Upp í vindinn - 01.05.1999, Síða 28

... UPP I VINDINN
The derivation of IDF curves for
precipitation from M5 values
Abstract
The generalised distribution adapted for
precipitation is in principle established for
24 hour values only. Nevertheless, the
same distribution applies for the observa-
tions of shorter duration precipitation
available in Iceland. By applying the prin-
ciple of identical statistical distribution
for standardized annual maxima of any
duration, IDF (Intensity - Duration -
Frequency) curves have been derived. An
associated program calculates the IDF-values on basis of M5 and
Cj, which are the two parameters that define the generalized pre-
cipitation distribution.
1 Introduction
A generalized formula for IDF-curves is suggested in Eliasson
1997.
1 = RCW f(T) g(tr) (1)
Here we have:
I rain intensity [m t'1]
period. Similarly we have for a fixed
return period
l(tr+ 1) < I(tr), T fixed (3)
To use this distribution it is necessary to
have a map that shows the value of the
index variable R(T0,tr0) at each locality.
2 The index variable
It has been suggested to use the 5 year
24h precipitation as index variable (Eliasson 1997). This makes
T0 = 5 and tro = 24 h = 1440 min. To use this particular index
variable was originally suggested in the Flood Studies Report
(NERC 1975) and later adapted by Norway (Förland et al.
1989).
Today a map with estimated five year 24h precipitation values,
called M5, exist for all Iceland in a large scale, suitable for esti-
mation of IDF curves for areas larger than 25 km2 (10 mi2). For
smaller areas there exist 3 maps for the south and the southwest
lowlands. They cover an area where over 75% of the Icelandic
population lives. These maps are prepared by the Engineering
Institute of the University of Iceland in cooperation with the
Icelandic Meteorological Bureau.
Jónas Elíasson lauk
fyrrihlutaprófi í
verkfræði frá H.í.
1959, prófi í
byggingarverkfræöi
frá DTH 1962,
lic.techn. 1973. Er nú
prófessor viö
umhverfis- og byggingarverkfræðiskor H.í.
T return period in years [t]
t duration [t[
f and g are functions [-]
tro fixed duration, g(tr) = 0 [t]
T0 fixed return period f(T ) = 0 [t]
R is an index parameter it varies with the locality, but not with
T or tr, in each locality R is fixed, once T0 and tr0 are chosen
Karl Imhoff (Novotny et al. 1989) originally proposed this
form of a generalized formula. Using this form of generalized
IDF relationship has the advantage that the variation with dura-
tion (T) and return period (tr) is the same everywhere and the
spatial variation is taken care of by a single index variable. This
is of course an approximation, but it can never be a very bad one
because (1) defines a set of lines in the T - t and the lines can
never intersect, not even in the outer limits where T goes to
infinity and tr to zero. This may be seen by comparing two lines,
one for a fixed value T and another for the fixed value T + 1. We
must always have
3 Distribution of 24h precipitation f(T)
It has been shown that the General Extreme Value no 1 (GEV
1) cunrulative distribution function (Gumbels CDF) fits rainfall
data very well. The best way to do this is to use the station - year
method. It has been shown that precipitation maxima of 24h
duration fit GEVl very well in unrelated areas such as
Washington State, Iceland (Eliason 1997) and goes for Denmark
to. It is necessary to use the station - year method to get enough
number of points. Estimating individual stations will presum-
ably result in a skewness that is somewhat different from 1.14
which is the skewness factor of the Gumbel distribution in the
GEV family of CDF’s. But accepting Gumbel instead of the more
general GEV has the advantage of using a two parameter CDF
instead of a three parameter CDE When using a two parameter
CDF we can work with standardized 24h annual maxima, stan-
dardized by subtracting the mean and dividing with standard
deviation. Then we use the station year method on the stan-
dardized annual maxima. In this manner annual precipitation
maxima for entire meteorological regions can be assembled on
one line (Eliasson 1997).
Written in terms of the M5 the distribution becomes.
x = MT = M5( 1 + Cj (y-1.5)) y < yUm (4)
I(T) < I(T + 1), tr fixed
(2) x Stochastic variable
In words, intensity for any duration must increase with return y = -logn(-logn(1 - 1/T))
28