Improved Numerical Methods for Distributed Hydrological Models

Abstract

Distributed hydrological models have been used for decades to calculate and predict the movement of water and energy within watersheds. These models have evolved from relatively simple empirical applications into complex spatially distributed and physically-based programs. However, the evolution of distributed hydrological models has not involved the improvement of the numerical methods used to calculate the redistribution of water and energy in the watershed. Because of this, many models still use numerical methods that are potentially inaccurate.

In order to simulate the transport of water and energy in a hydrological model, typical numerical methods employ an operator splitting approach. Operator splitting (OS) essentially breaks down the set of coupled ordinary differential equations (ODEs) that define a hydrological model into separate ODEs that can be solved individually. The dominant operator splitting method in surface water models is the ordered series approach. Because the ordered series approach treats parallel hydrological processes as if they happen in series, it is prone to errors that can significantly reduce the accuracy of model results. The impact that operator splitting errors have upon hydrologic model results is, to date, unknown.

Using a new distributed hydrological model, Raven, the impact of operator splitting errors is investigated. Understanding these errors will lead to better numerical methods for reducing errors in models and to shed light on the shortcomings of hydrological models with respect to numerical method choice. Alternative numerical methods - the explicit Euler and the implicit iterative Heun methods - are implemented and assessed in their ability to minimize errors and produce more accurate distributed hydrological models.