The Probability Distribution of Daily Precipitation at the Point and Catchment Scales in the United States

Ye, Lei; Hanson, Lars S.; Ding, Pengqi; Wang, Dingbao; Vogel, Richard M.

doi:10.5194/hess-2018-85

Cited by 7 publications

(9 citation statements)

References 33 publications

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“…Logistic distribution is a continuous probability distribution. It defined by two parameters for all the real numbers, which are a scale s and a location μ (Ye et al, 2018). Its PDF plot is always symmetric about the mean.…”

Section: Methodsmentioning

confidence: 99%

Statistical modeling of monthly rainfall variability in Soummam watershed of Algeria, between 1967 and 2018

Aieb

Lefsih

Scarpa

et al. 2020

Natural Resource Modeling

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The monthly precipitations obtained during 51 years of measurement in 24 stations of Soummam watershed in Algeria were analyzed to describe rainfall trends and aridity state of the area using statistical modeling. The choice of distribution laws was justified by comparing fitting results of different distributions laws used in literature reviews. Hence, the p values proved that Generalized Extreme Value, Weibull (3) and Logistic the distribution law are more adequate to analyze rainfall frequencies in different part of the watershed. The diagnostic given by Q‐Q plot, P‐P plot and survival regression curve showed the period of wetness and dryness in the northeastern and the southwestern part of the watershed, respectively. Moreover, the study given by the De Martonne index explains the consequences of climate change by a new form of aridity in the watershed between 1994 and 2018. Recommendations for Resource Managers The annual rainfall of Soummam watershed has a moderate and irregular rainfall distribution between 1967 and 2018. Using distribution function on monthly rainfall in each bioclimatic floor to analyze the trend of rainfall frequency gives a spatio‐temporal description of climate in the area. Fitting by Kolmogorov‐Smirnov test allows us to choose generalized extreme value, Weibull (3) and Logistic for modeling monthly rainfall variability in each part of the watershed. The diagnostic obtained by P‐P plot, Q‐Q plot and survival regression curve proved a change of aridity in the northeastern and southwestern part of the watershed between 1994 and 2018.

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Section: Methodsmentioning

confidence: 99%

Statistical modeling of monthly rainfall variability in Soummam watershed of Algeria, between 1967 and 2018

Aieb

Lefsih

Scarpa

et al. 2020

Natural Resource Modeling

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show abstract

“…Three distributions are chosen which are gamma, Log-Normal and Generalized Pareto distributions (GPD) are tested on multivariate rainfall data. These distributions are commonly used as potential candidates for the data generating mechanism of rainfall data [20][21][22]. Estimation of the parameters for each of the above sampled probability distributions are based on the summary statistics from the daily torrential rainfall data in Peninsular Malaysia.…”

Section: Simulation Procedures For Generating Synthetic Rainfall Datamentioning

confidence: 99%

Fitting statistical distribution of extreme rainfall data for the purpose of simulation

Shaharudin

Ahmad

Mohamed

et al. 2020

IJEECS

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<span>In this study, several types of probability distributions were used to fit the daily torrential rainfall data from 15 monitoring stations of Peninsular Malaysia from the period of 1975 to 2007. The study of fitting statistical distribution is important to find the most suitable model that could anticipate extreme events of certain natural phenomena such as flood and tsunamis. The aim of the study is to determine which distribution fits well with the daily torrential Malaysian rainfall data. Generalized Pareto, Lognormal and Gamma distributions were the distributions that had been tested to fit the daily torrential rainfall amount in Peninsular Malaysia. First, the appropriate distribution of the daily torrential rainfall was identified within the selected distributions for rainfall stations. Then, data sets were generated based on probability distributions that mimic a daily torrential rainfall data. Graphical representation and goodness of fit tests were used in finding the best fit model. The Generalized Pareto was found to be the most appropriate distribution in describing the daily torrential rainfall amounts of Peninsular Malaysia. The outputs can be beneficial for the purpose of generating several sets of simulated data matrices that mimic the same characteristics of rainfall data in order to assess the performance of the modification method compared to classical method. </span>

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“…On the basis of the results, the mixed exponential distribution showed the best fit for the data followed by the gamma and exponential distributions, respectively. Ye, Hanson, Ding, Wang, and Vogel (2018) evaluated the performance of 15 distributions in 237 rainfall gauge stations in the United States. The results indicated that the four‐parameter kappa distribution showed the best performance to describe the occurrence of daily rainfall in the rainfall gauge stations.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, assessing the applicability of CDFs with different structures is necessary to provide more accurate information on rainfall. In practice, precipitation is simulated using the gamma distribution that in most cases is able to adequately estimate low and moderate rainfall due to its flexibility (Kist & Virgens Filho, 2015; Papalexiou, Koutsoyiannis, & Makropoulos, 2013; Ye et al, 2018; Yoo, Jung, & Kim, 2005). However, the gamma distribution may not be adequate in cases of extreme precipitation values, as magnitude and frequency are often underestimated (Allard & Bourotte, 2015; Kleiber, Katz, & Rajagopalan, 2012).…”

Section: Introductionmentioning

confidence: 99%

Cumulative distribution function of daily rainfall in the Tocantins–Araguaia hydrographic region, Amazon, Brazil

Progênio

Blanco

2020

Natural Resource Modeling

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Knowing the temporal and spatial variability of the probability of rainfall occurrence is indispensable for the planning and management of agricultural and agroindustrial activities. This study aims to evaluate the applicability of four cumulative distribution functions (CDFs; exponential, two-parameter exponential, mixed exponential, and gamma) to estimate the probability of daily rainfall in the Tocantins-Araguaia hydrographic region (TAHR). The CDFs were applied to 196 rainfall gauge stations distributed in three homogeneous regions (HRs) of rainfall in the TAHR. In relation to the CDFs, the Kolmogorov-Smirnov test and the probability-probability plot showed that the mixed exponential best adhered to the observed data for most of the months of the year in the three HRs that were analyzed. In the few months that this function did not have a good statistical performance, the gamma function was the one with the best fit quality. This study can be used as a guide for studies in other river basins in Brazil and around the world to estimate CDFs of daily rainfall. Recommendations for Resource Managers• Stochastic models using cumulative distribution functions (CDFs) allow the simulation of rainfall data by means of their frequency of occurrence. Some CDFs have been used to verify the behavior and variability of precipitation over the years. For example, the mixed exponential, the Weibull with two parameters, the generalized Pareto, the lognormal, and the gamma with two parameters.• Daily rainfall modeling is important to recognize the occurrence patterns for the prediction of the climatic behavior of a region. Sectors such as agriculture, flood control, and human supply projects need knowledge of precipitation for planning, management, and operation.• The knowledge of the rainfall behavior is very important in Tocantins-Araguaia hydrographic region because it is located in the arc of deforestation in the Amazon. In this case, the dry season and temperatures have been increasing due to global climate change and deforestation itself. K E Y W O R D S adherence test, agroindustrial activities, ecotone, homogeneous regions, water resources

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The Probability Distribution of Daily Precipitation at the Point and Catchment Scales in the United States

Cited by 7 publications

References 33 publications

Statistical modeling of monthly rainfall variability in Soummam watershed of Algeria, between 1967 and 2018

Statistical modeling of monthly rainfall variability in Soummam watershed of Algeria, between 1967 and 2018

Fitting statistical distribution of extreme rainfall data for the purpose of simulation

Cumulative distribution function of daily rainfall in the Tocantins–Araguaia hydrographic region, Amazon, Brazil

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