Bayesian spectral likelihood for hydrological parameter inference

Schaefli, Bettina; Kavetski, Dmitri (2017). Bayesian spectral likelihood for hydrological parameter inference. Water resources research, 53(8), pp. 6857-6884. American Geophysical Union 10.1002/2016wr019465

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This paper proposes a spectral domain likelihood function for the Bayesian estimation of hydrological model parameters from a time series of model residuals. The spectral domain error model is based on the power-density spectrum (PDS) of the stochastic process assumed to describe residual errors. The Bayesian spectral domain likelihood (BSL) is mathematically equivalent to the corresponding Bayesian time domain likelihood (BTL) and yields the same inference when all residual error assumptions are satisfied (and all residual error parameters are inferred). However, the BSL likelihood function does not depend on the residual error distribution in the original time domain, which offers a theoretical advantage in terms of robustness for hydrological parameter inference. The theoretical properties of BSL are demonstrated and compared to BTL and a previously proposed spectral likelihood by Montanari and Toth (2007), using a set of synthetic case studies and a real case study based on the Leaf River catchment in the U.S. The empirical analyses confirm the theoretical properties of BSL when applied to heteroscedastic and autocorrelated error models (where heteroscedasticity is represented using the log-transformation and autocorrelation is represented using an AR(1) process). Unlike MTL, the use of BSL did not introduce additional parametric uncertainty compared to BTL. Future work will explore the application of BSL to challenging modeling scenarios in arid catchments and indirect calibration with nonconcomitant input/output time series.

Item Type:

Journal Article (Original Article)


08 Faculty of Science > Institute of Geography

UniBE Contributor:

Schaefli, Bettina


900 History > 910 Geography & travel




American Geophysical Union




Bettina Schäfli

Date Deposited:

15 Jan 2021 16:08

Last Modified:

15 Jan 2021 16:16

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Web of Science ID:


Additional Information:

Notes: ISI Document Delivery No.: FH5JN Times Cited: 0 Cited Reference Count: 61 Schaefli, Bettina Kavetski, Dmitri Swiss National Science Foundation (SNF) [PZ00P2_147366, PP00P2_157611] The research of the first author was supported by research grants of the Swiss National Science Foundation (SNF; PZ00P2_147366 and PP00P2_157611). A Matlab implementation of the HYMOD model, including the Leaf river data set, was provided by the model identification toolbox of Hoshin Gupta (University of Arizona). No other data sets were used for this theoretical study. An R implementation of the MTL likelihood was provided by Alberto Montanari (University of Bologna). We thank two anonymous reviewers, Anna Sikorska, and Chief Editor Alberto Montanari for their constructive comments during the review process. Amer geophysical union Washington
Custom 1: Article
Date: 2017

Uncontrolled Keywords:

hydrology Bayesian inference spectral domain inference rainfall-runoff modeling frequency domain inference model calibration time-series model calibration catchment models runoff models uncertainty heteroscedasticity autocorrelation prediction domain errors




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