The accuracy of a raingage network is judged by

!

how well its *estimate *of the mean areal rainfall over

the basin compares to the "true" value of mean areal

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

observe a storm is

where

(4-4)

F = standard deviation

4

The network size, N, is selected to reach the desired level of

= mean

accuracy as defined by *C*V. Now, since *T*obs is known from

direct analysis of watershed records or it is estimated from

watershed characteristics, *C*V is a function of the number of

expected to be to the true value. A low *C*V 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 *C*V 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 *C*V,

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 *C*V 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

(4-3)

&0.22

0.082*T*obs

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

of Federal and local sponsor resources available for