16 A NEW METHOD OF ESTIMATING STREAM-FLOW 
one inch of rainfall on one square mile of area. The question might well be asked, 
why use factors to convert the rainfall into units of 100 inch-miles, when the unit 
used in the observation equations is 0.001 foot of depth on the lake surface? The 
answer is that this unit, 100 inch-miles, was used in the very early stages of the 
investigation in an attempt to derive the law of run-off of the rainfall into the lake. 
When the unit was subsequently changed to 0.001 foot of depth on the lake surface, 
the factors were not changed, as complete use of them had already been made. 
Instead, the proper conversion factor was applied to the rainfall computed in the 
original unit to reduce it to the final unit used. 
FIRST APPROXIMATE VALUES OF h FOR LAKES MICHIGAN-HURON AND SUPERIOR 
It is proposed to state briefly the manner of obtaining the first approximations 
to I c for each of Lakes Michigan-Huron and Superior. At a subsequent place, the 
manner of revising these first approximations from the least-square computations 
will be set forth. 
For the land part of the drainage area of a lake, the following equation is true 
for the average year: 
(Rainfall on land) — (evaporation from land) — (run-off) = (7) 
from which the run-off from land can be computed, and this, converted to depth on 
the lake surface and divided by 365, gives the first estimate of I c for the lake; that 
is, the run-off into the lake in one day when (rainfall on land) — (evaporation from 
land) — (run-off) has been zero for a long time and the ground water is at its 
average level, expressed in depth on the lake area. 
In order to estimate I c from equation (7), it is necessary to know what the 
evaporation from the land surface is. At first this is not known, but there exist in 
the literature estimates of evaporation from the water surfaces of the Great Lakes 
in inches of depth per year. If one can determine the ratio of the rate of evaporation 
from the land surface to the rate of evaporation from the lake surface, the product of 
this ratio and the estimated evaporation from the water surface equals the evapo- 
ration from land. Call this ratio -~ in which E t is the evaporation from each 
E w 
unit of area of land expressed in depth of water evaporated per unit of time, and 
E w the corresponding evaporation from the water surface. 
W 
In order to calculate the ratio — ' for the Great Lakes region, we make use of 
E w 
the following equation: 
(Rainfall on drainage area) — (evaporation from land) — (evaporation from 
water) + (inflow from lakes above) — (outflow to lakes below) + (decrease in 
storage in lakes and streams and ground-water) = (8) 
By choosing the average year as the unit of time, the last term on the left- 
hand side of equation (8) vanishes ; that is, for the average year there is no decrease 
in storage in the lakes and streams and ground-water of the land part of the drain- 
age area. The remaining unknown, the evaporation from land, can then be de- 
termined in terms of the other four quantities, estimates of which are available in 
the literature on the hydrology of the Great Lakes drainage basin. 
