Direction of Change: a Simple Approach to Support the Diagnostic Evaluation of Hydrologic Models

Abstract:

Hydrologic models are used to simulate natural phenomena while making different assumptions about the level of complexity with which natural processes should be represented. Global Sensitivity Analysis is regularly applied to scrutinize these assumptions by analyzing how the inputs of hydrologic models (e.g. system forcings, parameters and initial states) control their outputs. A relatively little explored strategy to support such diagnostic analysis is the assessment of direction of change, which addresses the question whether the increase (or decrease) of a model input leads to a positive (or negative) change in the model output. Here we propose a metric, called Direction Index, to quantitatively assess the direction of change, and develop a simple approach to calculate it. The basic idea is two-folded: (1) Estimate the zero-th and first order term of the High Dimensional Model Representation (HDMR) decomposition of the model output. (2) Calculate the derivatives of the first order term of the HDMR decomposition with respect to a given input. We demonstrate our approach on a widely used conceptual lumped hydrological model with a time-varying analysis applied to US catchments. The results show that our approach provides new insights into the behaviour of the model, which can be used to guide model structure improvement or to improve calibration efficiency.