Enhancing Hydrological Modelling Through Global Sensitivity Analysis and Dimension Reduction.

Abstract

The global sensitivity analysis (GSA) process is pivotal in model development and evaluation, enhancing the understanding of model robustness and reliability, and informing model calibration and validation strategies through factor fixing, factor prioritisation and factor mapping. However, GSA in general encounters several challenges that can affect its reliability. Taking three hydrological models of different complexity as illustrative, namely the SWAT, SAC-SMA and IHACRES rainfall-runoff models, this thesis explores factors that affect global sensitivity analysis outcomes. These factors include: dependency on the choice of objective functions and climate forcings; the type of GSA estimation and sampling methods used; the way of assessing convergence and accuracy of sensitivity metrics; the role that GSA can play in reducing the number of parameters (the dimension) of hydrological models; and the potential for the Active Subspace method to yield a reproduction of a model's response surface. The thesis investigates the applicability of dimension reduction informed by GSA for the SAC-SMA model (factor fixing and factor prioritisation). The parameters ignored in model calibration were fixed at random values from their plausible parameter ranges to evaluate the variation of outcomes. It showed that a model calibrated with a subset of parameters (12 to 9 parameters in the SAC-SMA model) can often yield validation outcomes equal to or better than the original model, suggesting that an optimal model may not require the full parameter set. Based on the method to investigate the reduced-order model, this study proposes a guide to help modellers effectively minimise a model's dimensionality, thereby reducing parameter uncertainty. Numerical GSA methods rely on a finite number of samples to approximate the behaviour of a model over the entire input space. Consequently, the sensitivity metrics derived from the samples may vary depending on the context. Further experiments were conducted to investigate variations in the sensitivity rankings estimated by three GSA methods and three sampling methods, using a very large sample size as a benchmark. It demonstrates that the choice of both the GSA and sampling methods employed affect the resulting rankings, though the impact of the sampling method is smaller. The study proposes a way of measuring the accuracy and convergence of the GSA metrics. Sensitivity metrics estimated by the perturbation-based methods of Active Subspace and Morris methods are found to be unbiased for experiments using smaller sample sizes, but the Sobol' method appears to require many more samples to yield acceptable results. Based on the methods to assess the accuracy and convergence of the sensitivity metrics and the findings drawn from the methods, the study proposes a practical guide to achieve a statistically robust GSA. The relatively recent Active Subspace method warrants investigation of its applicability as a GSA method, but it also offers the additional feature of being able to produce surrogate models. The method defines the rotation of the parameter space that aligns the axes along the most significant directions. Linear fitting between active variables and the model's output can approximate the response surface. This study proposes new approaches for reconstructing the response surface, taking the 6-parameter IHACRES model as an illustration. A method utilising both the Jacobian and Hessian matrices at the central point of the parameter space produces 96.6% of the original model's output with only 28 model evaluations. The second method takes an average of a Jacobian in each subrange of the most sensitive parameter. This method is shown to explain 98.5% of the original model's response surface based on 35 model evaluations. This indicates the potential for developing the methods further to advance the utility of active subspace methods in deriving surrogate models.