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An investigation into the Flow Duration Curve in eastern United States : environmental controls and prediction… Wafa, Chouaib 2018

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AN INVESTIGATION INTO THE FLOW DURATION CURVE IN EASTERN UNITED STATES: ENVIRONMENTAL CONTROLS AND PREDICTIONS AT UNGAUGED BASINS by  Wafa Chouaib Eng., National Agronomic Institute of Tunis (INAT), 2007 M. Sc., Land and Water Management, IAM-Bari, Italy, 2009 M. Sc., Geomatics, National School of Engineers, Tunis, 2012  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Forestry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) May 2018  © Wafa Chouaib, 2018 ii  Abstract The Flow Duration Curve (FDC) is a probabilistic flow representation relevant to streamflow investigation and physical understanding given its use in wide range of hydrological and ecological applications. A regional study that investigates FDCs and their prediction at ungauged catchments is important to develop causal models and provide insights to solve issues of water resources planning and management of aquatic ecosystems and habitats. Hydrological modelling and model parametrization in gauged and ungauged catchments are fundamental steps preceding the regional investigation of flow response using FDC. By means of Sacramento rainfall-runoff model (SAC-SMA), in 73 catchments from the eastern United States, I investigated the effect of SAC-SMA a priori parameters in the constrained calibration of the model. This analysis revealed and discussed limitations of a priori parameters that are intensively used to facilitate model calibration and make predictions at ungauged basins (PUB). The PUB using parameter transfer within homogeneous regions of similar climate and flow characteristics outweighed in performance the a priori parameters. The FDC was advantageous in revealing the effect of lack of efficiency and bias. A parameter regionalization approach is more efficient for PUB than a priori parameters. The ultimate limitations of the within-region parameter transfer are recognized and discussed.  The interaction between climate and landscape properties was central to develop the physical understanding of the FDC. The high precipitation variability does not necessarily lead to FDC of a steep slope. Characteristics of the catchment— equivalent to a precipitation filter— interplayed with the precipitation and affected FDC shapes. The analysis highlighted the role of soil infiltration rates in specific conditions of soil moisture storage capacity and predominant runoff generation mechanism. The study revealed that processes underlying FDC and the FDC shapes are by far iii  more complex than being characterized in the wider literature using characteristics of landscape or climate.  In conditions of humid climate and perennial flow, a meta-analysis utilizing a process-based investigation showed that mean monthly runoff FDC —readily available at ungauged catchments—predicts only FDC middle third (exceedance probabilities between 33% and 66%). The method is constrained by the value of flow variability (slope of the FDC).  iv  Lay Summary This regional study analyzes the environmental controls of Flow Duration Curve (FDC) and explores ways to predict FDC at ungauged catchments. The FDC is a probabilistic flow representation that helps to solve issues of water resources planning and management of aquatic ecosystems and habitats. In order to meet the specified objectives, the study was undertaken in 73 catchments from the eastern United States and utilized the Sacramento model (SAC-SMA). The findings demonstrated that interaction between climate and landscape properties was central to advance understanding of FDC shapes. At ungauged catchments, the use of mean monthly runoff data —more readily available— allows prediction of FDC middle-third. The method is possible only in catchments with flatter slope of the FDC. The transfer of calibrated SAC-SMA model parameters from gauged catchments within homogeneous regions of similar climate and flow characteristics yielded higher predictive performance at ungauged catchments than soil-derived a priori parameters.           v  Preface All components of the research presented herein represent original work for which I have been the lead investigator. I conceived the research questions under the consultation of my supervisor and committee members. I collaborated with Pr. Murugesu Sivapalan in early stages of data collection and development of experimental design. I conducted the data analysis, interpretation, and drafted the manuscripts. Pr. Y. Alila supervised both the content and interpretations of several parts in this research project and edited the manuscripts. P.V Caldwell helped with fruitful discussions on the findings and edited the manuscripts. Chapters in this dissertation have been presented in international conferences, accepted for publication, or under review in peer review journals:  Chapter 3 A version of chapter 3 is under a Journal’s review  Chouaib, W., Alila, Y., Caldwell, PV., 2018. Evaluation of Sacramento a priori parameters and their effect on constrained calibration at regional scale. (under review)   Chapter 4 A version of Chapter 4 is published in the Journal of Hydrology  Chouaib, W., Alila, Y. and Caldwell, P.V., 2018. Parameter transferability within homogeneous regions and comparisons with predictions from a priori parameters in the eastern United States. Journal of Hydrology. A portion of this chapter has been presented at AGU Fall Meeting 2016, San Francisco.  Chapter 5  A version of chapter 5 is published in the Journal of Hydrology vi  Chouaib, W., Caldwell, P.V. and Alila, Y., 2018. Regional variation of flow duration curves in the eastern United States: Process-based analyses of the interaction between climate and landscape properties. Journal of Hydrology, 559, pp.327-346.  Parts of Chapter 5 have been presented in doctoral IUFRO meeting in Oregon State University, 2016 and in the 12th Kovacs Colloquium at UNESCO Headquarters in Paris  Chapter 6  A version of Chapter 6 is under Journal’s review. Chouaib, W., Alila, Y., Caldwell, PV., 2018. On the use of mean monthly runoff to predict the flow duration curve at ungauged catchments. (under review)    vii  Table of Contents  Abstract .......................................................................................................................................... ii Lay Summary ............................................................................................................................... iv Preface .............................................................................................................................................v Table of Contents ........................................................................................................................ vii List of Tables ............................................................................................................................... xii List of Figures ............................................................................................................................. xiii List of Symbols ......................................................................................................................... xviii List of Abbreviations ................................................................................................................. xix Acknowledgements .................................................................................................................... xxi Dedication ................................................................................................................................. xxiv Chapter 1: Introduction ................................................................................................................1 1.1 Motivation for the study.................................................................................................. 1 1.2 Research objectives ......................................................................................................... 5 1.3 Thesis overview .............................................................................................................. 6 Chapter 2: Dataset and study area ...............................................................................................8 2.1 Dataset............................................................................................................................. 8 2.2 Study area........................................................................................................................ 9 Chapter 3: Evaluation of Sacramento a priori parameters and their effect on constrained calibration at regional scale ........................................................................................................13 3.1 Introduction ................................................................................................................... 13 3.2 Methods......................................................................................................................... 16 viii  3.2.1 Overview ................................................................................................................... 16 3.2.2 The homogeneous regions used in the analysis ........................................................ 17 3.2.3 SAC-SMA model structure calibration ..................................................................... 18 3.2.3.1 Model parameters and physical meaning .......................................................... 18 3.2.3.2 SAC-SMA model constrained calibration ........................................................ 20 3.2.3.3 Topographic index distribution for each catchment ......................................... 21 3.3 Results ........................................................................................................................... 23 3.3.1 Model performance using a priori and calibrated parameters .................................. 23 3.3.2 Analysis of predictions from a priori parameters and constrained calibration: the catchment landscape properties and runoff processes .......................................................... 25 3.4 Discussion ..................................................................................................................... 29 3.5 Conclusions ................................................................................................................... 35 Chapter 4: Parameter transferability within homogeneous regions and comparisons with predictions from a priori parameters in the eastern United States.........................................37 4.1 Introduction ................................................................................................................... 37 4.2 The homogeneous regions used in parameter transfer: specific characteristics ........... 41 4.3 Methods......................................................................................................................... 43 4.3.1 Overview ................................................................................................................... 43 4.3.2 Evaluation of the prediction at ungauged catchments using a priori parameters ..... 44 4.3.3 Parameter transfer (TRANS_IN) .............................................................................. 44 4.3.4 TRANS_OUT ........................................................................................................... 45 4.3.5 Interpretation of SAC-SMA parameters transferability ............................................ 46 4.4 Results and discussion .................................................................................................. 47 ix  4.4.1 Performance of parameter transferability and a priori parameters ........................... 47 4.4.2 Evaluation, interpretation, and discussion of parameter transferability and a priori parameters ............................................................................................................................. 51 4.4.2.1 Which approach to use for PUB, the a priori parameters or the parameter regionalization? ................................................................................................................. 59 4.4.3 Comparison with previous studies ............................................................................ 60 4.5 Conclusions ................................................................................................................... 61 Chapter 5: Regional variation of flow duration curves in the eastern United States: Process-based analyses of the interaction between climate and landscape properties ..........63 5.1 Introduction ................................................................................................................... 63 5.2 Methods......................................................................................................................... 66 5.2.1 Storm separation ....................................................................................................... 68 5.2.2 Soil moisture storage capacity .................................................................................. 69 5.2.3 Slope of the empirical FDC ...................................................................................... 69 5.2.4 Precipitation duration curve and catchment filter ..................................................... 70 5.3 Results ........................................................................................................................... 71 5.3.1 Effects of landscape properties ................................................................................. 71 5.3.1.1 Climate clusters ................................................................................................. 71 5.3.1.2 Precipitation variability from slopes of precipitation duration curves .............. 72 5.3.1.3 Soil moisture storage capacity .......................................................................... 73 5.3.1.4 The regional variation of the FDC: categories of flow variability .................... 74 5.3.1.5 Effect of catchment filter on precipitation and flow duration curves ............... 78 5.3.2 Process understanding of the FDC regional variation .............................................. 80 x  5.3.2.1 Aspect of flow component FDCs ...................................................................... 80 5.3.2.2 Predominant runoff generation mechanism across the eastern US ................... 82 5.3.2.3 FDC regional variation in relation to the pattern of runoff generation mechanism ........................................................................................................................ 84 5.3.2.4 Flow components of the FDC with regards to precipitation: process understanding of the catchment filter ............................................................................... 86 5.4 Discussion ..................................................................................................................... 86 5.4.1 To what extent the diversity of FDC shapes can be explained by climate and landscape properties? ............................................................................................................ 87 5.4.2 Process-based understanding of the spatial pattern of FDCs .................................... 92 5.5 Conclusions ................................................................................................................... 95 Chapter 6: On the use of mean monthly runoff to predict the flow duration curve at ungauged catchments...................................................................................................................97 6.1 Introduction ................................................................................................................... 97 6.2 Methods: Analysis of the MM_FDC in relation to the FDC ...................................... 100 6.3 Results ......................................................................................................................... 101 6.3.1 Variation of the MM_FDC in comparison to the FDC ........................................... 101 6.3.2 FDC portions in comparison to the MM_FDC ....................................................... 104 6.4 Discussion ................................................................................................................... 108 6.4.1 Interpretation of the FDC portions in comparison to the MM_FDC ...................... 108 6.4.1.1 FDC upper third .............................................................................................. 108 6.4.1.2 FDC middle third ............................................................................................ 109 6.4.1.3 FDC lower third .............................................................................................. 111 xi  6.4.2 Catchments and flow conditions where it is possible to predict the FDC using MM_FDC ............................................................................................................................ 113 6.4.3 Conceptual model of the FDC and MM_FDC ........................................................ 115 6.5 Conclusion .................................................................................................................. 116 Chapter 7: Conclusions .............................................................................................................118 7.1 Novelty and contribution to the wider literature ......................................................... 118 7.2 Summary and conclusions .......................................................................................... 119 7.3 Limitations and future recommendations ................................................................... 121 7.3.1 Use of a priori parameters in constrained calibration ............................................. 121 7.3.2 Parameter regionalization for prediction at ungauged catchments ......................... 122 7.3.3 FDC environmental controls and process-based predictions of the FDC at ungauged catchments........................................................................................................................... 123 Bibliography ...............................................................................................................................125 Appendix .....................................................................................................................................150 Table A1: Study catchments’ descriptors ............................................................................... 150  xii  List of Tables  Table 3-1:    Correlation between NS and predominant soil hydrologic groups in the study regions ........................................................................................................................................... 26 Table 4-1:  region’s main descriptors ........................................................................................... 43 Table 4-2: average statistics of the different simulations across clusters in calibration and validation periods .......................................................................................................................... 47 Table 6-1: Correlation of SSFDC and FDC slopes using normalized curves ............................ 107  xiii  List of Figures  Figure 1-1: Flow chart of the study steps........................................................................................ 5 Figure 2-1: (a) catchment size distribution, (b) mean monthly precipitation (mm) ..................... 10 Figure 2-2: (a) HGB soils proportions, (b) HGC soils proportions, (c) HGA soils proportions. . 11 Figure 3-1: SAC-SMA model conceptualization .......................................................................... 19 Figure 3-2: (a) catchments classification according to Sawicz et al. (2011) and DEM, b) CDFs of NS coefficients across regions in  calibration period, CDFs of NS coefficients from APRIORI and CAL simulation during the calibration and validation (c) in C1, (d) in C2, (e) in C3, (f) in C5....................................................................................................................................................... 24 Figure 3-3: (a) CDFs of HGB soil proportions across regions, (b) CDFs of HGA soil proportions across regions, (c) CDFs of HGC soil proportions across regions ............................................... 25 Figure 3-4: The parameters variability in each region where Sdv_APRIORI and sdv_CAL denote the normalized standard deviations of each parameter by median of the parameters standard deviation during APRIORI and CAL, respectively.  We use the median for normalization same as in Gan and Burges et al. (2006). ............................................................................................... 27 Figure 3-5: (a) spatial distribution of TI groups designated as TI classification in the map (b) frequency distribution of topographic index per catchment. ........................................................ 29 Figure 4-1: (a) regions in the eastern US, the catchments highlighted in squares are the donor catchments in each region (b) whisker plots of snow day ratio (SDR), (c) whisker plots of aridity index (AI) ...................................................................................................................................... 42 Figure 4-2: (a) mean monthly hydrograph (MMH) and FDC of a typical catchment from C1 with NS 0.80, 0.74 at  APRIORI, and TRANS_IN, respectively, (b) MMH and FDC in a typical xiv  catchment from C5 with  NS 0.79, 0.78, 0.73 at APRIORI, TRANS_IN, and TRANS_OUT, respectively, (c) MMH and FDC in a typical catchment from C2 with NS 0.55, 0.6, 0.55 at APRIORI, TRANS_IN, and TRANS_OUT, respectively, (d) MMH and FDC in a typical catchment from C3 with NS 0.7, 0.72, 0.71 at APRIORI, TRANS_IN, and TRANS_OUT, respectively ................................................................................................................................... 49 Figure 4-3: The median percent error of the FDC at several flow percentiles (10%, 25%, 50%, 75%, and 90%) in each region ...................................................................................................... 50 Figure 4-4: The mean catchment elevation in each region ........................................................... 53 Figure 4-5: (a) whisker plots of HGB soils proportion across the regions; (b) whisker plots of HGC soils proportion across the regions;  (c) whisker plots of HGA soils proportion across the regions ........................................................................................................................................... 54 Figure 5-1: A conceptual diagram illustrating the workflow of the investitation. In the step 1, we identify the climate clusters. In the step 2, we analyze the precipitation duration curve (PDC) of each catchment in the cluster. In the step 3, we analyze the catchments’ properties (topography, soil hydrologic properties, soil moisture storage capacity (SMSC)) except from other factors that deals with the bedrock structure and geomorphology.  In the step 4, we investigate the SFDCs (slope of the FDCs) to study the regional variation of the FDCs that results from the interaction between the landscape properties and the precipitation variability (measured by the slope of the PDC). It is the catchment filter stage that assesses how strong the catchment system is in filtering the precipitation.  We complement the investigation with analyses of the runoff processes using the topographic index (TI) and the flow component FDCs. ......................................................... 68 Figure 5-2: (a) catchments classification into three clusters according to storm seasonality (b) seasonal variation of storm characteristics in C3 cluster (c) seasonal variation of storm xv  characteristics in C2 cluster (d) seasonal variation of storm characteristics in C1 cluster. The squares on the map denote the catchments with PDCs dipping at 50%. ...................................... 72 Figure 5-3: (a) CDFs of the slopes of PDCs across clusters (b) normalized PDCs in C2 cluster by mean annual daily precipitation (c) normalized PDCs in C3 cluster by mean annual daily precipitation (d) normalized PDCs in C1 cluster by mean annual daily precipitation. ................ 73 Figure 5-4: (a) Regional variation of soil moisture storage capacity (b) cumulative distribution function (CDF) of soil moisture storage capacity (c) CDF of forest cover for each cluster (d) CDF of mean elevation for each cluster (e) CDF of HGC soils for each cluster (f) correlation between forest cover and SMSC (g) correlation between catchment mean elevation and SMSC (h) correlation between HGC and SMSC. .................................................................................... 75 Figure 5-5: (a) Regional variation of FDC slopes; the square shape refers to catchments with small SMSC and flat FDC. The oval shape highlights catchments with large SMSC and steep FDC; (b) normalized FDCs in C3 cluster; (c) normalized FDCs in C2 cluster; (d) normalized FDCs in C1 cluster; (e) the CDFs of the SFDCs across clusters; (f) the SFDC-SMSC correlation; (g) SFDC-HGC correlation ........................................................................................................... 77 Figure 5-6: (a) The spatial pattern of rain filter; the oval shape highlights the catchments we used for the parameter permutation in section 4.2.3 (b) CDFs of the filter across clusters (c) the correlation between SMSC and the catchment filter (d) the correlation between the proportions of HGC soils and the catchment filter........................................................................................... 79 Figure 5-7: (a) Baseflow FDC, interflow FDC, and surface flow FDC for catchments with large SFDCs (b) Baseflow FDC, interflow FDC, and surface flow FDC for catchments with small SFDCs. All the curves are normalized by the mean annual daily flow as in Yokoo and Sivapalan et al. (2011) ................................................................................................................................... 80 xvi  Figure 5-8: (a) median baseflow FDC, median interflow FDC, and median surface flow FDC for catchments with large SFDCs (b) median baseflow FDC, median interflow FDC, and median surface flow FDC for catchments with small SFDCs. All the curves are normalized by the mean annual daily flow (Qm) as in Yokoo and Sivapalan et al. (2011)................................................. 81 Figure 5-9: (a) spatial distribution of TI groups designated as TI classification in the map across catchments of similar storm characteristics; (b) frequency distribution of topographic index per catchment. Three different groups were identified; the right skewed (predominant saturation excess), the middle, and left skewed (predominant subsurface stormflow). ................................ 83 Figure 5-10: a) The CDF of SMSCs in each TI cluster (b) the CDF of SFDCs in each TI cluster (c) the CDF of subsurface flow index per TI cluster (d) CDF of surface flow index per TI cluster (e) CDF of baseflow index per TI cluster (f) CDF of interflow index per TI cluster. The baseflow index was calculated from the ratio of base flow to total streamflow (Schaake et al., 2006). The other flow indices were determined using the same approach. The subsurface flow index was calculated after summing up the baseflow and the interflow. ...................................................... 83 Figure 5-11: Flow component FDCs for representative catchments from each TI cluster (a) a catchment from left skewed TI distribution, (b) a catchment from right skewed TI distribution, (c) a catchment from middle TI distribution. ................................................................................ 84 Figure 5-12: (a) flow component FDCs for a catchment with 55% HGC and 30% HGB (b) flow component FDCs for a catchment with 11% HGC and 74% HGB (c) flow components FDC for catchment in (b) using model parameters from catchment in (a). Qobs is observed flow response, Qsim is the simulated flow, P is the daily precipitation. The suffix “b” refers to base conditions prior to parameter permutations. The suffix “s” refers to the permutation scenario. ................... 85 xvii  Figure 6-1: (a) Regional variation of SFDC (modified from Fig. 5-5(a)), (b) regional variation of MM_FDC, (c) SFDC and SMM_FDC correlation ..................................................................... 102 Figure 6-2: (a) FDC and MM_FDC in catchments with small SFDC, (b) FDC and MM_FDC in catchments with large SFDC ...................................................................................................... 103 Figure 6-3: SFDC (slope of FDC) and SMM_FDC (slope of MM_FDC) in catchments with steeper slope of the FDC and milder slope of the FDC .............................................................. 104 Figure 6-4: normalized flow (nQ), normalized MM_FDCs (nQ_reg) (a) and (b) in catchments with steeper slope of the FDC, (c) and (d) in catchments with milder slope of the FDC. The curves were normalized by the mean annual daily flow (Qm) ................................................... 105 Figure 6-5: normalized flow (nQ), normalized simulated flow (nQsim), normalized subsurface flow (nQss) in catchments with steeper FDC (a) and (b); in catchments with milder FDC (c) and (d). The curves were normalized by the mean annual daily flow (Qm) ..................................... 106 Figure 6-6: Cumulative Distribution Function (CDF) of the SFDC and SSFDC in catchments with (a) steeper slope of the FDC and (b) catchments with milder slope of the FDC ................ 108 Figure 6-7: conceptual model of the FDC in conditions of humid climate and perennial runoff in (a) catchments with milder slope of the FDCs and (b) in catchments with steeper slope of the FDC. ............................................................................................................................................ 116  xviii  List of Symbols θfld               Water content at field capacity, %  θs                 Water content at saturation, % θwlt              Water content at wilting point, % Ks               hydraulic conductivity at saturation, m/s  xix  List of Abbreviations ADIMP Maximum fraction of an additional impervious area due to saturation AI    Aridity index APRIORI Prediction using SAC-SMA a priori parameters BFI Baseflow index CAL Prediction using calibrated SAC-SMA parameters ET Evapotranspiration, mm FDC Flow Duration Curve HGA Soil hydrologic group A, % HGB Soil hydrologic group B, % HGC   Soil hydrologic group C, % LZFPM   The lower layer primary free water capacity, mm LZFSM Lower layer supplemental free water capacity, mm LZPK   Depletion rate of the lower layer primary free water storage, day-1 LZSK   Depletion rate of the lower layer supplemental free water storage, day-1 LZTWM   Lower layer tension water capacity, mm MAP Mean annual precipitation MM_FDC Mean monthly flow FDC MOPEX Model Parameter Experiment NS Nash-Sutcliffe coefficient PCTIM Permanent impervious area fraction PDC    Precipitation Duration curve   xx  PET Potential evapotranspiration, mm PFREE   Percolation fraction that goes directly to the lower layer free water storages PRISM Planning Tool for Resource Integration, Synchronization, and Management REXP Shape parameter of the percolation curve SAC-SMA        Sacramento Soil Moisture Accounting Model SDR   Snow Day Ratio SFDC   Slope of the FDC SMM_FDC        Slope of the MM_FDC SMSC Soil moisture storage capacity, mm SPDC Slope of the precipitation duration curve SSFDC Subsurface flow FDC SSURGO Soil Survey Geographic Database STATSGO State Soil Geographic Database TI Topographic Index TRANS_IN        Calibrated model parameter transfer within homogeneous regions TRANS_OUT    Calibrated model parameter transfer irrespective of homogeneous regions UZFWM   Upper layer free water capacity, mm UZK Interflow depletion rate from upper layer free water storage, day-1 UZTWM The upper layer tension water capacity, mm ZPERC Ratio of maximum and minimum percolation rates  xxi  Acknowledgements It is until this moment when I realize that my PhD program comes to an end and I have to get ready for new challenges in life. I found that the quotation of Hellen Keller “Life is either a daring adventure or nothing at all!” the most suited to describe the wisdom I gained throughout my PhD journey. I became mother a couple of months after enrollment and found myself responsible for two new born; my son and my PhD. Both required huge attention and care. It was simply amazing watching my son developing new skills through days and myself grow in experience and understanding.  I owe a debt of thanks to many people since it is their generous help along that has led me here and let my work see the light. First and foremost, I present my sincere gratitude to my supervisor Pr. Younes Alila, who introduced me to research and shed the light on my way during the past four years. It is his passion for quality work that gave me the taste for research. I couldn’t have come to the position I am now without an insightful and supportive supervisor like Younes. Looking back, I see that I've learned a lot. The day-to-day discussions with a passionate supervisor allowed me to get to the bottom of my understanding and taught me that a hydrologist is not simply a scientist that happened to run a rainfall-runoff model. The great opportunities he gave me to work with outstanding people expanded further my knowledge.  I would like to thank from the core of my heart Dr. Peter Caldwell who provided thoughtful support and guidance for my work as advisory committee member. My sincere gratitude are also addressed to Pr. Murugesu Sivapalan for his insightful suggestions at early stages of my research project. I also want to thank the member of my advisory committee Dr. Ziad Shawwash. I am grateful to Dr. Chelcy Miniat from the United States Forest Services (USFS) for her generosity and welcome during my visit to Coweeta Hydrologic Laboratory. It was exciting to visit the xxii  experimental watersheds in the Appalachian Mountains where top scholars like Hewlett and Hibbert developed their first experiments and hypotheses.  I want to thank Pr. Andrew Thomas Black for his belief in my ability to do the work well. Being his teaching assistant for two years helped me grow my teaching experience and develop fabulous connections with the students. I thank Pr. Valerie Lemay and Dr. Susan Watt who encouraged me and made me appreciate my value as a mother and a young researcher. I express my deep consideration to Pr. R.D. Moore who was passionate to share with graduate students his experience in using R language to solve programming issues in hydrology. I want also to thank Pr. Cindy Prescott for the conversation we had at the beginning of my PhD program. Her words were inspiring and motivated me to thrive along my PhD journey. This research was financially supported by the prestigious PhD scholarship of the Islamic Development Bank (IDB). Partial funding was granted by NSERC Discovery Grant of Pr. Younes Alila (RGPIN 194388-11). More funding was granted for my GPA and fulfilment during my PhD program by internal awards from the Faculty of Forestry: Mary and David Macaree, 2015; Weldwood of Canada Limited H. Richard Whittall, 2016; Peter Rennie Memorial Award, 2017. A grant from IUFRO was awarded to give an oral presentation during the IUFRO doctoral meeting 2016 in Oregon State University and participate to several activities of the conference during a week.        xxiii   xxiv  Dedication This humble work is dedicated to  My Son, although thousands of miles away you were the flame illuminating my path with strong motivation to get to this fulfilment  My husband who willingly shouldered the burden of playing the dual role of mother and father during my absence. He was a constant source of support and encouragement to overcome challenges. My MOM and DAD whose unconditional support, affection, encouragement, and prays days and nights helped me to get to this stage My parents-in-law, for their constant support to my little family My sisters, my best friends, who were always there willing to help. Their success in winning a doctoral degree while being mothers inspired me to embark on the same adventure.  The soul of my brother, you are always present in my thoughts and down deep in my heart My brothers-in-law, thank you for your unconditional support     1  Chapter 1: Introduction  1.1 Motivation for the study Evaluation of the runoff processes at regional scale and assessment of the streamflow patterns beyond individual catchments are crucial for advancing the physical understanding and prediction of their hydrological behaviour (Dooge, 1986; Savenije, 2001; Sivapalan, 2003; McDonnell et al., 2007). Developing a degree of understanding and predictability at regional scale is important for water resources planning and management issues related to yield, storage, and extreme events, but increasingly to ecological studies across a wide range of spatial and temporal scales (Sanborn and Bladsoe, 2004; Kokkonen et al., 2003). The analysis of the streamflow regime encompasses the magnitude, timing, duration, and frequency of high and low flows, the rate of change of streamflow, and inter-annual variation. The streamflow regime is increasingly cited as a ‘master variable’ that structures aquatic ecosystems and habitats (Poff and Ward, 1989; Richter et al., 1996; Poff et al., 1997; Baron et al., 2002). The flowchart in Figure 1-1 ordinates the knowledge gaps in the literature as steps that are connected leading, namely, to assessment of streamflow pattern, advancing the physical understanding and predicting the hydrological behaviour.  Figure 1-1 serves at a later stage to formulate the objectives of this research project where the study components are those outlined in the flowchart.  The evaluation of the streamflow pattern and the understanding of the catchments hydrologic behaviour entails the need for hydrological modelling (e.g., streamflow prediction and simulation of flow components). In hydrological modelling one of the most common and significant challenges faced is the model parametrization and the reduction of parameters 2  uncertainty in gauged and ungauged catchments (Beven, 1995; Sivapalan and Kalma, 1995; Beven and Feyen, 2002; Duan et al., 2006) (Fig. 1-1, step 1). Over the past decades, among the main approaches that were developed to facilitate the parameter estimation is the a priori estimation technique that is based usually on the catchments characteristics (Koren et al., 2003). A priori parameter estimation may be used to obtain parameter values in ungauged catchments or to constrain the initial parameter ranges for calibration cited as ‘constrained calibration’ (e.g., Ao et al., 2006). While the technique of a priori parameter estimation is far from being perfect, it has been receiving increasing attention from hydrologists and water resources managers (e.g. Sivapalan et al., 2003a; Koren et al., 2003; Schaake et al., 2006; Duan et al., 2001). Parameters regionalization, which refers to assigning the same parameter set to catchments from the same homogeneous region, is another alternative of model parameterization that is usually used for streamflow assessment in ungauged catchments. Despite the plethora of studies, there is still no consensus regarding the most efficient approach for model parameter regionalization to make predictions at ungauged basins (PUB) (Hrachowitz et al., 2013; Parajka et al., 2013; Razavi and Couillibaly, 2013).  The hydrological modelling at regional scale in gauged and ungauged catchments is an initial step towards understanding the hydrological behaviour from assessment of streamflow pattern and evaluation of runoff processes (Fig. 1-1, step 2 and 3).  The Flow Duration Curve (FDC) is a flow representation that characterizes the flow regime within a stochastic framework (see Fig. 1-1 for an illustration of FDC). This flow representation is relevant for assessment of streamflow pattern and understanding of catchments’ hydrologic behaviour (e.g., Jencso et al., 2009).  The streamflow investigation and the physical understanding using FDC are pertinent in a wide range of hydrological and ecological applications (e.g., stream habitat assessment, 3  management of aquatic systems, reservoir and lake sedimentation studies, hydropower feasibility analysis, water quality management, waste load and water resources allocation) (Vogel and Fennessey, 1994; Vogel and Fennessey, 1995; Kokkonen et al., 2003).  The FDC graphically depicts the percentage of time (duration) that streamflow exceeds a given value over a historical period for a particular river basin (e.g., Vogel and Fennessey, 1994). If the streamflow is assumed to be a random variable, the FDC may also be viewed as the complement of the cumulative distribution function of the flow (CDF) (e.g., Vogel and Fennessey, 1994; LeBoutillier and Waylen, 1993). FDC is a stochastic representation of the flow. The understanding of the hydrological behaviour  focuses on explaining the physical causes of the flow response considering the succession of events thus the ‘frequency’ (Klemeš, 1978) (Fig. 1-1, step 3 and 4). The FDC is different from the deterministic flow representation (flow hydrograph) that considers instead the chronological change of flow response, which can be daily or over any time step. Both representations of the flow are of interest in science investigation and are critical for management of water resources and aquatic ecosystems (Poff et al, 1997) because they provide complementary understandings (Klemeš, 1978).    One of the most fundamental problems facing the hydrological community is the lack of understanding of the relative contribution of climate and watershed characteristics on the shape of FDCs (Yokoo and Sivapalan, 2011; Yaeger et al., 2012; Cheng et al., 2012). Solving this issue is central to advance the physical understanding of the hydrological behaviour within a stochastic framework using FDC (Fig. 1-1, step 3 and 4a). There is a need to investigate the regional variation of the FDC through a process-based analysis of the interaction between climate and landscape properties (Yokoo and Sivapalan, 2011). 4  The physical understanding of the hydrological behaviour using FDC forms the basis for developing process-based models that predict the FDC. Traditionally, the FDC is predicted using streamflow observations and curve fitting through manipulation of the statistical characteristics of probability distributions that does not resort much to understanding of hydrological processes (Booker and Snelder, 2012). Stochastic models to predict FDC using a process-based approach are not fully developed and have not been validated in actual catchments across a range of topographic and hydroclimatic settings (Botter et al., 2007a, b; Botter et al., 2009; Muneepeerakul et al., 2010, Yokoo and Sivapalan, 2011).    Therefore, there is a need to further develop process-based models of the FDC and study their use in improving predictions. Ideally, the theoretical development of the models should be extended to real catchments at regional scale of wide range of topographic and hydro-climatic settings.  The meta-analysis is of great value in this type of investigations at regional scale (Fig. 1-1, step 4b). Recently, meta-analysis aided in elucidating the hydrological response characteristics of Mediterranean catchments at different time scales (see Merheb et al., 2016). Extending theoretical developments to real catchments at regional scale is central because it allows to set hypotheses —while learning from the data— and to investigate the prediction tools that can be extrapolated to ungauged catchments. All of which are an initial step towards quantifying FDC using a model of physical bases (Fig. 1-1, step 5).  In this thesis, I used the data from the eastern United States (US) to conduct a regional study that addresses the knowledge gaps revealed by the current body of literature. The eastern US occasionally has hazardous flood, particularly in the Appalachian Mountains (Miller, 1990). The big event of April 1977 that affected four States (Kentucky, Tennessee, W. Virginia and Virginia) was linked to 22 deaths and 290,000 tons/day of sediment loss (Runner et al., 1977).  The total damages were around $400 Million (Runner et al., 1977). Rappaport (2000) from NOAA Tropical 5  Prediction Center found that one half of all flood-related deaths in the US between 1970 and 1999 were caused by floods in Appalachians. Thus, conducting a study in catchments of the eastern US within the wider scope of providing understanding and predictability of their hydrological behaviour is relevant from the scientific and social standpoints.   Figure 1-1: Flow chart of the study steps 1.2 Research objectives The objectives of this dissertation were motivated by the knowledge gaps in the current body of literature and was undertaken with the wider scope of facilitating the prediction at ungauged 6  catchments and advance the physical understanding of FDC. The following three objectives form the basis of this dissertation:  Assess the efficiency of constrained calibration and evaluate model parameterization in ungauged catchments using a priori parameters and regionalization approach   Determine the relative contribution of climate and watershed characteristics on the shape of FDCs within the framework of a process-based analysis  Explore the possibility to predict FDC at ungauged catchments using a process-based approach  1.3 Thesis overview To achieve the study objectives, this dissertation consists of six additional chapters. Chapter 2 provides details of study area and the dataset. By means of the Sacramento model (SAC-SMA), Chapter 3 and Chapter 4 focus on hydrological modelling at regional scale (step 1 and 2 in the flow chart in Fig. 1-1). Chapter 3 reveals the effect of a priori parameters limitations on modelled processes and determine the extent to which constrained calibration produces much more reliable model prediction. Chapter 4 investigates the model parameter transferability within regions of similar flow and climate characteristics. The findings of the parameter transfer are compared with predictions from the SAC-SMA a priori parameters designed to facilitate the prediction at ungauged catchments. In Chapter 5, the regional variation of the FDCs was analyzed and the environmental controls are investigated. The chapter presents a process-based analysis of the interaction between climate and landscape properties to explain further the regional variation of the FDC (step 3 and 4 in the flowchart in Fig. 1-1). This chapter employed results of calibration—developed in Chapter 3 for SAC-SMA model— to explore the runoff processes at regional scale. The findings advanced the physical understanding of the FDC and allowed to set 7  hypotheses about the environmental controls of FDC shapes.  Chapter 6 developed a meta-analysis using real catchments to explore the possibility of predicting FDC at ungauged catchments using a process-based approach (step 4b and step 5 in Fig. 1-1). This chapter builds on some physical understanding from Chapter 5 and provides more analyses to meet the objectives of the investigation. The chapter set hypotheses about the use of mean monthly runoff to develop a process-based approach that quantifies FDC at ungauged catchments.   8  Chapter 2: Dataset and study area   2.1 Dataset  The catchments used in this study are part of the database developed for the Model Parameter Estimation Experiment (MOPEX) (Duan et al., 2006; Schaake et al., 2006). The database contains historical hydro-meteorological data and land surface characteristics for many hydrological basins in the US and in other countries (Duan et al., 2006). MOPEX research has been driven by a series of international workshops that brought together interested hydrologists and modellers to exchange knowledge and experience in developing and applying model parameter estimation techniques. With its focus on parameter estimation, MOPEX plays a major role in the context of international initiatives such as Prediction in Ungauged Basins (PUB) (Hrachowitz et al., 2013). We extracted all the data of catchments located within the study area from the MOPEX database. We chose the MOPEX because it has relatively long record length (50 years on average) and it has been used repeatedly in several researches in the U.S (Koren et al., 2003; Cheng et al., 2012; Coopersmith et al., 2012; Ye et al., 2012; Berghuijs et al., 2014; Berghuijs et al., 2016).  The database is freely available and was retrieved from the following website:  www.nws.noaa.gov/oh/mopex/mo_datasets.htm. Air temperature, potential evapotranspiration (PET), and streamflow are all available with a daily time step. Precipitation data are representative of the catchment average and is available at both daily and hourly time steps. In this study, we use the hourly and daily precipitation, as well as the daily flow and daily PET. The record length ranges from 1948 to 2000. The MOPEX catchments are considered to be associated with a natural flow regime with limited human influence (Schaake et al., 2006).  9  2.2  Study area  We studied the spatial pattern of FDCs using 73 MOPEX catchments from the eastern US. The mean annual precipitation (MAP) in the study catchments varies between 702 mm to 2072 mm (Appendix, Table A1). The catchments have a humid climate. The aridity index (the ratio of the MAP to the potential evapotranspiration) is rather low according to Coopersmith et al. (2012) (see Appendix A, Table A1 where the catchments are sorted according to their site code). The catchment size ranged from 67 km2 to 8052 km2, as shown in Figure 2-1(a) and Table A1 (Appendix). Around 20% of the catchments have sizes larger than 4000 km2. The catchments are mainly forested with some proportions of agricultural lands and limited influence of urban areas (see Appendix, Table A1).  The catchments’ runoff ratio —that is annual runoff to precipitation ratio— has a minimum of 0.33, a maximum of 0.64, and a median of 0.44 (see Appendix, Table A1). Perennial snow cover is absent for most catchments and does not exceed 3% of the surface area for individual catchments (Berghuijs et al., 2014). The precipitation in the eastern US is of low seasonality (Fig. 2-1(b)) (Coopersmith et al., 2012; Sawicz et al., 2011). The mean monthly precipitation has limited fluctuation through seasons, whereas storm characteristics—in particular storm intensity—have systematic seasonal variation (Hershfield, 1961). Orographic thunderstorms are common in the Appalachian Mountains and produce large rainfall accumulations that may exceed 600 mm for 6-hour storms (Erskine, 1951; Eisenlohr, 1952; Miller, 1990; Smith et al., 1996). At the headwater scale, orographic thunderstorms lead to large floods that may exceed the 500-year return period, such as the event of November 1985 in Central Appalachian (see Miller, 1990).   10  The Appalachian Mountains create a contrast in elevations as shown by the Digital Elevation Model (DEM) in Figure 2-2. Catchments with low relief are mainly located in the eastern coast and in the state of Georgia, while the interior catchments have higher relief. The maximum elevation across the region is 2029 meters above sea level (m.a.s.l), and the minimum is -93 m.a.s.l. (Fig. 2-2). This area of low elevation refers to a wetland in Florida that lies below sea level. In this study, we do not make use of the detailed geomorphology and geology descriptors (e.g., impermeable areas, spring horizon, intermittent streams) covering such a large region because such information is not readily available.    Figure 2-1: (a) catchment size distribution, (b) mean monthly precipitation (mm) 11   Figure 2-2: (a) HGB soils proportions, (b) HGC soils proportions, (c) HGA soils proportions. 12  The variation in soil texture and structure across the study region affects the soil hydrologic properties and so the flow response (Wood et al., 1984). Figure 2-2 illustrates the spatial pattern of the main hydrologic groups HGA (soil with high infiltration rate), HGB (soil with medium infiltration rate) and HGC (soil with slow infiltration rate) (Wood et al., 1984). Note how the highest proportions of the HGA soils are in West Virginia. There is a gradual decrease of HGB soils from the southern to northern regions. In mid-latitudes, the soil is a combination of HGB and HGC, while in northeast it becomes predominantly HGC.           13  Chapter 3: Evaluation of Sacramento a priori parameters and their effect on constrained calibration at regional scale  3.1 Introduction  Over the past decades, among the main approaches that was developed to facilitate the parameter estimation is the a priori estimation technique. A priori parameter estimation may be used to minimize the number of parameters to be calibrated, obtain parameter values where calibration is not possible, constrain the initial parameter ranges for calibration, and use the parameters to make predictions at ungauged catchments (e.g., Ao et al., 2006). While the technique of a priori parameter estimation is far from being perfect, it has been receiving increasing attention from hydrologists and water resources managers (e.g. Sivapalan et al., 2003a; Schaake et al., 2006; Duan et al., 2001).  The a priori estimation procedures are only available for few hydrological models (e.g., Anderson et al., 2006). The most commonly used method to determine a priori parameters is the correlation between the model parameters and the catchment characteristics (primarily the soils and vegetation types). For instance, Abdulla et al. (1996) developed empirical equations that correlate the VIC-2LLSM parameters to determinable basin features. Duan et al. (1996) correlated the Simple Water Balance (SWB) model parameters and the catchment features for the southeast region of the United States of America (USA). Yokoo et al. (2001) related 16 parameters of the conceptual Tank model to land use and soil types through multiple linear regression. The correlation method, although it helps in streamflow assessment at regional scale, has limited success because the catchment characteristics are indirectly related to the model parameters (e.g., 14  the soil hydraulic properties and the soil depth) (Duan, 2001). In addition, the improperly calibrated parameters from catchments used to develop the correlations induce uncertainty in the relationships with the catchment features (e.g., Ao et al., 2006; Gupta et al., 1999).  For physically based models, the a priori parameters can be directly measured. However, this strategy poses problems due to the differences between the measurement and the grid scales (Beven, 1989). Recently, remote sensing (e.g., LIDAR measurements) and Digital Elevation Models have resolved some of the inaccuracies because fine resolution measurements have become available (e.g., Fang et al., 2010; Dornes et al., 2008). However, this alternative is less applicable in regional studies due to the high computing power required by distributed modelling to make predictions across thousands of square kilometers. The Sacramento Soil Moisture Accounting Model (SAC-SMA) is among the few lumped models that has soil-derived a priori parameters estimated from analytical and empirical equations (Koren et al., 2003). Hence, it is appropriate for streamflow investigation at a regional scale because i) lumped models are parsimonious (Beven, 2000), ii) the a priori expressions of the SAC-SMA parameters cope with improper simulations from other strategies and provide a globally applicable and physically realistic technique of a priori parameter estimation that can be used worldwide (Koren et al., 2003; Duan et al., 2006), and iii) the spatially-explicit soil data are widely available at resolutions appropriate for regional assessments. One area worth investigating is analyzing, at regional scale, the impact of a priori parameters and of parameters estimated by constrained calibration on predictions from SAC-SMA. A study of the kind would serve the scientific community in revealing the limitations of the globally applicable estimation technique of a priori parameters. 15  Within the framework of the Model Parameter Experiment (MOPEX), the SAC-SMA a priori parameters have been estimated in several catchments across the continental United States (Koren et al., 2000). All a priori parameters are soil derived and used the State Soil Geographic Database (STATSGO) map to estimate θwlt (the water content at wilting point), θs (the water content at saturation),  θfld (the water content at field capacity), and Ks (the hydraulic conductivity at saturation) (Duan et al., 2001; Koren et al., 2003). In the eastern United States and using few catchments from the mid-latitudes, Koren et al. (2003) found that flow simulation from a priori parameters led to similar model efficiencies as the calibrated parameters. Koren et al. (2003) underscored the benefit of a priori parameters as they provide reasonable estimate for ungauged basins and facilitate the calibration. The constrained calibration to the a priori parameters helps retain physical consistency and reduce equifinality (Koren et al., 2003; Duan, 2001). Nonetheless, in a study conducted over a few geographically distant MOPEX catchments in the United States, Gan and Burges (2006) obtained non-satisfactory predictions from both constrained calibration and a priori parameters. The lack of efficiency highlighted by Gan and Burges (2006) hints at uncertainty in the a priori values that did not appear in Koren et al. (2003). This would be related to the limited number of catchments used in both studies preventing us to make a conclusive statement about the extent of the a priori parameters’ limitations and whether these limitations vary with catchment properties. The limitations of SAC-SMA a priori parameters are mainly related to the lower layer free water storage assumptions (not exceeding a depth of 2.5 m) and to the interpolations in STATSGO to derive soil data on 1 × 1 km grids (Anderson et al., 2006; Koren et al., 2003). The implications of the a priori parameter limitations on predictions from SAC-SMA (from a priori values or constrained calibration) remain poorly understood.  16  Therefore, the objective of this thesis chapter is to 1) calibrate the SAC-SMA in catchments from the eastern United States using the constrained calibration approach, 2) analyze the effect of a priori parameters limitations on modelled processes and the prediction; determine the extent to which constrained calibration produces much more reliable model prediction.  By investigating the a priori parameters limitations and analyzing the constrained calibration, future improvements that are inevitable can be explored and help to foster a priori parameters operational use worldwide.  3.2 Methods 3.2.1 Overview Within the regional context of the study in this thesis chapter, the criterion of homogeneity in the hydrologic response is considered through the use of homogeneous regions in eastern US (Wagener et al., 2007). The homogeneity in the hydrologic response facilitates assessment of a priori parameter limitations per region and their effect on model performance.   Therefore, the analysis in this chapter uses the homogeneous regions determined by Sawicz et al. (2011). The evaluations of a priori parameters limitations and their effect on model performance take into account the catchment conditions. The analysis considers the soil hydrologic properties and predominant runoff generation mechanism in each catchment. Within each homogeneous region, the correlations of the model efficiency with dominant soil hydrologic groups are studied for simulations using calibrated and a priori parameters. In this chapter, the model simulation from constrained calibration is denoted by CAL and the prediction using a priori parameters is connoted by APRIORI. The variability of each parameter between catchments of the same region in CAL and APRIORI is analyzed. The increase (decrease) in parameter variability between catchments 17  of the same region—from APRIORI to CAL— indicates that there is much more (less) variability in the catchment properties affecting the runoff response than the a priori parameters would suggest. The larger the change in the parameter variability from APRIORI to CAL the larger is the improvement in the parameter value from APRIORI to CAL. This reasoning is applied here following Koren et al. (2003) and Gan and Burges (2006) that evaluated the improvement in constrained calibration in few catchments using the same logic. It is noteworthy that parameter variability along through the parameter physical meaning, indicates the model processes most critical to flow predictions.  The topographic index (TI) distribution at the catchment scale allowed to identify the dominant runoff generation mechanism in each catchment. Combining the outcomes of the parameters variability between catchments in each region and the dominant runoff generation mechanism provided translucent interpretations of the limitations of a priori parameters, their effect on modelled processes and the improvements after calibration. The knowledge of the landscape properties (e.g., soil and topography) revealed the catchment conditions where limitations of a priori parameters affected the performance from CAL the most.  3.2.2 The homogeneous regions used in the analysis Over the last decade, PUB studies have worked to identify appropriate schemes for homogeneous regions (Hrachowitz et al., 2013). According to Wagener et al. (2007), the homogeneous regions should be physically meaningful and provide a means to assess the dominant controls on the streamflow patterns (McDonnell and Woods, 2004). The analysis in this thesis chapter used the homogeneous regions identified by Sawicz et al. (2011). These regions are geographically contiguous and have been identified using six characteristics: the streamflow elasticity to precipitation, snow day ratio (SDR, the number of days per year where the precipitation is falling as snow), the baseflow index, runoff ratio, slope of the flow duration curve 18  (FDC), and the slope of the hydrograph rising limb.  The streamflow elasticity to precipitation and the climate were the most influential in the regionalization followed by the runoff ratio and the slope of the flow duration curve (Sawicz et al., 2011). The regionalization using the six characteristics employed the method of partitioning algorithm by Kennard et al. (2010). The novelty in Sawicz et al. (2011) is not in the characteristics themselves but in their combination to determine the homogeneous regions and, therefore, quantify the hydrologic similarity between catchments.  3.2.3 SAC-SMA model structure calibration 3.2.3.1 Model parameters and physical meaning  The SAC-SMA model has been applied worldwide and particularly in the different hydro-climate regimes of the United States (Koren et al., 2003). It allows for more detailed flow simulations by separating flow into runoff components, namely, the direct runoff, surface runoff, interflow, and baseflow (van Werkhoven et al., 2008; Burnash, 1995). The model has a two-soil-layer structure (Fig. 3-1). Each layer is made of tension and free water storages that interact to simulate soil moisture and five runoff components (Koren et al., 2000, 2003).  The tension water storages simulate the evapotranspiration (ET). The daily average PET from MOPEX data is one of the inputs necessary for ET simulations. The free water storage of the lower layer has two sub-storages that simulate supplemental (fast) and primary (slow) groundwater flows (Fig. 3-1). The storage in the tension and free water of the upper zone partitions the rainfall into surface runoff and infiltration into the lower zone storage.  19   Figure 3-1: SAC-SMA model conceptualization   The excess from the tension water capacity of the upper zone (UZTWM) becomes the excess rainfall, and the excess from above the free water capacity (UZFWM) generates the surface runoff. At saturation of the upper zone storages, the runoff rate is influenced by deficiencies in the lower zone reservoirs, the tension water, LZTWM, and the free water, LZFSM and LZFPM, capacities.  The runoff is generated at each free water reservoir depending on the depletion coefficients, namely, the UZK coefficient in the upper zone and LZSK and LZPK in the lower zone (see Fig. 3-1). The percolation rate into the lower zone is a nonlinear function of the deficiencies of the lower and upper reservoirs and includes two parameters: the maximum rate of 20  percolation, ZPERC, and an exponent value, REXP (Koren et al., 2003). The water from the deep percolation divides into three storages. The PFREE parameter determines the fractional split between the tension and free water storages. The parameters not estimated by the a priori expressions are ADIMP and PCTIM because they are not soil-derived (Koren et al., 2003). 3.2.3.2 SAC-SMA model constrained calibration The SAC-SMA model simulation is used to assess the effect of a priori parameters on the constrained calibration (Chapter 3).  The calibration results are employed to investigate the SAC-SMA model parameter transferability (Chapter 4). The calibrated parameters helped simulate soil moisture, surface and subsurface flows at catchment scale in analysis of Chapters 5 and 6.  Under the MOPEX project, default SAC-SMA parameters (a priori parameters) have been estimated for each catchment in the dataset to facilitate model calibration (Koren et al., 2003). ADIMP and PCTIM that deal with the fraction of impervious areas in a catchment do not have a soil-derived physical meaning. The default ranges by SAC-SMA were initially used for these two parameters. The model simulations of flows and soil moisture account for the role of the impervious areas. The SAC-SMA model parameters were calibrated using Shuffle Complex algorithm (SCE-UA) with 10,000 iterations (Sorooshian et al., 1993). This algorithm is extensively used for SAC-SMA calibration to achieve different research goals, such as studying model parameter transferability (e.g., Gan and Burges (2006)) and building a large database for the continental US (e.g., Newman et al., 2015). Similar to Gan and Burges (2006) and Koren et al. (2003), the calibration was constrained to the a priori value of each parameter to keep physical consistency and reduce equifinality. The value of ±35% was set as the range of deviations allowed from the default parameters. This range is larger than the range used in Koren et al. (2003) (e.g., ±25%). This interval was chosen to allow for more variability around the default parameters and 21  in the parameters space that is used by SCE-UA algorithm to find the global optimum.  The model was calibrated for the period of 1948-1963. The objective function minimized RMSE (Root Mean Square Error) between daily observed and simulated flows. The model calibration performance was evaluated by Nash-Sutcliffe coefficient (NS) (Nash and Sutcliffe, 1970). The catchments with the highest NS were tested for validation and considered in the analyses. Using a sample of 100 catchments for calibration, those with NS lower than 0.50 were disregarded from the study. The eliminated catchments should have a minimal effect on the outcomes. The same NS-based criterion was used by Berghuijs et al. (2014) for analysis of regional water balance in the continental US. In this study, the catchment sample decreased from 100 to 73 and the efficiency of daily simulated flows ranged from 0.50 and 0.92. The average NS value was 0.72.  3.2.3.3 Topographic index distribution for each catchment Analyses of the topographic index (TI) are helpful to explore the predominant runoff generation mechanism. TI represents the propensity of a point within a catchment to generate saturation excess overland flow (Beven and Kirkby, 1979) due to a topographic control on surface and subsurface flows (Rice and Hornberger, 1998). TI was first defined by Beven and Kirkby (1979) as follows: TI = ln⁡(atanβ)                                                                                                                             (1) where: TI is the topographic index of a point/pixel within a watershed; a  is the specific upslope area per unit contour length;   is the local topographic slope angle acting at the point. 22  In this study, TI was calculated at the pixel level using a DEM of 30-m resolution and algorithms necessary for the determination of specific upslope area “a” and the local slope angle β (Rousseau et al., 2005; Hentati et al., 2010). The TI calculation uses the properties of the stream network; namely, the flow directions and the flow accumulation, which both help to identify the riparian zone (see Hentati et al., 2010). Finer details about the stream network dynamics and the stream connectivity are difficult to get for each watershed. Therefore, the effects of intermittent streams and whether they affect the predominant runoff generation mechanism and the flow response are not considered in calculations of the topographic index and are beyond the scope of the study.  The frequency of TI distribution was then determined for each catchment after classification of TI pixel values. The differences in the TI frequency distribution at the catchment scale illustrate the wide differences in topographic properties between study catchments and, consequently, the effect of topography on the flow response. According to Beven and Kirkby (1979) and Beven and Wood (1983), large values of TI in tails of the distribution indicate the likelihood of runoff being generated by saturation excess overland flow, whereas smaller values in the tails hint to predominant subsurface processes in the runoff generation. The flow response depends also on the soil infiltration properties and permeability (Price, 2011; Ameli et al., 2015). Therefore, analyses of the runoff generation mechanism using TI serve to reveal the predominant mechanism that takes place as a response to topography while the effect of other factors (e.g., permeability) on the flow response is acknowledged.  The spatial pattern of the soil hydrologic properties is used as indicative of the soil infiltration rates and permeability (Wood et al., 1984).  23  3.3 Results  3.3.1 Model performance using a priori and calibrated parameters  The study regions are presented in Fig. 3-2(a) and the results of model performance over the calibration period are summarized in Fig. 3-2 (b).  The same regions’ notation is maintained in as Sawicz et al. (2011) for consistency. The cumulative distribution function (CDF) of the NS coefficients showed that the best model performance during the calibration period was in C5 (the Southeast) and C1 (the Center). The catchments with the poorest performance were in C3 (West Virginia) and C2 (the Northeast) (Fig. 3-2(b)). According to Fig.3, the major improvements from APRIORI to CAL during the calibration and the validation periods were in C1, C2, and C5 regions (Fig. 3-2 (c), (d), and (f), respectively). The simulations (calibration and validation periods) in C3 barely improved from APRIORI to CAL (Fig 3-2 (e)). Nonetheless, the calibrated parameters maintained the model efficiency higher than 0.5 after the validation, although the simulations from APRIORI dropped to 0.2 in one study catchment (see Fig. 3-2 (e)). 24   Figure 3-2: (a) catchments classification according to Sawicz et al. (2011) and DEM, b) CDFs of NS coefficients across regions in  calibration period, CDFs of NS coefficients from APRIORI and CAL simulation during the calibration and validation (c) in C1, (d) in C2, (e) in C3, (f) in C5    25  3.3.2 Analysis of predictions from a priori parameters and constrained calibration: the catchment landscape properties and runoff processes In C2 and C3, the soils are poorly drained and have a steep topography, whereas, in C5, the catchments have well-drained soils and are located at lower elevations. In Fig. 3-3, the large differences were observed in the spatial patterns of the soil hydrologic groups. The CDFs of HGB showed that it is predominant in C5 and C1 (Fig. 3-3(a)). The proportion of HGA soils is small across regions (soils with high infiltration, Wood et al., 1984), except in C3 (Figs. 3-3(b)). Meanwhile, HGC soils (slow infiltration rate) are prominent in C3 and C2 (Fig. 3-3(c)).    Figure 3-3: (a) CDFs of HGB soil proportions across regions, (b) CDFs of HGA soil proportions across regions, (c) CDFs of HGC soil proportions across regions  26  According to Table 3-1, in C1 as the percent of the HGB soils rises, the model efficiency in each catchment improves for APRIORI and CAL simulations. The increase in the proportion of the fine soil textures (HGC and HGBD (slow infiltration rate according to Wood et al., 1984)) affects the model efficiency in APRIORI and CAL.  The correlations of the NS coefficient with the different soil hydrologic groups are statistically significant (p-value <0.05).   Table 3-1:    Correlation between NS and predominant soil hydrologic groups in the study regions   Region SHG r R^2 p-valueCALC1 HGB 0.70 0.5 <0.0001HGBD* -0.67 0.46 <0.0001HGC -0.63 0.4 <0.0001C2 HGA 0.38 0.15 0.18HGB 0.36 0.13 0.22HGC -0.63 0.4 <0.05C3 HGA -0.67 0.45 <0.0001HGB 0.45 0.2 0.17HGC -0.14 0.02 0.59C5 HGA -0.76 0.57 <0.05HGB 0.64 0.41 0.06HGC -0.55 0.31 0.08APRIORIC1 HGB 0.59 0.35 <0.0001HGBD* -0.59 0.347 <0.0001HGC -0.55 0.3 <0.0001C2 HGA 0.42 0.18 0.14HGB 0.28 0.08 0.34HGC -0.63 0.4 0.03C3 HGA -0.70 0.49 <0.0001HGB 0.52 0.27 0.28HGC -0.13 0.018 0.64C5 HGA -0.45 0.2 0.22HGB 0.72 0.52 <0.05HGC -0.72 0.52 <0.05*SHG:  soil hydrologic group* HGBD: an SHG with very small infiltration rate * CAL: simulation using calibrated parameters* APRIORI: simulations using a priori parameters27     Figure 3-4: The parameters variability in each region where Sdv_APRIORI and sdv_CAL denote the normalized standard deviations of each parameter by median of the parameters standard deviation during APRIORI and CAL, respectively.  We use the median for normalization same as in Gan and Burges et al. (2006).   During the calibration, in C1, the main improvements were associated with an increase in the variability of the deep percolation parameters (ZPERC, REXP in Fig. 3-4(a)) and depletion from free water storage in the upper layer (UZK, Fig. 3-4(a)), which implies additional water leakages from the interflow and improved infiltration toward the lower layers. The increase in LZTWM variability (see Section 3.2.2.1 for physical meaning) suggests that the deep percolation permitted additional evapotranspiration from the lower layer.  28  In C2 region and according to Table 3-1, the increase in the HGA and HGB soil proportions increases the model efficiency. This effect was not statistically significant (p-value > 0.05). However, the increase in the HGC soils decreased the NS coefficients in APRIORI and CAL (p-value < 0.05). After calibration, the effect of the fine soil texture on the model performance was adjusted by increasing the variability of the deep percolation parameters (UZK and REXP in Fig. 3-4(b)). Therefore, additional water was needed to move downwards to increase the evapotranspiration from the deep soils (more variable LZTWM after calibration in Fig. 3-4(b)). As for C3 the results of the correlations in Table 3-1 indicate that the model performance improved in APRIORI and CAL as the amount of HGA soils decreased (p-value < 0.05). The effect of HGC and HGB soils was not statistically significant (p-value > 0.05). In Fig. 3-4(c), the depletion coefficient from the lower layer (LZPK) was the most variable parameter in both simulations. The variability of the drainage parameter from the upper layer and its depletion coefficient (UZFWM and UZK, respectively) slightly increased after calibration. In C5 (located in the State of Georgia), APRIORI was affected by HGA soils but more significantly by HGB and HGC soils (p-value < 0.05 in Table 1). The model efficiency improved as the HGB soils increased (p-value < 0.05). After calibration, the parameters responsible for the subsurface processes increased in variability, e.g., UZK, ZPERC, and REXP (Fig. 3-4(d)). In addition, the baseflow contribution was enhanced due to an increase in the LZFPM and LZSK variability (the lower layer depletion coefficients in Fig. 3-4(d)). In C1, C5 and in most catchments from C2, the saturation excess is predominant (large values of TI in tails in the right skewed distribution in Fig. 3-5). This is where the parameters simulating the model processes of deep percolation had the highest variability (particularly in C1 and C2) and those responsible of baseflow, particularly in C5, increased in variability after 29  calibration. In C3, all the catchments are at high altitudes in the Appalachians (Fig. 3-5(a)). The TI frequency distributions in C3 are all left skewed. This finding implies that subsurface processes are dominant (Beven and Kirkby, 1979). In these catchments, the parameters responsible for interflow had the highest variability after calibration.  Figure 3-5: (a) spatial distribution of TI groups designated as TI classification in the map (b) frequency distribution of topographic index per catchment.    3.4 Discussion  This study evaluates the limitations of a priori parameters and their effect on the constrained calibration and modelled processes at regional scale. The analysis sought to reveal the catchments characteristics where the predictions from the a priori parameters and the constrained calibration are less efficient.  The results demonstrated that CAL efficiency is low in catchments with poorly drained soils. The highest model efficiency was in C5 (in Georgia) with the best improvements from 30  APRIORI during calibration and validation periods. The CAL in C1 and C2 regions improved APRIORI, whereas, the improvement was less important than in C5 (Fig. 3-2(c), (d), and (f), respectively). The poorest efficiency was found in the C3 region. This pattern in the efficiency suggest that the uncertainty in the a priori parameter expressions is pronounced under poor soil drainage conditions.  The physiographic characteristics of the catchments in C5, primarily the low relief and the well-drained soils, are an indication of pronounced water infiltration. In C5 (Georgia), the increase in the variability of all parameters after calibration (Fig. 3-4(d)) suggests that there is much more variability in the soil properties that affect runoff across the catchments than the a priori parameters would suggest (see the average NS coefficients in C5 for APRIORI versus CAL). Remarkably, the groundwater processes are relevant to runoff predictions in C5 due to relatively large variability in LZFPM (a parameter responsible for drainage from the lower layer to baseflow). The prevalent groundwater processes is in agreement with TI analyses in C5 where saturation excess overland flow was predominant (Fig. 3-5) (Beven and Wood, 1983). The increase in LZFPM variability after CAL, in this region, could be related to the lack of reliability in a priori parameters of the lower layer in catchments with deep groundwater (such that in C5) because the soil information from STATSGO do not exceed 2.5 m depth. The higher values of NS coefficients in CAL suggest that some of the uncertainty has been reduced.   The decrease in CAL efficiency in C1 and C2 compared to C5 suggests that this decrease is most likely due to higher uncertainty in the a priori parameters. This uncertainty can be explained by differences in landscape properties (the topography and soil in Fig. 2-2). In C1 and C2, the catchments have either steep or subdued topography with a combination of HGC and HGB soils (lower soil drainage conditions compared to C5). It appears that, in addition to the limitation of 31  the STATSGO spatial resolution, the finer soil textures result in even more uncertain estimates of each of the soil physical properties (θwlt, θs, θfld, and Ks). In C1 and C2, the a priori parameters mostly affected by these uncertainties are LZPK (baseflow), ZPERC, and REXP (deep percolation) due to their large variability in CAL compared to APRIORI. In C1 and C2, the relatively poorly drained soils (a combination of HGC and HGB) would have resulted in less accurate estimation of a priori parameters dealing with deep percolation (REXP and ZPERC) such that it entailed corrections in CAL. The predominant mechanism of the saturation excess overland flow (Fig. 3-5) required more accurate baseflow depletion coefficient (LZPK) than those suggested by the a priori values.  The increase of the LZPK variability in CAL suggests some improvement.  The LZPK, ZPERC, and REXP were also among the most variable in CAL compared to APRIORI in studies by Gan and Burges (2006) and Koren et al. (2003). This similarity in results demonstrates that the major uncertainty in the a priori parameters for SAC-SMA is related to the deep percolation and groundwater processes. The free water drainage at the upper layer (UZK) is also highly variable between catchments in C1 and C2 because the subsurface processes were dominant in some catchments (Fig. 3-5) and, potentially, due to uncertainty in θwlt used in estimate of UZK (see the UZK equation in Koren et al. (2003) in page 252).  According to Koren et al. (2003), the limitation in STATSGO resolution is generated by interpolations that downscale soil data to a grid size of 1 km × 1 km. The lack of soil sampling (once per 100 or 200 km2) in some regions would also increase the uncertainty in the spatial interpolation and reduces the reliability of a priori parameters (Koren et al., 2003). In C1 and C2, the lower CAL performance, even though it improves APRIORI predictions under conditions of fine soil texture and steep topography, suggests that the average values of soil properties in each pixel of STATSGO are less representative of the real landscape complexities than  in conditions 32  of C5 (well-drained soils and flat topography). The steeper topography could have resulted in larger heterogeneity in the catchment soil characteristics than in conditions of flat topography. Therefore, in mountainous catchments of fine soil texture in C1 and C2, the lower performance after calibration deals with (i) uncertainty of measured physical properties in poorly drained soils, and (ii) lack of soil sampling that increases the uncertainty from spatial interpolation of soil physical properties in STATSGO. Both levels of uncertainty affect a priori parameters’ values and propagate to CAL.   In the C3, the region with poorest model efficiency that is covered by forested mountainous catchments of steepest topography in soils of fine texture (West Virginia), the increase in HGA soils reduced model performance. This finding is contradictory with results from other regions where better soil infiltration (primarily HGB soils) improved model efficiency. Notably, the most variable parameters in C3 are LZPK (the primary baseflow depletion coefficient) and UZK (the depletion coefficient from the upper layer) (Fig. 3-4(c)) due to the predominant subsurface stormflow. Physically, LZPK captures the role of baseflow and is computed from an exponential equation involving the hydraulic conductivity (Ks) and other variables (Koren et al., 2003). According to Bonell (1993), Ks is one of the most difficult hydraulic properties to assess, particularly in forested soils. The main responsible factors are the non-uniformity of the soil porosity with depth arising from biological activity and macropores resulting from decayed roots. In fact, in C3, all catchments are mountainous and forested (Sawicz et al., 2011) with poorly drained soils (HGC) of highest fraction of HGA (very high infiltration rates). Macropores have likely developed because of decayed roots in C3 catchments laying over steep slopes at high altitudes in Appalachian Mountains. Likely, lateral preferential flow is taking place under these conditions of landscape properties and predominant subsurface stormflow (Fig. 3-5). The 33  hypothesis of lateral preferential flow would also be applicable for the few highland catchments in C1. However, the large HGA proportions in C3 of most complex landscape properties suggest that this region is most prone to the effect of lateral preferential flow. Lateral preferential flow is thought to be one of the most relevant mechanisms in highland forested catchments (Weiler and McDonnell, 2007; McDonnell et al., 1990; Beven, 1982). The transient process of infiltration via macropores enables large volumes of water to be quickly delivered to stream channels (McDonnell, 1990; Beven, 1982). This mechanism is usually neglected in most conceptual and physically based models (Beckers and Alila, 2004; Beven, 1982).  In C3, given the very complex landscape properties compared to C1 and C2, the a priori parameters are mostly subject to : (i) the uncertainty in values of measured physical properties (particularly Ks), in addition to  the uncertainty explored in C1 and C2 due to less accurate spatial interpolation in STATSGO. Both sources of uncertainty would be pronounced in C3 as a result of complex landscape properties. The effect of preferential flow on the efficiency is applicable to predictions from a priori and calibrated parameters as this effect deals with model structure. However, the likelihood of preferential flow adds to the reasons explaining the uncertainty in the physical properties used to determine a priori values given that this flow is particularly dependent on hydraulic properties of soils including Ks (Simnek et al., 2002). Using another model to capture nonlinearity of lateral preferential flow, specifically in catchments from C3 is worth testing. Many research studies are in progress to understand the particularity of lateral preferential flow and develop most convenient models structure for accurate predictions (Beckers and Alila, 2004; Ameli et al., 2016).   The prediction from APRIORI and CAL is subject to uncertainty from measured precipitation, particularly, from measurements by rain gauges. Although a minimum of rain gauges 34  density had been met in MOPEX catchments based on criteria of basin size (Duan et al., 2006), precipitation depths could be difficult to estimate in complex topography of mountainous catchments in C3, C1 and C2.    Despite the limitations of a priori parameter values, the constrained calibration helped to obtain satisfactory predictions in most of the study catchments. This finding shows that the soil-derived a priori parameters—used to facilitate the calibration— can represent the spatial heterogeneity of land surface characteristics in most cases. To this effect, the calibrated parameters are physically consistent and yield predictions that are helpful in regional assessment of flow response.    In other studies from the literature using models other than SAC-SMA, the predictions from a priori parameters were less satisfactory when the a priori values were determined by means of regression between calibrated model parameters and basin attributes (Duan et al., 2001). The intrinsic uncertainty of the approach, primarily the errors in the correlations and the calibration techniques, tends to produce “noisy” parameter estimates such that many combinations of model parameters produce very similar model responses (e.g., equifinality) (Duan et al., 2001; Beven, 2006). Consequently, the improper a priori parameters led to poor model performances (e.g., Liston et al., 1994; Duan et al., 1996; Abdulla et al., 1996; Ao et al., 2006).  From the literature, the use of soil properties to estimate a priori parameters has been promising in other studies. For example, the approach to determine a priori parameters in Hughes and Kapangaziwiri (2007) allowed to reach reasonable efficiency when soil properties were used (e.g., soil texture, soil physical properties, soil depth). Dornes et al. (2008) emphasized the advantage of physically measurable parameters to run physically based models. A study by Anderson et al. (2006) provided promising results using SSURGO soil map (Soil Survey 35  Geographic Database) instead of STATSGO to determine SAC-SMA a priori parameters. However, the SSURGO is limited to a small number of catchments in the United States.   It appears that future venues to improve a priori parameter estimation for hydrological models including SAC-SMA should focus on improvements to measurable catchment properties (e.g., the soil physical properties). The current study found that there is a need to adjust a priori parameter values in highland catchments with fine soil texture to support complexity of the physiographic features and their effect in simulating flow response processes. There should be modifications that address subsurface processes, particularly, the uncertainty in lower layer parameters that are primarily dependent on soil hydraulic properties.  3.5 Conclusions The need to evaluate the a priori parameters and their effect on the constrained calibration at regional scale motivated the objective of this chapter of the thesis. The study used 73 catchments from the eastern United States. The findings showed that constrained calibration and a priori parameters have lower efficiency in catchments of fine soil texture. The constrained calibration provided predictions with higher efficiency in conditions of well-drained soils and flat topography where saturation excess overland flow is predominant. The study, therefore, suggests that the estimate of soil physical properties by STATSGO in poorly drained soils requires adjustments.  Particularly, those used in model parameters simulating subsurface processes, such as the saturated hydraulic conductivity.  The estimation of the saturated hydraulic conductivity should be revisited most importantly in catchments with the smallest efficiency where the subsurface stormflow dominated and the soils were poorly drained (predominantly HGC or a combination of HGC and HGB). Additionally, the likelihood of lateral preferential flow in these catchments would have 36  increased the uncertainty in the lower zone parameters including the estimates of saturated hydraulic conductivity given the effect of preferential pathways on soil hydraulic properties.  37  Chapter 4: Parameter transferability within homogeneous regions and comparisons with predictions from a priori parameters in the eastern United States   4.1 Introduction Over the past decade, different studies have developed techniques for prediction in ungauged basins (PUB), primarily via flow regionalization and model parameterization (Hrachowitz et al., 2013; Gan and Burges, 2006; Ren et al., 2016). Model parameterization in ungauged basins can be achieved using two primary approaches: parameter regionalization and a priori parameters determined from catchment properties (Hrachowitz et al., 2013). Regionalization for PUB involves the following steps: (i) identification of homogeneous regions where several criteria of homogeneity can be used and (ii) data transfer (observed flow data or calibrated parameters) from gauged to ungauged catchments of the same homogenous region.  In parameter regionalization, the rainfall-runoff model is calibrated for all the study catchments with observed flows. Then, using a regionalization method, the parameters are transferred from the donor gauged catchments to the recipient ungauged catchments within the same region. To examine the potential predictive performance of parameter regionalization at ungauged catchments, the simulated flows after parameter transfer are compared with the observed flows of a set of gauged recipient catchments that play the role of ungauged catchments (e.g., Hundesha and Bradossy, 2004; Jennings et al., 1994; Kokkonen et al., 2003; Norbiato et al., 2007). The three most common methods used for parameter regionalization are the regression-based 38  approach, spatial proximity, and physical similarity (e.g., Merz and Blöschl, 2004; Parajka et al., 2005; Sefton and Howarth, 1998; Young, 2006).  The regression-based approach correlates the calibrated model parameters with the physical properties of gauged catchments. The correlation is used to determine the model parameters in ungauged catchments (Merz and Blöschl, 2004). The spatial proximity approach consists of transferring parameters from neighboring catchments to the ungauged catchment, the rationale being that catchments that are close to each other should have similar hydrologic behaviour (e.g., Oudin et al., 2008; Parajka et al., 2007). The physical similarity approach consists of transferring the parameters between catchments of similar physical descriptors. This approach assumes that catchments with similar attributes exhibit similar hydrologic behaviours (e.g., McIntyre et al., 2005). A common issue among the three regionalization approaches is less-than-satisfactory efficiency (e.g., Arsenault and Brissette, 2004) and a strong dependence on the complexity of the terrain and scale at which the relations are derived (Bock et al., 2015). The model parameter definitions are by nature ambiguous and often difficult to determine from a small number of descriptors such as physical and climatic characteristics (Zhang et al., 2008). Previous studies have demonstrated that the regression-based approach yields the lowest efficiency because the high correlation between the model parameters and the catchment descriptors does not guarantee efficient model simulation of the flow response (Kokkonen et al., 2003; Oudin et al., 2010; Sefton and Howarth, 1998).   Studies of spatial proximity and physical similarity have yielded no evidence of the most efficient method. Spatial proximity yielded satisfactory predictions in a study by Koren et al. (2003), but it did not help as a criterion of hydroclimate homogeneity in studies conducted by Shu and Burn (2003) and Reed et al. (1999). Oudin et al. (2008) found that spatial proximity outperformed physical similarity. However, results from 39  Arsenault and Brissette (2014) demonstrated the opposite finding.  In the spatial proximity method, there is significant uncertainty in the estimates, mainly due to a lack of representativeness of catchment data, rainfall data, as well as identifiability problems of the runoff model parameters (Skøien and Blöschl, 2007). Other measurements, in addition to the distances between catchments, are needed for further refinement of the predictions. In terms of physical similarity, the homogeneity of the physical descriptors does not necessarily translate into representativeness of the model parameters and the flow response (Zhang et al., 2008). The most important component of the transfer of model parameters to ungauged catchments—critical to obtaining satisfactory efficiency—is the identification of the geographic extent to which there is homogeneity in the hydroclimate characteristics and therefore similarity in the hydrologic response (Bock et al., 2015).  Only a few recent studies have tested parameter transferability within homogeneous regions of similar hydroclimate characteristics and flow response without being limited to measures of either proximity or physical similarity.  All of the catchments geographically located in the same homogeneous region received the same parameter set (e.g., Kim and Kaluarachchi, 2008; Bock et al., 2015). Note that spatial proximity is considered to be one of the explanatory variables of the hydroclimate similarity (Sawicz et al., 2011) because of the first-order effects of climatic and topographic controls on hydrologic response (Smakhtin, 2001; Ali et al, 2012). Therefore, the similarity in the hydroclimate characteristics combines to some extent criteria of spatial proximity and physical similarity but with more robust measures of similarity in the hydrologic response. Kim and Kaluarachchi (2008) assessed parameter transferability within sub-basins of a large catchment (176,000 km2). The geographical limit of the sub-basin was the spatial extent within which the catchments had similar hydroclimate characteristics. Bock et al. (2015) used the flow data of gauged catchments to analyze the model 40  parameter sensitivity (PS) and geographically identify the regions of similar PS. The similarity in PS is indicative of the similarity in the model runoff processes. A similar principle has been used for decades in flood regionalization where the stream flow data of the gauged catchments determined the regional flood frequency distribution to predict floods at ungauged catchments of the same region (e.g., Ouarda et al. 2001; Farquharson et al., 1992; Mimikou and Gordios, 1989; Portela and Dias, 2005; Zrinji and Burn, 1994).  Bock et al. (2015) used the same parameter set for all of the catchments located in the same homogeneous region.  The evaluation of the regionalization approach in Bock et al. (2015) yielded satisfactory efficiency of the mean monthly flow predictions.  Additional research is needed to evaluate the predictions of the daily flow time series and to provide alternatives to PS while meeting the criteria of hydroclimate homogeneity in the parameter regionalization.  The lack of consensus regarding the most efficient approach among the common parameter regionalization methods and the need for more in-depth investigation of parameter transfer within homogenous regions of similar hydroclimate characteristics triggered the research goals of this component of this study. We investigate the Sacramento model (SAC-SMA) parameter transferability in the eastern United States (US) using the geographically contiguous hydroclimatic regions determined by Sawicz et al. (2011). The homogeneous regions have the uniqueness of being identified using a combination of climate and flow characteristics that quantify the hydrologic function and determine the spatial extent where the hydroclimate characteristics are consistent. The use of combined climate and flow characteristics in the regionalization adds to the novelty of this research compared with other parameter regionalization approaches.  Previous studies used the SAC-SMA model to investigate the parameter transferability on a few catchments 41  in the US following the criteria of spatial proximity (Koren et al., 2003) or with no specific criteria of parameter regionalization where the catchments were spatially distant (Gan and Burges, 2006).  The primary objective of this part of the thesis was to quantify the gain in the SAC-SMA model performance attained by the parameter transfer at ungauged catchments from calibrated model of gauged catchments within homogeneous hydroclimate regions (TRANS_IN) relative to 1) model parameterized with a priori parameters derived from soil properties (APRIORI), and 2) model parameterized with transferred parameters from a single best performing catchment in the study area (TRANS_OUT).  The study tests the hypothesis that the delineation of the study area into homogenous regions where there is similarity in the hydroclimate conditions will improve the efficiency of parameter transferability (TRANS_IN) relative to APRIORI and TRANS_OUT. TRANS_OUT is not meant to represent a regionalization scheme for PUB but instead aids in measuring the gain in performance and revealing limitations of the parameter regionalization TRANS_IN.  The comparison between TRANS_IN and APRIORI, where both having the ultimate goal of PUB will determine under what catchments’ conditions the predictions from a priori parameters is better (worse) than the prediction from the regionalization approach.  In this Chapter, the novelty lies in the comparison of the a priori parameterization to the parameter regionalization approach and the ultimate goal is to provide insights into the usage of the parameter transfer within homogeneous regions and the a priori parameters for PUB in the U.S and elsewhere.  4.2 The homogeneous regions used in parameter transfer: specific characteristics  The homogeneous regions of the eastern US identified by Sawicz et al. (2011) and presented in chapter 3 (section 3.2.1 from this dissertation) are the same used to study SAC-SMA parameter transferability. The homogeneous regions have the ultimate goal of facilitating 42  predictions at ungauged catchments using data transfer (e.g., flow, parameters) from gauged catchments. Below the specific climate and landscape properties are described across regions.   Figure 4-1: (a) regions in the eastern US, the catchments highlighted in squares are the donor catchments in each region (b) whisker plots of snow day ratio (SDR), (c) whisker plots of aridity index (AI)  The characteristics used to explore the specific characteristics of the climate in regions are namely the snow day ratio (SDR), the aridity index (AI), and the precipitation seasonality index (PSI).  The SDR is generally low across the study area and increases with the increasing latitude (R2 = 0.81, p-value <0.05) (Fig. 4-1(b)). The largest median value is 25% obtained in C2 (Fig. 4-1(b)). In C3, the median value is 22%. In C1, it drops to 12% followed by 2% in C5 (Fig. 4-1(b)). The storms have longer duration in C1, C2, and C3 than in the region of C5 (Chouaib et al., 2018). The AI is the mean annual Potential Evapotranspiration (PET) by the mean annual precipitation 43  (MAP) (Sawicz et al., 2011), describing the relative energy and water limitations on evapotranspiration of the catchments in each region (Fig. 4-1(c)). The catchments in C2 and C3 are more energy limited (low PET) than the catchments in C1 and C5 (large PET) (Fig. 4-1(c)). The PSI is nearly zero in all regions (Table 4-1). The forest cover proportions (FR) are large (Table 4-1). The smallest proportions of FR are in C5 where the median is 46% (Table 4-1). The median of agricultural lands is the largest in C5, but not exceeding 23.1% (Table 4-1).  The proportions of open water and wetlands are small in all the regions (Table 4-1).  Table 4-1:  region’s main descriptors    4.3 Methods  4.3.1 Overview  This chapter used the model simulations from a priori parameters (APRIORI) and the calibrated parameters of SAC-SMA developed in chapter 3 to undertake the steps detailed below: Step 1: identified calibrated catchment with best performance in each region to be used as donor catchments for a parameter transfer scheme (TRANS_IN). Step 2: performed model simulations using parameter transfer scheme TRANS_IN, calculated fit statistics during calibration and validation periods. region StatisticsMean elevation (m)slope (%)Urban areas (%)Forest (%)Agriculture (%)Open water (%)Wetland (%)MAP (mm)PSImin 76.7 2.0 1.9 39.2 0.3 0.00 0.00 982.1 0.026C1 max 1211.9 34.0 18.7 97.0 46.0 1.42 11.64 2072.0 0.45median 547.8 14.3 6.6 66.8 19.8 0.27 0.07 1201.8 0.065min 16.2 0.3 0.0 28.6 0.0 0.01 0.00 998.1 0.018C2 max 769.1 19.8 11.6 95.2 59.0 2.69 23.19 1520.2 0.127median 424.3 10.2 4.0 74.0 10.8 0.41 1.20 1145.2 0.076min 274.3 6.0 2.6 45.4 3.5 0.13 0.00 983.6 0.072C3 max 997.8 20.9 12.9 91.0 38.0 0.97 1.11 1385.5 0.117median 655.8 17.9 5.5 82.9 9.4 0.53 0.07 1158.9 0.083min 53.1 0.6 5.0 35.4 17.4 0.30 3.19 1206.0 0.032C5 max 269.6 4.8 15.8 55.7 31.3 1.35 19.66 1366.7 0.088median 217.7 3.4 9.0 46.0 23.1 0.62 5.65 1284.6 0.06644  Step 3: performed model simulations using parameters from the single best performing catchment for all 73 catchments irrespective of regions (TRANS_OUT), calculated fit statistics during calibration and validation period Step 4: compared model performance for the parameter transfer scheme TRANS_IN to both APRIORI and TRANS_OUT simulations, interpret SAC-SMA parameters transferability with respect to catchment characteristics.  4.3.2 Evaluation of the prediction at ungauged catchments using a priori parameters As highlighted in chapter 3, the a priori parameters are primarily designed to serve as an estimation technique for ungauged catchments (Koren et al., 2003; Young, 2006). In addition to the Nash–Sutcliffe (NS) coefficient (Nash and Sutcliffe, 1970), the predictions from a priori parameters (APRIORI) is evaluated in comparison to the parameter transfer (TRANS_IN) using percent bias (PBIAS), mean monthly hydrograph (MMH), and the flow duration curve (FDC).  The TRANS_IN and APRIORI comparison is fair as both approaches were intended to make PUB.   4.3.3 Parameter transfer (TRANS_IN) The parameter regionalization scheme (TRANS_IN) is investigated and evaluated for the transfer of parameter values from gauged to ungauged catchments within homogeneous regions to predict daily flow time series using SAC-SMA model.  In TRANS_IN, one single donor catchment is designated. After conducting the SAC-SMA model calibration, the catchment in each region with the highest NS coefficient at calibration was determined with the condition that the validation NS was quite stable and did not go below 85% of the calibration NS (e.g., Arsenault and Brissette, 2014). In Figure 4-1(a), the donor catchment of each region is highlighted with a square. The parameter set of the designated donor catchment is transferred to any of the catchments located in the same region of homogeneous climate and 45  flow characteristics (recipient catchments). Any ungauged catchment located in the same region uses the same parameter set to predict the flow data (Bock et al., 2015). Past studies demonstrated that  using the parameter set of the catchment with the highest NS helped to attain better efficiency from the parameter transfer than transferring the median parameter set of multiple donor catchments  (e.g., Kim and Kaluarachchi, 2008; Masih et al., 2010 ;Oudin et al., 2008). Evaluations of the predictive performance from TRANS_IN use the recipient catchments assuming they are ungauged, as in similar regional studies (e.g., Arsenault and Brissette, 2014; Bock et al., 2015; Kim and Kaluarachchi, 2008; Masih et al., 2010; Sanborn and Bladsoe, 2006). At individual catchments, the performance evaluation makes use of NS, PBIAS, predictions of the flow duration curve (FDC), and the mean monthly hydrograph (MMH). Besides, the median percent error of several flow percentiles of the FDC is assessed for a more in-depth evaluation.   4.3.4 TRANS_OUT TRANS_OUT takes into account all of the heterogeneities in the eastern United States (e.g., catchment energy conditions, landscape properties, predominant runoff generation mechanism, storm characteristics). TRANS_OUT is not a regionalization scheme for PUB, instead it is used to assess the gain in efficiency from TRANS_IN. The assessment of the gain in performance from the regionalization through comparisons of TRANS_IN with TRANS_OUT used the same performance measures noted above (NS, PBIAS, MMH, and FDC). In TRANS_OUT, one donor catchment was used to parameterize all catchments for all the regions (e.g., the original study region of eastern US). In this chapter, the donor catchment in TRANS_OUT had the highest NS of all of the 73 catchments.  Given that TRANS_IN uses the catchment with the best NS in each of the four regions of Sawics et al. (2011), the single best catchment across all regions is one of the four designated 46  catchments for TRANS_IN. This catchment coincides with the donor catchment of TRANS_IN in C1. Therefore, TRANS_OUT is not applicable for C1.  TRANS_OUT is a parameter transfer that includes all types of heterogeneities, therefore, comparisons of TRANS_IN with TRANS_OUT also reveal the extent to which the transferred parameters in TRANS_IN are representative of the catchments’ conditions. Particularly when TRANS_IN and TRANS_OUT have comparable efficiency.  This comparison is, therefore, indicative of the limitations of the parameter transferability using the parameter regionalization scheme (TRANS_IN). 4.3.5 Interpretation of SAC-SMA parameters transferability The study provides a quantitative interpretation of the performance from the parameter transfer TRANS_IN and TRANS_OUT in order to determine the representativeness of transferred parameters to the catchments’ conditions in each region. First, in each region, the catchment descriptors (climate, soil properties, and elevation) are used in combination with their measures of variation/inter-quantile variation to explain the satisfactory (lack of) efficiency of TRANS_IN in comparison with TRANS_OUT. The catchment descriptors employed are AI (Aridity Index), the mean elevation, and the soil hydrologic properties (HGC (low infiltration rates), HGB (medium infiltration rates), HGA (very large infiltration rates, Wood and Blackburn (1984)). Second, the correlation of these descriptors with the latitude and the mean elevation are analyzed in order to further understand the geographical extent of the variation, and therefore deduce the effect on the parameter transferability. Furthermore, the interpretations of the parameter transferability are complemented with the analysis of the predominant runoff generation mechanism in each catchment, using the Topographic Index (TI) distribution. The prevalent runoff generation mechanism is indicative of the runoff processes. This information is helps further to explain the 47  representativeness of the transferred parameters in each region from the perspective of runoff processes.  The approach to calculate the TI distribution at catchment site was developed in section 3.2.2.3 of Chapter 3. 4.4 Results and discussion  4.4.1 Performance of parameter transferability and a priori parameters Table 4-2: average statistics of the different simulations across clusters in calibration and validation periods Cluster  Period APRIORI TRANS_IN  TRANS_OUT NS         C1 Calibration 0.691 (0.075) 0.711 (0.079) N/A C1 Validation 0.681 (0.088) 0.710 (0.067) N/A C2 Calibration 0.604 (0.060) 0.604 (0.056) 0.622 (0.056) C2 Validation 0.617 (0.081) 0.588 (0.049) 0.604 (0.064) C3 Calibration 0.623 (0.065) 0.625 (0.058) 0.646 (0.070) C3 Validation 0.590 (0.133) 0.631 (0.068) 0.645 (0.063) C5 Calibration 0.749 (0.074) 0.762 (0.060) 0.757 (0.059) C5 Validation 0.707 (0.108) 0.771 (0.066) 0.705 (0.034) PBIAS         C1 Calibration 0.0245 (5.458) 0.483 (4.255) N/A C1 Validation -0.550 (4.841) 0.711 (0.079) N/A C2 Calibration -10.168 (5.549) 0.780 (0.032) -5.044 (5.934) C2 Validation -9.319 (7.226) -9.867 (6.318) -7.123 (7.051) C3 Calibration -4.213 (6.246) -4.416 (6.178) 0.557 (4.663) C3 Validation -3.835 (6.243) -11.688 (9.519) -3.665 (4.177) C5 Calibration -5.761 (9.076) -1.966 (7.646) -8.706 (9.727) C5 Validation 2.078 (11.009) -3.458 (6.866) -4.800 (4.272) * () numbers between parentheses refer to the standard deviation of the NS values across catchments in each cluster      TRANS_IN outperformed the prediction from TRANS_OUT for all of the homogeneous regions except the C3 region. The improvements are mainly a higher median NS and/or less-biased predictions with lower variation (see the values of NS and PBIAS with their respective variation listed in parentheses in Table 4-2). On the other hand, TRANS_IN outperformed the APRIORI with a particularly higher efficiency and/or less-biased predictions except for C3 (Table 4-2). Below, we present the performance results for C1 and C5 followed by C2 and C3; the former two regions exhibited the highest performance in TRANS_IN.   48  In C1, TRANS_OUT was not applicable. Meanwhile, TRANS_IN outperformed the APRIORI and led to predictions with higher median efficiency and limited bias (small median PBIAS in Table 4-2). The MMH and the FDC of a typical catchment exhibited a good fit of TRANS_IN and APRIORI with the observed flow (Fig. 4-2(a)). However, the median percent error of the FDC at several percentiles exhibited larger errors for APRIORI, particularly for the low and large flow percentiles (Fig. 4-3(a)).  In C5, TRANS_IN outperformed TRANS_OUT. The gain in performance due to TRANS_IN is mainly higher NS and less-biased predictions (Table 4-2). The MMH from the typical catchment did not exhibit a difference in performance between TRANS_IN and TRANS_OUT and the observed MMH (Fig. 4-2(b)). However, the FDC from TRANS_IN at the typical catchment had a better fit than the FDC from TRANS_OUT (Fig. 4-2(b)). The median percent errors of the FDC in TRANS_OUT were larger for all of the flow percentiles compared with TRANS_IN (particularly until the 75th percentile).  The APRIORI remained less efficient and more biased (see the large values of PBIAS with larger variation listed in Table 4-2). The MMH predicted by APRIORI in a typical catchment underestimates the large flows compared with the observed MMH and the one predicted from TRANS_IN (Fig. 4-2(b)). The predicted FDC from APRIORI in the same typical catchment deviates at the upper and lower tails from the observed FDC and from the FDC predicted using TRANS_IN (Fig. 4-2(b)). The median percent errors of the FDC are larger than those obtained from TRANS_IN in most of the percentiles (Fig. 4-3(b)).   In the remaining two regions, C2 and C3, the predictions from TRANS_IN were either of limited bias compared with those of TRANS_OUT (C2) or were outperformed by those of 49  TRANS_OUT (C3). Below, we present the performance of the parameter transferability in both regions that we compare with APRIORI.  Figure 4-2: (a) mean monthly hydrograph (MMH) and FDC of a typical catchment from C1 with NS 0.80, 0.74 at  APRIORI, and TRANS_IN, respectively, (b) MMH and FDC in a typical catchment from C5 with  NS 0.79, 0.78, 0.73 at APRIORI, TRANS_IN, and TRANS_OUT, respectively, (c) MMH and FDC in a typical catchment from C2 with NS 0.55, 0.6, 0.55 at APRIORI, TRANS_IN, and TRANS_OUT, respectively, (d) MMH and FDC in a typical catchment from C3 with NS 0.7, 0.72, 0.71 at APRIORI, TRANS_IN, and TRANS_OUT, respectively  50  In the C3 region, in contrast to previous regions, TRANS_OUT outperformed TRANS_IN and APRIORI (higher median NS and lower PBIAS of smaller variation during the calibration and validation periods; Table 4-2). TRANS_IN and APRIORI had similar performance in C3 (Table 4-2).  The differences in the efficiency were not visible based on the typical MMH and the typical FDC. All of the predicted FDCs deviated from the observed FDC at the lower tail (Fig. 4-2(d)). However, the median percent errors of the FDC revealed the differences in efficiency between TRANS_IN, TRANS_OUT and APRIORI. . The larger efficiency of TRAN_OUT yielded better predictions than TRANS_IN and APRIORI, mainly in the medium flows of the FDC (particularly between 30% and 70% exceedance probabilities), and was comparable to TRANS_IN and APRIORI at the low and high percentiles of the flow (Fig. 4-3(d)).   Figure 4-3: The median percent error of the FDC at several flow percentiles (10%, 25%, 50%, 75%, and 90%) in each region 51  4.4.2 Evaluation, interpretation, and discussion of parameter transferability and a priori parameters In this sub-section, the performance results for C1 and C5 are interpreted and discussed followed by C2 and C3. The good performance of TRANS_IN in C1 indicates that the transferred parameters are representative of the catchments conditions. In this region, most of the catchments are at low elevation, and a few are located in the Appalachian Mountains (Figs. 4-1(a)). AI (Aridity Index) was statistically correlated with the mean elevation (R2 = 0.33, p-value <0.05). This relation is mainly caused by the PET decrease with elevation as corroborated by the findings of Swift et al. (1988). The change in AI with elevation was not large according to the small inter-quantile range and the median value shown in Figure 4-1(c). Therefore, in C1 the catchments have similar energy conditions and most are water limited. The energy conditions are important for the predictions of flows because the PET is one of the inputs of the SAC-SMA model. Transferring parameters that are calibrated in similar energy conditions—as in the recipient catchments—has a large effect on the efficiency of TRANS_IN. Note that most of the soils in C1 are well drained (mainly HGB with some proportions of HGC (Figs. 2-2(a) and 4-5(a)). A saturation excess overland flow dominates in most of the catchments (Fig. 3-5(a)). On the other hand, subsurface storm flow is prevalent in few catchments at high elevations. The satisfactory prediction from TRANS_IN can be further explained using understanding of the runoff generation mechanism. In C1, and in conditions of predominant saturation excess overland flow, the large infiltration rates lead to an increase in the groundwater level, which enhances the groundwater contribution, mainly the surface flow from the saturated areas and the base flow. The saturated surface flow and base flow are both determined by the groundwater level (Huang et al., 2016). In the few catchments dominated by subsurface storm flow covered with well-drained soils, the groundwater contribution 52  is also important as a result of recharge in the vadose zone. According to isotope hydrology, in steep terrain with conductive soils, the new infiltrating water pushes the old subsurface runoff to induce stream flow in the channel (e.g., Buttle, 1994). This understanding demonstrates that groundwater contribution is important in catchments of C1 and is consistent with the base flow index (BFI) being large in this region (Sawicz et al., 2011).  The similarity in the groundwater effect between catchments further explains the efficiency from TRANS_IN and supports the claim that transferred parameters are representative of catchment conditions in C1. The smaller efficiency of APRIORI suggests that the soil-derived values of a priori parameters are less representative of the catchments’ conditions in C1 than the transferred parameters using the regionalization approach.  The catchments in C5 are all located at low elevations with the exception of one catchment of higher elevation (see the outlier in Fig. 4-4 and refer to the Digital Elevation Model (DEM) shown in Fig. 4-1(a)). Provided that the AI is correlated to the mean elevations (p-value< 0.05), there is homogeneity in the energy conditions where the catchments in C5 are all water limited with a very small inter-quantile range (Fig. 4-1(c)). Only one catchment is energy limited (see the outlier in Figure 4-1(c)).The Saturation excess overland flow is prevalent in all of the C5 regions where the soils are well drained (HGB soil proportions dominate compared with HGC for all catchments except for one: Figs. 2-2(a) and (b)). As in C1, these characteristics of the runoff processes and soil enhance the contribution of the groundwater and are consistent with BFI being the largest (larger than in C1) and the flow being the most attenuated (the smallest slope of the FDC), as found in Sawicz et al. (2011). 53   Figure 4-4: The mean catchment elevation in each region The catchments’ conditions and the predominant runoff generation mechanism explain the large efficiency in TRANS_IN that was not affected by the presence of one outlier (visible in Figs. 2-2(b) and 4-5(b)). On the other hand, transferring parameters from an outsider catchment (TRANS_OUT) (that belongs to C1) to make predictions of the flow leads to poor efficiency due to differences between C1 and C5, although the donor catchment in TRANS_OUT is geographically the closest to C5 (Fig. 4-1(a)). The differences between C1  and C5 are namely, the catchments in C5 have (i) the shortest duration of storms, (ii) the most stringent water-limited conditions (Fig. 4-1(c)) (iii), the lowest elevations (Fig. 4-4), and (iv) the smallest HGC proportions (Fig. 4-5(b)). In conditions of the predominant saturation excess, these attributes generate flows with characteristics different from those of C1. It has been shown that the interaction of the climate factors with the runoff generation mechanism influences the runoff response where, for instance, the semi-arid conditions fosters the dominance of the infiltration excess surface runoff (Huang et al., 2016). 54   Figure 4-5: (a) whisker plots of HGB soils proportion across the regions; (b) whisker plots of HGC soils proportion across the regions;  (c) whisker plots of HGA soils proportion across the regions  In C2, the lack of efficiency from TRANS_OUT is pertinent and reveals the extent to which the catchments are hydrologically similar and the transferred parameter set by TRANS_IN are representative of the catchments’ conditions leading to less-biased predictions. The catchments’ properties within C2 and their differences from C1 help to explain the gain in performance associated with TRANS_IN compared with TRANS_OUT. In C2, most of the catchments are energy limited (except two outliers) with a small range of variation compared with C1 (Fig. 4-1(c)). Hence, the catchments in C2 have homogeneous energy conditions with lower median AI than in C1. Furthermore, there is a very small range of variation in the value of the snow day ratio (SDR) in C2 (Fig. 4-1(b)), which further illustrates the homogeneity in the climate and its effect 55  on the runoff response and therefore on the efficiency from TRANS_IN. The SDR, although small in C2 (median 25%), influences the runoff response (Singh et al., 1997; Ye et al., 2012). In this region of the northeast, the soils are mostly characterized by poor drainage with a notable increase in the HGC proportion compared with the soils of C1 (Figs. 2-2(b) and 4-5(b)). The HGC proportions are the largest in this region. The runoff generation mechanism in C2 is mainly dominated by the saturation excess (Fig. 3-5(a), in Chapter 3). Only a few catchments belong to the middle category of the TI (Fig. 3-5(a), in Chapter 3) where the saturation excess and the subsurface storm flow are equivalent in their effect on the flow response (Beven and Kirkby, 1979; Beven and Wood, 1983).  Therefore, the interaction of the homogeneous climate, homogeneous soil, and homogeneous energy characteristics in C2 with the runoff generation mechanism (primarily saturation excess) fosters the hydrologic similarity between the catchments and explains the efficient performance of TRANS_IN. An illustrative example of the interaction between the climate, the landscape properties, and the runoff generation mechanism is presented in Bronstert et al. (2002). The transferred parameters within the geographical extent of C2 using one donor catchment from the same region are representative of the catchments’ conditions.  As shown above, the conditions in C2 are different from those in C1 making the characteristics of the flow response different in both regions (the catchments in C2 have steeper slope of the FDC s than those in C1; see Sawicz et al. (2011)), and therefore further explains the predictions of limited bias by TRANS_IN.  In C3, the poor efficiency of TRANS_IN compared to TRANS_OUT indicates the level of heterogeneity in C3 and helps to explain the performance from the parameter regionalization (TRANS_IN). In C3, although the catchments are energy limited (low PET), the AI (Aridity Index) 56  is characterized by large variations and a large inter-quantile range, suggesting that the catchments have heterogeneous energy conditions (Fig. 4-1(c)). There are catchments that are more energy limited (low PET) and others that are more water limited (high PET). The PET is one of the inputs into the SAC-SMA model. Hence, the transfer of parameters that are calibrated in different conditions of energy does not help to attain high efficiency. Furthermore, all of the catchments in C3 are forested (Table 4-1) and mountainous with higher elevations than other regions (Figs. 4-1(a) and 4-4). There is also large variation in the mean elevation among the catchments (Fig. 4-1). The soils are poorly drained (Fig. 4-5) with the lowest proportions of HGB (Fig. 4-5(a)) and among the highest proportions of HGC (Fig. 4-5(b)). The subsurface storm flow dominates in C3 (Fig. 3-5(a), in chapter 3). The disparity in the mean elevation likely leads to differences in the response between catchments because the hydraulic gradient is proportional to the topographic gradient in mountainous catchments (Butt et al., 2001).  The C3, according to findings from Chapter 3, is the region most subject to preferential flow. Current physically based and conceptual models—including SAC-SMA—often ignore the effect of preferential flow (Weiler and McDonnell, 2007). Therefore, we recognize its effect as a source of uncertainty in other predictions from C3 (APRIORI, TRANS_OUT). In ideal conditions where the preferential flow is simulated by the model structure, the parameter transfer within C3 (TRANS_IN) will not lead to high performance because (i) of the same reasons noted above related to disparity in catchment conditions, and because of (ii) the nature of preferential flow being specific to characteristics of each catchment (the density of preferential pathways changes between catchments as a result of soil texture/porosity, root zone density, and density of decayed/living roots) (Brammer, 1996; Bronstert, 1999; McDonnell et al., 2007; Weiler and McDonnell, 2007). Additional research is necessary to properly simulate lateral preferential flow and investigate 57  techniques to measure differences/similarities in the effects of this flow between catchments of the same region.  The relatively better performance of TRANS_OUT in C3 (limited to medium percentiles of the FDC), can be explained by the donor catchment in this parameter transfer (located in C1) being spatially close to the catchments in C3 (Fig. 4-1 (even closer compared to that in from C2) and being dominated, by the same runoff generation mechanism (the subsurface stormflow dominates the donor catchment of TRANS_OUT and the catchments in C3, Fig. 3-5(a), in Chapter 3). The results from TRANS_OUT and the likelihood of preferential flow indicate limitations of the parameter regionalization and suggest the need for other measures of similarity to relocate the catchments in C3. The findings, therefore, propose adding other characteristics in the regionalization  to assess the effect of preferential flow that can be complemented by physically based measures of the soil characteristics (e.g., porosity, permeability) and other measures related to the PET (e.g., AI) to reduce the heterogeneity in the energy conditions. Improving the efficiency from the parameter regionalization in regions of very complex landscape properties is a research venue that requires in-depth investigations.  In the eastern United States, the spatial pattern of soils pointed out how the HGC proportions are correlated with the latitude. This relation is statistically significant (R2 = 0.47, r = -0.68, p-value <0.05). The latitude explains 47% of the HGC variation in the eastern United States. It is difficult to conjecture the reasons for this tight correlation, but factors related to the geology structure that interacts with the topography in the eastern United States and the climate agents (e.g., storm characteristics) may be the potential factors. If the climate and the soil hydrologic properties (HGC proportions) are correlated with latitude and if these factors affect the flow response (Wagener et al., 2007), it is possible to use climate and physical descriptors (e.g., soils) 58  in identifying the homogeneous regions for parameter transfer.  However, the performance from the parameter transfer would probably not be as efficient as the parameter regionalization approach investigated in the current study considering that the climate and the physical descriptors do not capture the effect of interaction between all of the factors contributing to the flow response (e.g., climate, soil texture, runoff generation mechanism, groundwater, porosity, preferential pathways) (Troch et al., 2013). Note that a previous regional study by Oudin et al. (2010) demonstrated that only 60% of the hydrologically similar catchments are physically similar. This overlap was statistically significant. In 40% of the catchments, classified based on physical similarity, the parameters are not transferable. This finding supports the claim that emerges from the current analysis about the need to use catchments characteristics that capture the interaction between all factors contributing to the flow response in parameter regionalization approaches. Given that the flow is the product of this interaction and that using climate and flow characteristics in the regionalization leads to satisfactory efficiency from parameter transfer in most of the regions, the current study conjectures that the more the characteristics used in the regionalization capture the effect of interaction the more efficient are the predictions from the parameter transfer.  Furthermore, the analysis demonstrates that when MMHs do not exhibit differences between several predictions, the FDCs have diverse shapes according to the analyses of the median percent error in each simulation. Consequently, two main facts emerge concerning FDC use: (i) it reveals the bias effect on flow simulation inaccuracy, and (ii) it is advantageous for a more reliable parameter transfer assessment, which is urgently needed for reliable PUB. Several past studies have regarded FDC as essential for PUB (Archfield et al., 2013). For example, Kapangaziwiri et al. (2009, 2012) analyzed FDCs to assess predictions from parameter regionalization. Masih et al. (2010) delineated regions of homogenous hydrologic behaviour based on the similarity of the 59  FDC. Farmer et al. (2014) used the FDC of gauged basins to predict flow percentiles in ungauged basins using nonlinear spatial interpolations. Therefore, it is recommended to use FDC to better assess PUB in combination with the efficiency measures of NS and PBIAS.  Our assessments using FDC suggest giving new paradigms in the evaluation of model prediction a try. The use of summary metrics involving measures of the FDC (i.e., slope of the FDC, rising limb density, declining limb density) in Sadegh et al. (2015) and Vrugt and Sadegh (2013) showed great promises for prediction evaluations. It ensured that simulated response depicts accurately the observed flow behaviors. This finding is consistent with our results; FDC being more efficient in prediction evaluation than MMH and classic residual-based metrics. The problem resides in the convoluted error residuals of the observed and the simulated time-series. According to Sadegh et al. (2015), the summary metrics have the advantage to be relatively insensitive to forcing data errors, which is particularly desirable in the context of nonstationarity. The summary metrics, therefore, avoid proclaiming non-stationarity for the wrong reasons (errors on the rainfall data) (Sadegh et al., 2015). 4.4.2.1  Which approach to use for PUB, the a priori parameters or the parameter regionalization? In all of the regions, the comparisons of the efficiency from the parameter transfer with APRIORI highlighted the uncertainty in using the a priori parameters to make PUB compared to a parameter regionalization approach.  The lowest performance (low median NS and high PBIAS) from APRIORI was in C2 and C3 (Table 4-2).  APRIORI was equivalent to TRANS_IN in C3 where TRANS_IN was the least efficient across the regions. This finding does not allow to recommend the use of a priori parameters for PUB.  Slightly better predictions from APRIORI occurred in the catchments from C1 and C5 60  (Table 4-2) but never exceeded TRANS_IN. The limitations of a priori parameters developed in Chapter 3 explain the lack of performance of a priori parameters compared to a parameter regionalization approach.  The findings suggest that it is better to use a parameter regionalization approach, similar to what is presented in this study, to make predictions at ungauged basins. Future research would consider to compare the predictions from a priori parameters with predictions from other regionalization approaches (e.g., regression, spatial proximity, similarity in physical properties) to further evaluate the use of SAC-SMA a priori parameters in predictions at ungauged catchments.  4.4.3 Comparison with previous studies Comparisons of the efficiency results with the findings of other studies demonstrate that none of the catchments had predictions as poor and as biased as those reported by Gan and Burges (2006).  These authors used the same model to investigate the parameter transferability over geographically distant MOPEX catchments. These differences demonstrate the benefit of using hydrologically “similar” catchments for the parameter transfer. The results in this study outperform predictions from the spatial proximity, which provided better predictions than the physical similarity in a study by Oudin et al. (2008). The median NS attained 0.77 in this study, but it did not exceed 0.7 for spatial proximity and 0.69 for physical similarity in Oudin et al. (2008). In Arsenault and Brissette, (2014) the efficiency of the physical similarity did not exceed 0.75 at individual catchments. This efficiency is lower than the value of 0.85, the maximum obtained in this study at individual catchments. As stated previously, despite the limitations, the effect of the interaction between all factors contributing to the flow response—captured by the climate and flow characteristics employed in the regionalization—explain the better performance attained compared with the separate use of either criteria of spatial proximity or physical similarity.  61  Note that Oudin et al. (2008) considered the spatial proximity and physical similarity as complementary and that the average of the flow simulation from both approaches can be used to improve the prediction efficiency. Given the high performance obtained in this study and provided that homogeneous regions of similar hydroclimate characteristics implicitly combine aspects of spatial proximity and physical similarity, the proposition of Oudin et al. (2008) stating to combine predictions from two regionalization methods may represent a worth-testing approach to investigate in future researches. This so-called “multi-regionalization scheme” requires identification of a priori regionalization approaches to obtain the average of the flow simulation leading to the best performance after combination (Oudin et al., 2008).  Our prediction performance was consistent with other studies transferring the parameters between hydrologically similar catchments. Bock et al. (2015) obtained a median NS of 0.76 from the parameter transfer within regions of similar parameter sensitivity. The performance in individual catchments in our study exceeded the maximum value of 0.78 reported by Masih et al. (2010) who used the criterion of similarity in the FDC for the parameter regionalization.  4.5 Conclusions This Chapter evaluated the performance from the parameter transfer within homogeneous regions of similar climate and flow characteristics. Subsequently, it compared the performance from the parameter regionalization to the prediction efficiency from the soil-derived a priori parameters that are designed to make predictions at ungauged catchments. The study was conducted in the eastern US using 73 catchments. The analyses utilized the SAC-SMA model and the geographically contiguous regions determined by Sawicz et al. (2011) using criteria of similarity in climate and flow characteristics.   62  The results showed that parameter transfer within homogeneous regions reduced the bias and increased the predictions efficiency (it reaches a median NS of 0.77 and a NS of 0.85 at individual catchments). The use of the FDC was advantageous in revealing the effect of bias on the flow simulation inaccuracy. The satisfactory efficiency from the transferred parameters within the homogeneous regions was attained due to the similarity in the effect of interaction between climate, physiographic characteristics and predominant runoff generation mechanism. The use of the flow characteristics in the regionalization helped to capture the similarity in the effect of interaction. The transferred parameters within homogeneous regions outweighed in performance the soil derived a priori parameters. Therefore, it is better to use a regionalization approach to make predictions at ungauged catchments.  In one region of very complex landscape properties (e.g., forested mountainous catchments, steepest topography, higher fraction of the poorly drained soils) and heterogeneous energy conditions, the predictions from the a priori parameters had equivalent efficiency to those from transferred parameters within the same region. Both had poor performance. The use of the transferred parameters from an outsider donor catchment slightly improved the predictions (e.g., more accurate predictions of the medium flow percentiles). This finding underlined the limitations of the parameter regionalization approach used in this study.      63  Chapter 5: Regional variation of flow duration curves in the eastern United States: Process-based analyses of the interaction between climate and landscape properties   5.1 Introduction Over the past several decades, FDCs have been analyzed using a graphical representation (Ward and Robinson, 1990) or stochastic models in order to fit the appropriate statistical distribution to empirical FDCs (Cigizoglu and Bayazit, 2000; Sugiyama et al., 2003; Castellarin, 2004a; Iacobellis, 2008). These studies helped the hydrologic community in issues related to the prediction of the FDC without explicitly advancing the physical understanding of the FDC controls. Most often, the prediction studies at the ungauged catchments related the physiographic characteristics to the statistical moments of the FDC probability distributions to predict FDC at ungauged catchments (LeBoutillier and Waylen, 1993; Singh and Mishra, 2001; Claps and Fiorentino, 1997; Croker et al., 2003; Smakhtin and Hughes, 1997; Fennessey and Vogel, 1990; Castellarin et al., 2004b). This approach does not provide understanding of the FDC controls. Few researches dealing with the prediction at ungauged catchments provided implicit understanding of the FDC controls. For instance, Musiake et al. (1975) emphasized the prevalent effect of the geology structure on characterizing the baseflow after they classified the study catchments (small to medium sized) into physiographic classes and analyzed the baseflow data transfer between catchments of the same class. Sefton and Howarth (1998) derived the parameters’ values of a rainfall-runoff model from relationships with the morphometric and physiographic characteristics over 60 catchments in UK. These relationships indicated, through sensitivity analyses of the 64  parameters, the collective effect of the landscape characteristics (soil, land use, slope and elevation) on the FDC shapes. The effect of the geology structure and the landscape characteristics remained indicative and required a detailed physical and quantitative analyses. One of the rare studies that addressed thoroughly the effect of the vegetation types on the shape of the FDCs is Burt and Swank (1992). The study demonstrated that fertilized grass and the forest cover controlled similarly the discharge levels for all the frequency classes.  The existing literature can be used as base for our study towards a more comprehensive understanding of the FDC controls.  Another category of studies analyzed the FDCs from the perspective of runoff processes using stochastic modelling (Botter et al., 2007a; Muneepeerakul et al., 2010; Botter et al., 2009). The investigations contributed to advance the understanding of the FDC controls. Botter et al. (2007a) derived the slow-flow component FDC (baseflow) through analysis of the soil moisture dynamics and the statistical properties of the precipitation. Subsequently, Botter et al. (2009) included non-linearity in the subsurface storage discharge relationship, and Muneepeerakul et al. (2010) extended the same model to include a fast-flow component (surface flow). The ability of the model to reproduce observed FDCs has been tested in few small to medium sized catchments (Botter et al., 2007b; Ceola et al., 2010; Botter, 2010). However, this stochastic dynamic model builds on assumptions about precipitation (e.g., non-random events in Poisson rainfall arrival) and could only be applied seasonally with constant parameter values for each season (Botter et al., 2007 a,b). Therefore, overcoming the limitations of the stochastic dynamic framework reviewed above would further help in revealing the climatic and landscape controls of the FDCs.  In the continental US, a recent series of empirical studies analyzed the pattern of change of the FDCs in catchments from all the US (Cheng et al., 2012; Coopersmith et al., 2012; Ye et al., 2012). The study catchments had diverse climate and landscape properties. At a first stage, Cheng 65  et al. (2012) analyzed the FDC shape from the correlation of their statistical moments, when fitted to a gamma distribution, with first-order catchment characteristics (e.g., baseflow index, maximum daily precipitation, and a fraction of non-rainy days). Subsequently, in a study by Coopersmith et al. (2012), the study catchments were classified into climate clusters based on climate signatures (e.g., precipitation seasonality index, seasonality index of the precipitation, and day of peak precipitation). The climate clusters helped Yaeger et al. (2012) to investigate the spatial pattern of FDCs using the process controls of the seasonal flow response in the US; namely the aridity, the snowmelt, and the phenology. These processes were determined by the combined modelling and empirical water balance study of Ye et al. (2012). However, the large extent of the study area (e.g., the entire continental US) did not reveal sufficient detail about the climatic and landscape controls of FDCs. The characteristics of climate seasonality, aridity, and phenology that influenced the average seasonal flow response in Ye et al. (2012) were not sufficient to explain the diversity of FDC shapes across the continental US (Yaeger et al., 2012). A study by Yokoo and Sivapalan (2011) examined the shapes of FDCs under several theoretical combinations of landscape properties with climate. This study developed a conceptual framework to predict FDCs using a runoff process-based approach. The framework considered the FDC as constructed from precipitation variability that cascades through the catchment system and gets exposed to landscapes in order to generate runoff under its respective process controls (Cheng et al., 2012). This conceptual framework provided some understanding, but it required further analyses and testing using observed data (Yokoo and Sivapalan, 2011). Nonetheless, it can also serve as guidance for investigations focusing on the study of FDC controls.  Even with previous research regarding the factors that control the shapes of the FDCs, we remain far from understanding the physical mechanisms behind the regional variation of FDC. The 66  need for a process-based understanding motivated the research goals of this Chapter in the thesis. Therefore, here we propose to analyze the regional variation of FDCs in the eastern US to advance the current physical understanding of FDC controls. The following questions guided the investigation: 1) If the regional variation of FDCs is controlled by the interaction of climate and landscape properties, then to what extent is the diversity in the shapes of FDCs explained by each of the controls? and 2) In response to their effect, what is the aspect of the runoff processes that govern the regional variation of FDCs?  A number of methods are developed to answer the research questions. The overall goal was to provide a detailed analysis of the climate and landscape properties in the region of interest and to advance the process understanding of the physical relationships between the shapes of FDCs and the effect of climate and landscape properties.  5.2 Methods  The analysis of the regional variation of FDCs covered two main dimensions: (i) the study of FDC shapes in the context of landscape properties acting as a filter for precipitation at the catchment scale; and (ii) detailed analyses of the spatial pattern of the FDCs using flow components and runoff-generation mechanisms.  Prior to the FDC analyses, the study catchments were grouped into clusters of homogeneous storm characteristics in order to control for climate and isolate the effect of landscape properties on the regional variation of FDCs. The seasonality of storm characteristics was diagnosed in each catchment. This has been achieved by storm separation of hourly precipitation (see section 3.1 below). Analysis of the slope of FDCs (SFDCs) and their regional variation were conducted in this chapter of the thesis (e.g., the slope of the FDC is surrogate of the flow variability (Sawicz et al., 2011)). Categories of flow variability across study catchments were 67  defined based on the average value of SFDCs. Then, the differences in FDCs were investigated from the interaction of catchment filter with precipitation variability. The effect of catchment filter was assessed by means of the spatial pattern of FDCs and the precipitation duration curves (PDCs) using as guidance the conceptual framework of Yokoo and Sivapalan (2011). The slopes of the precipitation duration curve (PDC) are considered a surrogate of precipitation variability. The catchment filter effect on the precipitation collectively represent the impact of the landscape properties (e.g., soil hydrologic properties, surface topography, and vegetation type) and the geology structure. The limited availability of detailed descriptors of the vegetation (e.g., age, density, species) and the geology suggests focusing, in combination to the storm characteristics, on the impact of the landscape properties and the soil moisture storage capacity (SMSC).    The SAC-SMA model calibration (detailed description in Chapter 2, section 3.2.2.2) allowed to predict daily soil moisture and estimate the SMSC at the catchment scale.   The flow components provided by SAC-SMA simulations were utilized to meet the second dimension of the research goal. The analysis is aided by the predominant runoff generation mechanisms determined by TI distributions at the catchment scale (see section 3.2.2.3 of Chapter 3 for detailed description of TI calculations).  These process-based investigations explained the physical reasons for the regional variation of the FDCs. At this level, the effect of the catchment filter on precipitation (PDC) is reassessed to determine the flow component FDC that is directly affected by the precipitation variability. Figure 5-1 summarizes the several steps of the current study.  68   Figure 5-1: A conceptual diagram illustrating the workflow of the investitation. In the step 1, we identify the climate clusters. In the step 2, we analyze the precipitation duration curve (PDC) of each catchment in the cluster. In the step 3, we analyze the catchments’ properties (topography, soil hydrologic properties, soil moisture storage capacity (SMSC)) except from other factors that deals with the bedrock structure and geomorphology.  In the step 4, we investigate the SFDCs (slope of the FDCs) to study the regional variation of the FDCs that results from the interaction between the landscape properties and the precipitation variability (measured by the slope of the PDC). It is the catchment filter stage that assesses how strong the catchment system is in filtering the precipitation.  We complement the investigation with analyses of the runoff processes using the topographic index (TI) and the flow component FDCs.  5.2.1 Storm separation  The hourly rainfall data were obtained from the MOPEX database that is available for each study catchment. The hourly rainfall was separated into storm and inter-storm periods using an automated objective algorithm. The separation criterion is a specified minimum dry period between consecutive events equal to 6 hours (Erskine, 1951; Eisenlohr, 1952; Miller, 1990; Smith et al., 1996), which is similar to what other researchers have adopted: Hershfield (1961) and Huff (1967) used 6 hours; Koutsoyiannis and Foufoula-Georgiou (1993) used 7 hours.  Robinson and 69  Sivapalan (1997) used 7 hours in a study area belonging to the Appalachian region. The pulse events of intensity equal or lower than 0.01 mm/hour are considered as part of a no-event period. The storm separation generated a time series of storm intensity, storm duration, and storm depth. Subsequently, the mean monthly change of the storm depth, storm intensity, and the storm duration were investigated. The behaviour of the change was analyzed more closely in order to classify the catchments into clusters of homogeneous storm characteristics. From this perspective, using climate indices and a synoptic based approach (e.g., Verdon-Kidd and Kiem, 2009) would not help to get a detailed knowledge of the storm characteristics.   5.2.2 Soil moisture storage capacity  The soil moisture storage capacity (SMSC) is a surrogate of root zone depth, as described in Gao et al. (2014). It is a reservoir that acts as a dynamic buffer that moderates flows and retains tension water for plant use (Fenicia et al., 2008; Zhao and Liu, 1995). Therefore, SMSC was calculated using daily soil moisture (SM) estimates from the SAC-SMA model. Every year, each catchment has a maximum and minimum value of SM. The difference between the two figures is equivalent to the reservoir of catchment water storage capacity (Gao et al., 2014). The median storage capacity for each catchment was determined and taken as representative. 5.2.3 Slope of the empirical FDC The slope of the FDC (SFDC) is a surrogate of the flow variability in time (Sawicz et al., 2011). It is calculated between the 33rd and 66th flow quantiles, since at semi-log scale this represents a relatively linear part of the FDC (Yadav et al., 2007; Zhang et al., 2008). The entire daily record of the 50-year (on average) length was used to construct the empirical FDCs and to calculate their slopes. A high slope value indicates a variable flow regime, while a small value means a more damped flow response (Sawicz et al., 2011).  70  The SFDC is defined as: SFDC= ln(𝑄33%)−ln⁡(𝑄66%)(0.66−0.33)                                                                                                             (2) where SFDC is the slope of the flow duration curve, Q33% is the streamflow value at the 33rd percentile, and Q66% is its value at the 66th percentile. We normalized the empirical FDCs by the mean annual daily flows as in Yoko and Sivapalan (2011) and Yaeger et al. (2012) before we calculated the slopes of the curves.  5.2.4 Precipitation duration curve and catchment filter  The PDC is constructed in the same way as the FDC, however, it used daily precipitation instead of daily flows (Smakhtin and Masse, 2000). The entire daily record of 50 years (on average) was used to construct the empirical PDCs and calculate their slopes (SPDC). The PDCs were normalized by their respective mean daily precipitation before calculating the slopes. Unlike FDC, the slope of the PDC usually dips at a smaller percentile than the total 100% because precipitation may be null for many days in a year (Smakhtin and Masse, 2000). Then, the most linear part of the SPDC calculation will not be equal to that used for SFDC; instead, it will depend on the precipitation records. The linear portion of PDC across the study catchments ranged between 10% and 30%. According to the conceptual framework of Yokoo and Sivapalan (2011), the precipitation is filtered by the catchment system to generate daily flows of a given variability. Here we assumed that the catchment filter can be assessed using the ratio of SFDC to SPDC. Higher values of this ratio correspond to SFDC values that are closer to SPDC; this also corresponds to weaker catchment filters, leading to high flow variability.  71  5.3 Results  5.3.1 Effects of landscape properties  5.3.1.1 Climate clusters  The Figure 5-2(a) illustrates the catchments classified into three clusters according to monthly changes of average daily storm intensity, storm duration, and storm depth.  The storm intensity had the most systematic regional variation across the eastern US compared to the rest of storm metrics. Therefore, it was this criterion that helped to classify the study catchments into three clusters, or geographically defined regions, of homogeneous storm characteristics. The C3 cluster (Fig. 5-2(b)) had a peak storm intensity in summer (July). In C2, the storm intensity had no seasonality (Fig. 5-2(c)). However, in C1 (Fig. 5-2(d)), we observed two peaks: a first one in summer and a second in late winter. Meanwhile, the storm depth seasonality was similar in C2 and C1 clusters, declining dramatically during the summer and increasing during the fall and winter. In the C3 cluster (northeast), the storm depth was marginally higher in the summer compared to the fall and winter seasons. The duration did not exhibit a seasonal pattern, and its variation is correlated to storm intensity fluctuations.  Smaller storm intensities corresponded to larger durations and vice versa. The storms in C3 and C2 clusters had the longest duration (24h), while in C1 the duration did not go beyond 18h. 72   Figure 5-2: (a) catchments classification into three clusters according to storm seasonality (b) seasonal variation of storm characteristics in C3 cluster (c) seasonal variation of storm characteristics in C2 cluster (d) seasonal variation of storm characteristics in C1 cluster. The squares on the map denote the catchments with PDCs dipping at 50%.  5.3.1.2 Precipitation variability from slopes of precipitation duration curves  On average, the PDC curves dip at 70% of time exceedance in the C1 and C2 clusters and at 80% for the C3 cluster in the northeastern US (Fig. 5-3(b), (d), and (c), respectively). These high precipitation percentiles are illustrative of the humid climate in the eastern US. Three catchments in the C3 cluster dip at 50%. They are highlighted by a rectangle in Figure 5-2(a). These catchments have a larger number of days with zero precipitation than the rest of the catchments in the same cluster. The MAP for each of these three catchments is in the same range of the average value in the C3 cluster (1100 mm).  73   Figure 5-3: (a) CDFs of the slopes of PDCs across clusters (b) normalized PDCs in C2 cluster by mean annual daily precipitation (c) normalized PDCs in C3 cluster by mean annual daily precipitation (d) normalized PDCs in C1 cluster by mean annual daily precipitation.  The cumulative distribution function (CDFs) of SPDCs in each catchment for each cluster are shown in Figure 5-3(a). The clusters of C1 and C2 have the steepest PDCs (high variability of precipitation). In C3, the precipitation is less variable because of flatter PDCs (Fig. 5-3(a)). 5.3.1.3 Soil moisture storage capacity The SMSC (Soil Moisture Storage Capacity) was classified into two groups based on the average of 73 catchments in Figure 5-4(a). The figure shows that lowland areas (e.g., in North Carolina, Georgia, and some catchments in Virginia and Pennsylvania) have above average SMSCs compared to highland areas (e.g., high elevations of Appalachian Mountains) where SMSCs are below average. The C1 (Georgia) and C2 clusters are regions where most of the catchments have high SMSC compared to catchments in C3 (Fig. 5-4(b)). Overall, SMSC 74  increases along North-South and West-East directions. The Forest cover was the lowest in proportions in C2 and C3 (Fig. 5-4(c)). The SMSCs were the smallest in the C3 because of catchments with highest mean elevations (Fig. 5-4(d)), and poor drained soils (highest rates of HGC soils, Fig. 5-4(e).The SMSC was significantly negatively correlated (p-values <0.05) to forest cover, catchment mean elevation, and HGC soils (Fig. 5-4(f), (g), (h)). Consequently, SMSC is affected by the interaction between forest cover, topography, and soil hydrologic properties. In C2, the SMSC increased as the infiltration rates increased (lower HGC, Fig. 5-4(e)) and the mean elevation decreased (Fig. 5-4(a)). In C1, the SMSC was the largest with low mean elevations (Fig. 5-4(d)), and well-drained soils (lower HGC, Fig. 5-4(e)).  The catchments at high elevation happened to be the most forested (Fig. 5-4(c)). The SMSC decreased at the most forested catchments (Fig. 5-4(f)). 5.3.1.4 The regional variation of the FDC: categories of flow variability The FDC slopes were grouped into two categories: SFDCs below and above average. Figure 5-5 (a) shows the non-spatial correlation of SFDCs with climate clusters, which demonstrates the dominant effect of catchment landscape properties in the regional variation of the FDCs. The SFDC decreases from northern to southern regions. The SFDC is correlated with catchment latitude via a statistically significant relationship (R2=0.076, r =0.27, p-value <0.05). We do not show the figure of the regression for conciseness. The SFDC also decreases in a west-east direction (Fig. 5-5(a)) which explains the low R2 of the SFDC-latitude relationship. Figures 5-5(b), (c), and (d) illustrate the FDC of each catchment classified into clusters of homogeneous storm characteristics. The steepest FDCs (highest SFDC values) are mostly located in the C3 cluster and in some catchments from C1 and C2 (Fig. 5-5(e)).  75   Figure 5-4: (a) Regional variation of soil moisture storage capacity (b) cumulative distribution function (CDF) of soil moisture storage capacity (c) CDF of forest cover for each cluster (d) CDF of mean elevation for each cluster (e) CDF of HGC soils for each cluster (f) correlation between forest cover and SMSC (g) correlation between catchment mean elevation and SMSC (h) correlation between HGC and SMSC. 76  Most catchments in C1 and C2 had small SFDCs. In Figures 5-5(f) and (g), the change in the flow variability (SFDC) is related to the change in soil moisture storage capacity (SMSC) and soil hydrologic properties (HGC) (p-value<0.05). We notice that there is high variability of the SFDC in the 200-300 mm range of the SMSC. The SMSC explains only 4.5% (R2 =0.045) of the total variability of the SFDC. Thus, in the 200-300 mm range of the SMSC, the FDC may have low or large value of the slopes. This hints at other factors that caused this variability. Also, there is high variability around HGC 0-20% and a small decrease of the SFDC for HGC beyond the 70%. We admit that, in addition to the soil infiltration rates (indicated by proportions of the HGC) and properties of the SMSC, the structure of the subsurface geology and the deep groundwater would have contributed to this variability.  The spatial pattern of SFDC shows that in the northeastern US (C3), most catchments have high flow variability (large SFDCs) and small SMSCs at high elevations where HGC soils are predominant (Fig. 2-2(b)).  The few catchments in C1 (South East) and C2 (Center) with large SFDCS had small SMSCs and soils with medium to slow infiltration rates (half HGC and half HGB). They are mainly located in Kentucky and the interior parts of Virginia (Fig. 5-5(a)). Two main particularities in the spatial pattern of the FDCs are worth mentioning. First, there were few catchments in C2 where small SMSC was associated with limited flow variability (small SFDC). These catchments (highlighted by a rectangle in Fig. 5-5(a)) have predominant HGB soils (Fig. 2-2). Second, few catchments in North Carolina and South Georgia (highlighted by oval shape in Fig. 5-5(a)) had large flow variability (high SFDC) in soils with large SMSC and slow infiltration rates (HGC and HGD) (Fig. 5-4).  77   Figure 5-5: (a) Regional variation of FDC slopes; the square shape refers to catchments with small SMSC and flat FDC. The oval shape highlights catchments with large SMSC and steep FDC; (b) normalized FDCs in C3 cluster; (c) normalized FDCs in C2 cluster; (d) normalized FDCs in C1 cluster; (e) the CDFs of the SFDCs across clusters; (f) the SFDC-SMSC correlation; (g) SFDC-HGC correlation  78  5.3.1.5 Effect of catchment filter on precipitation and flow duration curves  After analysis of the spatial pattern of the SFDC that changes proportionally to patterns of the landscape properties (mean elevation, HGC, forest cover) and the SMSC, this section explores the pattern of the catchment filter. The catchment filter helps to implicitly measure the effect of the catchment system in filtering the precipitation and in generating flow characterized by some level of variability (a value of the SFDC). According to the way it is calculated (ratio of the SFDC by the SPDC), it points collectively to the effect of all the factors that contribute to filter the precipitation (e.g., landscape properties, deep groundwater, and the geology structure).  In Figure 5-6(a), the filter effect increased from the northern to southern regions. The weakest filters were found in the C3 cluster where SFDC to SPDC ratio was above average (Fig. 5-6(a), (b)). The filters in most catchments from C1 and C2 had below average ratios (Fig. 5-6(b)).  The CDFs representing the catchment filters in C1 and C2 illustrate the extent to which they have similar landscape characteristics (Fig. 5-6(b)).  The spatial pattern of the catchment filters in Fig. 5-6(a) reflects that of FDC in Fig. 5-5(a). Hence, the FDC shapes are a mirror of the catchment filter effect on PDC. The characteristics of the catchment filters are related to the soil hydrologic properties and soil moisture storage capacity (Fig. 5-6(c), (d)). The effect of the catchment filters on precipitation became more pronounced as HGC rates decreased and SMSC increased (p-value <0.05).  79   Figure 5-6: (a) The spatial pattern of rain filter; the oval shape highlights the catchments we used for the parameter permutation in section 4.2.3 (b) CDFs of the filter across clusters (c) the correlation between SMSC and the catchment filter (d) the correlation between the proportions of HGC soils and the catchment filter. 80  5.3.2 Process understanding of the FDC regional variation  5.3.2.1 Aspect of flow component FDCs  Figure 5-7: (a) Baseflow FDC, interflow FDC, and surface flow FDC for catchments with large SFDCs (b) Baseflow FDC, interflow FDC, and surface flow FDC for catchments with small SFDCs. All the curves are normalized by the mean annual daily flow as in Yokoo and Sivapalan et al. (2011)  Figure 5-7 displays the FDCs of each flow component with regard to SFDC categories (High SFDC versus low SFDC in Fig. 5-5(a)). The slopes of the baseflow FDCs are of larger values in Figure 5-7(a) for sites with high SFDCs than those in Figure 5-7(b) for sites with low SFDCs. We calculated the slope of the median baseflow FDC in each category. It was larger in the category of large SFDCs (slope 3.55) than that of small SFDCs (slope 2.42) (Fig. 5-7(a), and 5-7(b)). This suggests that the total flow variability is partly caused by the baseflow variability. Interflow has a more pronounced contribution to total flow in catchments with large SFDCs compared to those with flat small SFDCs. In fact, it dips between 20% and 70% of the flow 81  percentiles for high SFDC category, whereas this happens between 30% and 55% for low SFDC category (Fig. 5-7(b) and 5-7(e), respectively).   Figure 5-8: (a) median baseflow FDC, median interflow FDC, and median surface flow FDC for catchments with large SFDCs (b) median baseflow FDC, median interflow FDC, and median surface flow FDC for catchments with small SFDCs. All the curves are normalized by the mean annual daily flow (Qm) as in Yokoo and Sivapalan et al. (2011).  The normalized median curves confirm these differences (Fig. 5-8(a) it dips at 47% and at 35% in Fig. 5-8(b)). The surface flow FDCs in the upper tail and until 40% of the distribution are flatter for catchments with small flow variability (small SFDCs in Fig. 5-7(b)) compared to those with high flow variability (large SFDC catchments category in Fig. 5-7(a)). This flow lasts longer and has less irregularities at the lower tail for catchments exhibiting large SFDCs (it dips between 85% and 95% when SFDC is large and between 60% and 80% in when SFDC is small). The normalized surface flow FDCs in both categories is consistent with the differences in the upper 82  tail where surface flow FDC is more regular in the large SFDC category, whereas it showed an inflexion at 40% in the small SFDC category (Fig. 5-8(a) and Fig. 5-8(b), respectively).  Consequently, high flow variability stems from a highly variable baseflow, a predominant interflow, and a highly variable surface flow. However, in catchments where the response is dampened (small SFDCs), the baseflow and surface flow are less variable, and interflow contributes less to the total flow variability.  5.3.2.2 Predominant runoff generation mechanism across the eastern US The differences of flow component indices and their FDCs across TI categories (right-skewed, left-skewed and middle) (Fig. 5-9) explained the pattern of the runoff mechanisms. The baseflow indices were consistent (Fig. 5-10(a) and Fig. 5-10(d)). However, according to the CDFs of the surface flow index, this latter is higher in catchments with dominant saturation excess overland flow (right skewed and to some exent the middle TI clusters) (Figs. 5-9 and 5-10(d)). The subsurface flow and interflow indices are larger in catchments with predominant subsurface runoff processes (left-skewed TI cluster in Fig. 5-9) (Fig. 5-10(c) and Fig. 5-10(f), respectively). Figure 5-11 compares the FDC flow components using typical catchments in each TI category.  The interflow was dominant as a result of prevalent subsurface runoff processes—that is, it dips at 50% and 35% of the distribution in left skewed and middle TI category in Figures 5-11(a) and 5-11(c), respectively. The interflow effect on the response becomes of lesser importance whenever the saturation excess is dominant (e.g., interflow dips at 30% of the distribution  in Fig. 5-11(b)).   83   Figure 5-9: (a) spatial distribution of TI groups designated as TI classification in the map across catchments of similar storm characteristics; (b) frequency distribution of topographic index per catchment. Three different groups were identified; the right skewed (predominant saturation excess), the middle, and left skewed (predominant subsurface stormflow).   Figure 5-10: a) The CDF of SMSCs in each TI cluster (b) the CDF of SFDCs in each TI cluster (c) the CDF of subsurface flow index per TI cluster (d) CDF of surface flow index per TI cluster (e) CDF of baseflow index per TI cluster (f) CDF of interflow index per TI cluster. The baseflow index was calculated from the ratio of base flow to total streamflow (Schaake et al., 2006). The other flow indices were determined using the same approach. The subsurface flow index was calculated after summing up the baseflow and the interflow. 84   Figure 5-11: Flow component FDCs for representative catchments from each TI cluster (a) a catchment from left skewed TI distribution, (b) a catchment from right skewed TI distribution, (c) a catchment from middle TI distribution.  5.3.2.3 FDC regional variation in relation to the pattern of runoff generation mechanism From Figure 5-9, the catchments with predominant subsurface processes have large SFDCs (Figure 5-5(a) and limited soil moisture storage capacity (SMSC) (Fig. 5-4(a)).  In catchments with large SMSC (Fig. 5-4(a)), the prevalent saturation excess overland flow decreases the SFDCs (Fig. 5-5(a)). It is worth mentioning that in some catchments (highlighted by an oval shape in Fig. 5-9(a)) with predominant saturation excess and large SMSC (Fig. 5-4(a)), the SFDCs are of large values (Fig. 5-5(a)). Also, few catchments with predominant subsurface processes and limited SMSC (highlighted by square shape in Fig. 5-9(a)) exhibited low flow variability (small SFDCs) (Fig. 5-5(a)). This seems to conflict with the general pattern of the relationship between FDC shapes and predominant runoff generation mechanism. Other factors interacted with the topography  (e.g., soil structure). The soils in catchments highlighted by an oval shape is a combination of HGC and HGB proportions (Fig. 2-2). Moreover, the soils in catchments highlighted by a square are well drained (HGB, in Fig. 2-2). These combinations are pointing out to the following: Whenever saturation excess is predominant, the limited water infiltration could 85  make the flow response less dampened. Also, under predominant subsurface processes, the high infiltration rate mitigates the flow response.   Figure 5-12: (a) flow component FDCs for a catchment with 55% HGC and 30% HGB (b) flow component FDCs for a catchment with 11% HGC and 74% HGB (c) flow components FDC for catchment in (b) using model parameters from catchment in (a). Qobs is observed flow response, Qsim is the simulated flow, P is the daily precipitation. The suffix “b” refers to base conditions prior to parameter permutations. The suffix “s” refers to the permutation scenario.  In order to better understand the effect of the infiltration rate on the runoff processes and the FDC shape, we used the  parameter permutations between two catchments of different soil properties (HGC versus HGB) and located in the piedmont region (highlighted with ovale shape in Fig 5-6(a)). A detailed description of the catchments’ main characteristics is provided in Table A-1 (Appendix). The saturation excess is predominant in both catchments. The calibrated parameters of the catchment with poor drainage conditions (Fig. 5-12(a)) are used to simulate flows for the catchment with predominant HGB (Fig. 5-12(b)). The total flow FDC diverge in catchment number 02349500 from the base conditions (Fig. 5-12(c)). The interflow shifted upward, while baseflow diverged from base conditions. The surface flow curve kept the same shape after parameter permutation. Hence, the change in the FDC shapes of interflow and baseflow steepened the total flow FDC. 86  5.3.2.4 Flow components of the FDC with regards to precipitation: process understanding of the catchment filter The effect of the catchment filter on precipitation (precipitation duration curve, PDC) could be demonstrated through the aspect of subsurface and surface processes. From Figures 5-11 and 5-12, the surface flow is most sensitive to PDC. The PDC and the surface flow FDC dip at the same percentile contrary to the subsurface flow components (interflow and baseflow). They seem to be less dependent on precipitation and rather more dependent on subsurface processes such as the groundwater and properties of soils deep percolation.    Note that the surface flow FDC is almost parallel to the PDC in catchments with predominant subsurface processes and poorly drained soils (Figs. 5-11(a), (c)). However, according to Figures 5-11(b) and 5-12(b), the surface flow FDC deviates from the PDC at the upper tail in catchments with small SFDCs under conditions of predominant saturation excess and well-drained soils (HGB). Hence, the catchment filter, although it seems to directly affect subsurface processes, appears to affect surface flow response in catchments with limited flow variability. 5.4 Discussion  The goal of this paper was to elucidate the spatial pattern of FDCs over the eastern US and to evaluate the interaction between climate and landscape properties with respect to runoff processes in order to provide a comprehensive physical understanding of the regional variation of FDCs. We analyzed rainfall-runoff data from 73 MOPEX catchments. These catchments were classified into clusters of homogeneous storm characteristics in order to control for climate and better inspect the effect of landscape properties. 87  The storm intensity revealed the most distinct systematic seasonal variation across catchments and was used as a criterion for the classification. The use of other climatic variables (e.g., precipitation and temperature) for climate classification in past studies from the US were less relevant to delineate zones of similar climate (e.g., Fovell and Fovell, 1993). Our cluster delineation using similarity in storm characteristics was consistent with Hershfield (1961), where in the northeastern US (C3 cluster), the storm intensity has a peak in the summer, in the center it is evenly distributed through seasons (C2 cluster), and in the southeast (state of Georgia in C1 cluster) it shows two peaks during the summer and spring seasons. The climate classification by Coopersmith et al. (2012) in the US split our study area into two clusters based on a combination of climate indices (e.g., aridity, precipitation seasonality, peak of precipitation day) and the average runoff.  Most likely, the storm characteristics help to elucidate more details about climate homogeneity, which is critically needed for the study of interaction between climate and landscape properties. 5.4.1 To what extent the diversity of FDC shapes can be explained by climate and landscape properties?  In the cluster of low precipitation variability (flat PDC) in the northeastern US (C3 cluster) (Fig. 5-3(a)), the flows had high variability (large SFDCs) (Fig. 5-5(e)). Also, in clusters of high precipitation variability, (steep PDC) in the central regions (C2 cluster) (Fig. 5-3(a)), and in southeastern US (C1 cluster in Georgia), the flows had low variability (small SFDCs) (Fig. 5-5(e)). This finding underlines the effect of the catchments filter when interacting with the precipitation in the process of flow generation. As a result of the effect of the catchment filter, the overall pattern was a decrease in the value of slope of the FDC slopes from northern to southern regions and from 88  west to east directions (statistical significant correlation of the SFDC with the latitude, p-value<0.05)  This study underlines the effect of interaction between the soil moisture storage capacity (SMSC), the soil drainage conditions, and the topography in characterizing the catchment filter (Figs. 5-4 and 5-6) whose spatial pattern (Fig. 5-6(a)) mirrored the regional variation of the FDC (Fig. 5-5(a)). Most of the large (small) SFDCs are located at high (low) elevation (Fig. 5-5(a)). However, there are few catchments, in C1 and C2 clusters, despite they are at high (low) elevation they have small (large) SFDCs (highlighted by square and an oval shape in Fig. 5-5(a), respectively). In the following, we discuss first the reasons for large (small) SFDCs at high (low) elevation.  We found that most of the catchments in C1 and C2 acted as a strong precipitation filter (Fig. 5-6(b)) due to large SMSC (Figs. 5-4(b) and 5-6) and large soil infiltration rates (Fig. 5-4(e) and 5-6(d)). Whereas the catchment filter in C3 was weaker because of small SMSC at high elevation (Figs. 5-4(b) and 5-6) and poorly drained soils (Figs. 5-4(e) and 5-6). A study by Swift et al. (1988) demonstrated that the decreasing soil depth in steep topography resulted in less opportunity to store soil moisture before a rain. Also, the Swift et al. (1989) suggested that, at higher elevation, there is a limited evapotranspiration demand. In current study region, the potential evapotranspiration (PET) decreased with elevation. This finding supports the idea of decreased ET at high elevation and its effect on enhancing the flow variability. The map of PET spatial pattern decreasing with the mean elevation was not shown in this Chapter for brevity.  In conditions of catchments at high elevation, Butt et al. (2001) stated that the steep topography  indicates the hydraulic gradient of shallow soils. These physical explanations combining the decrease of soil moisture storage capacity with the decrease of ET and the increase of the hydraulic gradient—under conditions of steep topography— corroborate our findings and help to understand 89  the controls of large values of the SFDCs at high elevations (in catchments of the C3 cluster and a few in C1 and C2 clusters). The results, also underscored the effect of the soil properties on shapes of the FDCs (the increase in the HGC proportions steepened the slope of the FDCs (Fig. 5-5(g)). According to Price (2011), the influence of soil characteristics on water storage is can be understood through the tight correlations between soil properties and topography. The soil properties play a significant role in the rate of soil moisture loss due to surface or subsurface topographic gradients (Dodd and Lauenroth, 1997; Yeakley et al., 1998). Therefore, large values of the FDC slopes at high elevations in C3, and in a few catchments from C1 and C2, could be related to the interaction of shallow soils with poor drainage conditions. This effect is maximized in C3 where the SFDCs were the largest (Fig. 5-5(e)) and close to the precipitation variability (slope of PDC) (Fig. 5-6(a)). In contrast to conditions of large SFDCs, the mitigated flow response (small SFDCs) in most catchments from C1 and C2 could be explained by the interaction of flat topography with soils of high infiltration rates (HGB). The increased water storage capacity (large SMSC) dampened the flow variability despite the large precipitation variability.   We should mention that, in this study, the effect of vegetation cover on low variability was, overall, not as explicit as the effect of topography and soil drainage conditions. In fact, the contrast in types of the vegetation cover between the study catchments is not as pronounced as it is for topography and soil hydrologic properties. The vegetation cover is consistent and decreases in few catchments in piedmonts and the southeastern US (see Fig. 8 in Berghuijs et al. (2014)). Therefore, the vegetation cover effect was rather implicit to that of soil moisture storage capacity (statistically significant correlation between SMSC and forest cover proportions in Fig. 5-4(f)).  With regard to conditions of large SFDCs at low elevations (in southern Georgia (in C1) and in the east coast (in C2)) and small SFDCs at high elevations (in C2) (Fig. 5-5(a)), this finding 90  could explain the considerable scatter we found for the SFDC-SMSC correlation (p-value<0.05) (Fig. 5-5(f)) compared to the SFDC-HGC relationship (p-value<0.05) (Fig. 5-5(e)).   The decrease in SMSC, due to elevation, while it is associated with large SFDCs should not be taken as a general pattern. There are other factors, apart from the elevation, that control the FDC shapes. For instance, the effect of the groundwater (implicitly considered in soil moisture simulations of the SAC-SMA model) and the geology structure that are not investigated because of limited data availability.  Nonetheless, the landscape properties (e.g., soil hydrologic properties, forest cover) interacting with the SMSC pattern help in framing an explanation. The SMSC correlates with the forest cover, mean elevation, and soil hydrologic properties (Fig. 5-4(f), (g), and (h)).  At high elevations (small SMSC) in conditions of small SFDCs, the large infiltration rate allows for the rain water to move downward to the root zone. In presence of forest cover, the water might have been used by the forest (e.g., transpiration and interception) to allow for additional storage as ET takes place (Bonell, 1993). Hence, less water is stored in the soil leading to dry antecedent moisture conditions prior to the rain event. It has been shown repeatedly, particularly by isotope hydrology, that pre-event conditions, mainly the antecedent moisture conditions, affect the flow response (McDonnell 1990; Sklash and Farvolen, 1979). In a study by Burt and Swank (1992) the forest cover explicitly reduced the flow response by affecting flow magnitudes and their respective frequency. The FDCs were of lower value of the slope compared to those from other vegetation types.  The dry antecedent moisture conditions due to the effect of the forest cover mitigates the flow for all ranges of the precipitation events (small and extremes). This effect remains true for small to medium flows based on deterministic chronological pairing approach (Bathurst, 2014) as well as for extreme flows based on stochastic frequency pairing approach (Birkinshaw et al., 2011, Figure 8; Crooks and Davis 2001, Figure 6; Reynard et al., 2001, Figure 91  5). Therefore, it appears that, in the few fully forested catchments at high elevations, the small SFDCs are related to the effect of the interaction between the forest cover and the large infiltration rate on the antecedent moisture conditions and consequently on the flows’ magnitude and frequency. With regard to the condition of large SFDCs at low elevations, most likely the low infiltration rates (dominant HGC soils) did not allow to damp the flow response despite the large SMSC. Other factors are to mention, mainly those related to the effect of below surface geology and its role to advance the understanding of the flow variability controls, particularly in mountainous areas (e.g., Di Matteo et al., 2017; Kelson and Wells 1989). This dimension is again not covered in the present research because of lack of data. The findings from the empirical analysis partially agree with the hypothesis of Yokoo and Sivapalan (2011) that stems from a theoretical numerical study, where it has been suggested that slope of the FDCs in shallow soils are steeper than those in deep soils. It is true that most catchments in the present study region have large (small) SFDCs at high elevations in conditions of small (large) SMSC. However, the exceptions found make the generalization hampered by the soil hydrologic properties, in addition to other factors related to the subsurface geology.  The analyses suggest that when SMSC is large and the soil is poorly drained, the flow variability could be high (close to precipitation variability) because of limited infiltration rates. The FDCs may have flatter slope despite the small SMSC in well-drained soils. The effect of landscape properties on steepening the FDCs is maximized (in C3 cluster) if the poor drainage conditions and small SMSCs on steep topography are combined.  The several hypotheses that emerge from the empirical analyses require further testing using several degrees of landscape complexity when interacting with the climate.  92  5.4.2 Process-based understanding of the spatial pattern of FDCs The process-based analyses of the spatial pattern of SFDCs revealed that catchments with large SFDCs mainly (in C3 cluster and in few catchments from C1 and C2) have a larger proportion of interflow and steep slope of the surface flow FDCs (Figs. 5-7(a), 5-8(a)) than catchments with small SFDCs. The runoff flow components have different velocities: usually, surface flow is the fastest response followed by interflow and baseflow. Previous studies found that subsurface flow (sum of interflow and baseflow) can be as fast as surface flow (e.g., Sklash and Fervolen (1979)). These properties imply that high flow variability (large SFDCs) can be related to the predominance of fast-flow components on the response. Also, it has been shown that more variable total flow corresponds with steeper slope of the baseflow FDCs (as well as larger slopes of median baseflow FDCs; see Fig. 5-8). This result suggests that baseflow characteristics vary with catchment conditions. Although baseflow is a slow response, it affects the overall flow variability. This result hints at the effect of groundwater associated with geology of soils below surface (e.g., Di Matteo et al., 2017). The TI analyses showed that most catchments with large SFDCs had left-skewed TI distributions with small values in their tails. This fact leads to predominant subsurface flow processes in the runoff generation routine (Beven and Kirkby, 1979) illustrated by large interflow index hinting at limited groundwater effect. The predominant landscape properties in catchments with large SFDCs (limited SMSC, steep topography, and poor drainage conditions) and the properties of the surface and interflow responses indicate that the FDC shape illustrates the effect of limited runoff contributing area (small TIs in tails). Likely, the hydraulic gradient is the major regulator of the response (Hewlett and Hibbert, 1967).  93  Another significant aspect deals with the effect of soil infiltration rates in the runoff processes (a combination of HGB and HGC or fully HGC). In catchments of large SFDCs, the surface-flow FDCs were of more regular shape than in catchments of small SFDCs (all dip at 80% in Fig. 5-7(c) versus 60 to 80% in Fig. 5-7(f)). The small infiltration rates in catchments with large SFDCs —mostly located in hillslopes— suggest that the infiltration excess overland flow is dominant in the process of surface flow generation (Beven and Wood, 1983). Guebert and Gardner (2001) found that in steep slope catchments, the surface flow response becomes faster when it is dominated by the infiltration excess mechanism. Therefore, the large SFDCs illustrate the culminated effect of the infiltration excess surface flow  and the interflow. The effect of this combination could be of major impact in C3 catchments due to larger proportions of HGC soils compared to the rest of catchments in C1 and C2 of the same large SFDC category.  With respect to the small SFDCs, that represent most catchments in C1 and C2, the proportion of interflow from the total flow is low (Fig. 5-8(b)). The surface flow FDCs at the upper tail as well as the median slope of the baseflow FDCs are flat (see Fig. 5-8(b)). In these catchments, the increase of TIs in the tails make the TI distributions right-skewed (Fig. 5-9(b).) TI increases as contributing area increases and slope angle decreases (see equation (2)), hinting to a well-developed riparian zone (Beven and Wood, 1983). Usually, the more developed this zone the deeper the soils, allowing for more infiltration until saturation. The runoff response under these conditions is dominated by saturation excess overland flow .The excess water runs as surface runoff due to saturation excess overland flow (Beven and Wood, 1983). The aspect of runoff processes in most catchments from C1 and C2 and the landscape properties (large SMSCs and high proportions of HGB soils) suggest that the saturation excess dampens the flow response as a result of flat topography and large infiltration rates. Likely, the increase of groundwater levels, in 94  catchments with small SFDCs at low elevations, slows down the surface flow, limits the interflow contribution and enhances the baseflow.  As pointed out in the previous sub-section 5.4.1, the FDCs could be flat in conditions of small SMSC and well-drained soils. The TI analyses classified these catchments (highlighted by square shape in Fig. 5-9(a)) under a predominant subsurface runoff processes category. Likewise, other catchments with prevalent saturation excess have small SFDCs in presence of poorly drained soils (highlighted by oval shape in Fig. 5-9(a)). Both findings support the idea about the influence of infiltration rate in affecting the runoff processes. In the literature, the infiltration rate is associated with soil depth, topography, and hydrologic characteristics (Weiler and McDonnell, 2007), and it is a chief regulator of the flow response (Guebert and Gardner, 2001). Therefore, in the catchments with small values of SMSC and the SFDC, the impact of the predominant subsurface stormflow at hillslopes could have been lessened by the high infiltration rates that reduced the interflow contribution (Fig. 5-10(f), respectively). Under similar conditions, Guebert and Gardner (2001) stated that on catchments at high elevation, the landscape features in combination with high infiltration rate may produce a significant overland flow by saturation excess mechanism. The saturation in hillslope catchments is controlled by both the topography and the permeability of soil layers (Graham et al., 2010). More research is required to elucidate the relative role of saturation excess on the flow response when subsurface stormflow is dominant in hillslope catchments of well-drained soils.    The results from parameter permutations between catchments at low elevations and of opposite soil hydrologic properties (HGB versus HGC) explained the existence of catchments with steeper slope of the FDC at low elevations. The lower infiltration rate steepened the total flow FDC because the interflow shifted upward, and the baseflow diverged from base conditions (Fig. 95  5-12(c)). This outcome is consistent with Beven and Germann (1982), who stated that fine soil texture limits groundwater influence. Also, Bonell (1993) reported that in forest environments, the infiltration excess overland flow may occur in combination with saturation excess overland flow owing to properties of lower infiltration. Therefore, a predominant saturation excess may lead to a less dampened response because of limited drainage conditions. This is probably the most plausible physical explanation for the shapes of FDCs in the few catchments questioned here. With regard to the effect of the PDCs on the flow component FDCs as a response to the interaction with the catchment filter, the subsurface flow FDCs were not sensitive to the precipitation behaviour but were rather directly affected by the catchment conditions. Only surface flow FDC tracked the PDC, as suggested by Yokoo and Sivapalan (2011). However, in typical catchments with small SFDCs, the surface flow FDC and PDC were not parallel, as in the theoretical study of Yokoo and Sivapalan (2011), but rather  diverged at the upper tail (> 40% of the surface flow percentile) (Fig. 5-11(b) and Fig. 5-12(b)). Therefore, for conditions of dampened flow, catchment characteristics have a major role in filtering the precipitation even at the level of a fast response. 5.5 Conclusions The state of knowledge about FDCs lacked physical understanding of the controls underpinning their regional variation. The current study helped to advance the physical understanding by investigating the interaction of climate and landscape properties and the innate runoff processes responsible for the disparities in the shapes of FDCs. Using 73 catchments from the eastern US, the study highlighted strong regional differences within and across clusters of homogeneous storm characteristics.  96  The FDC shapes were attributed to the filter effect of landscape properties on precipitation. This effect was pronounced so that regions with high precipitation variability had limited flow variability (small SFDC). On the other hand, the regions with low precipitation variability had the highest flow variability (large SFDC). The flow response was dampened (small SFDC) in catchments at low elevations of well-drained soils and large storage capacity. These characteristics led to predominant saturation excess overland flow that allowed for more infiltration to lower layers, enhanced baseflow, and limited the interflow. The largest slope of the FDCs were associated with steep topography, soils of small storage capacity, and low infiltration rates. This interaction led to dominant subsurface stormflow and surface flow generated by infiltration excess overland flow.  This chapter also demonstrated that the effect of soil infiltration rate on FDC shapes was pronounced such that small (large) SFDCs at low (high) elevations is not always a general pattern. At low elevation and large soil moisture storage capacity, the catchments with predominant saturation excess experienced high flow variability (large SFDCs) because of poor drainage conditions. Also, in shallow, well-drained soils at high elevations, the prevalent subsurface stormflow led to limited flow variability and small SFDCs.  For all of the process-based analyses, the surface flow was the flow component most directly affected by the precipitation variability. However, this relationship became less important in catchments with small SFDCs. This result suggests that both the subsurface flow components (interflow and baseflow) and the surface flow, are highly affected by the dominant filter effect dictated by the landscape properties.  97  Chapter 6: On the use of mean monthly runoff to predict the flow duration curve at ungauged catchments    6.1 Introduction  The FDC prediction at ungauged catchments traditionally consists of two steps. The first step determines the FDC distribution parameters at gauged catchments using the streamflow observations and curve fitting (Booker and Snelder, 2012). The second step develops a regional regression model to predict the statistical distribution parameters at ungauged catchments from the physiographic and climatic characteristics of the catchments (e.g., LeBoutillier and Waylen, 1993; Smakhtin et al., 1997; Holmes et al., 2002; Singh et al., 2001; Croker et al., 2003; Sauquet and Catalogne, 2011). In other studies, a regional non-dimensional distribution is developed using daily flows of gauged catchments of a homogeneous region where it is subsequently multiplied by the index flow, at the ungauged catchments, determined by mapping and interpolations (e.g., Vandewiele and Elias, 1995; Arnell, 1995) or through correlations with the basin characteristics (e.g., Claps and Fiorentino, 1997; Castellarin et al., 2004).  The FDCs at ungauged sites can also be obtained by an observed FDC using a dissimilarity method whereby a matrix describing dissimilarities between all pairs of FDCs is related to a matrix describing dissimilarities between the catchment characteristics of all pairs of gauging stations (e.g., Ganora et al., 2009). These diverse techniques that are used to predict the FDC at ungauged catchments lack linkages with the catchment hydrological processes (Botter et al., 2009).  Despite their utility, process-based studies that contribute to the development of methods for prediction of the FDC at ungauged catchments are rare (e.g. Botter et al., 2007a and b; Botter 98  et al., 2009; Muneepeerakul et al., 2010; Yokoo and Sivapalan, 2011). Process-based stochastic models for prediction of the FDC have been tested but are not fully developed and have not been validated in actual catchments across a range of topographic and hydroclimatic settings (Botter et al., 2007a, b; Botter et al., 2009; Muneepeerakul et al., 2010, Yokoo and Sivapalan, 2011).   Botter et al. (2007a) developed a stochastic model of the subsurface flow to predict the overall streamflow response. The stochastic model used physical parameters that can be easily determined at ungauged catchments including soil, vegetation, and geomorphic attributes (mean residence time of subsurface flow, and the size of the basin) (Botter et al., 2007a, b). Muneepeerakul et al. (2010) complemented the work by Botter (2007a and b) and added the surface flow component (fast flow) using a stochastic model of rainfall-streamflow generation. Testing the model in a few catchments showed that complex streamflow processes can be captured by separately simulating the surface and subsurface flows. However, this stochastic modelling framework has not been validated at regional scale in watersheds of different sizes, geological settings, and climate (Ceola et al., 2010; Botter et al., 2010).  The theoretical study by Yokoo and Sivapalan (2011) tested the effect of several combinations of climate and landscape properties, using a hypothetical catchment, on the shape of the FDC in relation to the mean monthly runoff represented in its stochastic form of the FDC (MM_FDC). The study utilized three years of synthetic rainfall time series to run a water balance model that makes use of climate, geographic parameters (e.g., depth of soil layer, average thickness of saturated zone), and soil parameters (e.g., hydraulic conductivity, porosity). The investigation invoked the simulated flow components of the FDC (surface flow FDC and subsurface flow FDC). The study tested the effect of climate dryness (humid versus dry), soil type (silt versus sand), and soil depth (shallow versus deep soil) in conditions of different climate seasonality (precipitation in 99  phase/out of phase with potential evapotranspiration). Yokoo and Sivapalan (2011) conjectured that the upper third of the FDC is determined by a non-linear transformation of the precipitation. In catchments with perennial flow and humid climate, Yokoo and Sivapalan (2011) hypothesized that the middle and the lower third are represented by the mean monthly runoff data that might need corrections to account for the effect of evapotranspiration (ET) on low flows in order to predict the FDC lower third. In catchments with ephemeral flows, the conjectures about the use of the mean monthly runoff data are not applicable. The conceptual model by Yokoo and Sivapalan (2011) is intended to facilitate the predictions at ungauged catchments—at least in humid climate— through extrapolations from the gauged catchments of the daily precipitation data, monthly flow data, climate dryness, and storage capacity (needed for the effect of ET). Precipitation data are often available at ungauged catchments (e.g., weighted average from rain gauges or by means of PRISM data (Schaake et al., 2006)) while mean monthly runoff is relatively easy to obtain at ungauged catchments from predictions of global runoff models (e.g., Nijssen et al., 2001; Xie et al., 1996). The use of the mean monthly data would also be valuable when the flow data at daily time scale are not available in the neighbouring gauged catchments. The findings and hypotheses in Yokoo and Sivapalan (2011) were based on a conceptual investigation using one theoretical catchment and hypothetical combinations of climate and landscape characteristics. Therefore, there is a need to develop and test hypotheses on actual catchments to further the process understanding and prediction of FDC at ungauged catchments using the monthly flow data.  The objective of this component of the thesis is to extend the work of Yokoo and Sivapalan (2011) to real catchments with varying characteristics and flow regime behaviours. The mean monthly flow— represented in its stochastic form (MM_FDC)—was investigated in order to 100  determine whether it can be used to estimate FDC across many catchments at the regional scale. The following research question guided the objective of the study: What are the catchment characteristics and the flow conditions that make the use of the MM_FDC in predictions of the FDC plausible? The answers that will be provided by our regional study will advance the understanding and will contribute to the wider objective of developing FDC prediction models with physical bases.  The analysis is not limited to knowledge of typical landscape characteristics and climate but takes advantage of the diversity in characteristics of the study catchments in combination with properties of the flow variability (steep versus milder slope of the FDC). The investigation of the relation between MM_FDC and FDC within the framework of a meta-analysis is key to meeting the objectives of this study and to furthering the understanding of conditions that limit the use of MM_FDC to predict FDC. Meta-analysis type of studies are of great value in hydrology and has recently aided in elucidating the hydrological response characteristics of Mediterranean catchments at different time scales (see Merheb et al., 2016).  6.2 Methods: Analysis of the MM_FDC in relation to the FDC Similarly to Chapter 5, the entire daily flow record of the 50-year (on average) length was used to construct the empirical FDCs. The slope of the FDC (SFDC) was calculated using equation 1 from Chapter 5.  The calculation of the MM_FDC slope (SMM_FDC) did not use the Q33% and Q66% as in FDC but rather utilized the higher and the lower values of the MM_FDC (Yaeger et al., 2012). The empirical FDCs and the MM_FDCs were normalized by the mean annual daily flows as in Yoko and Sivapalan (2011) and Yaeger et al. (2012) before calculating the slopes.  The correlation between the MM_FDC and the FDC slopes was examined first in order to determine how well the two curves are correlated before undertaking a detailed analysis of the 101  MM_FDC at each watershed.  The value of flow variability (slope of the FDC) was used as a criterion to distinguish between the study catchments and their flow response. The catchments that had an SFDC below the mean across all catchments were considered to have low flow variability (flatter slope of the FDC) while those with an SFDC above the mean had high flow variability (steeper slope of the FDC). The spatial pattern of the SMM_FDCs was compared to that of the SFDCs in order to find out whether a catchment with steeper slope of the FDC also had a steeper slope of the MM_FDC. This comparison revealed at a preliminary stage whether the differences in the regional variation of the FDC were similar to that of the MM_FDC. Each of the FDC portions (the FDC upper, middle, and lower thirds) was compared to the MM_FDC as in Yokoo and Sivapalan (2011). However, in this study the comparison distinguished between each category of the flow variability and is conducted at individual real catchments instead of hypothetical catchments.  The meta-analysis between the study catchments considers the differences in landscape properties. The real combinations of the catchment characteristics reveal the physical conditions under which the prediction of FDC from the MM_FDC is (or is not) possible.  The flow components FDC were used in the meta-analysis to reveal the processes underlying each of the FDC portions and further explore the plausibility of using the MM_FDC to predict the FDC.  6.3 Results  6.3.1 Variation of the MM_FDC in comparison to the FDC The regional variation of the slope of MM_FDC (SMM_FDC) is equivalent to the regional variation of the slope of FDC (Figs. 6-1(a), (b)). The catchments with large SFDCs in Figure 6-1(a) are mostly those having steeper slope of the MM_FDC in Figure 6-1(b).   This is corroborated by a statistically significant correlation between the FDC middle thirds (SFDC) and the MM_FDC 102  slopes (SMM_FDC) (p-value < 0.05) (Fig. 6-1(c)). However, the SMM_FDC explains 38% of the SFDC variability.  Figure 6-1: (a) Regional variation of SFDC (modified from Fig. 5-5(a)), (b) regional variation of MM_FDC, (c) SFDC and SMM_FDC correlation 103   Figure 6-2: (a) FDC and MM_FDC in catchments with small SFDC, (b) FDC and MM_FDC in catchments with large SFDC The differences in shapes of the FDCs based on their slopes (steeper slope of the FDC vs milder slope of the FDC) is equivalent to the difference in shapes of the MM_FDCs. The MM_FDCs of catchments with large SFDCs have steeper slopes than those in catchments with small SFDCs (Figs. 6-2(a), (b)). 104   Figure 6-3: SFDC (slope of FDC) and SMM_FDC (slope of MM_FDC) in catchments with steeper slope of the FDC and milder slope of the FDC From Figure 6-3, there are differences in values between slopes of FDCs and MM_FDCs slopes. The differences are larger in catchments with high flow variability than in catchments with low flow variability (Fig. 6-3). Form Figure 6-3(a), the median SFDC is nearly double the median SMM_FDC for catchments with steeper slope of the FDC (Fig. 6-3(a)).   6.3.2 FDC portions in comparison to the MM_FDC With regards to the upper third, the MM_FDC showed no differences between categories of flow variability, despite the changes in FDC shapes across the study catchments (Figure 6-4). The changes in the upper third of the FDCs are mainly due to differences in shapes of the surface flow FDC, also, it is due to the effect of subsurface flow FDC that tracks the total flow FDC (Fig. 6-5). At the upper third, the surface flow and subsurface flow FDCs are steeper in catchments with large flow variability (Fig. 6-5(a) and Fig. 6-5(b)) than those with small flow variability (Fig. 6-5(c) and Fig. 6-5(d)).   105   Figure 6-4: normalized flow (nQ), normalized MM_FDCs (nQ_reg) (a) and (b) in catchments with steeper slope of the FDC, (c) and (d) in catchments with milder slope of the FDC. The curves were normalized by the mean annual daily flow (Qm)  106   Figure 6-5: normalized flow (nQ), normalized simulated flow (nQsim), normalized subsurface flow (nQss) in catchments with steeper FDC (a) and (b); in catchments with milder FDC (c) and (d). The curves were normalized by the mean annual daily flow (Qm)  107  Table 6-1: Correlation of SSFDC and FDC slopes using normalized curves    In the middle third of the FDC, the MM_FDCs deviate from the FDCs in catchments with large flow variability (steeper slope of the FDC) and track the FDCs in catchments with small flow variability (milder slope of the FDC) (Fig. 6-4).  In this portion of the FDC, the surface flow FDC extend to lower flow percentiles (80%) in all the study catchments irrespective of their flow variability (Fig. 6-5). The subsurface flow FDC track the total flow FDC in the middle third in all study catchments. The slopes of both curves (SSFDC and SFDC, respectively) are proportional with a statistically significant correlation (p-value <0.05) (Table 6-1). The slopes of the SSFDCs are larger than those of the SFDCs in both categories of flow variability (Fig. 6-6). In some catchments of steepest slope of the FDC, the subsurface flow is confounded with the total flow where the slope of the SSFDC is nearly equal to SFDC (Fig. 6-6(a)). The FDC lower third is the range of low flows where the evapotranspiration (ET) effect is dominant (e.g., Vitvar et al., 2002).  At the lower third, the MM_FDC deviates from FDC regardless of the level of flow variability (Fig. 6-4). The catchments with steeper slope of the FDC have sharper dip than the catchments with flatter slope of the FDC (Fig. 6-4). At the lower third, the subsurface flow FDC displays the same differences in shapes as those of the FDC in catchments with steeper slope of the FDC (Fig. 6-5).  In catchments with flatter slope of the FDC, the subsurface flow FDC has a flatter dip at lower third than total flow FDC (Fig. 6-5).    R2 R p-value Catchments with milder FDC  0.81 0.9 <0.001 catchments with steeper FDC  0.88 0.93 <0.001 108   Figure 6-6: Cumulative Distribution Function (CDF) of the SFDC and SSFDC in catchments with (a) steeper slope of the FDC and (b) catchments with milder slope of the FDC   6.4 Discussion  6.4.1 Interpretation of the FDC portions in comparison to the MM_FDC 6.4.1.1 FDC upper third  The FDC upper third is made of the largest flows. The MM_FDC diverged from FDC upper third independently from the value of flow variability (flatter/steeper slope of the FDC). The MM_FDC did not help to distinguish between FDC upper thirds in catchments from different categories of flow variability (Fig. 6-4). It is, therefore, not possible to use the MM_FDC in predictions of FDC upper third. The shapes of FDC upper third result from the combined effect of 109  surface and subsurface flow FDCs (Fig. 6-5). The distinguished shapes of FDC between different categories of flow variability illustrate the effect of antecedent moisture condition (AMC) dynamics in this range of flows (Q0%>Q>Q33%). At the upper third, the AMC dynamics effect is likely pronounced in catchments of low flow variability considering the flatter shape of flow components FDCs (surface and subsurface flow FDCs in Fig. 6-6). Flood analyses using the derived flood frequency approach, demonstrated that surface runoff generation mechanisms (saturation excess and infiltration excess overland flow) are influencing flood frequency shapes (e.g., Sivapalan et al., 1990).  This finding suggested that antecedent moisture conditions have to vary between the storms to make predictions of flood frequency curve.  The AMC dynamics effect has been underscored in several studies investigating streamflow predictions within deterministic framework (e.g., Kirchner, 2009). Notably, isotope hydrology emphasized the large contribution of pre-event water to the hydrograph compared to event water (e.g., Buttle et al., 1994; Uhlenbrook et al., 2002).  These findings from other studies support the claim about AMC dynamics affecting the upper third of the FDC. Muneepeerakul et al. (2010) showed that surface flow FDC can be derived from the precipitation. Based on this statement, we conjecture that the derivation of large flows should not use a simple function of precipitation but rather account for the AMC effect.   6.4.1.2 FDC middle third  The MM_FDC diverged from FDC middle third in catchments with steeper slope of the FDC. This finding is consistent with the large difference between median values of FDC and MM_FDC slopes (Fig. 6-3(b)). However, the MM_FDC tracked the FDC middle third in catchments with flatter slope of the FDC; the difference between the median value of FDC and MM_FDC slopes is not as large as in catchments with high flow variability. It is therefore possible to use the MM_FDC to predict FDC middle third only in catchments with low flow variability. 110  These findings can be further understood using the catchments characteristics and runoff processes across catchments from different categories of flow variability.  In FDC middle third (Q33%>Q>Q66%), the surface flow effect on the response was maintained irrespective of the value of flow variability (the surface flow FDC extends to lower flow percentiles (80%) in Fig. 6-5). Thus, surface and subsurface flow FDCs jointly affect the flow variability.  Previous studies demonstrated that surface runoff is dominant in the rising limb and to a lesser extent in the falling limb of the hydrograph (McDonnell, 2003), which further explains the interaction between surface and subsurface flow in this range of FDC made of medium flows. The subsurface flow FDC displays the effect of subsurface processes, namely the deep percolation and the evapotranspiration (e.g., Botter et al., 2009). The steeper slope of subsurface flow FDC in comparison to total flow FDC suggests that subsurface flow response is more sensitive to the effect of subsurface processes than the total flow (Fig. 6-6).  Given the complex combined effect of surface and subsurface flow in this range of FDC, the mean monthly runoff did not fully capture the variation of FDC slopes across the study catchments. The slopes of MM_FDCs explain only 38% of the total variation of FDC slopes (Fig. 6-1 (c)).  This value would refer to the fact that MM_FDC tracks FDC only in catchments with low flow variability. Hence, the differences between high and low flows of the mean monthly runoff —used to calculate MM_FDC slope— can approximate the combined effect of surface and subsurface flow and so the value of flow variability in catchments with flatter slope of the FDC. In catchments with high flow variability, the slopes of subsurface flow FDCs are larger than their values in catchments with low flow variability (Fig. 6-6(a) versus Fig. 6-6(b)). In these catchments, the subsurface stormflow is predominant (see Fig. 5-9 of chapter 5). In some mountainous forested catchments the slope of the subsurface flow FDC is the largest and 111  equivalent to the slope of FDC (Fig. 6-6(a)). Under these conditions, most likely the surface and subsurface flows are confounding and therefore cannot be distinguished in terms of runoff generation mechanisms making the subsurface flow variability equivalent to the total flow variability.  McDonnell (2013) considered that the lateral connectivity in the subsurface zone increases as the catchments topography is getting steeper. The lateral connectivity is larger in catchments at hillslopes and fosters patches of saturation making surface and subsurface runoff generation mechanisms less distinguishable.  Therefore, the findings in catchments with steeper slope of the FDC suggest that the interaction between surface and subsurface flow responsible for the total flow variability cannot be represented by mean monthly runoff. The monthly averaging attenuates the flow response and masks the behaviour of the flow regime when expressed as FDC.   6.4.1.3 FDC lower third  The MM_FDC diverged from FDC lower third independently from the value of flow variability (milder/steeper slope of the FDC). The MM_FDC did not help to distinguish between FDC lower thirds in catchments from different categories of flow variability. It is, therefore, not possible to use the MM_FDC in predictions of the FDC lower third. This finding can be further understood using differences in shapes of FDC and subsurface flow FDC at lower thirds between both categories of flow variability.  The FDC lower third had sharp dip in catchments with high flow variability and a flatter dip in catchments with low flow variability (Fig. 6-5). Note that in eastern US, independently from the value of flow variability, all mountainous catchments have smaller soil moisture storage capacity (SMSC) (<280mm) and all catchments at lowlands have larger SMSC (>280mm) (see Fig. 5-4(a)). This finding suggests that, in these conditions of humid climate, the dominant effect 112  of ET during low flows do not distinguish between the value of SMSC and rather changes with the value of flow variability (steeper versus milder slope of the FDC).   In conditions of high flow variability (steeper slope of the FDC), the effect of ET was not distinguished between the total flow and the subsurface flow where both had a sharp dip (Figs. 6-5(a), (b)). In this category, all catchments have limited infiltration rates (HGC predominant in Fig. 2-2(b)).  The sharp dips of subsurface and total flow suggest that the limited infiltration rates in presence of large/ small SMSCs is a chief regulator of the influence of ET on  FDC lower third.   In catchments with low flow variability the subsurface flow had a flatter dip than the total flow. The subsurface flow is then more sensitive to the effect of ET at the lower third. The subsurface zone is the area where rain water infiltrates and infiltration rates change non-linearly with depth (Ameli et al., 2016). In this category of catchments, the improved soil drainage in conditions of large/small SMSC and the non-linear change of infiltration rates with depth help to explain the ET effect and hence the flatter shape of subsurface and total flow FDCs at the lower tail.  Moore (1997) demonstrated —in a forested catchment of steep slope in British Columbia—that at early stages when the catchment is wetted up, the hydrograph recession limb is exponential (linear). However, at later stages, as the drainage from the upslope zones or the recharge from the vadose zone starts, the recession limb becomes non-linear and fits better the power law function. The two stages of the recession could not be distinguished in absence of ET (during dormant season) (Moore, 1997). This explanation of the hydrograph recession limb explains further the dominant ET effect on low flows. Further, findings from the hydrograph recession limb demonstrates that ET is one of the major factors making low flows prediction non-linear and highly affected by catchment characteristics (e.g., the soil infiltration rates). The studies by Botter et al. 113  (2009) and Botter et al. (2010) are consistent with findings from Moore (1997) regarding the non-linear aspect of low flows that should be met in the pursuit of prediction. Botter et al. (2009) and Botter et al. (2010) showed that in conditions of humid climate of northern Italy, the prediction of FDC from the probability of observing the water volume in the subsurface zone provided more accurate low flows’ assessment when the power law (non-linear) is fitted instead of the exponential distribution (linear). This understanding supports the claim about FDC lower third and explains the diverging MM_FDC in this portion of the FDC irrespective of the value of flow variability. The averaging in mean monthly runoff does not capture, therefore, the non-linearity in the low flow response.  The ET impact changed with properties of soil infiltration rates in conditions of small/large SMSC. There are opportunities to explore further predictions of low flows in lower portions of the FDC, at ungauged basins, using statistical models such as the quantiles Qd,y of the lowest mean discharge over a consecutive d-day period corresponding to a recurrence interval  (return period) of y-years (i.e.,  et al., 2008).   6.4.2 Catchments and flow conditions where it is possible to predict the FDC using MM_FDC According to analysis of each of FDC portions in comparison with MM_FDC in real catchments, it appears that the prediction of the FDC using the MM_FDC is only partially applicable. Given the effect of averaging in the mean monthly runoff that smooths the flow response, the method is limited to specific characteristics of flow variability (milder vs steeper slope of the FDC) and landscape properties. The catchments with milder slope of the FDC are mostly dominated by saturation excess overland flow, whereas, those with steeper slope of the FDC are mostly dominated by subsurface stormflow (see Fig. 6-5 (a)).   114  In catchments with flatter slope of the FDC, the findings lead one to conclude that MM_FDC can be used to predict medium flows, that is the FDC middle third but not the upper and lower thirds. In these catchments, the soil is well-drained (Fig. 2-2(a)) and most are located in lowland areas of predominant saturation excess overland flow, with a few other catchments that are mountainous and with well-drained soils (Fig. 2-2(a)).  In catchments with steeper slope of the FDC, it does not appear that the FDC portions can be predicted from MM_FDC, including the middle third. In these catchments, the soil is poorly-drained (Fig. 2-2(a)) and most are located in highland areas of predominant subsurface stormflow, with a few other catchments at lowlands with poorly drained soils (Fig. 2-2(a)).   MM_FDC slopes were smaller than those of the FDCs. Thus, even when it is possible to use MM_FDC to predict FDC, the assessment of FDC middle third might be used, but only as indicative rather than a firm estimation.  Our findings partially agree with the theoretical study of Yokoo and Sivapalan (2011) who suggested that middle and lower thirds of FDC can be estimated by mean monthly runoff in catchments with perennial streamflow and humid climate. The method is constrained by the value of flow variability and is applicable only for FDC middle third. The upper third prediction should involve non-linear filtering of the precipitation that has to account for AMC effect on large flows. At the lower third, the FDC predictions ought to consider the non-linear effect of ET on low flows.  The meta-analysis in real catchments and large dataset made our results complementary to findings from Yokoo and Sivapalan (2011) using a hypothetical catchment. The regional scale helped to combine wide range of flow response properties with complexity in physiography of real catchments. Analysis of observed flows and simulated flow components allowed to reveal facets about the use of MM_FDC not explored within the context of a theoretical study.  115  6.4.3 Conceptual model of the FDC and MM_FDC A conceptual illustrative model of the FDC in relation to the MM_FDC is elaborated in Figure 6-7 based on findings from the meta-analysis in this chapter. The conceptual model will serve as guidance for future studies about process-based FDC prediction. The upper and middle thirds of the FDC are controlled by the subsurface and surface flow. In catchments with flat slope of the FDC, the upper third is flatter due to the effect of well-drained soils and predominant saturation excess overland flow in most of the catchments. The middle third of the FDC can be represented by the MM_FDC. At the lower third, the subsurface flow is more sensitive to the ET effect than the total flow.  The subsurface flow FDC has a flatter dip than the total flow FDC due to large soil infiltration rates in catchments of large/ small SMSCs (Fig. 6-7(a)).  The MM_FDC does not capture the dominant effect of ET during low flows and deviates from FDC at the lower third. In catchments with steeper slope of the FDC, the upper third is steeper due to the effect of poorly-drained soils and predominant subsurface stormflow in most of the catchments. The FDC middle third is very steep and cannot be represented by the MM_FDC. The subsurface flow FDC and FDC are confounded and have equal slopes in the steepest mountainous catchments. At the lower third, the subsurface flow and total flow are equally sensitive to the ET effect where both have a sharp dip irrespective of the value of SMSC (large/ small SMSCs) (Fig. 6-7(b)). The MM_FDC does not capture the dominant effect of ET during low flows and deviates from the FDC at the lower third. 116   Figure 6-7: conceptual model of the FDC in conditions of humid climate and perennial runoff in (a) catchments with milder slope of the FDCs and (b) in catchments with steeper slope of the FDC.   6.5 Conclusion This Chapter sought to determine under what conditions the mean monthly runoff represented in the stochastic form of FDC (MM_FDC) can be used in prediction of the FDC portions. Answering this question is an initial step in gaining understanding that will help to quantify the FDC in ungauged catchments using more readily available monthly flow data. The mean monthly flows are available from predictions of global models and from neighboring gauged catchments of similar characteristics. The study used 73 catchments from the eastern US where the climate is humid and the precipitation is of limited seasonality. In these catchments of perennial runoff, the results showed that it is applicable to use the MM_FDC in predictions of FDC middle third. However, the MM_FDC does not distinguish the shapes of the upper or lower thirds dominated by the varying effect of antecedent moisture conditions and the effect of evapotranspiration, respectively. The averaging in the mean monthly runoff smooths the flow 117  response. Our results showed that the use of MM_FDC to predict FDC middle-third is primarily constrained by the characteristics of the flow variability and landscape properties. Only in catchments of low flow variability (milder slope of the FDC) that the MM_FDC tracked the FDC middle third.  These catchments have mostly predominant saturation excess overland flow in well-drained soils of large SMSC.  Few other catchments are mountainous with soils of large infiltration rates and limited SMSC. It is important to recognize that the non-applicability of the method in catchments with steeper slope of the FDC (high flow variability) indicates the complexity of the hydrological response and highlights the scope for further research.     118  Chapter 7: Conclusions  7.1  Novelty and contribution to the wider literature  This dissertation has two main novel contributions to the literature: it solves issues related to poor efficiency in PUB and it advances the physical understanding of the FDC that can be extrapolated to develop prediction models of the FDC with physical bases.  In terms of PUB, the current research project presented the research directions to improve the prediction from a priori parameters. To the best of my knowledge, unlike the flood regionalization studies, the combined use of climate and flow characteristics in parameter regionalization for daily streamflow prediction is investigated for the first time. The analyses also demonstrated that the flow regime representation using FDC is beneficial to assess the efficiency of PUB. The satisfactory predictions of daily streamflow from the parameter regionalization in this study can be even useful to estimate floods at ungauged catchments such as in Requena et al. (2017) who estimated floods at ungauged catchments using regionalized FDCs. Despite the use of FDC in wide hydrological and ecological applications, there is little research in the literature on the physical controls of FDC.  Most knowledge related to streamflow especially on the understanding of physics is dominated by the deterministic approach. Research seeking to deduce understanding to the physics of FDCs is rare if not non-existent.  The question raised here is why FDC studies lack physically-based explanations. Several decades ago, Klemeš (1978) recognized that there has been failure to see that statistical and stochastic properties of hydrologic processes have definite physical causes and are amenable to explanations. There were tendencies, and still are today, to limit the scope to description and manipulation of the statistical characteristics. The transition from description to explanation has already been made much earlier for the flood frequency analysis using the derived flood frequency approach (e.g., Eagleson, 1972; 119  Sivapalan et al., 1990) also for other branches of science (e.g., climatology, statistical mechanics). The term stochastic incorporates both an element of randomness and an element of determinism. (Klemeš, 1978). Therefore, linking the deterministic understanding to the physics of FDC allows to provide an explanation of the physical causes. This is where the contribution of this research project is unique to the wider literature. This dissertation used deterministic interpretations (e.g., results from isotope hydrology, flow hydrograph analysis in experimental catchments, soil infiltration properties) and deterministic hydrological modelling to advance the understanding of physical controls of FDC. At regional scale, the modelling using SAC-SMA determined the runoff processes and the soil moisture storage capacity.  The topographic index at fine resolution investigated the underlying runoff generation mechanisms. Learning from the data made the hypotheses of physical controls emerging from the different analyses plausible and insightful so that it can be tested in a following phase by numerical modelling as suggest the downward approach (Sivapalan et al., 2003).  7.2 Summary and conclusions The evaluation of the use of SAC-SMA a priori parameters on the constrained calibration at large scale pointed to the limitations of the estimation technique of a priori parameters. The study highlighted the areas of improvements that once covered promotes the operational use of a priori parameters in prediction at ungauged basins (PUB) and constrained calibration. Within the same framework of PUB, the hydrological modelling from parameter regionalization (Chapter 4) revealed the advantage of parameter transfer within regions of similar climate and flow characteristics. The climate and flow characteristics helped to identify the geographical extent to which there is similarity in hydroclimate characteristics. This combination resulted in better performance as opposed to the criteria of climate and/or landscape characteristics 120  or measures of distances between catchments used in other parameter regionalization approaches.   This finding is related to the fact that flow characteristics capture the effect of interaction between all factors contributing to the flow response (i.e., climate, landscape properties, and runoff generation mechanism). In practice, it is better to combine the similarity in climate and flow characteristics in parameter regionalization to make PUB. The use of a priori parameters for PUB is less efficient and remains dependent on improvements as stated in Chapter 3.   The idea of interaction between climate and landscape properties was central to developing an understanding of the environmental controls of FDC (Chapter 6). By means of observed data analysis, the findings helped to set hypotheses that serve in developing causal models to predict FDC.  The study revealed that the precipitation of high variability does not necessarily lead to FDC of steep slope. Further, contrary to hypotheses in previous studies, the catchments at high elevations do not necessarily have steep slope of the FDC. The catchments with flat (steep) slope of the FDC can be at high (low) elevations. Characteristics of the catchment— equivalent to a precipitation filter— interact and affect the shape of the FDC. The analysis demonstrated the major role of soil infiltration rates and the predominant runoff generation mechanism in specific conditions of soil moisture storage capacity. From a process-based perspective, the increase of the FDC slope is related to an increase of the interflow contribution.  The understanding gained in this study showed that in practice, it is not rational to characterize FDCs or predict their shapes according to categories of climate or landscape characteristics alone. The processes underlying the FDC shapes are by far more complex. This understanding is an initial step towards developing a process-based model to predict FDC.  The meta-analysis in Chapter 6 further advanced the understanding of FDC. The study evaluated the use of mean monthly runoff to make a process-based prediction of the FDC at 121  ungauged catchments. The humid climate and perennial flow are not the only conditions constraining the applicability of the method. This conclusion is consistent with Chapter 5 where the underlying processes responsible for FDC shapes are more complex than can be characterized by climate or landscape properties alone. In conditions of humid climate and perennial flow, predicting FDC using the mean monthly runoff is conditioned by the value of flow variability (slope of the FDC). Only in catchments with low flow variability, the mean monthly runoff data can be used to predict FDC middle-third. The upper and lower thirds depended on the varying effect of antecedent moisture conditions and the dominant effect of evapotranspiration during low flows, respectively. The meta-analysis using a large number of catchments was an opportunity to formulate alternative hypotheses in real catchments. In practice, learning from the data is a step that should precede developing the causal model.  7.3 Limitations and future recommendations 7.3.1 Use of a priori parameters in constrained calibration  There should be more research to improve the existing globally applicable technique of determining the SAC-SMA a priori values and improve the predictions from the constrained calibration. In US and using the STATSGO, more research is needed to test the effect of making the calibration less constrained to a priori values in regions of complex landscape properties (larger range than ±35% that is already larger than the ±25% of Koren et al. (2003)). In US and elsewhere, a soil map of high resolution with less uncertainty in the interpolations and where the soil information in each pixel is representative of the local conditions could yield better performance from a priori parameters and therefore from the constrained calibration particularly in zones of complex properties of the terrain. The remotely sensed imagery, although it may be subject of uncertainty, if methods to deal with this uncertainty are discovered it may support spatial 122  interpolations of sparse data coverage in existing soil maps (e.g., STATSGO). The remotely sensed data from existing platforms and planned missions offer an important source to improve incomplete spatial data (e.g., Mulder et al., 2011).    7.3.2 Parameter regionalization for prediction at ungauged catchments  Chapter 4 identifies that the within-region parameter transfer yields the best predictive performance except one specific region of very complex landscape properties where the prediction accuracy was less satisfactory and equivalent to that obtained from the a priori parameters. The limitations of the approach are in part explained by differences in the characteristics (e.g., elevation, energy conditions) between catchments of this specific region and the likelihood of lateral preferential flow that fostered the heterogeneity in this same region. There is room to improve the prediction from parameter regionalization in similar catchments’ conditions. Adding other measures of similarity in the regionalization beyond those used could improve model parameterization. Examples of these measures could be the aridity index, and measures of the effect of preferential flow supported by specific measures of soil characteristics (e.g., porosity, permeability). Expanding our results using much larger dataset will have the potential to provide further insights into the prediction from parameter regionalization using similarity in climate and flow characteristics.  More limitations of the parameters regionalization are related to the implications of climate variability and change on the homogeneity in each region and consequently on the parameter transferability. This limitation remains unexplored and is recommended in future research of parameter regionalization. One way to address this issue would be to analyze the non-stationarity of the climate and flow characteristics used in the regionalization, then analyze the change of the regionalization scheme accordingly.  123  7.3.3 FDC environmental controls and process-based predictions of the FDC at ungauged catchments  The study in Chapter 5 investigating the environmental controls of the FDC lacks understanding of the subsurface controls (see as example Di Matteo et al., 2017) and vegetation. This is largely related to the limited availability of detailed descriptors of geology, geomorphology, and the groundwater levels (covering a large region). In addition, there is a need to study in more detail the impact of the stream hydrological properties (e.g., stream connectivity) and the vegetation type (i.e., species, age, density) on the FDC shapes. Additionally, more research is needed to study the regional change of flow variability in other regions in US and elsewhere to either corroborate or refute the hypothesized conclusions and address the limitations of the analysis. Numerical experiments, following the principle of top-down approach (Sivapalan et al., 2003), where complexity is added gradually to a base model should be developed to investigate the effect of climate interactions with complex physical features on flow variability in order to test the hypotheses from Chapter 5.   Chapter 6 determined the conditions allowing to use the mean monthly runoff in predictions of FDC at ungauged catchments. Therefore, similar empirical analyses in other regions of different climate and flow characteristics are recommended. The precipitation seasonality would have an impact when compared to seasonality of the ET (being in phase versus being out of phase) given the dominant effect of ET during low flow periods.  The empirical study in Chapter 6 can also be aided by numerical experiments to test the several hypotheses and investigate the prediction of the FDC using MM_FDC under several combinations of climate and physiographic characteristics that mimic the complexity of real catchment conditions.  124  In this research project, the effect of non-stationarity in FDC investigations is not evaluated. The non-stationarity in the study catchments is mainly caused by the climate variability considering that the anthropogenic activity is limited. Therefore, non-stationarity in streamflow is due mainly to natural fluctuation caused by ENSO (El Niño Southern Oscillation) and PDO (Pacific Decadal Oscilliations) (Sivapalan and Samuel, 2009). The fifty years of observed flow data would be subject to cyclical fluctuations of wet and dry years. 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Journal of Hydrology 153:1–21.  149        150   Appendix Table A1: Study catchments’ descriptors   ID Long Lat HGA HGB HGCMEAN ELEVSLOPE URB FST AGROPEN WATERWET LANDMAP PET SDR AI RR PSIArea (km2)01031500 -69.315 45.175 4.5 14.3 41.4 299.4 6.5 2.2 77.4 1.8 2.13 5.67 1180.0 512.5 39.3 0.43 0.54 0.03 769.0501057000 -70.540 44.304 15.3 13.6 59.2 281.8 11.7 4.2 83.9 3.6 1.57 3.61 1083.3 559.3 36.2 0.52 0.51 0.03 190.9201127000 -71.985 41.598 11.0 34.5 37.1 164.4 5.1 11.4 60.9 10.1 2.69 12.97 1273.3 624.1 27.8 0.49 0.47 0.03 1846.7001170100 -72.671 42.703 2.4 25.4 54.2 410.9 13.6 3.0 90.8 4.4 0.38 1.28 1307.8 563.3 34.3 0.43 0.56 0.02 106.9901334500 -73.378 42.939 5.8 21.6 55.4 430.1 15.4 7.2 74.4 13.6 0.33 2.12 1198.9 573.8 30.3 0.48 0.43 0.09 1320.9001371500 -74.166 41.686 8.3 6.9 64.9 196.1 6.1 11.6 41.8 30.5 1.27 13.45 1186.2 652.2 22.6 0.55 0.45 0.06 1841.4801372500 -73.873 41.653 8.6 38.9 46.4 166.4 7.1 9.0 56.1 24.2 0.70 4.37 1148.4 645.7 24.4 0.56 0.46 0.07 468.8001411300 -74.821 39.307 12.0 45.7 14.7 16.2 0.3 1.2 73.8 9.8 0.01 13.31 1125.0 751.7 13.3 0.67 0.37 0.02 79.3701413500 -74.653 42.145 0.0 0.0 74.1 769.1 19.8 0.6 98.2 0.3 0.09 0.60 1520.2 502.5 34.1 0.33 0.51 0.08 434.0001423000 -77.957 42.122 4.4 2.2 88.3 591.6 15.7 3.9 65.8 27.5 0.24 1.12 1120.1 554.8 28.7 0.50 0.44 0.09 859.9001445500 -74.979 40.831 6.9 32.0 37.7 204.0 6.4 9.9 49.1 26.2 1.42 11.64 1245.8 646.8 22.7 0.52 0.45 0.07 274.5001541500 -78.406 40.972 6.8 24.2 61.2 520.5 9.5 7.1 74.2 15.8 0.98 0.00 1062.0 593.0 24.0 0.56 0.46 0.11 960.9001543500 -78.103 41.317 0.5 47.9 51.0 521.9 18.3 1.5 89.2 2.7 0.08 0.60 1096.0 593.1 25.4 0.54 0.46 0.10 1774.2001547700 -75.140 42.166 6.8 32.3 50.0 395.7 17.8 4.7 84.4 10.9 0.01 0.00 1048.5 635.4 21.9 0.61 0.43 0.10 113.5401552000 -78.103 41.317 1.6 3.3 88.0 509.3 13.0 2.6 81.6 10.7 0.37 0.18 1134.1 580.8 26.5 0.51 0.49 0.08 1129.4901552500 -77.606 41.060 0.0 0.9 91.1 562.6 15.7 2.6 75.5 8.6 0.17 0.00 1228.5 561.5 27.9 0.46 0.55 0.07 60.6401574000 -76.720 40.082 2.9 51.4 35.6 189.7 4.8 9.3 28.6 59.0 0.59 0.95 1086.1 720.6 17.2 0.66 0.35 0.05 1320.9001608500 -78.654 39.447 14.4 21.4 54.6 655.8 20.9 3.9 80.4 15.2 0.48 0.00 1003.3 642.9 17.4 0.64 0.47 0.09 3809.9001610000 -78.458 39.537 16.1 18.1 55.4 583.0 17.8 4.8 80.0 13.9 0.66 0.06 1022.7 647.9 18.2 0.63 0.46 0.08 8052.3001628500 -78.755 38.322 0.4 55.4 37.0 540.5 11.3 11.6 49.8 38.2 0.32 0.00 1056.1 678.7 14.5 0.64 0.39 0.08 2807.6001631000 -78.211 38.914 0.4 53.0 38.6 500.9 12.7 10.5 55.4 33.5 0.59 0.01 1070.9 685.9 14.4 0.64 0.38 0.07 4252.8001634000 -78.336 38.977 0.7 42.4 44.0 442.6 12.8 6.8 58.4 34.4 0.43 0.00 982.1 697.6 13.6 0.71 0.37 0.09 1989.1001664000 -77.814 38.531 0.0 59.0 35.5 237.2 10.0 4.1 59.3 35.9 0.26 0.19 1135.9 730.4 11.8 0.64 0.35 0.08 1605.8001667500 -77.975 38.350 0.0 56.3 37.2 263.4 10.4 6.2 56.4 36.5 0.40 0.26 1185.5 741.6 10.6 0.63 0.36 0.07 1222.5001668000 -77.518 38.322 0.0 44.5 42.5 202.3 8.0 4.5 55.6 38.1 0.42 0.30 1145.1 748.6 10.9 0.65 0.36 0.07 4133.6002016000 -79.760 37.792 1.0 40.9 41.3 661.1 18.0 3.6 87.7 8.3 0.39 0.00 1063.9 667.7 16.0 0.63 0.44 0.05 1194.0002018000 -79.912 37.666 0.4 53.3 33.4 635.0 18.1 3.1 90.1 6.4 0.34 0.00 1089.2 668.2 11.3 0.61 0.39 0.07 852.1002030500 -78.378 37.703 0.0 71.1 16.6 157.1 3.8 2.8 73.9 12.3 0.22 1.40 1145.4 775.4 8.5 0.68 0.37 0.04 585.3002055000 -79.939 37.258 0.9 35.7 56.1 575.1 17.2 18.7 70.8 10.3 0.09 0.01 1058.5 687.4 10.8 0.65 0.36 0.07 1023.1002083500 -77.533 35.894 10.1 55.3 19.0 76.7 2.0 7.5 47.4 27.5 0.65 7.80 1181.9 835.9 4.3 0.71 0.35 0.05 5654.0002102000 -79.116 35.627 1.3 55.7 38.7 171.0 3.3 11.7 55.4 22.7 0.58 0.85 1203.3 839.9 4.2 0.70 0.37 0.04 3714.1002116500 -80.386 35.857 1.0 78.9 16.6 395.2 9.5 12.8 58.1 23.1 0.43 0.21 1238.8 773.2 7.7 0.62 0.47 0.06 5905.2002118000 -80.659 35.845 0.0 87.1 11.0 317.4 6.5 7.1 49.1 37.0 0.11 0.41 1237.0 788.2 6.9 0.64 0.44 0.06 792.5002143000 -81.403 35.684 0.0 75.4 23.0 445.2 13.0 5.9 76.6 12.2 0.03 0.05 1310.9 783.8 6.5 0.60 0.46 0.04 214.5002143040 -81.567 35.591 0.0 75.0 21.4 547.8 15.7 2.6 90.2 3.9 0.01 0.02 1364.8 768.5 6.3 0.56 0.48 0.04 67.3302143500 -81.264 35.422 0.0 88.5 9.7 289.5 3.8 8.6 39.2 46.0 0.15 0.58 1246.2 826.4 4.3 0.66 0.44 0.03 178.7002192000 -82.770 33.974 0.0 91.0 6.6 217.7 4.3 7.7 53.3 22.7 0.59 3.60 1305.7 871.0 2.7 0.67 0.42 0.06 3703.6802202500 -81.416 32.191 10.0 54.4 14.8 90.4 1.8 5.0 43.7 22.9 0.31 13.77 1206.0 957.9 0.4 0.79 0.33 0.03 6863.50151    *AGR: percentage of agricultural areas in each catchment (%)       *PET: potential evapotranspiration     *AI: Aridity Index (%)                                                                       *PSI: precipitation seasonality index           *FST: percentage of forest areas in each catchment (%)                   *RR: runoff ratio (%) *Long: Longitude in °                                                                        *SDR: snow day ratio (%)  *Lat: Latitude in °                                                                               *SLOPE: catchments slope in (%)                                      *MAP: Mean Annual Precipitation                                                    *URB: percentage of urban areas in each catchment (%)                                                                       *MEAN ELEV: catchments mean elevation (m)                                *WET LAND:  percentage of wet land per catchment in %    *OPEN WATER: percentage of open water per catchment in % ID Long Lat HGA HGB HGCMEAN ELEVSLOPE URB FST AGROPEN WATERWET LANDMAP PET SDR AI RR PSIArea (km2)02217500 -83.423 33.947 0.0 95.1 4.9 269.6 4.8 15.8 45.1 26.0 0.60 3.19 1346.7 864.3 2.6 0.64 0.44 0.07 1030.8102218500 -83.273 33.581 0.0 95.0 4.7 240.6 4.4 13.7 48.7 23.3 0.94 3.73 1309.9 879.3 2.4 0.67 0.41 0.07 2823.1002219500 -83.349 33.609 0.0 96.9 2.7 226.6 3.4 9.0 45.8 27.3 0.96 5.30 1284.6 891.7 2.0 0.69 0.40 0.06 1129.2002228000 -81.868 31.221 4.1 14.0 32.4 53.1 0.6 6.7 35.4 23.1 0.30 19.66 1264.7 1003.1 0.0 0.79 0.33 0.08 7226.1002329000 -84.384 30.554 4.8 54.9 10.8 75.6 1.8 6.7 39.5 31.3 0.62 12.67 1366.7 1021.0 0.0 0.75 0.39 0.07 2952.6002347500 -84.233 32.721 0.0 91.5 3.8 241.3 3.4 12.5 55.7 17.4 1.35 5.65 1281.6 903.2 1.2 0.70 0.39 0.09 4791.5002349500 -84.044 32.298 8.9 73.6 11.3 208.4 3.4 9.3 55.4 17.7 1.00 7.08 1263.2 923.5 0.9 0.73 0.38 0.08 7511.0003024000 -79.956 41.438 13.2 2.3 59.8 418.5 4.0 7.4 49.0 35.3 1.41 3.67 1152.0 603.7 24.4 0.52 0.41 0.10 2662.5003032500 -79.394 40.994 1.2 13.8 73.5 474.4 9.4 8.8 64.8 22.7 0.44 0.37 1141.9 607.9 23.8 0.53 0.41 0.11 1367.5003050500 -79.879 38.925 4.5 18.5 57.1 828.5 20.1 5.5 84.9 8.3 0.47 0.07 1346.0 597.2 23.3 0.44 0.54 0.08 704.5003051000 -79.936 39.029 8.4 17.0 56.2 779.3 18.0 6.0 83.5 8.9 0.55 0.07 1332.8 604.0 22.4 0.45 0.53 0.08 1056.7003054500 -80.040 39.150 9.7 11.0 65.1 712.4 16.6 6.2 82.9 9.4 0.53 0.04 1369.0 621.2 21.1 0.45 0.50 0.07 2372.4003065000 -79.622 39.072 14.6 18.2 64.8 997.8 20.5 2.6 91.0 4.4 0.22 0.06 1364.6 570.9 24.3 0.42 0.52 0.07 893.6003070000 -79.666 39.347 17.1 13.3 63.6 922.3 19.8 3.7 89.6 3.5 0.66 0.77 1385.5 584.5 24.0 0.42 0.52 0.07 2426.8003075500 -79.426 39.422 17.1 9.8 67.9 794.8 9.8 7.9 65.7 22.8 0.50 1.11 1315.1 592.1 25.2 0.45 0.50 0.08 347.1003109500 -80.541 40.676 1.2 16.8 65.8 346.3 6.0 12.9 45.4 38.0 0.97 0.62 983.6 655.6 19.7 0.67 0.37 0.12 1284.6003111500 -80.734 40.193 0.0 19.3 77.7 342.7 8.9 10.0 54.6 30.2 0.93 0.19 1020.9 683.3 18.0 0.67 0.37 0.11 318.6003114500 -80.997 39.475 0.0 8.9 53.2 314.3 17.6 4.5 88.3 6.6 0.23 0.00 1158.9 700.7 15.6 0.60 0.43 0.09 1186.2003155500 -81.278 39.119 0.0 8.9 54.3 293.7 14.3 5.4 86.1 7.8 0.13 0.00 1145.7 709.5 14.9 0.62 0.43 0.08 1170.7003159500 -82.088 39.329 0.0 36.9 55.1 274.3 7.3 9.5 58.7 29.6 0.66 0.12 1022.7 682.4 16.8 0.67 0.37 0.08 2442.4003161000 -81.407 36.393 0.2 94.5 4.2 1023.7 17.0 9.6 66.8 19.8 0.09 0.12 1418.0 625.8 13.0 0.44 0.50 0.12 531.0003167000 -80.887 36.939 0.8 47.2 44.1 765.6 12.0 7.1 50.8 41.6 0.04 0.06 1019.4 649.0 12.7 0.64 0.44 0.08 639.7003168000 -80.746 36.937 0.5 74.0 21.9 869.0 14.3 6.3 61.2 30.4 0.27 0.09 1201.8 640.0 13.0 0.53 0.48 0.07 5703.2003183500 -80.642 37.724 8.3 31.7 45.6 834.0 18.1 4.5 83.3 11.2 0.54 0.07 1152.1 619.1 20.3 0.54 0.48 0.06 3532.8003184000 -80.805 37.640 7.7 31.7 48.0 804.5 17.9 4.7 82.2 12.1 0.56 0.06 1133.6 627.6 19.7 0.55 0.47 0.06 4193.2003186500 -80.484 38.379 6.3 21.7 70.9 1074.7 22.4 1.9 97.0 0.3 0.21 0.02 1504.5 582.8 24.3 0.39 0.53 0.06 331.5003281500 -83.677 37.479 0.0 61.8 27.2 366.3 22.2 5.9 83.6 4.6 0.31 0.00 1264.7 742.2 10.7 0.59 0.45 0.06 1870.0003443000 -82.624 35.299 0.0 89.1 4.3 862.6 17.9 7.8 82.9 7.9 0.32 0.16 1877.7 694.4 6.9 0.37 0.64 0.04 766.6003504000 -83.619 35.127 0.0 99.1 0.0 1211.9 26.9 1.9 97.0 0.3 0.02 0.15 2072.0 626.1 12.6 0.30 0.57 0.09 134.4003512000 -83.354 35.461 0.5 95.2 3.3 1147.9 34.0 3.8 94.0 1.4 0.00 0.04 1655.4 611.1 13.6 0.37 0.54 0.06 476.6003524000 -82.155 36.945 0.1 61.6 36.1 760.9 18.3 8.0 57.9 30.8 0.08 0.01 1159.1 662.0 13.6 0.57 0.45 0.08 1367.5003531500 -83.095 36.662 0.0 47.5 48.6 658.9 21.8 8.3 71.9 4.0 0.20 0.00 1383.8 703.2 12.4 0.51 0.50 0.08 826.2003550000 -83.981 35.139 0.2 87.0 9.6 762.5 24.2 6.6 87.1 5.4 0.05 0.24 1756.7 687.3 10.9 0.39 0.54 0.10 269.4004221000 -75.139 42.166 3.3 2.4 90.6 629.8 10.9 3.6 54.3 36.7 0.07 0.08 998.1 558.7 27.5 0.56 0.38 0.13 745.9004256000 -76.912 41.325 34.3 2.1 45.9 497.3 5.1 0.0 64.6 0.0 1.93 23.19 1242.0 526.8 37.2 0.42 0.62 0.08 238.28

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