466 HYDROLOGY
often this basic question of dependence or independence is
not discussed until after many primary statistical measures
have been defi ned. It is basic to the analysis, to the selec-
tion of variables and to the choice of technique to have some
idea of whether data is related or independent. For example,
it is usually reasonable to assume that annual fl ood peaks
are independent of each other, whereas daily streamfl ows are
usually closely related to preceding and subsequent events:
they exhibit what is termed serial correlation.
The selection of data for multiple correlation studies
is an example where dependence of the data is in confl ict
with the underlying assumptions of the method. Once the
true nature of the data is appreciated it is far less diffi cult to
decide on the correct statistical technique for the job in hand.
For example, maximum daily temperatures and incoming
radiation are highly correlated and yet are sometimes both
used simultaneously to describe snowmelt.
In many hydrological studies it has been demonstrated
that the assumption of random processes is not unreason-
able. Such an assumption requires an understanding of sta-
tistical distribution and probabilities. Real data of different
types has been found to approximate such theoretical distri-
butions as the binomial, the Poisson, the normal distribution
or certain special extreme value distributions. Especially, in
probability analysis, it is important that the correct assump-
tion is made concerning the type of distribution if extrapo-
lated values are being read from the graphs.
Probabilities and return periods are important con-
cepts in design studies and require understanding. The term
“return period” can be somewhat misleading unless it is
clearly appreciated that a return period is in fact a probabil-
ity. Therefore when we speak of a return period of 100 years
we imply that a magnitude of fl ow, or some other such event,
has a one percent probability of occurring in any given year.
It is even more important to realize that the probability of a
certain event occurring in a number of years of record is muchhigher than we might be led to believe from considering only
its annual probability or return period. As an example, the
200 year return period fl ood or drought has an annual prob-
ability of 0.5%, but in 50 years of record, the probability that
it will occur at least once is 22%. Figure 1 summarizes the
probabilities for various return periods to occur at least once
as a function of the number of years of record. From such a
graph it is somewhat easier to appreciate why design fl oods
for such critical structures as dam spillways have return of
1,000 years or even 10,000 years.ANALYSIS OF PRECIPITATION DATABefore analyzing any precipitation data it is advisable to
study the method of measurement and the errors inherent
in the type of gauge used. Such errors can be considerable
(Chow,^1 and Ward^5 ).
Precipitation measurements vary in type and precision,
and according to whether rain or snow is being measured.
Precipitation gauges may be read manually at intervals of a
day or part of a day. Alternatively gauges may be automatic
and yield records of short-term intensity. Wind and gauge
exposure can change the catch effi ciency of precipitation
gauges and this is especially true for snow measurements.
Many snow measurements are made from the depth of new
snow and an average specifi c gravity of 0.10 is assumed
when converting to water equivalent.
Precipitation data is analyzed to give mean annual values
and also mean monthly values which are useful in assessing
seasonal precipitation patterns. Such fi gures are useful for
determining total water supply for domestic, agricultural and
hydropower use, etc.
More detailed analysis of precipitation data is given for
individual storms and these fi gures are required for design of
drainage systems and fl ood control works. Analysis shows the100.2.4.6.81.020 30 40 50 60 70 80 90 100
No. Years Record200 YR. RP.1000 YR. RP.100 YR. RP.50 YR. RP.20 YR. RP.10 YR. RP.ProbabilityFIGURE 1 Probability of occurrence of various annual return period events as a function of years of
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