480 HYDROLOGY
as the “principle of parsimony.” The fi nal optimization of
the model parameters is done when the whole model is com-
plete. One parameter at a time is adjusted in a step by step
process until best fi t values are obtained.
To illustrate the process we shall consider a simple
model, Quick and Pipes.^47WATERSHED MODELING IN MOUNTAIN
CATCHMENTSThe rain and snowmelt run-off processes in rugged moun-
tain catchments appear, at fi rst sight, to be highly complex.
Rain, snow, temperature, and soil and rock composition of
the watershed all are highly variable at different elevation
levels in the watershed.
In reality this apparent complexity is simplifi ed by the
orographic infl uences. The strong orographic gradients of
behavior impose a useful discipline on the various processes.
In particular, there tends to be a greater areal uniformity of
precipitation and temperature within each elevation zone.
This uniformity of behavior by elevation zone, if proved to
be real, offers a great simplifi cation of the most diffi cult of
hydrologic behavior, namely the variation of rain and snow
and temperature over an area.
The UBC Watershed model was designed to take advan-
tage of the strong orographic discipline which exists in a
mountain watershed. The primary purpose in designing the
model was to provide a tool for forecasting fl ood run-off, but
in reality, its most useful purpose has become the day to day
forecasting of run-off for hydropower production. The model
can also be used as a research tool to investigate the total
system behavior of a mountain catchment. Such research
investigations are highly dependent on the accuracy and dis-
tribution of the meteorological and hydrological data base.Design of the UBC Watershed ModelThere are fi ve main subdivisions of the total model namely
meteorological data processing, snowmelt calculation, soil
moisture budget, routing of fl ow components to channel outfl ow
point, and statistical evaluation of model performance. These
subdivisions will be discussed briefl y. A complete description
of model design and use is given in Quick and Pipes.^49
Meteorological data processing Meteorological data is
available only at discrete points. In many situations, only
one data station may exist and that station may be in the
valley and perhaps not even in the watershed itself. Even
when more than one data station exists, there is still the tech-
nical problem of distributing the point data to all elevations
and regions of the watershed.
It is assumed that the orographic infl uences are the stron-
gest and that these orographic effects are modifi ed by the
moisture content of the air mass. Usually there is no direct
information on vapor pressure values, and therefore indirect
indications of moisture status are used. For example, tempera-
ture range during the day is used as an indicator of relative
humidity. A low daily temperature range is associated withhumid conditions when the temperature lapse rate will be
approximately equal to the saturated adiabatic rate. A high
daily temperature range is assumed to indicate that maxi-
mum temperature will vary at the dry adiabatic rate, but min-
imum temperature will tend to show a very low lapse rate.
A simple functional relationship is therefore defi ned between
temperature lapse rate and the daily temperature range.
Orographic precipitation gradients are made functionally
dependent on the rates of saturated dry adiabatic lapse rates
corresponding to the observed temperatures. The larger the
difference between saturated, L S , and dry, L D , lapse rates, the
greater is the convective instability of the air mass, so that
convective instability is measured byLL
LDS
D.^ (47)
If the air mass is already very unstable, then the orographic
effects will be moderate. The orographic opportunity is
therefore expressed asorographic opportunity
1LL
LL
LDS
DS
D≡.
(48)When this ratio approaches 1, the orographic effect on pre-
cipitation is high, whereas when the ratio decreases, the
orographic effect is weaker. It will therefore be appreciated
that orographic effects will be large during the winter, when
temperatures are low, and L S is more nearly equal to L D. On
the other hand, in the warm summer weather, because L S
is then much lower than L D , the orographic effects will be
much weaker.
This simple functional variation of precipitation gra-
dients has proved to be a very valuable tool in distribut-
ing meteorological data and has resulted in considerable
improvement in forecast accuracy.
Snowmelt calculation The strong elevation dependence
of snowmelt supports the use of temperature indices for the
calculation of snowmelt. The simple degree day method
probably accounts for 80% of the snowmelt process, but there
are periods of extreme melt when radiation and condensa-
tion melt become important additional factors. The snowmelt
algorithms used in the UBC Watershed model have been
discussed in a previous paper, but, in summary, additional
temperature terms are added to account for radiation and
condensation, Quick and Pipes.^46 Radiation is represented by
the daily temperature range and condensation is handled by
using the minimum temperature as an approximation for the
dew point temperature. Under warm summer conditions this
dew point assumption is usually good and this is the only time
when the extra terms are signifi cant. The snowmelt equation,
for forested areas, when slightly simplifi ed, isBM TMTX TN
kTNTN
k PTM
12⎛
⎝⎜⎞
⎠⎟∗⎧
⎨⎪⎩⎪⎫
⎬⎪⎭⎪∗ (49)C008_003_r03.indd 480C008_003_r03.indd 480 11/18/2005 10:29:30 AM11/18/2005 10:29:30 AM