On the identification of model structure in hydrological and environmental systems

144

[1] In the absence of model deficiencies, simulation results at the correct parameter values lead to an unbiased description of observed data with remaining deviations due to observation errors only. However, this ideal cannot be reached in the practice of environmental modeling, because the required simplified representation of the complex reality by the model and errors in model input lead to errors that are reflected in biased model output. This leads to two related problems: First, ignoring bias of output in the statistical model description leads to bias in parameter estimates, model predictions and, in particular, in the quantification of their uncertainty. Second, as there is no objective choice of how much bias to accept in which output variable, it is not possible to design an ''objective'' model calibration procedure. The first of these problems has been addressed by introducing a statistical (Bayesian) description of bias, the second by suggesting the use of multiobjective calibration techniques that cannot easily be used for uncertainty analysis. We merge the ideas of these two approaches by using the prior of the statistical bias description to quantify the importance of multiple calibration objectives. This leads to probabilistic inference and prediction while still taking multiple calibration objectives into account. The ideas and technical details of the suggested approach are outlined and a didactical example as well as an application to environmental data are provided to demonstrate its practical feasibility and computational efficiency.Citation: Reichert, P., and N. Schuwirth (2012), Linking statistical bias description to multiobjective model calibration, Water Resour.

Section: Discussionmentioning

confidence: 99%

Linking statistical bias description to multiobjective model calibration

Reichert

Schuwirth

2012

144

“…This method also postulates an error covariance structure that is estimated along with the rest of the model parameters. Kalman‐type approaches to fusing model predictions and measurements online are ubiquitous in many disciplines, including watershed modeling, and have been used as a technique to estimate the values of time‐varying parameters [e.g., Moradkhani et al , 2005; Lin and Beck , 2007].…”

Section: Methodsmentioning

confidence: 99%

“…Although the underlying assumption of stationarity is a valuable way to account for structural uncertainty while constraining the added complexity of temporally varying parameters, we may not expect a parameter to be stationary with respect to the (always somewhat arbitrary) study time frame, e.g., the intensity of in‐stream attenuation would be expected to vary with dry and wet years. Lin and Beck [2007] used a first‐order random walk, a nonstationary process, in a dissolved oxygen model of a managed pond. Their analysis shows how time varying parameters can be used to identify structural improvements to models of environmental systems.…”

Section: Methodsmentioning

confidence: 99%

A Bayesian methodological framework for accommodating interannual variability of nutrient loading with the SPARROW model

Wellen

Arhonditsis

Labencki

et al. 2012

[1] Regression-type, hybrid empirical/process-based models (e.g., SPARROW, PolFlow) have assumed a prominent role in efforts to estimate the sources and transport of nutrient pollution at river basin scales. However, almost no attempts have been made to explicitly accommodate interannual nutrient loading variability in their structure, despite empirical and theoretical evidence indicating that the associated source/sink processes are quite variable at annual timescales. In this study, we present two methodological approaches to accommodate interannual variability with the Spatially Referenced Regressions on Watershed attributes (SPARROW) nonlinear regression model. The first strategy uses the SPARROW model to estimate a static baseline load and climatic variables (e.g., precipitation) to drive the interannual variability. The second approach allows the source/sink processes within the SPARROW model to vary at annual timescales using dynamic parameter estimation techniques akin to those used in dynamic linear models. Model parameterization is founded upon Bayesian inference techniques that explicitly consider calibration data and model uncertainty. Our case study is the Hamilton Harbor watershed, a mixed agricultural and urban residential area located at the western end of Lake Ontario, Canada. Our analysis suggests that dynamic parameter estimation is the more parsimonious of the two strategies tested and can offer insights into the temporal structural changes associated with watershed functioning. Consistent with empirical and theoretical work, model estimated annual in-stream attenuation rates varied inversely with annual discharge. Estimated phosphorus source areas were concentrated near the receiving water body during years of high in-stream attenuation and dispersed along the main stems of the streams during years of low attenuation, suggesting that nutrient source areas are subject to interannual variability.

“…The most popular method to date is probably Bayesian multimodel averaging (BMA) [Hoeting et al, 1999;Neuman, 2003aNeuman, , 2003b, which uses multiple structures to characterize the uncertainty in our knowledge of the mechanics of underlying hydrological processes Georgakakos et al, 2004;Ajami et al, 2006;Duan et al, 2007]. Other methods seek not just to characterize model structure uncertainty but to also improve the structure of the hydrological model; examples include time-variable parameter methods such as the state-dependent parameter (SDP) estimation method [Young et al, 2001;Young and Ratto, 2009], the recursive prediction error (RPE) approach [Lin and Beck, 2007], and the time-dependent parameters approach [Reichert and Mieleitner, 2009]. Recently, a new method called the Bayesian estimation of structure (BESt) approach [Bulygina and Gupta, 2009 has been proposed to resolve the underlying structure of the model via data assimilation conducted on the raw data.…”

Section: Introductionmentioning

confidence: 99%

Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach

Gong

Gupta

Yang

et al. 2013

108

[1] With growing interest in understanding the magnitudes and sources of uncertainty in hydrological modeling, the difficult problem of characterizing model structure adequacy is now attracting considerable attention. Here, we examine this problem via a model-structureindependent approach based in information theory. In particular, we (a) discuss how to assess and compute the information content in multivariate hydrological data, (b) present practical methods for quantifying the uncertainty and shared information in data while accounting for heteroscedasticity, (c) show how these tools can be used to estimate the best achievable predictive performance of a model (for a system given the available data), and (d) show how model adequacy can be characterized in terms of the magnitude and nature of its aleatory uncertainty that cannot be diminished (and is resolvable only up to specification of its density), and its epistemic uncertainty that can, in principle, be suitably resolved by improving the model. An illustrative modeling example is provided using catchment-scale data from three river basins, the Leaf and Chunky River basins in the United States and the Chuzhou basin in China. Our analysis shows that the aleatory uncertainty associated with making catchment simulations using this data set is significant ($50%). Further, estimated epistemic uncertainties of the HyMod, SAC-SMA, and Xinanjiang model hypotheses indicate that considerable room for model structural improvements remain.