 37 ITK(days) 7 4 7 5 7 6 Table 4-34. Parameter values before and after calibration in Test #10 (Revelstoke) 1 elevation band 2 bands 8 bands before after before after before after SREP 0.0 0.12 0.0 0.20 0.0 0.28 RREP 0.0 -0.45 • 0.0 0.10 0.0 -0.05 GRADL 8 8 8 2 8 0 I H 01 GRADM 3 4 3 9 3 11 e EOLMID (m) 1940 1100 1940 1600 1940 1410 83 U C3 FTK (days) 1 1.2 1 1.0 1 1.2 CH IMPA 0.26 0.15 0.26 0.23 0.26 0.23 -a DZSH 0.53 0.50 0.53 0.40 0.53 0.33 © UGTK (days) 30 30 30 50 30 70 DZTK (days) 210 200 210 200 210 200 GWFR 0.90 0.98 0.90 0.97 0.90 0.95 ITK(days) 7 4 7 5 7 6 155 O l - O c t - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 l - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 -Qobs - Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a i (after c a l i b r a t i o n ) O l - O c t - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M ar -74 3 0 - J u n - 7 4 2 9 - S c p - 7 4 - Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a i (after c a l i b r a t i o n ) 01 - O c t-7 2 3 I - D ec -72 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D ec-7 3 3 I - M ar -74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 - Q c a i ( b e f o r e c a l i b r a t i o n ) - Q c a i (after c a l i b r a t i o n ) _j Figure 4-56. Test #1 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 700 600 500 4 0 0 O l - O c t - 7 2 3 l - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 I - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S c p - 7 4 Q c a l (after c a l i b r a t i o n ) O l - O c t - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D c c - 7 3 3 l - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (after c a l i b r a t i o n ) O l - O c t - 7 2 3 l - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D c c - 7 3 3 l - M a r - 7 4 1 Q o b s Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (a fte r 3 0 - J u n - 7 4 c a l i b r a t i o n ) 2 9 - S e p - 7 4 Figure 4-57. Test #2 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 157 O l - O c t - 7 2 3 ! - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D c c - 7 3 3 l - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S c p - 7 4 Q o b s Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a i (after c a l i b r a t i o n i 700 -r 600 -O l - O c t - 7 2 3 1 - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D e c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 | Q o b s — Q c a i (b e f o r c c a l i b r a t i o n ) — Q c a i (after c a l i b r a t i o n ) | 700 O l - O c t - 7 2 3 1 - D ec -72 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D ec -73 3 1 - M ar-74 3 0 - J u n - 7 4 2 9 - S c p - 7 4 — — Q o b s Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a i (after c a l i b rat ion ) Figure 4-58. Test #3 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 158 600 e O l - O c t - 7 2 3 1 - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D c c 73 3 1 - M ar -74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q o b s Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (after c a l i b r a t i o n ) 7 00 6 0 0 O l - O c t - 7 2 3 1 - D e e - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D c c - 7 3 3 l - M a r - 7 4 30 - J u n - 7 4 2 9 - S c p - 7 4 Q o b s Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a i (after c a lib ra t ion ) 700 600 A O l - O c t - 7 2 3 1 - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M ar-7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q ob t Q c a l ( b e f o r e c a l i b r a t i o n ) Q c a l (after c a l i b r a l i o n ) I Figure 4-59. Test #4 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 159 700 600 500 O l - O c t - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 S e p - 7 3 3 0 - D c c - 7 3 3 I - M ar-74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 [ Q o b s Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a i (after c a l i b r a t i o n ) 500 O l - O c t - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 0 1 - J u l - 7 3 30 - S e p - 7 3 3 0 - D e c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q o b s Q c a l (be fo re c a l ib rat io n ) Q c a i (after c a l i b r a t i o n ) | O l - O c t - 7 2 3 t - D c c - 7 2 O l - A p r - 7 3 0 1 - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D e c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 * Q o b g Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a i (after c a l i b r a t i o n ) | Figure 4-60. Test #5 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 160 O I - O c c - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 30 - S e p - 7 3 3 0 D e c - 7 3 3 1 - M ar -74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 - ( J o b s - Q c a l ( b e f o r e c a l i b r a t i o n ) - Q c a l (after c a l i b r a t i o n ) O l - O c t - 7 2 3 1 - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D c c - 7 3 3 1 - M ar-74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q c a l ( b e f o r e c a l i b r a t i o n ) - Q c a l (after c a l i b r a t i o n ) O l - O c t - 7 2 3 l - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D e c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 - Q o b s Q c a l | b c fo rc c a l i b rat io n ) - Q c a l (after c a l i b r a t i o n ) Figure 4-61. Test #6 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 161 700 • 600 5 00 O l - O c t - 7 2 3 1 - D e c - 7 2 01 . -Ap .r -7 3 O l - J u l - 7 3 3 0 - S c p - 7 3 3 0 - D e c - 7 3 .1 I - M ar-74 30 - J u n - 7 4 2 9 - S e p - 7 4 I Q o b s Q c a I | b e f o r e c a l i b r a t i o n ) _ _ Q c a l ( a f t e r c a l i b r a t i o n ) 500 Q o b s Q c a i ( b e f o r e c a l i b r a t i o n ) Q c a i (after c a l i b r a t i o n ) Figure 4-62. Test #7 calibration results (top to bottom: l band, 2 bands, 8 bands) (Revelstoke) Figure 4-63. Test #8 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) O l - O c t - 7 2 3 l - D c c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 - Q c a l ( b e f o r e c a l i b r a t i o n ) 3 0 - S e p - 7 3 3D - D e c - 7 3 3 I - M ar -74 3 0 - J u n - 7 4 2 9 S c p - 7 4 Q c a l (after c a l i b r a t i o n ) J 500 4 5 0 -| 400 3 5 0 | 300 2 5 0 -200 150 I 00 -I O l - O c t - 7 2 3 l - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D c c - 7 3 3 1 - M a r - 7 4 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q c a l ( b e f o r e c a l i b r a t i o n ) - Q c a l (after c a l i b r a t i o n ) O l - O c t - 7 2 3 1 - D e c - 7 2 O l - A p r - 7 3 O l - J u l - 7 3 3 0 - S e p - 7 3 3 0 - D c c - 7 3 3 1 - M ar -74 3 0 - J u n - 7 4 2 9 - S e p - 7 4 Q c a l Ibefort- c a l i b r a t i o n ) Figure 4-64. Test #9 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) 164 Figure 4-65. Test #10 calibration results (top to bottom: 1 band, 2 bands, 8 bands) (Revelstoke) Table 4-35. Comparison of model statistics before and after calibration (Revelstoke) Coefficient of Efficiency (E!) Volume Error (° /„) 1970-1997 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after Max. -3.49 0.81 -1.19 0.82 -0.95 0.85 117.1 33.04 115.5 28.93 112.8 20.35 CA cu Min. -9.29 0.41 -6.37 0.44 -6.33 0.55 56.21 -8.99 57.76 -12.37 55.66 -17.91 H Average -5.82 0.65 -3.31 0.70 -2.93 0.72 87.62 9.66 85.08 8.25 82.02 8.22 T T Max. -0.69 0.82 -0.40 0.81 -0.27 0.84 105.9 9.39 104.1 26.49 102.1 19.63 - * H CA CU Min. -5.27 0.52 -4.79 0.41 -4.80 0.51 46.37 -24.28 51.31 -15.41 48.64 -20.47 H Average -2.34 0.70 -1.83 0.67 -1.69 0.71 77.26 12.08 74.58 8.49 72.69 10.79 «*-) Max. -0.21 0.84 0.40 0.88 0.49 0.93 92.38 19.13 88.39 22.08 82.29 15.52 CA CU Min. -2.47 0.43 -1.84 0.66 -1.75 0.74 43.16 -14.31 36.04 -17.24 32.87 -21.06 H Average -1.10 0.62 -0.50 0.77 -0.33 0.84 66.79 6.35 62.39 6.92 57.90 5.66 Max. 0.69 0.92 0.68 0.92 0.73 0.93 75.58 17.20 71.22 22.04 68.72 16.17 CA CU Min. -0.69 0.67 -0.90 0.70 -0.94 0.67 30.09 -20.07 24.09 -15.36 21.34 -20.84 H Average 0.13 0.81 0.16 0.82 0.20 0.85 50.81 6.71 46.87 7.35 44.33 5.34 Max. -0.22 0.85 0.45 0.91 0.54 0.93 93.05 22.55 88.56 17.60 82.67 23.27 CA CU Min. -2.33 0.33 -1.73 0.66 -1.63 0.71 41.83 -11.00 35.42 -19.12 31.96 -16.57 H Average -1.07 0.60 -0.41 0.77 -0.24 0.84 66.38 8.13 62.03 5.85 57.58 8.52 00 Max. 0.74 0.92 0.74 0.93 0.79 0.94 75.87 22.01 71.26 22.42 68.82 20.56 -*-» CA CU Min. -0.58 0.70 -0.78 0.72 -0.82 0.62 28.69 -17.20 23.29 -15.07 20.45 -17.79 H Average 0.22 0.82 0.26 0.83 0.31 0.84 50.43 8.32 46.54 7.17 44.02 6.50 O N Max. 0.63 0.91 0.67 0.90 0.70 0.94 75.83 24.72 71.66 17.63 69.24 19.01 CA CU Min. -1.24 0.67 -1.48 0.67 -1.50 0.62 31.30 -13.60 25.87 -18.99 22.80 -18.57 H Average -0.07 0.82 -0.02 0.83 0.04 0.85 51.29 9.33 47.31 6.28 44.69 6.06 o Max. 0.66 0.91 0.68 0.92 0.73 0.94 86.57 28.01 79.37 22.11 75.14 17.92 -*-» o Min. -1.09 0.66 -1.20 0.71 -1.21 0.68 33.29 -12.94 26.28 -18.15 22.87 -20.83 H Average 0.02 0.82 0.09 0.84 0.15 0.86 57.53 10.91 51.73 6.62 48.11 5.69 * Detailed annual statistics for each test are shown in the Appendix B * * The maximum Volume Error values and the maximum efficiency values are not from the same year 166 4.4.2.1 Comments on Results of Model Calibration Using a Single Low-Altitude Station: As expected, using a low altitude station below the watershed elevation range yielded somewhat inferior results than those obtained with the station located well within the watershed elevation range. However, it seems reasonable to conclude that use of each of these two stations individually produced good results. With regard to the proposed different model structures, presented calibration results (Table 4-35 and Figures 4-56 through 4-65) lead to conclusions that are similar to those drawn from the tests based on the high-elevation station. Model structures 3 through 6, i.e. accounting for the surface as well as the sub-surface runoff component, caused "order of magnitude" improvements in model efficiency and most of the improvements in efficiency occurred when Model structure 3 was introduced (Tests #5 and #6). In Model structure 3 (Figure 3-3) total runoff is divided into a faster surface component and a slower sub-surface component. Further divisions of sub-surface runoff into components with different time delay signatures resulted in rather small improvements (Tests #7 through #10). Also, similarly to the high elevation station results, representing watershed with two or eight elevation bands produced better results than using a single elevation band approach, with the two-elevation bands approach produced essentially the same results as eight-elevation bands approach. Thus in the case of the Illecillewaet watershed with point input data, regardless of the altitude at which the data are input, the minimum degree of distribution required to obtain realistic representation of runoff processes is achieved by Test #6 with two elevation bands. However, the important difference is that when a low-altitude station is used, model calibration becomes much more important and improvements from non-calibrated to calibrated results are significantly greater. This again brings up the finding observed after the sensitivity analysis: when using point input data from high elevations within watershed elevation range, one needs 167 simple modelling concepts whereas the use of data from low elevations requires complicated modelling concepts to compensate for the unrepresentative climate. Table 4-36 serves to illustrate how large is the difference between improvements from non-calibrated to calibrated model when using low versus high elevation stations. The results shown are from the Tests #6 and #9 only, but they are typical for all other tests. Table 4-36. Coefficient of efficiency (27-year average) before and after calibration Mt. Fidelity (1875 m) Revelstoke (443 m) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after Test #6 0.84 0.87 0.88 0.91 0.87 0.91 0.13 0.81 0.16 0.82 0.20 0.85 Test #9 0.85 0.89 0.89 0.92 0.89 0.91 -0.07 0.82 -0.02 0.83 0.04 0.85 Table 4-36 indicates that in the cases of Tests #6 and #9, the quality of input data from the high elevation station, Mt. Fidelity is such that results with non-calibrated model are better than calibrated results with low elevation station, Revelstoke. 4.5 Two Meteorological Stations as Input 4.5.1 General Discussion Thus far, the effect that the degree of distribution in model structure and spatial representation of a watershed have on final runoff simulation has been analysed. Al l experiments used data from single point station as meteorological input. In watershed modelling, input data, usually comprising precipitation and temperatures, have at least equal effect on model output as does the model structure. Generally, more distributed meteorological input should provide better model 168 efficiency all other factors being equal, because by using more meteorological stations, one gets closer to estimating the true precipitation over a given area. However, station density by itself does not guarantee good modelling results. Density in certain areas can be achieved by having many valley stations and no high altitude stations. Valley stations can be located in "micro-climate" areas and be totally unrepresentative of watershed's overall precipitation patterns. For example, if two out of three meteorological stations available for modelling are not representative of the watershed climate, using all three stations for simulation may result in lower model efficiency than using one single but representative station. The runoff-generating mechanism also has an effect on the density of meteorological input data. Snowpacks are likely to be more uniform over large areas, especially as they result from many storms during the whole winter. Also, snowmelt is governed by air temperature, which may be reasonably constant and uniform on a daily basis. This implies that watersheds that are dominated by snow generated runoff may require a lower density of meteorological data network than watersheds dominated by rainfall, which is less uniform. From the Illecillewaet example, it can be summarised that splitting a watershed into two elevation bands results in better simulation than using the single band approach. However, further spatial distribution into eight elevation bands does not improve results achieved with the two-band approach. These analyses are performed using point input data from a single meteorological station. In the first case, using Test #9 (i.e., current UBCWM) and data from Mt. Fidelity for 28 years of continuous simulation produced an average annual Nash-Sutcliffe efficiencies of 0.92 and 0.91 for two-bands and eight-bands approach, respectively. The same analysis but with the use of Revelstoke data, yielded average annual Nash-Sutcliffe efficiencies of 0.83 and 0.85 for 2-bands and 8-bands approach, respectively. Therefore it is reasonable to conclude that the use of each of these two stations individually in watershed modelling produced 169 good results. If the data from two meteorological stations are highly correlated, then it is expectable that use of each station individually would produce results of similar efficiency. On the other hand, if the data from two meteorological stations are not well correlated, and yet use of each of them in modelling the same watershed yields good results, there must be added value in using those two stations together, i.e. increasing the degree of distribution in meteorological input. This is the case in this study example where both Mt. Fidelity and Revelstoke produced good results and yet their mutual correlation is not that high. More precisely, 'correlation coefficient for daily precipitation between these two stations for the available 28-year period is 0.665 (the R 2 coefficient is 0.437). When precipitation is summed over 5-day periods to account for the time delay in storms the correlation coefficient increased to 0.792 (the R coefficient is 0.623). Temperatures, as expected, are very well correlated with a correlation coefficient of over 0.91. To investigate the added value or the amount of extra-information obtained when using more than 1 station for input, the Illecillewaet watershed is modelled using both meteorological stations simultaneously. To accomplish this goal we can use any one of the proposed model structures since the goal is not to compare different model structures but rather to see the change in results from using a single input station to two input stations used together. The current version of the UBC Watershed Model, or Test #9 from this study, is utilised for this experiment. Options with two and eight elevation bands are investigated. In the case of two elevation bands, the lower half of the watershed uses input from Revelstoke and upper half of the watershed uses input from Mt. Fidelity. In the case of eight elevation bands, the lowest two elevation bands (below an elevation of approximately 1400 m) use input from Revelstoke while the rest of the watershed (from 1400 m up to 3271 m) use input from Mt. Fidelity. 170 4.5.2 Model Calibration Results The starting values of the parameters are obtained from the results of calibration with a single point input station. Their values are shown in Tables 4-37 and 4-38. Table 4-37. Parameter values for one and two input stations in Test #9 (2 elevation bands) Rev From Tbl. 4-33 Fid From Tbl. 4-22 Rev&Fid Starting values Rev&Fid (calibrated) SREP 0.20 -0.09 0.20/-0.09 0.10/-0.10 RREP 0.10 -0.34 0.10/-0.34 0.10/-0.50 GRADL 2 1 2 o -*-» GRADM 9 4 4 cu E EOLMID (m) 1590 1345 1345 «i-C 3 FTK (days) 1.1 1.0 1.0 CM IMPA 0.235 0.41 cu " O DZSH 0.40 0.27 0.34 o UGTK (days) 50 39 45 DZTK (days) 208 261 235 PERC (mm/day) 30 30 30 ITK(days) 5 9 7 Table 4-38. Parameter values for one and two input stations in Test #9 (8 elevation bands) Rev From Tbl. 4-33 Fid From Tbl. 4-22 Rev&Fid Starting values Rev&Fid (calibrated) SREP 0.40 -0.12 0.40/-0.12 0.50/-0.10 RREP 0.00 -0.25 0.00/-0.25 -0.05/-0.30 GRADL 0 2 0 u cu .*-» GRADM 12 2 2 cu E EOLMID (m) 1500 1180 1500 [Para FTK (days) 1.3 1.1 1.2 [Para IMPA 0.23 0.41 0.40 cu •o DZSH 0.40 0.38 O UGTK (days) 71 25 50 DZTK (days) 160 243 200 PERC (mm/day) 37 24 30 ITK(days) 6 3 4 171 Calibration is performed only on precipitation adjustment parameters, because the other parameters are already calibrated with a single station and their values should be independent of precipitation input. The calibration results are compared with the results obtained without calibration as well as with the single-station results (Table 4-39). Table 4-39. Model statistics for single and multiple input stations (Test #9) Water Year Coefficient of ifficiency (E!) 2 bands 8 bands 1 st. (Fid) 1 st. (Rev) 2 st. 2 st. calib. 1 st. (Fid) 1 st. (Rev) 2 st. 2 st. calib. 1970-1971 0.94 0.74 0.87 0.91 0.94 0.76 0.93 0.9*3" 1 1971-1972 0.94 0.90 0.90 0.93 0.95 0.85 0.93 0.93 1 • 1972-1973 0.95 0.82 0.95 0.96 0.94 0.86 0.94 0.95 : ! 1973-1974 0.95 0.90 0.94 0.94 0.97 0.94 0.94 0.94 ! | 1974-1975 0.94 0.88 0.93 0.96 0.94 0.90 0.97 0.97 | I 1975-1976 0.92 0.84 0.93 0.93 0.94 0.88 0.93 0.93 : 1976-1977 0.91 0.82 0.90 0.93 0.90 0.88 0.93 0.93 1977-1978 0.93 0.81 0.92 0.94 0.93 0.87 0.94 0.94 1978-1979 0.88 0.87 0.88 0.91 0.87 0.89 0.93 0.93 1979-1980 0.95 0.85 0.93 0.95 0.94 0.84 0.94 0.95 1980-1981 0.87 0.82 0.84 0.87 0.87 0.84 0.88 0.88 1981-1982 0.93 0.84 0.88 0.93 0.91 0.79 0.93 0.93 1982-1983 0.89 0.82 0.89 0.89 0.89 0.78 0.89 0.89 1983-1984 0.94 0.83 0.94 0.95 0.91 0.88 0.92 0.93 1984-1985 0.91 0.83 0.89 0.92 0.93 0.88 0.94 0.93 1985-1986 0.93 0.89 0.91 0.92 0.91 0.87 0.91 0.91 1986-1987 0.93 0.85 0.91 0.94 0.92 0.89 0.95 0.95 1987-1988 0.91 0.84 0.88 0.92 0.89 0.89 0.94 0.95 1988-1989 0.84 0.83 0.82 0.88 0.83 0.82 0.92 0.92 1989-1990 0.92 0.88 0.89 0.92 0.92 0.93 0.93 0.93 1990-1991 0.90 0.80 0.86 0.89 0.90 0.86 0.91 0.91 1991-1992 0.92 0.84 0.90 0.92 0.92 0.88 0.93 0.93 1992-1993 0.84 0.67 0.77 0.83 0.81 0.62 0.86 0.85 1993-1994 0.94 0.81 0.93 0.94 0.93 0.84 0.93 0.94 1994-1995 0.93 0.78 0.92 0.92 0.92 0.82 0.92 0.92 1995-1996 0.88 0.78 0.90 0.92 0.88 0.75 0.90 0.90 1996-1997 0.92 0.90 0.93 0.92 0.92 0.89 0.90 0.90 Maximum 0.95 0.90 0.95 0.96 0.97 0.94 0.97 0.97 Minimum 0.84 0.67 0.77 0.83 0.81 0.62 0.86 0.85 Average 0.9152 0.8311 0.8967 0.9200 0.9104 0.8481 0.9237 0.9248 172 4.5.2.1 Comments on Results of Model Calibration Using Mt. Fidelity and Revelstoke The results show that using two point input stations instead of one improved, although only slightly, modelling efficiency. It should be noted that the results achieved with Mt. Fidelity station were very good in the first place and there was not much room for improvement. Calibration had greater effect in the case of two elevation bands; i.e. average annual model efficiency went from 0.8967 to 0.92. The possible reason for this is that too much of the watershed (one half) was represented by the Revelstoke data. This "misrepresentation" had to be fixed through calibration. In the case of eight elevation bands, calibration was almost unnecessary and improvement was negligible, probably because representing the lower quarter of the watershed with the Revelstoke station was a correct initial assumption. It is also interesting to note that just combining two stations without calibration surpassed efficiency achieved with the Mt. Fidelity data only. At this point the following questions are relevant: What is the amount of extra-information when using more than one station for input and how does the ability to extract that extra-information depend on the runoff generating mechanism? To address these questions, it is important to distinguish between rain and snow outflows. As previously mentioned, snowpacks are likely to be more uniform over large areas, since they result from many storms during the whole winter. Also, snowmelt is influenced by air temperature, which may be reasonably constant and uniform on a daily basis as proven by the high correlation of temperature data between the Mt. Fidelity and Revelstoke stations. This implies that even though precipitation values are not well correlated, use of each station individually would yield similar results in snow outflow simulation as long as both stations 173 produce reasonably similar snowpack accumulation throughout elevation bands. In that case subsequent snowmelt will be similar due to highly correlated temperature data from the stations. It is an entirely different mechanism in case of rain outflow. Unlike snow, rainfall does not accumulate and appears in the outflow rather quickly; therefore if certain rain events were not recorded at the one station they will not be simulated when that station is used individually. If those rain events are recorded at another station, thus implying low correlation between precipitation data from the two stations, there should be improvement in the simulation results when data from the second station are added to data from the first. This, of course, applies only if both stations produce reasonably good results when used individually. To summarise, the starting assumption was that if the data from two meteorological stations are not well correlated, and yet use of each of them in modelling the same watershed yields good results, there should be added value in using those two stations together. That assumption was proven through a modelling exercise indicating that even though modelling with Revelstoke data achieved good results and modelling with Mt. Fidelity achieved even better results, an added value was obtained when using both station together - each representing an adequate portion of the watershed. 174 CHAPTER 5 EVALUATION OF WATERSHED MODEL STRUCTURES ON A RAIN-DOMINATED WATERSHED 5.1 Runoff Generating Mechanism In the previous chapter, different model structures of varying complexity were tested and it was concluded that minimum degree of distribution required to obtain realistic representation of runoff processes was achieved by Test #6 with two elevation bands. This test used two land cover representations and Model structure 3 (Figure 3-3), where total runoff is divided into a faster surface component and a slower sub-surface component or groundwater with routing time constants of 1 and 60 days, respectively (Table 4-12). Running this model structure continuously for 28 years produced an average annual Nash-Sutcliffe efficiency of over 0.9, which was very satisfactory. More complex model structures and division in more than two elevation bands did not bring significant improvement in runoff simulation. The analysis of different model structures was performed on the lllecillewaet watershed that is fairly large (1150 km2) and a typical snow-dominated watershed. In other words, the majority of runoff appearing at the watershed outflow is generated by snowmelt. The obvious way to validate the conclusions obtained by applying various modelling structures on the snow-dominated watershed is to confirm the findings on the example of a rain-dominated watershed. The runoff-generating mechanism is an important factor in watershed modelling. It affects the degree of distribution in meteorological input. Snowpacks are likely to be more uniform over 175 large areas, especially as they result from many storms during the winter period. Also, snowmelt is influenced by air temperature, which may be reasonably constant and uniform on a daily basis. This implies that watersheds that are dominated by snow generated runoff may require a lower degree of distribution in meteorological data input than watershed dominated by rainfall which is less uniform. The runoff-generating mechanism also affects the degree of detail in the watershed physical description. For example, we may simulate rain-dominated watersheds with only one elevation band, whereas a watershed with a significant snow component will likely require division in more than one elevation band to properly simulate snowpack accumulation/depletion processes. In the later case, a question is whether only two bands are sufficient or whether more elevation bands would assure a better simulation. Regarding land cover representation, it is known that snow melts differently under different land cover conditions. Regarding hydrograph shape, snow-dominated watersheds produce annual hydrographs that have fairly regular triangular shape, whereas hydrographs from rain-dominated watersheds are much flashier and irregular in their nature. This "flashiness vs. regularity" in hydrograph shape explains the fact that calculated model statistics for the rain-dominated watersheds were consistently lower than those for the snow-dominated watersheds. Therefore, it would be convenient to validate conclusions from the Illecillewaet example on a watershed that is rain-dominated and preferably of different size. It would be a bonus if that watershed could be located in a different climatic zone from the Illecillewaet watershed. This all means that we are looking for a rain-dominated, small size watershed from the Coastal BC rainfall-rich climatic zone. The watershed that fits this profile is the Coquitlam watershed. 176 5.2 Coquitlam Watershed 5.2.1 General Information Location, size and topography: The Coquitlam Lake Watershed (Figure 5-1) lies in the southernmost extension of the Pacific Ranges of the Coast Mountains of British Columbia immediately to the north of the Lower Fraser Valley and about 30 km north-east of the downtown Vancouver. The Coquitlam watershed above the Coquitlam Dam has a drainage area of 187.9 km 2 ranging in elevation from 153 m to 1773 m. With steep valley slopes, the Coquitlam Lake has a long and narrow shape with a length of 13 km and a width that varies between 0.5 and 1.5 km. Climate: The Coquitlam basin is open to southwesterly flows of warm, moist air responsible for the heaviest rainfalls for durations greater than one or two hours. The abrupt rise of the Coast Mountains exerts strong orographic influence on these airflows. The critical months of the year for heavy precipitation are November through March. During this period frontal storms arriving from the southwest off the Pacific Ocean and carried up the Fraser Valley are associated with strong, moist winds that bring heavy precipitation for durations of a few hours to several days. The accumulated snowpack may vary appreciably throughout the winter, particularly at low elevations. Typically, a period of cooler weather in which the snowpack increases may be followed by a large Pacific disturbance that raises temperatures and melts a portion of the snowpack. There are two climate stations, Coquitlam Lake forebay and Coquitlam River above Lake located within the watershed. Location and altitude of the stations are shown in Figure 5-1. 177 Figure 5-1: Coquitlam watershed Hydrologic regime: The periods of highest streamflow in the Coquitlam Watershed coincide with the heavy winter rains at which time the air temperature may be above freezing at all altitudes in the basin. A winter storm commonly produces high runoff lasting less than four days. The annual floods are generated almost exclusively from rainfall and occur in the November - March period. The Coquitlam Watershed is a small basin with a very flashy response to rainfall events. This type of watershed is generally challenging in terms of watershed 178 modelling. The observed flows often change from almost no flow (~1 m3/s) to floods (-300 m3/s) in a couple of days (late November 1990, late January 1991, late August 1991). Table 5-1 summarises the historical daily inflows by month and highlights the variability of inflows observed at the Coquitlam Dam watershed. Table 5-1. Coquit am Lake Reservoir daily inflows (1954-1998) Month Minimum Daily Inflow (m3/s) Maximum Daily Inflow (m3/s) Mean Daily Inflow (m3/s) October Less than 1 536 28 November Less than 1 463 37 December Less than 1 478 30 January Less than 1 432 26 February Less than 1 281 25 March Less than 1 354 21 April Less than 1 245 23 May 3 282 28 June 1 160 26 July Less than 1 250 15 August Less than 1 291 7 September Less than 1 161 11 5.2.2 Degree of Detail in Watershed Description Following the lllecillewaet example, different degrees of spatial distribution and their effects on the overall model efficiency are tested. Tables 5-2, 5-3 and 5-4 show the physical structure of the Coquitlam watershed divided into eleven elevation bands, two elevation bands and described as one area. 179 Table 5-2. Coquitlam watershed description (11 elevation bands) Elevation Band 1 2 3 4 5 6 7 8 9 10 11 Mean elevation (m) 200 381 533 685 838 990 1143 1295 1448 1600 1753 Area (km2) 30.2 16.9 16.9 23.1 25.5 23.5 24.4 15.3 7.8 3.6 0.7 Forested fraction 0.2 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.8 0.7 Orientation (0=N; 1=S) 1 1 1 1 1 1 1 1 1 1 1 bnpermeable fraction 0.9 0.15 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 Table 5-3. Coquitlam watershed description (2 elevation bands) Elevation Band 1 2 Mean elevation (m) 455 924 Area (km2) 94.1 93.8 Forested fraction 0.61 0.89 Orientation (0=North; l=South) 1 1 Impermeable fraction 0.41 0.34 Table 5-4. Coquitlam watershed description (1 ele Elevation Band 1 Mean elevation (m) 787 Area (km ) 187.9 Forested fraction 0.78 Orientation (0=North; l=South) 1 Impermeable fraction 0.376 Starting values of impermeable area and forest cover for Coquitlam were estimated from digital land cover maps (Baseline Thematic Mapping (BTM) from the Provincial Ministry of Sustainable Resource Management), which can recognise 20 land cover classes including forest, barren surface, alpine regions, wetlands, urban areas, etc. These land cover types can be used to make a starting estimate of "impermeable areas". According to 1:250,000 BTM, there are six land cover classes within Coquitlam dam watershed (alpine, avalanche chutes, old forest, young forest, recently logged and fresh water). The values of impermeable fraction in Table 5-2 were obtained by assuming that all of the fresh water area, most of the alpine and avalanche areas, and some of the forested areas were impermeable. The all of the alpine and avalanche areas are located at higher altitude, hence there is greater impermeable fraction in the upper bands. It is 180 also assumed that the portion of forested area which is impermeable increases with elevation. The numbers in Tables 5-3 and 5-4 were simply aggregated from Table 5-2. It should be noted that the values of impermeable fraction in Table 5-2 are rather roughly estimated from the BTM, because they are starting estimates only and are significantly modified during calibration as shown later in Tables 5-5 and 5-6. Alternatively, in the lllecillewaet example, because BTM was not available for the area, an approximate estimate was derived using Federal (Natural Resources Canada Centre for Mapping) 1:250,000 topographic maps and the "impermeable fraction = lack afforest cover" rule, in which all forested areas are assumed permeable and the unforested area are assumed impermeable. It is arguable which method of impermeable fraction estimation is more accurate, because the true value of impermeable area is quite complex, as explained earlier in Section 3.1. It is possible, and expected even for a 100% forested watershed, to have a certain fraction of impermeable area. The impact of starting error estimates of impermeable fraction is very small because the final, calibrated value may differ significantly from the starting estimate ("IMPA" in Tables 5-5 and 5-6). 5.2.3 Input Data - Meteorological and Streamflow As shown in Figure 5-1, there are two climate stations available to provide input data for the modelling of the Coquitlam watershed. The stations are Coquitlam Lake forebay at 160 m and Coquitlam River above Lake at 290 m. Obviously, unlike in the lllecillewaet example, a high-altitude climate station well within the Coquitlam watershed elevation range (153 m - 1773 m) is not available. That is unfortunate since the value of such a station was proven in the previous 181 chapter. Considering that both stations were located in the bottom part of the watershed elevation range, the meteorological data will have to be increased from the station elevation to the top of the watershed. Therefore the only added value that can be obtained from using these stations together is in their spatial distance. The two stations are located on the opposite sides of the watershed, as shown in Figure 5-1, and it is possible that some localised storms could be recorded at one and missed at another station. That is why the best option is to create so called "index" station by averaging data from these two meteorological stations. Meteorological input data from this index station for the period 01/10/1990 to 30/09/1992 is shown in Figure 5-2. 01-Oct-90 31-Dec-90 Ol-Apr-91 Ol-Jul-91 30-Sep-91 30-Dcc-9l 30-Mar-92 29-Jun-92 28-Sep-92 | Tmax Tmin Precipitation | Figure 5-2. Averaged meteorological data used for Coquitlam watershed Comparison of the data from Figure 5-2 with the data from Figures 4-4 and 4-49 shows that the Coquitlam watershed receives several times more precipitation than the Illecillewaet watershed. 182 The Coquitlam Lake inflow was calculated by BC Hydro staff from reservoir elevation, generation, and spill (spillways, low-level outlets and fish valves) records using a computer program called FLOCAL. Flow data was then quality controlled as part of the Water Use Planning (WUP) process (BC Hydro, 2002); missing data were filled by BC Hydro Operations personnel using some kind of regional correlation and an engineering judgement. Therefore, it is quite possible that the inflow data are not always correct, which may be an excuse for the occasional poor match between the observed and the simulated flow. The meteorological and streamflow data were available for the period from 01/10/1985 to 30/09/1999. The model calibration was, similarly to the Illecillewaet case, performed on a six-year continuous period from 01/10/1990 to 30/09/1996. 5.3 Model Calibration Results The analysis performed on a snow-dominated large watershed showed that the minimum complexity of model structure required to obtain realistic representation of runoff processes was achieved by Test #6. More complex model structures, including the most complex one (Test #9 - current version of the UBC Watershed Model) did not significantly improve runoff simulation. To validate this finding on a very different watershed (rainfall-dominated, relatively small, receives much more precipitation), it is sufficient to run Test #6 and compare it with the Test #9. The parameter values before calibration were taken from the Coquitlam watershed model currently used in BC Hydro for inflow forecasting. The values of the model parameters and the calculated statistics before and after calibration are shown in Tables 5-5 through 5-8. Because of the hydrograph flashiness, plotting 2 years, as done for the Illecillewaet tests, would be visually 183 unclear. That is why the hydrographs for only one year are shown in the following figures. The year chosen (01/10/1990 to 30/09/1991) was the wettest on the record and can illustrate how the model handles extreme conditions. Figures 5-3 and 5-5 show comparison of observed flow and flow simulated after calibration. Figures 5-4 and 5-6 show hydrographs simulated by the model before and after calibration. Table 5-5. Parameter values before and after calibration in Test #6 (Coquitlam) 1 elevation band 2 bands 11 bands before after before after before after SREP 0.025 -0.266 0.025 0.09 0.025 -0.27 O ) -*-» RREP 0.105 0.154 0.105 -0.08 0.105 0.13 = GRADL 2 1 2 4 2 1 93 S -93 GRADM 10 13 10 8 10 12 CH EOLMID (m) 1370 900 1370 863 1370 1417 O ) •o FTK (days) 0.15 0.2 0.15 0.20 0.15 0.22 o IMPA 0.376 0.32 0.376 0.632 0.376 0.604 GTK (days) 60 98 60 71 60 82 Table 5-6. Parameter values before and after calibration in Test #9 (Coquitlam) 1 elevation band 2 bands 11 bands before after before after before after SREP 0.025 -0.287 0.025 0.099 0.025 -0.205 RREP 0.105 0.069 0.105 0.107 0.105 0.064 GRADL 2 2 2 1 2 2 GRADM 10 8 10 13 10 13 E EOLMID (m) 1370 764 1370 1085 1370 1258 93 S-93 FTK (days) 0.14 0.27 0.14 0.21 0.14 0.21 CH IMPA 0.376 0.253 0.376 0.530 0.376 0.357 V t 3 DZSH 0.58 0.63 0.58 0.62 0.58 0.46 O UGTK (days) 21 22 21 29 21 11 DZTK (days) 96 97 96 132 96 51 PERC (mm/day) 13 19 13 15 13 17 ITK(days) 1 0.6 1 1.3 1 0.5 184 0 I - O c t 90 3 I - D ec • 90 Q c a l (after c a l i b r a t i o n ) 30 S e p - 9 1 200 ISO L L 0 I -0 c t -90 3 1 -D e c - 9 0 Q c a l (after c a l i b r a t i o n ) 3 0 - S e p - 9 I 350 300 01 - A pr -9 I -Q o b s - Q c a l (after c a l ib ratio n ) Figure 5-3. Test #6 calibration results (top to bottom: 1 band, 2 bands, 11 bands) (Coquitlam) 185 3 I - D ec -90 - Q c a i ( b e f o r e c a l i b r a t i o n } - Q c a i (after c a l i b r a t i o n ) 30 S e p - 9 1 - Q c a i ( b e f o r e c a l i b r a t i o n ) - Q c a i (after c a l i b r a t i o n ) 3 0 - S c p - 9 I - Q c a l ( b e f o r e c a l i b r a t i o n ) - Q c a i (a fte r c a l ib ra 1 Jo n ) Figure 5-4. Test #6 hydrographs before and after calibration (top to bottom: 1, 2 and 11 bands) 186 450 400 3 50 300 250 0 1 - O c t - 9 0 3 1 - D e c - 9 0 0 ] - A p r - 9 1 O l - J u l - 9 1 3 0 - S e p - 9 1 Q o b s — — Q c a i (after c a l i b r a t i o n ) Figure 5-5. Test #9 calibration results (top to bottom: 1 band, 2 bands, 11 bands) (Coquitlam) 187 3 I - D c c - 9 0 - Q c a l ( b e f o r e c aj i b ra t ion > Q c a l (after c a l i b r a t i o n ) 0 I - O c t - 9 0 3 1 - D ec -90 3 0 - S c p - 9 1 - Q c a l ( b e f o r e c a l l b r a d o n ) - Q c a l (after c a l i b r a t i o n ) 0 I - A p r - 9 I 3 0 - S e p - 9 1 - Q c a l ( b e f o r e c a l i b r a t i o n ) - Q c a l (after c a l i b r a t i o n ) Figure 5-6. Test #9 hydrographs before and after calibration (top to bottom: 1, 2 and 11 bands) 188 Table 5-7. Model statistics before and after calibration for Test #6 (Coquitlam) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 11 bands 1 band 2 bands 11 bands before after before after before after before after before after before after 1985-1986 0.64 0.69 0.65 0.68 0.67 0.71 17.43 14.88 15.07 11.79 18.56 17.63 1986-1987 0.72 0.75 0.73 0.74 0.79 0.79 8.87 6.62 6.58 1.12 9.25 5.41 1987-1988 0.52 0.60 0.54 0.52 0.57 0.55 14.64 11.45 12.22 7.24 15.63 12.99 1988-1989 0.64 0.69 0.67 0.71 0.72 0.76 6.97 1.58 4.96 2.70 6.83 0.25 1989-1990 0.73 0.78 0.73 0.77 0.74 0.77 3.04 -3.33 1.36 -0.20 4.01 -2.77 ; 1990-1991 0.84 0.84 0.85 0.86 0.85 0.86 3.21 -2.69 1.27 -0.64 3.31 -2.87 \ 1 1991-1992 0.80 0.83 0.81 0.82 0.84 0.85 14.46 11.83 11.99 7.04 15.42 70.591 j 1992-1993 0.46 0.54 0.54 0.56 0.61 0.63 13.42 5.72 10.81 9.06 13.76 6.45 j ; 1993-1994 0.73 0.72 0.73 0.73 0.69 0.70 -6.28 -8.21 -8.69 -11.80 -6.61 -10.85; 1 1994-1995 0.67 0.69 0.67 0.69 0.63 0.65 3.41 -3.31 0.56 -0.66 2.25 -4.49 1 1995-1996 0.83 0.81 0.83 0.82 0.84 0.83 2.76 -0.16 0.66 -3.92 4.02 -0.07 1996-1997 0.70 0.67 0.70 0.70 0.68 0.67 -13.31 -17.23 -15.69 -17.25 -13.84 -18.57 1997-1998 0.73 0.74 0.74 0.74 0.77 0.77 -3.88 -5.77 -6.01 -10.81 -3.57 -8.60 1998-1999 0.53 0.56 0.54 0.55 0.62 0.59 -27.39 -29.94 -29.19 -31.26 -27.75 -31.17 Maximum 0.84 0.84 0.85 0.86 0.85 0.86 17.43 14.88 15.07 11.79 18.56 17.63 Minimum 0.46 0.54 0.54 0.52 0.57 0.55 -27.39 -29.94 -29.19 -31.26 -27.75 -31.17 Average 0.68 0.71 0.70 0.71 0.72 0.72 9.93 8.77 8.93 8.33 10.34 9.56 Table 5-8. Model statistics before and after calibration for Test #9 (Coquitlam) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 11 bands 1 band 2 bands 11 bands before after before after before after before after before after before after 1985-1986 0.60 0.73 0.61 0.70 0.63 0.77 19.00 13.37 16.62 13.00 20.16 14.21 1986-1987 0.65 0.73 0.68 0.73 0.76 0.79 8.38 4.46 6.10 1.19 8.78 4.30 1987-1988 0.34 0.53 0.38 0.51 0.40 0.49 15.47 10.38 13.03 6.89 16.44 12.32 1988-1989 0.52 0.68 0.59 0.71 0.68 0.75 6.11 -0.85 4.10 -0.01 6.08 -0.29 1989-1990 0.63 0.76 0.64 0.75 0.65 0.72 3.07 -4.67 1.46 -1.72 4.07 -2.52 ; 1990-1991 0.84 0.85 0.87 0.87 0.88 0.88 3.99 -2.81 2.02 -1.08 4.19 -1.82; 1 1991-1992 0.73 0.81 0.76 0.82 0.80 0.84 14.22 9.36 11.72 6.75 14.92 9.45 1 j 1992-1993 0.27 0.47 0.41 0.53 0.53 0.61 12.45 3.74 9.91 6.29 12.88 6.02 j ! 1993-1994 0.73 0.75 0.75 0.75 0.73 0.73 -6.41 -10.41 -8.87 -12.73 -6.84 -12.1 j ! 1 1994-1995 0.64 0.70 0.67 0.70 0.65 0.66 3.79 -3.73 0.92 -2.58 2.77 -3.71 1 ' 1995-1996 0.82 0.80 0.82 0.81 0.84 0.83 2.69 -1.78 0.61 -3.55 3.87 -0.44 '• 1996-1997 0.72 0.69 0.74 0.70 0.73 0.69 -12.48 -17.50 -14.87 -18.12 -12.90 -17.99 1997-1998 0.72 0.73 0.74 0.74 0.78 0.77 -5.35 -9.02 -7.46 -11.22 -5.24 -10.04 1998-1999 0.47 0.51 0.50 0.53 0.58 0.57 -27.40 -31.03 -29.22 -31.75 -27.69 -31.36 Maximum 0.84 0.85 0.87 0.87 0.88 0.88 19.00 13.37 16.62 13.00 20.16 14.21 Minimum 0.27 0.47 0.38 0.51 0.40 0.49 -27.40 -31.03 -29.22 -31.75 -27.69 -31.36 Average 0.62 0.70 0.65 0.70 0.69 0.72 10.06 8.97 9.07 8.55 10.49 9.14 189 5.3.1 Comments on Results of Model Calibration After analysing the statistics calculated for Tests #6 and Test #9, and visually observing the hydrographs, it appears that the findings from an experiment with the snow-dominated watershed hold true for the case of rain-dominated watershed. It was confirmed that model complexity represented by Test #6 is sufficient for both snow and rain dominated watersheds. This test uses two land cover representations and Model structure 3 (Figure 3-3), where total runoff is divided into a faster surface component and a slower sub-surface component with routing time constants of 1 and 60 days, respectively (Table 4-12). More complex model structure, i.e. Test #9 did not result in further improvement in runoff simulation. As expected, the statistics are much lower that those calculated in the lllecillewaet example because of several reasons: a high-altitude station that would better represent watershed overall precipitation patterns was not available; flashier hydrographs produce lower Nash-Sutcliffe efficiencies due to the nature of the Nash-Sutcliffe statistic itself; and there are likely errors in both streamflow and climate input data. However, the goal was to show that a simplified model structure applied in Test #6 is good enough and that making it more complex by introducing additional parameters would not improve overall simulation results. The annual statistics in Tables 5-7 and 5-8 show that splitting the watershed in more elevation bands generally does not bring significant improvement. However, careful examination of the hydrographs from Figures 5-3 and 5-5 reveals that in early summer of 1991 there is gradual improvement from one to two and from two to eleven elevation bands. This can be explained by more realistic representation of snowpack with more elevation bands. In both tests, using the one elevation band approach resulted in snowpack melting too soon and consequent discrepancy between the observed and calculated hydrographs. Using more elevation bands fixed the 190 problem (Figures 5-3 and 5-5). However this could not be noticed through the statistical evaluation presented in Tables 5-7 and 5-8, because the effect of these relatively short discrepancies gets dampened when the model efficiency is analysed on a larger time scale (one year in this example). It appears that the nature of the coefficient of model efficiency is such that different modelling structures wil l seem statistically closer as the period of statistical evaluation becomes longer. 191 CHAPTER 6 THE ROLE OF NON-LINEARITY IN WATERSHED MODELLING 6.1 Types of Non-Linearity in Watershed Behaviour Considering that natural watersheds have non-linear response, there must be concepts implemented to account for watershed non-linearity. Generally, the non-linearity concepts in watershed modelling can be classified in two types or groups. The first group consists of the non-linearity concepts that influence the determination of the water budget and its allocation in different vertical zones of a watershed. These concepts are concentrated in vertical cross section of the soil matrix, i . e., in soil moisture accounting. A few examples of representation of watershed non-linearity from this group are: • the concept of limiting percolation to groundwater (slow runoff component) and allocating a portion of runoff to interflow (not as slow runoff component); • the concept of soil moisture accounting where an actual evapotranspiration rate is computed as a function of soil moisture deficit; • the concept of limiting infiltration to permeable soil in case of high-intensity rainfall; • the concept where the watershed permeable area is not a constant value, but changes as a function of soil moisture deficit. The second group is comprised of the non-linearity concepts that influence the temporal distribution of already determined water quantities or the time distribution of runoff. Different components of total watershed runoff can be recognised in the outflow hydrograph because of 192 their characteristically different time delays, which can vary by an order of magnitude. It is debatable how many flow components should be modelled. Routing of the runoff components could be non-linear, further increasing model complexity. It should also be mentioned that non-linearity in watershed behaviour could also be captured by increasing the accuracy of watershed physical description. This concept is closely linked with the time distribution of runoff and they both could be used to achieve the same goal. It was shown previously in the Coquitlam watershed example that splitting the watershed into more bands delays snowmelt runoff, thus achieving the same result that could have been achieved through some routing (linear or non-linear) concept. A similar observation is true for land cover representation, where forest canopy delays snowmelt runoff. Al l of these concepts contribute to more realistic runoff modelling, but not to an equal extent. Some of them are absolutely necessary while some cause only minor improvements. On the other hand, some of them come into effect only occasionally, usually during extreme hydrological events. Many of the mentioned non-linearity concepts were implemented and tested in earlier chapters with the goal of determining which ones have the most effect on modelling accuracy. Different model structures of varying complexity were tested and it was concluded that the minimum degree of distribution required to obtain realistic representation of runoff processes was achieved by Test #6 with two elevation bands. This test used two land cover representations and Model structure 3 (Figure 3-3), where total runoff is divided into a faster surface component and a slower sub-surface component or groundwater with routing time constants of 1 and 60 days (Table 4-12). Therefore, the introduction of a soil moisture sub-model into the model structure 3, i.e., accounting for the surface as well as the sub-surface runoff component, caused order of magnitude improvement in model efficiency. More complex model structures, including the current UBC Watershed Model (Test #9) were also tested. Their 193 greater complexity compared to Test #6 is reflected in a more detailed/complex time distribution of runoff and a routing of runoff components. However, they did not bring significant improvement in runoff simulation. This implies that the most important non-linearity representation concepts are concentrated in the aforementioned first group that influences the determination of available water quantities, i . e., in soil moisture accounting. This agrees with the findings reported by Franchini and Pacciani (1991) and Cordova and Rodriguez-Iturbe (1983) who reported that determining what to route is more important than the way of routing it. Finally, it is believed that non-linear hydrological behaviour of a watershed is emphasised during extreme events such as floods, or droughts. As mentioned earlier, two watershed models may have similar efficiencies on an annual basis, and yet very different efficiencies during storms of weekly duration. The better model will be able to capture less frequent non-linear behaviour that the watershed exhibits only during those extreme events. At that time, parameters or non-linearity concepts that previously appeared unimportant could have a significant effect on model simulation. Because of this, further investigations and experiments will be focused on modelling several of the largest historical storms on record. Because of their short duration, in most cases a few days, the computational time step within a model will be decreased from one day to one hour. This will also require that meteorological and flow data be provided in hourly time steps. 6.2 Modelling Extreme Events A total of five historical floods, four from the Coquitlam watershed and one from the lllecillewaet watershed are simulated using an hourly time step and the model structures 194 described in Tests #6 and #9. The five mentioned floods include the highest floods on record for each watershed. Table 6-1 shows these flood events and their time of occurrence. Table 6-1. Historical floods at Coquitlam and 11 ecillewaet watersheds Coquitlam (drainage area 188 km2) lllecillewaet (drainage area 1150 km2) Time of occurrence Hourly peak (m3/s) Time of occurrence Hourly peak (m3/s) 23 November 1990 679.0 12 July 1983 590.1 08 November 1995 649.7 19 March 1997 523.1 07 January 2002 528.4 It is interesting to observe from Table 6-1 that the lllecillewaet watershed, although six times larger in size, has a much smaller maximum historical flood than the Coquitlam watershed, proving that their hydrological regimes are indeed very different. For both watersheds, the calibration was performed using the same starting parameter sets as presented earlier in Chapters 4 and 5. Those starting parameter values and parameter values after calibration are shown in Tables 6-2 and 6-3. Note that calibration is conducted manually using individual judgement and thus a minimal number of parameters changed their starting values. In case of the Coquitlam watershed only one parameter was changed; the rainfall routing time constant was reduced from 0.15 days to 0.10 days to account for the extremely fast watershed response during the flood event. In the lllecillewaet case, besides reducing the rainfall routing time constant, a rainfall adjustment factor had to be applied at Mt. Fidelity, probably because the station was undercatching rainfall at the time of storm. 195 Table 6-2. Parameter values before and after calibration in Test #6 Illecil ewaet Coquitlam before after before after SREP 0.0 0.0 0.025 0.025 CU RREP 0.0 0.25 0.105 0.105 CU E GRADL 8 8 2 2 I Para GRADM 3 3 10 10 I Para EOLMID (m) 1940 1940 1370 1370 cu FTK (days) 1 0.6 0.15 0.10 © IMPA 0.26 0.26 0.376 0.376 GTK (days) 60 60 60 60 Table 6-3. Parameter values before and after calibration in Test #9 Illecil ewaet Coquitlam before after before after SREP 0.0 0.0 0.025 0.025 RREP 0.0 0.14 0.105 0.105 GRADL 8 8 2 2 O +-» GRADM 3 3 10 10 CJ s EOLMID (m) 1940 1940 1370 1370 93 I* 93 FTK (days) 1 0.55 0.14 0.10 CH IMPA 0.26 0.26 0.376 0.376 cu •a DZSH 0.53 0.53 0.58 0.58 o UGTK (days) 30 30 21 21 DZTK (days) 210 210 96 96 PERC (mm/day) 18 18 13 13 ITK(days) 7 7 1 1 6.2.1 lllecillewaet Results Figures 6-1 and 6-2 show the results of watershed model simulation of the largest historical flood in the lllecillewaet watershed before and after calibration. Hourly data from a single station, Mt. Fidelity are used as meteorological input. 196 lllecillewaet - July 1983 Flood The presented results are obtained by representing the watershed with two elevation bands. Since the modelled event is a large rainstorm in nature, using more elevation bands is not expected to significantly improve simulation. Indeed, as illustrated in Figure 6-3, there is not much difference between hydrographs simulated with two and eight elevation bands. Illecillewaet - July 1983 Flood - Calibrated 500 400 g> 300 200 100 0 Observed Flow Test #9 (2 elevation bands) (RREP=0.14; FRTK=0.55) • Test #9 (8 elevation bands) (RREP=0.14; FRTK=0.55) ! Jul 5 0:00 Jul 7 0:00 Jul 9 0:00 Jul 11 0:00 Jul 13 0:00 Jul 15 0:00 Jul 17 0:00 Jul 19 0:00 Figure 6-3. Illecillewaet flood event simulation using 2 and 8 elevation bands Considering that the transition from Figure 6-1 (poor simulation) to Figure 6-2 (good simulation) is achieved by changing two parameters, important conclusions can be made. Both of the changed parameters, the rainfall adjustment factor (RREP) and fast runoff routing time constant (FTK), exhibited low sensitivity when examined during long-term simulation earlier in Chapter 4. More precisely, the changes in RREP (from 0 to 0.14) and FTK (from 1 to 0.55) that were applied for the storm event calibration in Test #9 would be rather irrelevant during long-term simulation according to Figure 4-33. The same can be concluded for Test #6 from Figure 198 4-27. However, these very changes in the value of both parameters during storm event calibration caused significant improvement in simulation as shown in Figures 6-1 and 6-2. These conclusions confirmed the previously made suggestion that parameter sensitivity should not be seen as universal, i.e., it might change depending on what time scale is being observed. Another observation from Figure 6-2 is that Test #9 with a more complex model structure and greater number of parameters performs better than Test #6, especially at the recession limb of the hydrograph (Figure 6-2). During long-term daily calibration both tests, as reported earlier, perform equally well. The reason for this change is explained with an examination of the flow components shown in Figures 6-4 and 6-5. The model structure used in Test #6 splits total runoff in only two components, namely faster (with response time of 0.55 day in this case) and slower or groundwater (with response time of 60 days in this example). The rising limb of the flood hydrograph is simulated well, because it is created by a fast responding runoff component which is included in the modelling concept used in Test #6. However, the recession limb could not be modelled adequately, as shown in Figure 6-4, because it is caused not only by fast runoff and groundwater but also by a part of total runoff that is responding slower than fast runoff and faster than groundwater. If we tried to slow down the fast runoff component to better fit the recession limb, by increasing FTK from 0.55 day to 1 day and consequently stretched the red line from Figure 6-4 to the right, the result would be similar to the "uncalibrated" hydrograph from Figure 6-1. In Figure 6-2 FTK has a value of one day which assures closer fit to the recession limb, but dramatically reduces the peak. Evidently, to adequately simulate this flood, or its recession part, we need an additional flow component that is slightly slower than the fast runoff component. That component exists in the model structure used in Test #9 and is the main reason that Test #9 produces a much better runoff simulation for this flood event than Test #6. The component is called interflow, or medium runoff, shown as the green line in Figure 6-5 199 which has the response time constant of 7 days. Therefore, compared with Test #6 which has only two total runoff components, Test #9 "took" a certain amount of water from the slowest (groundwater) component and gave it to this additional medium speed runoff component, thereby matching the recession limb better without compromising the peak flow. Nash-Sutcliffe efficiencies for the two tests are shown in Figures 6-4 and 6-5 indicating that Test #9 improved simulation efficiency from 0.75 calculated for Test #6, to 0.85. It should also be observed that splitting groundwater into upper (faster) and lower (slower) component in the model structure used in Test #9 did not improve runoff simulation, indicating that the concept of groundwater separation in two components is rather unimportant in both long-term and event runoff simulation. To summarise, the calibration of the largest flood recorded at the Illecillewaet watershed indicates that the increased complexity introduced in the model structure used in Test #9 indeed helps to more accurately represent non-linearity in the runoff process that is emphasised during the extreme events. However, this advantage could be observed only during such a rare extreme event, since that is the only time when non-linearity in watershed response is sufficiently elevated that it can be captured by modelling concepts that seem unnecessary during rest of the time. In the presented example it is obvious that introduction of the interflow component during mid-July 1983 in the Illecillewaet basin is not only useful but also necessary. Using Model structure from Test #6, i.e., without the interflow component, it would be impossible to achieve the recession effect simulated by Test #9. However, for almost all of the other time, the interflow concept and additional parameters associated with it is unnecessary and the simpler model structures are quite sufficient. Thus, it seems that the choice of model depends on the needs; do we need a simpler model that is easier to run and calibrate and have decent simulation almost all of the time, or do we need a more complicated model that will be accurate at all times. 200 Test #6 - lllecillewaet - July 1983 Flood - Calibrated 0 I Jul 5 0:00 Jul 7 0:00 Jul 9 0:00 Jul 11 0:00 Jul 13 0:00 Jul 15 0:00 Jul 17 0:00 Jul 19 0:00 Figure 6-4. lllecillewaet flood simulation using Tests #6 (total runoff components) Test #9 - lllecillewaet - July 1983 Flood - Calibrated 600 | Jul 5 0:00 Jul 7 0:00 Jul 9 0:00 Jul 11 0:00 Jul 13 0:00 Jul 15 0:00 Jul 17 0:00 Jul 19 0:00 Figure 6-5. lllecillewaet flood simulation using Tests #9 (total runoff components) 6.2.2 Coquitlam Results There are four historical floods available for the modelling of the Coquitlam watershed, including the largest on record, which happened on November 23, 1990. The peak hourly flow recorded is 679 m3/s. In terms of unit flow that is 3.61 m3/s/km2 which is a massive flood by all standards. Thus it is reasonable to expect increased non-linearity in watershed hydrological behaviour. The other three modelled floods are also rather large as shown in Table 6-1. As mentioned previously (Tables 6-2 and 6-3), only one model parameter, namely fast runoff routing time constant (FTK) is modified during calibration. That is reasonable because long-term calibration contains the majority of small and medium-sized storms during which the watershed response time is expected to be slightly slower than during several of the largest storms. Al l four events are modelled using the same set of parameters, i.e., nothing is modified from event to event. Similar to the lllecillewaet example, the analysis focuses on the investigation of whether the two different model structures from Tests #6 and #9, which proved equally successful in long-term modelling would perform equally well during simulation of extreme events. The following are the results. Figures 6-6 through 6-13 show the results of flood-event modelling for the Coquitlam watershed before calibration (the same parameters as in long-term simulation) and after calibration, i.e., using a modification of the fast runoff routing time constant (FTK). 202 November 21 to 27,1990 700 Nov20,90 0:00 Nov21.900:00 Nov22.900:00 Nov 23. 90 0:00 Nov 24 , 90 0:00 Nov 25. 90 0:D0 Nov 26, 90 0:00 Nov27.900:00 Nov2fl,900:00 Nov29.900:00 Figure 6-6. Coquitlam flood simulation using Tests #6 and #9 - Storm 1 (before calibration) November 6 to 10,1995 Nov5.950:00 Nov6.95 0:00 Nov7.950:00 Nov8.950:00 Nov9.950:00 Nov 10.950:00 Nov11,950:00 Nov 12,950:00 Figure 6-8. Coquitlam flood simulation using Tests #6 and #9 - Storm 2 (before calibration) November 6 to 10,1995 Nov5,950:00 Nov6.950.00 Nov7,950:00 Novo.950:00 Nov9.950:00 Nov10.95 0:00 Nov 11,95 0:00 Nov12,950:00 Figure 6-9. Coquitlam flood simulation using Tests #6 and #9 - Storm 2 (after calibration) 204 March 15 to 22,1997 Mar 14. 97 0:00 Mar 15. 97 0:00 Mar 16. 97 0:00 Mar 17. 97 0:00 Mar 18, 97 0:00 Mar 19. 97 0:00 Mar 20. 97 0:00 Mar 21. 97 0:00 Mar 22. 97 0:00 Mar 23, 97 0:00 Mar 24, 97 0:00 Figure 6-10. Coquitlam flood simulation using Tests #6 and #9 - Storm 3 (before calibration) March 15 to 22,1997 r 14, 97 0:00 Mar 15, 97 0:00 Mar 16, 97 0:00 Mar 17. 97 0:00 Mar 16. 97 0:00 Mar 19. 97 0:00 Mar 20. 97 0:00 Mar 21. 97 0:00 Mar 22, 97 0:00 Mar 23. 97 0:00 Mar 24, 97 0:00 Figure 6-11. Coquitlam flood simulation using Tests #6 and #9 - Storm 3 (after calibration) 205 December 31, 2001 to January 12, 2002 Dec 30. 01 0:00 Jan 1, 02 0:00 Jan 3, 02 0:00 Jan 5. 02 0:00 Jan 7, 02 0:00 Jan 9. 02 0:00 Jan 11. 02 0:00 Jan 13. 02 0:00 Jan 15. 02 0:00 Figure 6-12. Coquitlam flood simulation using Tests #6 and #9 - Storm 4 (before calibration) December 31, 2001 to January 12, 2002 600 -Observed Flow -Test #6 -Test #9 Dec 30. 01 0:00 J a m . 0 2 0:00 Jan 3. 02 0:00 Jan5,020:00 Jan 7. 020:00 Jan 9. 02 0:00 Jan 11,020:00 Jan 13,020:00 Jan 15. 02 0:00 Figure 6-13. Coquitlam flood simulation using Tests #6 and #9 - Storm 4 (after calibration) 206 It can be concluded that the largest historical flood in the Coquitlam watershed (Storm 1) is simulated very well and the second largest (Storm 2) is simulated even better. Storm 3 simulation can be seen as satisfactory, whereas Storm 4 simulation indicates an input data problem, either precipitation or observed flows. The assumption about the input data problem could be made because it is highly unlikely that both models would "switch" peak flows when using accurate input data, especially considering successful simulation of the other events. After analysing the results from Figures 6-6 through 6-13, the first obvious difference from the Illecillewaet example is that Test #6 and Test #9 are much closer in terms of modelling accuracy. It appears that the more complex model structure in Test #9 could not significantly improve over what was achieved with the simpler concept used in Test #6. The reason for this is the intensity of floods in the Coquitlam watershed in general and the analysed flood in particular. In the Coquitlam watershed during these extreme events streamflow increases from single-digit values to almost 700 m3/s within a day or two, and then almost equally quickly drops back again. The intensity of the flood event that produces this sharp triangular hydrograph shape causes the watershed to behave linearly. This means that everything flows fast from the watershed and may as well be modelled as only one component - fast runoff. That is why more complexity in the model structure in Test #9, i.e., introduction of the interflow component by limiting percolation to groundwater does not significantly improve simulation. The components of the total runoff for both tests for the largest flood (Storm 1) are shown in Figures 6-14 and 6-15 and it seems that in Test #9 (Figure 6-15) the interflow component does increase the peak a little bit compared with the results of Test #6 (Figure 6-14). However, this increase in peak may be achieved in Test #6 simply by increasing the precipitation adjustment factor. 207 November 21 to 27,1990 700 Nov 20. 90 0:00 Nov 21. 90 0:00 Nov 22. 90 0:00 Nov 23. 90 0:00 Nov 24, 90 0:00 Nov 25, 90 0:00 Nov 26, 90 0:00 Nov 27, 90 0:00 Nov 28. 90 0:00 Nov 29. 90 0:00 Figure 6-14. Coquitlam flood simulation using Tests #6 (total runoff components) November 21 to 27,1990 700 Nov 20. 90 0:00 Nov 21. 90 0:00 Nov 22. 90 0:00 Nov 23. 90 0:00 Nov 24. 90 0:00 Nov 25. 90 0:00 Nov 26. 90 0:00 Nov 27. 90 0:00 Nov 28. 90 0:00 Nov 29. 90 0:00 Figure 6-15. Coquitlam flood simulation using Tests #9 (total runoff components) 208 6.2.3 General Comments on Modelling of Extreme Events After the attempt to simulate several large floods in the lllecillewaet and Coquitlam watersheds, it can be concluded that the more complex model structure was indeed necessary in the case of the lllecillewaet flood because it was able to simulate part of the hydrograph that could not be simulated with simpler concepts. However, in the case of the Coquitlam floods it appears that the simpler model concept applied in Test #6 was not as inferior. The reason is likely due to the simplicity of the flood hydrographs from Coquitlam watershed - they are very intense and caused almost entirely by the fast runoff component and thus could be simulated reasonably well using a simple linear approach. Therefore, the simple concept of only two flow components, fast runoff and groundwater, can provide a realistic representation of runoff processes in most cases. Such cases comprise long-term runoff simulation from both snow-dominated and rain-dominated watersheds as well as extreme flood simulation from watersheds that are subject to heavy and intense flood events resulting in simple flood hydrographs. However there are times, although not very often, when the simple model structure is not good enough. On those occasions, like the case of the lllecillewaet flood, certain runoff processes could not be represented with the simpler structure. The interflow component was needed, and there was no way to simulate it using only two flow components. It is important to recognise shortcomings of the model structure and not try to compensate for it by calibrating other model parameters to ridiculous values. In the case of Test #6, it was shown that one could not compensate for the interflow (stretching the fast runoff component reduced the peak) even if one wanted to. This was actually good, because it enables us to realise that model is not appropriate for the given task. The model structure used in Test #6 was simple and had clearly defined, meaningful parameters whose ranges were logically defined. 209 Sometimes, as reported by Uhlenbrook et al. (1999), it is possible to achieve many equally good simulations with the simple model that has many uncertain parameters that could take on almost any value. Klemes (1982) also cautioned that models often might provide the right answers for the wrong reasons. This issue will be further explored in the next section using an experiment with Test #9 and the "variable source area" concept. 6.3 Variable Source Area as Non-Linearity Concept It was argued earlier that the more important group of non-linearity concepts in watershed modelling are the concepts that concentrate on the vertical cross section of the soil matrix, i . e., on soil moisture accounting. One of the typical representatives of this group is the so called variable source area (VSA), in which the watershed impermeable area is not a constant value, but changes as a function of the soil moisture deficit. Therefore there is some minimum of impermeable area in the watershed that is constant (usually bedrock areas, glaciers, or lakes), but as precipitation increases, parts of the watershed that were initially permeable become saturated and act as impermeable areas. This concept is implemented in both Tests #6 and Test #9 presented earlier. The detailed description of the algorithm is given in Quick, 1995 (page 250) as well as in UBCWM Manual, 1995 (page A-8). In the next experiment with Test #9, this important non-linearity concept will be removed from the model structure and the effects will be studied by trying to simulate flood events. Obviously by removing the VSA concept from the model structure, the model becomes more "linear' or less "non-linear". The fraction of impermeable area in the watershed, in this case, becomes a constant value independent of precipitation and soil moisture. It is interesting to see whether it is possible to compensate for 210 the loss of this important non-linearity representation by manipulating the parameters of the resulting simplified model. The simplified model structure resulting from the removal of the VSA concept from Test #9 was named "Test #9noVSA". First, we compared the simulated Coquitlam flood hydrographs produced by Test #9 and "Test #9noVSA", thereby observing the effect that the removal of the VSA non-linearity concept has on overall simulation accuracy. After that we tried to compensate for the lack of VSA concept by calibrating other parameters in the "Test #9noVSA" model. It turned out that the parameter that needed to be modified in order to compensate for the lack of VSA concept was the fraction of impermeable area (IMPA). IMPA values were increased according to Table 6-4. Table 6-4. IMPA modifications in the model without VSA concept - Coquit Elevation Band 1 2 3 4 5 6 7 8 9 10 11 Total Area (km2) 30.2 16.9 16.9 23.1 25.5 23.5 24.4 15.3 7.8 3.6 0.7 187.9 IMPA-Test #9 0.90 0.15 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.376 IMPA-Test #9noVSA 0.90 0.30 0.39 0.48 0.54 0.60 0.68 0.75 0.84 0.92 0.88 0.619 am watershed Therefore in Test #9, the starting fraction of impermeable area was 0.376, but it was dynamically changing according to the VSA concept, i.e., increasing during precipitation events as the soil was being saturated and decreasing back towards starting values as the soil was drying during periods without precipitation. As shown earlier (Figures 6-6 through 6-13), Test #9 simulated the Coquitlam extreme floods rather well while having VSA concept implemented in its structure. However, essentially the same quality of simulation was achieved with "Test #9noVSA" in which the fraction of impermeable area of the watershed was a constant value of 0.619. This test did not have the VSA concept implemented in its structure and the IMPA had the same values regardless of precipitation and soil moisture account. The hydrographs obtained with (Test #9) and without (Test #9noVSA) VSA concept for the Coquitlam floods are shown in Figures 6-16 through 6-19. 211 November 21 to 27,1990 Nov 20. 90 0:00 Nov 21. 90 0:00 Nov 22, 90 0:00 Nov 23. 90 0:00 Nov 24, 90 0:00 Nov 25. 90 0:00 Nov 26, 90 0:00 Nov 27. 90 0,00 Nov 28. 90 0:00 Nov 29. 90 0:00 Figure 6-16. Coquitlam flood simulation using Test #9 without VSA concept - Storm 1 November 6 to 10,1995 •Observed Flow -Test #9 -Test#9noVSA - Test #9noVSA (calibrated) Nov 5, 95 0:00 Nov 6, 95 0:00 Nov 7. 95 0:00 Nov 8, 95 0:00 Nov 9, 95 0:00 Nov 10, 95 0:00 Nov 11, 95 0:00 Nov 12, 95 0:00 Figure 6-17. Coquitlam flood simulation using Test #9 without VSA concept - Storm 2 212 March 15 to 22,1997 600 500 400 ~g 300 a 200 100 0 --Observed Flow Test #9 Test #9no VSA — Test #9noVSA (calibrated) 1 -Mar 14, 97 0:00 Mar 15, 97 0:00 Mar 16, 97 0:00 Mar 17. 97 0:00 Mar 18, 97 0:00 Mar 19, 97 0:00 Mar 20, 97 0:00 Mar 21, 97 0:00 Mar 22, 97 0:00 Mar 23, 97 0:00 Mar 24, 97 0:00 Figure 6-18. Coquitlam flood simulation using Test #9 without VSA concept - Storm 3 December 31, 2001 to January 12, 2002 500 400 6 300 O 200 100 0 ^^"Observed Flow Test #9 Test #9noVSA — Test #9noVSA (calibrated) I J 1 Dec 30. 01 0:00 Jan 1.02 0:00 Jan 3, 02 0:00 Jan 5, 02 0:00 Jan 7, 02 0:00 Jan 9, 02 0:00 Jan 11, 02 0:00 Jan 13, 02 0:00 Jan 15, 02 0:00 Figure 6-19. Coquitlam flood simulation using Test #9 without VSA concept - Storm 4 213 Figures 6-16 through 6-19 indicate that it is indeed possible to compensate for the lack of a non-linear representation in model structure by manipulating parameters of the much simpler model. Coquitlam historical extreme floods were successfully modelled using both modelling approaches - incorporating the VSA concept and leaving it out of the model structure. Clearly, the latter is the less realistic concept because impermeable fraction of a watershed is not a constant value. It is obvious from the Figures 6-16 through 6-19 that neglecting the VSA concept resulted in poor simulation (see the green line) with the original IMPA values. Only when the IMPA values were dramatically increased according to Table 6-4, could a good simulation be achieved. This brings us to the important issue in conceptual modelling, namely the definition of the model parameters and the ability to realistically identify their values. In the presented case, it was easy to determine that the modelling approach without the VSA concept was inadequate even though it produced satisfactory results after calibration of the extreme events. The extreme event calibration changed values of the fraction of impermeable area in the watershed to 62% at all times, implying vast areas of bedrock outcrop, glaciers and lakes in the Coquitlam watershed, which is clearly unrealistic. This is why the application of this simplified model to the more ordinary events outside of the extreme storm events simulation would not work, i.e., a separate calibration would be required to reduce the IMPA value. Therefore, if focused on a group of special events only, and without testing the model on a whole range of conditions, it may seem that a linear model without soil moisture accounting is not inferior to the more complex model with the VSA concept implemented. That is why the model performance should, whenever possible, be tested over a whole range of different conditions. 214 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS 7.1 Conclusions Completely accurate modelling of the hydrology of a natural watershed is not possible because of its tremendous complexity. Therefore, the only reasonable approach to watershed modelling for practical applications seems to be some kind of a conceptual approach. Conceptual watershed models have been, and are still being, widely applied in the design, planning and management of water resources projects all over the world. In terms of the model structure, the conceptual watershed models vary from very simple ones to rather comprehensive and complex models. The more complex models try to improve representation of watershed hydrological behaviour by capturing more physical processes and, consequently, introducing additional parameters. At some point, this improvement becomes so small that it does not justify an increase in model complexity, and the input requirements associated with it. Finding that optimum complexity is a rather challenging task. Therefore, given point input data, this study attempts to determine, what degree of model complexity, is required to obtain realistic representation of the runoff processes. To investigate this model complexity, six model structures, with a gradual increase in complexity from 1 to 6, were formulated and their performance was tested. The degree of distribution in watershed physical description was also tested by representing a watershed with a 215 different number of land cover classes and dividing it in a different number of sub-areas, or elevation bands. The effect of point input meteorological data was also investigated in terms of both location and number of stations. Al l the tests were performed on two distinctly different watersheds. The Illecillewaet watershed is a snow-dominated relatively large watershed, whereas the Coquitlam watershed is a small, extremely flashy, rain-dominated watershed receiving large amounts of precipitation. And finally, the same tests were performed firstly for long-term calibration periods using a daily time step and then, for extreme event calibration using an hourly time step for shorter-term calibration periods. It should also be mentioned that the results and conclusions from this work are most relevant to the prediction of streamflow from watersheds in temperate climates under relatively constant land-cover conditions. In arid regions in which heavy droughts and soil moisture deficits sufficient to cause transpiration restriction occur regularly, the presented model structure would likely be too simple for accurate soil moisture accounting. 7.1.1 Long-Term Simulation Model Structures 1 and 2 (Figures 3-1 and 3-2), which are fully linear, do not model any infiltration, and assume that all runoff from a watershed occurs as surface runoff. The very simple Model Structure 1 could not model the watershed runoff process realistically. Model Structure 2 introduced some delay in the surface runoff response, and this improved results over the instantaneous concept used in Model Structure 1, but the simulation results remained well bellow acceptable level. 216 Introduction of the soil moisture sub-model into the Model Structure 3 (Figure 3-3), accounted for a surface as well as a sub-surface runoff component, and this feature produced an "order of magnitude" improvement in model efficiency. It is important to note that most of this improvement in efficiency occurred because some non-linearity was introduced (Tests #5 and #6). In this model structure (Figure 3-3) total runoff is divided into a faster surface component and a slower sub-surface component. Further divisions of sub-surface runoff into multiple components with different time delay signatures resulted in rather small, or no improvement (Tests #7 through #10). The degree of spatial distribution was also investigated. It was found that representing the watershed with two or more elevation bands produced better results than using a single elevation band. This is reasonable, especially in the case of a snow-dominated watershed, because snow will melt unrealistically fast from a single elevation band, because the temperature lapse rate, which is so important in mountainous watersheds cannot be represented. Introduction of more elevation bands will decrease temperature in the higher bands, and therefore delay the snowmelt, improving the simulation results. However, rather surprisingly, the two-elevation bands approach was satisfactory enough and produced essentially the same results as eight or eleven-elevation bands. In addition, the two types of land cover representation, forested and open area, was superior to the single land cover because of the different timing of the snowmelt mechanisms in forested and open areas. Therefore, the present study shows that, for long-term simulation with point input data, for both snow-dominated and rain-dominated watersheds, the minimum degree of distribution required to obtain realistic representation of runoff processes was achieved by Test #6 using two elevation bands. This test uses two land cover representations, open and forested, and Model Structure 3 217 (Figure 3-3), where total runoff is divided into only two components, a faster surface component and a slower sub-surface component. This model structure does not attempt to model channel phase runoff mechamisms within a watershed but, represents the total watershed runoff processes by using only the land, or hillslope phase, thus avoiding channel routing algorithms. The justification for this approach is that the land phase is the main control of the watershed runoff process and the much faster channel phase may be neglected in modelling, as argued previously in Micovic and Quick (1999). More complex model structures and division into more than two elevation bands did not bring significant improvement in the runoff simulation. These findings indicate that model structure can be surprisingly simple and yet provide good simulation of the runoff processes. The probable reason for this is in the nature of the runoff process, i.e. storage effects and internal averaging at the watershed scale, so that the watershed hydrographs are generally better correlated than the meteorological inputs causing them. This question of correlation of watershed input and output data was theoretically investigated by examining two synthetic uncorrelated precipitation inputs and the resulting hydrograph outputs generated by assuming a simple linear unit hydrograph storage concept. This study showed that the output hydrographs were reasonably correlated, even though the input precipitation events were totally uncorrelated. Furthermore, when measured on a longer time window, the correlation between hydrographs caused by two totally uncorrelated precipitation events kept increasing. This finding has important implications for the statistical measures of watershed modelling efficiency because, similar to the correlation coefficient, the Nash-Sutcliffe coefficient will be higher when applied to longer simulation periods. It is shown that this can lead to the conclusion that certain parameters are insensitive, while the truth is that they are effective only for short time periods, and their sensitivity is dampened when analysed on a 218 longer time window. That is why the parameter sensitivity should always be reported along with the time frame for which it was analysed. The investigation of the effects of point input meteorological data focused on the location and number of stations. In terms of the location of the meteorological station, the focus was on its elevation. A l l tests were performed first with a single station located at high elevation well within the watershed elevation range and then with a single station located at low elevation close to the watershed outlet. The sensitivity analysis of the model parameters, performed on a 6-year calibration period, showed that the most sensitive parameters were the meteorological representation parameters and the fraction of impermeable area. The meteorological representation, specifically the precipitation adjustment parameters, control the simulated volume and have to be very sensitive. Also the time distribution of runoff is very important and is controlled in Model Structure 3 (Test #6) by the fraction of impermeable area. This factor controls how much water becomes fast runoff, and how much enters the slow sub-surface runoff system, and was found to exhibit high sensitivity. Introduction of extra parameters that further divided sub-surface runoff into more components did not improve model performance. This was demonstrated by the model structure used in Test #6 (only two runoff components, fast, surface runoff and slower, groundwater), which produced similar results to those produced by the more complex model structures in Tests #7, #8, #9 and #10. This conclusion will be re-examined below when modelling extreme historical storm events. Testing of meteorological stations at different altitudes produced rather surprising results. For example, experiments with a single high altitude station indicated low sensitivity of the precipitation distribution parameters (GRADL, GRADM and EOLMID) which are used to model the orographic enhancement of precipitation. When using such a high meteorological station, 219 the precipitation data are entered in the model approximately in the middle of the watershed elevation range. Therefore the precipitation gradients used in the model reduced precipitation in the lower half of the watershed and increased precipitation in the upper half of the watershed. This situation dampened the effect that precipitation gradients have on the amount of simulated runoff volume, resulting in their low sensitivity. Conversely, when using a low altitude meteorological station, the precipitation distribution parameters proved to be quite sensitive because most watersheds show an increase in precipitation with altitude. These precipitation gradient parameters were able to represent these processes by modelling the distribution of precipitation from the station elevation at the bottom of the watershed to the top of the watershed. Another important observation was that all parameters exhibited significantly higher sensitivity when data from a low elevation station were used. This observed difference in parameter sensitivity has important implications. It suggests that when using point-input data from high elevations that are well within the watershed elevation range, one can represent the runoff processes reasonably well with relatively simple modelling concepts, because most of the parameters have low sensitivity. Conversely, when using data from a low elevation station below or close to the watershed outlet, one is forced to use more complex modelling concepts to compensate for the unrepresentative climate input data. Unfortunately, in the majority of watersheds in mountainous areas, input data is often only available at valley stations that are at the bottom, or below the watershed elevation range. The use of more than one meteorological station should help to reduce data error and produce better results, especially if the data from two meteorological stations are not well correlated, and even more so if the separate use of each station for modelling the same watershed yields good 220 results. This assumption was tested through a modelling exercise which indicated that, even though modelling of the lllecillewaet watershed with Revelstoke data achieved good results and modelling with Mt. Fidelity data achieved even better results, an added value was found in using both stations together, where each represented a portion of the watershed. It should be noted that the results achieved with Mt. Fidelity station, alone, were very good, so that there was not much room for improvement. 7.1.2 Extreme Event Simulation It is believed that non-linear hydrological behaviour of a watershed is emphasised during the extreme events such as floods, or droughts. Two watershed models may have similar efficiencies on an annual basis, and yet very different efficiencies during storms of weekly duration. The better model will be able to capture less frequent non-linear behaviour that watersheds exhibit only during those extreme events. At that time, parameters representing non-linearity concepts, that previously appeared unimportant, could have a significant effect on model simulation. Thus, in order to examine the role of non-linearity in model design, several of the largest historical storms on record were modelled using hourly time steps. The relatively simple modelling concept applied in Test #6, that was proven to be satisfactory during long-term calibration, was tested on the extreme events and compared against more complex modelling structure applied in Test #9. In the case of the Coquitlam floods, the simpler model concept applied in Test #6 produced satisfactory results. 221 The reason was likely due to the simplicity of the flood hydrographs from the Coquitlam watershed, which are very intense and are caused almost entirely by the fast runoff component, and thus could be simulated reasonably well using a simple linear approach. However, the more complex model structure was necessary in the case of the Illecillewaet flood, because the watershed response was more complex, and could not be simulated with the simpler concept applied in Test #6. The interflow component (Section 3.2.5), activated by the infiltration limiting effect of extreme rain, was needed in addition to the fast and slow groundwater components, so that there was no way to simulate this extra runoff using only two flow components. This demonstrated that it is important to recognise shortcomings of the model structure and not try to compensate for it by calibrating other model parameters to ridiculous values. In the case of Test #6, it was shown that one could not compensate for the lack of an interflow component even if one wanted to. This was valuable, because it enabled us to realise that a model was not appropriate for the given task. There are times, however, when it is possible to compensate for the lack of more complex model structure by manipulating model parameters. This was illustrated in this study by experimenting with the Variable Source Area (VSA) concept, which represents a strong non-linearity in watershed hydrological behaviour. In this concept, the watershed impermeable fraction is not a constant value, but changes as a function of the soil moisture deficit, or with the intensity of the precipitation (infiltration limiting Flash Share in the UBCWM). In other words, the impermeable fraction of the watershed increases with increase in precipitation. During the experiment with the extreme storm events, the VSA concept was replaced with a constant value of the watershed impermeable fraction. Such a simple model, initially, produced poor simulation results, but after calibration of the 222 impermeable fraction parameter, it produced the same flood simulation as did the model with the implemented VSA concept. Therefore, the lack of non-linearity representation, in the simpler model was successfully compensated by increasing the constant fraction of impermeable area to a much higher value. However, due to a constant and unrealistically high value of the impermeable fraction, this simple linear concept works only for the special case for which the calibration was forced and would require a separate calibration for the more ordinary events. Conversely, the more complex model structure with the VSA concept produces realistic results over a whole range of conditions with a single calibration which includes a dynamically changing fraction of impermeable area. This example illustrates that, if focused only on a group of similar events, the parameters of a simple linear model could be manipulated so that the model produces the results equal to those produced by a more complex model. However, expanding the focus to the entire range of conditions would reveal that this simple linear model is inadequate and inferior to the more complex modelling approach. 7.1.3 Final Discussion This work set out to investigate the minimal degree of complexity in a watershed model structure required to represent the runoff process realistically. As might have been expected, the answer is not straightforward. It was argued before that the physically based, fully distributed watershed modelling approach which attempts to achieve completely accurate representation of runoff processes, does not succeed because of many constraints. The results of this work indicate that, in most cases, the relatively simple conceptual modelling approach presented in Test #6 will provide a satisfactory representation of watershed hydrological behaviour. This 223 finding has been shown to apply to the long-term runoff simulation of large and small, snow-dominated and rain-dominated watersheds. For some watersheds that always exhibit high amounts of fast runoff, even extreme rain floods were adequately simulated with this same simple model structure. For these fast reacting watersheds, the additional effort required to introduce more complexity into the model structure and to utilise additional input data, can only be justified if there is an equivalent improvement in watershed runoff representation. The model structure used in Test #6 divides the total watershed runoff in only two components, the fast responding (order of magnitude 1 day) and the slower responding (order of magnitude 1 -3 months). The model structure does not attempt to model the channel phase within a watershed, but rather represents the whole watershed through the land or hillslope phase, thus avoiding channel routing algorithms. The routing of both runoff components from the land phase is linear, which conserves water balance and adds great efficiency to the computation process. Watershed response in this model structure is represented by division of the watershed land cover into two classes, open and forested, and into two elevation bands. The algorithm describing the impermeable fraction of the watershed divides total runoff into surface (fast) and sub-surface (slow) component and activates the soil moisture accounting which further captures watershed non-linearity by dynamically keeping track of the soil moisture deficit and changing the value of the impermeable fraction accordingly. In a physical sense, the fast runoff component may be explained as a combination of surface or overland flow and earlier mentioned "pipeflow" within shallow sub-surface layer, because these two phenomena have the shortest response times. The significant difference between them is that surface, overland flow is non-linear whereas sub-surface pipeflow is shown to be linear (Loukas and Quick 1992). This difference has important implications considering that overland flow as such never (or almost 224 never) occurs while the existence of pipeflow in mountainous watersheds has been observed fairly frequently. It can then be concluded that majority, if not all, of fast runoff component comes from the pipeflow and thus exhibits linear behaviour. That may explain why linear routing worked well in this type of model structure. Input to the model is relatively simple, consisting of precipitation and temperature data from a single point station. The model is easy to set up and calibrate due to a small number of calibration parameters, all of which are logically defined and understandable. In the case of the lllecillewaet watershed and using a single high-altitude point station as a meteorological input, this modelling approach produced average annual Nash-Sutcliffe model efficiency over simulation period of 28 years of 0.91, with maximum of 0.96 and minimum of 0.80, which is considered very good. However there are occasions, although not very often, when this simple model structure is not good enough, as in the case of extreme flood event simulation for the lllecillewaet watershed. In that case, more complexity was needed and was achieved by using the model structure represented by Test #9, which included extra parameters that represented a higher degree of non-linearity, and modelled an additional, third, flow component. 7.2 Recommendations In the watershed modelling concept that uses point input data, especially in mountainous watersheds, it is recommended to use high altitude stations well within watershed elevation range. It is likely that the meteorological data recorded at such a station will be representative of 225 the watershed precipitation and temperature patterns. This will result in less model complexity, since no unrepresentative input data will have to be compensated by the model structure. In addition, precipitation may not occur at low altitude station, and in that case there is no way to compensate for it. The model performance should, whenever possible, be tested over a whole range of conditions, because it is possible that, an otherwise inadequate model, might perform well when tested only on an individual event or on a group of similar events. In regard to future research opportunities, the presented work offers an insight into the dependence of the "optimal" model complexity on the temporal resolution. It was shown that the importance of certain algorithms, process representations and parameters was masked during the long-term continuous simulation. Change in focus to the individual extreme events and the reduction in the computational time step from daily to hourly revealed the importance of the parameters and algorithms that appeared unimportant during the long-term simulation. 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World Meteorological Organisation, 1981. Guide to Hydrological Practices, Volume 1 - Data Acquisition and Processing, WMO Report No. 168, pg. 313. 233 APPENDIX A THEORETICAL INVESTIGATION OF WATERSHED RESPONSE AND STATISTICAL MEASURES OF M O D E L EFFICIENCY 234 A . l Uncorrelated Inputs, Correlated Outputs It is relatively easy to show that two totally uncorrelated rainfall events will produce instantaneous unit hydrographs having certain mutual correlation. Two rainfall events are shown in Figure A - l below. Both rainfall event #1 and rainfall event #2 are assumed to be two-day events. Rainfall #1 represents scenario in which rain "a" occurs on the first day and no rain occurs on the second day. Rainfall #2 represents scenario in which no rain occurs on the first day and rain "b" occurs on the second day. Rainfall #1 Rainfall #2 day 1 day 2 t i m e day 1 day 2 t i m e Figure A - l . Different scenarios for a two-day rainfall event It is obvious that Rainfall event #1 and Rainfall event #2 do not have good correlation. The actual coefficient of correlation (/?), between these two rainfall events can be calculated using standard equation as follows: 235 Px.Y = • j (« - 1) • » V (Ty (-\<PXJ<\) (A-l) where, jr = -^— Y = J = i — (A.2) and, CTy=- (A.3) Therefore correlation between Rainfall #1 and Rainfall #2 from Figure A - l is: a —-(2-1)-0 - -+ (2-1) + 0-- b — = -\ 2 f b) 0 — + b-I 2) y 2, (A.4) (2-1) It remains to be proven that responses of a watershed, i.e., outflow hydrographs for each of these two rainfall events will have better mutual correlation than the rainfalls that caused them. To prove this, the simple concept of a linear reservoir is applied. A watershed can be thought of as a single reservoir with linear outflow-storage relationship as follows, 236 S = KO where, S= storage [L 3], K = routing time constant [T], 0 = (A.5) outflow from the reservoir [L3/T]. From the principle of continuity, 1 - 0 = ^- (A.6) dt • where, I = inflow into the reservoir [L3/T] and t = time. Combining Equations (A.5) and (A.6), I-0 = K— (A.7) dt In order to solve this equation numerically, as shown in Quick and Pipes (1975) the following substitutions have to be made, AO = O(i+0 - O0) (A.8) and, dt = t (A.9) Equation (A.7) becomes, - O0+l) = fO0+i) - O0)] KJt (A.10) Adding and subtracting 0$, [I(i+0 - Ori]] - [0(i+1) - 0(i)] = [O(i+0 - O(0J -KJt (A. 11) 237 The terms in the square brackets are the incremental changes in the inflow and the outflow, as follows, AI-AO = AOK/t (A.12) Therefore, the change in the outflow is, AO = AI (A.13) l + K/t The outflow at any time step t can be calculated as, 0(l) = 0(i.,) + AO(l) (A. 14) or, O(0 = O ( M , + T T ^ 7 7 - ( / ( / ) - O ( M , ) ( A . 1 5 ) Equation (A. 15) is now used to calculate the outflow hydrograph ordinates for both previously mentioned rainfall events. The calculation uses daily time steps to respond to rainfall input, which implies that in Equation (A.15) time t is equal to 1 day. Daily rainfall intensities [L/T] from Rainfall events #1 and #2 have to be converted to inflow [L3/T] by multiplying them with the watershed area [L2]. Inflows caused by rainfall a and b are called Ia and ID, respectively. The following tables show the inflows and outflows for Rainfall events #1 and #2. Note that the outflow on day zero is assumed to be 0. 238 Table A - l . Inflow and Outflow from Rainfall #1 Day Inflow from Rainfall #1 [L3/T] Outflow hydrograph [L3/T] 1 la h l+K 2 0 h l + K f>- ' 1 3 0 K l + K 1 T , i + ^ J 4 0 K l + K \- ' Y Etc. 0 Table A-2.1 nflow and Outflow from Rainfall #2 Day Inflow from Rainfall #2 [L3/T] Outflow hydrograph [L3/T] 1 0 0 2 h h l + K 3 0 h l + K I l + K, 4 0 h l + K ' 1 , l + K) 2 Etc. 0 239 The outflow hydrograph ordinates can be written in generalised terms for both cases. Therefore for Rainfall #1, f 1 \ + + O = " ,;) UK i = 1, 2, 3, ...,n (A.16) And for Rainfall #2, O(i) = 0 and 0(i) = /. r. i v ' " 2 ) l + K i = 2, 3, 4, ...,« (A. 17) The outflow hydrographs from Rainfall events #1 and #2 are shown in Figure A-2. Figure A-2. Outflow hydrographs for rainfalls #1 and #2 240 It is obvious from Figures A-2 and A - l that the two outflow hydrographs have better correlation than the rainfall events that caused them. Furthermore, if the comparison started on day 2 (Figure A-2), the two hydrographs would be perfectly correlated, i.e., the correlation coefficient would be equal to 1. Theoretically, and according to Equations (A. 16) and (A. 17), these outflow hydrographs are of infinite duration, which means that the correlation calculation using Equations (A.l) and (A.4) would eventually yield the following result, 1 (A.18) implying maximum correlation. However, in reality we are not interested in hydrograph ordinates of extremely small value such as, for example, values after day 8 on Figure A-2. A point in time at which the hydrograph ordinates reach near-zero values depends directly on watershed storage that is reflected through the routing time constant K. The smaller the K, the less storage watershed has and sooner the outflow hydrograph ordinates reach near-zero value. In the special case of K = 0, the change in the outflow will exactly equal the change in inflow, because the storage is zero when K = 0. The correlation coefficient between the two outflow hydrographs from our example for the special case of K = 0 can be calculated using Equation (A.l) as follows, P = f I \ ( f ( r o f \ n) 0 - b + 0 - a h _ 2b_ + « • b V nj « j V n j ( I "\ V n ) 2 ( I } ( 1} 2 ( + n- a • J o— b - + h _ zb_ v n) V K n) n J 2 f + n-V n J (A.19) Note that when s- —»0 and — —> 0, so that Equation (A. 19) becomes, n n 241 (A.20) / Equations (A.4) and (A.20), show that even in the extreme case of no storage (K = 0), the outflow hydrographs have better mutual correlation than the rainfall events that caused them. As the routing time delay constant K, i.e. the watershed storage increases, the outflow hydrographs resulting from totally uncorrelated rainfall events become even more correlated. This has important implications in understanding and subsequently modelling natural watershed behaviour. Flashy, fast-responding watersheds may require better, more representative precipitation data for successful modelling. On the other hand, slower responding watersheds may be less dependent on quality and representativness of meteorological input data. A.2 Coefficient of Correlation vs. Coefficient of Efficiency When dealing with the observed and simulated (calculated) hydrographs, one can examine various statistical relationships between the two. For example, for the two mentioned hydrographs we can calculate the correlation coefficient (p) as well as the coefficient of modelling efficiency (E!), also known as Nash-Sutcliffe coefficient. It is possible to derive the relationship between the coefficient of correlation (p) and Nash-Sutcliffe coefficient by combining Equations A . l , A.2, and A.3 from this Chapter and Equation 4.5 from Chapter 4. The resulting relationship looks like this: 242 (Px,r)2 = El (A.21) where, X and Y represent the ordinates of observed and calculated hydrographs, respectively. Several examples from model simulations performed in Test #9 using Mt. Fidelity data shown in Figure A-3 illustrate that good correlation between hydrographs does not automatically mean good model efficiency. The examples are monthly runs from both summer and winter months. E!= -0.504 ; p = 0.939 E!= 0.114 ; p = 0.495 Figure A-3. Differences between coefficients of correlation and efficiency 243 Let us now assume that inflows caused by rainfall a and b from Tables A - l and A-2, Ia and ID, are equal, i.e., Ia=I0= I. Let us also, using information from Tables A - l and A-2, substitute: —— = Z (A.22) l + K Therefore, Tables A - l and A-2 can now be shown as follows: Table A-3. Inflow and Outflow from Rainfall #1 anc I Rainfall #2 Day Inflow from Rainfall #1 [L3/T] Observed flow Qobs [L3/T] Inflow from Rainfall #2 [L3/T] Calculated flow Qca. [L3/T] 1 / / \ + K 0 0 2 0 1 (i z) l + K I I l + K 3 0 1 (i zf l + K V ' 0 1 (i z) l + K ' 4 0 1 a zy l + K ' 0 1 •(! Zf l + K Etc. 0 0 It is now possible to calculate the Nash-Sutcliffe coefficient of efficiency for these two hydrographs that are caused by two entirely uncorrelated rainfalls. We can calculate the components of the Equation 4.5 from Chapter 4, as follows (note that n represents time step): 244 E(fi* - &„ y = (' •z? • {1+z2 • h - 2)°]+r- • [(i - zy f +r- • \\ - zy- J +...+r- • \\ - zr1 J} (A.23) Z(a*-e,*)2 = (/z)2 \ n - 1 ) - a - z) - (i - zy- - (i - z)> -... - (i - zy' -i + (n-\)(\-z)-o-zy--(i-z)'-...-o-zy->~ - l - ( l - Z ) + ( « - l ) ( l - Z ) : - ( l - Z ) 3 - . . . - ( l - Z ) " - 1 - (I - Z) - (1 - Z ) 2 - (1 - Z ) 1 - . . . + ( « - 1 ) • (1 - z)-1 (A.24) Therefore for the example case of a routing time constant K = 1, from Equation A.22 it follows that Z = 0.5. The hydrographs resulting from Rainfall #1 and Rainfall #2, for the case of K =1, are shown in Figure A-4. For the purpose of calculating the coefficient of efficiency, the hydrograph caused by Rainfall # 1 is assumed to be the observed flow and the hydrograph caused by Rainfall #2 is assumed to be the calculated flow. Using the Nash-Sutcliffe efficiency Equation 4.5 from Chapter 4, and Equations A.23 and A.24, the efficiency coefficient (E!) for different time steps is calculated and shown in Table A-4. The corresponding values of correlation coefficient (p) are also shown in Table A-4. In addition, Table A-4 shows the values of El and p calculated without the first time step. 245 Figure A - 4 . Hydrographs resulting from Rainfall #1 ( Q o b s ) and Rainfall #2 ( Q c a i ) for K=l Table A - 4 . Coefficients of efficiency (E!) and correlation (p) for the routing time constant K=l Time step (n) 4 5 6 7 8 9 10 20 E! -1.956 -1.292 -0.940 -0.730 -0.593 -0.497 -0.427 -0.176 E! -3.500 -1.956 -1.292 -0.940 -0.730 -0.593 -0.497 -0.187 (without first time step) P -0.331 -0.104 0.043 0.140 0.205 0.252 0.287 0.412 P 1 1 1 1 1 1 1 1 (without first time step) 246 The results shown in Table A-4 represent a theoretical illustration of the observed fact that Nash-Sutcliffe efficiency is higher when measured on longer periods of model run. Using the same calculation presented in Table A-4, it can be shown that Nash-Sutcliffe efficiency increases with n for any value of routing time constant K, i.e., regardless of watershed storage. The example case of a routing time constant K = 2 is shown in Figure A-5 and Table A-5. Figure A-5. Hydrographs resulting from Rainfall #1 ( Q 0 b s ) and Rainfall #2 ( Q c a i ) for K=2 247 Table A-5. Coefficients of efficiency (E!) and correlation (p) for the routing time constant K=2 Time step (n) 4 5 6 7 8 9 10 20 E! -3.210 -1.896 -1.224 -0.832 -0.582 -0.411 -0.290 0.111 E! -1.625 -0.540 -0.074 0.170 0.314 0.408 0.471 0.661 (without first time step) P -0.457 -0.208 -0.015 0.126 0.229 0.304 0.360 0.556 P 1 1 1 1 1 1 1 1 (without first time step) 248 APPENDIX B DETAILED STATISTICS FROM CHAPTER 4 The following annual statistics apply to Illecillewaet watershed. Data from a single meteorological station (either Mt. Fidelity or Revelstoke) were used as input into the models. The name of the station used is indicated in the table captions. The statistics for the tests are presented in the same order in which they appeared in the main body of the text. 249 Input Data from Mt. Fidelity 250 4.3.1 Watershed Represented with Single Elevation Band Table 4-6. Detailed statistics of Test #5 without calibration (Mt. Fidelity; 1 elevation band) Water Year Coeff. of Eff. El Coeff. of Det. Dl Volume Error (%) 1969-1970 0.53 0.76 6.65 1970-1971 0.50 0.74 22.21 1971-1972 0.66 0.85 23.74 1972-1973 0.47 0.73 30.72 1973-1974 0.72 0.83 14.64 1974-1975 0.41 0.71 36.66 1975-1976 0.46 0.70 22.20 1976-1977 0.53 0.81 37.62 1977-1978 0.47 0.68 19.82 1978-1979 0.35 0.76 35.00 1979-1980 0.58 0.78 26.29 1980-1981 0.48 0.71 16.96 1981-1982 0.70 0.86 24.96 1982-1983 0.65 0.74 22.91 1983-1984 0.56 0.73 15.58 1984-1985 0.52 0.82 35.12 1985-1986 0.72 0.86 22.70 1986-1987 0.49 0.76 33.87 1987-1988 0.31 0.72 41.95 1988-1989 0.22 0.78 44.72 1989-1990 0.46 0.77 30.71 1990-1991 0.36 0.75 32.01 1991-1992 0.34 0.61 27.93 1992-1993 0.64 0.78 24.48 1993-1994 0.48 0.69 19.54 1994-1995 0.59 0.74 19.20 1995-1996 0.72 0.80 10.64 1996-1997 0.85 0.86 7.11 Maximum 0.85 0.86 44.72 Minimum 0.22 0.61 6.65 Average 0.53 0.76 25.21 251 Table 4-7. Detailed statistics of Test #6 without calibration (Mt. Fidelity; 1 elevation band) Water Year Coeff. of Eff. El Coeff. of Det. DI Volume Error (%) 1969-1970 0.89 0.90 -7.17 1970-1971 0.86 0.87 5.12 1971-1972 0.90 0.91 7.60 1972-1973 0.86 0.88 15.97 1973-1974 0.92 0.93 -0.99 1974-1975 0.82 0.86 22.48 1975-1976 0.89 0.90 8.38 1976-1977 0.76 0.85 26.94 1977-1978 0.87 0.88 7.83 1978-1979 0.82 0.89 20.42 1979-1980 0.85 0.88 15.33 1980-1981 0.81 0.82 5.99 1981-1982 0.85 0.88 12.71 1982-1983 0.83 0.85 12.98 1983-1984 0.85 0.86 3.49 1984-1985 0.84 0.87 18.88 1985-1986 0.86 0.87 11.49 1986-1987 0.82 0.88 22.00 1987-1988 0.78 0.89 28.60 1988-1989 0.71 0.88 31.51 1989-1990 0.84 0.89 16.18 1990-1991 0.81 0.88 17.80 1991-1992 0.77 0.79 15.95 1992-1993 0.85 0.88 14.85 1993-1994 0.86 0.87 7.69 1994-1995 0.88 0.89 9.46 1995-1996 0.86 0.87 -3.09 1996-1997 0.89 0.90 -3.39 Maximum 0.92 0.93 31.51 Minimum 0.71 0.79 -7.17 Average 0.84 0.88 13.37 252 Table 4-8. Detailed statistics of Test #7 without calibration (Mt. Fidelity; 1 elevation band) Water Year Coeff. of Eff. El Coeff. ofDet. Dl Volume Error (%) 1969-1970 0.51 0.72 0.73 1970-1971 0.48 0.69 17.87 1971-1972 0.64 0.81 21.45 1972-1973 0.41 0.68 33.91 1973-1974 0.68 0.78 13.76 1974-1975 0.40 0.68 36.90 1975-1976 0.43 0.64 20.41 1976-1977 0.51 0.78 39.99 1977-1978 0.42 0.62 20.93 1978-1979 0.33 0.71 33.80 1979-1980 0.53 0.73 26.59 1980-1981 0.43 0.66 16.86 1981-1982 0.69 0.83 24.77 1982-1983 0.62 0.71 23.15 1983-1984 0.52 0.68 16.81 1984-1985 0.52 0.79 33.79 1985-1986 0.72 0.84 22.69 1986-1987 0.48 0.72 33.04 1987-1988 0.29 0.66 41.73 1988-1989 0.20 0.73 45.15 1989-1990 0.46 0.73 29.83 1990-1991 0.36 0.71 30.83 1991-1992 0.28 0.55 31.00 1992-1993 0.59 0.74 27.70 1993-1994 0.42 0.62 18.04 1994-1995 0.56 0.69 20.04 1995-1996 0.70 0.77 9.47 1996-1997 0.82 0.84 6.62 Maximum 0.82 0.84 45.15 Minimum 0.20 0.55 0.73 Average 0.50 0.72 24.92 253 Table 4-9. Detailed statistics of Test #8 without calibration (Mt. Fidelity; 1 elevation band) Water Year Coeff. of Eff. El Coeff. of Det. DI Volume Error (%) 1969-1970 0.89 0.90 -11.74 1970-1971 0.86 0.86 1.54 1971-1972 0.92 0.93 5.56 1972-1973 0.86 0.89 18.38 1973-1974 0.91 0.94 -1.52 1974-1975 0.85 0.88 22.36 1975-1976 0.90 0.90 7.01 1976-1977 0.80 0.88 28.12 1977-1978 0.85 0.86 9.04 1978-1979 0.84 0.89 19.71 1979-1980 0.85 0.87 14.93 1980-1981 0.80 0.81 6.04 1981-1982 0.88 0.90 12.78 1982-1983 0.83 0.85 12.87 1983-1984 0.85 0.86 5.00 1984-1985 0.88 0.90 17.84 1985-1986 0.88 0.89 11.01 1986-1987 0.84 0.88 21.22 1987-1988 0.80 0.88 28.45 1988-1989 0.74 0.89 31.86 1989-1990 0.88 0.91 15.85 1990-1991 0.85 0.89 16.80 1991-1992 0.76 0.79 18.25 1992-1993 0.84 0.87 17.55 1993-1994 0.83 0.84 6.44 1994-1995 0.88 0.89 10.02 1995-1996 0.88 0.89 -3.50 1996-1997 0.91 0.93 -4.12 Maximum 0.92 0.94 31.86 Minimum 0.74 0.79 -11.74 Average 0.85 0.88 13.55 254 Table 4-10. Detailed statistics of Test #9 without calibration (Mt. Fidelity; 1 elevation band) Water Year Coeff. of Eff. El Coeff. of Det. Dl Volume Error (%) 1969-1970 0.90 0.91 -7.17 1970-1971 0.88 0.88 1.85 1971-1972 0.91 0.91 7.38 1972-1973 0.86 0.89 16.68 1973-1974 0.94 0.95 -0.92 1974-1975 0.82 0.88 23.16 1975-1976 0.88 0.90 8.22 1976-1977 0.81 0.90 27.02 1977-1978 0.86 0.87 8.97 1978-1979 0.81 0.91 20.81 1979-1980 0.85 0.89 14.28 1980-1981 0.79 0.82 6.34 1981-1982 0.87 0.90 13.82 1982-1983 0.86 0.88 12.59 1983-1984 0.83 0.86 5.87 1984-1985 0.86 0.90 16.97 1985-1986 0.88 0.90 11.69 1986-1987 0.81 0.89 22.01 1987-1988 0.77 0.89 28.87 1988-1989 0.70 0.89 30.82 1989-1990 0.86 0.91 16.25 1990-1991 0.83 0.89 17.23 1991-1992 0.76 0.80 17.85 1992-1993 0.83 0.88 16.74 1993-1994 0.84 0.86 6.82 1994-1995 0.89 0.91 10.43 1995-1996 0.89 0.90 -5.12 1996-1997 0.93 0.93 -2.29 Maximum 0.94 0.95 30.82 Minimum 0.70 0.80 -7.17 Average 0.85 0.89 13.51 255 Table 4-11. Detailed statistics of Test #10 without calibration (Mt. Fic elity; 1 elev. band) Water Year Coeff. of Eff. El Coeff. of Det. Dl Volume Error (%) 1969-1970 0.90 0.92 -4.00 1970-1971 0.89 0.89 6.16 1971-1972 0.92 0.93 9.11 1972-1973 0.86 0.90 22.02 1973-1974 0.93 0.94 2.17 1974-1975 0.83 0.89 26.68 1975-1976 0.89 0.91 10.87 1976-1977 0.77 0.90 33.74 1977-1978 0.87 0.90 14.92 1978-1979 0.81 0.91 25.39 1979-1980 0.85 0.90 20.51 1980-1981 0.81 0.84 11.17 1981-1982 0.87 0.90 17.52 •1982-1983 0.85 0.88 17.68 1983-1984 0.86 0.88 9.02 1984-1985 0.85 0.90 22.65 1985-1986 0.88 0.90 15.67 1986-1987 0.81 0.90 26.66 1987-1988 0.75 0.90 34.70 1988-1989 0.67 0.90 37.36 1989-1990 0.85 0.91 20.63 1990-1991 0.83 0.90 21.01 1991-1992 0.76 0.82 24.81 1992-1993 0.83 0.90 23.97 1993-1994 0.85 0.87 12.16 1994-1995 0.88 0.91 16.74 1995-1996 0.89 0.90 -0.71 1996-1997 0.93 0.93 -0.29 Maximum 0.93 0.94 37.36 Minimum 0.67 0.82 -4.00 Average 0.85 0.90 17.44 256 4.3.3 Comparison of Calculated Statistics (for 1, 2 and 8 elevation bands; without calibration) Comparison of model statistics for Test #4 (Mt. Fidelity) without calibration Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands 1969-1970 0.15 0.51 0.55 24.84 19.99 18.09 1970-1971 0.28 0.65 0.72 28.07 25.24 23.54 1971-1972 0.56 0.72 0.80 27.46 24.33 22.38 1972-1973 0.11 0.54 0.59 33.10 29.68 27.22 1973-1974 0.62 0.85 0.89 19.84 15.99 14.26 1974-1975 0.12 0.44 0.51 43.95 39.98 37.85 1975-1976 0.31 0.61 0.65 29.03 23.88 22.09 1976-1977 -0.13 0.26 0.28 39.14 35.93 33.19 1977-1978 0.11 0.65 0.66 30.24 23.80 21.78 1978-1979 -0.26 0.27 0.30 38.29 35.06 33.11 1979-1980 -0.01 0.58 0.63 32.94 26.34 22.92 1980-1981 -0.01 0.63 0.61 22.25 18.20 16.03 1981-1982 0.30 0.49 0.52 35.50 31.45 29.57 1982-1983 0.21 0.63 0.63 27.20 22.33 19.75 1983-1984 0.17 0.63 0.64 22.26 18.34 16.53 1984-1985 0.18 0.49 0.56 39.79 34.19 32.78 1985-1986 0.40 0.72 0.69 28.21 24.53 22.12 1986-1987 -0.04 0.36 0.43 40.13 36.16 33.79 1987-1988 -0.31 0.29 0.32 51.40 44.40 42.50 1988-1989 -0.77 -0.14 -0.03 51.37 48.17 44.71 1989-1990 0.09 0.48 0.46 36.80 32.84 31.20 1990-1991 0.06 0.54 0.53 36.90 32.04 30.46 1991-1992 -0.03 0.54 0.61 34.19 28.84 26.89 1992-1993 -0.13 0.23 0.24 33.37 28.58 25.32 1993-1994 0.00 0.63 0.69 27.53 22.58 20.28 1994-1995 0.07 0.63 0.62 31.69 26.85 24.10 1995-1996 0.49 0.76 0.75 15.65 10.88 8.85 1996-1997 0.68 0.85 0.87 13.13 10.09 7.93 Maximum 0.68 0.85 0.89 51.40 48.17 44.71 Minimum -0.77 -0.14 -0.03 13.13 10.09 7.93 Average 0.12 0.53 0.56 31.94 27.52 25.33 257 Comparison of model statistics for Test #5 (Mt. Fidelity) without calibration Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands 1969-1970 0.53 0.82 0.85 6.65 3.22 1.34 1970-1971 0.50 0.80 0.88 22.21 17.73 14.51 1971-1972 0.66 0.87 0.92 23.74 19.88 16.33 1972-1973 0.47 0.78 0.86 30.72 25.00 21.07 1973-1974 0.72 0.91 0.97 14.64 9.39 6.67 1974-1975 0.41 0.81 0.86 36.66 31.37 26.66 1975-1976 0.46 0.84 0.90 22.20 15.86 12.28 1976-1977 0.53 0.67 0.78 37.62 . 31.49 26.13 1977-1978 0.47 0.88 0.92 19.82 12.37 7.90 1978-1979 0.35 0.66 0.77 35.00 29.09 25.61 1979-1980 0.58 0.87 0.91 26.29 17.91 12.43 1980-1981 0.48 0.78 0.84 16.96 9.37 6.45 1981-1982 0.70 0.83 0.88 24.96 20.58 17.14 1982-1983 0.65 0.82 0.86 22.91 15.52 11.57 1983-1984 0.56 0.85 0.89 15.58 9.58 6.54 1984-1985 0.52 0.76 0.83 35.12 28.04 24.59 1985-1986 0.72 0.86 0.89 22.70 17.81 14.32 1986-1987 0.49 0.77 0.84 33.87 27.29 23.45 1987-1988 0.31 0.71 0.79 41.95 34.25 30.04 1988-1989 0.22 0.56 0.66 44.72 38.17 32.85 1989-1990 0.46 0.73 0.80 30.71 26.04 22.41 1990-1991 0.36 0.71 0.80 32.01 26.52 23.43 1991-1992 0.34 0.82 0.88 27.93 21.34 17.69 1992-1993 0.64 0.79 0.82 24.48 16.64 12.15 1993-1994 0.48 0.84 0.91 19.54 13.04 8.94 1994-1995 0.59 0.87 0.90 19.20 15.01 9.66 1995-1996 0.72 0.84 0.90 10.64 5.32 1.35 1996-1997 0.85 0.93 0.95 7.11 1.50 -1.45 Maximum 0.85 0.93 0.97 44.72 38.17 32.85 Minimum 0.22 0.56 0.66 6.65 1.50 -1.45 Average 0.53 0.80 0.86 25.21 19.26 15.53 258 Comparison of model statistics for Test #6 (Mt. Fidelity) without calibration Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands 1969-1970 0.89 0.91 0.91 -7.17 -8.89 -10.55 1970-1971 0.86 0.90 0.91 5.12 3.24 -0.08 1971-1972 0.90 0.88 0.87 7.60 4.99 2.14 1972-1973 0.86 0.90 0.90 15.97 12.97 10.06 1973-1974 0.92 0.88 0.88 -0.99 -4.65 -6.61 1974-1975 0.82 0.90 0.89 22.48 17.22 15.65 1975-1976 0.89 0.89 0.89 8.38 3.24 0.97 1976-1977 0.76 0.80 0.80 26.94 21.01 18.33 1977-1978 0.87 0.97 0.96 7.83 0.85 -2.28 1978-1979 0.82 0.86 0.86 20.42 15.35 13.11 1979-1980 0.85 0.91 0.92 15.33 7.98 3.22 1980-1981 0.81 0.84 0.83 5.99 -0.84 -3.56 1981-1982 0.85 0.87 0.86 12.71 6.94 5.35 1982-1983 0.83 0.89 0.90 12.98 5.87 3.26 1983-1984 0.85 0.90 0.90 3.49 -1.05 -3.51 1984-1985 0.84 0.84 0.82 18.88 12.92 11.11 1985-1986 0.86 0.85 0.83 11.49 5.19 3.67 1986-1987 0.82 0.87 0.88 22.00 15.86 13.07 1987-1988 0.78 0.87 0.87 28.60 21.38 18.06 1988-1989 0.71 0.80 0.82 31.51 24.60 20.82 1989-1990 0.84 0.83 0.80 16.18 13.12 10.28 1990-1991 0.81 0.82 0.79 17.80 12.80 11.14 1991-1992 0.77 0.89 0.91 15.95 11.89 8.72 1992-1993 0.85 0.90 0.91 14.85 7.03 3.32 1993-1994 0.86 0.95 0.94 7.69 0.31 -2.48 1994-1995 0.88 0.94 0.95 9.46 3.97 0.37 1995-1996 0.86 0.79 0.75 -3.09 -8.11 -10.62 1996-1997 0.89 0.86 0.85 -3.39 -8.24 -10.05 Maximum 0.92 0.97 0.96 31.51 24.60 20.82 Minimum 0.71 0.79 0.75 -7.17 -8.89 -10.62 Average 0.84 0.88 0.87 13.37 9.30 7.94 259 Comparison of model statistics for Test #7 (Mt. Fidelity) without calibration Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands 1969-1970 0.51 0.82 0.85 0.73 -1.43 -2.96 1970-1971 0.48 0.81 0.90 17.87 14.16 11.24 1971-1972 0.64 0.88 0.94 21.45 17.68 14.19 1972-1973 0.41 0.77 0.85 33.91 28.05 24.06 1973-1974 0.68 0.92 0.97 13.76 8.62 5.82 1974-1975 0.40 0.83 0.88 36.90 31.58 26.99 1975-1976 0.43 0.85 0.91 20.41 14.72 11.03 1976-1977 0.51 0.68 0.78 39.99 33.21 28.07 1977-1978 0.42 0.87 0.91 20.93 13.44 9.04 1978-1979 0.33 0.69 0.80 33.80 28.10 24.41 1979-1980 0.53 0.86 0.90 26.59 18.15 12.85 1980-1981 0.43 0.78 0.85 16.86 9.49 6.45 1981-1982 0.69 0.85 0.90 24.77 19.75 16.36 1982-1983 0.62 0.82 0.86 23.15 16.12 12.16 1983-1984 0.52 0.85 0.89 16.81 10.52 7.47 1984-1985 0.52 0.80 0.87 33.79 26.92 23.41 1985-1986 0.72 0.87 0.91 22.69 17.60 14.15 1986-1987 0.48 0.79 0.86 33.04 27.04 23.12 1987-1988 0.29 0.72 0.80 41.73 33.97 29.86 1988-1989 0.20 0.59 0.70 45.15 38.38 33.16 1989-1990 ; 0.46 0.77 0.85 29.83 25.32 21.67 1990-1991 0.36 0.75 0.84 30.83 25.65 22.41 1991-1992 0.28 0.81 0.86 31.00 23.90 20.40 1992-1993 0.59 0.77 0.80 27.70 19.78 15.24 1993-1994 0.42 0.84 0.91 18.04 11.66 7.56 1994-1995 0.56 0.86 0.89 20.04 15.31 10.20 1995-1996 0.70 0.85 0.92 9.47 4.72 0.55 1996-1997 0.82 0.93 0.95 6.62 0.78 -2.21 Maximum 0.82 0.93 0.97 45.15 38.38 33.16 Minimum 0.20 0.59 0.70 0.73 -1.43 -2.96 Average 0.50 0.81 0.87 24.92 19.14 15.61 260 Comparison of model statistics for Test #8 (Mt. Fidelity) without calibration Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands 1969-1970 0.89 0.92 0.91 -11.74 -12.43 -13.81 1970-1971 0.86 0.91 0.92 1.54 0.18 -2.81 1971-1972 0.92 0.90 0.89 5.56 3.00 0.14 1972-1973 0.86 0.92 0.91 18.38 15.47 12.39 1973-1974 0.91 0.89 0.90 -1.52 -5.09 -7.10 1974-1975 0.85 0.93 0.93 22.36 17.28 15.59 1975-1976 0.90 0.91 0.91 7.01 2.15 -0.06 1976-1977 0.80 0.84 0.84 28.12 22.22 19.54 1977-1978 0.85 0.96 0.96 9.04 1.97 -0.99 1978-1979 0.84 0.89 0.90 19.71 14.55 12.21 1979-1980 0.85 0.92 0.92 14.93 7.83 3.22 1980-1981 0.80 0.86 0.85 6.04 -0.57 -3.34 1981-1982 0.88 0.90 0.89 12.78 6.50 4.82 1982-1983 0.83 0.90 0.90 12.87 6.03 3.46 1983-1984 0.85 0.92 0.92 5.00 0.00 -2.44 1984-1985 0.88 0.88 0.87 17.84 12.03 10.06 1985-1986 0.88 0.87 0.86 11.01 4.94 3.35 1986-1987 0.84 0.90 0.91 21.22 15.26 12.63 1987-1988 0.80 0.89 0.90 28.45 21.20 17.94 1988-1989 0.74 0.85 0.86 31.86 24.93 21.15 1989-1990 0.88 0.88 0.85 15.85 12.60 9.84 1990-1991 0.85 0.87 0.84 16.80 12.06 10.21 1991-1992 0.76 0.89 0.92 18.25 13.76 10.82 1992-1993 0.84 0.89 0.90 17.55 9.98 6.19 1993-1994 0.83 0.95 0.95 6.44 -0.74 -3.49 1994-1995 0.88 0.93 0.95 10.02 4.31 0.69 1995-1996 0.88 0.81 0.78 -3.50 -8.42 -11.06 1996-1997 0.91 0.87 0.86 -4.12 -9.13 -10.96 Maximum 0.92 0.96 0.96 31.86 24.93 21.15 Minimum 0.74 0.81 0.78 -11.74 -12.43 -13.81 Average 0.85 0.89 0.89 13.55 9.45 8.23 261 Comparison of model statistics for Test #9 (Mt. Fidelity) without calibration Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands 1969-1970 0.90 0.92 0.91 -7.17 -8.53 -10.45 1970-1971 0.88 0.92 0.93 1.85 0.30 -2.34 1971-1972 0.91 0.91 0.91 7.38 4.85 1.97 1972-1973 0.86 0.92 0.92 16.68 13.76 10.58 1973-1974 0.94 0.92 0.92 -0.92 -4.26 -6.28 1974-1975 0.82 0.92 0.91 23.16 18.38 16.45 1975-1976 0.88 0.91 0.91 8.22 3.53 1.39 1976-1977 0.81 0.84 0.84 27.02 20.66 17.42 1977-1978 0.86 0.97 0.96 8.97 1.77 -1.07 1978-1979 0.81 0.86 0.87 20.81 15.72 13.53 1979-1980 0.85 0.94 0.94 14.28 6.79 2.07 1980-1981 0.79 0.86 0.85 6.34 -0.11 -2.53 1981-1982 0.87 0.87 0.85 13.82 7.99 6.23 1982-1983 0.86 0.92 0.92 12.59 5.70 2.89 1983-1984 0.83 0.91 0.91 5.87 0.54 -1.73 1984-1985 0.86 0.88 0.86 16.97 11.84 9.70 1985-1986 0.88 0.88 0.86 11.69 5.43 3.95 1986-1987 0.81 0.89 0.89 22.01 16.06 13.36 1987-1988 0.77 0.86 0.87 28.87 21.69 18.19 1988-1989 0.70 0.81 0.83 30.82 24.06 20.49 1989-1990 0.86 0.85 0.82 16.25 13.65 10.98 1990-1991 0.83 0.84 0.81 17.23 12.89 11.05 1991-1992 0.76 0.92 0.94 17.85 12.57 9.36 1992-1993 0.83 0.85 0.85 16.74 9.48 5.54 1993-1994 0.84 0.96 0.96 6.82 -0.69 -3.18 1994-1995 0.89 0.95 0.95 10.43 4.83 0.97 1995-1996 0.89 0.82 0.78 -5.12 -8.61 -10.95 1996-1997 0.93 0.90 0.89 -2.29 -8.39 -10.16 Maximum 0.94 0.97 0.96 30.82 24.06 20.49 Minimum 0.70 0.81 0.78 -7.17 -8.61 -10.95 Average 0.85 0.89 0.89 13.51 9.40 8.03 262 Comparison of model statistics for Test #10 (Mt. Fidelity) without calibration Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands 1969-1970 0.90 0.93 0.92 -4.00 -7.01 -9.43 1970-1971 0.89 0.92 0.93 6.16 3.47 -0.07 1971-1972 0.92 0.91 0.90 9.11 5.53 2.39 1972-1973 0.86 0.92 0.92 22.02 17.34 13.69 1973-1974 0.93 0.91 0.92 2.17 -2.70 -5.03 1974-1975 0.83 0.92 0.92 26.68 20.08 17.63 1975-1976 0.89 0.91 0.91 10.87 4.29 1.83 1976-1977 0.77 0.83 0.83 33.74 25.55 21.34 . 1977-1978 0.87 0.97 0.97 14.92 5.15 1.26 1978-1979 0.81 0.87 0.87 25.39 18.20 15.09 1979-1980 0.85 0.93 0.94 20.51 10.62 4.92 1980-1981 0.81 0.86 0.85 11.17 2.32 -1.18 1981-1982 0.87 0.89 0.88 17.52 9.51 7.25 1982-1983 0.85 0.92 0.91 17.68 8.74 5.18 1983-1984 0.86 0.92 0.92 9.02 2.81 -0.37 1984-1985 0.85 0.87 0.86 22.65 15.28 12.58 1985-1986 0.88 0.88 0.86 15.67 7.74 5.57 1986-1987 0.81 0.89 0.90 26.66 18.65 15.02 1987-1988 0.75 0.86 0.87 34.70 24.96 20.84 1988-1989 0.67 0.80 0.83 37.36 28.39 23.37 1989-1990 0.85 0.86 0.83 20.63 15.69 12.34 1990-1991 0.83 0.86 0.82 21.01 14.65 12.52 1991-1992 0.76 0.90 0.93 24.81 17.51 13.23 1992-1993 0.83 0.88 0.88 23.97 13.73 8.57 1993-1994 0.85 0.96 0.96 12.16 2.52 -0.89 1994-1995 0.88 0.94 0.96 16.74 7.89 3.02 1995-1996 0.89 0.82 0.79 -0.71 -6.78 -9.63 1996-1997 0.93 0.89 0.88 -0.29 -6.85 -9.33 Maximum 0.93 0.97 0.97 37.36 28.39 23.37 Minimum 0.67 0.80 0.79 -4.00 -7.01 -9.63 Average 0.85 0.89 0.89 X1AA 11.57 9.06 263 4.3.6 Model Calibration Results (for 1, 2 and 8 elevation bands; before and after calibration) Model statistics before and after calibration for Test #3 (Mt. Fidelity) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after 1969-1970 -1.60 0.76 -0.13 0.83 -0.01 0.81 34.33 -14.43 29.51 -9.44 26.89 -7.98 j 1970-1971 -1.45 0.72 0.01 0.76 0.23 0.78 38.38 -1.30 35.94 1.71 33.39 1.92 j ; 1971-1972 -0.81 0.81 0.26 0.82 0.48 0.81 37.38 -0.54 35.86 0.74 32.43 0.89 ; 1 1972-1973 -1.63 0.76 -0.20 0.82 0.09 0.82 43.92 3.92 38.65 5.38 36.20 4.91 1 j 1973-1974 -0.75 0.79 0.54 0.80 0.65 0.82 29.94 -7.74 26.27 -6.72 23.80 -6.43 j • 1974-1975 -1.45 0.73 -0.06 0.83 0.11 0.84 55.03 13.71 50.58 12.39 47.22 12.05' • 1975-1976 -1.29 0.69 0.15 0.84 0.35 0.87 38.95 0.31 34.48 -2.72 31.54 -3.40 1976-1977 -1.35 0.54 -0.45 0.72 -0.17 0.74 48.99 20.05 44.32 13.85 41.02 10.93 1977-1978 -1.45 0.72 0.24 0.83 0.31 0.86 39.46 3.17 33.31 -2.65 30.34 -4.38 1978-1979 -2.08 0.65 -0.51 0.83 -0.22 0.82 47.99 14.94 44.94 11.07 41.97 9.99 1979-1980 -1.39 0.69 0.07 0.80 0.21 0.81 41.57 13.39 35.18 3.16 31.45 -0.25 1980-1981 -1.49 0.63 0.19 0.74 0.31 0.75 30.38 6.69 26.99 -2.32 24.08 -4.20 1981-1982 -0.78 0.74 0.07 0.86 0.25 0.84 44.91 6.87 41.46 3.35 38.82 3.00 1982-1983 -0.63 0.56 0.32 0.69 0.37 0.72 35.97 13.78 31.19 1.91 27.93 -1.79 1983-1984 -1.14 0.71 0.31 0.80 0.36 0.83 30.92 0.18 26.94 -5.03 24.75 -6.40 1984-1985 -1.46 0.68 -0.14 0.74 0.16 0.73 50.24 11.28 44.53 10.24 42.28 10.07 1985-1986 -0.67 0.64 0.44 0.67 0.46 0.63 37.13 5.54 34.28 1.07 30.95 -0.46 1986-1987 -1.33 0.60 -0.23 0.74 0.05 0.75 49.44 20.61 45.98 10.27 42.67 8.12 1987-1988 -1.97 0.68 -0.45 0.82 -0.20 0.83 61.94 22.40 55.10 16.89 52.42 14.85 1988-1989 -2.58 0.44 -0.97 0.63 -0.68 0.64 61.92 28.69 59.06 20.69 55.00 18.37 1989-1990 -1.49 0.75 -0.04 0.85 0.17 0.85 46.49 7.67 42.67 6.99 39.99 6.37 1990-1991 -1.67 0.70 -0.06 0.83 0.26 0.80 46.96 4.98 42.37 5.98 39.97 6.18 1991-1992 -1.68 0.69 0.12 0.80 0.22 0.84 43.27 5.88 37.78 3.43 35.22 1.77 1992-1993 -1.12 0.49 -0.12 0.70 -0.14 0.71 41.02 27.12 36.71 9.26 33.13 5.23 1993-1994 -1.53 0.77 -0.02 0.84 0.25 0.86 36.36 4.90 32.56 0.27 29.34 -1.40 1994-1995 -1.16 0.70 0.27 0.83 0.25 0.89 40.05 8.03 35.79 2.50 32.56 -0.29 1995-1996 -0.70 0.75 0.46 0.76 0.67 0.77 25.02 -7.63 21.37 -9.38 18.31 -11.29 1996-1997 -0.05 0.71 0.58 0.79 0.72 0.79 21.52 -8.31 17.74 -12.78 15.18 -14.28 Maximum -0.05 0.81 0.58 0.86 0.72 0.89 61.94 28.69 59.06 20.69 55.00 18.37 Minimum -2.58 0.44 -0.97 0.63 -0.68 0.63 21.52 -14.43 17.74 -12.78 15.18 -14.28 Average -1.31 0.68 0.02 0.78 0.20 0.79 41.41 10.14 37.20 6.86 34.24 6.33 264 Model statistics before and after calibration for Test #4 (Mt. Fidelity) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after 1969-1970 0.15 0.80 0.51 0.80 0.55 10.78 24.84 -5.55 19.99 -5.57 18.09 -4.47 1970-1971 0.28 0.72 0.65 0.88 0.72 0.90 28.07 1.58 25.24 0.45 23.54 1.21 I 1971-1972 0.56 0.82 0.72 0.90 0.80 0.94 27.46 0.26 24.33 -0.65 22.38 0.05 1 '• 1972-1973 0.11 0.75 0.54 0.84 0.59 0.84 33.10 4.65 29.68 2.09 27.22 2.64 '• ! 1973-1974 0.62 0.86 0.85 0.91 0.89 0.96 19.84 -6.05 15.99 -7.22 14.26 -6.66! | 1974-1975 0.12 0.81 0.44 0.88 0.51 0.87 43.95 12.56 39.98 9.79 37.85 10.381 I 1975-1976 0.31 10.85 0.61 0.90 0.65 0.90 29.03 -2.32 23.88 -5.76 22.09 -4.08 : 1976-1977 -0.13 0.69 0.26 0.78 0.28 0.76 39.14 10.56 35.93 5.56 33.19 5.13 1977-1978 0.11 0.80 0.65 0.88 0.66 0.86 30.24 -2.10 23.80 -6.04 21.78 -4.78 1978-1979 -0.26 0.73 0.27 0.81 0.30 0.75 38.29 9.94 35.06 7.31 33.11 7.94 1979-1980 -0.01 0.74 0.58 0.89 0.63 0.85 32.94 1.91 26.34 -5.25 22.92 -4.92 1980-1981 -0.01 0.65 0.63 0.91 0.61 0.86 22.25 -3.18 18.20 -8.26 16.03 -8.17 1981-1982 0.30 0.81 0.49 0.84 0.52 0.85 35.50 3.13 31.45 0.73 29.57 2.20 1982-1983 0.21 0.69 0.63 0.78 0.63 0.80 27.20 -1.31 22.33 -7.93 19.75 -7.90 1983-1984 0.17 0.81 0.63 0.87 0.64 0.85 22.26 -5.89 18.34 -9.60 16.53 -8.46 1984-1985 0.18 0.66 0.49 0.81 0.56 0.86 39.79 10.31 34.19 7.45 32.78 7.87 1985-1986 0.40 0.67 0.72 0.79 0.69 0.84 28.21 -0.70 24.53 -3.57 22.12 -3.00 1986-1987 -0.04 0.71 0.36 0.85 0.43 0.86 40.13 8.30 36.16 3.55 33.79 4.20 1987-1988 -0.31 0.75 0.29 0.83 0.32 0.79 51.40 15.94 44.40 10.53 42.50 11.79 1988-1989 -0.77 0.52 -0.14 0.69 -0.03 0.66 51.37 18.77 48.17 13.57 44.71 13.82 1989-1990 0.09 0.84 0.48 0.85 0.46 0.84 36.80 7.13 32.84 4.63 31.20 5.76 1990-1991 0.06 0.71 0.54 0.83 0.53 0.84 36.90 7.05 32.04 5.08 30.46 5.69 1991-1992 -0.03 0.79 0.54 0.88 0.61 0.88 34.19 3.07 28.84 -0.52 26.89 1.07 1992-1993 -0.13 0.73 0.23 0.67 0.24 0.61 33.37 6.30 28.58 -1.47 25.32 -2.47 1993-1994 0.00 0.73 0.63 0.88 0.69 0.88 27.53 0.06 22.58 -3.34 20.28 -3.66 1994-1995 0.07 0.86 0.63 0.90 0.62 0.84 31.69 2.01 26.85 -4.42 24.10 -3.62 1995-1996 0.49 0.84 0.76 0.82 0.75 0.87 15.65 -10.53 10.88 -14.44 8.85 -13.55 1996-1997 0.68 0.82 0.85 0.87 0.87 0.93 13.13 -14.16 10.09 -17.11 7.93 -16.13 Maximum 0.68 0.86 0.85 0.91 0.89 0.96 51.40 18.77 48.17 13.57 44.71 13.82 Minimum -0.77 0.52 -0.14 0.67 -0.03 0.61 13.13 -14.16 10.09 -17.11 7.93 -16.13 Average 0.12 0.76 0.53 0.84 0.56 0.84 31.94 6.26 27.52 6.20 25.33 6.13 265 Model statistics before and after calibration for Test #5 (Mt. Fidelity) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after 1969-1970 0.53 0.80 0.82 0.91 0.85 0.92 6.65 -15.37 3.22 -11.29 1.34 -10.15 1970-1971 0.50 0.77 0.80 0.88 0.88 0.94 22.21 0.74 17.73 1.38 14.51 0.41 I 1971-1972 0.66 0.86 0.87 0.94 0.92 0.96 23.74 1.66 19.88 3.95 16.33 2.14 | '• 1972-1973 0.47 0.73 0.78 0.91 0.86 0.93 30.72 8.86 25.00 5.71 21.07 4.72 '• ! 1973-1974 0.72 0.89 0.91 0.92 0.97 0.97 14.64 -6.01 9.39 -4.54 6.67 -6.54 ! | 1974-1975 0.41 0.75 0.81 0.94 0.86 0.95 36.66 11.36 31.37 12.44 26.66 10.481 I 1975-1976 0.46 0.74 0.84 0.90 0.90 0.94 22.20 -2.77 15.86 -3.65 12.28 -2.38 : 1976-1977 0.53 0.79 0.67 0.88 0.78 0.90 37.62 12.03 31.49 9.17 26.13 9.11 1977-1978 0.47 0.73 0.88 0.92 0.92 0.95 19.82 -6.29 12.37 -6.94 7.90 -5.90 1978-1979 0.35 0.78 0.66 0.87 0.77 0.92 35.00 10.04 29.09 10.23 25.61 10.07 1979-1980 0.58 0.80 0.87 0.91 0.91 0.93 26.29 -0.50 17.91 -3.58 12.43 -2.36 1980-1981 0.48 0.74 0.78 0.83 0.84 0.88 16.96 -7.80 9.37 -10.00 6.45 -7.71 1981-1982 0.70 0.87 0.83 0.94 0.88 0.96 24.96 -0.92 20.58 0.51 17.14 2.36 1982-1983 0.65 0.71 0.82 0.81 0.86 0.88 22.91 -3.95 15.52 -6.61 11.57 -3.94 1983-1984 0.56 0.77 0.85 0.90 0.89 0.93 15.58 -8.61 9.58 -9.75 6.54 -7.33 1984-1985 0.52 0.82 0.76 0.90 0.83 0.94 35.12 11.49 28.04 11.58 24.59 9.59 1985-1986 0.72 0.83 0.86 0.90 0.89 0.94 22.70 -1.59 17.81 -0.92 14.32 -0.74 1986-1987 0.49 0.76 0.77 0.93 0.84 0.94 33.87 4.97 27.29 4.95 23.45 7.00 1987-1988 0.31 0.71 0.71 0.90 0.79 0.90 41.95 11.99 34.25 11.50 30.04 13.35 1988-1989 0.22 0.75 0.56 0.86 0.66 0.86 44.72 14.37 38.17 14.29 32.85 15.68 1989-1990 0.46 0.80 0.73 0.91 0.80 0.93 30.71 6.59 26.04 6.96 22.41 7.06 1990-1991 0.36 0.71 0.71 0.87 0.80 0.92 32.01 8.31 26.52 10.05 23.43 8.44 1991-1992 0.34 0.66 0.82 0.89 0.88 0.93 27.93 5.09 21.34 2.33 17.69 2.37 1992-1993 0.64 0.82 0.79 0.90 0.82 0.91 24.48 -4.56 16.64 -5.72 12.15 -3.19 1993-1994 0.48 0.73 0.84 0.92 0.91 0.94 19.54 -4.12 13.04 -3.61 8.94 -4.51 1994-1995 0.59 0.79 0.87 0.90 0.90 0.93 19.20 -6.62 15.01 -5.96 9.66 -3.95 1995-1996 0.72 0.82 0.84 0.82 0.90 0.89 10.64 -10.88 5.32 -13.82 1.35 -12.21 1996-1997 0.85 0.81 0.93 0.89 0.95 0.92 7.11 -15.21 1.50 -15.79 -1.45 -14.18 Maximum 0.85 0.89 0.93 0.94 0.97 0.97 44.72 14.37 38.17 14.29 32.85 15.68 Minimum 0.22 0.66 0.56 0.81 0.66 0.86 6.65 -15.37 1.50 -15.79 -1.45 -14.18 Average 0.53 0.78 0.80 0.89 0.86 0.93 25.21 7.24 19.26 7.40 15.53 6.71 266 Model statistics before and after calibration for Test #6 (Mt. Fidelity) Coefficient of Efficiency (E!) Volume Error (%) Water Year 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after 1969-1970 0.89 0.89 0.91 0.90 0.91 0.92 -7.17 -8.81 -8.89 -6.10 -10.55 -9.13 1970-1971 0.86 0.92 0.90 0.94 0.91 0.95 5.12 -0.73 3.24 0.25 -0.08 -1.98 I 1971-1972 0.90 0.95 0.88 0.95 0.87 0.96 7.60 -0.69 4.99 0.85 2.14 -0.49 1 ' 1972-1973 0.86 0.89 0.90 0.93 0.90 0.94 15.97 7.82 12.97 5.71 10.06 5.47 '• ! 1973-1974 0.92 0.95 0.88 0.96 0.88 0.97 -0.99 -7.15 -4.65 -6.87 -6.61 -8.97! | 1974-1975 0.82 0.89 0.90 0.93 0.89 0.95 22.48 11.55 17.22 11.87 15.65 9.20 | I 1975-1976 0.89 0.92 0.89 0.92 0.89 0.93 8.38 -4.65 3.24 -3.04 0.97 -3.03 : 1976-1977 0.76 0.86 0.80 0.88 0.80 0.90 26.94 10.70 21.01 9.30 18.33 8.88 1977-1978 0.87 0.83 0.97 0.94 0.96 0.92 7.83 -6.77 0.85 -4.85 -2.28 -6.44 1978-1979 0.82 0.88 0.86 0.86 0.86 0.88 20.42 6.10 15.35 9.23 13.11 7.84 1979-1980 0.85 0.87 0.91 0.94 0.92 0.93 15.33 -2.55 7.98 -2.19 3.22 -3.40 1980-1981 0.81 0.81 0.84 0.89 0.83 0.86 5.99 -10.99 -0.84 -7.84 -3.56 -9.05 1981-1982 0.85 0.93 0.87 0.91 0.86 0.94 12.71 -1.06 6.94 1.69 5.35 -0.31 1982-1983 0.83 0.75 0.89 0.88 0.90 0.87 12.98 -7.73 5.87 -5.20 3.26 -5.24 1983-1984 0.85 0.87 0.90 0.93 0.90 0.92 3.49 -11.37 -1.05 -8.38 -3.51 -8.89 1984-1985 0.84 0.90 0.84 0.89 0.82 0.93 18.88 9.77 12.92 9.03 11.11 6.21 1985-1986 0.86 0.91 0.85 0.92 0.83 0.93 11.49 -2.05 5.19 -1.42 3.67 -1.61 1986-1987 0.82 0.90 0.87 0.92 0.88 0.93 22.00 1.84 15.86 6.13 13.07 5.23 1987-1988 0.78 0.86 0.87 0.88 0.87 0.90 28.60 11.13 21.38 12.37 18.06 11.64 1988-1989 0.71 0.78 0.80 0.80 0.82 0.83 31.51 12.12 24.60 15.87 20.82 13.97 1989-1990 0.84 0.88 0.83 0.90 0.80 0.92 16.18 5.91 13.12 6.68 10.28 6.38 1990-1991 0.81 0.86 0.82 0.89 0.79 0.90 17.80 9.20 12.80 8.18 11.14 7.55 1991-1992 0.77 0.83 0.89 0.92 0.91 0.91 15.95 5.44 11.89 3.33 8.72 2.18 1992-1993 0.85 0.81 0.90 0.80 0.91 0.83 14.85 -8.50 7.03 -2.40 3.32 -4.39 1993-1994 0.86 0.85 0.95 0.94 0.94 0.94 7.69 -4.84 0.31 -3.36 -2.48 -6.62 1994-1995 0.88 0.86 0.94 0.93 0.95 0.91 9.46 -4.01 3.97 -3.62 0.37 -5.50 1995-1996 0.86 0.90 0.79 0.87 0.75 0.89 -3.09 -14.15 -8.11 -14.27 -10.62 -14.31 1996-1997 0.89 0.91 0.86 0.92 0.85 0.92 -3.39 -17.24 -8.24 -14.93 -10.05 -16.30 Maximum 0.92 0.95 0.97 0.96 0.96 0.97 31.51 12.12 24.60 15.87 20.82 13.97 Minimum 0.71 0.75 0.79 0.80 0.75 0.83 -7.17 -17.24 -8.89 -14.93 -10.62 -16.30 Average 0.84 0.87 0.88 0.91 0.87 0.91 13.37 7.32 9.30 6.61 7.94 6.84 267 Model statistics before and after calibration for Test #7 (Mt. Fidelity) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after 1969-1970 0.51 0.80 0.82 0.90 0.85 0.90 0.73 -13.27 -1.43 -14.65 -2.96 -14.13 1970-1971 0.48 0.77 0.81 0.86 0.90 0.94 17.87 4.42 14.16 -0.39 11.24 -0.47 I 1971-1972 0.64 0.85 0.88 0.94 0.94 0.96 21.45 5.20 17.68 3.32 14.19 2.10 1 '• 1972-1973 0.41 0.75 0.77 0.90 0.85 0.91 33.91 14.69 28.05 8.85 24.06 11.85' • ! 1973-1974 0.68 0.89 0.92 0.92 0.97 0.96 13.76 -2.39 8.62 -5.21 5.82 -5.50 ! I 1974-1975 0.40 0.75 0.83 0.94 0.88 0.96 36.90 16.26 31.58 12.96 26.99 13.391 I 1975-1976 0.43 0.75 0.85 0.89 0.91 0.93 20.41 0.37 14.72 -4.27 11.03 -4.35 : 1976-1977 0.51 0.80 0.68 0.88 0.78 0.90 39.99 16.93 33.21 10.70 28.07 12.05 1977-1978 0.42 0.72 0.87 0.89 0.91 0.91 20.93 -2.93 13.44 -6.93 9.04 -5.73 1978-1979 0.33 0.79 0.69 0.88 0.80 0.93 33.80 13.11 28.10 9.60 24.41 9.49 1979-1980 0.53 0.79 0.86 0.89 0.90 0.90 26.59 3.15 18.15 -3.28 12.85 -2.86 1980-1981 0.43 0.73 0.78 0.83 0.85 0.86 16.86 -5.20 9.49 -10.13 6.45 -9.72 1981-1982 0.69 0.87 0.85 0.94 0.90 0.96 24.77 2.12 19.75 -0.74 16.36 0.40 1982-1983 0.62 0.70 0.82 0.77 0.86 0.82 23.15 -0.94 16.12 -6.24 12.16 -5.67 1983-1984 0.52 0.77 0.85 0.88 0.89 0.92 16.81 -5.46 10.52 -9.65 7.47 -8.27 1984-1985 0.52 0.82 0.80 0.93 0.87 0.94 33.79 15.44 26.92 10.85 23.41 10.07 1985-1986 0.72 0.83 0.87 0.89 0.91 0.94 22.69 2.34 17.60 -0.79 14.15 -0.21 1986-1987 0.48 0.78 0.79 0.93 0.86 0.94 33.04 8.17 27.04 4.80 23.12 5.45 1987-1988 0.29 0.72 0.72 0.89 0.80 0.92 41.73 15.60 33.97 11.09 29.86 11.39 1988-1989 0.20 0.74 0.59 0.86 0.70 0.89 45.15 18.71 38.38 14.16 33.16 14.68 1989-1990 0.46 0.81 0.77 0.92 0.85 0.93 29.83 10.61 25.32 7.08 21.67 6.69 1990-1991 0.36 0.72 0.75 0.89 0.84 0.92 30.83 12.75 25.65 9.91 22.41 9.73 1991-1992 0.28 0.66 0.81 0.87 0.86 0.92 31.00 11.05 23.90 4.51 20.40 8.16 1992-1993 0.59 0.81 0.77 0.86 0.80 0.86 27.70 -1.16 19.78 -4.30 15.24 -2.10 1993-1994 0.42 0.73 0.84 0.90 0.91 0.92 18.04 -1.68 11.66 -5.22 7.56 -6.04 1994-1995 0.56 0.80 0.86 0.87 0.89 0.90 20.04 -3.06 15.31 -6.12 10.20 -5.47 1995-1996 0.70 0.83 0.85 0.82 0.92 0.87 9.47 -8.48 4.72 -13.46 0.55 -13.61 1996-1997 0.82 0.83 0.93 0.87 0.95 0.89 6.62 -12.37 0.78 -16.16 -2.21 -15.82 Maximum 0.82 0.89 0.93 0.94 0.97 0.96 45.15 18.71 38.38 14.16 33.16 14.68 Minimum 0.20 0.66 0.59 0.77 0.70 0.82 0.73 -13.27 -1.43 -16.16 -2.96 -15.82 Average 0.50 0.78 0.81 0.89 0.87 0.91 24.92 8.14 19.14 7.69 15.61 7.69 268 Model statistics before and after calibration for Test #8 (Mt. Fidelity) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after 1969-1970 0.89 0.89 0.92 0.91 0.91 0.91 -11.74 -9.32 -12.43 -7.55 -13.81 -6.54 1970-1971 0.86 0.92 0.91 0.94 0.92 0.95 1.54 -1.55 0.18 -1.29 -2.81 -1.16 1 1971-1972 0.92 0.95 0.90 0.95 0.89 0.96 5.56 -0.93 3.00 -0.45 0.14 -0.09 1 ' 1972-1973 0.86 0.90 0.92 0.94 0.91 0.93 18.38 9.03 15.47 8.28 12.39 7.71 '• ! 1973-1974 0.91 0.95 0.89 0.95 0.90 0.97 -1.52 -7.07 -5.09 -7.55 -7.10 -7.52 ! | 1974-1975 0.85 0.90 0.93 0.94 0.93 0.94 22.36 12.03 17.28 12.21 15.59 77.031 I 1975-1976 0.90 0.92 0.91 0.92 0.91 0.93 7.01 -4.20 2.15 -3.01 -0.06 -7.52 : 1976-1977 0.80 0.87 0.84 0.88 0.84 0.88 28.12 12.16 22.22 11.84 19.54 72.73 1977-1978 0.85 0.84 0.96 0.94 0.96 0.93 9.04 -5.38 1.97 -3.33 -0.99 -3.22 1978-1979 0.84 0.89 0.89 0.88 0.90 0.87 19.71 7.02 14.55 9.06 12.21 9.52 1979-1980 0.85 0.87 0.92 0.94 0.92 0.93 14.93 -1.11 7.83 -0.35 3.22 -0.81 1980-1981 0.80 0.82 0.86 0.87 0.85 0.87 6.04 -9.57 -0.57 -6.99 -3.34 -6.65 1981-1982 0.88 0.93 0.90 0.94 0.89 0.92 12.78 -0.22 6.50 1.66 4.82 2.45 1982-1983 0.83 0.76 0.90 0.89 0.90 0.88 12.87 -6.09 6.03 -3.20 3.46 -2.57 1983-1984 0.85 0.88 0.92 0.94 0.92 0.92 5.00 -9.82 0.00 -6.74 -2.44 -5.95 1984-1985 0.88 0.91 0.88 0.92 0.87 0.92 17.84 9.51 12.03 8.25 10.06 8.08 1985-1986 0.88 0.90 0.87 0.93 0.86 0.92 11.01 -1.19 4.94 -0.46 3.35 0.09 1986-1987 0.84 0.91 0.90 0.92 0.91 0.91 21.22 3.10 15.26 7.49 12.63 8.13 1987-1988 0.80 0.87 0.89 0.89 0.90 0.89 28.45 12.25 21.20 13.36 17.94 14.36 1988-1989 0.74 0.80 0.85 0.83 0.86 0.81 31.86 13.66 24.93 17.14 21.15 17.01 1989-1990 0.88 0.90 0.88 0.92 0.85 0.90 15.85 6.22 12.60 6.53 9.84 7.74 1990-1991 0.85 0.87 0.87 0.91 0.84 0.89 16.80 9.11 12.06 7.59 10.21 8.40 1991-1992 0.76 0.84 0.89 0.91 0.92 0.92 18.25 6.75 13.76 5.90 10.82 5.65 1992-1993 0.84 0.82 0.89 0.82 0.90 0.81 17.55 -5.14 9.98 1.39 6.19 0.96 1993-1994 0.83 0.85 0.95 0.94 0.95 0.94 6.44 -4.71 -0.74 -3.94 -3.49 -4.71 1994-1995 0.88 0.87 0.93 0.93 0.95 0.92 10.02 -3.18 4.31 -2.12 0.69 -2.31 1995-1996 0.88 0.91 0.81 0.86 0.78 0.88 -3.50 -13.42 -8.42 -13.86 -11.06 -12.76 1996-1997 0.91 0.91 0.87 0.92 0.86 0.93 -4.12 -16.53 -9.13 -14.56 -10.96 -14.11 Maximum 0.92 0.95 0.96 0.95 0.96 0.97 31.86 13.66 24.93 17.14 21.15 17.01 Minimum 0.74 0.76 0.81 0.82 0.78 0.81 -11.74 -16.53 -12.43 -14.56 -13.81 -14.11 Average 0.85 0.88 0.89 0.91 0.89 0.91 13.55 7.15 9.45 6.65 8.23 6.59 269 Model statistics before and after calibration for Test #9 (Mt. Fidelity) Coefficient of Efficiency (E!) Volume Error (%) Water Year 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after 1969-1970 0.90 0.90 0.92 0.92 0.91 0.92 -7.17 -11.56 -8.53 -7.48 -10.45 -7.63 1970-1971 0.88 0.94 0.92 0.94 0.93 0.94 1.85 -2.48 0.30 -2.02 -2.34 -2.10 I 1971-1972 0.91 0.94 0.91 0.94 0.91 0.95 7.38 -0.67 4.85 -0.77 1.97 0.83 | '• 1972-1973 0.86 0.91 0.92 0.95 0.92 0.94 16.68 12.18 13.76 4.41 10.58 5.41 '• ! 1973-1974 0.94 0.94 0.92 0.95 0.92 0.97 -0.92 -6.39 -4.26 -8.58 -6.28 -7.58! | 1974-1975 0.82 0.90 0.92 0.94 0.91 0.94 23.16 14.20 18.38 9.63 16.45 11.54\ I 1975-1976 0.88 0.93 0.91 0.92 0.91 0.94 8.22 -3.83 3.53 -4.20 1.39 -1.37 \ 1976-1977 0.81 0.89 0.84 0.91 0.84 0.90 27.02 15.52 20.66 8.21 17.42 10.33 1977-1978 0.86 0.86 0.97 0.93 0.96 0.93 8.97 -4.57 1.77 -6.59 -1.07 -4.14 1978-1979 0.81 0.91 0.86 0.88 0.87 0.87 20.81 7.23 15.72 7.71 13.53 9.33 1979-1980 0.85 0.90 0.94 0.95 0.94 0.94 14.28 -1.17 6.79 -3.35 2.07 -2.34 1980-1981 0.79 0.85 0.86 0.87 0.85 0.87 6.34 -9.04 -0.11 -8.95 -2.53 -6.67 1981-1982 0.87 0.94 0.87 0.93 0.85 0.91 13.82 -0.30 7.99 -0.80 6.23 2.88 1982-1983 0.86 0.78 0.92 0.89 0.92 0.89 12.59 -5.54 5.70 -6.02 2.89 -3.59 1983-1984 0.83 0.89 0.91 0.94 0.91 0.91 5.87 -9.20 0.54 -9.08 -1.73 -6.25 1984-1985 0.86 0.89 0.88 0.91 0.86 0.93 16.97 9.87 11.84 5.36 9.70 7.11 1985-1986 0.88 0.90 0.88 0.93 0.86 0.91 11.69 0.01 5.43 -2.57 3.95 -0.15 1986-1987 0.81 0.92 0.89 0.93 0.89 0.92 22.01 3.59 16.06 5.27 13.36 7.34 1987-1988 0.77 0.90 0.86 0.91 0.87 0.89 28.87 13.27 21.69 11.00 18.19 13.91 1988-1989 0.70 0.84 0.81 0.84 0.83 0.83 30.82 13.83 24.06 13.83 20.49 16.11 1989-1990 0.86 0.90 0.85 0.92 0.82 0.92 16.25 6.87 13.65 5.92 10.98 7.76 1990-1991 0.83 0.88 0.84 0.90 0.81 0.90 17.23 9.80 12.89 6.81 11.05 8.60 1991-1992 0.76 0.87 0.92 0.92 0.94 0.92 17.85 10.16 12.57 2.72 9.36 3.83 1992-1993 0.83 0.82 0.85 0.84 0.85 0.81 16.74 -3.92 9.48 -2.59 5.54 -0.92 1993-1994 0.84 0.89 0.96 0.94 0.96 0.93 6.82 -5.19 -0.69 -5.42 -3.18 -5.49 1994-1995 0.89 0.90 0.95 0.93 0.95 0.92 10.43 -2.39 4.83 -5.71 0.97 -3.26 1995-1996 0.89 0.89 0.82 0.88 0.78 0.88 -5.12 -14.06 -8.61 -15.08 -10.95 -12.92 1996-1997 0.93 0.90 0.90 0.92 0.89 0.92 -2.29 -16.27 -8.39 -16.54 -10.16 -14.56 Maximum 0.94 0.94 0.97 0.95 0.96 0.97 30.82 15.52 24.06 13.83 20.49 16.11 Minimum 0.70 0.78 0.81 0.84 0.78 0.81 -7.17 -16.27 -8.61 -16.54 -10.95 -14.56 Average 0.85 0.89 0.89 0.92 0.89 0.91 13.51 7.61 9.40 6.73 8.03 6.57 270 Model statistics before and after calibration for Test #10 (Mt. Fidelity) Coefficient of Efficiency (E!) Volume Error (%) Water Year 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after 1969-1970 0.90 0.92 0.93 0.93 0.92 0.94 -4.00 -5.20 -7.01 \J0.50 -9.43 -9.97 1970-1971 0.89 0.92 0.92 0.95 0.93 0.94 6.16 1.73 3.47 -3.89 -0.07 -2.04 I 1971-1972 0.92 0.95 0.91 0.94 0.90 0.94 9.11 2.75 5.53 -2.72 2.39 0.76 | '• 1972-1973 0.86 0.89 0.92 0.96 0.92 0.95 22.02 15.28 17.34 4.93 13.69 6.95 '• ! 1973-1974 0.93 0.94 0.91 0.94 0.92 0.95 2.17 -2.93 -2.70 -10.18 -5.03 -7.60 ! | 1974-1975 0.83 0.87 0.92 0.96 0.92 0.95 26.68 18.76 20.08 8.71 17.63 11.75\ I 1975-1976 0.89 0.92 0.91 0.92 0.91 0.94 10.87 1.87 4.29 -7.13 1.83 -1.30'. 1976-1977 0.77 0.86 0.83 0.93 0.83 0.93 33.74 22.98 25.55 8.25 21.34 12.59 1977-1978 0.87 0.88 0.97 0.94 0.97 0.94 14.92 4.24 5.15 -7.57 1.26 -4.30 1978-1979 0.81 0.89 0.87 0.90 0.87 0.91 25.39 15.55 18.20 6.59 15.09 10.04 1979-1980 0.85 0.90 0.93 0.95 0.94 0.94 20.51 9.05 10.62 -4.68 4.92 -1.19 1980-1981 0.81 0.85 0.86 0.87 0.85 0.87 11.17 -0.10 2.32 -10.43 -1.18 -6.15 1981-1982 0.87 0.92 0.89 0.94 0.88 0.93 17.52 7.80 9.51 -2.57 7.25 3.06 1982-1983 0.85 0.84 0.92 0.87 0.91 0.89 17.68 4.83 8.74 -7.54 5.18 -2.57 1983-1984 0.86 0.90 0.92 0.94 0.92 0.93 9.02 -1.14 2.81 -10.65 -0.37 -5.92 1984-1985 0.85 0.89 0.87 0.91 0.86 0.93 22.65 16.03 15.28 4.99 12.58 7.60 1985-1986 0.88 0.91 0.88 0.93 0.86 0.92 15.67 6.92 7.74 -3.77 5.57 0.90 1986-1987 0.81 0.89 0.89 0.95 0.90 0.95 26.66 13.47 18.65 3.14 15.02 7.82 1987-1988 0.75 0.85 0.86 0.93 0.87 0.92 34.70 21.99 24.96 9.24 20.84 14.51 1988-1989 0.67 0.79 0.80 0.88 0.83 0.88 37.36 24.03 28.39 12.35 23.37 16.43 1989-1990 0.85 0.89 0.86 0.93 0.83 0.93 20.63 12.72 15.69 3.91 12.34 8.32 1990-1991 0.83 0.87 0.86 0.91 0.82 0.91 21.01 14.32 14.65 5.46 12.52 9.70 1991-1992 0.76 0.82 0.90 0.93 0.93 0.92 24.81 17.02 17.51 3.61 13.23 5.82 1992-1993 0.83 0.87 0.88 0.87 0.88 0.88 23.97 9.02 13.73 -3.37 8.57 -0.85 1993-1994 0.85 0.88 0.96 0.95 0.96 0.94 12.16 3.09 2.52 -6.47 -0.89 -5.01 1994-1995 0.88 0.91 0.94 0.94 0.96 0.93 16.74 6.11 7.89 -6.92 3.02 -3.67 1995-1996 0.89 0.91 0.82 0.85 0.79 0.86 -0.71 -8.34 -6.78 -17.94 -9.63 -12.75 1996-1997 0.93 0.93 0.89 0.90 0.88 0.91 -0.29 -9.24 -6.85 -18.50 -9.33 -14.69 Maximum 0.93 0.95 0.97 0.96 0.97 0.95 37.36 24.03 28.39 12.35 23.37 16.43 Minimum 0.67 0.79 0.80 0.85 0.79 0.86 -4.00 -9.24 -7.01 -18.50 -9.63 -14.69 Average 0.85 0.89 0.89 0.92 0.89 0.92 17.44 9.88 11.57 7.53 9.06 6.94 271 Input Data from Revelstoke 272 4.4.2 Model Calibration Results (for 1, 2 and 8 elevation bands; before and after calibration) Model statistics before and after calibration for Test #3 (Revelstoke) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after 1970-1971 -8.45 0.59 -5.13 0.58 -4.43 0.58 100.8 -0.05 97.52 -1.18 94.55 -3.05 j 1971-1972 -3.96 0.73 -2.50 0.82 -1.87 0.85 93.31 2.37 88.34 -2.26 84.83 -6.63 j ; 1972-1973 -3.73 0.70 -2.06 0.73 -1.80 0.70 56.21 -7.28 57.76 -12.37 55.66 -15.23; 1 1973-1974 -4.05 0.80 -1.58 0.82 -1.36 0.80 70.39 -4.22 68.16 -8.28 66.27 -12.811 j 1974-1975 -4.25 0.78 -2.54 0.81 -2.27 0.78 81.45 1.84 79.03 -2.08 75.79 -6.80' • 1975-1976 -3.52 0.69 -1.19 0.75 -0.95 0.73 66.12 -8.99 60.78 -11.39 57.85 -17.91> 1976-1977 -4.31 0.56 -2.40 0.64 -1.91 0.67 70.90 4.92 67.68 -0.56 63.99 -8.20 1977-1978 -7.01 0.67 -4.28 0.66 -3.66 0.69 107.5 13.79 101.6 13.04 98.83 5.40 1978-1979 -4.96 0.69 -2.93 0.76 -2.42 0.78 62.44 5.33 64.88 -0.78 62.33 -6.44 1979-1980 -6.78 0.52 -4.58 0.59 -3.98 0.68 108.3 20.50 104.9 17.27 100.5 8.35 1980-1981 -8.47 0.53 -4.53 0.55 -3.85 0.59 94.26 12.18 90.65 6.76 87.51 -0.58 1981-1982 -6.82 0.72 -3.98 0.81 -3.91 0.84 116.5 17.40 112.9 13.92 110.2 8.70 1982-1983 -5.84 0.54 -3.44 0.64 -3.34 0.69 100.6 21.15 97.35 15.39 93.78 7.23 1983-1984 -6.21 0.74 -2.87 0.77 -2.48 0.78 85.61 4.24 83.60 -0.25 79.32 -5.60 1984-1985 -5.91 0.59 -3.18 0.68 -2.84 0.73 88.29 8.65 83.19 3.94 80.88 -2.35 1985-1986 -4.48 0.64 -1.94 0.73 -2.09 0.78 79.67 6.63 78.59 3.30 77.66 -3.18 1986-1987 -3.87 0.57 -2.46 0.63 -1.94 0.69 81.21 9.86 81.73 8.07 78.02 0.06 1987-1988 -6.09 0.66 -3.38 0.71 -3.03 0.77 103.7 17.45 101.8 13.86 97.35 6.70 1988-1989 -6.71 0.48 -4.98 0.51 -4.47 0.60 106.1 21.04 103.1 19.40 100.1 11.17 1989-1990 -5.94 0.74 -2.90 0.81 -2.30 0.80 79.57 6.09 77.81 -0.91 74.34 -6.61 1990-1991 -5.97 0.68 -3.08 0.68 -2.62 0.66 78.88 -2.25 77.87 -4.81 74.30 -8.81 1991-1992 -4.84 0.62 -2.24 0.71 -2.10 0.75 74.48 4.72 71.27 -1.10 69.44 -6.35 1992-1993 -9.29 0.41 -6.37 0.44 -6.33 0.55 117.1 33.04 115.5 28.93 112.8 20.35 1993-1994 -7.03 0.70 -4.00 0.70 -3.56 0.66 84.92 6.12 83.32 3.56 80.55 -1.15 1994-1995 -6.13 0.81 -3.78 0.75 -3.51 0.72 75.17 -3.36 72.29 -6.31 69.57 -10.02 1995-1996 -9.11 0.68 -4.94 0.73 -4.26 0.73 102.9 10.40 99.93 4.85 95.92 0.23 1996-1997 -3.49 0.71 -1.98 0.80 -1.72 0.82 79.48 -1.38 75.71 -5.61 72.13 -10.88 Maximum -3.49 0.81 -1.19 0.82 -0.95 0.85 117.1 33.04 115.5 28.93 112.8 20.35 Minimum -9.29 0.41 -6.37 0.44 -6.33 0.55 56.21 -8.99 57.76 -12.37 55.66 -17.91 Average -5.82 0.65 -3.31 0.70 -2.93 0.72 87.62 9.66 85.08 8.25 82.02 8.22 273 Model statistics before and after calibration for Test #4 Revelstoke) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after i 1970-1971 -3.21 0.52 -2.65 0.49 -2.43 0.59 88.07 -8.48 85.54 -0.02 83.95 -7.78 j I 1971-1972 -1.07 0.81 -1.07 0.81 -0.84 0.84 80.78 -12.59 73.52 -4.77 72.54 -12.60\ ! 1972-1973 -0.98 0.71 -0.68 0.72 -0.57 0.71 46.37 -22.56 52.29 -15.41 50.03 -20.47\ j 1973-1974 -0.69 0.76 -0.41 0.80 -0.28 0.80 59.88 -18.52 57.61 -11.21 56.82 -18.07\ I 1974-1975 -1.17 0.82 -1.12 0.80 -0.96 0.81 70.04 -13.18 68.22 -4.37 66.78 -11.04] 1975-1976 -0.89 0.63 -0.40 0.76 -0.27 0.76 56.58 -24.28 51.31 -10.99 48.64 -17.19 1976-1977 -1.77 0.66 -1.28 0.62 -1.04 0.66 61.94 -16.76 59.86 -2.41 56.93 -8.30 1977-1978 -3.01 0.67 -2.50 0.55 -2.24 0.64 95.90 -4.51 90.36 13.55 88.46 6.71 1978-1979 -1.64 0.75 -1.40 0.73 -1.26 0.76 52.75 -16.23 54.91 -5.53 53.52 -10.62 1979-1980 -3.44 0.71 -2.72 0.61 -2.55 0.72 98.81 -0.98 94.18 15.72 90.75 8.34 1980-1981 -3.63 0.54 -2.51 0.54 -2.29 0.60 83.95 -7.68 79.68 4.67 77.75 -2.84 1981-1982 -2.92 0.82 -2.65 0.79 -2.54 0.84 103.8 -0.23 99.41 12.96 98.29 6.28 1982-1983 -2.80 0.68 -2.28 0.69 -2.21 0.73 90.41 -2.13 87.49 12.36 85.21 6.36 1983-1984 -2.33 0.72 -1.63 0.71 -1.36 0.74 75.16 -12.73 72.90 -0.24 70.16 -7.33 1984-1985 -2.38 0.70 -1.66 0.60 -1.43 0.65 78.40 -9.91 73.27 1.82 72.06 -4.86 1985-1986 -1.77 0.79 -1.14 0.78 -1.23 0.79 69.67 -12.75 68.54 -0.85 68.55 -7.27 1986-1987 -1.76 0.71 -1.57 0.65 -1.36 0.68 72.52 -9.63 72.49 7.44 69.78 1.17 1987-1988 -3.17 0.79 -2.25 0.69 -2.27 0.74 93.71 -2.97 90.99 12.97 87.89 6.35 1988-1989 -3.62 0.64 -3.29 0.47 -3.20 0.58 95.51 1.11 91.98 18.81 90.03 11.53 1989-1990 -2.56 0.69 -1.53 0.75 -1.44 0.79 70.92 -12.52 67.85 -3.21 65.87 -9.88 1990-1991 -2.09 0.61 -1.55 0.62 -1.35 0.64 69.11 -14.67 67.23 -5.50 65.59 -12.39 1991-1992 -1.82 0.73 -1.31 0.75 -1.22 0.74 65.28 -14.02 61.62 -4.31 60.69 -9.08 1992-1993 -5.27 0.66 -4.79 0.41 -4.80 0.51 105.9 9.39 104.1 26.49 102.1 19.63 1993-1994 -2.85 0.63 -2.10 0.64 -1.99 0.68 74.46 -9.25 72.75 2.00 71.15 -4.63 1994-1995 -1.73 0.76 -1.35 0.63 -1.19 0.64 65.11 -14.08 62.56 -7.47 60.88 -14.29 1995-1996 -3.38 0.65 -2.66 0.63 -2.47 0.71 90.97 -5.10 86.23 2.97 84.29 -5.50 1996-1997 -1.31 0.79 -0.98 0.81 -0.91 0.81 69.85 -16.60 66.87 -5.70 63.93 -11.78 Maximum -0.69 0.82 -0.40 0.81 -0.27 0.84 105.9 9.39 104.1 26.49 102.1 19.63 Minimum -5.27 0.52 -4.79 0.41 -4.80 0.51 46.37 -24.28 51.31 -15.41 48.64 -20.47 Average -2.34 0.70 -1.83 0.67 -1.69 0.71 77.26 12.08 74.58 8.49 72.69 10.79 274 Model statistics before and after calibration for Test #5 (Revelstoke) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after i 1970-1971 -2.21 0.58 -1.33 0.73 -1.05 0.77 67.16 -1.24 64.24 -0.20 62.47 4.23 i I 1971-1972 -0.56 0.84 -0.31 0.88 -0.05 0.91 72.77 6.81 67.13 6.08 62.85 7.15 : ! 1972-1973 -0.21 0.54 0.18 0.66 0.29 0.78 45.43 -7.47 45.23 -2.82 41.28 -1.76! j 1973-1974 -0.42 0.55 0.19 0.87 0.28 0.93 50.09 -8.02 47.81 -4.72 44.60 -4.62 j I 1974-1975 -0.49 0.62 -0.07 0.75 0.08 0.84 62.47 0.97 57.46 1.70 53.25 1.94 : 1975-1976 -0.34 0.61 0.40 0.80 0.49 0.84 43.16 -14.31 36.04 -17.24 32.87 -21.06 1976-1977 -0.51 0.49 0.05 0.67 0.27 0.81 53.67 -2.94 47.64 -4.58 42.42 -10.15 1977-1978 -1.49 0.56 -0.81 0.74 -0.53 0.86 75.88 6.14 69.33 7.05 64.94 1.02 1978-1979 -0.59 0.60 -0.23 0.77 -0.01 0.87 53.34 -0.47 51.32 0.70 47.99 -3.19 1979-1980 -1.42 0.75 -0.92 0.82 -0.66 0.85 82.25 9.45 76.91 12.95 70.63 6.43 1980-1981 -2.17 0.63 -1.03 0.76 -0.78 0.84 73.48 4.93 67.71 5.99 62.38 1.39 1981-1982 -1.60 0.67 -0.93 0.85 -0.89 0.87 90.79 14.79 86.33 17.87 82.10 15.30 1982-1983 -1.20 0.65 -0.62 0.77 -0.57 0.74 83.90 14.60 76.96 13.89 72.44 7.76 1983-1984 -1.29 0.53 -0.44 0.77 -0.22 0.86 65.42 2.85 60.85 2.91 55.38 -0.92 1984-1985 -1.07 0.70 -0.31 0.78 -0.14 0.88 69.33 7.55 62.13 6.40 58.09 3.35 1985-1986 -0.53 0.84 -0.06 0.85 -0.07 0.89 62.47 1.03 59.92 3.77 56.77 1.62 1986-1987 -0.46 0.66 -0.14 0.76 0.08 0.86 63.06 0.68 59.54 3.75 54.25 -3.19 1987-1988 -1.27 0.68 -0.60 0.80 -0.43 0.89 78.11 10.26 75.52 11.51 68.84 5.58 1988-1989 -1.36 0.50 -1.09 0.77 -0.84 0.85 81.69 10.70 77.58 13.03 71.91 7.53 1989-1990 -1.26 0.53 -0.38 0.83 -0.16 0.92 61.60 2.87 58.16 0.91 53.61 -2.02 1990-1991 -1.30 0.50 -0.49 0.75 -0.30 0.83 59.54 -0.84 56.13 0.38 51.47 0.21 1991-1992 -0.69 0.60 -0.09 0.71 0.02 0.84 58.01 1.83 51.86 1.59 47.86 -0.96 1992-1993 -2.08 0.81 -1.84 0.74 -1.75 0.75 92.38 19.13 88.39 22.08 82.29 15.52 1993-1994 -1.48 0.59 -0.73 0.73 -0.53 0.80 62.47 1.26 59.49 3.19 54.67 1.84 1994-1995 -0.94 0.50 -0.40 0.73 -0.28 0.79 54.65 -0.43 51.23 1.71 47.28 1.73 1995-1996 -2.47 0.43 -1.46 0.71 -1.20 0.74 79.29 11.63 74.91 12.66 70.27 12.60 1996-1997 -0.25 0.71 0.04 0.86 0.16 0.89 61.04 -0.35 54.62 -0.71 50.40 -3.88 Maximum -0.21 0.84 0.40 0.88 0.49 0.93 92.38 19.13 88.39 22.08 82.29 15.52 Minimum -2.47 0.43 -1.84 0.66 -1.75 0.74 43.16 -14.31 36.04 -17.24 32.87 -21.06 Average -1.10 0.62 -0.50 0.77 -0.33 0.84 66.79 6.35 62.39 6.92 57.90 5.66 275 Model statistics before and after calibration for Test #6 (Revelstoke) Coefficient of Efficiency (E!) Volume Error (° Water Year 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after i 1970-1971 -0.19 0.74 -0.21 0.73 -0.15 0.79 44.99 3.91 44.24 2.24 43.27 -1.13 i I 1971-1972 0.30 0.85 0.20 0.85 0.26 0.87 51.71 9.43 44.91 7.09 43.44 1.42 : ! 1972-1973 0.63 0.76 0.68 0.78 0.71 0.84 33.07 3.37 34.21 2.09 33.32 1.03 \ j 1973-1974 0.69 0.92 0.68 0.92 0.71 0.93 31.41 -5.69 29.77 -6.51 27.46 -11.51\ I 1974-1975 0.55 0.89 0.51 0.87 0.57 0.88 45.21 6.57 41.71 4.51 40.29 0.04 : 1975-1976 0.61 0.78 0.68 0.85 0.73 0.86 30.09 -20.07 24.09 -15.36 21.34 -20.84 1976-1977 0.30 0.72 0.46 0.78 0.57 0.86 41.72 -9.66 36.91 -2.72 33.92 -5.08 1977-1978 -0.04 0.82 0.04 0.81 0.13 0.87 59.69 -0.22 53.14 4.58 49.88 0.20 1978-1979 0.50 0.85 0.48 0.87 0.51 0.88 37.51 -7.10 35.84 -0.52 34.16 -4.63 1979-1980 -0.29 0.83 -0.20 0.82 -0.16 0.86 69.15 5.96 62.79 13.83 58.39 6.29 1980-1981 -0.33 0.80 -0.18 0.80 -0.12 0.85 57.71 2.12 52.53 7.90 48.57 1.24 1981-1982 -0.26 0.86 -0.28 0.85 -0.26 0.85 72.22 16.58 67.13 19.95 65.79 13.14 1982-1983 -0.10 0.69 -0.03 0.79 -0.01 0.80 71.41 12.90 65.16 16.59 63.08 10.08 1983-1984 0.19 0.77 0.28 0.83 0.36 0.87 48.65 0.19 46.14 4.14 42.05 -1.21 1984-1985 0.11 0.85 0.29 0.83 0.38 0.88 51.90 3.36 46.56 6.39 43.99 2.51 1985-1986 0.31 0.87 0.36 0.90 0.32 0.89 46.86 1.71 44.44 3.43 43.16 -0.65 1986-1987 0.29 0.82 0.22 0.84 0.29 0.88 50.08 -3.11 47.09 3.87 43.83 -0.86 1987-1988 -0.18 0.84 -0.05 0.83 -0.05 0.89 63.43 5.69 60.12 12.35 55.31 6.05 1988-1989 -0.24 0.80 -0.22 0.81 -0.20 0.84 67.10 8.64 61.67 13.78 58.75 9.96 1989-1990 0.08 0.84 0.24 0.87 0.25 0.93 47.15 -1.40 44.04 3.14 40.88 -3.15 1990-1991 0.16 0.80 0.23 0.80 0.29 0.86 43.08 5.17 39.98 0.91 38.20 -2.80 1991-1992 0.36 0.81 0.38 0.81 0.41 0.85 43.91 1.84 37.30 2.72 36.24 0.16 1992-1993 -0.69 0.72 -0.90 0.70 -0.94 0.67 75.58 17.20 71.22 22.04 68.72 16.17 1993-1994 0.09 0.73 0.14 0.77 0.18 0.82 45.62 4.97 44.23 4.37 40.93 0.30 1994-1995 0.52 0.84 0.55 0.81 0.60 0.80 36.31 6.72 33.23 0.49 30.34 -3.46 1995-1996 -0.25 0.67 -0.27 0.74 -0.24 0.80 58.08 14.62 53.90 11.88 50.97 5.14 1996-1997 0.34 0.89 0.34 0.88 0.37 0.88 48.32 0.51 43.06 1.92 40.59 -3.22 Maximum 0.69 0.92 0.68 0.92 0.73 0.93 75.58 17.20 71.22 22.04 68.72 16.17 Minimum -0.69 0.67 -0.90 0.70 -0.94 0.67 30.09 -20.07 24.09 -15.36 21.34 -20.84 Average 0.13 0.81 0.16 0.82 0.20 0.85 50.81 6.71 46.87 7.35 44.33 5.34 276 Model statistics before and after calibration for Test #7 (Revelstoke) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after i 1970-1971 -2.02 0.49 -1.08 0.70 -0.80 0.82 56.71 3.74 55.43 1.13 53.98 0.68 i I 1971-1972 -0.46 0.82 -0.17 0.91 0.09 0.91 68.44 9.26 63.35 5.66 59.29 9.42 : ! 1972-1973 -0.31 0.57 0.14 0.66 0.26 0.75 50.83 -7.69 49.97 -4.50 46.23 9.35 \ j 1973-1974 -0.42 0.53 0.24 0.84 0.35 0.93 48.21 -5.33 46.10 -5.34 42.87 -1.52 j I 1974-1975 -0.51 0.63 -0.05 0.72 0.10 0.84 63.42 2.90 58.62 0.11 54.41 9.52 : 1975-1976 -0.34 0.61 0.45 0.76 0.54 0.83 41.83 -11.00 35.42 -19.12 31.96 -16.57 1976-1977 -0.56 0.51 0.05 0.66 0.27 0.80 57.01 -0.95 50.20 -8.65 45.40 -1.21 1977-1978 -1.44 0.51 -0.70 0.71 -0.42 0.87 74.53 10.55 67.89 3.55 63.63 5.10 1978-1979 -0.66 0.61 -0.22 0.77 0.01 0.86 53.49 1.53 51.42 -2.52 48.09 2.72 1979-1980 -1.33 0.72 -0.77 0.83 -0.52 0.84 80.43 13.62 75.30 9.17 69.06 11.23 1980-1981 -2.12 0.55 -0.88 0.76 -0.61 0.86 72.54 8.35 66.91 3.70 61.54 6.33 1981-1982 -1.49 0.64 -0.79 0.84 -0.74 0.88 90.15 18.44 85.48 16.05 81.10 20.58 1982-1983 -1.17 0.65 -0.56 0.76 -0.51 0.71 84.19 17.67 77.39 9.90 72.96 15.70 1983-1984 -1.31 0.50 -0.38 0.76 -0.16 0.85 67.13 5.73 62.68 0.33 57.19 5.55 1984-1985 -1.08 0.69 -0.26 0.80 -0.09 0.87 70.55 10.08 62.86 4.02 58.94 9.80 1985-1986 -0.51 0.85 0.01 0.87 -0.01 0.87 61.88 3.46 58.91 2.17 55.86 7.02 1986-1987 -0.42 0.68 -0.06 0.77 0.16 0.85 62.49 3.69 59.80 -0.69 54.55 3.14 1987-1988 -1.20 0.67 -0.46 0.80 -0.29 0.89 77.79 13.77 74.87 8.38 68.25 11.23 1988-1989 -1.33 0.49 -1.02 0.74 -0.76 0.84 82.48 14.14 78.48 9.00 72.71 14.53 1989-1990 -1.25 0.48 -0.27 0.82 -0.03 0.91 60.38 5.86 57.47 -0.61 52.71 2.73 1990-1991 -1.26 0.46 -0.39 0.72 -0.20 0.84 58.84 1.37 55.34 -1.33 50.76 4.58 1991-1992 -0.71 0.62 -0.04 0.73 0.06 0.83 60.81 3.48 54.65 -1.08 50.65 7.46 1992-1993 -2.05 0.77 -1.73 0.81 -1.63 0.72 93.05 22.55 88.56 17.60 82.67 23.27 1993-1994 -1.49 0.55 -0.64 0.71 -0.44 0.81 61.86 3.66 58.83 1.07 54.01 6.60 1994-1995 -1.01 0.48 -0.42 0.67 -0.29 0.78 56.32 1.16 52.60 0.29 48.43 7.58 1995-1996 -2.33 0.33 -1.23 0.69 -0.95 0.80 76.27 14.59 72.10 11.56 67.37 15.06 1996-1997 -0.22 0.73 0.11 0.87 0.23 0.89 60.58 2.27 54.26 -2.22 50.07 1.60 Maximum -0.22 0.85 0.45 0.91 0.54 0.93 93.05 22.55 88.56 17.60 82.67 23.27 Minimum -2.33 0.33 -1.73 0.66 -1.63 0.71 41.83 -11.00 35.42 -19.12 31.96 -16.57 Average -1.07 0.60 -0.41 0.77 -0.24 0.84 66.38 8.13 62.03 5.85 57.58 8.52 277 Model statistics before and after calibration for Test #8 (Revelstoke) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after j 1970-1971 0.00 0.77 0.00 0.72 0.07 0.77 36.50 0.32 37.00 -0.36 36.20 0.41 j I 1971-1972 0.45 0.85 0.34 0.86 0.40 0.86 47.97 9.39 41.75 4.96 40.38 4.86 : j 1972-1973 0.63 0.79 0.70 0.81 0.73 0.83 37.01 7.97 37.89 1.26 37.00 4.92 ! j 1973-1974 0.74 0.92 0.74 0.93 0.77 0.94 30.09 -3.93 28.50 -5.52 26.33 -6.96 j I 1974-1975 0.60 0.90 0.55 0.89 0.62 0.88 45.95 9.39 42.47 4.26 40.93 4.67 : 1975-1976 0.66 0.79 0.74 0.84 0.79 0.87 28.69 -17.20 23.29 -15.07 20.45 -/7.7P 1976-1977 0.33 0.73 0.50 0.78 0.60 0.85 44.36 -5.86 39.07 -4.35 36.31 -2.58 1977-1978 0.08 0.84 0.16 0.83 0.25 0.86 58.57 2.37 52.09 4.88 48.99 3.32 1978-1979 0.52 0.87 0.52 0.88 0.55 0.87 37.92 -3.61 36.06 -1.94 34.35 -2.20 1979-1980 -0.13 0.85 -0.03 0.82 0.01 0.85 66.80 8.77 60.84 12.90 56.39 9.73 1980-1981 -0.19 0.82 0.00 0.80 0.06 0.85 57.13 5.41 51.90 7.49 47.98 4.61 1981-1982 -0.07 0.87 -0.12 0.86 -0.10 0.83 72.00 20.54 66.80 20.29 65.15 17.76 1982-1983 0.01 0.74 0.07 0.82 0.08 0.76 70.94 17.28 64.88 16.16 62.89 14.04 1983-1984 0.24 0.80 0.35 0.85 0.43 0.86 50.90 4.83 48.07 5.18 44.16 3.02 1984-1985 0.16 0.86 0.35 0.85 0.44 0.86 53.12 7.13 47.41 5.80 44.87 6.28 1985-1986 0.39 0.89 0.44 0.91 0.40 0.87 46.05 5.07 43.53 3.63 42.27 2.89 1986-1987 0.38 0.84 0.31 0.85 0.38 0.87 49.50 0.25 47.06 2.71 43.87 1.87 1987-1988 -0.05 0.85 0.09 0.84 0.09 0.89 63.09 9.78 59.67 12.29 54.96 9.49 1988-1989 -0.14 0.81 -0.12 0.83 -0.10 0.83 67.77 12.54 62.58 13.08 59.51 13.24 1989-1990 0.15 0.85 0.36 0.88 0.38 0.93 46.26 1.76 43.25 3.76 40.08 0.38 1990-1991 0.28 0.82 0.35 0.82 0.40 0.86 42.64 7.19 39.47 1.31 37.52 1.04 1991-1992 0.40 0.83 0.44 0.84 0.47 0.85 46.22 6.30 39.83 2.26 38.78 3.84 1992-1993 -0.58 0.73 -0.78 0.72 -0.82 0.62 75.87 22.01 71.26 22.42 68.82 20.56 1993-1994 0.14 0.76 0.23 0.78 0.27 0.81 45.32 6.83 43.61 3.83 40.53 3.39 1994-1995 0.54 0.87 0.56 0.85 0.62 0.82 38.12 7.98 34.89 0.40 31.91 0.83 1995-1996 -0.05 0.70 -0.06 0.77 -0.02 0.78 55.66 17.18 51.41 11.93 48.38 9.94 1996-1997 0.45 0.90 0.45 0.90 0.47 0.88 47.16 3.67 42.12 1.00 39.60 -0.01 Maximum 0.74 0.92 0.74 0.93 0.79 0.94 75.87 22.01 71.26 22.42 68.82 20.56 Minimum -0.58 0.70 -0.78 0.72 -0.82 0.62 28.69 -17.20 23.29 -15.07 20.45 -17.79 Average 0.22 0.82 0.26 0.83 0.31 0.84 50.43 8.32 46.54 7.17 44.02 6.50 278 Model statistics before and after calibration for Test #9 (Revelstoke) Coefficient of Efficiency (E!) Volume Error (° /0) Water Year 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after i 1970-1971 -0.58 0.70 -0.44 0.74 -0.33 0.76 45.57 2.73 45.46 -0.20 43.98 3.74 i I 1971-1972 0.24 0.87 0.06 0.90 0.19 0.85 51.14 8.76 44.82 0.69 43.69 4.99 '. ! 1972-1973 0.63 0.82 0.67 0.82 0.70 0.86 32.14 5.15 32.59 -6.49 31.04 0.16 ! j 1973-1974 0.61 0.91 0.61 0.90 0.66 0.94 31.56 -4.09 30.49 -11.78 28.65 -7.83 j I 1974-1975 0.44 0.90 0.34 0.88 0.43 0.90 45.84 8.69 42.32 -3.14 40.49 2 . i o : 1975-1976 0.52 0.82 0.62 0.84 0.68 0.88 31.30 -13.60 25.87 -18.99 22.80 -18.57 1976-1977 0.30 0.77 0.42 0.82 0.53 0.88 41.67 -1.52 36.40 -5.86 32.84 -4.08 1977-1978 -0.22 0.82 -0.14 0.81 -0.02 0.87 62.27 6.66 55.01 2.48 52.13 3.40 1978-1979 0.40 0.88 0.33 0.87 0.37 0.89 36.13 -1.50 34.80 -5.28 33.40 -2.89 1979-1980 -0.52 0.83 -0.36 0.85 -0.30 0.84 68.70 11.64 62.34 8.46 57.59 8.69 1980-1981 -0.67 0.76 -0.33 0.82 -0.25 0.84 57.86 8.07 52.67 2.35 49.13 4.14 1981-1982 -0.53 0.84 -0.63 0.84 -0.56 0.79 75.71 21.84 70.32 14.53 68.76 17.63 1982-1983 -0.35 0.77 -0.27 0.82 -0.23 0.78 70.43 19.69 63.47 10.14 61.15 12.28 1983-1984 -0.07 0.79 0.04 0.83 0.17 0.88 50.45 7.41 48.34 -1.05 43.94 1.45 1984-1985 -0.22 0.84 0.08 0.83 0.21 0.88 53.18 10.24 47.62 2.42 44.79 4.94 1985-1986 0.08 0.87 0.16 0.89 0.10 0.87 46.52 7.16 43.70 -1.29 43.11 2.52 1986-1987 0.17 0.86 0.06 0.85 0.15 0.89 49.35 3.35 47.31 -0.43 43.66 0.37 1987-1988 -0.50 0.84 -0.27 0.84 -0.29 0.89 63.81 13.26 60.61 8.13 56.03 8.95 1988-1989 -0.44 0.81 -0.53 0.83 -0.49 0.82 67.33 16.69 62.32 10.01 58.91 11.76 1989-1990 -0.20 0.82 0.04 0.88 0.08 0.93 47.09 4.78 44.35 -1.66 41.40 -0.13 1990-1991 -0.02 0.80 0.10 0.80 0.18 0.86 44.14 6.97 40.42 -4.30 38.47 0.06 1991-1992 0.25 0.85 0.26 0.84 0.30 0.88 44.51 6.95 38.10 -2.65 36.66 1.54 1992-1993 -1.24 0.67 -1.48 0.67 -1.50 0.62 75.83 24.72 71.66 17.63 69.24 19.01 1993-1994 -0.15 0.75 -0.06 0.81 0.01 0.84 45.35 7.69 43.75 -0.61 40.53 2.96 1994-1995 0.39 0.86 0.40 0.78 0.48 0.82 38.14 6.55 34.44 -5.68 31.49 -1.72 1995-1996 -0.46 0.69 -0.44 0.78 -0.38 0.75 58.29 17.22 54.25 5.47 51.68 9.80 1996-1997 0.22 0.90 0.26 0.90 0.28 0.89 50.45 5.08 43.96 -3.77 41.13 -1.31 Maximum 0.63 0.91 0.67 0.90 0.70 0.94 75.83 24.72 71.66 17.63 69.24 19.01 Minimum -1.24 0.67 -1.48 0.67 -1.50 0.62 31.30 -13.60 25.87 -18.99 22.80 -18.57 Average -0.07 0.82 -0.02 0.83 0.04 0.85 51.29 9.33 47.31 6.28 44.69 6.06 279 Model statistics before and after calibration for Test #10 (Revelstoke) Water Year Coefficient of Efficiency (E!) Volume Error (%) 1 band 2 bands 8 bands 1 band 2 bands 8 bands before after before after before after before after before after before after i 1970-1971 -0.25 0.70 -0.23 0.77 -0.14 0.78 45.28 4.30 44.25 0.72 42.76 7.77 i I 1971-1972 0!33 0.86 0.22 0.90 0.30 0.88 53.00 10.46 45.67 1.78 44.10 1.95: ! 1972-1973 0.59 0.82 0.63 0.83 0.67 0.85 42.80 6.85 42.25 -2.75 39.73 -2.72! j 1973-1974 0.66 0.91 0.67 0.91 0.71 0.94 34.90 -3.44 32.47 -10.42 30.11 -10.03\ I 1974-1975 0.48 0.91 0.44 0.88 0.52 0.88 51.61 9.89 46.78 -0.55 44.13 -0.44 : 1975-1976 0.58 0.83 0.68 0.84 0.73 0.86 33.29 -12.94 26.28 -18.15 22.87 -20.83 1976-1977 0.26 0.78 0.41 0.82 0.54 0.86 51.45 -0.33 44.51 -2.69 39.52 -6.32 1977-1978 -0.16 0.83 -0.04 0.82 0.08 0.87 66.84 8.32 57.86 5.33 53.45 1.78 1978-1979 0.42 0.89 0.39 0.89 0.43 0.89 44.81 0.85 41.24 -1.95 38.45 -4.49 1979-1980 -0.44 0.82 -0.26 0.85 -0.20 0.87 75.46 13.71 66.37 11.77 60.69 7.11 1980-1981 -0.47 0.77 -0.22 0.83 -0.13 0.86 63.11 9.27 56.08 4.09 51.49 1.23 1981-1982 -0.34 0.83 -0.34 0.87 -0.31 0.84 77.95 22.71 71.17 15.09 69.07 13.82 1982-1983 -0.25 0.76 -0.14 0.84 -0.10 0.80 77.69 21.16 69.12 12.40 66.02 9.35 1983-1984 0.07 0.79 0.18 0.85 0.29 0.88 56.95 8.80 52.55 1.69 47.48 -0.70 1984-1985 -0.02 0.83 0.20 0.85 0.31 0.88 60.81 12.27 53.19 6.10 49.19 3.45 1985-1986 0.21 0.87 0.30 0.92 0.25 0.90 52.88 8.74 48.65 1.29 46.68 0.36 1986-1987 0.18 0.86 0.14 0.85 0.24 0.89 57.68 5.85 52.94 3.36 48.16 -0.86 1987-1988 -0.35 0.84 -0.14 0.84 -0.11 0.90 71.28 14.70 65.68 11.22 59.57 6.96 1988-1989 -0.45 0.80 -0.40 0.83 -0.35 0.85 76.27 19.09 68.41 13.64 64.03 10.07 1989-1990 -0.05 0.83 0.19 0.88 0.22 0.94 53.31 7.25 47.92 0.96 43.90 -1.90 1990-1991 0.09 0.80 0.18 0.81 0.27 0.86 48.57 9.21 44.11 -2.04 41.31 -2.09 1991-1992 0.23 0.85 0.28 0.84 0.32 0.87 54.92 10.32 46.35 2.26 43.69 0.75 1992-1993 -1.09 0.66 -1.20 0.71 -1.21 0.68 86.57 28.01 79.37 22.11 75.14 17.92 1993-1994 -0.07 0.75 0.03 0.81 0.09 0.83 54.63 11.16 50.72 3.87 46.14 1.75 1994-1995 0.42 0.87 0.45 0.78 0.53 0.81 46.00 9.81 40.47 -2.23 36.09 -3.29 1995-1996 -0.33 0.67 -0.29 0.80 -0.24 0.80 61.76 18.94 56.02 7.08 52.58 6.96 1996-1997 0.30 0.90 0.33 0.90 0.37 0.89 53.55 6.33 46.21 -2.24 42.63 -4.10 Maximum 0.66 0.91 0.68 0.92 0.73 0.94 86.57 28.01 79.37 22.11 75.14 17.92 Minimum -1.09 0.66 -1.20 0.71 -1.21 0.68 33.29 -12.94 26.28 -18.15 22.87 -20.83 Average 0.02 0.82 0.09 0.84 0.15 0.86 57.53 10.91 51.73 6.62 48.11 5.69 280 

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