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Article

Tuning the Bivariate Meta-Gaussian Distribution Conditionally in Quantifying Precipitation Prediction Uncertainty

by 1,2
1
National Weather Service, Office of Water Prediction, 1325 East-West Highway, Silver Spring, MD 20910, USA
2
Lynker, 202 Church Street, SE/Suite 536, Leesburg, VA 20175, USA
Forecasting 2020, 2(1), 1-19; https://doi.org/10.3390/forecast2010001
Received: 25 November 2019 / Revised: 2 January 2020 / Accepted: 10 January 2020 / Published: 15 January 2020
(This article belongs to the Special Issue Advances in Hydrological Forecasting)
One of the ways to quantify uncertainty of deterministic forecasts is to construct a joint distribution between the forecast variable and the observed variable; then, the uncertainty of the forecast can be represented by the conditional distribution of the observed given the forecast. The joint distribution of two continuous hydrometeorological variables can often be modeled by the bivariate meta-Gaussian distribution (BMGD). The BMGD can be obtained by transforming each of the two variables to a standard normal variable and the dependence between the transformed variables is provided by the Pearson correlation coefficient of these two variables. The BMGD modeling is exact provided that the transformed joint distribution is standard normal. In real-world applications, however, this normality assumption is hardly fulfilled. This is often the case for the modeling problem we consider in this paper: establish the joint distribution of a forecast variable and its corresponding observed variable for precipitation amounts accumulated over a duration of 24 h. In this case, the BMGD can only serve as an approximate model and the dependence parameter can be estimated in a variety of ways. In this paper, the effect of tuning this parameter is studied. Numerical simulations conducted suggest that, while the parameter tuning results in limited improvements in goodness-of-fit (GOF) for the BMGD as a bivariate distribution model, better results may be achieved by tuning the parameter for the one-dimensional conditional distribution of the observed given the forecast greater than a certain large value. View Full-Text
Keywords: meta-Gaussian distribution; Gaussian copula; mallows distance; earth mover’s distance; precipitation; precipitation intermittency; uncertainty quantification meta-Gaussian distribution; Gaussian copula; mallows distance; earth mover’s distance; precipitation; precipitation intermittency; uncertainty quantification
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MDPI and ACS Style

Wu, L. Tuning the Bivariate Meta-Gaussian Distribution Conditionally in Quantifying Precipitation Prediction Uncertainty. Forecasting 2020, 2, 1-19. https://doi.org/10.3390/forecast2010001

AMA Style

Wu L. Tuning the Bivariate Meta-Gaussian Distribution Conditionally in Quantifying Precipitation Prediction Uncertainty. Forecasting. 2020; 2(1):1-19. https://doi.org/10.3390/forecast2010001

Chicago/Turabian Style

Wu, Limin. 2020. "Tuning the Bivariate Meta-Gaussian Distribution Conditionally in Quantifying Precipitation Prediction Uncertainty" Forecasting 2, no. 1: 1-19. https://doi.org/10.3390/forecast2010001

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