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Handbook of Hydrometeorological Ensemble Forecasting pp 1429–1462Cite as

Probability and Statistical Theory for Hydrometeorology

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Abstract

The hydrometeorological forecasting plays an important role in water resources planning and management. The fundamentals of probability and statistics in hydrometeorology are reviewed in this chapter to aid the forecasting practices. We first introduce the elements of probability theory in the classical statistics, including random variables, probability distribution, joint probability, and total probability theorem. The probability estimation is among the key topics in hydrometeorology for statistical inferences, such as uncertainty analysis and statistical forecasting. The probability inference in the univariate case is first introduced with different methods, including parametric distribution, nonparametric distribution, and mixed distribution. Many hydroclimatic variables are mutually correlated, and the dependence modeling of multivariate random variables through the construction of the joint distribution is then introduced. Most of the context is introduced from the view of classical statistics, while a preliminary introduction of the Bayesian approach is also provided. At last, some commonly used methods for hydrometeorological forecasting are introduced, along with a short summary of this chapter.

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Authors and Affiliations

  1. College of Water Sciences, Beijing Normal University, Beijing, China

    Zengchao Hao

  2. Department of Biological and Agricultural Engineering and Zachry Department of Civil Engineering, Texas A&M University, College Station, TX, USA

    Vijay P. Singh

  3. State Key Laboratory of Earth Surface Processes and Resource Ecology, Faculty of Geographical Science, Beijing Normal University, Beijing, China

    Wei Gong

  4. Institute of Land Surface System and Sustainable Development, Faculty of Geographical Science, Beijing Normal University, Beijing, China

    Wei Gong

Authors
  1. Zengchao Hao
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  2. Vijay P. Singh
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  3. Wei Gong
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Corresponding author

Correspondence to Zengchao Hao .

Editor information

Editors and Affiliations

  1. Faculty of Geographical Science, Beijing Normal University, Beijing, China

    Qingyun Duan

  2. European Centre for Medium-Range Weather Forecasts, ECMWF, Reading, UK

    Florian Pappenberger

  3. National Center for Atmospheric Research, Boulder, CO, USA

    Andy Wood

  4. Department of Meteorology, Reading University, Reading, UK

    Hannah L. Cloke

  5. U.S. National Weather Service (retired), Annapolis, MD, USA

    John C. Schaake

Section Editor information

  1. Hydrologic Solutions Limited, Southampton, UK

    James Brown Director

  2. College of Global Change and Earth System Science, Beijing Normal University, Beijing, China

    Wei Gong

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Hao, Z., Singh, V.P., Gong, W. (2019). Probability and Statistical Theory for Hydrometeorology. In: Duan, Q., Pappenberger, F., Wood, A., Cloke, H., Schaake, J. (eds) Handbook of Hydrometeorological Ensemble Forecasting. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39925-1_61

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