scholarly journals Modelling Extreme Rainfall Using Adjusted Sandwich Estimator

2020 ◽  
pp. 1-5
Author(s):  
Nur Farhanah Kahal Musakkal ◽  
Darmesah Gabda
Keyword(s):  
Maximum Likelihood ◽  
Extreme Rainfall ◽  
Extreme Value ◽  
Annual Maximum ◽  
Generalized Extreme Value ◽  
Maximum Rainfall ◽  
Penalized Maximum Likelihood ◽  
Sandwich Estimator ◽  
Annual Maximum Rainfall ◽  
Site Dependence

The Generalized Extreme Value (GEV) distribution is often used to describe the frequency of occurrence of extreme rainfall. Modelling the extreme event using the independent Generalized Extreme Value to spatial data fails to account the behaviour of dependency data. However, the wrong statistical assumption by this marginal approach can be adjusted using sandwich estimator. In this paper, we used the conventional method of the marginal fitting of generalized extreme value distribution to the extreme rainfall then corrected the standard error to account for inter-site dependence. We also applied the penalized maximum likelihood to improve the generalized parameter estimations. A case study of annual maximum rainfall from several stations at western Sabah is studied, and the results suggest that the variances were found to be greater than the standard error in the marginal estimation as the inter-site dependence being considered. Key words: Generalized Extreme Value theory, sandwich estimator, penalized maximum likelihood, annual maximum rainfall

scholarly journals Analysis of extreme rainfall in Oti River Basin (West Africa)

2021 ◽  
Author(s):  
Komi S. Klassou ◽  
Kossi Komi
Keyword(s):  
River Basin ◽  
Heavy Rainfall ◽  
Extreme Rainfall ◽  
Value Theory ◽  
Extreme Value ◽  
Return Periods ◽  
Maximum Rainfall ◽  
Daily Data ◽  
Dry Spell ◽  
Annual Maximum Rainfall

Abstract Understanding how extreme rainfall is changing locally is a useful step in the implementation of efficient adaptation strategies to negative impacts of climate change. This study aims to analyze extreme rainfall over the middle Oti River Basin. Ten moderate extreme precipitation indices as well as heavy rainfall of higher return periods (25, 50, 75, and 100 years) were calculated using observed daily data from 1921 to 2018. In addition, Mann–Kendall and Sen's slope tests were used for trend analysis. The results showed decreasing trends in most of the heavy rainfall indices while the dry spell index exhibited a rising trend in a large portion of the study area. The occurrence of heavy rainfall of higher return periods has slightly decreased in a large part of the study area. Also, analysis of the annual maximum rainfall revealed that the generalized extreme value is the most appropriate three-parameter frequency distribution for predicting extreme rainfall in the Oti River Basin. The novelty of this study lies in the combination of both descriptive indices and extreme value theory in the analysis of extreme rainfall in a data-scarce river basin. The results are useful for water resources management in this area.

scholarly journals On the Smoothing of the Generalized Extreme Value Distribution Parameters Using Penalized Maximum Likelihood: A Case Study on UVB Radiation Maxima in the Mexico City Metropolitan Area

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 329
Author(s):  
Alejandro Ivan Aguirre-Salado ◽  
Carlos Arturo Aguirre-Salado ◽  
Ernesto Alvarado ◽  
Alicia Santiago-Santos ◽  
Guillermo Arturo Lancho-Romero
Keyword(s):  
Maximum Likelihood ◽  
Mexico City ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Generalized Extreme Value Distribution ◽  
Uvb Radiation ◽  
Generalized Extreme Value ◽  
Penalized Maximum Likelihood ◽  
Distribution Parameters ◽  
Smoothing Functions

This paper concerns the use and implementation of penalized maximum likelihood procedures to fitting smoothing functions of the generalized extreme value distribution parameters to analyze spatial extreme values of ultraviolet B (UVB) radiation across the Mexico City metropolitan area in the period 2000–2018. The model was fitted using a flexible semi-parametric approach and the parameters were estimated by the penalized maximum likelihood (PML) method. In order to investigate the performance of the model as well as the estimation method in the analysis of complex nonlinear trends for UVB radiation maxima, a simulation study was conducted. The results of the simulation study showed that penalized maximum likelihood yields better regularization to the model than the maximum likelihood estimates. We estimated return levels of extreme UVB radiation events through a nonstationary extreme value model using measurements of ozone (O3), nitrogen oxides (NOx), particles of 10 μm or less in diameter (PM10), carbon monoxide (CO), relative humidity (RH) and sulfur dioxide (SO2). The deviance statistics indicated that the nonstationary generalized extreme value (GEV) model adjusted was statistically better compared to the stationary model. The estimated smoothing functions of the location parameter of the GEV distribution on the spatial plane for different periods of time reveal the existence of well-defined trends in the maxima. In the temporal plane, a presence of temporal cyclic components oscillating over a weak linear component with a negative slope is noticed, while in the spatial plane, a weak nonlinear local trend is present on a plane with a positive slope towards the west, covering the entire study area. An explicit spatial estimate of the 25-year return period revealed that the more extreme risk levels are located in the western region of the study area.

scholarly journals A New Look at Storm Separation Technique in Estimation of Probable Maximum Precipitation in Mountainous Areas

Water ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 1177
Author(s):  
Yifan Liao ◽  
Bingzhang Lin ◽  
Xiaoyang Chen ◽  
Hui Ding
Keyword(s):  
Extreme Rainfall ◽  
Separation Technique ◽  
Annual Maximum ◽  
Return Periods ◽  
Mountainous Areas ◽  
Maximum Rainfall ◽  
Probable Maximum Precipitation ◽  
Maximum Precipitation ◽  
L Moments ◽  
Annual Maximum Rainfall

Storm separation is a key step when carrying out storm transposition analysis for Probable Maximum Precipitation (PMP) estimation in mountainous areas. The World Meteorological Organization (WMO) has recommended the step-duration-orographic-intensification-factor (SDOIF) method since 2009 as an effective storm separation technique to identify the amounts of precipitation caused by topography from those caused by atmospheric dynamics. The orographic intensification factors (OIFs) are usually developed based on annual maximum rainfall series under such assumption that the mechanism of annual maximum rainfalls is close to that of the PMP-level rainfall. In this paper, an alternative storm separation technique using rainfall quantiles, instead of annual maximum rainfalls, with rare return periods estimated via Regional L-moments Analysis (RLMA) to calculate the OIFs is proposed. Based on Taiwan’s historical 4- and 24-h precipitation data, comparisons of the OIFs obtained from annual maximum rainfalls with that from extreme rainfall quantiles at different return periods, as well as the PMP estimates of Hong Kong from transposing the different corresponding separated nonorographic rainfalls, were conducted. The results show that the OIFs obtained from rainfall quantiles with certain rare probabilities are more stable and reasonable in terms of stability and spatial distribution pattern.

Statistical Modeling for One Hour Rainfall Data in Kuala Lumpur and Selangor

2014 ◽  
Vol 1030-1032 ◽  
pp. 665-668
Author(s):  
Amanda Lee Sean Peik ◽  
Choong Wee Kang ◽  
Andy Chan
Keyword(s):  
Extreme Value Distribution ◽  
Extreme Rainfall ◽  
Extreme Value ◽  
Distribution Functions ◽  
Rainfall Data ◽  
Kuala Lumpur ◽  
Maximum Rainfall ◽  
Two Phases ◽  
Annual Maximum Rainfall ◽  
The One

The purpose of this study is to assess patterns of extreme rainfall and this study focused on the changes between two phases for extreme rainfall, for the period of 1971 to 2011 and from 1995 to 2011 in Kuala Lumpur and Selangor. The generalised extreme value distribution appears to outperform other distribution functions such as two-parameter Gumbel and lognormal and the three-parameter generalized extreme value (GEV), lognormal (LN3) and log Pearson (LP3) in modeling the one-hour annual maximum rainfall series from 14 stations. The estimated return period of 20, 50, 100-year for each stations based on the best fitting model for the periods of entire record data and from 1995-2011 have been computed. More than 70% of estimated quantiles using rainfall data from 1995-2011 are higher compared to estimation using the entire recorded data.

scholarly journals Heavy rainfall equations for Santa Catarina, Brazil

2011 ◽  
Vol 35 (6) ◽  
pp. 2127-2134 ◽  
Author(s):  
Álvaro José Back ◽  
Alan Henn ◽  
José Luiz Rocha Oliveira
Keyword(s):  
Coastal Region ◽  
Daily Rainfall ◽  
Rain Gauge ◽  
Annual Maximum ◽  
Santa Catarina ◽  
Maximum Rainfall ◽  
Rainfall Events ◽  
Significance Level ◽  
Intensity Duration Frequency ◽  
Annual Maximum Rainfall

Knowledge of intensity-duration-frequency (IDF) relationships of rainfall events is extremely important to determine the dimensions of surface drainage structures and soil erosion control. The purpose of this study was to obtain IDF equations of 13 rain gauge stations in the state of Santa Catarina in Brazil: Chapecó, Urussanga, Campos Novos, Florianópolis, Lages, Caçador, Itajaí, Itá, Ponte Serrada, Porto União, Videira, Laguna and São Joaquim. The daily rainfall data charts of each station were digitized and then the annual maximum rainfall series were determined for durations ranging from 5 to 1440 min. Based on these, with the Gumbel-Chow distribution, the maximum rainfall was estimated for durations ranging from 5 min to 24 h, considering return periods of 2, 5, 10, 20, 25, 50, and 100 years,. Data agreement with the Gumbel-Chow model was verified by the Kolmogorov-Smirnov test, at 5 % significance level. For each rain gauge station, two IDF equations of rainfall events were adjusted, one for durations from 5 to 120 min and the other from 120 to 1440 min. The results show a high variability in maximum intensity of rainfall events among the studied stations. Highest values of coefficients of variation in the annual maximum series of rainfall were observed for durations of over 600 min at the stations of the coastal region of Santa Catarina.

scholarly journals Evaluation of Rainfall Temporal Distribution Models with Annual Maximum Rainfall Events in Seoul, Korea

Water ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 1468 ◽  
Author(s):  
Wooyoung Na ◽  
Chulsang Yoo
Keyword(s):  
Root Mean Square Error ◽  
Peak Flow ◽  
Temporal Distribution ◽  
Mean Square ◽  
Annual Maximum ◽  
Block Method ◽  
Maximum Rainfall ◽  
Rainfall Events ◽  
Pattern Correlation ◽  
Annual Maximum Rainfall

This study evaluated five models of rainfall temporal distribution (i.e., the Yen and Chow model, Mononobe model, alternating block method, Huff model, and Keifer and Chu model), with the annual maximum rainfall events selected from Seoul, Korea, from 1961 to 2016. Three different evaluation measures were considered: the absolute difference between the rainfall peaks of the model and the observed, the root mean square error, and the pattern correlation coefficient. Also, sensitivity analysis was conducted to determine whether the model, or the randomness of the rainfall temporal distribution, had the dominant effect on the runoff peak flow. As a result, the Keifer and Chu model was found to produce the most similar rainfall peak to the observed, the root mean square error was smaller for the Yen and Chow model and the alternating block method, and the pattern correlation was larger for the alternating block method. Overall, the best model to approximate the annual maximum rainfall events observed in Seoul, Korea, was found to be the alternating block method. Finally, the sensitivity of the runoff peak flow to the model of rainfall temporal distribution was found to be much higher than that to the randomness of the rainfall temporal distribution. In particular, in small basins with a high curve number (CN) value, the sensitivity of the runoff peak flow to the randomness of the rainfall temporal distribution was found to be insignificant.

scholarly journals Mapping an index of extreme rainfall across the UK

1998 ◽  
Vol 2 (2/3) ◽  
pp. 183-194 ◽  
Author(s):  
D. S Faulkner ◽  
C. Prudhomme
Keyword(s):  
Regression Models ◽  
Digital Terrain Model ◽  
Extreme Rainfall ◽  
Maximum Rainfall ◽  
Mountainous Regions ◽  
Terrain Model ◽  
Rainfall Frequency ◽  
Flood Estimation ◽  
Annual Maximum Rainfall ◽  
The Uk

Abstract. Distance from the sea, proximity of mountains, continentality and elevation are all useful covariates to assist the mapping of extreme rainfalls. Regression models linking these and other variables calculated from a digital terrain model have been built for estimating the median annual maximum rainfall, RMED. This statistic, for rainfall durations between 1 hour and 8 days, is the index variable in the rainfall frequency analysis for the new UK Flood Estimation Handbook. The interpolation of RMED between raingauge sites is most challenging in mountainous regions, which combine the greatest variation in rainfall with the sparsest network of gauges. Sophisticated variables have been developed to account for the influence of topography on extreme rainfall, the geographical orientation of the variables reflecting the prevailing direction of rain-bearing weather systems. The different processes of short and long-duration extreme rainfall are accounted for by separate regression models. The technique of georegression combines estimates from regression models with a map of correction factors interpolated between raingauge locations using the geostatistical method of kriging, to produce final maps of RMED across the UK.

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