Sensitivity analysis, calibration, and testing of a distributed hydrological model using error‐based weighting and one objective function

[1] We evaluate the utility of three interrelated means of using data to calibrate the fully distributed rainfall-runoff model TOPKAPI as applied to the Maggia Valley drainage area in Switzerland. The use of error-based weighting of observation and prior information data, local sensitivity analysis, and single-objective function nonlinear regression provides quantitative evaluation of sensitivity of the 35 model parameters to the data, identification of data types most important to the calibration, and identification of correlations among parameters that contribute to nonuniqueness. Sensitivity analysis required only 71 model runs, and regression required about 50 model runs. The approach presented appears to be ideal for evaluation of models with long run times or as a preliminary step to more computationally demanding methods. The statistics used include composite scaled sensitivities, parameter correlation coefficients, leverage, Cook's D, and DFBETAS. Tests suggest predictive ability of the calibrated model typical of hydrologic models.

[1]  Stefano Tarantola,et al.  Estimating the approximation error when fixing unessential factors in global sensitivity analysis , 2007, Reliab. Eng. Syst. Saf..

[2]  Keith Beven,et al.  Equifinality and the problem of robust calibration in nitrogen budget simulations , 1999 .

[3]  Mary C. Hill,et al.  Methods and Guidelines for Effective Model Calibration , 2000 .

[4]  C. W. Thornthwaite.  THE WATER BALANCE , 1955 .

[5]  Three Water-Balance Maps of Eastern North America , 1959 .

[6]  Keith Beven,et al.  Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology , 2001 .

[7]  Soroosh Sorooshian,et al.  Effect of rainfall‐sampling errors on simulations of desert flash floods , 1994 .

[8]  S. E. Rantz,et al.  Measurement and computation of streamflow , 1982 .

[9]  B. Croke.  Representing uncertainty in objective functions: extension to include the influence of serial correlation , 2008 .

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

[11]  Michael D. Dettinger,et al.  First order analysis of uncertainty in numerical models of groundwater flow part: 1. Mathematical development , 1981 .

[12]  Heidi Christiansen Barlebo,et al.  Investigating the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, using a three‐dimensional inverse flow and transport model , 2004 .

[13]  David W. Pollock,et al.  A Controlled Experiment in Ground Water Flow Model Calibration , 1998 .

[14]  N. Draper,et al.  Applied Regression Analysis , 1967 .

[15]  Mary C. Hill,et al.  Predictive modeling of flow and transport in a two‐dimensional intermediate‐scale, heterogeneous porous medium , 2001 .

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

[17]  W. Graf.  Fluvial Hydraulics: Flow and Transport Processes in Channels of Simple Geometry , 1998 .

[18]  D. Legates,et al.  Evaluating the use of “goodness‐of‐fit” Measures in hydrologic and hydroclimatic model validation , 1999 .

[19]  Mary C Hill,et al.  Determining Extreme Parameter Correlation in Ground Water Models , 2003, Ground water.

[20]  Heidi Christiansen Barlebo,et al.  Concentration data and dimensionality in groundwater models: evaluation using inverse modelling , 1998 .

[21]  L. Band.  Topographic Partition of Watersheds with Digital Elevation Models , 1986 .

[22]  E. Poeter,et al.  Inverse Models: A Necessary Next Step in Ground‐Water Modeling , 1997 .

[23]  Keith Beven,et al.  Flood frequency estimation by continuous simulation for a catchment treated as ungauged (with uncertainty) , 2002 .

[24]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information , 1998 .

[25]  S. Sorooshian,et al.  Effective and efficient algorithm for multiobjective optimization of hydrologic models , 2003 .

[26]  John Doherty,et al.  Comparison of hydrologic calibration of HSPF using automatic and manual methods , 2007 .

[27]  S. Sorooshian,et al.  Evaluation of Maximum Likelihood Parameter estimation techniques for conceptual rainfall‐runoff models: Influence of calibration data variability and length on model credibility , 1983 .

[28]  Henrik Madsen,et al.  Automatic calibration of a conceptual rainfall-runoff model using multiple objectives. , 2000 .

[29]  L Foglia,et al.  Testing Alternative Ground Water Models Using Cross‐Validation and Other Methods , 2007, Ground water.

[30]  J. Brian Gray,et al.  Applied Regression Including Computing and Graphics , 1999, Technometrics.

[31]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[32]  Mario L. V. Martina,et al.  Flood forecasting using a fully distributed model: application of the TOPKAPI model to the Upper Xixian Catchment , 2005 .

[33]  S. Sorooshian,et al.  Automatic calibration of conceptual rainfall-runoff models: sensitivity to calibration data , 1996 .

[34]  M. Hill,et al.  A Comparison of Solute‐Transport Solution Techniques and Their Effect on Sensitivity Analysis and Inverse Modeling Results , 2001, Ground water.

[35]  N. Draper,et al.  Applied Regression Analysis: Draper/Applied Regression Analysis , 1998 .

[36]  J. Nash,et al.  River flow forecasting through conceptual models part I — A discussion of principles☆ , 1970 .

[37]  Keith Beven,et al.  Functional classification and evaluation of hydrographs based on Multicomponent Mapping (Mx) , 2004 .

[38]  D. Helsel,et al.  Statistical methods in water resources , 2020, Techniques and Methods.

[39]  J. Doherty,et al.  Role of the calibration process in reducing model predictive error , 2005 .

[40]  Michael N. Gooseff,et al.  Sensitivity analysis of conservative and reactive stream transient storage models applied to field data from multiple-reach experiments , 2005 .

[41]  Steen Christensen,et al.  Prediction of Regional Ground Water Flow to Streams , 1998 .

[42]  Jason W. Kean,et al.  Generation and verification of theoretical rating curves in the Whitewater River basin, Kansas , 2005 .

[43]  Mary C. Hill,et al.  A new multistage groundwater transport inverse method: presentation, evaluation, and implications , 1999 .

[44]  Mary C Hill,et al.  Parameter and observation importance in modelling virus transport in saturated porous media-investigations in a homogenous system. , 2005, Journal of contaminant hydrology.

[45]  Keith Beven,et al.  Estimation of flood inundation probabilities as conditioned on event inundation maps , 2003 .

[46]  Ashish Sharma,et al.  A comparative study of Markov chain Monte Carlo methods for conceptual rainfall‐runoff modeling , 2004 .

[47]  Henrik Madsen,et al.  Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling , 2008 .

[48]  Jan Feyen,et al.  Use of sensitivity and uncertainty measures in distributed hydrological modeling with an application to the MIKE SHE model , 2002 .

[49]  Reply to comment by F. Molz et al. on “Investigating the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, using a three‐dimensional inverse flow and transport model” , 2006 .

[50]  George Kuczera,et al.  Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm , 1998 .

[51]  Armando Brath,et al.  Analysis of the effects of different scenarios of historical data availability on the calibration of a spatially-distributed hydrological model , 2004 .

[52]  Mary C. Hill,et al.  Two-dimensional advective transport in ground-water flow parameter estimation , 1996 .

[53]  Harvey M. Wagner,et al.  Global Sensitivity Analysis , 1995, Oper. Res..

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

[55]  V. T. Chow.  Open-channel hydraulics , 1959 .

[56]  R. L. Cooley.  A theory for modeling ground-water flow in heterogeneous media , 2004 .

[57]  C. Tiedeman,et al.  Effective Groundwater Model Calibration , 2007 .

[58]  Rolland W. Carter,et al.  Accuracy of Current Meter Measurement , 1963 .

[59]  Stephen R. Workman,et al.  STATISTICAL PROCEDURES FOR EVALUATING DAILY AND MONTHLY HYDROLOGIC MODEL PREDICTIONS , 2004 .

[60]  Mary C. Hill,et al.  UCODE_2005 and six other computer codes for universal sensitivity analysis, calibration, and uncertainty evaluation constructed using the JUPITER API , 2006 .

[61]  Mary C Hill,et al.  The Practical Use of Simplicity in Developing Ground Water Models , 2006, Ground water.

[62]  D. M. Ely,et al.  A method for evaluating the importance of system state observations to model predictions, with application to the Death Valley regional groundwater flow system , 2004 .

[63]  Richard M. Yager,et al.  Detecting influential observations in nonlinear regression modeling of groundwater flow , 1998 .

[64]  Mary C. Hill,et al.  Death valley regional ground-water flow model calibration using optimal parameter estimation methods and geoscientific information systems , 1999 .

[65]  Mary C Hill,et al.  Numerical methods for improving sensitivity analysis and parameter estimation of virus transport simulated using sorptive-reactive processes. , 2005, Journal of contaminant hydrology.

[66]  Hoshin Vijai Gupta,et al.  Do Nash values have value? , 2007 .

[67]  K. Bencala,et al.  Automated calibration of a stream solute transport model: implications for interpretation of biogeochemical parameters , 2003, Journal of the North American Benthological Society.

[68]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods , 2000 .

[69]  J. Doherty,et al.  METHODOLOGIES FOR CALIBRATION AND PREDICTIVE ANALYSIS OF A WATERSHED MODEL 1 , 2003 .

[70]  V. Singh,et al.  The TOPKAPI model. , 2002 .

[71]  Richard L. Cooley,et al.  Regression modeling of ground-water flow , 1990 .

[72]  R. M. Yager,et al.  Effects of Model Sensitivity and Nonlinearity on Nonlinear Regression of Ground Water Flow , 2004, Ground water.