Adjustment of extreme rainfall statistics accounting for multidecadal climate oscillations
Introduction
Several authors reported on the existence of dependence in the occurrence of rainfall extremes in time (e.g. Aryal et al., 2009, De Jongh et al., 2006, Gershunov and Cayan, 2003, Grimm and Tedeschi, 2009, Kamruzzaman et al., 2011, May and Hitch, 1989, Ntegeka and Willems, 2008). This phenomenon of temporal clustering is most likely linked to the large-scale, low-frequency oscillations in atmospheric circulation. Decadal and multi-decadal climate oscillations have indeed been observed in many regions of the world. The most well-known for the Atlantic region is the North Atlantic oscillation (NAO, e.g. Hurrell, 1995). It is defined by an index, the NAO index, which represents a normalized sea level pressure difference between a station on the Azores and one on Iceland. Other indices that exist for the Atlantic region, and which all reflect some type of long-term oscillations, is the AMO (Atlantic Multidecadal Oscillation) index (Enfield et al., 2001, Kerr, 2000, Knight, 2005), the Arctic Oscillation (AO) index (Noren et al., 2002) and the Antarctic Oscillation index (AOI) (Gong and Wang, 1999). For the Pacific, well-known indices are the El Niño southern oscillation (ENSO, e.g. Philander, 1990) index, the Pacific Decadal Oscillation (PDO) index (Mantua et al., 1997), the Southern Oscillation Index (SOI) (Trenberth, 1984), the Indian Ocean Dipole (IOD) index (Saji et al., 1999) and the Southern Annular Mode (SAM) (Thompson and Solomon, 2002).
Although the scientific proof turns out to be difficult – probably because of the high natural variability of precipitation – some authors (see next) have shown that the temporal oscillations in the occurrence of high rainfall intensities is somehow linked to the above-mentioned atmospheric and oceanographic oscillations. The link between rainfall extremes and the Pacific-related indices such as the ENSO, SOI and PDO turns out to be most clear. See the research by Gershunov and Cayan (2003) for the link between the frequency of heavy daily rainfall and the ENSO in the North Pacific; Schreck and Semazzi (2004) for eastern Africa; Grimm and Tedeschi (2009) and Haylock et al. (2006) for South America; Cayan et al. (1999) and Gershunov (1998) for the contiguous and western USA; Aryal et al. (2009) and Kamruzzaman et al. (2011) for Australia.
These oscillations in climate and related rainfall extremes over decadal to multidecadal time scales may have several complications in hydrology, which are often overlooked. One of the complications is their effect on rainfall design statistics. This paper deals with the rainfall statistics typically used in urban drainage design. Urban drainage systems are typically designed using design storms or rainfall statistics derived from rainfall intensity–duration–frequency (IDF) relationships. These can be seen as a “design rainfall atlas”, which provides information on rainfall depths accumulated or averaged over various time durations and for different return periods (or average recurrence intervals) (WMO, 2009a, WMO, 2009b). They thus combine information on both the frequency and intensity of the rainfall events.
This paper shows how extreme rainfall statistics may be biased when based on time series of limited duration. When the time series duration is less than one oscillation cycle it may coincide with an oscillation high period or an oscillations low period. Hence, rainfall statistics derived from such periods may be biased from the longer-term statistics. This is demonstrated in the paper based on a time series of 107 years of 10 min rainfall intensities at Uccle, Brussels. This series is worldwide unique because of its length and high temporal resolution, but also because the same instrument recorded the series during the entire period and the series was thoroughly quality checked (Demarée, 2003). The series thus is not affected by measurement inhomogeneities due to instrumental differences.
Section snippets
Analysis of multidecadal oscillations
Independent extremes were extracted from the full Uccle rainfall series based on an independence criterion. This was done for different temporal scales in the range between 10 min and 15 days. For each temporal scale, a moving average operation with time step of 10 min was applied to the full original 10 min series, and the rainfall extremes extracted from the moving average series. In the cases of temporal scales less than 12 h, two successive extremes were defined to be independent if they are
Rainfall statistical analysis
IDF relationships were obtained for the Uccle rainfall data before by Willems (2000). He used the Uccle 10 min rainfall series for the period 1967–1993. A two-component exponential distribution was calibrated to the rainfall extremes above a selected threshold. The optimal threshold was defined as the threshold above which the mean squared error of the estimated distribution is minimal. The distribution parameters were calibrated based on all empirical quantiles above that threshold based on
Conclusions and discussion
This paper has shown based on a unique time series of 10 min rainfall observations since 1898 at Brussels, Belgium, that rainfall extremes are temporarily clustered due to the presence of multidecadal climate oscillations. Although it was not the intention of this paper to explain these oscillations, it is expected that they are linked to the multidecadal oscillations in large-scale atmospheric and oceanographic indices reported before by several authors (see introduction).
It is shown that the
Acknowledgements
The 10 min Uccle rainfall series was made available by the Royal Meteorological Institute of Belgium. The author also acknowledges the data providers in the ECA&D project.
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