wherek is a basin factor which depends on the predominant aspect of the slopes, and is 2.5 when north and south facing slopes are equal in area,
F is the average basin forest canopy cover, as a decimal fraction Ii is incoming solar radiation, observed or estimated, in langleys
(gm cal/cm )2 a is snow surface albedo, as a fraction
(2) M
=
0.04lF (T )rl a
where T is mean air temperature
°c
a
3.3
o •
~ assuming that the snow surface is at 0 C durlng melt periods.
(3) M
cc 3.4
where K is a basin factor dependent upon relative exposure to wind and varies from 2.5 for an open plain to 0.8 for a heavily forested area;
(4) per day.
V is the average daily wind speed (m/s) at the 15 m. level, and T
d is the average daily dewpoint °C.
M
=
.004 P (T) where P is the average basin rainfall in cm.r r w r
3.5
T is the wet-bulb temperature oC and is generally taken as equal
w
to T on rain days.
a
(5) M can be taken as a constant
g 0.05 cm/day.
Both of these sno,vrnelt computation methods are described in greater detail in the WMO Guide to Hydrometeorological Practices, Annex "All (2).
Before using either of these snowmelt computation procedures it is necessary to test them for the basin in question in order to determine basin values of the coefficients involved. These tests involve making trial predictions of the snowmelt runoff .by estimating, for available years of
meteorological and streamflow record, the melt rates during a melt period, assessing the percentage of this melt which will appear as streamflow and the timing of this flow due to snowmelt at the stream gauging stations. These trial "predictions" are then compared with the streamflmv actually observed, and the various coefficients and assumptions may be adjusted until the
prediction procedure yields figures which closely fit the observed flow data.
This type of trial and adjustment procedure is most readily performed by computer, and is discussed in Section 4.4. However. where computers are not available such analyses can be done by hand, especially in regions where information on snowmelt-runoff ratios is available and where degree-day and energy balance coefficients have been worked out for nearby river basins. It should be noted that the coefficients that must be evaluated in using the energy balance equations are closely linked to physical characteristics of the drainage basin and can be readily estimated. This is not the case in the
degree-day approach in which the coefficient allows for a multitude of factors and inter-relationships. In addition, i t is generally found that the
coefficient in a degree-day relationship is not a constant for a given basin, but gradually increases as the snowmelt season progresses. The degree-day approach also tends to excessively IIsmoothll the snowmelt estimates, by over-estimating on days with little melt and under-over-estimating on high melt-rate days (1).
In testing the energy balance equations for the Manicouagan and Outardes River basins, the example used earlier, the values of k, K, F and a were first selected from those given in references (2) and (4) and then
confirmed and/or modified by hydrologic trials in a method such as that out-lined in Section 4.4.
The albedo of the snow surface '~'l was taken as 80% on a day of
130 ESTIMATION OF MAXIMillij FLOODS
new snow with an exponential decrease to a minimum of 40% for a snow surface age of 18 days or longer. Due to the orientation and topography of the Manieouagan and Outardes basins a value of 2.5 for k was accepted. K was
taken as 1.0 and F was estimated as 40%, based on the horizontal projection of an effective forest canopy of 80%.
In the trials, daily values of insolation were estimated for the Manicouagan basin by averaging amounts observed at Normandin and Knob Lake.
Lake Manuan, Nitchequon and Seven Islands data w"ere used to obtain daily air temperatures, dew points, wind velocities, snowfall and rainfall values.
One other factor which was difficult to evaluate but needed in the hydrologic trials was the percentage of the watershed contributing to snowmelt, particularly during the period when the contributing area decreases in the latter part of the season. This factor was determined by trial and error for the 3 years of study 1957, 1958 and 1960 using as an initial guide, values suggested in references (4) and (5). By plotting a factor representing
the fraction of the pack already melted, (such as the potential snow melt in inches accumulated from the beginning of the melt season, divided by the water equivalent of the snow pack at the beginning of melt season) versus the fraction
of area contributing to snowmelt runoff, the three years gave similar curves.
The mean of these "curves could be then used in reconstruction of a design flood.
3.3.2 Maximum Melt Rates 3.3.2.1 Temperature
In anplication of either the energy balance equations or the degree-day method, the most critical sequences of air temperature must be determined.
To do this, the first step is to develop curves of highest maximum (or mean) temperatures for the sno~~elt season, by analysis of the temperature records
at a representative 10ng-rec9rd station or stations within the basin. This involves determination of the greatest recorded temperatures for durations, for example, of 3 days, 7 days, 15 days and 20 days. For smaller drainage basins, periods shorter than 3 days may have to be considered. It may be thought that the greatest recorded temperature from a record of 30-50 years duration may be very much less than the highest possible temperature, but most experience suggests that this is not the case. It appears that plotting of highest 3 day or 7 day temperatures gives curves in which the maximum recorded values are approached asymptotically. This is likely because of the air mass temperature limitations imposed by the characteristics of the source region of the warmest air mass that can affect a region at a particular time of year.
Thus a moderately long (30-50 year) air temperature record serves to give the upper limits to snowmelt temperature sequences that can occur.
Once these limiting curves are derived it is necessary to postulate temperature sequences' for a season which fall within these limits and which yield maximum snowmelt floods. In general this usually means low temperatures during the latter part of the snow accumulation period so as to prohibit
premature melt. Then the temperatures are allowed to increase rapidly to maximum values and remain that way for as long as the limiting curves permit.
The limiting curves, in the example of the Manicouagan and Outardes basin are given in Fig3,4 along with a sample critical t~mperature
sequence which is kept within the 3 day, 7 day and 30 day limits imposed by the limiting curves. In this case the critical sequence suggested assumes snow accumulation to April 30~ moderate snow melt for the first half of May to permit ripening of the snow pack, and saturation of the soil by melt water, then melt factors are assumed to build up to maximum values by May 20-30. By trial this was found to yield critical spring flows for the basin projects.