Technical Report - Methods: A diagnostic approach to analyze the direction of change in model outputs based on global variations in the model inputs

Hydrologic models are used to simulate natural phenomena while making different assumptions about the levels of complexity with which natural processes should be represented. Global Sensitivity Analysis is regularly applied to understand how the inputs (including forcing, parameters and initial states) of these models control their outputs. A less widely explored strategy to support such diagnostic analysis is the assessment of direction of change (DOC) which addresses the question whether the increase (or decrease) of a model input leads to a positive (or negative) change in the model output. We propose a metric, called Direction Index, to quantitatively assess the direction of change and develop an approach to calculate it. The basic idea of our approach is two-folded: (1) Estimate the zero-th and first order term of the High Dimensional Model Representation (HDMR) decomposition. (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 (Hymod) with a time-varying analysis applied to the Leaf River Catchment in the USA. 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.