ETL 1110-2-540
30 Sep 96
The accuracy of a raingage network is judged by
A = basin area
!
how well its estimate of the mean areal rainfall over
the basin compares to the "true" value of mean areal
N = number of gages
rainfall. One measure of how well the network
measures rainfall is a statistical parameter called the
The appropriate observation period for a flood warning
coefficient of variation (CV). The coefficient of
situation is a balance between waiting long enough to get
variation is the ratio between the standard deviation
sufficient information and getting a forecast out soon enough
and the mean of a sample of measurements
to be valuable to the recipients. Assume a reasonable time to
monitor the developing storm is equal to 25 percent of the
F
(4-2)
basin time of concentration. Then the time, Tobs, required to
Cv '
observe a storm is
where
Tc
(4-4)
Tobs '
F = standard deviation
4
The network size, N, is selected to reach the desired level of
= mean
accuracy as defined by CV. Now, since Tobs is known from
direct analysis of watershed records or it is estimated from
CV provides an indication of how close a measured value is
watershed characteristics, CV is a function of the number of
expected to be to the true value. A low CV means that the
raingages for a given watershed of size A. The network size,
measured value is expected to be near the true value with a
N, is selected to reach a desired level of accuracy as defined
high degree of certainty. A high value of CV indicates a
by CV. To illustrate the impact of network size on CV,
much lower degree of certainty.
consider a given watershed having a specific TC area and
corresponding observation time. Using equations 4-3 and 4-4
For example, consider a relatively high value of CV,
and presenting the results graphically as shown in Figure 4-2,
!
say 0.25, for mean areal rainfall. This means that,
one can see very clearly how adding gages to a relatively
for a measured mean areal rainfall value of 127 mm
small network dramatically improves network accuracy.
(5.0 in.), the true value of mean areal rainfall is
Eventually, however, the gains in accuracy diminish to
expected to be in the range between 63.5 and
insignificant levels for each additional gage. This could be
191 mm (2.50 and 7.50 in.) (i.e., 2F) about
shown for any given watershed in the same manner.
95 percent of the time. When CV is lower, say
0.05, the measurement is more certain. Then, for a
The diminishing return of network performance for
!
rainfall estimate of 5.0 in., the true value of mean
additional gages provides important information for
areal rainfall is expected to be in the range between
network size.
The accuracy of rainfall
114 and 140 mm (4.50 and 5.50 in.) about
measurements is a vital aspect of any hydrologic
95 percent of the time, a much narrower range.
model performance in a flood warning -
preparedness program.
In fact, model
Since flood forecast model performance is sensitive
performance is much more sensitive to errors in the
!
to the accuracy of rainfall estimates, narrowing the
rainfall input than to errors in any other parameter -
range of possibilities for the true rainfall amounts
especially in flash flood situations. Therefore, it
translate directly to more accurate and reliable
seems reasonable that a measure of rainfall accuracy
forecasts. Therefore, the coefficient of variation is a
such as CV can be used as a surrogate measure of
reasonable surrogate to use to evaluate improve-
hydrologic model performance. Equations 4-3 and
ments in forecast accuracy. An empirical equation is
4-4 can be used to develop a curve, as in Figure 4-
available (GKY & Associates 1981) to estimate the
2, for any watershed to help determine the sensitivity
coefficient of variation of the mean areal rainfall
between the number of gages and the estimate of
basin average precipitation.
&0.602
N
(4-3)
&0.22
Cv '
0.082Tobs
A
The information described above will help deter-
!
where
mine the minimum and most effective number of
gages for an initial estimate. The cost and amount
Tobs = observation period in hours
of Federal and local sponsor resources available for
4-3
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