158 
A NEW METHOD OF ESTIMATING STREAM-FLOW 
(34) and (36). This computation should cover a period of about a month preceding 
the approximate date when the decrease in melting is assumed to take place, and 
extend past that date a week or more. The difference between the flow as com- 
puted and the observed flow gives a set of residuals which are mostly negative, 
since the observed flow during such a period is generally made up of surface as well 
as sub-surface flow, whereas equation (33) accounts only for the sub-surface flow. 
The date on which the first differences of the residuals changed sign, from a large 
negative to a large positive, is taken as the date of the beginning of the period of 
decreased rate of melting. 
To the extent that assumption No. 10, page 140, is true, it is a simple matter to 
fix the beginning date of the period of decreased rate of melting from the flood flow 
formula, equation (37). From equation (37), the lag between a change in storage 
above ground surface and its maximum effect upon the stream-flow can be deter- 
mined from the derived R'/s. This lag amounts to three days, as a rule, as will be 
seen later from the numerical values of the R'/s to be given. Therefore, by this 
method, three days preceding the date on which maximum discharge took place is 
the date on which the maximum amount of water was stored above the ground 
surface by melting, hence that is assumed to be the last date on which the melting 
took place at its maximum rate. 
Having fixed the beginning of the period of decreased rate of melting and the 
assumed law of decrease in rate of melting, equation (67), the end of the freezing- 
melting period was taken as the date on which the melting as computed from equa- 
tion (67) was for the last time in excess of 0.005 inch. 
EXAMPLE OF ESTIMATE OF BEGINNING OF PERIOD OF DECREASED RATE OF MELTING 
On Stream A in the spring of 1913 it was not possible, as already stated, to 
fix the beginning date of the period of decreased rate of melting by the first method 
stated above. The condition at the 19 snow gages on Watershed A was as follows 
on the various dates: 
Water equivalent of 
No. of gages 
the snow 
Date 
at which 
there was 
some snow 
Maximum at 
Mean 
any gage 
1913 
inches 
inches 
Mar. 27 
19 
7.68 
4.70 
30 
15 
7.07 
4.24 
Apr. 2 
15 
7.13 
4.05 
5 
15 
8.40 
4.36 
8 
17 
8.74 
4.41 
11 
15 
9.20 
4.59 
14 
13 
9.07 
3.97 
17 
12 
8.70 
3.13 
20 
10 
7.66 
2.49 
23 
9 
6.61 
1.83 
26 
7 
6.48 
1.71 
29 
5 
5.04 
1.08 
May 2 
4 
2.52 
0.44 
5 
1 
0.97 
0.02 
From the above record, it was estimated that April 1 1 was the day of the begin- 
ning of the decrease of rate of melting, at which time the mean water equivalent of 
the snow on the ground — the A of equation (67) — was 459, in units of 0.01 inch. 
