Geoscience Reference
In-Depth Information
100
10
1
Figure 13.10
Relationship
between the greatest
magnitude rainfalls and
duration for the world as a
whole. (Redrawn selecting
extreme values from
Brutsaert, 2005, after WMO,
1986, published with
permission.)
0.1
Minutes
Hours
Days
Months
Years
0.01
1
10
100
1 000
Duration (minutes)
10 000
100 000
1 000 000
storm drainage, for example. The most important result to emerge from such
studies is that the maximum intensity attained for different durations at a location
are interrelated, and that this interrelationship can be represented relatively simply
both mathematically and graphically.
The form of the relationship between maximum intensity and duration changes
with region and the assumed form will generally need to be calibrated over a
portion of the range before application. One commonly adopted assumed
relationship between maximum intensity and its duration is the
McCullum
model
which has the form:
n
I t
−
=
(13.10)
where
I
is the intensity (mm hr
−1
) that is sustained for a duration
t
(in hours), and
k
and
n
are location dependent constants obtained by calibration. Interestingly,
this relationship (which yields a straight line when values are plotted on log-log
graph paper) seems to apply at the global scale and also within individual storms
both of convective and frontal nature. Figure 13.10 shows the greatest magnitude
rainfalls and their duration for the world as a whole, while Fig. 13.11 shows
intensity-duration relationships (a) at Dar es Salaam, Tanzania for several storms
of convective origin and (b) at Lampeter in Wales for several storms of frontal
origin. Note the very different axes used in parts (a) and (b) of Fig. 13.11.
Statistics of extremes
Calibrating intensity-duration relationships over the usually longer duration and
lower intensity portion of their range and then using the resulting curve to estimate
the duration of more intense rainfalls (mentioned above) is one example of a more
general approach. Hydrologists and hydrometeorologists are often concerned with
