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-22-6519-2018

Cited by 59 publications

(44 citation statements)

References 38 publications

(51 reference statements)

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“…Therefore, KAP is the best distribution model among the employed distributions for QDM to bias-correct the simulated precipitation in South Korea. These results are consistent with the analysis results of the probability distribution for daily precipitation in the United States [20]. They report that KAP is the best distribution for modeling the daily precipitation on a wet day.…”

Section: Discussionsupporting

confidence: 90%

Probability Distributions for a Quantile Mapping Technique for a Bias Correction of Precipitation Data: A Case Study to Precipitation Data Under Climate Change

Heo

Ahn

Shin

et al. 2019

Water

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The quantile mapping method is a bias correction method that leads to a good performance in terms of precipitation. Selecting an appropriate probability distribution model is essential for the successful implementation of quantile mapping. Probability distribution models with two shape parameters have proved that they are fit for precipitation modeling because of their flexibility. Hence, the application of a two-shape parameter distribution will improve the performance of the quantile mapping method in the bias correction of precipitation data. In this study, the applicability and appropriateness of two-shape parameter distribution models are examined in quantile mapping, for a bias correction of simulated precipitation data from a climate model under a climate change scenario. Additionally, the impacts of distribution selection on the frequency analysis of future extreme precipitation from climate are investigated. Generalized Lindley, Burr XII, and Kappa distributions are used, and their fits and appropriateness are compared to those of conventional distributions in a case study. Applications of two-shape parameter distributions do lead to better performances in reproducing the statistical characteristics of observed precipitation, compared to those of conventional distributions. The Kappa distribution is considered the best distribution model, as it can reproduce reliable spatial dependences of the quantile corresponding to a 100-year return period, unlike the gamma distribution.Eden et al. [6] attempted to identify any sources of climate model error, and reported that precipitation data corrected by a statistical correction method can be a good predictor for the observed data set at a global scale. Teng et al. [7] assessed the performances of several bias correction methods for precipitation data, and evaluated their impact on a runoff model. They reported that the quantile mapping (QM) and two-state gamma distribution mapping methods provide good performance. The QM method shows better performance than a simpler bias correction for the mean and variation in the precipitation data [8][9][10]. Themeßl et al. [11] reported that QM leads to the best performance for precipitation, particularly to large amounts of quantiles. While the QM method provides a good performance for the bias correction of stationary data, it leads to less reliable results for nonstationary data, such as simulation data under a climate change scenario. To address this drawback, Cannon et al. [12] suggested the quantile delta mapping (QDM) method which explicitly preserves relative changes in all of the quantiles of the distribution. They claimed that the QDM method is superior to the traditional QM method and the detrended quantile mapping (DQM) method, which considers trends in the mean.The QM method assumes that the distribution of simulated or estimated data preserves the distribution of any observed data. In QM, simulated data corresponding to a given probability is replaced by an observed quantile corresponding to the same probabili...

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Section: Discussionsupporting

confidence: 90%

Probability Distributions for a Quantile Mapping Technique for a Bias Correction of Precipitation Data: A Case Study to Precipitation Data Under Climate Change

Heo

Ahn

Shin

et al. 2019

Water

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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.…”

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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).…”

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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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“…Each distribution has different parameters, and they can all be conveniently computed and parameterized for series. Since the extremes of water systems are often needed to determine the infrastructure design and management plans, improving the prediction using the most reasonable distribution as a model can greatly improve water management practices [26].Second, we will evaluate the non-stationary statistics for hydrological extremes. One example of a non-stationary statistic is the Hurst exponent, first developed to quantify the long-term persistence of water storage of reservoirs by Hurst [27].…”

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confidence: 99%

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confidence: 99%

Statistical Analysis of Extreme Events in Precipitation, Stream Discharge, and Groundwater Head Fluctuation: Distribution, Memory, and Correlation

Dawley

Zhang

Liu

et al. 2019

Water

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Hydrological extremes in the water cycle can significantly affect surface water engineering design, and represents the high-impact response of surface water and groundwater systems to climate change. Statistical analysis of these extreme events provides a convenient way to interpret the nature of, and interaction between, components of the water cycle. This study applies three probability density functions (PDFs), Gumbel, stable, and stretched Gaussian distributions, to capture the distribution of extremes and the full-time series of storm properties (storm duration, intensity, total precipitation, and inter-storm period), stream discharge, lake stage, and groundwater head values observed in the Lake Tuscaloosa watershed, Alabama, USA. To quantify the potentially non-stationary statistics of hydrological extremes, the time-scale local Hurst exponent (TSLHE) was also calculated for the time series data recording both the surface and subsurface hydrological processes. First, results showed that storm duration was most closely related to groundwater recharge compared to the other storm properties, while intensity also had a close relationship with recharge. These relationships were likely due to the effects of oversaturation and overland flow in extreme total precipitation storms. Second, the surface water and groundwater series were persistent according to the TSLHE values, because they were relatively slow evolving systems, while storm properties were anti-persistent since they were rapidly evolving in time. Third, the stretched Gaussian distribution was the most effective PDF to capture the distribution of surface and subsurface hydrological extremes, since this distribution can capture the broad transition from a Gaussian distribution to a power-law one.process-based models requiring intensive data that are typically not available for many study sites, statistical analysis of hydrological extremes is an attractive tool to interpret these extreme events within and across systems from simple measurements [7-10].There are two major challenges when applying basic statistics to analyze hydrologic extremes. First, hydrologic processes in the water cycle are interconnected, while basic statistical analysis of extremes often does not consider multiple systems and tends to oversimplify the complexity of the correlated processes like precipitation and groundwater table fluctuations [11,12]. Understanding how the subtle properties of one system's extreme events can affect the other interconnected systems requires more in-depth analysis and use of advanced statistical techniques. Second, these basic statistical techniques often rely on assumptions or major simplifications of properties for water systems, such as stationarity in both space and time, which may not always be valid for real world dynamics [13][14][15]. These issues motivated this study.One example of the assumption/simplification used by basic statistical studies in hydrological extremes is the well-known Gumbel distribution. Statistics of extremes is one of th...

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The probability distribution of daily precipitation at the point and catchment scales in the United States

Cited by 59 publications

References 38 publications

Probability Distributions for a Quantile Mapping Technique for a Bias Correction of Precipitation Data: A Case Study to Precipitation Data Under Climate Change

Probability Distributions for a Quantile Mapping Technique for a Bias Correction of Precipitation Data: A Case Study to Precipitation Data Under Climate Change

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

Statistical Analysis of Extreme Events in Precipitation, Stream Discharge, and Groundwater Head Fluctuation: Distribution, Memory, and Correlation

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