Eficiencia o rendimiento del transformador η

Rossi et al. (1984) and Katz et al. (2002) apply extreme value modelling to the river flooding applications with long spans of overlapping time series (Table 2.4). Similarly, Cooley et al. (2007), Keef et al. (2009a), Keef et al. (2009b), Grigg and Tawn (2012), and Wyncoll and Gouldby (2013) investigate the extreme value theory models for flood frequency analysis and associated flood intensity (Table 2.4). However, they have done multivariate extreme models for local scale river and fluvial flooding, but not for regional scale (i.e. the UK’s East Coast).

Table 2.4. Summary of extreme value analysis models.

Authors Summary

Rossi et al. (1984)

A regionalized two-component extreme value analysis for 39 stream-gauging stations in central and southern Italy for which the longest annual instantaneous flood series were available (34-49 years with an average of 40 years)

Tawn (1990)

Extreme value modelling to 40 years of trivariate sea level annual maxima at 3 sites on the south- east coast of England.

Bruun and Tawn

(1998)

Univariate and multivariate extreme value method for estimating the probability of coastal flooding at several sites along a Dutch Coastline.

Dixon et al. (1998)

Spatial modelling extreme sea level of UK east coast, providing a set of design level estimates along the entire coastline.

Bortot et al. (2000)

Multivariate Gaussian tail model at Newlyn (UK) by modelling a trivariate dataset of oceanographic variables (sea surge, wave period and wave height).

Katz et al. (2002)

Univariate analysis: Precipitation (US); annual total economic damage due to floods (US) for the time period 1932–1997; sea level (Fremantle, Western Australia) for the time period 1897–1989 where only 86 years of data available (i.e., values for 1902, 1907, 1910–1911, 1924, and 1942 are missing).

Multivariate analysis: maximum of daily precipitation amount for the month of January (Chico, US), for the time period 1907–1988, with 4 years being eliminated because of missing values; Slat River peak flow (USA) for the time period 1924-1999 (1986 missing).

Svensson and Jones

(2002)

Trivariate dependence model (extreme sea surge, river flow and precipitation) for the period 1965–97: hourly sea surge and total sea level data for 8 stations on the east coast of Britain (Lowestoft and Immingham have the most complete data set with only 2.3% and 3.2% missing data respectively, but about 20% of the data are missing at North Shields, Sheerness and Aberdeen), daily mean river flows for 40 stations in catchments draining to the North Sea (36 of the stations have fewer than 88 days missing, 0.7% of the record), and daily precipitation accumulations (without missing values) at 20 stations in eastern Britain.

Svensson and Jones

(2004)

Trivariate dependence model (extreme sea surge, river flow and precipitation) for the period 1963-2001: hourly sea surge and total sea level data for 19 stations on the British south and west, daily mean river flows for 72 stations and daily precipitation accumulation for 27 stations in catchments draining to the south and west coast of Great Britain.

Bernier and Thompson

(2006)

Extreme model in the northwest Atlantic (36 tide gauges located along the east coast of Canada and the northeaster United States): total sea levels reconstructed using the hindcast surges, and tides and higher-frequency variability predicted from short, observed sea level records.

Butler et al. (2007a)

Storm surge model for the North Sea for the period 1955-2000. Butler et

al. (2007b)

Storm surge event model in the southern and central North Sea over the period 1955–2000, using surge levels at sites for which sufficiently long observational records are available.

Cooley et al. (2007)

Bayesian analysis for spatial extremes for daily precipitation (Fort Collins, US) above a high threshold at 56 weather stations.

Pirazzoli and Tomasin

(2007)

Extreme sea level model (Joint Probability Model) for the French Atlantic coast and 3 ports in the southwest of the UK. The length of the records varies from almost 130 equivalent full years at Brest and more than 84 years at Newlyn to less than 20 years at 9 stations, less than 13 years at 6 stations and even only 1.3 years at Le Crouesty.

Authors Summary Keef et al.

(2009a)

Spatial dependence of extreme daily mean river flows of 271 stations and precipitation of 256 rain-gauges across Great Britain. For the rain-gauges almost all of the selected sites have on average 40 years of data, since 1961, so have long records with limited missing data and long spans of overlapping series from gauge to gauge.

Keef et al. (2009b)

Extension of the Heffernan and Tawn (2004) method which accounts for missing values by assessing spatial dependence over four fluvial sites in Scotland.

Haigh et al. (2010)

Extreme value model of sea level records (derived from data archaeology) at 18 sites around the English Channel (at least 50 years of records).

Lamb et al. (2010)

Joint probability of extreme river flows and seal levels at multiple locations. There are two studies: 2 locations (Leeds and York, UK) and regional (145 gauges in and around the northeast of England).

Martucci et al. (2010)

Statistical trend analysis and extreme distribution of wave height (1958-1999) for 27 representative geographical sites around the Italian coasts.

Olbert and Harnett

(2010)

Numerical surge model: meteorological forcing and hydrographic records for the Irish and west British coastline.

Keef et al. (2011)

Environment Agency’s report to analysis the risk of widespread flooding from rivers and coasts. The gauges were selected according to the length and quality of record, and spatial coverage. The river flow gauging stations considered the number of gauges chosen in each catchment and the population density of the area in which each gauge was located.

Galiatsatou et al. (2012)

Extreme marine events model in Varna in the Western Black Sea: annual and monthly maxima of wave height, storm surges and wave period. The length of the records varies from a period of 61 years (1948-2008) for wave heights and wave periods, while storm surge data cover a period of 80 years (1928-2007).

Grigg and Tawn (2012)

Extreme river flow model from five UK rivers stations with distinct catchment characteristics, accounting for appropriate hydrological covariates. The data from each site are for the same period (January 1984–December 2001) and between 0% and 15% of the days have some hourly flow data missing.

Oliver et al. (2012)

Extreme current speeds model of non-tidal currents and tidal currents (1988-2004) of the northwest Atlantic Ocean.

Batstone et al. (2013)

Skew Surge Joint Probability Method along the UK coastline. The lengths of records from the 45 gauges available range from 92 years at Newlyn to 8 years at Moray Firth, with a median length of 19 years.

Eastoe et al. (2013)

Extreme sea surface elevation model for the Atlantic coastline: time series of measured 3h maximum sea surface elevations from the 8m array at the Field Research Facility (Duck, North Carolina, US), for the period from January to December 2005 at 15 pressure gauges.

Wyncoll and Gouldby

(2013)

Extreme value models for fluvial. The case study analysis the 27 years of time series rainfall of 248 representative nodes spanning the river network for the Eden catchment in the north-west of England.

Li et al. (2014)

Univariate and multivariate extreme storm model along the Dutch coast using Gaussian copula model for the Dutch wave climate data (1979-2009).

Zheng et al. (2014)

Bivariate extreme model for the Hawkesbury-Nepean catchment near Sydney (Australia): rainfall (21 daily rainfall gauges) and storm tides (at the catchment outlet) for a period of approximately 92 years.

The extremes of storm surges, sea levels and tides are studied (Table 2.4) in the coastline of the UK (e.g. Tawn, 1990; Dixon et al., 1998; Bortot et al., 2000; Svensson and Jones, 2002; Svensson and Jones, 2004; Butler et al., 2007a; Butler et al., 2007b; Haigh et al., 2010; Batstone et al., 2013), and in other sites, Dutch coastline (e.g. Bruun and Tawn, 1998; Li et al., 2014), Irish coastline (e.g. Olbert and Harnett, 2010), French coastline (e.g. Pirazzoli and Tomasin, 2007), Italian coastline (Martucci et al., 2010), Atlantic coastline (e.g. Bernier and Thompson, 2006; Oliver et al., 2012; Eastoe et al. 2013), Australian coastline (e.g. Zheng et al., 2014) and Asian coastline (e.g. Galiatsatou et al., 2012).

Until recently, the problem of estimating the probability of extreme sea levels along a coastline has received little attention. Most of the existing analyses are univariate approaches that are applied independently to data from individual sites (e.g. Bruun and Tawn, 1998; Katz et al., 2002; Li et al., 2014). Dixon et al. (1998) present a spatial extension of the methods, an approach for obtaining extreme sea level probabilities along the whole UK East Coast. However, a multivariate extreme value model on this large scale is intractable.

An advance on this work was to analyse multiple sites, including temporal aspects (Keef et al., 2009a). These descriptions are the first step in assessing widespread river flood risk, but do not enable estimates of the occurrence probability of events, such as the UK events of summer 2007. Keef et al (2009a) adopt a model-based approach using the methods of Heffernan and Tawn (2004) for modelling dependences in multivariate extreme analysis extending the method to handle missing data and temporal dependences.

Working with river flow data from 197 sites, Keef et al. (2011) present extensions to the statistical model used by Keef et al. (2009a) over multiple locations to simulate synthetic events. This approach (Keef et al., 2011) provides new information about the probability of river flooding at a broad spatial scale, regional or national spatial scale. It is possible to estimate the probability of an entire event, rather than simply stating probabilities at individual sites.

Keef et al (2011) examine two previous studies that revise daily data from the UK to assess the risk of widespread river floods: Svensson and Jones (2002, 2004) and Keef et al. (2009b). The work of Svensson and Jones (2002, 2004) is an investigation of the pairwise dependence between extreme sea surge, river flow and precipitation around the coast of Britain. One of the main outcomes of these studies was a set of maps describing pairs of variables that have a non-zero probability of their very largest observations occurring in the same event. All possible same-variable pairs were examined. The work of Keef et al. (2009b) uses a summary measure to estimate the level of dependence between a single gauging station and surrounding gauging stations within defined distances.