TY - JOUR
T1 - Transformation of point rainfall to areal rainfall
T2 - Intensity-duration-frequency curves
AU - Sivapalan, Murugesu
AU - Blöschl, Günter
N1 - Funding Information:
The authors would like to thank the Austrian Science Foundation (FWF), project no. M00298-TEC, for financial support. We thank Dr Mike Hutchinson of the Australian National University and two other anonymous reviewers, and Dr Roman Krzyszto-fowicz, Editor, for their constructive comments which helped to substantially improve the manuscript.
PY - 1998/1/30
Y1 - 1998/1/30
N2 - Current approaches to constructing catchment intensity-duration-frequency (IDF) curves are dominated by the use of empirically-derived areal reduction factors (ARFs). In this paper we present an alternative methodology which is based on the spatial correlation structure of rainfall. It represents an attempt to link current scientific theories of space-time rainfall fields with design methods. The starting point is to derive the parent distribution of catchment average rainfall intensity from that of point rainfall intensity. The parameters of the two parent distributions are related through a variance reduction factor which is a function of the spatial correlation structure of rainfall and catchment area. Assuming that the parent distribution is of the 'exponential type', it is then transformed to an extreme value distribution of the Gumbel type. The crucial step is to match the parameters of the extreme rainfall distribution derived above, for the particular case of zero catchment area, with those of empirical point IDF curves which have also been fitted to the Gumbel distribution. With this match, the proposed theory then naturally generalises to yield catchment IDF curves for catchments of any size, and for rainfall of any spatial correlation structure. The new catchment IDF curves have the attractive property that, with a minimum number of assumptions, they can reproduce a range of observed properties of catchment rainfall. For example, not only the mean and the standard deviation of extreme rainfall, but also its coefficient of variation, decrease with increasing catchment area. We also find that computed ARFs using the new approach depend not only on catchment area and storm duration, but also on the return period. We estimate ARFs using the new methodology for two major observed storms in Austria, and find that these estimates compare favourably with our understanding of the rainfall generating mechanisms associated with these two particular storm types.
AB - Current approaches to constructing catchment intensity-duration-frequency (IDF) curves are dominated by the use of empirically-derived areal reduction factors (ARFs). In this paper we present an alternative methodology which is based on the spatial correlation structure of rainfall. It represents an attempt to link current scientific theories of space-time rainfall fields with design methods. The starting point is to derive the parent distribution of catchment average rainfall intensity from that of point rainfall intensity. The parameters of the two parent distributions are related through a variance reduction factor which is a function of the spatial correlation structure of rainfall and catchment area. Assuming that the parent distribution is of the 'exponential type', it is then transformed to an extreme value distribution of the Gumbel type. The crucial step is to match the parameters of the extreme rainfall distribution derived above, for the particular case of zero catchment area, with those of empirical point IDF curves which have also been fitted to the Gumbel distribution. With this match, the proposed theory then naturally generalises to yield catchment IDF curves for catchments of any size, and for rainfall of any spatial correlation structure. The new catchment IDF curves have the attractive property that, with a minimum number of assumptions, they can reproduce a range of observed properties of catchment rainfall. For example, not only the mean and the standard deviation of extreme rainfall, but also its coefficient of variation, decrease with increasing catchment area. We also find that computed ARFs using the new approach depend not only on catchment area and storm duration, but also on the return period. We estimate ARFs using the new methodology for two major observed storms in Austria, and find that these estimates compare favourably with our understanding of the rainfall generating mechanisms associated with these two particular storm types.
KW - Areal reduction factors
KW - Catchments
KW - Extreme value distributions
KW - Flood estimation
KW - IDF curves
KW - Rainfall fields
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U2 - 10.1016/S0022-1694(97)00117-0
DO - 10.1016/S0022-1694(97)00117-0
M3 - Article
AN - SCOPUS:0032579427
SN - 0022-1694
VL - 204
SP - 150
EP - 167
JO - Journal of Hydrology
JF - Journal of Hydrology
IS - 1-4
ER -