1052 
K is the slope of this line. More interesting, however, 
is the possibility of solving (5) by means of least squares 
in which the C’s become regression constants, or by 
multiple graphical correlation yielding a chart such as 
Fig. 2. The latter method has the advantage of per- 
| (@) 30 40 50 
60 0 e} 2 
50 
[TAD STAGE (0,) 
it if 
40 
30 
fr 
“ye 40 
CAIRO STAGE (1)) 
20 t+ 
NOTE: NOT APPLICABLE WHEN 
NEW MADRID FLOODWAY IS 
OPEN FORECASTS MUST BE _} 5 a 
ADJUSTED WHEN IT IS KNOWN 
THAT THE FLOODWAY WILL BE 
OPENED, 
DATA RANGE: I-1-43 TO 
4-30-44 (DATA FOR 1937 
FLOOD WERE GIVEN SOME 
WEIGHT.) 10 
MISSISSIPPI RIVER 
ROUTING PROCEDURE 
ZB CAIRO - NEW MADRID 
eo M.A.K. 7-7-44 
NEW MADRID STAGE ONE DAY LATER (02) 
0 
Fic. 2.—Stage routing relation between Cairo, Ill. and New 
Madrid, Mo. developed by multiple graphical correlation. 
mitting curvilinear and joint functions without the 
complexities of the analytical solution. 
Recently an electronic circuit has been devised for 
the solution of the differential form of the storage equa- 
tion (I — O = dS/dt) by analogy with the flow of 
electricity in a circuit containing capacitors [6]. 
Forecasting the Runoff from Rainfall. The forecaster 
dealing with small headwater basins cannot make use 
of upstream flows as a basis for forecasts, and he must 
turn to the ultimate inflow to the basin—precipitation. 
The first step in headwater forecasting is therefore the 
determination of the quantity of water which will actu- 
ally reach the stream. This step is a detailed evaluation 
of one small portion of the hydrologic cycle. The fore- 
caster must determine the portion of the precipitation 
which will be held in the basin as interception on vege- 
tation, in puddles on the ground surface, and as sub- 
surface storage (soil-moisture and ground water). The 
amount of this “basin recharge” in any storm is a func- 
tion of (1) the moisture conditions in the basin prior 
to the storm, and (2) the intensity, amount, duration, 
and distribution of the precipitation. Much has been 
written on the theoretical considerations which may 
ultimately lead to a completely rational solution of 
this problem [7]. For the time being at least, the com- 
plexities introduced by superimposing the varying char- 
acteristics of a storm with respect to area over a basin 
which itself has varying soil types, vegetal cover, and 
HYDROMETEOROLOGY 
antecedent moisture conditions have forced the adop- 
tion of empirical techniques. 
Many methods have been employed, ranging upward 
in complexity from a simple correlation between rain- 
fall and runoff, but the procedure which has proven 
most successful in the experience of the U.S. Weather 
Bureau is a multiple graphical correlation such as that 
shown in Fig. 3. Here the moisture condition of the 
5 
5 
E 4 : 
<a RUNOFF RELATION FOR 
ag MONOGAGCY RIVER AT 
ipa) JUG BRIDGE, MD. 
a2 
a= 
QZ 
i>) 
uy i} 
ee 
2 
a 
0 5 
Fic. 3.—Rainfall-runoff relation for the Monocacy River 
above Frederick, Md. 
basin is introduced in terms of an antecedent precipi- 
tation index, a weighted summation of precipitation 
for approximately thirty days prior to the storm with 
the highest weights assigned to the most recent days. 
The significance of this antecedent index is modified 
by the introduction of the week of the year to reflect 
at least the normal evapotranspiration characteristics 
and the extent of interception by foliage. Storm char- 
acteristics are expressed in terms of duration and 
amount of precipitation. If the variation in depth of 
precipitation is great, the average over the basin may 
not reflect the true runoff because of the curvilinear 
relations involved. In this case runoff may be com- 
puted for subareas of the basin and averaged to get the 
best estimate of average runoff. 
Runoff Distribution After the total volume of runoff 
is computed, usually in terms of the depth in inches 
over the basin, the final step is the determination of 
the time distribution of this runoff in terms of the 
stream flow at the outlet of the basin. Sherman [12] 
observed that the hydrograph shapes for storms of 
like distribution and equal duration were character- 
istically similar on any basin. This led to the concept 
of the unit hydrograph which is almost universally used 
today for determining hydrograph shape. The unit hy- 
drograph (Fig. 4) is a composite of the hydrographs of 
storms of equal duration and similar areal distribution 
of rainfall, all reduced to a volume of one inch of runoff 
by dividing their ordinates by the runoff depth in 
inches. A series of such graphs must be available for 
