The challenge of parameter uncertainty

Abstract

Conceptual hydrological model parameters represent characteristics of a catchment. They are an integration of spatial heterogeneous parts of the system. Finding adequate parameter values based on field observations, which represents the heterogeneity of a catchment on the spatial resolution and scale of the model, is considered challenging since the scale of the observations do not meet the scale of the parameters.

The objective of this thesis is to analyze the extent to which it is possible to make an estimation of parameter distributions based on field observations (the precipitation, evaporation and discharge) and a given hydrological model structure. The goal is to avoid the use of uninformed prior parameter distributions during calibration by using available field data to generate informed prior distributions.

In this research, six different expert-knowledge inverse modelling methods are developed to find four parameter distributions. Each method uses sub-periods in the data and is coupled to the parameter of the model component representing that specific type of sub-period.

To test the methods, the study was conducted in a synthetic environment, which made it easier to validate the parameter distributions obtained with the methods. In this synthetic experiment, discharge data was produced by a model driven by real rainfall data and potential evaporation data. All forms of uncertainty were excluded in this test.

The effect of data uncertainty in the methods was investigated separately by conducting a sensitivity analysis. The same synthetic data was used; however the synthetic data was corrupted to simulate data uncertainty.

Last, an application of the methods upon real measured data was completed. The performance of the methods to find parameter distributions can no longer be assessed since in the real world the “correct” parameter values are not known. However, a comparison of the informed prior parameter distributions of the methods with uninformed prior parameter distributions could be made with a Monte-Carlo sampling strategy calibration.

In the synthetic experiment, all parameter distributions of the investigated model were correctly determined using the expert-knowledge inverse modelling methods. The sensitivity analysis revealed that the method to determine the maximum percolation rate parameter (Pmax) distribution was sensitive to data uncertainty. The determined Pmax parameter distributions did not include the original parameter of the corrupted synthetic data. However, this issue does not lead to other parameter distributions that do not include the original parameters.

In real-world application, insight is gained into the performance of the developed methods to find parameter distributions. An uncertainty interval was constructed with the Generalized Likelihood Uncertainty Estimation (GLUE) method. The total area of the constructed uncertainty interval using the calibration results of the informed prior parameter distributions was less than half than the uncertainty interval constructed using the uninformed prior parameter distributions. The posterior parameter distributions of the informed parameter distributions was two to five times smaller than for the uninformed parameter distribution. The model performance of both calibrations did not deviate significantly, indicating a sufficient model structure for the catchment and an adequate performance of the methods to find parameters.