478 HYDROLOGY
This is the aim of streamfl ow generation studies. Whether
the methods currently in use are adequate or valid is still
under debate. The aims are sound and the methods promis-
ing, if used with caution and an awareness of the intrinsic
assumptions.
It is worthwhile comparing the artifi cial generation
methods with the approaches previously used. It has been
customary to construct a test period or sequence from the
recorded data. As an example, it was not unusual to use the
three driest years of record and assume that they occur in suc-
cessive years. This became the design drought. Without care
to evaluate just how extreme an event this might be, such a
method might lead to either over or under design. Hopefully,
streamfl ow generation will lead to more balanced designs,
especially as experience with the techniques and the tech-
niques themselves improve.
To consider the generation techniques, it is fi rst of all
important to appreciate that streamfl ow forms a time series
which can be highly dependent or almost entirely indepen-
dent according to the time interval chosen. Daily fl ows are
usually highly correlated with each other; monthly fl ows may
still have a reasonable serial correlation, but annual fl ows
may be almost totally independent. Certainly it is usual to
assume that annual fl ood peaks are independent.
The simplest streamfl ow model assumes that there is no
long term trend in the run-off pattern, so that the mean fl ow
for the period of record is a reasonably good estimate of the
long term mean. Also it is assumed that the standard devia-
tion from the mean is a good measure of the dispersion of
fl ows around the mean. The model expresses:
Generated fl ow = Mean fl ow + Random Component
i.e. ,QQtijijs (44)i refers to synthetic sequence, j to historic sequence.Q i = synthetic streamfl ow for month i
= is mean fl ow for same month
t i is random normal deviate with mean zero and vari-
ance unity (Available in most computer libraries)
σ j is standard deviation of fl ows for month j.The random component is seen to be made up of the cal-
culated standard deviation multiplied by a random variable
t i which is generated by a random number generation, and
has a statistical distribution which is the same as the normal
random error. The variable t i therefore redistributes σ j in a
random Gaussian fashion.
A more sophisticated model by Thomas and Fiering 42,43
includes the memory that this month’s fl ow has of last month’s
fl ow. This memory is described by serial correlation:
Generated Flow Mean Flow Serial Component
Random Component
i.e.,QQ bQQ tijji++ 11 j ij 1 rj^212
1
()()s (45)The additional symbols areb j is regression coeffi cient for serial correlation of j
and j 1 month
r j is correlation coeffi cient between j and j 1 month.It will be noticed that when a serial component is intro-
duced, the random component must be correspondingly
decreased by the factor (1rj^2 ) 1/2 so that there is not a net
increase in fl ow.
Many other synthetic streamfl ow methods have been
tried or suggested but at the present time only the simple
models [Eq. (44) and (45)]. Thomas and Fiering’s model^43
seem to be in use by practising hydrologists. Also, the reader
should appreciate, that the methods are not without their
problems, for generated fl ows may go negative, so that mod-
eling of droughts is questionable. However, a study of the
statistical frequency of failure may still be better than the
old methods.
So far, generation techniques have been discussed only
for a single streamfl ow record. If a whole river basin with
several reservoirs on different tributaries and on the main
stream is being studied, then a much more diffi cult prob-
lem arises. It is not diffi cult to generate artifi cial data for
each tributary or for the main stream. But such data will have
none of the cross-correlation which exists in real data. That
is to say, with the real data, if fl ows are high in one tributary,
then probably the other tributaries are also reasonably high.
This cross-correlation is diffi cult to preserve in generating
techniques. It is discussed at great length by Fiering but the
method suggested for preserving cross-correlations is very
demanding on computer storage and time.
The writer wonders whether use of a physically based
computer model of a river basin, coupled to a random gen-
eration of precipitation events both for one area of storm and
intensity of storm might not produce data more economi-
cally and with the correct statistical interdependence.HYDROLOGICAL SIMULATIONSimulation is a very broad term covering many types of
mathematical and physical procedures. The streamfl ow gen-
eration techniques already discussed are one type of simula-
tion. Analogue computer models and physical fl ow models
are also simulations. Digital computer models for simulation
may be based on statistics entirely or on the physical behav-
ior of various components of the system. Some models may
be a mixture of both physical and statistical methods.
Although the types of simulation models vary widely,
their aims are similar, namely to describe the behavior of
a complex system so that predictions of system behavior
can be made from some specifi ed input. These predictions
may be short-term fl ood-fl ow predictions to give fl ood warn-
ing, especially for operation of fl ood protection schemes.
Alternatively, predictions may be needed to evaluate water
resource schemes and to examine the infl uence of storage,
diversion, consumptive use, etc. on the system of operation.C008_003_r03.indd 478C008_003_r03.indd 478 11/18/2005 10:29:29 AM11/18/2005 10:29:29 AM