Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time‐dependent parameters

Reichert, Peter; Mieleitner, Johanna

doi:10.1029/2009wr007814

Cited by 154 publications

(202 citation statements)

References 60 publications

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“…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

Water Resources Research

104

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[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.

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Section: Introductionmentioning

confidence: 99%

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

Gong

Gupta

Yang

et al. 2013

Water Resources Research

104

View full text Add to dashboard Cite

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“…Abramowitz et al [2006] model systematic deviations between the model simulations and observed data; Kuczera et al [2006] and Reichert and Mieleitner [2009] treat parameters as stochastic variables with possible time or state dependency; Kennedy and O'Hagan [2001] stochastically estimate the model equations themselves when all model inputs, states, and outputs are observable.…”

Section: Introductionmentioning

confidence: 99%

Correcting the mathematical structure of a hydrological model via Bayesian data assimilation

Bulygina

Gupta

2011

Water Resources Research

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[1] The goal of model identification is to improve our understanding of the structure and behavior of a system so the model can be used to make inferences about its input-state-output response. It is conventional to preselect some model form and evaluate its "suitability" against historical data. If deemed unsuitable, ways must be found to "correct" the model through some intuitive process. Here, we discuss a Bayesian data assimilation process by which historical observations can be used to diagnose what might be wrong with the presumed mathematical structure of the model and to provide guidance toward fixing the problem. In previous work we showed how, given a suitable conceptual model for the system, the Bayesian estimation of structure (BESt) method can estimate the stochastic form for structural equations of a model that are consistent with historical observations at the spatiotemporal scale of the data while explicitly estimating model structural contributions to prediction uncertainty. However, a prior assumption regarding the form of the equations (an existing model) is often available. Here, we extend BESt to show how the mathematical form of the prior model equations can be corrected/improved to be more consistent with available data while remaining consistent with the presumed physics of the system. Conditions under which convergence will occur are stated. The potential of the extended BESt approach is demonstrated in the context of basin-scale hydrological modeling by correcting the equations of the HyMod model applied to the Leaf River catchment and thereby improving its representation of system input-state-output response.Citation: Bulygina, N., and H. Gupta (2011), Correcting the mathematical structure of a hydrological model via Bayesian data assimilation, Water Resour. Res., 47, W05514,

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“…Some previous studies, such as the study of Reichert and Mieleitner [33], have analyzed the input uncertainty of lumped conceptual nonlinear models by observing the variation of rainfall input multipliers for optimal results; however, by using the distributed hydrological models, such as the DYRIM in this study, the uncertainty quantization of rainfall input would be more complicated and difficult. In this study, we focus on the change of uncertainty corresponding to the number of rainfall stations.…”

Section: Uncertainty Quantization Of Basin Rainfall and Simulated Runoffmentioning

confidence: 95%

“…To alleviate the influence of rainfall spatial uncertainty, Blume et al [32] proposed an event-based runoff coefficient in combination with simple statistical models that could improve the understanding of the rainfall-runoff response of catchments with sparse data. Reichert and Mieleitner [33] proposed a time-dependent rainfall multiplier at the input side of a hydrological model, which was adjusted according to the goodness of fit of model results.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Influence of Rainfall Spatial Uncertainty on Hydrological Simulations Using the Bootstrap Method

Zhang

Shi

et al. 2018

Atmosphere

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Abstract:Rainfall stations of a certain number and spatial distribution supply sampling records of rainfall processes in a river basin. Uncertainty may be introduced when the station records are spatially interpolated for the purpose of hydrological simulations. This study adopts a bootstrap method to quantitatively estimate the uncertainty of areal rainfall estimates and its effects on hydrological simulations. The observed rainfall records are first analyzed using clustering and correlation methods and possible average basin rainfall amounts are calculated with a bootstrap method using various combinations of rainfall station subsets. Then, the uncertainty of simulated runoff, which is propagated through a hydrological model from the spatial uncertainty of rainfall estimates, is analyzed with the bootstrapped rainfall inputs. By comparing the uncertainties of rainfall and runoff, the responses of the hydrological simulation to the rainfall spatial uncertainty are discussed. Analyses are primarily performed for three rainfall events in the upstream of the Qingjian River basin, a sub-basin of the middle Yellow River; moreover, one rainfall event in the Longxi River basin is selected for the analysis of the areal representation of rainfall stations. Using the Digital Yellow River Integrated Model, the results show that the uncertainty of rainfall estimates derived from rainfall station network has a direct influence on model simulation, which can be conducive to better understand of rainfall spatial characteristic. The proposed method can be a guide to quantify an approximate range of simulated error caused by the spatial uncertainty of rainfall input and the quantified relationship between rainfall input and simulation performance can provide useful information about rainfall station network management in river basins.

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Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time‐dependent parameters

Cited by 154 publications

References 60 publications

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

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

Correcting the mathematical structure of a hydrological model via Bayesian data assimilation

Analysis of the Influence of Rainfall Spatial Uncertainty on Hydrological Simulations Using the Bootstrap Method

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