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Performance assessment of short-term hydrological forecasts in small, coastal watersheds with complex… VanWerkhoven, Curtis 2015

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   PERFORMANCE ASSESSMENT OF SHORT-TERM HYDROLOGICAL FORECASTS IN SMALL, COASTAL WATERSHEDS WITH COMPLEX TERRAIN USING FULLY-DISTRIBUTED HYDROLOGICAL AND METEOROLOGICAL MODELS  by  CURTIS VANWERKHOVEN B.A.Sc., The University of British Columbia, 2010     A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCES in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Civil Engineering)    THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)     August 2015 © Curtis VanWerkhoven, 2015   ii ABSTRACT Accurate and reliable short-term streamflow forecast systems are beneficial for non-storage hydroelectric operators to minimize costs associated with foregoing electricity market opportunities because of held reserves due to forecast error and those making decisions based on flood risks. Accurate real-time forecasting on hourly and daily intervals with lead times less than three days remains a challenge in small, coastal, mountainous watersheds of the Pacific Northwest. This thesis examines a real-time streamflow forecasting system in which a physically-based, fully-distributed coupled MIKE SHE/MIKE 11 hydrologic model is driven by the distributed output of a 1.3 km gridded high-resolution numerical weather prediction (NWP) model. The model performance in simulating hydrological processes is evaluated in the model calibration and validation phases, and the forecast accuracy and reliability is evaluated in the forecast verification phase. Both performance evaluations are completed with graphical and statistical techniques based on a wide range of statistical metrics. In addition to the performance, the forecast skill is evaluated relative to alternative reference forecasts including persistence and historical climatological forecasts. The hydrologic model and forecasting system are applied to the Coquitlam River above Coquitlam Lake watershed located in the coastal mountains of southwestern British Columbia, Canada. The hydro-climate regime in the watershed is pluvio-nival, flashy, and with negligible glacier melt. High flows have a bi-modal distribution, characterized by high flows in May and June due to snowmelt and in fall (November) due to Pacific frontal systems that can bring significant precipitation. The MIKE SHE/MIKE 11 model performs well during the model calibration and validation phases, demonstrating accuracy and reliability in simulating the hydrological processes in the watershed with a one year calibration period. In addition, the forecast system provides a reliable forecast for hourly and daily mean streamflow with considerable forecast skill in comparison to reference forecasts for lead times of one to three days. MIKE SHE/MIKE 11 is demonstrated as a suitable fully-distributed, physically-based model for river forecasts based on high-resolution NWP models, and that there is the opportunity for short-term forecast skill in small, mountainous, Pacific Northwest watersheds with limited observed data. iii PREFACE The work completed for this thesis is completed as original work, and is not comprised of work from published, submitted, or in-preparation works. Funding for this research was provided in part by the Canadian Natural Sciences and Engineering Research Council (NSERC) through an Alexander Graham Bell Canada Graduate Scholarship. Dr. Robert Millar, PhD, contributed to research design, study development, reviewing, and editing. Dr. Ziad Shawwash, PhD, contributed reviewing and editing and into the research design and study development. Daniel Terpstra, BS, contributed to the development of MATLAB scripts used in data processing and analysis. Dr. Dominique Bourdin, PhD, contributed to research design and data collection. Gaven Tang, MASc, contributed to editing. No manuscripts resulting from the work presented in this thesis have been published to date.   iv TABLE OF CONTENTS ABSTRACT .................................................................................................................................... ii PREFACE ...................................................................................................................................... iii TABLE OF CONTENTS ............................................................................................................... iv LIST OF TABLES ....................................................................................................................... viii LIST OF FIGURES ....................................................................................................................... ix LIST OF EQUATIONS .................................................................................................................. x LIST OF SYMBOLS AND ABBREVIATIONS .......................................................................... xi ACKNOWLEDGEMENTS ......................................................................................................... xiii 1 INTRODUCTION ................................................................................................................... 1 1.1 STATEMENT OF PROBLEM ........................................................................................ 2 2 LITERATURE REVIEW ........................................................................................................ 4 2.1 CURRENT PRACTICE ................................................................................................... 4 2.1.1 HYDROLOGIC MODEL SELECTION .................................................................. 4 2.1.2 MODEL CALIBRATION AND VALIDATION TO OBSERVED DATA ............ 5 2.1.3 HYDROLOGIC FORECASTING............................................................................ 6 2.2 RIVER FORECASTING USING HYDROLOGICAL MODELS AND NUMERICAL WEATHER PREDICTIONS ...................................................................................................... 7 2.2.1 MIKE SHE AND SWAT MODEL COMPARISON ............................................... 8 2.2.2 EVALUATION OF HYDROMETEOROLOGICAL FORECAST SYSTEM FOR MOUNTAINOUS WATERSHEDS........................................................................................ 9 2.2.3 EVALUATION OF HYDROLOGICAL FORECASTING SYSTEM USING THE UNIVERSITY OF BRITISH COLUMBIA WATERSHED MODEL AND NWP FORECASTS......................................................................................................................... 10 2.2.4 EVALUATION OF PROBABILISTIC HYDROLOGICAL FORECASTS USING MULTIPLE HYDROLOGICAL AND NWP MODELS ...................................................... 11 v 2.2.5 SUPER-ENSEMBLE ARTIFICIAL INTELLIGENCE FLOOD-FORECAST MODEL FOR A PACIFIC NORTHWEST RIVER ............................................................. 13 2.2.6 INTERCOMPARISON STUDY OF PROCESS-ORIENTED WATERSHED MODELS ............................................................................................................................... 13 2.2.7 DHI MIKE SHE AND MIKE 11 FLOOD FORECASTING SYSTEM ................ 15 2.2.8 CONCLUSIONS..................................................................................................... 15 2.3 GRAPHICAL AND STATISTICAL MODEL PERFORMANCE ............................... 17 2.4 HYDROLOGICAL FORECAST SKILL ...................................................................... 18 2.5 CONCLUSIONS ............................................................................................................ 21 3 METHODS ............................................................................................................................ 22 3.1 CASE STUDY WATERSHED AND DATA ................................................................ 22 3.1.1 COQUITLAM RIVER WATERSHED ABOVE COQUITLAM LAKE .............. 22 3.1.2 AVAILABLE WATERSHED AND REGIONAL INFORMATION .................... 24 3.1.2.1 SPATIAL GEOGRAPHIC INFORMATION ................................................. 24 3.1.2.2 METEOROLOGICAL RECORDS ................................................................. 24 3.1.2.3 HYDROMETRIC RECORDS ........................................................................ 25 3.1.2.4 WATERSHED PARAMETERS ..................................................................... 26 3.1.2.5 NUMERICAL WEATHER PREDICTION MODELS ................................... 27 3.2 MODELLING METHODOLOGY ................................................................................ 28 3.2.1 MODEL SETUP ..................................................................................................... 28 3.2.1.1 APPLICATION OF DATA ............................................................................. 28 3.2.1.2 MIKE SHE/MIKE 11 MODEL PROCESSES ................................................ 29 3.2.2 MODEL CALIBRATION AND VALIDATION ................................................... 30 3.2.2.1 MODEL CALIBRATION ............................................................................... 30 3.2.2.2 MODEL VALIDATION ................................................................................. 31 3.2.3 FORECAST MODELLING ................................................................................... 32 vi 3.2.4 MODEL PERFORMANCE AND FORECAST VERIFICATION ........................ 33 3.2.4.1 HYDROLOGIC MODEL PERFORMANCE ................................................. 33 3.2.4.2 FORECAST VERIFICATION ........................................................................ 34 4 RESULTS AND DISCUSSION ............................................................................................ 36 4.1 CALIBRATION AND VALIDATION PERFORMANCE ........................................... 36 4.2 FORECAST PERFORMANCE AND SKILL ............................................................... 41 4.2.1 FORECAST PERFORMANCE.............................................................................. 41 4.2.1.1 FORECAST PERFORMANCE FOR DAILY MEAN STREAMFLOWS .... 41 4.2.1.2 FORECAST PERFORMANCE FOR HOURLY STREAMFLOWS ............. 45 4.2.2 FORECAST SYSTEM SKILL ............................................................................... 48 4.2.2.1 SKILL REFERENCED TO PERSISTENCE FORECAST ............................ 48 4.2.2.2 SKILL REFERENCED TO CLIMATOLOGICAL FORECAST................... 49 4.2.2.3 SKILL REFERENCED TO HINDCAST MODELLING OF OBSERVED METEOROLOGY ............................................................................................................. 50 5 SUMMARY........................................................................................................................... 51 5.1 CONCLUSIONS ............................................................................................................ 51 5.1.1 SUITABILITY OF MIKE SHE AND MIKE 11 MODEL ..................................... 51 5.1.2 CALIBRATION AND VALIDATION PERFORMANCE ................................... 52 5.1.3 FORECAST PERFORMANCE AND SKILL........................................................ 52 5.1.4 RESEARCH CONTRIBUTION ............................................................................. 53 5.2 LIMITATIONS .............................................................................................................. 53 5.3 FUTURE WORK ........................................................................................................... 54 REFERENCES ............................................................................................................................. 55 APPENDIX A – MODEL PERFORMANCE VERIFICATION METRICS ............................... 63 A-1 STATISTICAL VERIFICATION METRICS ................................................................... 63 vii A-2 SKILL SCORE METRICS ................................................................................................ 67 APPENDIX B – MODELLING PARAMETERS ........................................................................ 68  viii LIST OF TABLES Table 1-1: Performance of modelled Coquitlam River streamflow during model calibration and validation phases. .......................................................................................................................... 36 Table 1-2: Performance of modelled Coquitlam River streamflow during forecasting period for daily mean streamflow .................................................................................................................. 41 Table 1-3: Performance of modelled Coquitlam River streamflow during forecasting period for hourly streamflow ......................................................................................................................... 45 Table 1-4: Skill score of NWP - hydrological model forecast relative to a persistence forecast . 48 Table 1-5: Skill score of NWP - hydrological model forecast relative to a climatological forecast (historical daily mean flows for the forecasted day) ..................................................................... 49 Table 1-6: Skill score of NWP - hydrological model forecast relative to the hindcast modelling of streamflow using observed meteorological data ........................................................................... 50 Table B-1: Watershed parameter sources of information and values ........................................... 68    ix LIST OF FIGURES Figure 3-1: Map of the Coquitlam River watershed above Coquitlam Lake, located in southwestern BC, including regional climate, hydrometric and, snow survey stations. .............. 23 Figure 3-2: Historical data from Environment Canada Station 08MH141 (1982-2012 averages) 26 Figure 3-3: Flowchart illustrating forecast modelling process. (© Bourdin, 2013, adapted with permission) .................................................................................................................................... 33 Figure 4-1: Coquitlam River daily mean streamflow during model calibration ........................... 39 Figure 4-2: Coquitlam River hourly streamflow during model calibration .................................. 39 Figure 4-3: Coquitlam River daily mean streamflow during model validation ............................ 40 Figure 4-4: Coquitlam River hourly streamflow during model validation ................................... 40 Figure 4-5: Coquitlam River forecasted daily mean streamflow for 1-day lead time .................. 43 Figure 4-6: Coquitlam River forecasted daily mean streamflow for 2-day lead time .................. 44 Figure 4-7: Coquitlam River forecasted daily mean streamflow for 3-day lead time .................. 44 Figure 4-8: Coquitlam River forecasted hourly streamflow for 1-day lead time ......................... 46 Figure 4-9: Coquitlam River forecasted hourly streamflow for 2-day lead time ......................... 47 Figure 4-10: Coquitlam River forecasted hourly streamflow for 3-day lead time ....................... 47  x LIST OF EQUATIONS Equation 2-1: General Skill Score Equation modified from USDOC (2006) .............................. 20 Equation A-1: Mean Absolute Error (MAE) ................................................................................ 63 Equation A-2: Percent Bias (PBIAS) ............................................................................................ 64 Equation A-3: Nash-Sutcliffe Efficiency (NSE)........................................................................... 64 Equation A-4: Coefficient of Determination (R2) ......................................................................... 65 Equation A-5: Root Mean Square Error (RMSE) ......................................................................... 65 Equation A-6: Mean Squared Logarithmic Error (MSLE) ........................................................... 65 Equation A-7: Average Percent Error in Peak Flows (APEP) ...................................................... 66 Equation A-8: Absolute Average Percent Error in Peak Flows (AAPEP) ................................... 66 Equation A-9: Mean Absolute Error Skill Score (MAESS) ......................................................... 67 Equation A-10: Root Mean Square Error Skill Score (RMSESS) ................................................ 67  xi LIST OF SYMBOLS AND ABBREVIATIONS ABBREVIATIONS ANN   =  Artificial neural network  BC   = British Columbia BC Hydro  = British Columbia Hydro and Power Authority DCP    = Data Collection Platform DDMC   = Degree Day Melt Coefficient DEM   = Digital Elevation Model DHSVM  = Distributed-Hydrology-Soil-Vegetation Model DHI   = Danish Hydraulic Institute EC   = Environment Canada GDCFDC  = Geophysical Disaster Computational Fluid Dynamics Centre GRU   = Grouped Response Unit HBV-EC  = Hydrologiska Bryans Vattenbalansavdelning model HRU   = Hydrologic Response Units km2   = Square kilometers LAI   = Leaf Area Index LNSE   = NSE of log-transformed flows m   = meters MAE   = Mean Absolute Error MAESS  = Mean Absolute Error Skill Score masl   = meters above sea level mm   = millimeters mm/oC/day  =  millimeters per degrees Celsius per day (mm per degree day) m/s   = meters per second MM5   = Fifth-generation Mesoscale Model MSLE   = Mean Squared Logarithmic Error M2M   = Member-to-Member NSE   = Nash-Sutcliffe Efficiency NWP   = Numerical Weather Prediction xii NWSRFS  = National Weather Service River Forecasting System PBIAS   = Percent Bias NCAR   =  National Center for Atmospheric Research PET   = Potential Evapotranspiration RFC   = River Forecast Centre RFS   = River Forecast System RMSE   = Root Mean Square Error RMSESS  = Root Mean Square Error Skill Score SS   = Skill Score SWE   = Snow-water equivalent SWAT   = Soil and Water Assessment Tool UBC   = University of British Columbia UBCWM  = University of British Columbia Watershed Model USDOC  = United Stated Department of Commerce WaSiM  = Water balance Simulation Model  SYMBOLS %   =  percent oC   = Degrees Celsius ot   = observed streamflow at time t o̅t   = mean observed value over all t in 𝑇 mt   = modelled (or forecast) streamflow at time t m̅t   = mean modelled (or forecast) value over all t in 𝑇 R2   = coefficient of determination T   = set of time points for the evaluation  ‖T‖   = The size of T (varies for analysis time step) t   = internal counter for the evaluation set of time points T ∞   = Infinity  xiii ACKNOWLEDGEMENTS Large thanks to Dr. Robert Millar, my supervisor at the University of British Columbia for guidance, support and most of all, patience.  Gratitude also goes to: Dr. Ziad Shawwash for reviewing this thesis, Daniel Terpstra for analysis assistance,  Dr. Dominique Bourdin for significant help in archiving weather forecasts and guidance, Gaven Tang for camaraderie, memories, and proofreading assistance, Golder Associates Ltd. for providing the flexibility to complete this work, Lynne Campo (Environment Canada) and Tim Ashman (BC Hydro) for help with data requests, My parents for their constant support, And most of all, to my wife, Britteny, for her unwavering support, patience, tough love and encouragement to see this to the end.   1 1 INTRODUCTION Short-term river forecasts with lead times of one to five days are of particular interest to the owners of electric system with non-storage hydro components and to those assessing flood risks in small, mountainous watersheds. Reliable and accurate short-term river forecasts are important to optimize the integration of non-storage hydro components within an electric system by reducing the day-ahead opportunity costs (the costs associated with held water reserves due to forecast uncertainty and to provide system flexibility), and for increasing the trade opportunity of forecast electricity (BC Hydro, 2010 and Guzman, 2005). In addition, reliable forecasts are important to predict critical conditions related to the potential risk of flooding or precipitation events potentially related to debris flows or landslides, potentially resulting in damage to infrastructure or communities (Brayfield, 2013 and Fleming et al., 2015).  Flow forecasting is usually undertaken using computational hydrologic models.  Hydrologic models have been applied for spatial scales ranging over many orders of magnitude, to temporal scales from sub-hourly to annually, and for hydro-climates over the entire earth (Graham and Butts, 2005). Computer based hydrologic models are commonly used in simulation of the hydrologic cycle within a watershed to forecast hydrologic outputs such as snow-water equivalent (SWE), reservoir inflows, and streamflow. Predictions may be used to assess the impacts of land-use or climate change, provide forecasts for hydroelectric reservoir operators or electricity system operators, and to provide streamflow flood forecasting. In general, forecasts are used to support informed decision-making. Real-time streamflow forecasting with lead-times in the range of 1 to 5 days remains a challenge in small, coastal, mountainous watersheds of the Pacific Northwest (Westrick et al., 2002 and Bourdin, 2013). These watersheds can generally be characterized as having a pluvio-nival regime, with high flows occurring both in May to June from snowmelt and in the fall due to rainfall from Pacific frontal systems (BC Hydro, 2010).  In these watersheds, meteorological forecasts are typically more accurate than climatological averages (Weber et al. 2006) and may be more accurate than persistence-based forecasts, due to the rapid watershed response to precipitation events. Real-time meteorological forecasts, in the form of distributed Numerical Weather Prediction (NWP) models, can be used as input into a hydrologic model. NWP models within Pacific Northwest watersheds are complicated by complex mountainous terrain that can 2 lead to large orographic precipitation gradients (Tangborn and Rasmussen, 1976), cold air damming episodes, and challenges in forecasting temperature lapse rates (the variation in temperature with elevation) and therefore precipitation phasing (Bourdin, 2013). These complications in the NWP models can lead to challenges in the prediction of streamflow. The challenge of short-term streamflow forecasting in small watersheds with complex terrain has direct applicability to the management of non-storage hydroelectric projects within an electricity system. These projects are an intermittent renewable energy source with energy production limited to the availability of real-time instream flows, unlike hydroelectric facilities downstream of reservoirs with large storage capabilities. Streamflow forecasts in small watersheds with complex terrain also have applicability to the users of forecasts of flood or potential debris flows in risk management. The challenges of short-term streamflow forecasting in small watersheds with complex terrain has led to numerous model intercomparison studies that review model suitability, performance and limitations. In these studies, the fully-distributed, physically-based coupled hydrologic MIKE SHE and hydraulic MIKE 11 model has often not been reviewed or has been stated as not being successfully demonstrated in complex and steep terrain (Beckers et al., 2009). 1.1 STATEMENT OF PROBLEM The statement of problems that this research includes the following, which are discussed below:  Challenges remain in short-term streamflow forecasting in small, coastal, mountainous watersheds of the Pacific Northwest; and,  Previous studies are based on lumped or semi-distributed models and have a long-period of record used for calibration or model learning. Small, coastal, mountainous watersheds in the Pacific Northwest present streamflow forecast challenges as the complex terrain can lead to highly variable precipitation and temperature gradients, and sensitive precipitation phasing. High-resolution NWP models (1.3 km spacing now available over southwest British Columbia [BC]) may be able to simulate processes such as strong orographic gradients in the precipitation fields or cold air damming episodes and difficulties in forecasting temperature lapse rates and therefore precipitation phasing. There is 3 interest in reliable, skillful forecasts for applications such as non-storage (run-of-river) hydro, reservoir inflows, or flood forecasting in small watersheds. To take full advantage of the high-resolution NWP models, fully-distributed hydrological models are required, as opposed to lumped, conceptual, or empirical models (Bourdin et al., 2012).  A common challenge to the verification of model forecasts outside of research watersheds is the availability of long-term observed data sets suitable for the calibration of models and the assessment of statistical performance or forecast skill (Brun and Band, 2000; Eckhardt and Ulbrich, 2003). However, research based model calibration and validation studies are primarily based in watersheds with long-term measurements of input parameters (i.e.: soil hydraulic conductivity, evaporation, rainfall, meteorological stations, etc.) and long-term data sets of outputs used for calibration (i.e.: discharge records) within the study basin. Physically-based watershed models are expected to require less training and calibration than lumped or conceptual models (El-Nasr et al., 2005). The Coquitlam River watershed, above the Coquitlam Lake Reservoir, will be used as a case study representing a small watershed in the Pacific Northwest’s Coastal Mountain range A fully-distributed, physically-based hydrological model, MIKE SHE (coupled with MIKE 11) will be used to forecast Coquitlam River streamflow above Coquitlam Lake. The model will be calibrated to a short-period of record, and then short-term 1- to 3-day deterministic river forecasts will be produced using a high-resolution NWP model. The model calibration and forecast verification performance measures will be assessed in addition to forecast skill relative to persistence forecasts and climatological forecasts. 4 2 LITERATURE REVIEW 2.1 CURRENT PRACTICE The general approach to short-term streamflow forecasting in small Pacific Northwest watersheds with complex terrain typically follows the following procedure: 1) Select appropriate hydrologic model(s) to simulate the hydrologic processes of interest in the study watershed; 2) Use an observed meteorological record to simulate hydrologic processes and perform model calibration and validation to an observed model output (i.e., streamflow, water levels, SWE, etc.) based on performance metrics; 3) Use a meteorological forecast(s), such as NWP model(s), as driving data in the hydrologic model(s) to create hydrologic forecasts and access the forecast performance and skill. A brief discussion of the procedure steps are provided below. 2.1.1 HYDROLOGIC MODEL SELECTION A large number of hydrologic watershed models have been developed to simulate and forecast streamflow. Each model has varying degrees of complexity, user support, data needs, physically-based algorithms, flexibility, and performance. Current watershed models have a wide range of applications.  The ability of hydrologic models to simulate hydrologic processes in watersheds of interest using observed meteorological data as input has been assessed using artificial neural network (ANN)-based streamflow models, WATFLOOD, the UBC Watershed Model (UBCWM), Environment Canada’s version of the Hydrologiska Bryans Vattenbalansavdelning model (HBV-EC), the National Weather Service River Forecasting System (NWSRFS), the University of Washington Distributed-Hydrology-Soil-Vegetation Model (DHSVM) (Brayfield, 2013, Conestoga-Rovers, 2010, Fleming et al., 2015, Hugget, 2012, and Weber et al., 2006). This is not intended as a complete list of all modelling work, but rather to demonstrate that a variety of models have been applied to small, coastal mountainous, Pacific Northwest watersheds. The most relevant studies to this thesis are discussed in greater detail in Section 2.2. 5 In addition to model performance evaluation, the forecast skill evaluation of small, coastal mountainous, Pacific Northwest hydrologic watershed models using NWP models for meteorological input data have been completed using models including the UBCWM (Weber et al. 2006), the DHSVM (Westrick et al. 2002), WATFLOOD, and the Water balance Simulation Model (WaSiM) (Bourdin, 2013). These studies are discussed in greater detail in Section 2.2.  Limited use of the physically-based, fully-distributed MIKE SHE model to evaluate forecast skill using a calibrated and validated model with NWP input in small, coastal, mountainous watershed has been completed. For applications with limited data and high-resolution NWP model output, a fully-distributed, physically-based model should be considered (Bourdin, 2013; and El-Nasr et al., 2005).  2.1.2 MODEL CALIBRATION AND VALIDATION TO OBSERVED DATA The current practice of model calibration (parameter optimization) is to compare records of a modelled output (i.e., streamflow, water levels, etc.) to the concurrent observed records and evaluate the model performance by qualitative methods (i.e., graphical) and quantitative methods (i.e., widely used statistical verification metrics).  Optimization is typically carried out by trial-and-error (manually or by automated process) until the agreement between the modeled output and the observations meet an objective function. This objective function could be based on one statistical verification metric, multiple metrics, or on a user-defined criteria, however, use of a single metric will typically lead to a biased calibration (Duan et al., 2007). Model validation is completed by using the fixed optimized parameters to model a different period of meteorological inputs, and then to compare records of a modelled output to the concurrent observed records and evaluate the model performance by qualitative methods (i.e., graphical) and quantitative methods (i.e., widely used statistical verification metrics). Calibration and validation periods are generally ten years of observed meteorological input and hydrologic output (BC Hydro, 2010).     Current modelling practice is to use sub-daily meteorological time steps and sub-daily computational time-steps, but to use daily, monthly, or annual streamflow averages to evaluate the model or forecast performance. Streamflow response to precipitation events in steep, small, mountainous watersheds is rapid, and therefore generally requires meteorological input at an hourly scale, and the hydrologic processes to be modelled on an hourly basis (Brayfield, 2013).  6 The evaluation of model performance in simulating hydrologic processes or the evaluation of NWP as input into hydrologic models should be evaluated on sub-daily time step. The use of daily (or greater) averages to evaluate small watershed models likely results in an inflation of apparent forecast quality due to lengthening the accumulation period used for verification (Bourdin, 2013, Mass et al., 2002, Moriasi et al., 2007, and Stensrud and Yussouf, 2007).  While this is well documented and sub-daily evaluation intervals are recommended (Bourdin, 2013, Brayfield, 2013, and Hugget, 2012), studies, including model intercomparison studies, evaluate the performance of model or forecast performance on daily average streamflow (BC Hydro, 2010, Bourdin, 2013, El-Nasr et al., 2005, and Weber et al. 2006), sometimes due to poor, or noisy, hourly data. 2.1.3 HYDROLOGIC FORECASTING Hydrologic forecasting can be completed by a number of methods including the use of  historical records to predict future values (i.e., past mean daily flows for the forecast days, also known as climatology forecasts), persistence (where the observations at the time the forecast is issued are persisted out over the forecast lead-time), or by using a meteorological forecasts as the input to drive a hydrologic model. In small, coastal watersheds with complex terrain, NWP models are generally used to force hydrologic models and provide the most accurate forecasts (Bourdin, 2013 and Weber at al., 2006). There are a multitude of NWP models available with different mesoscale models, grid sizes (highest resolution is currently 1.3 km), and forecast lead-times. The NWP models are available from an ensemble suite created on a daily basis by the Geophysical Disaster Computational Fluid Dynamics Centre (GDCFDC), in the Department of Earth, Ocean, and Atmospheric Sciences at the University of British Columbia (UBC). The NWP model results are typically used in real-time to provide short-term hydrologic forecasts. In these pairings of NWP model output and hydrologic models, the initial conditions of the watershed are spun-up to the NWP issue date and time using observed meteorological data to avoid accumulating errors in the hydrologic states (i.e., SWE), due to incorrect NWPs. Then, at the NWP forecast time, the hydrologic model is run using the NWP data to provide a real-time hydrologic forecast. 7 The forecasted hydrologic model outputs are then compared to the observed concurrent observed records and the model performance is evaluated by qualitative methods (i.e., graphical) and quantitative methods (i.e., widely used statistical verification metrics). The forecast skill, or the relative performance (relative accuracy) of the forecast to some reference forecast can be assessed. The skill score, as a percentage, can be interpreted as the improvement of the modeled forecast over a reference forecast, such as a climatological or persistence forecast (Weber et al., 2006). 2.2 RIVER FORECASTING USING HYDROLOGICAL MODELS AND NUMERICAL WEATHER PREDICTIONS To forecast river flows in small, Pacific Northwest watersheds with complex terrain within lead times of a few days, is it typically not sufficient to forecast using climatological (i.e., historical) records or persistence records (Weber et al., 2006). Meteorological forecasts (i.e., NWP models) are more accurate to predict the watershed response to flashy precipitation events, of which the precipitation form depends on temperature forecasts and elevation (BC Hydro, 2010). Furthermore, long-term input and observed data of 5 to 10 years within the modelled watershed are typically used to set-up, calibrate and train hydrological models (BC Hydro, 2010; and Moriasi et al., 2007).    There have been relatively few attempts at assessing the predictive forecast skill of hydrological models in Pacific Northwest watersheds with complex terrain with lead times of a few days, using short-term period of observed records for model calibration and validation. A review of the literature has provided a significant amount of hydrological model calibration and validation studies, and to a lesser extent, assessment of forecast skill using NWP models. Selected studies are discussed below to represent the current use of hydrological models to predict the forecast skill in Pacific Northwest watersheds with complex terrain with lead times of a few days using NWP models. In addition, a general discussion of the description, use, and performance of the physically-based, fully-distributed MIKE SHE model is provided.   8 2.2.1 MIKE SHE AND SWAT MODEL COMPARISON The study by El-Nasr et al. (2005) assessed and compared the performance of the fully-distributed, physically-based MIKE SHE model and the semi-distributed Soil and Water Assessment Tool (SWAT) model to simulate catchment hydrology. The assessment was performed against observed data and no assessment of forecast skill was completed. In MIKE SHE, the hydrological processes are modelled by finite difference representations of partial differential equations to conserve mass, momentum and energy, which are solved for state variables at each modelling element (or grid cell) (El-Nasr et al., 2005). To solve for the state variables such as evapotranspiration or overland flow at each element, several parameters are required as input, which theoretically should be unique to each element (Beven, 2000). However, due to limited input in many catchments, parameters may be applied to sub-sections or the entire basin, therefore increasing the uncertainty in the model. According to DHI (Danish Hydraulic Institute; 1999), successful modelling can be completed using limited spatial input data.  In the SWAT model, the catchment is divided into sub-catchments and further divided into hydrologic response units, which have common attributes assigned. Processes are lumped at the hydrologic response unit level, to provide the output for the sub-catchment, and are described as one-dimensional, average values for each sub-catchment (Arnold and Allen, 1996). The assessment and comparison of the two described models was for the Jeker River Basin in Belgium, a 465 km2 catchment with rolling topography. Rainfall input for the model was available at seven rainfall stations in and around the catchment. Six years of observed discharge was available for a split sample calibration and validation for both models, and in addition, the MIKE SHE model was calibrated using an internal catchment discharge and observation wells time series (El-Nasr et al., 2005).  The performance of the models was assessed based on qualitative assessments (hydrographs and correlation plots) in addition to statistical indices based on daily observed and modelled flows. The comparison of model performance indicated that the fully-distributed MIKE SHE model predicted river flows slightly better than the semi-distributed SWAT model, however, both provided acceptable simulations of the catchment hydrology (El-Nasr et al., 2005). 9 2.2.2 EVALUATION OF HYDROMETEOROLOGICAL FORECAST SYSTEM FOR MOUNTAINOUS WATERSHEDS The study by Westrick et al. (2002) described and evaluated a river forecasting system at six watersheds in the Cascade Mountains of western Washington for the prediction of peak flows. The forecast system used the University of Washington DHSVM to simulate the hydrological processes and the Pennsylvania State University-National Center for Atmospheric Research (NCAR) fifth-generation Mesoscale Model (MM5) to provide meteorological input (NWP models) into DHSVM. Both the MM5 forecasts and the long-term precipitation bias corrected MM5 forecasts were modelled. The assessment was performed for peak flow events against observed data to calculate the percent error of the forecasted peak, and to assess the effect of long-term precipitation bias corrections of the forecasted NWP.  DHSVM, a physically-based distributed hydrologic model, includes channel routing and an energy balance snowpack model (Westrick et al., 2002). The model was applied to the Cascade Mountain range, where large orographically induced precipitation gradients (precipitation lapse rates) (Tangborn and Rasmussen, 1976), the scarcity of real-time rain gauge data, and flashy watersheds create a challenge in real-time river forecasting. The Penn State-NCAR MM5 atmospheric model was used to provide NWP inputs to the hydrologic model. The output from the 4-km high-resolution nest over the study area was applied with and without bias correction. A finding in the study area was that the MM5 over predicts precipitation upwind of major orographic barriers for light to moderate precipitation amounts (Colle et al. 1999). The assessment was for six watersheds on the western (windward) slopes of the Cascade Mountain range in the Pacific Northwest. These watersheds range in size from 106 to 1849 km2 and receive annual precipitation in the range of 2 to 3 metres. Observed climate input for the model was available at 33 locations in and around the watersheds. The model calibration period was eight years using observed discharge at the outlet of each watershed (Westrick et al., 2002). No performance metrics were provided for the model calibration or validation, but only for model performance of forecasting the peak flows. The performance of the coupled DHSVM and Penn State-NCAR MM5 model to forecast peak river flows was assessed for bias corrected NWP forecasts and non-bias corrected NWP forecasts 10 for six events over 1998 to 1999. The average absolute peak error was 38% for the bias corrected input and 45% for the non-bias corrected input for all watersheds. However, the bias-corrected output, which were completed as a single fixed fraction during all precipitation events, provided poorer predictions of long-term mass balance volumes. The study concludes that the bias-correction, as applied, did not improve the overall model performance of peak flows. 2.2.3 EVALUATION OF HYDROLOGICAL FORECASTING SYSTEM USING THE UNIVERSITY OF BRITISH COLUMBIA WATERSHED MODEL AND NWP FORECASTS  The study by Weber et al. (2006) explored the use of statistical verification measures and the use of statistical skill scores to evaluate the performance of BC Hydro’s hydrological forecasts for short-term 5 day forecasts. The evaluation was completed on two watersheds within British Columbia, of which the Stave basin, a coastal, mountainous basin dominated by rainfall, is of relevance to this thesis. The discussion of this study is limited to the Stave basin and to the deterministic forecast evaluation (the study also assesses ensemble forecasts). The study is based on BC Hydro’s River Forecast System (RFS), which uses the calibrated UBCWM (Quick, 1995) and historical input and output data, to run short- and long-term forecasts. The UBCWM is a semi-distributed model which uses lumped elevation zones, with water balance calculations completed independently for each zone, but does not include channel routing calculations (BC Hydro, 2010). The RFS was calibrated using long-term data for the Stave basin. To create a short-term forecast, the RFS was first run up to the forecast date using observed data, and then NWP temperature and precipitation input data (bias-corrected) were used as inputs into the RFS for the five-day forecast (Weber at al., 2006).    The statistical verification of the deterministic forecast was evaluated for lead times of one to five days over two calendar years using the relative bias, mean absolute error (MAE), and the coefficient of determination (R2) performance measures. In addition, an assessment of the probability of detection of high-flow events was completed. To assess the performance of the deterministic forecasts relative to reference forecasts, such as historical mean flows or persistence, a MAE-based skill score was calculated.  11 Conclusions of the study include that the deterministic, short-term forecasts were generally over-predicted, but provided skill above reference forecasts for most scenarios except two to five-day lead time spring forecasts and four to five-day lead time winter forecasts. Also, due to the challenges of predicting large rainfall events on the west coast of British Columbia, especially in mountainous terrain, large flow events were not predicted well for lead times greater than one day, but were determined to be advantageous compared to naïve forecasts (Weber at al., 2006). 2.2.4 EVALUATION OF PROBABILISTIC HYDROLOGICAL FORECASTS USING MULTIPLE HYDROLOGICAL AND NWP MODELS  The dissertation study by Bourdin (2013) presented the methodology and evaluation of a probabilistic hydrological forecasting system for reservoir inflows. The system used gridded climate forecasts derived from an ensemble of NWP models which then are used as input into two distributed hydrologic models to create a 72 Member-to-Member (M2M) ensemble. Each hydrologic model was optimized based on statistical verification scores using historical records, and the initial conditions of each hydrological model were updated each forecast day based on the meteorological observations. The 72 M2M ensemble was evaluated for short-term forecast lead times of one to two days over a period of three water years. In addition to statistical evaluation of the M2M ensemble, an uncertainty analysis of all stages of the modelling process was completed to identify and quantity (where possible), the uncertainty. The forecasting system was applied to the Daisy Lake hydroelectric reservoir, on the Cheakamus River in southwestern BC. The watershed above the reservoir is characterized as a mountainous watershed with complex terrain, minor glacier content, and having a drainage area of 721 km2. The watershed is subject to flashy fall and winter flows due to Pacific frontal systems and spring and summer flows dominated by snow and glacier melt. (Bourdin, 2013) Two distributed hydrologic models are used in the M2M ensemble forecasts, selected for their suitability to the study watershed, to receive high-resolution distributed NWP models, and a capability to model hydrological processes in complex terrain with limited input data. The first is the Water balance Simulation Model (WaSiM; Schulla, 2012), a full-distributed, physically-based model, for which potential evapotranspiration (PET) is based on the Penman-Monteith equation (Monteith, 1965), and snowmelt is modelled using a temperature index algorithm (or 12 the degree-day method) (Anderson, 1973). The WaSiM model was run with 1 km grid cells and an hourly time step. For hydrologic forecasts using NWP models, gridded NWP hourly precipitation, temperature, wind speed, humidity, and global radiation (global radiation only available as output for some NWP forecasts), were used as input, with wind speed, humidity, and global radiation used in the PET algorithm. The second model used was WATFLOOD, a physically-based, semi-distributed model. WATFLOOD uses the Grouped Response Units (GRU) approach that lumps together Hydrologic Response Units (HRU), or areas with similar land cover, and models each HRU to generate a total GRU outflow (Kouwen at al., 1993). WATFLOOD uses the Hargreaves equation to estimate PET, and snowmelt is modelled using the temperature index algorithm, also known as the degree-day method (Anderson, 1973).  The M2M ensemble forecast system uses multiple NWP models, downscaled with multiple interpolation schemes and then uses two distributed hydrologic models. The NWP models were obtained from the operational ensemble suite run by the GDCFDC, in the Department of Earth, Ocean, and Atmospheric Sciences at UBC. Three independent high-resolution mesoscale models were used, which are centered over southwestern BC (Bourdin, 2013).  The three mesocale models were:  The Mesoscale Compressible Community model (Benoit et al., 1997);  The fifth-generation Pennsylvania State University-Nation Center for Atmospheric Research Mesoscale Model (MM5; Grell et al., 1994); and,  Version 3 of the Weather Research and Forecasting (WRF) mesoscale model (Skamarock et al. 2008). Both hydrologic models were calibrated and validated each with ten years of observed flows based on the Nash-Sutcliffe Efficiency (NSE; Nash and Sutcliffe, 1970), the NSE of log-transformed flows (LNSE), R2, MAE, and Root Mean Square Error (RMSE). Similarly, the inflow forecasts performance were evaluated based on the NSE, LNSE, R2, MAE, RMSE, and the RMSESS relative to a persistence reference forecast. Conclusions of the study relevant to this thesis include that both hydrologic models performed well during calibration and validation according the statistical verification scores, and that the use of the multi-state, multi-parameter M2M components into the multi-NWP, multi-distributed-13 hydrologic-model ensemble increased forecast resolution by improving the final inflow forecast ensembles. A limitation identified in this study was that the use of daily observed data to verify the results likely resulted in an over-estimate of apparent forecast quality relative to what might be determined using shorter sub-daily periods of assessment (Stensrud and Yussouf, 2007). The study recommends that hydrologic forecasting applications that make use of high-resolution NWP forecasts, and that require forecasts with sub-daily time steps, should be using sub-daily time steps for validation or skill assessments (Bourdin, 2013).     2.2.5 SUPER-ENSEMBLE ARTIFICIAL INTELLIGENCE FLOOD-FORECAST MODEL FOR A PACIFIC NORTHWEST RIVER  The Study by Fleming et al. (2015) developed a super-ensemble operational forecast system for the Englishman River, a river on Vancouver Island in southwest British Columbia, with an upstream drainage area of 319 km2. The forecasting system was developed to predict daily flood events for lead times of 1 to 3 days. The modelling system used up to 42 NWP model outputs from the North American Ensemble Forecast System, along with an ensemble of six different ANN-based streamflow models to create a super-ensemble of 252 daily probabilistic streamflow forecasts. The ANN-based streamflow models were trained using only high-flow observed data from the hydrometric station, and as such, the modelling system is not intended to forecast the compete hydrograph, but rather only flood events. The system was trained on data from 1995 to 2011 and the forecast was tested during the 2013 to 2014 storm season by British Columbia’s flood forecasting agency. The forecast system does not provide detailed hydrologic process information, and the 2013 to 2014 period did not yield high-flow events for statistical comparisons, however, the results were promising and the operational forecasts was found to be robust and easy to use on a daily basis. Continued forecast verification was recommended as part of this study. 2.2.6  INTERCOMPARISON STUDY OF PROCESS-ORIENTED WATERSHED MODELS  The Intercomparison Study of Process-Oriented Watersheds report completed by Conestoga-Rovers & Associates on behalf of the British Columbia Hydro and Power Authority (BC Hydro; BC Hydro, 2010) reviewed several process-based models to assess hydrologic performance and 14 suitability of the model for operational forecasting at BC Hydro. The assessment of hydrologic performance was limited to the observed period of data during the calibration and validation phases and did not consider NWP model input. The models reviewed in the study included the UBCWM, HBV-EC, NWSRFS, and WATFLOOD.  The four models used in the study are characterized below (BC Hydro, 2010):  The UBCWM is a semi-distributed model which uses lumped elevation zones, with water balance calculations completed independently for each zone, but does not include channel routing calculations;  The HBV-EC model is a semi-distributed model in which unique combinations of climate, elevation, land class, aspect, and slope groups define computational GRUs;   The NWSRFS model is a system of lumped models which sub-divide the watershed into homogeneous modelling areas which are independently modelled; and  WATFLOOD is a physically-based, semi-distributed model. WATFLOOD uses the Grouped Response Units approach that lumps together HRUs, or areas with similar land cover, and models each HRU to generate a total GRU outflow. The study included the calibration and validation of each model based on historical data to three watersheds in BC, of which the Alouette watershed was a small, steep, coastal, mountainous watershed with a drainage area of 203 km2 that is most relevant to this thesis. The study considered ten-year long calibration and validation periods, and the simulated results of discharges were compared to observed discharge records at hydrometric stations. Model performance was evaluated based on the ability of the model to reproduce the main hydro-climate processes found in the study watersheds and the accuracy in simulated streamflow. To assess the overall performance, mean annual and monthly flow volumes, snow accumulation, and melt simulation, rain-on-snow simulation, hydrograph separation, baseflow simulation, daily flow simulation, and peak flow simulation were evaluated. These criteria provided a wide-angle characterization of the model performance, but to create a basis for relative model performance, four statistical verification metrics were used and included the NSE of daily flows, R2 for annual flow volumes, the annual flow volume bias, and the weighted monthly flow volume bias. 15 Overall, the NWSRFS model simulated the flashy hydro-climate of the Alouette watershed the best for peak flow and daily flow simulation.  However, considering all three watersheds and all evaluation criteria, the UBCWM was identified as providing the best overall hydrological performance. 2.2.7 DHI MIKE SHE AND MIKE 11 FLOOD FORECASTING SYSTEM A coupled MIKE SHE/MIKE 11 pilot flood forecasting model was used in real-time to model streamflow in the 350 km2 Urumea basin in Spain with complex terrain in a Larsen et al. study (2010). In this study, MIKE SHE was used to model surface water and groundwater processes and MIKE 11 was coupled with MIKE SHE to model hydraulic channel processes and routing. The model was calibrated and validated based on observed meteorology and streamflow data, and then the calibrated model was used in real-time with forecasted meteorological input. The calibration procedure included a sensitivity analysis and an optimization of the most sensitive parameters. During the forecasting period the precipitation was applied to the catchment as a constant value (with elevation adjustment) over the entire watershed.  The study concluded that a coupled MIKE SHE/MIKE 11 model was suitable to real-time flood forecasting and provided good predictions of streamflow magnitude and timing. However, a limitation of the study was the meteorological data was applied to the entire catchment as lumped data, rather than as fully-distributed data, which can affect precipitation phasing and streamflow timing.   2.2.8 CONCLUSIONS Based on the review of literature, MIKE SHE has not been widely used in calibration-validation and NWP short-term forecasting studies in Pacific Northwest watersheds of interest, but has been widely applied to watershed modelling (Graham and Butts, 2005). Most studies, other than Westrick et al. (2002), have considered lumped or semi-distributed models to simulate hydrologic processes in Pacific Northwest small, steep, coastal watersheds with complex terrain. High-resolution NWP models (1.3 km spacing) may be able to simulate processes such as strong orographic gradients in the precipitation fields or cold air damming episodes and difficulties in forecasting temperature lapse rates and therefore precipitation phasing. To take full advantage of the high-resolution NWP models, distributed hydrological models are required, as opposed to 16 lumped, conceptual, or empirical models (Bourdin et al., 2012). Intercomparison studies (El-Nasr et al., 2005 and BC Hydro, 2010) were evaluated only using observed point source climate data as inputs and therefore did not evaluate the model forecast performance using NWP models as input. In addition, as higher-resolution NWP models are made available for longer forecast lead times, the conclusions of past studies should be re-assessed. For example, in Weber et al. (2006), forecast precipitation and temperature for 0 to 48 hours and from 48 to 120 hours were from approximately 15 km and 100 km gridded resolution, respectively. Current availability of NWP forecasts could provide 1.3 km grid resolution for 0 to 84 hours and then a 12 km grid resolution for 84 to 120 hours (GDCFDC, 2015), which could change the conclusions and increase forecast skill. The above observations indicate an opportunity to assess the forecast skill using a model such as MIKE SHE. The reviewed studies of small, steep, coastal watersheds with complex terrain in the Pacific Northwest typically used long periods of observed records within the study watershed to calibrate and train the hydrologic model parameters. For calibration periods, greater than ten years were used in Weber et al. (2006), ten years were used in BC Hydro (2010) and Bourdin (2013), and eight years were used in Westrick et al. (2002). The long-term period of records of high-quality, watershed-specific data available for model training, calibration, and validation in academic studies, may not be available for industrial or commercial applications. The above observations indicate an opportunity to assess the forecast skill, with the use of short-term, out of watershed observations using a physically-based model such as MIKE SHE. Evaluation of model or forecast system performance in the reviewed studies is completed on a daily, monthly, or annual time interval. This may be applicable for uses such as simulating reservoir levels, or streamflow in large watersheds, but sub-daily time intervals may be of greater concern for applications such as non-storage (run-of-river) hydro or flood forecasting in small watersheds. There is an opportunity to study the performance of hydrologic model or forecast skill on a sub-daily time step that makes use of hourly high-resolution, NWP forecasts. 17 2.3 GRAPHICAL AND STATISTICAL MODEL PERFORMANCE Graphical and statistical verification metrics pair the modelled or forecast hydrologic output (i.e., streamflow, water level, SWE) to an observed concurrent data set to characterize the relationship between the two (Welles et al. 2007). Graphical and statistical verification metrics are critical to assessing the performance of hydrologic models using observed records during model calibration and validation, and hydrologic models using a NWP model as meteorological input. These assessments are important to understand the model accuracy and the forecast skill, both which are valuable to decision makers in evaluating the likelihood of outcomes and risk. In addition, the use of statistical verification metrics enables objective criteria to evaluate how well, or how poorly, a model performs based on generally accepted performance ratings found in the body of literature (Moriasi, et al., 2007). This section is intended to summarize the studies completed by others regarding key graphical and statistical verification metrics and acceptable values for which performance ratings can be made. Not all graphical or statistical methods are discussed, as significant number of methods have been used over past studies (Moriasi et al., 2007). Previous studies have completed this and can be found in studies such as Borah and Bera (2004), Boyle et al. (2000), El-Nasr et al., (2005), Gupta et al., (2009), Legates and McCabe (1999), Moriasi et al. (2007), USDOC (2006), and Wilks (1995), among others. Common recommendations from the studies above include:  Assessments should not be only completed for one verification measure or metric, but include multiple evaluation methods to provide a complete assessment of overall model performance and avoid undue emphasis on matching one feature of the hydrograph while reducing the skill of other hydrograph features (Boyle et al., 2000);   Assessments should consider at least one dimensionless statistic, one absolute error statistic with the observed standard of deviation, and one graphical technique;  Graphical technique includes a visual inspection of modelled and observed hydrographs to assess bias and accuracy; and  Assessments should consider statistical verification metrics that assess high-flow, low-low and mass balance performance. 18 To meet the above recommendations, and based on similar studies (BC Hydro, 2010, Bourdin, 2013, Hugget, 2012, and Weber et al. 2006), the following approach is suggested to evaluate the performance of modelled or forecasted streamflow:  Visual assessment of overall model performance, bias, and accuracy based on a hydrographs. Hydrographs are useful to identify model bias, identify performance of peak flows (both magnitude and timing), and the shape of rising and recession curves (ASCE, 1993 and Moriasi et al. 2007);   Evaluation of the error and absolute error in a sub-set of selected modelled peak streamflows to assess the model performance in predicting the timing and magnitude of peak flows.  Evaluation of the overall model performance by calculating the NSE, MAE, Percent Bias (PBIAS), RMSE, and R2 will be evaluated to assess overall mode performance; and  Assessment of the low-flow model performance by using the Mean Squared Logarithmic Error (MSLE) (BC Hydro, 2010). The above performance metrics may be computed on hourly, daily, monthly, or annual time periods of assessments based on the modelling purpose and intended use (Moriasi et al., 2007). The above approach is intended to summarize the wide range of evaluation methods and metrics used to evaluate model performance based on both literature summary studies, and methods applied in studies relevant to this thesis. All statistical verification metrics, including equations and descriptions, that are included used in this thesis are provided in Appendix A (Section A-1).   2.4 HYDROLOGICAL FORECAST SKILL In addition to calculating the statistical performance metrics for hydrological forecast, the forecast skill, or the relative performance (relative accuracy) of the forecast to some reference forecast can be assessed. This provides the forecast user with a relative assessment of performance and context to interpret the performance metrics compared to a reference (or baseline) model (Gupta et al., 2009 and Welles et al., 2007). The skill score, as a percentage, can be interpreted as the improvement of the modeled forecast over a reference forecast (Weber et al., 2006). 19 The forecast skill is generally referenced to an unskilled (also referred to as a dumb, or zero-skill) forecast such as persistence or climatology (USDOC, 2006), but can also be referenced to the modelled outputs when observed inputs are used in hindcasting (therefore not in real-time). Persistence reference forecasts are the observations at the time the forecast is issued, persisted out into the future (Welles et al., 2007). The time interval that observations are persisted depends on the forecast lead time. If a three-day lead time forecast is considered, observations on the forecast issue day are persisted over the entire three-day forecast period. A common persisted observation is daily average discharge or water levels. Climatology reference forecasts are derived from long-term records of observed data and commonly use daily mean values for short-term forecasts or the annual mean values for long-term forecasts (Weber et al., 2006). Skill of hydrological forecasts can also be assessed (not on a real-time basis) with reference to the outputs of models which use the observed meteorological inputs to provide a comparison of the skill of the forecasts using meteorological NWP models. It should also be noted that the NSE can be interpreted as a classic skill score, where skill is assessed to the reference model, in this case, the mean of the observations (Gupta et al., 2009). 20 Skill Score (SS) is defined as the percentage difference between statistical verification scores for two sets of forecasts (i.e., the operational forecasts and the reference forecast) and have the general form of the following equation. Equation 2-1: General Skill Score Equation modified from USDOC (2006) 𝑆𝑆 = 1 −𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑎𝑙 𝑉𝑒𝑟𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑆𝑐𝑜𝑟𝑒 (𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡)𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑎𝑙 𝑉𝑒𝑟𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑆𝑐𝑜𝑟𝑒 (𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡) X 100%  The statistical verification scores used to calculate the skill score in relevant studies include the MAE (Weber et al., 2006), the RMSE (Bourdin, 2013, USDOC, 2006, and Welles et al., 2007), and the MSE (USDOC, 2006). In addition, the reference forecasts include both the persistence and climatological average forecasts. Skill scores can be negative if the reference forecast is a better predictor of observed values, is 0% if the forecast and the reference forecast have the same skill, and is 100% for a perfect forecast. The Weber et al. (2006) study, using BC Hydro’s RFS calculated annual MAESS of 45% to 10% (average of 29%) over climatology forecasts and 42% to 32% (average of 38%) over persistence forecasts for lead times of 1 to 5 days. The assessments were based on deterministic forecasts in the Stave basin, a coastal, mountain watershed with a drainage area of 956 km2. The Bourdin (2013) study, using the median forecasts derived from the 72 M2M ensembles, calculated RMSESS between 80% and 70% over persistence forecasts for lead times of 1- to 3-days. The assessments were completed for the Cheakamus basin above the Daisy Lake Reservoir, a coastal, mountain watershed with a drainage area of 721 km2. The equations for skill scores used in this study are provided in Appendix A (Section A-2). Skill scores provide an objective score of relative improvement for NWP model driven forecasts compared to the best alternative options of hydrologic forecasts such as climatological averages or persistence. The use of skill scores such as the MAESS or the RMSESS, which are based on widely used metrics, allows for comparison across studies.  21 2.5 CONCLUSIONS The literature review of hydrologic modelling and NWP based-hydrological forecasting studies in Pacific Northwest mountainous watershed and the MIKE SHE and MIKE 11 models has indicated that additional research is warranted. The investigation into the performance of the coupled MIKE SHE/MIKE 11 model to forecast streamflows on a sub-daily basis for lead times of 1- to 3-days using high-resolution NWP models to force the hydrologic model builds upon completed research in Pacific Northwest watersheds with complex terrain. The evaluation of the model performance is completed based on the results of the literature review for assessing hydrologic model performance and evaluating forecasting quality or skill score.22 3 METHODS The Coquitlam River watershed above Coquitlam Lake is used as a case study representing a small watershed in the Pacific Northwest’s Coastal Mountain range with limited observed input data within the watershed boundaries. A fully-distributed, physically-based hydrological model, MIKE SHE coupled with MIKE 11 (MIKE SHE/MIKE 11), is used to forecast Coquitlam River streamflow above Coquitlam Lake at a hydrometric station. The coupled MIKE SHE/MIKE 11 model has the capability to model groundwater flow, surface water flow both overland and in a routed through a hydraulic channel. The model is calibrated to a short-period of observed flows from June 24, 2010 to June 23, 2011, representing the possible short-term observational records for many of the non-academic study watersheds or those without long-term monitoring. Using the calibrated model and optimized parameters, the observed meteorological records are used to force the model from June 24, 2011 to June 23, 2012 to validate the model performance. Also, during separate modelling over the period from June 24, 2011 to June 23, 2012, the model was forced by high-resolution NWP model output and short-term 1- to 3-day deterministic river forecasts. The model validation and forecasting periods are the same due to limited data availability and NWP model output archiving timing restrictions. The model calibration and forecast verification performance measures are assessed in addition to forecast skill relative to persistence forecasts and climatological forecasts.  Section 3.0 provides an overview of the case study watershed, the available input and verification data, and modelling methods.  3.1 CASE STUDY WATERSHED AND DATA 3.1.1 COQUITLAM RIVER WATERSHED ABOVE COQUITLAM LAKE The Coquitlam River watershed is a coastal basin located in the Coast Mountain range in southwestern BC. The watershed area of study used in the hydrologic modelling and forecasting is located upstream of Environment Canada (EC) hydrometric station 08MH141 on the Coquitlam River, upstream of the Coquitlam Lake reservoir. The watershed is shown in Figure 3-1.  23  Figure 3-1: Map of the Coquitlam River watershed above Coquitlam Lake, located in southwestern BC, including regional climate, hydrometric and, snow survey stations.  The watershed is a steep, mountainous, coastal watershed with significant forest cover and limited disturbance due to access and logging restrictions (Koop, 1994). The watershed has a drainage area of 54.7 km2 to Station 08MH141 and surface elevations that range from 280 to 1,750 meters above sea level (masl) with an average elevation of 1,000 masl. Glacier coverage in this basin is minimal, due to its southern, coastal location, and elevations.  The hydro-climate regime in the watershed is pluvio-nival, flashy, and with negligible glacier melt. High flows have a bi-modal distribution, characterized by high flows in May and June due to snowmelt and in fall (November) due to Pacific frontal systems that can bring significant precipitation. The snowmelt contribution to annual runoff is 30 to 40% (Weber et al., 2006) and the mean annual discharge is 6.6 m3/s.  COQUITLAM LAKE COQUITLAM RIVER 24 3.1.2 AVAILABLE WATERSHED AND REGIONAL INFORMATION 3.1.2.1 SPATIAL GEOGRAPHIC INFORMATION Limited publically available spatial geographic information is available for the Coquitlam River watershed above Coquitlam Lake. The watershed elevation data is Canadian Digital Elevation Data from the National Topographic Data Base. This data was processed in Global Mapper to provide a stream network, watershed boundaries, and a Digital Elevation Model (DEM).   3.1.2.2 METEOROLOGICAL RECORDS Meteorological records were obtained from the network of EC Stations and BC Hydro’s Data Collection Platform (DCP) Stations. EC Station 08MH141 and the BC Hydro Station CQM, both named the Coquitlam River above Coquitlam Lake station, the were used as primary sources of meteorological data. Surrounding climate stations were used for quality checks, to fill in missing data using linear regression if data from 08MH141 and CQM were missing, and to derive estimated daily temperature lapse rates. Surrounding stations include the North Vancouver Grouse Mountain Resort EC Station 1105658, and the BC Hydro, Coquitlam Lake Forebay (COQ), Gold Creek (GOC) Stave River above Stave Lake (STA), and Stave River Upper (STV) sites. EC Squamish Airport climate station (WSK) was not used for any infilling of data or to derive temperature lapse rates.    EC Station 08MH141 reports real-time hourly temperature and hourly accumulated precipitation. However, no hourly or daily data are currently archived or uploaded within Environment Canada, but rather only reported as real-time data online (Lynne Campo, Environment Canada, personal communication, June 30, 2011). All hourly meteorological data from EC Station were raw unapproved data, subject to errors and additional caution was provided regarding using hourly temperature records from Station 08MH141. At the start of the data acquisition period of this study, the data from Environment Canada’s Real-Time Hydrometric Data website were downloaded providing hourly temperature and hourly accumulated precipitation data from April 2010 to the end of the study, June 23, 2012. The real-time data were available at http://wateroffice.ec.gc.ca/report/report_e.html?type=realTime&stn=08MH141. 25 Daily maximum and minimum temperatures and 24-hour accumulated precipitation observations are available for all BC Hydro stations. Data from CQM was used as a primary quality check and to fill in missing hourly data at EC Station 08MH141. During periods of infill or correction, the daily minimum and maximum temperatures were transformed in hourly time steps using a sine curve with the daily minimum temperature occurring at 0400 PST and the daily maximum temperature occurring at 1600 PST. Daily accumulated precipitation totals were divided into 24 equal amounts over the 24-hour daily time steps. Primary quality checks for the corrected meteorological time series from 08MH141 and CQM were completed by comparisons to the COQ site. The corrected and complete meteorological data set was composed primarily of hourly data from 08MH141, with corrections and minor infilling with daily data from CQM.    3.1.2.3 HYDROMETRIC RECORDS EC collects streamflow data at Station 08MH141 on the Coquitlam River above Coquitlam Lake (Figure 3-1). Data are available from 1982 to 2015, and as of July 9, 2015 is reporting real-time data. A high-level review of the historical mean daily data from 1982 to 2012, in Figure 3-2, shows the flashy nature of the watershed and high-flow events that have short duration occurring throughout the entire year due to precipitation events. The bi-modal distribution of high daily mean flows can also be seen on Figure 3-2. 26  Figure 3-2: Historical data from Environment Canada Station 08MH141 (1982-2012 averages) EC also collects streamflow data at Seymour River below Orchid Creek (Station 08GA077) over the period of interest. This is a nearby station with a similar drainage area of 63 km2, and has a similar hydro-climate. Data from this station were used for data quality checks, but were not used as model input. Snow survey data were available from the BC River Forecast Center (RFC), reported as SWE from the RFC’s Manual Snow Survey Data archives. Manual snow surveys were completed four to eight times per year from January to June with concentrated surveys in May and June over the period of model calibration and forecasting. Three stations were found within 20 km of the modelled watershed; however, only the two closest stations were used for model verification. The two stations used are the Dog Mountain Station (3A10) at 1,007 masl and the Grouse Mountain Station (3A01) at 1,126 masl.  3.1.2.4 WATERSHED PARAMETERS Limited publically available information is available for the Coquitlam River watershed above Coquitlam Lake. Watershed parameters or rates used as input for the hydrologic model were 020406080100120Daily Discharge (m3/s)DateDaily MaximumDaily MeanDaily Minimum27 compiled from various literature sources for regional studies, studies in similar hydro-climates and studies in similar geographic locations. Table B-1 provides a list of sources of information used to estimate the watershed input parameters or rates, the range of acceptable values based on previous similar studies, and the final parameter value used in the calibrated model. 3.1.2.5 NUMERICAL WEATHER PREDICTION MODELS The NWP models produced by the GDCFDC include three independent high-resolution mesoscale models that have forecast domains over southwest BC. These mesoscale models produce forecasts at 36, 12, 4, and 1.3 km horizontal grids with varying lead times. The 1.3 km grid size was desired because of the small study watershed, the orographic effects in steep, mountain watersheds, and to make full use of the fully-distributed MIKE SHE model. The Version 3 Weather Research and Forecasting (WRF3) mesoscale model was selected for archiving and input into the hydrologic model for forecasting because it was available at both the 1.3 km high-resolution and the 1- to 3-day forecast period. The WRF3 mesoscale model is fully-compressible and non-hydrostatic and has been developed in the public domain for community use (Skamarock et al., 2008). The WRF3 NWP forecast is initialized at 0000 UTC (1600 PST) and then the WRF3 NWP model is computed for different grid sizes: 36, 12, 4, and 1.3 km. The nested 1.3 km grid starts running at 0100 PST after the larger grid sizes runs, and the first valid hourly forecast issued after model spin-up is at 0500 PST. The WRF3 NWP model provides precipitation and temperature forecasts at an hourly timestep. The WRF3 NWP forecasts were archived over the period of June 24, 2011 to June 23, 2012 to provide forecasts spanning one year. The WRF3 NWP forecasts were not issued for a total of 21 days (August 18 to 19; August 24 to 31; September 5 to 6, 11, 21, and 23; November 10 and 25; December 14, 22 to 24; January 7; May 13 and 30; and June 10). Only congruent pairings of forecasted and observed data were used in verification or skill score metrics. 28 3.2 MODELLING METHODOLOGY The modelling methodology of setting up the coupled MIKE SHE/MIKE 11 hydrologic model, calibrating and validating the model performance when forced by meteorological observations, and forecasting streamflows with the calibrated model forced with NWP outputs are described in the following sections. A description of the methods to qualitatively and quantitatively assess model performance of the hydrologic model, and verification of the forecast performance and skill are also discussed.   3.2.1 MODEL SETUP A coupled MIKE SHE/MIKE 11 physically-based, fully-distributed hydrologic model was selected to model the high-resolution distributed NWP model forecasts. Within the coupled model, MIKE SHE simulates the surface water and groundwater processes, and MIKE 11 simulates the one dimensional hydraulic open-channel flow routing processes. Prior to forecasting streamflows using the NWP model output, the hydrologic model was set-up, calibrated, and validated using observed meteorological data. The application of available data and the model processes are described below. 3.2.1.1 APPLICATION OF DATA The spatial extent of the Coquitlam River watershed above Coquitlam Lake and above EC station 08MH141 was defined using the DEM and watershed boundary delineated in Global MapperTM. The DEM was bilinearly interpolated within the watershed boundary in MATLAB to the hydrologic model grid cell size of 200 m. This grid cell size was selected based on assessment model runs to balance model performance and model run-time. MIKE 11 channel cross-sections were derived from the available DEM to represent estimated channel geometry along the MIKE 11 river network that was limited to the Coquitlam River main stem. During the model calibration and validation period, the observed meteorological records forced the hydrologic model. The corrected and infilled precipitation record from 08MH141 was distributed across the watershed within MIKE SHE as a constant value adjusted for elevation using a calibrated constant precipitation lapse rate. The corrected and infilled temperature record from 08MH141 was also distributed across the watershed as a constant value adjusted for 29 elevation using a daily temperature lapse rate. Processing in MATLAB was required to create a gridded temperature file with hourly time steps using a variable daily temperature lapse rate as MIKE SHE only provides the option of a constant temperature lapse rate value. Daily temperature lapse rates were required to model observed temperature inversions, cold air draining and ponding, and local daily variability that effects precipitation phasing (Minder et al., 2010 and Stahl et al., 2006). The gradient-plus-inverse-distance-squared model presented in Stahl et al. (2006) was used to derive daily temperature lapse rates using regional stations.  Hourly precipitation and temperature NWP forecast data described in Section 3.1.2.5 was downscaled to the hydrologic model scale in MATLAB using bilinear interpolation without elevation adjustment or smoothing during the forecasting stage. A gridded temperature and precipitation file with hourly time steps was produced for each forecast day for lead times of 1- to 3-days. 3.2.1.2 MIKE SHE/MIKE 11 MODEL PROCESSES The set-up MIKE SHE/MIKE 11 model incorporates mainly physically-based hydrologic and hydraulic processes, and provides multiple user-selected methods to simulate hydrologic and hydraulic processes. A summary of available hydrologic processes in MIKE SHE and MIKE 11 are available in Graham et al. (2005). The following methods were used for this study and model set-up:  Evapotranspiration is estimated from the Kristensen and Jensen model (Kristensen and Jensen, 1975);  Snowmelt is modelled using the temperature index algorithm (Anderson, 1973) due to poor (or non-exisitent) wind and radiation data, and includes thermal melting due to rain;  Overland flow modelled using the 2-Dimension finite difference method;   Saint Venant 1-Dimension flow and Muskingum routing for channel flow in MIKE 11;  Unsaturated zone flow (infiltration) is estimated from the 1-Dimension finite difference Richards equation (Refsgaard & Storm, 1995); and  Saturated groundwater flow is simulated using the finite difference method and the successive over-relaxation technique. 30 3.2.2 MODEL CALIBRATION AND VALIDATION 3.2.2.1 MODEL CALIBRATION Model calibration is the process of determining the optimal value of model parameters that result in the best agreement between a modelled output and an observed output. The determination of the best agreement can be based on graphical comparisons, or an objective function relating to the maximization or minimization of statistical verification metrics. In this study, the parameters of the MIKE SHE/MIKE 11 coupled model were optimized on daily mean streamflow observations of the Coquitlam River at 08MH141 from June 24, 2010 to June 23, 2011 using observed meteorological inputs. The model was spun up (initialized) from snow-free initial conditions using daily observed meteorological data from September 1, 2009 to January 31, 2010 and hourly observed meteorological data from April 1, 2010 to June 23, 2010. Model parameters were optimized to minimize the MAE and peak flow errors, and to maximize the NSE. Graphical comparisons of streamflow hydrographs were used to support the qualitative evaluation of modelled streamflow and were useful to assess timing and magnitude errors. The SWE depths at proxy site grid cells with equivalent elevations as the 3A01 and 3A10 snow survey stations were used to provide a graphical comparison, which were used to support model calibration and ensure that the optimized parameter distribution led to physically reasonable snowpacks. The manual survey observations of SWE were not directly used in quantitative parameter optimization because of a limited number of observations and because of the uncertainty of using a proxy site.  The complete set of statistics used in the model calibration phase is provided in Appendix A-1.  The MIKE SHE/MIKE 11 coupled model was manually calibrated following the procedures recommended in Moriasi et al. (2007). The statistics were computed, recorded and tracked for each model run. The following describes the calibration process:  Based on watershed information or literature sources, each parameter was provided an initial estimate and upper and lower bound to ensure that a physically-based set of model parameters is used that are applicable to the study watershed. The parameters and sources of information are in Table B-1 in Appendix B. 31  The initial assessment included model runs for each parameter value at an upper, lower and estimated value while all other model parameters were unchanged to assess the model sensitivity to parameter values. Performance of the parameter value was also assessed based on modelling quality of baseflow, peak flow, flow routing, and snowmelt, and adjusted accordingly.  The sensitivity analysis revealed that the Degree Day Melt Coefficient (DDMC), the precipitation lapse rate, detention storage depth, and the Strickler roughness number for overland sheet flow had the greatest effects on the model performance.  A series of model runs with incremental perturbations of the selected model parameters within the reasonable bounds defined were completed while all other model parameters remained at the best estimated values based on literature and initial calibration assessment.  Selection of the combination of model parameters providing the least MAE and peak flow error, and greatest NSE were selected as the optimized parameter set.    Table B-1 provides a list of the final parameter value used in the calibrated model. The values of the parameters most sensitive, and therefore calibrated based on quantitative statistics, were a variable DDMC ranging from 0.5 to 3.75 mm/oC/day in July and August, a precipitation lapse rate of 0.040 %/m (increasing with elevation), a variable daily temperature lapse rate based on observed meteorological records, an annual canopy interception of 25% of all rainfall, and a Strickler Roughness Number of 10 for overland sheet flow.  3.2.2.2 MODEL VALIDATION Validation of the hydrologic model performance to simulate the hydrologic processes in the watershed requires an assessment during a period of time for which model parameters are not optimized. This split-sample technique uses one year of data for model calibration (June 24, 2010 to June 23, 2011), and one year of data for model validation (June 24, 2011 to June 23, 2012). The evaluation of model performance during the validation phase is based on the same set of graphical comparisons and statistical verification metrics used during the calibration phase and therefore the resulting statistics are representative of the evaluation periods. Due to the short 32 period of available meteorological data, the validation period is the same period used for forecast modelling. 3.2.3 FORECAST MODELLING The calibrated MIKE SHE/MIKE 11 model was then used to simulate 1-3 day streamflow forecasts using downscaled gridded NWP forecast fields as meteorological input. Hourly precipitation and temperature output from the 1.3 km NWP grids are downscaled using bilinear interpolation in MATLAB to create a gridded time series input file for MIKE SHE sized at the hydrologic model grid size. No elevation adjustment to precipitation and temperature NWP grids or smoothing is completed, consistent with downscaling methodology in Bourdin (2013).  Streamflow forecasts over the period of June 24, 2011 to June 23, 2012 were produced using a method similar to real-time operational forecasts, however, the streamflow forecasts using NWP model output were hindcast to reduce the overall modelling time span. The initial hydrologic model states from the calibrated model were used at the start of the forecast modelling period at 0500 PST June 24, 2011. For each day of the forecast study period, the observed meteorological data are used as input into the calibrated hydrologic model to provide the initial hydrologic model states used in the forecast model. This was done as part of the validation procedure, and hydrologic model states for all variables and grid cells in the model were saved on a daily basis providing a ‘hot-start’ file for which the forecast model initialized from. This process eliminates the potential for large accumulated errors in the hydrologic states due to errors in the NWP forecasts (Bourdin, 2013 and Westrick et al., 2002). The procedure to update the initial hydrologic model states using observed meteorology, to simulate streamflow using observed meteorology, and to forecast streamflow using NWP model outputs on a daily interval is illustrated in Figure 3.3, adapted from Bourdin (2013), with permission. Grey arrows indicate the use of input data to drive the hydrologic model, black arrows represent model runs initialized from hydrologic state driven by observed meteorology. Solid lines show the use of meteorological observations and dashed lines show the flow of NWP forecasts. The time associated with the procedure is shown by the dot-dashed line at the top of Figure 3.3. 33  Figure 3-3: Flowchart illustrating forecast modelling process. (© Bourdin, 2013, adapted with permission)  3.2.4 MODEL PERFORMANCE AND FORECAST VERIFICATION Assessment of the modelled streamflow in comparison to observed streamflow is completed for two separate phases of the study. The first was assessment of the hydrologic model performance during the calibration and validation periods when observed meteorological data was used as input. The second was verification of the forecasted streamflow during the forecasting period when a NWP model was used as meteorological input into the calibrated model. For both of these phases, the modelled or forecasted streamflow was compared to the observed streamflow at EC Station 08MH141 on both a daily and hourly basis. The methods are discussed below.    3.2.4.1 HYDROLOGIC MODEL PERFORMANCE Assessment of the modelled streamflow in the calibration and validation periods was completed to evaluate the performance of the model in reproducing hydrologic processes when forced by meteorological observations. Parameters were optimized in the calibration phase, and then the Meteorological Observations Sept 1, 2009 to Jun 23, 2011 NWP Forecast Issued Jun 24, 2011 Forecast Streamflow Jun 24-26, 2011  Initial State Conditions from Calibrated Model Oct 1, 2009 Simulated Streamflow Jun 24, 2011 Forecast Streamflow Jun 25-27, 2011  Forecast Streamflow Jun 26-28, 2011  Simulated Streamflow Jun 25, 2011 Simulated Streamflow Jun 26, 2011 Jun 24 05PST Updated State Jun 25 05PST Updated State Jun 26 05PST Updated State Meteorological Observations Jun 24, 2011 Meteorological Observations Jun 25, 2011 Meteorological Observations Jun 26, 2011 NWP Forecast Issued Jun 25, 2011 NWP Forecast Issued Jun 26, 2011 34 validity of the model was assessed by running the calibrated model with input from the validation period. For both the calibration and validation period, the following graphical techniques and statistical verification metrics will be calculated by comparing the modelled streamflow with the observed values for both daily mean streamflow and hourly streamflow:  Graphical evaluation of model performance using streamflow hydrographs; and,  Statistical evaluation of the model performance by several statistical verification metrics (as listed in Appendix A-1) to assess peak flows, low-flows, and overall performance. 3.2.4.2   FORECAST VERIFICATION Verification of the forecasted streamflow for 1- to 3-days lead time was completed by comparing the forecasted streamflow to the observed streamflow. For the forecast period, the following graphical techniques and statistical verification metrics will be calculated by comparing the modelled streamflow with the observed values for both daily mean streamflow and hourly streamflow for 1, 2, and 3 day lead times:  Graphical evaluation of forecast performance using streamflow hydrographs; and,  Statistical evaluation of the forecast performance by several statistical verification metrics (as listed in Appendix A-1) to assess peak flows, low-flows, and overall performance. In addition to the above assessments of forecast quality relative to the observed streamflow records, the relative forecast performance, or forecast skill, compared to two reference forecasts and one hindcast is completed. The forecast skill is assessed using the MAESS and the RMSESS skill scores according to the methods and equations in Appendix A-2 using the following three baseline streamflow series:  The forecast skill score is calculated using daily persistence forecasts as a reference forecast to evaluate the potential improvement of using the paired MIKE SHE and NWP model streamflow forecast over a daily persistence model.  The forecast skill score is calculated using a historical daily climatological forecast as a reference forecast to evaluate the potential improvement of using the paired MIKE SHE 35 and NWP model streamflow forecast over a historical climatological model using long-term daily mean streamflow.  The forecast skill score is calculated using the validation period streamflow hindcasts from the calibrated model driven by observed meteorology as a reference forecast to evaluate the skill (or lack of skill) using the paired MIKE SHE and NWP model streamflow forecast over a hindcast model using the calibrated model and meteorological observations. This is completed for a daily interval.  36 4 RESULTS AND DISCUSSION 4.1 CALIBRATION AND VALIDATION PERFORMANCE The results of the calibration and validation periods are presented together for both hourly and daily mean flows and are discussed in this section. The results from the calibration and validation periods are used to provide an evaluation of the MIKE SHE/MIKE 11 model performance in simulating hydrological processes and to provide confidence in the model and parameter optimization used for forecast simulations. The hourly and daily model performance metrics for both calibration (June 24, 2010 to June 23, 2011) and validation (June 24, 2011 to June 23, 2012) are presented in Table 4-1. Table 1-1: Performance of modelled Coquitlam River streamflow during model calibration and validation phases.  PERFORMANCE METRIC UNIT DAILY Calibration       Validation HOURLY Calibration       Validation MAE [m3/s] 2.18 1.85 2.46 2.12 PBIAS [%] -3.44 -1.89 -3.39 -2.64 NSE [-] 0.69 0.83 0.62 0.78 R2 [-] 0.72 0.84 0.66 0.79 MSLE [ln (m3/s)2] 0.22 0.13 0.25 0.16 RMSE [m3/s] 3.80 3.08 4.68 3.82 APEPa [%] -8.02 -10.7 -22.3 -13.7 AAPEPa  [%] 34.3 18.3 35.6 26.8 a) For peak flows greater than the 95th percentile. The performance metrics for the calibration and validation phases shown in Table 4-1 provide a representative set of metrics to describe how well the modelled streamflow replicates the observed streamflow for low, average, and high flows. The performance of metrics are in comparison to existing studies, including BC Hydro (2010), Bourdin (2013), Hugget (2012), and Moriasi et al. (2007). 37 The MAE, PBIAS, NSE and R2 provide an assessment of the overall model performance for accuracy and hydrograph fit. All values for both hourly and daily streamflow during the calibration and validation phase indicate a very good overall agreement of modelled streamflow with observed streamflow both in magnitude and timing. The PBIAS indicates a general under-prediction. There is improvement in all performance metrics from hourly to daily mean streamflow evaluation, and also from calibration to validation. Improvements from hourly to daily mean interval evaluation is related to the flashy nature of the watershed and challenges in modelling hourly streamflow using only one meteorological station within the watershed. Improvements from calibration to validation periods indicate that the calibrated model parameters that were optimized in the calibration period are also applicable and provide good model results in the validation period.  The MSLE provides an assessment of low-flow performance. The error is small for low flow events for both hourly and daily assessment intervals during both the calibration and validation periods, and indicates a good simulation of low, base flows. The errors are below those reported in the intercomparison study for all four models used (BC Hydro, 2010). This metric also provides an improvement from hourly to daily mean data, which is related to the flashy nature of the watershed and challenges in modelling hourly streamflow using only one meteorological station within the watershed. Improvements from calibration to validation periods indicate that the calibrated model parameters that were optimized in the calibration period are also applicable and provide good model results in the validation period for the simulation of base flow. The performance of base flow (related to groundwater flows in dry periods), is a challenge for many models (Hugget, 2012). The good performance of low (or base) flows may be due to the integrated surface and groundwater modelling system in MIKE SHE.  The RMSE, APEP, and AAPEP provide an assessment of the model performance in simulating errors related to large flows and peak flow events. The RMSE considers all paired hourly and daily streamflows, while the APEP and AAPEP consider only observed streamflows during each of the calibration and validation periods that are greater than the 95th percentile of streamflows over the entire hydrometric station record. In comparison to existing studies of peak flow performance in Pacific Northwest watersheds (BC Hydro, 2010 and Westrick et al., 2002), the current model performs well in simulating the peak flows. Peak flows are on average under-38 estimated for both the calibration and validation stages. In addition, the RMSE is considered low (Moriasi et al., 2007). Performance of peak flow simulation is a challenge due to uncertainty in meteorological and hydrometric data collection in heavy rainfall and streamflow events and orographic and precipitation phasing effects during typically fall or winter rainfall events.  While not a performance metric for hourly or daily streamflow simulation, the SWE data for two nearby stations, the Dog Mountain Station (3A10) at 1,007 masl and the Grouse Mountain Station (3A01) at 1,126 masl, were compared to model proxy stations. These observation stations are manual stations, and therefore the sample size for each period is approximately eight each year. These indicate a good agreement in SWE during the calibration and validation periods with coefficient of determination (R2) values of 0.99 and 0.96 at Grouse Mountain and Dog Mountain respectively during the calibration period, and values of 0.96 and 0.71 at Grouse Mountain and Dog Mountain respectively during the validation period. Visual comparison of the hourly and daily modelled and observed hydrographs during both the calibration and validation periods are provided below. These indicate a general good agreement with the greatest predictive errors related to peak flows and late summer snowmelt. The daily mean hydrograph for the calibration period is shown in Figure 4-1, the hourly hydrograph for the calibration period is shown in Figure 4-2, the daily mean hydrograph for the validation period is shown in Figure 4-3, and the hourly hydrograph for the validation period is shown in Figure 4-4. 39  Figure 4-1: Coquitlam River daily mean streamflow during model calibration  Figure 4-2: Coquitlam River hourly streamflow during model calibration 0102030405060Daily Mean Discharge (m3/s)DateObserved 08MH141Modelled020406080100120Hourly Discharge (m3/s)DateObserved 08MH141Modelled40  Figure 4-3: Coquitlam River daily mean streamflow during model validation  Figure 4-4: Coquitlam River hourly streamflow during model validation 0102030405060Daily Mean Discharge (m3/s)DateObserved 08MH141Modelled020406080100120Hourly Discharge (m3/s)DateObserved 08MH141Modelled41 4.2 FORECAST PERFORMANCE AND SKILL 4.2.1 FORECAST PERFORMANCE This section assesses the performance of the MIKE SHE/MIKE 11 model (forced with NWP model outputs) forecasting system accuracy compared to the observed streamflow record for lead times of 1- to 3-days. The forecast performance is evaluated for both daily and hourly intervals for the hydrograph agreement, overall accuracy, and for low-flow and high-flow performance based on hydrographs and statistical metrics. The performance of daily metrics are in comparison to existing studies, including Bourdin (2013), Weber et al. (2006), and Westrick et al. (2002). The period of forecast and observed streamflow data used for forecast verification is June 24, 2011 to June 25, 2012, for an entire year of 1- to 3-day forecasts. 4.2.1.1 FORECAST PERFORMANCE FOR DAILY MEAN STREAMFLOWS The daily mean streamflow forecast verification performance metrics are presented in Table 4-2, for daily forecasts of 1, 2, and 3-day lead times. Table 1-2: Performance of modelled Coquitlam River streamflow during forecasting period for daily mean streamflow PERFORMANCE METRIC UNIT DAILY 1-DAY                       2-DAY                       3-DAY MAE [m3/s] 2.42 2.70 2.73 PBIAS [%] -22.2 -20.6 -11.4 NSE [-] 0.73 0.69 0.43 R2 [-] 0.80 0.74 0.53 MSLE [ln (m3/s)2] 0.22 0.32 0.29 RMSE [m3/s] 3.92 4.15 5.47 APEPa [%] -33.7 -28.4 -28.7 AAPEPa  [%] 34.3 30.6 36.4 a) For peak flows greater than the 95th percentile. 42 The MAE, PBIAS, NSE and R2 provide an assessment of the overall forecast performance for accuracy and hydrograph fit for lead times of 1 to 3 days. The MAE ranges from 2.4 and 2.7 m3/s for lead times of 1 to 3 days, respectively, with increasing error as lead time increases. The PBIAS decreases with increasing lead times, from -22% to -11% showing improvement with increasing lead times and general under-prediction. Both the NSE and the R2 values indicate good forecast performance for lead times of 1 to 2 days, but decrease to a fair forecast performance for lead-times of 3 days. Based on the combination of metrics to assess the overall accuracy and hydrograph fit, the forecast performs well in forecasting streamflow magnitude and timing for lead times of 1 to 2 days and decreases in performance for a lead time of 3 days.  The MSLE provides an assessment of low-flow forecast performance. The error is small for low flow events for all lead times and indicates a good simulation of low, base flows. There is no large decrease in forecast performance for increased lead times. The errors are below those reported in the calibration and validation intercomparison study for all four models used (BC Hydro, 2010). Good low-flow performance may be due to reducing the significance of high-flow event prediction error attributed to erroneous NWP forecasts in magnitude and timing. The RMSE, APEP, and AAPEP provide an assessment of the forecast performance in prediction errors related to large flows and peak flow events. The RMSE considers all paired daily streamflows, while the APEP and AAPEP consider only observed daily streamflows that are greater than the 95th percentile of daily streamflows over the entire hydrometric station record. In comparison to existing studies of peak flow performance in Pacific Northwest watersheds (Westrick et al., 2002), the current model performs well in simulating the peak flows. Peak flows are on average under-estimated. RMSE increases as lead times increase; however, APEP and AAPEP remain relatively constant of the forecast lead time. Forecasting peak flows is a challenge due to uncertainty NWP model outputs for the magnitude and timing of peak events, as can be seen in the daily hydrographs below.  Visual comparison of the daily forecasted and observed hydrographs for lead times of 1, 2, and 3 days are provided below. These indicate a general good agreement, with the greatest forecasted errors related to high-flow events which may have been forecasted but didn’t occur. An example of such a forecasted event, which leads to large errors, can be seen during November 9 to 10, 2011 for the 3-day lead time. The daily mean hydrograph for 1-day lead time is shown in Figure 43 4-5, the daily mean hydrograph for 2-day lead time is shown in Figure 4-6, and the daily mean hydrograph for 3-day lead time is shown in Figure 4-7.  Figure 4-5: Coquitlam River forecasted daily mean streamflow for 1-day lead time  0102030405060Daily Mean Discharge (m3/s)DateObserved 08MH1411-Day Ahead Daily Forecasted44  Figure 4-6: Coquitlam River forecasted daily mean streamflow for 2-day lead time  Figure 4-7: Coquitlam River forecasted daily mean streamflow for 3-day lead time  0102030405060Daily Mean Discharge (m3/s)DateObserved 08MH1412-Day Ahead Daily Forecasted0102030405060Daily Mean Discharge (m3/s)DateObserved 08MH1413-Day Ahead Daily Forecasted67 m3/s 45 4.2.1.2 FORECAST PERFORMANCE FOR HOURLY STREAMFLOWS The hourly forecast verification performance metrics are presented in Table 4-2, for hourly streamflow forecasts for 1 to 24 hrs (1-day), 25 to 48 hours (2-day), and 49 to 72 hours (3-day) lead times. The hourly forecast performance and errors are useful for the assessment of the expected streamflow forecast error for applications such as non-storage run-of-river hydro facilities. Table 1-3: Performance of modelled Coquitlam River streamflow during forecasting period for hourly streamflow PERFORMANCE METRIC UNIT HOURLY 1-DAY                       2-DAY                       3-DAY MAE [m3/s] 3.06 3.08 2.99 PBIAS [%] -22.2 -20.6 -11.4 NSE [-] 0.56 0.53 0.27 R2 [-] 0.61 0.62 0.45 MSLE [ln (m3/s)2] 0.32 0.37 0.33 RMSE [m3/s] 5.46 5.56 6.73 APEPa [%] -34.9 -28.6 -25.6 AAPEPa  [%] 44.5 40.0 44.0 a) For peak flows greater than the 95th percentile. The performance of forecast hourly streamflow is similar to the daily mean performance in that the 1- to 2-day lead time provides a good forecast, which deteriorates for the 3-day lead time. There is a decrease in accuracy and forecast performance for all metrics for hourly intervals compared to daily intervals, as is expected when considering shorter time steps that increase the error associated with forecasted streamflow timing.  Visual comparison of the hourly forecasted and observed hydrographs for lead times of 1, 2, and 3 days are provided below. These indicate a general good agreement, with the greatest forecasted errors related to high-flow events which may have been forecasted but didn’t occur, or streamflow peaks were significantly less than forecasted. Examples of such forecasted events which lead to large errors include October 11, 2011 for the 1-day lead time, November 27, 2011 46 for the 2-day lead time, and November 9, 2011 for the 3-day lead time. The hourly hydrograph for a 1-day lead time is shown in Figure 4-8, the hourly hydrograph for a 2-day lead time is shown in Figure 4-9, and the hourly hydrograph for a 3-day lead time is shown in Figure 4-10.  Figure 4-8: Coquitlam River forecasted hourly streamflow for 1-day lead time 020406080100120Hourly Discharge (m3/s)DateObserved 08MH1411-Day Ahead Hourly Forecasted122 m3/s 47  Figure 4-9: Coquitlam River forecasted hourly streamflow for 2-day lead time  Figure 4-10: Coquitlam River forecasted hourly streamflow for 3-day lead time  020406080100120Hourly Discharge (m3/s)DateObserved 08MH1412-Day Ahead Hourly Forecasted020406080100120Hourly Discharge (m3/s)DateObserved 08MH1413-Day Ahead Hourly Forecasted114 m3/s 48 4.2.2 FORECAST SYSTEM SKILL This section assesses the improvements of the MIKE SHE/MIKE 11 model (forced with NWP model outputs) forecasting system accuracy over alternative naïve, or unskilled, alternative daily forecasts such as persistence and climatological forecasts. In addition, the forecasts skill relative to hindcast modelling using observed meteorological data is also included. Skill is assessed for daily mean streamflow. 4.2.2.1 SKILL REFERENCED TO PERSISTENCE FORECAST Improvements of the forecasting system over a persistence reference forecast, where the daily streamflow observed at the start of the forecast period is forecasted over the 1- to 3-day forecast period, are measured by the MAE and RMSE skill scores. The skill scores are shown in Table 4-4, and show forecast skill compared to persistence based forecasts for both metrics for 1- to 3-day lead times.  Table 1-4: Skill score of NWP - hydrological model forecast relative to a persistence forecast SKILL SCORE METRIC UNIT DAILY 1-DAY                       2-DAY                       3-DAY MAESS [%] 27.3 42.1 46.0 RMSESS [%] 40.3 52.4 39.4  MAESS show an increasing improvement for greater lead times with 1-day forecasts having a MAESS of 27% and 3-day forecasts having a MAESS of 46%, indicating that the persistence based forecasts deteriorates as lead times increase. RMSESS have the same skill for 1- and 3-day lead times of 40%, with an increased skill of 52% for a 2-day lead time, possibly due to individual storm event predictions in the short forecast period. The skill scores evaluated over a 1- to 3-day lead time indicate that the MIKE SHE/MIKE 11 model using NWP model outputs provides a considerable more skillful forecast relative to persistence forecasts for all evaluated lead times. This large skill can be attributed to the flashy nature of the Coquitlam River Watershed, for which high streamflow events are predominately triggered by rainfall or rain-on-snow events and have durations shorter than the forecast lead time. While challenges exist in 49 meteorological forecasting in watersheds such as the Coquitlam River watershed, there is considerable skill in forecasts from the fully-distributed MIKE SHE/MIKE 11 hydrological modelling using high-resolution NWP model outputs compared to persistence based forecasts.    4.2.2.2 SKILL REFERENCED TO CLIMATOLOGICAL FORECAST Improvements of the forecasting system over a climatological reference forecast, where the daily streamflow for the forecasted date is derived from averaging the daily mean streamflow from all historical observed records for that date (see Section 3.1.2.3 for historical records), are measured by the MAE and RMSE skill scores. The skill scores are shown in Table 4-5, and show forecast skill compared to climatological based forecasts for both metrics for 1- to 3-day lead times.  Table 1-5: Skill score of NWP - hydrological model forecast relative to a climatological forecast (historical daily mean flows for the forecasted day) SKILL SCORE METRIC UNIT DAILY 1-DAY                       2-DAY                       3-DAY MAESS [%] 51.9 46.2 44.2 RMSESS [%] 48.1 44.6 24.4  MAESS show a decrease in skill for increased lead times, with 1-day forecasts having a MAESS of 52% and 3-day forecasts having a MAESS of 44%, indicating that the accuracy of the hydrological model forecast declines as lead times increase. RMSESS also show a decrease in skill with increased lead times, with 1-day forecasts having a RMSESS of 48% and 3-day forecasts having a RMSESS of 24%. This decrease in skill scores for increased lead times is expected as meteorological forecasting error increases with longer lead times. The skill scores evaluated over a 1- to 3-day lead time indicate that the MIKE SHE/MIKE 11 model using NWP model outputs provides a considerable more skillful forecast relative to climatological forecasts for all evaluated lead times. This large skill can be attributed to the flashy nature of the Coquitlam River Watershed, for which high streamflow events are predominately triggered by rainfall or rain-on-snow events and have durations shorter than the forecast lead time and significant variations for long-term historical averages, as shown in Figure 3-2. While challenges 50 exist in meteorological forecasting in watersheds such as the Coquitlam River watershed, there is considerable skill in forecasts from the fully-distributed MIKE SHE/MIKE 11 hydrological modelling using high-resolution NWP model outputs compared to climatological based forecasts on a daily evaluation. 4.2.2.3 SKILL REFERENCED TO HINDCAST MODELLING OF OBSERVED METEOROLOGY Skill scores of the forecasting system over a hindcast model using the observed meteorological record are measured by the MAE and RMSE skill scores. The skill scores are shown in Table 4-6, and show no forecast skill for both metrics for 1- to 3-day lead times.  Table 1-6: Skill score of NWP - hydrological model forecast relative to the hindcast modelling of streamflow using observed meteorological data SKILL SCORE METRIC UNIT DAILY 1-DAY                       2-DAY                       3-DAY MAESS [%] -31.2 -46.3 -47.5 RMSESS [%] -27.2 -34.8 -77.5  The MAESS and the RMSESS for comparison of the hindcast streamflow to the forecasted streamflow are included to assess the relative skill and uncertainty reflected in the NWP model output versus the observed meteorological records. For both metrics, negative skill scores are determined for 1- to 3-day lead times with skill scores decreasing as forecasting lead times increases. The RMSESS decreases rapidly as lead time increases, indicating that the forecasted NWP model temperature and precipitation values for large precipitation events, leading to large streamflow events, decrease in accuracy as lead time increases. These results are expected as they reflect the uncertainty in the temperature and precipitation forecasts in the small, coastal, mountainous watersheds of the Pacific Northwest. 51 5 SUMMARY 5.1 CONCLUSIONS The main goals of this study were to assess the suitability of the MIKE SHE/MIKE 11 coupled model by completing a calibration and validation study using a short period of record for model calibration, and then to assess the skill of streamflow forecasts derived from the NWP model meteorological forecasts and the MIKE SHE/MIKE 11 hydrological model. The results of the study and the research contributions related to these goals are discussed below. 5.1.1 SUITABILITY OF MIKE SHE AND MIKE 11 MODEL The case study watershed and the modelling methodology are discussed in Section 3.0, and it is found that the MIKE SHE/MIKE 11 coupled model is suitable for modelling hydrologic processes in small, coastal, watersheds with complex terrain in the Pacific Northwest. In addition, the hydrologic model is suitable for using NWP model output to force the hydrologic model for streamflow forecasts. The model has not been included in recent intercomparison studies and has not been recommended due to limited validation in small watersheds with steep terrain (Pike et al., 2010). This study serves to expand the validation case studies in small watersheds with steep terrain. The following are strengths of the MIKE SHE/MIKE 11 model related to short-term forecasting using NWP model output to drive the model:  The model is fully-distributed, therefore capable of using high-resolution NWP model output without lumping meteorological inputs, and is suitable for complex terrain watersheds where precipitation phasing and orographic effect modelling are important.  The model is a fully-integrated surface and groundwater model allowing simulation of the entire hydrological cycle.  The coupled model combines hydrological modelling with hydraulic channel modelling to integrate surface water modelling and enable modelling of flow routing.  The model is a physically-based model relying on physical watershed parameters and processes, which may reduce long-period model training time.    52 5.1.2 CALIBRATION AND VALIDATION PERFORMANCE The coupled MIKE SHE/MIKE 11 model used in calibration to optimize the model parameters and in validation to validate the set of optimized parameters with a different set of meteorological input parameters performed well with good agreement for high, average and low flows. The modelled streamflow was compared to the observed gauge station data on the Coquitlam River above Coquitlam Lake. In comparison to similar studies and the guidelines for model calibration and validation, the MIKE SHE/MIKE 11 performed well for both hourly and daily mean streamflow based on hydrographs and a wide range of performance metrics, and in many cases better than values reported for similar modelling studies. Based on the results of this study, the MIKE SHE/MIKE 11 coupled model should be considered for watershed modelling in small, coastal, mountainous watersheds of the Pacific Northwest in addition to the currently used models. It should be noted that the resulting statistics are representative of the short periods of calibration and validation.  5.1.3 FORECAST PERFORMANCE AND SKILL A set of performance metrics and hydrograph comparisons were used to assess the forecast performance in predicting the overall accuracy, hydrograph fit, and agreement of base and peak streamflow with observed streamflow records on the Coquitlam River above Coquitlam Lake. The forecast performance was evaluated for both daily mean streamflow and hourly streamflow. Forecasts performed well at predicting base-flows for all lead times and for overall hydrograph fit and accuracy for lead times of 1- to 2-days. The forecast performance decreased for the 3-day lead times as expected due to the difficultly of correctly forecasting large rainstorms for coastal watersheds in the Pacific Northwest for lead times greater than 2 days. In addition, the forecast performance was sensitive to the evaluation interval with the daily mean streamflow performance metrics being better than those for the hourly streamflow.   Deterministic short term streamflow forecasts for 1- to 3-day lead times using the MIKE SHE/MIKE 11 model driven by NWP model output were skillful for all lead times compared to persistence and climatological reference forecasts, with forecast skill generally between 25 and 50% for MAESS  and RMSESS. This forecast skill is an effective performance measure for forecast users to provide a comparison to alternative forecasts. Use of short-term forecasts from 53 hydrologic models driven with high-resolution NWP outputs allows for improved forecasts for non-storage hydro electricity production and flood risk management. These improved forecasts also allow for improved decision making when compared to decisions based on persistence or climatological forecasts.   5.1.4 RESEARCH CONTRIBUTION Research into this area indicates that MIKE SHE/MIKE 11 should be considered as a suitable fully-distributed, physically-based model for river forecasts based on high-resolution NWP models, and that there is the opportunity for short-term forecast skill in small, mountainous, Pacific Northwest watersheds with limited observed data. Forecasts from hydrological models with NWP input to provide real-time modelling have provided forecast skill in comparison to persistence or historical average based forecasts. In addition, the investigation into daily and sub-daily time intervals for model evaluation indicate that the results are sensitive to the time interval selected for evaluation, and that sub-daily time-intervals for model evaluation should be considered in studies of small, mountainous, Pacific Northwest watersheds. 5.2 LIMITATIONS The following are limitations of this hydrologic forecast system study:  This study is for a deterministic forecast considering one NWP model output rather than an ensemble of forecasts to provide a range and probability distribution of predictions. The numerical results of this study are therefore applicable to the selected NWP model, with the methodology and applicability relevant for ensemble forecasts.  The selected watershed has not been previously assessed for short-term streamflow forecasts, and therefore there is no comparison to evaluate the site-specific skill over alternative modelling systems.  Due to a short data period-of-record, performance of the short-term forecasts is subject to limited sample size, and is therefore influenced by individual events. The performance and skill determined in this study are representative of the forecast period (June 2011 to June 2012).  54 5.3 FUTURE WORK Future work for this research should further study the use of the coupled MIKE SHE/MIKE 11 hydrologic model relative to alternative models when using distributed, high-resolution NWP models to forecast hydrologic processes and investigate the benefits of the application of the forecasting system. A number of the areas for future work are outlined in the limitations section, with additional suggestions below:  Use MIKE SHE/MIKE 11 in a model intercomparison study to assess performance and forecast skill using hydrologic and NWP models in small, coastal watersheds with complex terrain.  Increase period-of-record for the assessment of forecast performance and skill by using archiving NWP model output for a selected watershed over a greater time period.  Use MIKE SHE/MIKE 11 with ensemble NWP forecasts, and therefore ensemble streamflow forecasts, to study the probabilistic forecast performance and skill.  Study the applications short-term forecasting with a hydrologic model driven with high-resolution NWP forecasts in small, mountainous coastal watersheds. 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The range of metrics are intended to provide suitable characterization of the model predictive skill over the entire hydrograph (low, high, and average streamflows), and responses to both precipitation events and snowmelt. For the metrics, the following definitions apply:  𝑇 = set of time points for the evaluation   ‖𝑇‖ = The size of 𝑇 (varies for analysis time step)  𝑡 = internal counter for the evaluation set of time points 𝑇  𝑚𝑡 = modelled (or forecast) streamflow at time 𝑡  ?̅?𝑡 = mean modelled (or forecast) value over all t in 𝑇  𝑜𝑡 = observed streamflow at time 𝑡  ?̅?𝑡 = mean observed value over all t in 𝑇  Mean Absolute Error (MAE) The MAE is an accuracy metric characterizing the average absolute agreement between modelled (or forecasted) and observation pairs, useful for evaluation over the entire range of flows. It is a reliable and robust measure less sensitive to large residuals and errors in the timing of flows than squared error statistics (Weber et al., 2006). A perfect score is zero, and the score is in the units of the parameter of interest.   Equation A-1: Mean Absolute Error (MAE) 𝑀𝐴𝐸 =1‖𝑇‖∑|𝑚𝑡 − 𝑜𝑡|𝑡∈𝑇  64 Percent Bias (PBIAS) PBIAS measures the average propensity of modelled (or forecasted) data to be greater or less than the observed pair. Low values suggest accurate model simulation of flow volumes. Negative values indicate model underestimation, and positive values indicate model overestimation (Moriasi et al., 2007). The optimal value of PBIAS is zero.   Equation A-2: Percent Bias (PBIAS) 𝑃𝐵𝐼𝐴𝑆 = [∑ (𝑚𝑡 − 𝑜𝑡)𝑡∈𝑇  × 100∑ (𝑜𝑡)𝑡∈𝑇]  Nash-Sutcliffe Efficiency (NSE) The NSE is commonly the measure of choice for reporting (and comparing) model performance (Gupta et al., 2009). It is an indicator of statistical association that determines the relative magnitude of the residual variance in reference to the observed data variance (Nash and Sutcliffe, 1970). Gupta et al. (2009) decibes it in this way, “NSE can be interpreted as a classic skill score (Murphy, 1988), where skill is interpreted as the comparative ability of a model with regards to a baseline model, which in the case of NSE is taken to be the ‘mean of the observations’ (i.e., if NSE = 0, the model is no better than using the observed mean as a predictor)”. NSE can range from -∞ to 1, and is subject to maximization, where 1 indicates a perfect forecast.   Equation A-3: Nash-Sutcliffe Efficiency (NSE) 𝑁𝑆𝐸 = 1 −∑ (𝑜𝑡 −𝑚𝑡)2𝑡∈𝑇∑ (𝑜𝑡 − ?̅?𝑡)2𝑡∈𝑇     65 Coefficient of Determination (R2) R2 provides the percentage of the variance that is explained by a linear relationship between the model (or forecast) and the observations, or the degree of collinearity. R2 ranges from 0 to 1, with greater values indicating less error variance. R2 is sensitive to extreme values and are insensitive to proportional differences between modelled and observed data (Legates and McCabe, 1999). A perfect score is 1.   Equation A-4: Coefficient of Determination (R2) 𝑅2 = [∑ (𝑚𝑡 − ?̅?𝑡)𝑡∈𝑇 (𝑜𝑡 − ?̅?𝑡)√∑ (𝑚𝑡 − ?̅?𝑡)2𝑡∈𝑇 ∑ (𝑜𝑡 − ?̅?𝑡)2𝑡∈𝑇]2  Root Mean Square Error (RMSE) The RMSE is an indicator of overall performance in forecasting the hydrograph, but places greater emphasis on large streamflow error than MAE. Perfect modelled or forecast hydrographs have an RMSE of zero, and the score is in the units of the parameter of interest. Equation A-5: Root Mean Square Error (RMSE) 𝑅𝑀𝑆𝐸 = √1‖𝑇‖∑(𝑚𝑡 − 𝑜𝑡)2𝑡∈𝑇  Mean Squared Logarithmic Error (MSLE) The MSLE is a metric that evaluates the performance of the low-flow modelled (or forecast flows). A perfect score is zero.   Equation A-6: Mean Squared Logarithmic Error (MSLE) 𝑀𝑆𝐿𝐸 =1‖𝑇‖∑(𝑙𝑛(𝑚𝑡) − 𝑙𝑛(𝑜𝑡))2𝑡∈𝑇 66 Average Percent Error in Peak Flows (APEP) APEP measures the average percent error of a sub-set of streamflows that are selected as peak events. In studies with long period-of-records, this may be annual maximum peaks. However in this study, selected observed peak events were chosen as observations greater than the 95th percentile to provide an adequate sample size, but also to represent the hydrologic processes that may cause peak flows (both snowmelt and precipitation events). The average error of the modelled (or forecasted) peak and observed pairing represents the error in timing and magnitude.  Equation A-7: Average Percent Error in Peak Flows (APEP) 𝐴𝑃𝐸𝑃 =1‖𝑇‖∑(𝑚𝑡 − 𝑜𝑡)𝑜𝑡× 100𝑡∈𝑇  Absolute Average Percent Error in Peak Flows (AAPEP) Similarly to APEP, AAPEP measures the average percent error of a sub-set of streamflows that are selected as peak events, but considers the absolute value of the error. Equation A-8: Absolute Average Percent Error in Peak Flows (AAPEP) 𝐴𝑃𝐸𝑃 =1‖𝑇‖∑|𝑚𝑡 − 𝑜𝑡|𝑜𝑡× 100𝑡∈𝑇  67 A-2 SKILL SCORE METRICS The skill score metrics described in this Appendix were applied to the forecast streamflow to assess forecast skill relative to reference forecasts. Reference forecasts include daily persistence, climatological (historical mean daily flows), and hindcast streamflows derived from the hydrologic model when observed meteorological data is used to drive the model. The methods for all of the skill assessments are provided in the main body. The forecast skill, also known as the relative performance or relative accuracy, of the forecast to some reference forecast is assessed using two statistical verification metrics, namely the MAE and the RMSE. Skill Score (SS) is defined as the percentage difference between statistical verification scores for two sets of forecasts (i.e., the operational forecasts and the reference forecast). The equations used for the skill assessments have the following form:  Mean Absolute Error Skill Score (MAESS) Equation A-9: Mean Absolute Error Skill Score (MAESS) 𝑀𝐴𝐸𝑆𝑆 = 1 −𝑀𝐴𝐸 (𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡)𝑀𝐴𝐸 (𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡) X 100%  Root Mean Square Error Skill Score (RMSESS) Equation A-10: Root Mean Square Error Skill Score (RMSESS) 𝑅𝑀𝑆𝐸𝑆𝑆 = 1 −𝑅𝑀𝑆𝐸 (𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡)𝑅𝑀𝑆𝐸 (𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡) X 100%  68 APPENDIX B – MODELLING PARAMETERS  Table B-1: Watershed parameter sources of information and values Model Input Parameter or Rate Units Range of Values Calibrated Model Value(s) Data Source Precipitation Lapse Rate %/m 0.025 – 0.062 0.040 (BCMOE, 2015)  (Dickerson, 2010) (Jakob and Weatherly, 2003) (Stahl et al., 2008) Temperature Lapse Rate oC/km   -3.5 – -6.25  (monthly or annual averages) Daily variable based on paired regional meteorological stations (90% of data within +0.15 and -0.84) (BCMOE, 2015)  (Bunnell et al., 1985)  (Dickerson, 2010) (Minder et al., 2010) (Stahl et al., 2006) (Stahl et al., 2008) Degree Day Melt Coefficient (DDMC) mm/oC/day 1.8 – 6.0 Seasonal variable to a maximum of 3.75 in July and August (Graves and Chang, 2007) (Pipes and Quick, 1987) (Moore et al., 2011) (Rango and Martinec, 1995) (Stahl et al., 2008) (USACE, 1998) Max Wet Snow Fraction - 0.10 – 0.19 0.12 (Singh et al., 1998) (USACE, 1998) (Williams et al., 1999) Melting Coefficient for Thermal Energy in Rain / oC N/A 0.0125 (Fickenscher, 2006)  (USACE, 1998) Leaf Area Index (LAI) - 3.0 - 8.6 7 (Humphreys et al., 2006) (Sias, 2003) Canopy Interception % 14 – 40 25 (Bunnell et al., 1985)  (Moore et al., 2011) (Sias, 2003) (Bixby, 2011) (Plamondon et al., 1984) 69 Root Depth Constant m 0.6 – 1.4 0.9 (D’Anjou, 2002)  (Eis, 1973) (Humphreys et al., 2006) Detention Storage Depth mm 3.0 – 10.0 6.4 (Masch, 1984) (Pike et al., 2010) Surface Layer Lateral Hydraulic Conductivity m/s 1.0x10-6 – 1.0x10-3 1.0x10-5 (Dickerson, 2010) (Saxton et al., 1986) Surface Layer Vertical Hydraulic Conductivity m/s 1.0x10-6 – 1.0x10-3 1.0x10-5 (Dickerson, 2010) (Saxton et al., 1986) Surface Layer Depth m 0.7 – 3.5 1.5 (BCMOE, 2015) (D’Anjou, 2002) (Dickerson, 2010) (Jakob and Weatherly, 2003) Lower Layer Hydraulic Conductivity m/s 1.0x10-8 – 1.0x10-5 1.0x10-6 (BCMOE, 2015) (D’Anjou, 2002) (Dickerson, 2010) (Jakob and Weatherly, 2003) Mannings Number for Channel Flow  (m1/3/s)-1 0.03 – 0.07 0.04 (Masch, 1984) Strickler Number for Overland Sheet Flow m1/3/s 1 – 20 10 (Masch, 1984)  

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