HYDROLOGY 467
relationship between rain intensity (inches per hour) with both
duration and area. In general terms, the longer the duration
of storm, the lower will be the average intensity of rainfall.
Similarly, the larger the area of land being considered, the
lower will be the average intensity of rainfall. For example, a
small catchment area of, say, four square miles may be sub-
jected to a storm lasting one hour with an average intensity of
two inches per hour while a catchment of two hundred square
miles would only experience an average intensity of about one
inch per hour. Both these storms would have the same return
period or probability associated with them. Such data is pre-
pared by weather agencies like the U.S. Weather Bureau and
is available in their publications for all areas of the country.
Typical data is shown in Figure 2. The use of these data sheets
will be discussed further in the section on run-off.
Winter snowpacks represent a large water storage which
is mainly released at a variable rate during spring and early
summer. In general, the pattern of snowfall is less important
than the total accumulation. In the deep mountain snowpacks,
snowtube and snowpillow measurements appear to give fairly
reliable estimates of accumulated snow which can be used for
forecasts of run-off volumes as well as for fl ood forecasting.
On the fl at prairie lands, where snow is often quite moderate
in amounts, there is considerable redistribution and drifting
of snow by wind and it is a considerable problem to obtain
good estimates of total snow accumulation.
When estimates of snow accumulation have been made
it is a further problem to calculate the rate at which the snow
will melt and will contribute to stream run-off. Snow there-
fore represents twice the problem of rain, because fi rstly we
must measure its distribution and amount and secondly, it
may remain as snow for a considerable period before it con-
tributes to snowmelt.EVAPORATION AND EVAPO-TRANSPIRATIONOf the total precipitation which falls, only a part fi nally dis-
charges as streamfl ow to the oceans. The remainder returns
to the atmosphere by evaporation. Linsley^2 points out that ten
reservoirs like Lake Mead could evaporate an amount equiv-
alent to the annual Colorado fl ow. Some years ago, studies
of Lake Victoria indicated that the increased area resulting
from raising the lake level would produce such an increase in
evaporation that there would be a net loss of water utilization
in the system.
Evaporation varies considerably with climatic zone,
latitude and elevation and its magnitude is often diffi cult to
evaluate. Because evaporation is such a signifi cant term in
many hydrological situations, its proper evaluation is often a
key part of hydrological studies.
Fundamentally, evaporation will occur when the vapor
pressure of the evaporating surface is greater than the vapor
pressure of the overlying air. Considerable energy is required to
sustain evaporation, namely 597 calories per gram of water or
677 calories per gram of snow or ice. Energy may be supplied
by incoming radiation or by air temperature, but if this energy
supply is inadequate, the water or land surface and the air willcool, thus slowing down the evaporation process. In the long
term the total energy supply is a function of the net radiation
balance which, in turn, is a function of latitude. There is there-
fore a tendency for annual evaporation to be only moderately
variable and to be a function of latitude, whereas short term
evaporation may vary considerably with wind, air temperature,
air vapor pressure, net radiation, and surface temperature.
The discussion so far applies mainly to evaporation from
a free water surface such as a lake, or to evaporation from a
saturated soil surface. Moisture loss from a vegetated land
surface is complicated by transpiration. Transpiration is the
term used to describe the loss of water to the atmosphere
from plant surfaces. This process is very important because
the plant’s root system can collect water from various depths
of the underlying soil layers and transmit it to the atmosphere.
In practice it is not usually possible to differentiate between
evaporation from the soil surface and transpiration from the
plant surface, so it is customary to consider the joint effect and
call it evapo-transpiration. This lumping of the two processes
has led to thinking of them as being identical, however, we do
know that the evaporation rate from a soil surface decreases
as the moisture content of the soil gets less, whereas there
is evidence to indicate that transpiration may continue at a
nearly constant rate until a plant reaches the wilting point.
To understand the usual approach now being taken to the
calculation of evapo-transpiration, it is necessary to appreciate
what is meant by potential evapo-transpiration as opposed to
actual evapo-transpiration. Potential evapo-transpiration is the
moisture loss to the atmosphere which would occur if the soil
layers remained saturated. Actual evapo-transpiration cannot
exceed the potential rate and gradually reduces to a fraction
of the potential rate as the soil moisture decreases. Various
formulae exist for estimating potential evapo-transpiration in
terms of climatic parameters, such as Thornthwaites method,
or Penman or Turk’s formulae. Such investigations have shown
that a good fi eld measure of potential evapo-transpiration is
pan evaporation from a standard evaporation-pan, such as the
Class A type, and such measurements are now widely used. To
turn these potential estimates into actual evapo-transpiration
it is commonly assumed that actual equals potential after the
soil has been saturated until some specifi c amount of mois-
ture has evaporated, say two inches or so depending on the
soil and crop. It is then assumed that the actual rate decreases
exponentially until it effectively ceases at very low moisture
contents. In hydrological modeling an accounting procedure
can be used to keep track of incoming precipitation and evapo-
ration so that estimates of evapo-transpiration can be made.
The potential evapo-transpiration rate must be estimated from
one of the accepted formulae or from pan-evaporation mea-
surements, if available. Details of such procedures are well
illustrated in papers by Nash^17 and by Linsley and Crawford^44
in the Stanford IV watershed model.RUN-OFF: RAINIt is useful to imagine that we start with a dry catchment,
where the groundwater table is low, and the soil moistureC008_003_r03.indd 467C008_003_r03.indd 467 11/18/2005 10:29:26 AM11/18/2005 10:29:26 AM