Comparison of estimators of the Gumbel distribution for modelling annual maximum rainfall

2013 ◽  
Vol 8 (3) ◽  
pp. 166-172
Author(s):  
N. Vivekanandan
Keyword(s):  
Gumbel Distribution ◽  
Annual Maximum ◽  
Maximum Rainfall ◽  
Annual Maximum Rainfall

Best-fit probability distribution model for predicting annual maximum rainfall of Pusa (Bihar)

2018 ◽  
Vol 3 (01) ◽  
pp. 100-104
Author(s):  
J. Kumar ◽  
R. Suresh ◽  
Jyoti .
Keyword(s):  
Probability Distribution ◽  
Gumbel Distribution ◽  
Annual Rainfall ◽  
Annual Maximum ◽  
Distribution Models ◽  
Maximum Rainfall ◽  
Type Iii ◽  
Pearson Type ◽  
Annual Maximum Rainfall ◽  
Pearson Type Iii Distribution

In present study an attempt has been made to evaluate the suitable probability distribution models for predicting 1, 2, 3, 4, 5, 6 and 7-days annual maximum rainfall amounts based on 39 years (1964 to 2002) daily rainfall data. Three probability distribution models namely: Log Normal distribution, Log Pearson Type-III distribution and Gumbel distribution models were considered to evaluate their goodness of fit. The Weibull’s method was used for computation of observed rainfall values at1, 5, 20, 30, 50, 95 and 99 percent probability levels. The Log Pearson type –III distribution was found suitable for 1 and 2 days maximum annual rainfall, while Gumbel distribution was found to be the best for predicting 3, 4, 5, 6 and 7- days annual maximum rainfall amounts. The relationships between annual maximum rainfall and return periods were also developed. The non – linear relationships (i.e. logarithmic) were found to be most suitable for all the cases.

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 Potential of plotting positions for intensity-duration-frequency curves with short rainfall records

2017 ◽  
Vol 13 (4-1) ◽  
pp. 394-399
Author(s):  
Noratiqah Mohd Ariff ◽  
Abdul Aziz Jemain ◽  
Mohd Aftar Abu Bakar
Keyword(s):  
Probability Distribution ◽  
Empirical Distribution ◽  
Annual Rainfall ◽  
Annual Maximum ◽  
Distribution Fitting ◽  
Maximum Rainfall ◽  
Gev Distribution ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
Annual Maximum Rainfall

Intensity-duration-frequency (IDF) curves represent the relationship between storm intensity, storm duration and return period. The IDF curves available are mostly done by fitting series of annual maximum rainfall intensity to parametric distributions. However, the length of annual rainfall records, especially for small scaled data, are not always enough. Rainfall records of less than 50 years are usually deemed insufficient to unequivocally identify the probability distribution of the annual rainfall. Thus, this study introduces an alternative approach that replaces the need for parametric fitting by using empirical distribution based on plotting positions to represent annual maximum rainfall series. Subsequently, these plotting positions are used to build IDF curves. The IDF curves found are then compared to the IDF curves yielded from the parametric GEV distribution which is a common basis for IDF curves. This study indicates that IDF curves obtained using plotting positions are similar to IDF curves found using GEV distribution for storm events. Hence, researchers could model and subsequently build IDF curves for annual rainfall records of less than 50 years by using plotting positions and avoid any probability distribution fitting of insufficient data.

scholarly journals Rainfall statistics changes in Sicily

2013 ◽  
Vol 10 (2) ◽  
pp. 2323-2352 ◽  
Author(s):  
E. Arnone ◽  
D. Pumo ◽  
F. Viola ◽  
L. V. Noto ◽  
G. La Loggia
Keyword(s):  
Extreme Events ◽  
Daily Rainfall ◽  
Negative Trend ◽  
Rainfall Series ◽  
Annual Maximum ◽  
Maximum Rainfall ◽  
Rainfall Events ◽  
Rainfall Characteristics ◽  
Annual Maximum Rainfall ◽  
Rainfall Statistics

Abstract. Changes in rainfall characteristics are one of the most relevant signs of current climate alterations. Many studies have demonstrated an increase in rainfall intensity and a reduction of frequency in several areas of the world, including Mediterranean areas. Rainfall characteristics may be crucial for vegetation patterns formation and evolution in Mediterranean ecosystems, with important implications, for example, in vegetation water stress or coexistence and competition dynamics. At the same time, characteristics of extreme rainfall events are fundamental for the estimation of flood peaks and quantiles which can be used in many hydrological applications, such as design of the most common hydraulic structures, or planning and management of flood prone areas. In the past, Sicily has been screened for several signals of possible climate change. Annual, seasonal and monthly rainfall data in the entire Sicilian region have been analyzed, showing a global reduction of total annual rainfall. Moreover, annual maximum rainfall series for different durations have been rarely analyzed in order to detect the presence of trends. Results indicated that for short durations, historical series generally exhibit increasing trends while for longer durations the trends are mainly negative. Starting from these premises, the aim of this study is to investigate and quantify changes in rainfall statistics in Sicily, during the second half of the last century. Time series of about 60 stations over the region have been processed and screened by using the non parametric Mann–Kendall test. Particularly, extreme events have been analyzed using annual maximum rainfall series at 1, 3, 6, 12 and 24 h duration while daily rainfall properties have been analyzed in term of frequency and intensity, also characterizing seasonal rainfall features. Results of extreme events analysis confirmed an increasing trend for rainfall of short durations, especially for one hour rainfall duration. Instead, precipitation of long durations have exhibited a decreased trend. With regard to the spatial distribution, increase in short duration precipitation has been observed especially in stations located along the coastline; however, no clear and well-defined spatial pattern have been outlined by the results. Outcomes of analysis for daily rainfall properties have showed that heavy-torrential precipitation tends to be more frequent at regional scale, while light rainfall events exhibited a negative trend at some sites. Values of total annual precipitations confirmed a significant negative trend, mainly due to the reduction during the winter season.

scholarly journals Characteristics of the Underestimation Error of Annual Maximum Rainfall Depth Due to Coarse Temporal Aggregation

Atmosphere ◽  
2018 ◽  
Vol 9 (8) ◽  
pp. 303 ◽  
Author(s):  
Renato Morbidelli ◽  
Carla Saltalippi ◽  
Alessia Flammini ◽  
Tommaso Picciafuoco ◽  
Jacopo Dari ◽  
...  
Keyword(s):  
Central Italy ◽  
Statistical Characteristics ◽  
Temporal Aggregation ◽  
Annual Maximum ◽  
Maximum Rainfall ◽  
Normal Distributions ◽  
Average Value ◽  
Mathematical Relation ◽  
Rainfall Depth ◽  
Annual Maximum Rainfall

This study analyzed all characteristics of the error committed in evaluating annual maximum rainfall depth, Hd, associated with a given duration, d, when data with coarse temporal aggregation, ta, were used. It is well known that when ta = 1 min, this error is practically negligible while coarser temporal aggregations can determine underestimation for a single Hd up to 50% and for the average value of sufficiently numerous series of Hd up to 16.67%. By using a mathematical relation between average underestimation error and the ratio ta/d, each Hd value belonging to a specific series could be corrected through deterministic or stochastic approaches. With a deterministic approach, an average correction was identically applied to all Hd values with the same ta and d while, for a stochastic correction, a thorough knowledge of the statistical characteristics of the underestimation error was required. Accordingly, in this work, rainfall data derived from many stations in central Italy were analyzed and it was assessed that single and average errors, which were both assumed as random variables, followed exponential and normal distributions, respectively. Furthermore, the single underestimation error was also found inversely correlated to the corresponding annual maximum rainfall depth.

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