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Rainfall extremes: Toward reconciliation after the battle of distributions.

Serinaldi F, Kilsby CG - Water Resour Res (2014)

Bottom Line: A twofold effect is recognized.First, as the threshold decreases, and nonextreme values are progressively incorporated in the POT samples, the variance of the GP shape parameter reduces and the mean converges to positive values denoting a tendency to heavy tail behavior.Res., 50, 336-352, doi:10.1002/2013WR014211.

View Article: PubMed Central - PubMed

Affiliation: School of Civil Engineering and Geosciences, Newcastle University Newcastle Upon Tyne, UK ; Willis Research Network London, UK.

ABSTRACT
[1] This study attempts to reconcile the conflicting results reported in the literature concerning the behavior of peak-over-threshold (POT) daily rainfall extremes and their distribution. By using two worldwide data sets, the impact of threshold selection and record length on the upper tail behavior of POT observations is investigated. The rainfall process is studied within the framework of generalized Pareto (GP) exceedances according to the classical extreme value theory (EVT), with particular attention paid to the study of the GP shape parameter, which controls the heaviness of the upper tail of the GP distribution. A twofold effect is recognized. First, as the threshold decreases, and nonextreme values are progressively incorporated in the POT samples, the variance of the GP shape parameter reduces and the mean converges to positive values denoting a tendency to heavy tail behavior. Simultaneously, the EVT asymptotic hypotheses are less and less realistic, and the GP asymptote tends to be replaced by the Weibull penultimate asymptote whose upper tail is exponential but apparently heavy. Second, for a fixed high threshold, the variance of the GP shape parameter reduces as the record length (number of years) increases, and the mean values tend to be positive, thus denoting again the prevalence of heavy tail behavior. In both cases, i.e., threshold selection and record length effect, the heaviness of the tail may be ascribed to mechanisms such as the blend of extreme and nonextreme values, and fluctuations of the parent distributions. It is shown how these results provide a link between previous studies and pave the way for more comprehensive analyses which merge empirical, theoretical, and operational points of view. This study also provides several ancillary results, such as a set of formulae to correct the bias of the GP shape parameter estimates due to short record lengths accounting for uncertainty, thus avoiding systematic underestimation of extremes which results from the analysis of short time series. Citation: Serinaldi, F., and C. G. Kilsby (2014), Rainfall extremes: Toward reconciliation after the battle of distributions, Water Resour. Res., 50, 336-352, doi:10.1002/2013WR014211.

No MeSH data available.


Related in: MedlinePlus

Location of GHCN rainfall records used in the analyses.
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fig01: Location of GHCN rainfall records used in the analyses.

Mentions: [11] The data set used in the analyses is a subset of the Global Historical Climatology Network (GHCN) data set available at the web site (www.ncdc.noaa.gov/oa/climate/ghcn-daily). GHCN-Daily data set contains daily data from over 80,000 surface stations worldwide, about two thirds of which are for precipitation only [Menne et al., 2012]. The data set was retrieved and handled by the R contributed package GhcnDaily [Mosher, 2012]. Since the POT analysis requires possibly complete time series, only a limited subset of the available time series was retained. In more detail, two subsets of data are selected: (1) rainfall series spanning from 1970 to 2011 with less than 5% of missing values and (2) rainfall series spanning from 1900 to 2011 with less than 5% of missing values (Figure 1). The additional selection criteria based on the quality flags used by Papalexiou et al. [2013] were also applied along with a check of the random distribution of missing values and a visual check of each time series and its empirical distribution function to detect possible macroscopic inconsistencies related to measurement errors. Our selection differs from that of Papalexiou et al. [2013] as we decided to use only time series covering the same periods (i.e., 1970–2011 and 1900–2011) so that the series reflect the worldwide climate conditions over homogeneous time windows. Obviously, this criterion is more restrictive than the 50 year minimum length used by Papalexiou et al. [2013] and resulted in a smaller number of time series, namely, 1898 for the shortest series and 113 for the longest ones.


Rainfall extremes: Toward reconciliation after the battle of distributions.

Serinaldi F, Kilsby CG - Water Resour Res (2014)

Location of GHCN rainfall records used in the analyses.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4016761&req=5

fig01: Location of GHCN rainfall records used in the analyses.
Mentions: [11] The data set used in the analyses is a subset of the Global Historical Climatology Network (GHCN) data set available at the web site (www.ncdc.noaa.gov/oa/climate/ghcn-daily). GHCN-Daily data set contains daily data from over 80,000 surface stations worldwide, about two thirds of which are for precipitation only [Menne et al., 2012]. The data set was retrieved and handled by the R contributed package GhcnDaily [Mosher, 2012]. Since the POT analysis requires possibly complete time series, only a limited subset of the available time series was retained. In more detail, two subsets of data are selected: (1) rainfall series spanning from 1970 to 2011 with less than 5% of missing values and (2) rainfall series spanning from 1900 to 2011 with less than 5% of missing values (Figure 1). The additional selection criteria based on the quality flags used by Papalexiou et al. [2013] were also applied along with a check of the random distribution of missing values and a visual check of each time series and its empirical distribution function to detect possible macroscopic inconsistencies related to measurement errors. Our selection differs from that of Papalexiou et al. [2013] as we decided to use only time series covering the same periods (i.e., 1970–2011 and 1900–2011) so that the series reflect the worldwide climate conditions over homogeneous time windows. Obviously, this criterion is more restrictive than the 50 year minimum length used by Papalexiou et al. [2013] and resulted in a smaller number of time series, namely, 1898 for the shortest series and 113 for the longest ones.

Bottom Line: A twofold effect is recognized.First, as the threshold decreases, and nonextreme values are progressively incorporated in the POT samples, the variance of the GP shape parameter reduces and the mean converges to positive values denoting a tendency to heavy tail behavior.Res., 50, 336-352, doi:10.1002/2013WR014211.

View Article: PubMed Central - PubMed

Affiliation: School of Civil Engineering and Geosciences, Newcastle University Newcastle Upon Tyne, UK ; Willis Research Network London, UK.

ABSTRACT
[1] This study attempts to reconcile the conflicting results reported in the literature concerning the behavior of peak-over-threshold (POT) daily rainfall extremes and their distribution. By using two worldwide data sets, the impact of threshold selection and record length on the upper tail behavior of POT observations is investigated. The rainfall process is studied within the framework of generalized Pareto (GP) exceedances according to the classical extreme value theory (EVT), with particular attention paid to the study of the GP shape parameter, which controls the heaviness of the upper tail of the GP distribution. A twofold effect is recognized. First, as the threshold decreases, and nonextreme values are progressively incorporated in the POT samples, the variance of the GP shape parameter reduces and the mean converges to positive values denoting a tendency to heavy tail behavior. Simultaneously, the EVT asymptotic hypotheses are less and less realistic, and the GP asymptote tends to be replaced by the Weibull penultimate asymptote whose upper tail is exponential but apparently heavy. Second, for a fixed high threshold, the variance of the GP shape parameter reduces as the record length (number of years) increases, and the mean values tend to be positive, thus denoting again the prevalence of heavy tail behavior. In both cases, i.e., threshold selection and record length effect, the heaviness of the tail may be ascribed to mechanisms such as the blend of extreme and nonextreme values, and fluctuations of the parent distributions. It is shown how these results provide a link between previous studies and pave the way for more comprehensive analyses which merge empirical, theoretical, and operational points of view. This study also provides several ancillary results, such as a set of formulae to correct the bias of the GP shape parameter estimates due to short record lengths accounting for uncertainty, thus avoiding systematic underestimation of extremes which results from the analysis of short time series. Citation: Serinaldi, F., and C. G. Kilsby (2014), Rainfall extremes: Toward reconciliation after the battle of distributions, Water Resour. Res., 50, 336-352, doi:10.1002/2013WR014211.

No MeSH data available.


Related in: MedlinePlus