Evaluation of Model Complexity and Input Uncertainty of Field‐Scale Water Flow and Salt Transport

Abstract

Prediction of large‐scale vadose zone water flow and salt transport is affected by errors due to uncertainties in model structure, that is, complexity of representation of hydrologic processes and model input uncertainties such as parameter values, boundary conditions, and initial conditions. Selection of an appropriate level of model complexity must consider these two sources of uncertainty. We illustrate this selection process for the prediction of field‐scale crop transpiration and salt drainage in irrigated agriculture given a limited number of point‐scale measurements. Various levels of model input uncertainty in hydraulic properties and infiltration rates are considered, representative of a range of spatial heterogeneities. Model complexity is defined relative to a “true” model, in terms of the level of spatial and temporal averaging used in the approximate model. This set‐up allows for the separation of the total model error into different terms representing the model input error and the structural model error. Results show that the relative contribution of structural model error to the total model error decreases as spatial heterogeneity or uncertainty in the model input increases. Model input uncertainty may be reduced by taking a larger number of point‐scale measurements. Our analysis further illustrates that there exists an optimal trade‐off between model complexity and model input uncertainty. It suggests that complex models may be replaced by more simple ones as long as the resulting structural model error is smaller than the prediction errors due to input uncertainty. The methodology provides a straightforward and objective approach to identifying an optimal level of model complexity as a function of the degree of field‐scale heterogeneity and data availability.