Complexity, Uncertainty, and Systematic Error in Hydrologic Models

Abstract

Issues of complexity, parameter and input variable uncertainty, and systematic model errors are reviewed and assessed. Simple measures are derived to represent degree of complexity, degree of uncertainty, and degree of systematic error for a simple subset of hydrologic models. Model complexity is represented by a complexity number, Nc = nm + 1. The quantity n is the number of model parameters and input variables and m is the number of simulation runs (around base or nominal values) required to assess noninteractive model sensitivity. Model uncertainty is represented by a summed coefficient of variation, CVm, computed from the sum of the individual coefficients of variations of the n parameters and input variables. Systematic error, NSm, is related to how well the model mimics nature and is represented as a function of the number of the basic concepts of conservation of mass, momentum, and energy, and of the basic variables position, velocity, and acceleration included in each model component. Three infiltration models: Phi Index, Runoff Curve Number, and the Green-Ampt Infiltration Equation; Two peak discharge estimation procedures: The Rational Formula and the coupled Green-Ampt Kinematic Wave Model are used as example illustrations. These examples are used to illustrate the highly interactive and important concepts of model complexity, uncertainty, and systematic error. The model quantification methodology and examples are also used to formulate the hypothesis that simple measures can be derived and used to objectively evaluate model complexity and its relationships with uncertainty and systematic error. Possible future applications of the model quantification methodology include selection of appropriate simulation models within decision support systems and contributions to development of a systematic approach for development and application of appropriate technology.KeywordsSystematic ErrorDecision Support SystemHydrologic ModelSaturated Hydraulic ConductivityWater Quality ModelingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.