US 12,105,250 B2
Method for calibrating daily precipitation forecast by using bernoulli-Gamma-Gaussian distribution
Tongtiegang Zhao, Guangdong (CN); and Zeqing Huang, Guangdong (CN)
Assigned to SUN YAT-SEN UNIVERSITY, Guangdong (CN)
Appl. No. 17/793,050
Filed by SUN YAT-SEN UNIVERSITY, Guangdong (CN)
PCT Filed Apr. 16, 2021, PCT No. PCT/CN2021/087676
§ 371(c)(1), (2) Date Jul. 15, 2022,
PCT Pub. No. WO2022/217568, PCT Pub. Date Oct. 20, 2022.
Prior Publication US 2023/0152488 A1, May 18, 2023
Int. Cl. G01W 1/18 (2006.01); G01W 1/10 (2006.01); G01W 1/14 (2006.01); G06F 17/18 (2006.01)
CPC G01W 1/18 (2013.01) [G01W 1/10 (2013.01); G01W 1/14 (2013.01); G06F 17/18 (2013.01)] 16 Claims
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1. A method for calibrating daily precipitation forecast by using a Bernoulli-Gamma-Gaussian distribution, comprising the following steps:
S1, acquiring raw forecast data of a daily average precipitation in a watershed area and corresponding observed data of an average precipitation in the watershed area;
S2, using a Bernoulli distribution to perform a precipitation occurrence analysis on the raw forecast data and observed data;
S3, using a Gamma distribution to perform a precipitation amount analysis on the raw forecast data and the observed data that precipitation occurs;
S4, performing a normal transformation on the raw forecast data and the observed data according to analysis results of the Bernoulli distribution and the Gamma distribution, and obtaining normalized variable F and normalized variable Ô corresponding to the raw forecast data and the observed data;
S5, constructing a bivariate joint normal distribution according to the normalized variable F and normalized variable Ô;
S6, using the normalized variable F of the raw forecast data as a predictor and using the normalized variable Ô of the observed data as a predictand to construct a conditional probability distribution of the predictand Ô; and
S7, determining whether forecast data to be calibrated is that a precipitation event occurs, determining the conditional probability distribution of the predictand Ô, further randomly sampling the conditional probability distribution of the predictand Ô, and finally obtaining the calibrated forecast according to an inverse normal quantile transform, wherein the calibrated forecast be used in an engineering application of precipitation forecast for improving a predictive performance of a daily precipitation forecast;
wherein the step of performing the normal transformation on the raw forecast data and the observed data comprises:
S4.1, transforming the raw forecast data and the observed data into corresponding cumulative distribution function values according to the analysis results of the Bernoulli distribution and the Gamma distribution, wherein the calculation formula thereof is as follows:

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wherein Pfi and Poi denote the cumulative distribution function values of the raw forecast data fi and the observed data oi in an i-th year, and i=1,2, . . . , K; CDFf, βf) and CDFo, βo) respectively denote cumulative distribution functions of the Gamma distribution of the raw forecast data and the observed data; and mf and mo respectively denote the cumulative distribution function values of the raw forecast data and the observed data that no precipitation event occurs;
S4.2, transforming the cumulative distribution function values Pfi and Poi into variables obeying a standard normal distribution by means of an inverse function of the cumulative distribution function in the standard normal distribution, wherein the expression formulas thereof are as follows:

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wherein CDF′N(0,12)( ) denotes the inverse function of the cumulative distribution function in the standard normal distribution; and fi and ôi respectively denote a variable of raw forecast and a variable of observation which were normal quantile transformed; therefore, the normalized variable F=[f1, f2, . . . , fK] of the raw forecast data and the normalized variable Ô=[ô1, ô2, . . . , ôK] of the observed data obey a normal distribution.