Toward improved identifiability of hydrologic model parameters: The information content of experimental data

We have developed a sequential optimization methodology, entitled the parameter identification method based on the localization of information (PIMLI) that increases information retrieval from the data by inferring the location and type of measurements that are most informative for the model parameters. The PIMLI approach merges the strengths of the generalized sensitivity analysis (GSA) method [Spear and Hornberger, 1980], the Bayesian recursive estimation (BARE) algorithm [Thiemann et al., 2001], and the Metropolis algorithm [Metropolis et al., 1953]. Three case studies with increasing complexity are used to illustrate the usefulness and applicability of the PIMLI methodology. The first two case studies consider the identification of soil hydraulic parameters using soil water retention data and a transient multistep outflow experiment (MSO), whereas the third study involves the calibration of a conceptual rainfall-runoff model

Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling?

In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchment

New Insights into History Matching via Sequential Monte Carlo

The aim of the history matching method is to locate non-implausible regions of the parameter space of complex deterministic or stochastic models by matching model outputs with data. It does this via a series of waves where at each wave an emulator is fitted to a small number of training samples. An implausibility measure is defined which takes into account the closeness of simulated and observed outputs as well as emulator uncertainty. As the waves progress, the emulator becomes more accurate so that training samples are more concentrated on promising regions of the space and poorer parts of the space are rejected with more confidence. Whilst history matching has proved to be useful, existing implementations are not fully automated and some ad-hoc choices are made during the process, which involves user intervention and is time consuming. This occurs especially when the non-implausible region becomes small and it is difficult to sample this space uniformly to generate new training points. In this article we develop a sequential Monte Carlo (SMC) algorithm for implementation which is semi-automated. Our novel SMC approach reveals that the history matching method yields a non-implausible distribution that can be multi-modal, highly irregular and very difficult to sample uniformly. Our SMC approach offers a much more reliable sampling of the non-implausible space, which requires additional computation compared to other approaches used in the literature

An efficient estimation of time-varying parameters of dynamic models by combining offline batch optimization and online data assimilation

It is crucially important to estimate unknown parameters in earth system models by integrating observation and numerical simulation. For many applications in earth system sciences, an optimization method which allows parameters to temporally change is required. In the present paper, an efficient and practical method to estimate the time-varying parameters of relatively low dimensional models is presented. In the newly proposed method, called Hybrid Offline Online Parameter Estimation with Particle Filtering (HOOPE-PF), an inflation method to maintain the spread of ensemble members in a sampling-importance-resampling particle filter is improved using a non-parametric posterior probabilistic distribution of time-invariant parameters obtained by comparing simulated and observed climatology. The HOOPE-PF outperforms the original sampling-importance-resampling particle filter in synthetic experiments with toy models and a real-data experiment with a conceptual hydrological model especially when the ensemble size is small. The advantage of HOOPE-PF is that its performance is not greatly affected by the size of perturbation to be added to ensemble members to maintain their spread while it is critically important to get the optimal performance in the original particle filter. Since HOOPE-PF is the extension of the existing particle filter which has been extensively applied to many earth system models such as land, ecosystem, hydrology, and paleoclimate reconstruction, the HOOPE-PF can be applied to improve the simulation of these earth system models by considering time-varying model parameters

Application of temporal streamflow descriptors in hydrologic model parameter estimation

This paper presents a parameter estimation approach based on hydrograph descriptors that capture dominant streamflow characteristics at three timescales (monthly, yearly, and record extent). The scheme, entitled hydrograph descriptors multitemporal sensitivity analyses (HYDMUS), yields an ensemble of model simulations generated from a reduced parameter space, based on a set of streamflow descriptors that emphasize the timescale dynamics of streamflow record. In this procedure the posterior distributions of model parameters derived at coarser timescales are used to sample model parameters for the next finer timescale. The procedure was used to estimate the parameters of the Sacramento soil moisture accounting model (SAC-SMA) for the Leaf River, Mississippi. The results indicated that in addition to a significant reduction in the range of parameter uncertainty, HYDMUS improved parameter identifiability for all 13 of the model parameters. The performance of the procedure was compared to four previous calibration studies on the same watershed. Although our application of HYDMUS did not explicitly consider the error at each simulation time step during the calibration process, the model performance was, in some important respects, found to be better than in previous deterministic studies. Copyright 2005 by the American Geophysical Union

The role of hydrograph indices in parameter estimation of rainfall-runoff models

A reliable prediction of hydrologic models, among other things, requires a set of plausible parameters that correspond with physiographic properties of the basin. This study proposes a parameter estimation approach, which is based on extracting, through hydrograph diagnoses, information in the form of indices that carry intrinsic properties of a basin. This concept is demonstrated by introducing two indices that describe the shape of a streamflow hydrograph in an integrated manner. Nineteen mid-size (223-4790 km2) perennial headwater basins with a long record of streamflow data were selected to evaluate the ability of these indices to capture basin response characteristics. An examination of the utility of the proposed indices in parameter estimation is conducted for a five-parameter hydrologic model using data from the Leaf River, located in Fort Collins, Mississippi. It is shown that constraining the parameter estimation by selecting only those parameters that result in model output which maintains the indices as found in the historical data can improve the reliability of model predictions. These improvements were manifested in (a) improvement of the prediction of low and high flow, (b) improvement of the overall total biases, and (c) maintenance of the hydrograph's shape for both long-term and short-term predictions. Copyright © 2005 John Wiley & Sons, Ltd