Function applicability to class conditional probability density of hourly rainfall

Shen, Tieyuan; Yiheng, Xiang; Liao, Yuhong; Huang, Qi; Wang, Junchao; Dekang, Yu

doi:10.18307/2023.0230

Cited by 1 publication

(2 citation statements)

References 7 publications

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“…Three classes of the class-conditional probability density (CCPD) of hourly rainfall were defined [57]. Then, the applicability of multiple functions was theoretically explored, and three kinds of applicable functions of the CCPD were deduced and screened out [58]. These included GΓD, generalized normal distribution (GND), and Weibull distribution.…”

Section: Object Of Studymentioning

confidence: 99%

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Optimization of Probability Density Functions Applicable for Hourly Rainfall

Shen

Xiang

2023

Atmosphere

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In order to improve the calculation accuracy of the rainfall probability distribution in related applications, this study aimed to select a theoretical function from applicable functions for three classes of the class-conditional probability density function (CCPD) of hourly rainfall series. The three applicable functions are generalized gamma distribution (GΓD), generalized normal distribution (GND), and Weibull distribution. For the reason that it is hard to distinguish the advantages and disadvantages of the three functions by the probability plot and error analysis of fitted values, optimization criteria are proposed, which are the Bayesian information criterion (BIC) and the estimated accuracy of both the annual average rainfall (AAR) and the annual average continuous rainfall (AACR). The results show that by using three applicable functions in 15 regions, the relative fitting deviations for CCPD1 were less than 2.3% and less than 3.3% for ln(CCPD1). The goodness-of-fit values were all above 0.98 for CCPD1 and greater than 0.94 for ln(CCPD1). The fitting effect of the Weibull distribution was relatively poor from the perspective of the probability plot and error analysis of the fitted values, while the three applicable functions could be used to fit CCPD. GΓD had the highest fitting accuracy for the three classes of CCPDs, but there is concern about overfitting due to its broad spectrum. GND, with fewer parameters, had comparable performance to GΓD, and when fitting CCPD1 using GND, the mean relative fitting deviation was 0.6%, the coefficient of determination was 0.999, and for ln(CCPD1), they were 1.45% and 0.989. At the same time, GND performed well in estimating the AARs, with an 8.6% relative error and a 0.92 correlation coefficient in the fifteen regions, indicating that GND can well reflect the spatial variation characteristics of the AAR. Moreover, the function form of GND is simple. GND follows the parsimonious principle, and it is suitable for the whole domain. Therefore, GND is recommended as the theoretical density function based on the optimization criteria. The genetic algorithm was adopted to obtain the approximate solution of the parameters through optimization, which can simplify the derivation and calculation steps. The multiplicative and additive fitting errors were both used in the objective functions, which gave comprehensive consideration to both ends of the fitting curve.

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Section: Object Of Studymentioning

confidence: 99%

“…All of the curves are convex and decreasing in Figure 4a and concave and decreasing in Figure 4b. According to these and other characteristics, three distributions were chosen as applicable functions by filtering using theoretical derivation [58].…”

Section: Empirical Function Of Three Ccpd Classesmentioning

confidence: 99%

Optimization of Probability Density Functions Applicable for Hourly Rainfall

Shen

Xiang

2023

Atmosphere

View full text Add to dashboard Cite

show abstract

Function applicability to class conditional probability density of hourly rainfall

Cited by 1 publication

References 7 publications

Optimization of Probability Density Functions Applicable for Hourly Rainfall

Optimization of Probability Density Functions Applicable for Hourly Rainfall

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