Non-parametric kernel-based estimation and simulation of precipitation amount

Pavlides, Andrew; Agou, Vasiliki D.; Hristopulos, Dionissios T.

doi:10.1016/j.jhydrol.2022.127988

Cited by 9 publications

(4 citation statements)

References 64 publications

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“…In addition, the kernel method effectively estimates the overall form and shape of fuzzy probability density functions, excelling at capturing their complex structure 22 . However, it lacks the capability to identify the specific mixture of probability distributions that contribute to the formation of the fuzzy density function.…”

Section: Literature Reviewmentioning

confidence: 99%

The fuzzy Kullback–Leibler divergence for estimating parameters of the probability distribution in fuzzy data: an application to classifying Vietnamese Herb Leaves

Le,

Sang,

Lam Thuy

et al. 2023

Sci Rep

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In this paper, we address the challenge of estimating probability distributions which are typically represented by parameter-based values. However, this estimation is prone to errors and does not comprehensively capture the nature of real-world data. Additionally, real-world data often follows a mixed form of probability distributions, where sub-datasets may contain incomplete information. To enhance flexibility, especially in classification problems, we propose a new method for describing parameters estimated through Bayesian statistics. Our method introduces fuzzy parameters and assesses the similarity between probability distributions using the fuzzy extended Kullback–Leibler divergence. We demonstrate the practical application of our approach in Vietnamese Herb Leaves classification. By incorporating fuzzy parameters and leveraging Bayesian statistics, our method provides more robust estimations of probability distributions and enables improved flexibility in classification tasks.

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Section: Literature Reviewmentioning

confidence: 99%

The fuzzy Kullback–Leibler divergence for estimating parameters of the probability distribution in fuzzy data: an application to classifying Vietnamese Herb Leaves

Le,

Sang,

Lam Thuy

et al. 2023

Sci Rep

View full text Add to dashboard Cite

show abstract

“…When choosing a PDF for a parametric rainfall model to describe the probability distribution, the domain of definition, curve flexibility, and simplicity of the function should be deliberated [39]. The normal (denoted as N), Weibull (denoted as W), lognormal (denoted as L), gamma (denoted as G), and GEV (denoted as E) distribution functions [30] were used to fit the observed RFs of each period using the maximum likelihood function. More specifically, the parameters of each PDF are the maximum likelihood estimates.…”

Section: Probability Distribution Functions (Pdfs)mentioning

confidence: 99%

“…Similarly, they can be divided into three groups based on the parameters used, i.e., parametric [27], semiparametric, and nonparametric models. Parametric models have strong extrapolation capabilities, such as gamma [28], generalized gamma, lognormal, Weibull [29], and generalized extreme value (GEV) [30]. In addition, some machine-learning-based methods have emerged for randomly generating monthly rainfall [31].…”

Section: Introductionmentioning

confidence: 99%

An Event-Based Stochastic Parametric Rainfall Simulator (ESPRS) for Urban Stormwater Simulation and Performance in a Sponge City

Yang

Liu

2023

Water

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The temporal heterogeneity of rainfall is substantial in urban catchments, and it often has huge impacts on stormwater simulation and management. Using a design storm with a fixed pattern may cause uncertainties in hydrological modeling. Here, we propose an event-based stochastic parametric rainfall simulator (ESPRS) for stormwater simulation in a sponge city with green roofs, permeable pavements, and bioretention cells. In the ESPRS, we used five distributions to fit the measured rainfall events and evaluated their performance using Akaike’s Information Criterion, Anderson—Darling goodness-of-fit test, and p-values. The vast rainfall time series data generated using the ESPRS were used to run the storm water management model for outflow simulations in the catchment, thus revealing the influence of temporal rainfall characteristics on the hydrological responses. The results showed the following: (1) The ESPRS outperforms the Chicago method in predicting extreme precipitation events, and its control factors are the rainfall peak period, rainfall peak fraction, and cumulative rainfall fraction at the peak period. (2) The best-fit functions for the rainfall depth in each period have different distributions, mostly being in lognormal, gamma, and generalized extreme value distributions. (3) Rear-type precipitation events with high peak fractions are the most negative pattern for outflow control. The developed ESPRS can suitably reproduce rainfall time series for urban stormwater management.

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“…As an alternative to frequency histogram methods for estimating the PDFs of the rainfall data, the kernel density estimation (KDE) is a non-parametric method to estimate the PDF of a random variable based on kernels as weights [28,29]. Ref.…”

Section: Introductionmentioning

confidence: 99%

KDE-Based Rainfall Event Separation and Characterization

Cao

Diao

Wang

et al. 2023

Water

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Rainfall event separation is mainly based on the selection of the minimum inter-event time (MIET). The traditional approach to determining a suitable MIET for estimating the probability density functions is often using the frequency histograms. However, this approach cannot avoid arbitrariness and subjectivity in selecting the histogram parameters. To overcome the above limitations, this study proposes a kernel density estimation (KDE) approach for rainfall event separation and characterization at any specific site where the exponential distributions are suitable for characterizing the rainfall event statistics. Using the standardized procedure provided taking into account the Poisson and Kolmogorov–Smirnov (K-S) statistical tests, the optimal pair of the MIET and rainfall event volume threshold can be determined. Two climatically different cities, Hangzhou and Jinan of China, applying the proposed approach are selected for demonstration purposes. The results show that the optimal MIETs determined are 12 h for Hangzhou and 10 h for Jinan while the optimal event volume threshold values are 3 mm for both Hangzhou and Jinan. The KDE-based approach can facilitate the rainfall statistical representation of the analytical probabilistic models of urban drainage/stormwater control facilities.

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Non-parametric kernel-based estimation and simulation of precipitation amount

Cited by 9 publications

References 64 publications

The fuzzy Kullback–Leibler divergence for estimating parameters of the probability distribution in fuzzy data: an application to classifying Vietnamese Herb Leaves

The fuzzy Kullback–Leibler divergence for estimating parameters of the probability distribution in fuzzy data: an application to classifying Vietnamese Herb Leaves

An Event-Based Stochastic Parametric Rainfall Simulator (ESPRS) for Urban Stormwater Simulation and Performance in a Sponge City

KDE-Based Rainfall Event Separation and Characterization

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