Influence diagnostics in hydrological modeling

Abstract

Accurate hydrological model predictions play an important role in designing infrastructure for domestic water supply, agriculture, industry, and flood and drought protection. A key step in model development is model calibration where hydrologists fit a model to historical data to make predictions into the future. The original contribution to knowledge of this thesis is to evaluate and develop influence diagnostics to understand the extent to which model calibration outcomes are determined by a small number of data points that may be erroneous or unrepresentative of overall catchment behaviour. Influence diagnostics can be implemented to describe changes in model predictions, calibrated parameters and model performance. Broadly, these diagnostics can be categorised into two different classes; “case-deletion” influence diagnostics and “regressiontheory” influence diagnostics. Although influence diagnostics have previously been applied to a small number of hydrological studies, there is a need to address the following two major limitations with the currently available influence diagnostics before they can be applied to broader hydrological applications: 1. Case-deletion influence diagnostics are too computationally expensive to apply in hydrological modelling applications because of the length of data and therefore number of model recalibrations that are required (e.g. 10 years requires approximately 3650 model re-calibrations). 2. Regression theory influence diagnostics are computationally efficient, but only linear Cook’s distance has been applied which has strong assumptions of linear model response and Gaussian residual error that are typrically not valid in hydrological modeling. This thesis by publication presents three papers in Chapter 2 to Chapter 4. The first paper investigates the application of influence diagnostics in the context of a series of common hydrological case-studies including a rating curve model and a daily hydrological model with two years of calibration data. In the second paper we generalise regression xii theory influence diagnostics and evaluate the performance in reproducing the computationally expensive case-deletion influence diagnostics on eleven case studies with a variety of model structures and inference scenarios including: nonlinear model response, heteroscedastic residual errors, data uncertainty and Bayesian priors. Finally, in the third paper we present a hybrid framework for influence assessment that combines the strengths of the two classes of influence diagnostics in order to overcome the key limitations listed above. The hybrid framework presented in the third paper in this thesis will provide a foundation for all hydrological modellers to have greater insight into the influence of individual data points on model calibration, thereby providing a basis for identifying disinformative points or understanding how sensitive model predictions are to a small proportion of the dataset. xiii