The importance of topography-controlled sub-grid process heterogeneity and semi-quantitative prior constraints in distributed hydrological models

Abstract. Heterogeneity of landscape features like terrain, soil, and vegetation properties affects the partitioning of water and energy. However, it remains unclear to what extent an explicit representation of this heterogeneity at the sub-grid scale of distributed hydrological models can improve the hydrological consistency and the robustness of such models. In this study, hydrological process complexity arising from sub-grid topography heterogeneity was incorporated into the distributed mesoscale Hydrologic Model (mHM). Seven study catchments across Europe were used to test whether (1) the incorporation of additional sub-grid variability on the basis of landscape-derived response units improves model internal dynamics, (2) the application of semi-quantitative, expert-knowledge-based model constraints reduces model uncertainty, and whether (3) the combined use of sub-grid response units and model constraints improves the spatial transferability of the model. Unconstrained and constrained versions of both the original mHM and mHMtopo, which allows for topography-based sub-grid heterogeneity, were calibrated for each catchment individually following a multi-objective calibration strategy. In addition, four of the study catchments were simultaneously calibrated and their feasible parameter sets were transferred to the remaining three receiver catchments. In a post-calibration evaluation procedure the probabilities of model and transferability improvement, when accounting for sub-grid variability and/or applying expert-knowledge-based model constraints, were assessed on the basis of a set of hydrological signatures. In terms of the Euclidian distance to the optimal model, used as an overall measure of model performance with respect to the individual signatures, the model improvement achieved by introducing sub-grid heterogeneity to mHM in mHMtopo was on average 13 %. The addition of semi-quantitative constraints to mHM and mHMtopo resulted in improvements of 13 and 19 %, respectively, compared to the base case of the unconstrained mHM. Most significant improvements in signature representations were, in particular, achieved for low flow statistics. The application of prior semi-quantitative constraints further improved the partitioning between runoff and evaporative fluxes. In addition, it was shown that suitable semi-quantitative prior constraints in combination with the transfer-function-based regularization approach of mHM can be beneficial for spatial model transferability as the Euclidian distances for the signatures improved on average by 2 %. The effect of semi-quantitative prior constraints combined with topography-guided sub-grid heterogeneity on transferability showed a more variable picture of improvements and deteriorations, but most improvements were observed for low flow statistics.

[1]  Jeffrey J. McDonnell,et al.  Scale effects on headwater catchment runoff timing, flow sources, and groundwater‐streamflow relations , 2004 .

[2]  Wesley W. Wallender,et al.  Multi-criteria optimization of a regional spatially-distributed subsurface water flow model , 2005 .

[3]  Hoshin Vijai Gupta,et al.  A spatial regularization approach to parameter estimation for a distributed watershed model , 2008 .

[4]  Felix Naef,et al.  Identifying runoff processes on the plot and catchment scale , 2006 .

[5]  R. J. Granger,et al.  Storage dynamics and streamflow in a catchment with a variable contributing area , 2009 .

[6]  W. Bastiaanssen,et al.  Constraining model parameters on remotely sensed evaporation: Justification for distribution in ungauged basins? , 2008 .

[7]  Keith Beven,et al.  A manifesto for the equifinality thesis , 2006 .

[8]  Ophélie Fovet,et al.  Hydrological hysteresis and its value for assessing process consistency in catchment conceptual models , 2015 .

[9]  Keith Beven,et al.  The sensitivity of hydrological models to spatial rainfall patterns: an evaluation using observed data , 1994 .

[10]  Dirk Eilander,et al.  Predicting the ungauged basin: model validation and realism assessment , 2015, Front. Earth Sci..

[11]  K. Verdin,et al.  New Global Hydrography Derived From Spaceborne Elevation Data , 2008 .

[12]  Hubert H. G. Savenije,et al.  Process consistency in models: The importance of system signatures, expert knowledge, and process complexity , 2014 .

[13]  M. Wigmosta,et al.  A distributed hydrology-vegetation model for complex terrain , 1994 .

[14]  Nicola Fohrer,et al.  Comparing model sensitivities of different landscapes using the ecohydrological SWAT model , 2009 .

[15]  Vijay P. Singh,et al.  Effect of spatial and temporal variability in rainfall and watershed characteristics on stream flow hydrograph , 1997 .

[16]  P. Jones,et al.  A European daily high-resolution gridded data set of surface temperature and precipitation for 1950-2006 , 2008 .

[17]  Erwin Zehe,et al.  Comparison of conceptual model performance using different representations of spatial variability , 2008 .

[18]  Hoshin Vijai Gupta,et al.  A process‐based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model , 2008 .

[19]  K. Beven,et al.  A physically based, variable contributing area model of basin hydrology , 1979 .

[20]  Pierre Le Pape,et al.  Trace element behavior and partition versus urbanization gradient in an urban river (Orge River, France) , 2012 .

[21]  Jeroen C. J. H. Aerts,et al.  Comparing model performance of two rainfall-runoff models in the Rhine basin using different atmospheric forcing data sets , 2007 .

[22]  Massimiliano Zappa,et al.  Does model performance improve with complexity? : A case study with three hydrological models , 2015 .

[23]  M. Sivapalan,et al.  Catchment classification: Empirical analysis of hydrologic similarity based on catchment function in the eastern USA , 2011 .

[24]  Hubert H. G. Savenije,et al.  HESS Opinions "Topography driven conceptual modelling (FLEX-Topo)" , 2010 .

[25]  Peter Reichert,et al.  On the usefulness of overparameterized ecological models , 1997 .

[26]  Thomas C. Winter,et al.  THE CONCEPT OF HYDROLOGIC LANDSCAPES 1 , 2001 .

[27]  N. Fohrer,et al.  Modelling hydrological processes in mesoscale lowland river basins with SWAT—capabilities and challenges , 2008 .

[28]  Hubert H. G. Savenije,et al.  Modelling subsurface storm flow with the Representative Elementary Watershed (REW) approach: application to the Alzette River Basin , 2006 .

[29]  J. V. Soares,et al.  HAND, a new terrain descriptor using SRTM-DEM: Mapping terra-firme rainforest environments in Amazonia , 2008 .

[30]  C. Perrin,et al.  Does a large number of parameters enhance model performance? Comparative assessment of common catchment model structures on 429 catchments , 2001 .

[31]  Hubert H. G. Savenije,et al.  Using expert knowledge to increase realism in environmental system models can dramatically reduce the need for calibration , 2013 .

[32]  Salvatore Manfreda,et al.  Space‐time modeling of soil moisture: Stochastic rainfall forcing with heterogeneous vegetation , 2006 .

[33]  Luis Samaniego,et al.  Seasonal Soil Moisture Drought Prediction over Europe Using the North American Multi-Model Ensemble (NMME) , 2015 .

[34]  Hubert H. G. Savenije,et al.  Rainfall-runoff modelling in a catchment with a complex groundwater flow system: application of the Representative Elementary Watershed (REW) approach , 2005 .

[35]  Ezio Todini,et al.  TOPKAPI: a model for the representation of the rainfall‐runoff process at different scales , 2002 .

[36]  Dennis P. Lettenmaier,et al.  Development of regional parameter estimation equations for a macroscale hydrologic model , 1997 .

[37]  Ralf Ludwig,et al.  An ensemble approach to assess hydrological models' contribution to uncertainties in the analysis of climate change impact on water resources , 2012 .

[38]  Hoshin Vijai Gupta,et al.  Model identification for hydrological forecasting under uncertainty , 2005 .

[39]  András Bárdossy,et al.  Comparison of four regionalisation methods for a distributed hydrological model , 2007 .

[40]  M. J. Booij,et al.  Impact of climate change on river flooding assessed with different spatial model resolutions , 2005 .

[41]  Murugesu Sivapalan,et al.  Modelling water balances in an Alpine catchment through exploitation of emergent properties over changing time scales , 2003 .

[42]  Nicholas Kouwen,et al.  Watershed modeling using land classifications , 1992 .

[43]  Hubert H. G. Savenije,et al.  A framework to assess the realism of model structures using hydrological signatures , 2012 .

[44]  Kevin J. McGuire,et al.  Topographic controls on shallow groundwater dynamics: implications of hydrologic connectivity between hillslopes and riparian zones in a till mantled catchment , 2010 .

[45]  J. Kirchner.  Getting the right answers for the right reasons: Linking measurements, analyses, and models to advance the science of hydrology , 2006 .

[46]  J. Ihringer,et al.  Modeling water flow and mass transport in a loess catchment , 2001 .

[47]  D. Lettenmaier,et al.  A simple hydrologically based model of land surface water and energy fluxes for general circulation models , 1994 .

[48]  B. Arheimer,et al.  Development and testing of the HYPE (Hydrological Predictions for the Environment) water quality model for different spatial scales , 2010 .

[49]  Kevin Bishop,et al.  Groundwater dynamics along a hillslope: A test of the steady state hypothesis , 2003 .

[50]  Ralf Ludwig,et al.  On the need for bias correction in regional climate scenarios to assess climate change impacts on river runoff , 2012 .

[51]  Luis Samaniego,et al.  Streamflow prediction in ungauged catchments using copula‐based dissimilarity measures , 2010 .

[52]  Denis A. Hughes,et al.  A review of 40 years of hydrological science and practice in southern Africa using the Pitman rainfall-runoff model , 2013 .

[53]  Derek Karssenberg,et al.  Towards closure relations in the Representative Elementary Watershed (REW) framework containing observable parameters: Relations for Hortonian overland flow , 2012 .

[54]  Thibault Mathevet,et al.  A downward structural sensitivity analysis of hydrological models to improve low-flow simulation , 2011 .

[55]  Dominique Thiéry,et al.  Benchmarking hydrological models for low-flow simulation and forecasting on French catchments , 2013 .

[56]  Dmitri Kavetski,et al.  The influence of conceptual model structure on model performance: a comparative study for 237 French catchments , 2013 .

[57]  Murugesu Sivapalan,et al.  Extension of the Representative Elementary Watershed approach for cold regions: constitutive relationships and an application , 2007 .

[58]  Keith Beven,et al.  Uniqueness of place and process representations in hydrological modelling , 2000 .

[59]  Luis Samaniego,et al.  Implications of Parameter Uncertainty on Soil Moisture Drought Analysis in Germany , 2013 .

[60]  Hubert H. G. Savenije,et al.  Climate controls how ecosystems size the root zone storage capacity at catchment scale , 2014 .

[61]  Jeffrey J. McDonnell,et al.  Threshold relations in subsurface stormflow: 2. The fill and spill hypothesis , 2006 .

[62]  András Bárdossy,et al.  Modeling of the effect of land use changes on the runoff generation of a river basin through parameter regionalization of a watershed model , 2004 .

[63]  Z. Samani,et al.  Reference crop evapotranspiration from ambient air temperature , 1985 .

[64]  Bruno Merz,et al.  Effects of spatial variability on the rainfall runoff process in a small loess catchment , 1998 .

[65]  Kevin Bishop,et al.  Simulating interactions between saturated and unsaturated storage in a conceptual runoff model , 2003 .

[66]  Yuqiong Liu,et al.  Reconciling theory with observations: elements of a diagnostic approach to model evaluation , 2008 .

[67]  W. Briggs.  Statistical Methods in the Atmospheric Sciences , 2007 .

[68]  S. Uhlenbrook,et al.  Hydrological process representation at the meso-scale: the potential of a distributed, conceptual catchment model , 2004 .

[69]  J. Doherty,et al.  A hybrid regularized inversion methodology for highly parameterized environmental models , 2005 .

[70]  Hubert H. G. Savenije,et al.  Testing the realism of a topography driven model (FLEX-Topo) in the nested catchments of the Upper Heihe, China , 2013 .

[71]  Praveen Kumar,et al.  Typology of hydrologic predictability , 2011 .

[72]  Soroosh Sorooshian,et al.  The role of hydrograph indices in parameter estimation of rainfall–runoff models , 2005 .

[73]  V. Smakhtin.  Low flow hydrology: a review , 2001 .

[74]  M. Sivapalan,et al.  A unifying framework for watershed thermodynamics: balance equations for mass, momentum, energy and entropy, and the second law of thermodynamics , 1998 .

[75]  H. Winsemius,et al.  The effect of forcing and landscape distribution on performance and consistency of model structures , 2015 .

[76]  Jeffrey J. McDonnell,et al.  Gauging the Ungauged Basin: Relative Value of Soft and Hard Data , 2015 .

[77]  Murugesu Sivapalan,et al.  Extension of the representative elementary watershed approach for cold regions via explicit treatment of energy related processes , 2006 .

[78]  Thibault Mathevet,et al.  All that glitters is not gold: the case of calibrating hydrological models , 2012 .

[79]  S. Sorooshian,et al.  Effective and efficient global optimization for conceptual rainfall‐runoff models , 1992 .

[80]  Keith Beven,et al.  Prophecy, reality and uncertainty in distributed hydrological modelling , 1993 .

[81]  Sabine Attinger,et al.  Multiscale and Multivariate Evaluation of Water Fluxes and States over European River Basins , 2016 .

[82]  Wolfgang-Albert Flügel,et al.  Delineating hydrological response units by geographical information system analyses for regional hydrological modelling using PRMS/MMS in the drainage basin of the River Bröl, Germany , 1995 .

[83]  Bryan A. Tolson,et al.  Dynamically dimensioned search algorithm for computationally efficient watershed model calibration , 2007 .

[84]  Jeffrey J. McDonnell,et al.  On the dialog between experimentalist and modeler in catchment hydrology: Use of soft data for multicriteria model calibration , 2002 .

[85]  Harald Kunstmann,et al.  Inverse distributed hydrological modelling of Alpine catchments , 2005 .

[86]  Alain Pietroniro,et al.  Grouped Response Units for Distributed Hydrologic Modeling , 1993 .

[87]  Julien Lerat,et al.  Crash testing hydrological models in contrasted climate conditions: An experiment on 216 Australian catchments , 2012 .

[88]  C. Rennó,et al.  Height Above the Nearest Drainage – a hydrologically relevant new terrain model , 2011 .

[89]  Erwin Zehe,et al.  HESS Opinions: From response units to functional units: a thermodynamic reinterpretation of the HRU concept to link spatial organization and functioning of intermediate scale catchments , 2014 .

[90]  Sabine Attinger,et al.  Implications of distributed hydrologic model parameterization on water fluxes at multiple scales and locations , 2013 .

[91]  Günter Blöschl,et al.  Comparative predictions of discharge from an artificial catchment (Chicken Creek) using sparse data , 2009 .

[92]  P. Matgen,et al.  Understanding catchment behavior through stepwise model concept improvement , 2008 .

[93]  Michael N. Gooseff,et al.  Hydrologic connectivity between landscapes and streams: Transferring reach‐ and plot‐scale understanding to the catchment scale , 2009 .

[94]  Peter C. Young,et al.  Parallel Processes in Hydrology and Water Quality: A Unified Time‐Series Approach , 1992 .

[95]  Zhao Ren-jun,et al.  The Xinanjiang model applied in China , 1992 .

[96]  Tom Rientjes,et al.  Flux parameterization in the representative elementary watershed approach: Application to a natural basin , 2005 .

[97]  Ming Ye,et al.  Towards a comprehensive assessment of model structural adequacy , 2012 .

[98]  D. Seo,et al.  Overall distributed model intercomparison project results , 2004 .

[99]  S. Attinger,et al.  Multiscale parameter regionalization of a grid‐based hydrologic model at the mesoscale , 2010 .

[100]  Martyn P. Clark,et al.  Comparison of hydrological model structures based on recession and low flow simulations , 2011 .

[101]  Luis Samaniego,et al.  Toward computationally efficient large‐scale hydrologic predictions with a multiscale regionalization scheme , 2013 .

[102]  E. Toth,et al.  Calibration of hydrological models in the spectral domain: An opportunity for scarcely gauged basins? , 2007 .

[103]  S. Gharari,et al.  Using expert knowledge to increase realism in environmental system models can dramatically reduce the need for calibration , 2013 .

[104]  Thibault Mathevet,et al.  Hydrology and Earth System Sciences Hess Opinions " Crash Tests for a Standardized Evaluation of Hydrological Models " , 2022 .

[105]  Denis A. Hughes,et al.  A semi-distributed, variable time interval model of catchment hydrology—structure and parameter estimation procedures , 1994 .

[106]  C. Perrin,et al.  Improvement of a parsimonious model for streamflow simulation , 2003 .

[107]  Luis Samaniego,et al.  Influence of soil textural properties on hydrologic fluxes in the Mississippi river basin , 2015 .

[108]  Sabine Attinger,et al.  The effects of spatial discretization and model parameterization on the prediction of extreme runoff characteristics , 2010 .

[109]  Markus Weiler,et al.  Uncertainty of Precipitation Estimates Caused by Sparse Gauging Networks in a Small, Mountainous Watershed , 2011 .

[110]  M. Sivapalan,et al.  Process controls of water balance variability in a large semi-arid catchment: downward approach to hydrological model development , 2001 .

[111]  A. Thomsen,et al.  WATBAL: A Semi-Distributed, Physically Based Hydrological Modelling System , 1986 .

[112]  J. Refsgaard,et al.  Operational Validation and Intercomparison of Different Types of Hydrological Models , 1996 .

[113]  H. Savenije,et al.  Hydrology and Earth System Sciences Hydrological Landscape Classification: Investigating the Performance of Hand Based Landscape Classifications in a Central European Meso-scale Catchment , 2022 .

[114]  Thorsten Wagener,et al.  Incorporating uncertainty in hydrological predictions for gauged and ungauged basins in southern Africa , 2012 .