SMALL DAMS

Chapter II
STATISTICAL RAINFALL AND RUNOFF DISTRIBUTIONS
Figure 2 (p. 35) shows rainfall and runoff on the vertical scale versus the standardised
GUMBEL u.
The concave shape of the two curves is explained by the fact that events of very short
return periods are plotted. The asymptotic rainfall distribution appears if we limit
ourselves to the 27 most severe events (one event per year). It is not unusual for the
most severe event (September 13th, 1968) to lie some distance off the curve.
Since there is considerable sampling uncertainty in a 27 value sample, the computations
were run on the 150 most severe rainfall events observed for each of the durations
considered in determining the asymptote slopes, proportional to the standard deviations.
For this example, the fitting method would appear to overestimate the frequency of
the highest values. This is attributable to the sampling alone, and application of this
fitting method to samples of other rainfall durations yields estimates that are either
entirely consistent, or underestimated (points concave downwards). Results are listed
in table 4.
Duration (h) 1 2 4 8 12 24
Runoff (L) a 2.24 4.43 7.72 11.9 14.9 22.3
(mm) b 3.90 7.60 13.5 22.4 29.3 44.2
Rainfall (P) a 6.82 10.9 15.9 22.5 26.8 34.3
(mm) b 20.1 31.5 46.5 66.2 79.7 106
33
Table 4 - GUMBEL parameters a and b for rainfall or runoff: P (or L) = au + b
Application of these equations to a recurrence interval of 0.95 (u = 2.97) was the
basis for preparing table 3.
The rise in the GRADEX and therefore the trend in the a values (slope of the rainfall
distribution line) matches duration perfectly and can be expressed as:
GRADEX (t) = 7,4 t 0,51
Rare runoff is derived directly from these equations; by setting the pivot point at 0.95
(u = 2.97), runoffs of different duration at recurrence intervals of 0.999 are estimated at the
values shown in table 5.
Duration 1 2 4 8 12 24
(hours)
Runoff 37.2 63.3 98.6 146 179 245
(mm)
Table 5 - Estimation of runoff at recurrence interval 0.999