Calibration of rainfall‐runoff models: Application of global optimization to the Sacramento Soil Moisture Accounting Model

Conceptual rainfall-runoff models are difficult to calibrate by means of automatic methods; one major reason for this is the inability of conventional procedures to locate the globally optimal set of parameters. This paper investigates the consistency with which two global optimization methods, the shuffled complex evolution (SCE-UA) method (developed by the authors) and the multistart simplex (MSX) method, are able to find the optimal parameter set during calibration of the Sacramento soil moisture accounting model (SAC-SMA) of the National Weather Service River Forecast System (NWSRFS). In the first phase of this study, error-free synthetic data are used to conduct a comparative evaluation of the algorithms under “ideal” conditions. In 10 independent trials of each algorithm in which 13 parameters of the SAC-SMA model were optimized simultaneously, the SCE-UA method achieved a 100% success rate in locating the precise global optimum (i.e., the “true” parameter values) while the MSX method failed in all trials even with more than twice the number of function evaluations. In the second phase, historical data from the Leaf River watershed are used to conduct a comparative evaluation of the algorithms under “real” conditions, using two different estimation criteria, DRMS and HMLE; the SCE-UA algorithm obtained consistently lower function values and more closely grouped parameter estimates, while using one-third fewer function evaluations than the MSX algorithm.

[1]  David R. Dawdy,et al.  Mathematical Models of Catchment Behavior , 1965 .

[2]  Peter K. Kitanidis,et al.  Adaptive filtering through detection of isolated transient errors in rainfall‐runoff models , 1980 .

[3]  S. Sorooshian,et al.  Uniqueness and observability of conceptual rainfall‐runoff model parameters: The percolation process examined , 1983 .

[4]  Larry Brazil,et al.  Multilevel calibration strategy for complex hydrologic simulation models , 1988 .

[5]  Stephen J. Burges,et al.  An assessment of a conceptual rainfall‐runoff model's ability to represent the dynamics of small hypothetical catchments: 2. Hydrologic responses for normal and extreme rainfall , 1990 .

[6]  G. Pickup.  TESTING THE EFFICIENCY OF ALGORITHMS AND STRATEGIES FOR AUTOMATIC CALIBRATION OF RAINFALL-RUNOFF MODELS , 1977 .

[7]  Jene Diane Hendrickson,et al.  Comparison of Newton-type and direct search algorithms for calibration of conceptual rainfall-runoff models , 1988 .

[8]  Jacob D Goldstein,et al.  Applications of Kalman Filtering and Maximum Likelihood Parameter Identification to Hydrologic Forecasting , 1980 .

[9]  S. Sorooshian,et al.  Shuffled complex evolution approach for effective and efficient global minimization , 1993 .

[10]  S. Burges,et al.  An assessment of a conceptual rainfall‐runoff model's ability to represent the dynamics of small hypothetical catchments: 1. Models, model properties, and experimental design , 1990 .

[11]  P. R. Johnston,et al.  Parameter optimization for watershed models , 1976 .

[12]  R. Ibbitt,et al.  Systematic parameter fitting for conceptual models of catchment hydrology , 1970 .

[13]  Q. Duan,et al.  A global optimization strategy for efficient and effective calibration of hydrologic models. , 1991 .

[14]  P. D. Hutchinson,et al.  Model Parameter Consistency and Fitting Criteria , 1984 .

[15]  S. Sorooshian,et al.  Stochastic parameter estimation procedures for hydrologie rainfall‐runoff models: Correlated and heteroscedastic error cases , 1980 .

[16]  S. Sorooshian,et al.  The Automatic Calibration of Conceptual Catchment Models Using Derivative‐Based Optimization Algorithms , 1985 .

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

[18]  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 .

[19]  George Kuczera,et al.  On the relationship between the reliability of parameter estimates and hydrologic time series data used in calibration , 1982 .

[20]  Soroosh Sorooshian,et al.  The Analysis of Structural Identifiability: Theory and Application to Conceptual Rainfall-Runoff Models , 1985 .

[21]  John C. Monro.  Direct search optimization in mathematical modeling and a watershed model application , 1971 .

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

[23]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[24]  E. L. Peck,et al.  Catchment modeling and initial parameter estimation for the National Weather Service River Forecast System , 1976 .

[25]  L. Brazil,et al.  Calibration Procedures Use with the National Weather Service River Forecast System , 1980 .

[26]  G. Kuczera.  Improved parameter inference in catchment models: 1. Evaluating parameter uncertainty , 1983 .

[27]  S. Sorooshian,et al.  Automatic calibration of conceptual rainfall-runoff models: The question of parameter observability and uniqueness , 1983 .

[28]  Peter K. Kitanidis,et al.  Real‐time forecasting with a conceptual hydrologic model: 1. Analysis of uncertainty , 1980 .

[29]  Witold F. Krajewski,et al.  Optimization of Complex Hydrologic Models Using Random Search Methods , 1987 .

[30]  S. Sorooshian.  Parameter estimation of rainfall-runoff models with heteroscedastic streamflow errors — The noninformative data case , 1981 .

[31]  S. Sorooshian,et al.  A maximum likelihood criterion for use with data collected at unequal time intervals , 1988 .