Journal of Hydrology, 77 (1985) 1--18 1 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands [4] A NONLINEAR TIME-VARIANT CONSTRAINED MODEL FOR RAINFALL--RUNOFF BITHIN DATTA and DENNIS P. LETTENMAIER Water Resources Management Laboratory, Engineering Experiment Station, University of Arkansas, Fayetteville, AR 72701 (U.S.A.) Department of Civil Engineering, FX-I O, University of Washington, Seattle, WA 98195 (U.S.A.) (Received August 3, 1984; revised and accepted August 20, 1984) ABSTRACT Datta, B. and Lettenmaier, D.P., 1985. A nonlinear time-variant constrained model for rainfall--runoff. J. Hydrol., 77: 1--18. Models of the rainfall--runoff process can be segregated into two classes: those based on input-output (black box) techniques, and those based, directly or indirectly, on the laws of physics. Both approaches have limitations and advantages. In this paper a com- bined model is described which incorporates an approximate description of the physical process to estimate effective precipitation and uses the input--output estimation pro- cedure of the constrained linear system (CLS) model to relate effective precipitation to runoff. Results are presented which demonstrate that certain problems of poor calibration and prediction encountered with the CLS model are significantly reduced by using estimated effective precipitation in place of actual precipitation. Use of the precipitation preprocessor with the CLS runoff model effectively incorporates nonlinear and time- variant dynamics without the necessity for multiple-parameter vectors and antecedent precipitation thresholds required by the original version of CLS. Additional refinements, including time variability of some of the parameters, can easily be accommodated in the new formulation. 1. INTRODUCTION The transformation of rainfall to runoff is a complex physical phenome- non, which is yet to be fully understood. Ideally, a conceptual model based on sound physical principles would be the best approach to predicting runoff given rainfall. In practice, the complexity of the process, and its inherent variability in time and space, together with the limitations imposed by computational feasibility, resource constraints and data availability, force the incorporation of simplifying assumptions and empiricism. However, it often is possible to simplify the rainfall--runoff process description and still retain satisfactory model performance, since simpler models require fewer parameters and therefore a reduced loss of degrees of freedom in the parameter estimation stage. 0022-1694/85/$03.30 © 1985 Elsevier Science Publishers B.V.