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THE DERIVATION OF IDF CURVES FOR PRECIPITATION FROM M5 VALUES
M5 : The 5-year event (x for probability 0.8 or y =
1.5)
MT : The T-year event
y>yiim=>x = xPM (5)
yUm = 10.7 - 0.0071 M5, 25 < M5 < 200 mm/day (6)
C 1 1 - °'78
' C2 C' | ys-C> ~C„+0.72 (7)
v c2
Cv • i/cv
Cv = Coefficient of variation
To use this distribution C| has to be known. This
parameter is really an index variable too, but from
(7) it can be seen that its variation is very limited so
C( is used as regional constant. Chapter 4 discusses
the Cj values found in Iceland so far.
The function f now becomes:
f(T) = 1 + Ci(yl - 1,5) (8)
Ts I 2 5 y 10 20 50
Ta 1,6 2,5 5,5 10,5 20,5 50,5
Fig. 1 Comparison of different f functions
In fig. 1 are different f(T) functions compared to
(8) that is labelled WHI with two different C( values.
One can see that they are all very similar. The func-
tion labelled Vatnaskil is previously suggested by
Vatnaskil Consulting Eng. in a report to Reykjaviks
City Engineer. Their analysis is based on 10 years of
observations in a research area in Breiðholt in
Reykjavik. It is very close to the VVHI curves but
cover a little narrower range as must be expected
when a 10 years series is compared to a 40 years
series. The two USA relations compare very well to
(ASCE no 9).
There are two scales for return periods on fig. 1.
One is for annual maxima and the other for partial
duration series.
Fig 2 shows how the distribution of precipitation
of the duration’s 10, 20, 30, 60 and 120 minutes com-
pare to General Extreme Value no 1 (GEV 1) cumu-
lative distribution function (Gumbels CDF). Note
that fig. 2 shows standardized annual maxima (nX)
against Gumbels frequency parameter y = -ln(-ln(l -
1/T))
The data is from the Icelandic Meteorological Bureau. It consists of the
maximum rain intensity of the respective duration in over 40 years of
observations. Fig. 2 is previously published in Qónas Elíasson 1996). Fig.
2 shows that all the points follow the theoretical line very closely, except the
highest point in the 60 and 120 min. series. This very exceptional rain-
shower, recorded 1991, is shown in table 1. By studying the table it may be
seen that it rained with almost constant intensity for 100 minutes (from 20
to 120 minutes). This is very unusual, and besides that is the fact that it
rained in a limited area only. The reason for this behaviour of this particu-
lar rainshower is, that it was raining from a convective weather system that
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