Hydrological model simulations are often complicated by inevitable uncertainties in initial conditions, boundary conditions, and parameter fields. A proper identification and quantification of such uncertainties are nowadays a must for any modern hydrologist. In this mini symposium, beside presentations focusing on how uncertainty quantification can be properly performed for problems typical of hydrological sciences (e.g., flow and transport in porous media, river and karst spring discharge predictions, surface water-groundwater interaction…), we want to emphasize why uncertainty quantification is relevant in hydrology and its implication for engineering applications.
The minisimposium received funding from the International Graduate School of Science and Engineering of the Technical University of Munich.
Better informed than uncertain – Information theory as a framework for uncertainty quantification
Uwe Ehret | Karlsruhe Institute of Technology | Germany
Uncertainty is a crucial aspect of hydrological analysis and prediction because the systems of interest are typically complex and include multiple and non-linear interdependencies, while related observations are rare and influenced by many factors. In this talk, I will argue that information theory (IT), whose roots date back to the seminal work by Claude Shannon (Shannon, 1948) is a promising framework to address such problems. I will first introduce key concepts of IT (information, entropy, conditional and cross entropy) and explain how they are related to probabilistic concepts of uncertainty. I will then present some arguments why working with information (the log-transform of probability) rather than directly working with probabilities is useful, and why it is equally useful to focus on information that data or models contain about a question rather than stressing the remaining uncertainty. I will briefly talk about how maximum entropy concepts provide upper bounds for uncertainty, and how IT with its core unit of 'bit' facilitates evaluation of computer-based approaches to modeling (which is the standard today).
I will give application examples for information-based uncertainty quantification from rainfall-runoff detection in hydrological time series, spatial rainfall interpolation and spatial modeling, hydrological model building and evaluation.
Shannon, C. E. (1948). A Mathematical Theory of Communication, Bell System Technical Journal, 27 (3): 379–423.
Solving a Bayesian Inverse Problem for a Karst Aquifer Model with Active Subspaces
Mario Teixeira Parente | Technical University of Munich | Germany
We present a parameter study of the karst hydrological model LuKARS. The study consists of a high‐dimensional Bayesian inverse problem and a global sensitivity analysis. The active subspace (AS) method, a recent set of tools for dimension reduction, is applied to find directions in the space of parameters that dominate the Bayesian update from the prior to the posterior distribution. These directions are found by computing an eigendecomposition of a matrix involving the gradient of the negative log-likelihood. They span a linear subspace, the AS, which can be exploited for an adjusted, low-dimensional Markov chain Monte Carlo algorithm constructing samples from a posterior type distribution defined on the active subspace. The AS can be used to construct sensitivity metrics on each of the individual parameters and to construct a natural model surrogate that can be evaluated very fast. Our model consists of 21 parameters to reproduce the hydrological behavior of the Kerschbaum spring in Austria. It is demonstrated and visualized that this particular case study has implicit low dimensionality which can be seen from a quickly decaying spectrum in the mentioned eigendecomposition. Finally, we discuss also possibilities for improvement of this approach that could lie, for example, in the construction of a different surrogate that is aware of uncertainties introduced by the fact that the active subspace is constructed based on the prior, and not on the posterior distribution.
From uncertainty quantification to uncertainty attribution: what we can learn through global sensitivity analysis and how it can help in the calibration and evaluation of hydrological models
Valentina Noacco | University of Bristol | United Kingdom
Computer models are essential tools in hydrology research and practice. However, building and using hydrological models effectively is complicated by various sources of error and uncertainty, such as: simplifying assumptions underpinning the model structure; uncertainties in the input data that are used to force the model simulation; and errors in the output observations that are used to evaluate the model predictions. To understand the implications of these uncertainties, we can rely on increasingly powerful Global Sensitivity Analysis (GSA) methods. While most Uncertainty Analysis methods mainly focus on quantifying output uncertainty, GSA focuses on the attribution of such uncertainty to the model’s uncertain input factors. This attribution enable modellers to set priorities for effective uncertainty reduction, to identify potential for model simplification, and to investigate more comprehensively the interactions between inputs and their effects on the model’s response, resulting in better evaluation of the model behaviour. In this talk I will discuss the key working principles of GSA, and review some key lessons that our community has learnt through the application of GSA over the years - and what they mean for improving the way we calibrate, evaluate and improve our models.
Model ambiguity in subsurface flow in the presence of limited knowledge in hydraulic conductivities
Xavier Sanchez Vila | Universitat Politècnica de Catalunya | Spain
After decades of studies focused on unveiling the mysteries of complex transport processes in the subsurface, we have found that most misinterpretations associated with realistic applications stem from misunderstanding groundwater flow patterns due to the difficulties linked to proper (hydro)geologic reconstruction. This work is keyed to a critical review of a variety of aquifer characterization approaches. We highlight the possible sources of interpretive errors associated with popular techniques such as hydraulic tomography, use of training images, or the one-model-solves-all multiGaussian fields. All of these elements can lead to the formulation of often competing conceptual models, then translated to ambiguity of ensuing flow and transport fields. Moreover, typical observables of flow or solute transport do not allow proper model discrimination, and estimated model parameters become just apparent quantities with no expectation of attaining predictive capabilities. We then focus on a general recently developed model (based on the concept of Generalized Sub-Gaussian fields), which has been shown to best represent some key features of the hydraulic conductivity spatial structure. Here we rely on numerical simulations in a three-dimensional bounded porous medium and Quadratic Discriminant Analysis to document how different conservative transport observables might help in the non-univocal discrimination of model and parameters, thus translating into uncertain model outcomes.