The FORGEX method of rainfall growth estimation III: Examples and confidence intervals

Abstract

Abstract. This paper illustrates the performance of the FORGEX method of rainfall growth estimation. Results are presented for three regions of the United Kingdom: the East Midlands, north-west England and south-west England. Focused rainfall growth curves are compared between regions and between different sites within each region. Typical growth curve shapes are discussed with reference to the climate of each region. Daily growth curves are derived from a large number of records of annual maximum rainfalls. A smaller number of hourly annual maximum series is available for estimation sub-daily rainfall growth curves. Rainfall growth rates are compared with the results of a widely used method. The present method allows more local and regional variation in growth rates. The new growth rates are higher for durations of 1 and 2 days in parts of south-west England, but lower for moderate return periods at some focal points in the north-west. In the East Midlands, the new 1-hour growth rates are considerably higher for long return periods. Confidence limits for growth rates are derived by bootstrapping. This is accomplished by fitting a large number of growth curves to resampled sets of rainfall data.

Use of a Gaussian copula for multivariate extreme value analysis: Some case studies in hydrology

“…The multivariate MFSH return period T M was finally calculated as follows: (1) (1) ( ) ( ) have been introduced in equation (16). However, it should be noticed that there is no simple relationship similar to the equation 1 cc = − which holds in the univariate case.…”

Canadian RCM Projected Changes to Extreme Precipitation Characteristics over Canada

“…Therefore, an estimate of uncertainty in the regional growth curves for the reference (R1-R5) and future (F1-F5) simulations is carried out. For each studied region, B 5 1000 resamples for each of the ensemble members are used to develop confidence intervals using two different approaches: 1) the standard error-based approach (Cunnane 1989;Hall et al 2004) and (2) the test-inversion approach (Carpenter 1999;Faulkner and Jones 1999;Burn 2003). Let y T be the T-yr regional growth factor for either of the R1-R5/F1-F5 simulations, and y i T the corresponding T-yr regional growth factor for the ith resample.…”

The use of resampling for estimating confidence intervals for single site and pooled frequency analysis / Utilisation d'un rééchantillonnage pour l'estimation des intervalles de confiance lors d'analyses fréquentielles mono et multi-site

“…The elements of the concatenated sample are randomly permutated and the permutated sample is then divided into B samples of length n. A total of B estimates for the quantile of interest are then obtained and are used to estimate the desired confidence intervals. The procedure to find the 100(1 -2α)% confidence intervals, following Faulkner & Jones (1999), is: 1. Generate B resampled data sets using balanced resampling, as described above.…”

“…The confidence interval defined in step 5 uses what is known as a test-inversion approach (for details, see Faulkner & Jones, 1999;Carpenter, 1999).…”

“…Once the pooled data set has been assembled, quantiles can be estimated in accordance with the pooling method employed and confidence intervals calculated following the approach outlined above for single site analysis. Faulkner & Jones (1999) presented a similar approach for rainfall frequency analysis.…”