Encyclopedia of Environmental Science and Engineering, Volume I and II

486 HYDROLOGY

single data station and combinations of data stations. None

of the data stations were in the watershed. One valley data

station exhibited far less precipitation than the mountain sta-

tions, varying in frequency, duration, and amount. The study

showed that the nearest station, which was also near the mid-

elevation of the basin and in a similar climatic zone, gave the

best results, superior even to a combination of stations. Such

a mid-elevation station reduced data extrapolation errors and

is more representative of amount, duration, and frequency of

precipitation and of the actual basin temperature regime. For

the data tested, the errors of maximum peak fl ow, monthly

volumes and hydrograph shape, measured by residual vari-

ance, were all less than 5%.

In summary, simulation techniques should be kept as

simple as possible, provided that representation of reality is

not jeopardized. As much precalibration as possible for each

element of the model should be done during the model con-

struction, using good common sense. The value of graphi-

cal fi tting should be utilized because, by use of graphical

representation, the mind is able to handle large quantities of

data simultaneously. Final fi tting of the model is done when

the main simulation blocks have been assembled, and at this

point it is useful to have a simple quantitative measure of

the goodness of fi t. Several measures have been proposed,

but Nash’s^23 is as good as any. This measure is calculated by

subtracting the recorded output from the simulated output

for each time increment. These differences are squared and

summed to give a residual variance. The optimization can

then proceed to minimize this residual variance.

REPRESENTATIVE DESIGN APPLICATIONS

Minor Design Problems

Such structures as small dam spillways, road culverts,

small bridges, etc. require estimation of a design fl ood. The

approach by which such a design fl ood can be estimated is

shown diagrammatically in the fl ow diagram Figure 13.

First it must be decided whether rain fl oods or snowmelt

fl oods are likely to be limiting and it may be necessary to

calculate each before a conclusion can be reached.

Secondly, the response time of the catchment must be

considered and this is typically characterized by the unit

hydrograph, especially the time from the start of run-off to

the peak.

Thirdly, the precipitation records for rain events must

be examined. In many instances data for the catchment may

not exist, but representative data from adjacent areas may

be available. Such data must be analyzed to yield duration-

intensity plots for given return periods, or probabilities and

for the catchment area in question.

The unit hydrograph data and the precipitation data must

now be combined to determine the critical period of run-off.

As an example, starting with the 1 hour unit hydrograph, it

is easy to superimpose several 1 hour unit hydrographs to

obtain 2 hour, 3 hour, 4 hour, etc. unit hydrographs. These

longer duration unit hydrographs have relatively lower peaks

as is illustrated in Figure 14. However, the greater volume

of rain in longer duration storms may give a higher resultant

peak and such a situation is illustrated in the fi gure.

A similar calculation for snowmelt would yield a maxi-

mum fl ow for run-off. Note that, for small catchments, the

diurnal temperature variations impose limitations on the

maximum snowmelt run-off because the high temperatures

only last for a limited number of hours each day. 30,31,32

Once the peak fl ow has been determined for a given

rain or snow event probability, a fi rst design of the struc-

ture should be made. The costs can be estimated and

also damages resulting from higher fl oods can be at least

approximated. At this point the cost of added protection

can be considered and the assumed risk can be reevaluated.

Maximum Event

Rain Snow

Response Time

of

Catchment

Precipitation

Records

Duration-

Intensity

Critical Time

Period

Snow Records

Maximum

Melt

Pattern

Risk

Soil

Storage

Run-Off

Cost-Benefit

Analysis

Design

of

Structure

Run-Off

Soil

Storage

FIGURE 13 Estimation of design flood for a small spillway or road

culvert, etc.

RECORDED HYDROGRAPH

HYDROGRAPH GENERATED

BY THE UBC WATERSHED

MODEL

DAILY STREAMFLOW (MEAN CFS)

0

1000

2000

3000

4000

6000

7000

8000

9000

10000

11000

5000

FIGURE 12 Spillimacheen River hydrograph.

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