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Bayesian uncertainty decomposition for hydrological projections

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Abstract

There is a considerable uncertainty in a hydrological projection, which arisen from the multiple stages composing the hydrological projection. Uncertainty decomposition analysis evaluates contribution of each stage to the total uncertainty in the hydrological projection. Some uncertainty decomposition methods have been proposed, but they still have some limitations: (1) they do not consider nonstationarity in data and (2) they only use summary statistics of the projected data instead of the full time-series and lack a principled way to choose the summary statistic. We propose a novel Bayesian uncertainty decomposition method which can alleviate such problems. In addition, the proposed method provides probabilistic statements about the uncertainties. We apply the proposed method to the streamflow projection data for Yongdam Dam basin located at Geum River in South Korea.

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Notes

  1. Throughout this article, we refer to selected emission scenarios, GCMs, bias correction techniques and hydrological models as “simulators” to simplify sentences, e.g., we write “simulator uncertainties” instead of “model/scenario/technique uncertainties”.

  2. This result is valid for the scenario period. For the control period, we use an observed emission scenario and thus have 60 (\(=5\times 3\times 4\)) projected values.

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Acknowledgements

This work was supported by Korea Environmental Industry & Technology Institute(KEITI) through Advanced Water Management Research Program, funded by Korea Ministry of Environment (Grant no. 83082).

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Authors and Affiliations

  1. Department of Statistics, Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul, 08826, Korea

    Ilsang Ohn, Seonghyeon Kim & Yongdai Kim

  2. Water and Land Research Group, Korea Environment Institute, Seoul, South Korea

    Seung Beom Seo

  3. Department of Civil and Environmental Engineering, Seoul National University, Seoul, South Korea

    Young-Oh Kim

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  1. Ilsang Ohn
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  5. Yongdai Kim
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Correspondence to Yongdai Kim.

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Appendix A. Bias correction techniques

Appendix A. Bias correction techniques

In this section, we briefly explain bias correction steps in BCSD and BCCA. For more details, we refer to Pierce et al. (2013) and Maurer (2010).

BCSD starts with monthly GCM output (e.g., temperature or precipitation). BCSD first removes the linear trend in the GCM data over years in each month and then applies the quantile mapping to the detrended data for each month. Through the quantile mapping, the GCM output value z is adjusted to the bias corrected value \({\hat{z}}\) as

$$\begin{aligned} {\hat{z}}=F_o^{-1}(F_m(z)), \end{aligned}$$

where \(F_m\) and \(F_o\) denote the cumulative distribution functions of the GCM output and the observed data, respectively. In practice, \(F_m\) and \(F_o\) usually assumed to be in a parametric family, for example, normal distribution for temperature and gamma distribution for precipitation, and their parameters are determined for each month based on the GCM ouput data and the observed data in the control period, respectively. Lastly BCSD added the subtracted linear trend back to the adjusted GCM output through the quantile mapping.

BCCA is almost identical to BCSD, but the quantile mapping is applied to the daily data instead of the monthly data. BCCA does not remove the linear trend in the data since the motivation for trend removal is not strong for daily data. The cumulative distribution functions of the GCM output and the observed data are estimated from the GCM output values and observed data in the control period, respectively, for each month.

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Ohn, I., Kim, S., Seo, S.B. et al. Bayesian uncertainty decomposition for hydrological projections. J. Korean Stat. Soc. 49, 953–975 (2020). https://doi.org/10.1007/s42952-019-00042-8

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