470 HYDROLOGY
e vapor pressure for 6 hr period
h station elevation (feet)
D melt in inches per 6 hr periodThe U.S. Corps Equation is^36Mk I a NTNTk’ iac0 00508 1 10 0212 0 84 0 02900.....()()()()()()(^0084 UT T0 22..a0 78d)M = Incident Radiation incoming clear air longwave
cloud longwave [Conduction Condensation]k ′ and k are approximately unity.
N fraction of cloud cover
I i incident short wave radiation (langleys/day)
a albedo of snow surface
T a daily mean temperature °F above 32°F at 10′ level
T c cloud base temperature
T d dew point temperature °F above 32°F
U average wind speed—miles/hour at 50′ level.Putting in some representative data for a day when the mini-
mum temperature was 32°F and the maximum 70°F, incom-
ing radiation was 700 langleys per day and relative humidity
varied from 100% at night to 60% at maximum temperature,
the results were:Light Equation
D Air temp melt and Condensation melt
1.035 0.961 inches/day
1.996 inches/dayU.S. Corps Equation
M incoming shortwave incoming longwave
air temp. Condensation
1.424 0.44 0.351 0.59
1.925 inches/day.Note the large amount attributed to radiation which the Light
equation splits between air temperature and radiation. It is
a worthwhile operation to attempt to manufacture data for
these equations and to compare them with real data. The
high correlations between air temperature and radiation is
immediately apparent, as is the close relationship between
diurnal air temperature variation and dewpoint temperature
during the snowmelt season. Further comparison of the for-
mulae at lower temperature ranges leave doubts about the
infl uence of low overnight temperatures.
There is enough evidence of discrepancies between real
and calculated snowmelt to suggest that further study may
not be wasted effort. Perhaps this is best illustrated from
some recent statements made at a workshop on Snow and Ice
Hydrology.^39 Meier indicates that, using snow survey data,
the Columbia forecast error is 8 to 14% and occasionally
40 to 50%. Also these errors occurred in a situation wherethe average deviation from the long-term mean was only
12 to 20%. For a better comparison of errors it would be
interesting to know the standard error of forecast compared
with standard “error” of record from the long-term mean.
Also, later in the same paper it is indicated that a correct heat
exchange calculation for the estimation of snowmelt cannot
be made because of our inadequate knowledge of the eddy
convection process. At the same workshop the study group
on Snow Metamorphism and Melt reported: “we still cannot
measure the free water content in any snow cover, much less
the fl ux of the water as no theoretical framework for fl ow
through snow exists.”
Although limitations of data often preclude the use of the
complex melt equations, various investigators have used the
simple degree-day method with good success (Linsley^32 and
Quick and Pipes 40,46,47 ). There may be reasonable justifi ca-
tion for using the degree-day approach for large river basins
with extensive snowfi elds where the air mass tends to reach a
dynamic equilibrium with the snowpck so that energy supply
and the resulting melt rate may be reasonably well described
by air temperature. In fact there seems to be no satisfactory
compromise for meteorological forecasting; either we must
use the simple degree-day approach or on the other hand we
must use the complex radiation balance, vapour exchange
and convective heat transfer methods involving sophisticated
and exacting data networks.COMPUTATION OF RUN-OFF—
SMALL CATCHMENTSTotal catchment behavior is seen to be made up of a number
of complex and interrelated processes. The main processes
can be reduced to evapo-transpiration losses, soil moisture
and groundwater storage, and fl ow of water through porous
media both as saturated fl ow and unsaturated fl ow. To describe
this complex system the hydrologist has resorted to a mix-
ture of semi-theoretical and empirical calculation techniques.
Whether such techniques are valid is justifi ed by their abil-
ity to predict the measured behavior of a catchment from the
measured inputs.
The budgeting techniques for calculating evapo-
transpiration losses have already been described. From an
estimation of evapo-transpiration and soil moisture and mea-
sured precipitation we can calculate the residual precipita-
tion which can go to storage in the catchment and run-off
in the streams. A method is now required to determine at
what rate this effective precipitation, as it is usually called,
will appear at some point in the stream drainage system. The
most widely used method is the unit hydrograph approach
fi rst developed by Sherman in 1932.^16
To reduce the unit hydrograph idea to its simplest form,
consider that four inches of precipitation falls on a catch-
ment in two hours. After allowing for soil moisture defi cit
and evaporation losses, let us assume that three inches of this
precipitation will eventually appear downstream as run-off.
Effecitvely this precipitation can be assumed to have fallen
on the catchment at the rate of one and a half inches per hourC008_003_r03.indd 470C008_003_r03.indd 470 11/18/2005 10:29:26 AM11/18/2005 10:29:26 AM