Volume 28, Number 3
Transactions, American Geophysical Union
June 1947
FURTHER STUDIES OF THE BALANCED WATER CYCLE ON EXPERIMENTAL WATERSHEDS
J. A. Lieberman and P. W. Fletcher
Abstract--In the field of land-use hydrology it is frequently of value to keep a
chronological account or balance of the components of the water resource of a watershed. In this paper a time period for studying this balance is described. Essentially
it is the annual period between times of maximum watershed storage at the end of the
dormant season. Changes in ground-water storage are taken into account, and by
choosing the beginning and end points of the year at times of field capacity, water
storage changes in the soil mass are eliminated. Sample data for an experimental
watershed are given.
In the management of water resources, it is of considerable value to be able to keep accounts
of the resource in all of its phases of the hydrologic cycle. This is particularly true when an attempt is made to evaluate the effects of land use changes and land management practices on several components of the water cycle. Much progress has been made in establishing practical accounting methods with the use of the storage equation inflow = outflow + storage and other balancing procedures [see "References" at end of paper; HURSH, HOOVER, and FLETCHER, 1942;
HOYT and others, 1936; HOUK, 1921; VERMULE, 1894].
At the Coweeta Experimental Forest, an expansion of a study of these methods is continuously
being carried on. The experimental forest which is part of the Appalachian Forest Experiment
Station is located in the high rainfall area of the southern Appalachian Mountains. The data presented in Table 1 give a general summary of the rainfall and runoff for the period of record for
the experimental drainage basin (no. 18) used in the present paper. This watershed is 30.8 acres
in area and is at an average elevation of 2700 feet. The basic geology is the Carolina gneiss of
Pre-Cambrian age. The soil is more than 4 feet in average depth and lies over soft, disintegrated
rock. The vegetal cover is a typical hardwood forest stand of the southern Appalachian Mountains.
Table 1--Average monthly precipitation, runoff, and temperature for
the period 1936 to 1945. Coweeta watershed 18
Month
Precipitation
Runoff
Temperature
in
in
per cent
Nov.
Dec.
Jan.
4.32
7.24
5.79
1.10
1.93
3.37
25.5
26.7
58.2
43.9
38.8
38.1
Feb.
Mar.
Apr.
7.50
7.64
5.89
4.83
5.41
4.76
64.4
70.8
80.8
39.9
47.3
56.4
May
June
July
4.21
4.56
7.34
3.47
2.09
1.93
82.4
45.8
26.3
64.1
71.1
72.0
Aug
Sep
Oct.
5.76
4.413.08
1.66
1.19
0.94
28.8
27.0
30.5
71.5
65.6
55.8
In this paper an effort is made to keep a more logical account of the factors of the water cycle
by using the same basic expression of the hydrologic cycle given in the above equation but for periods which are believed to be of more hydrologic significance. Previous similar analyses have
421
LJEBERMAN and FLETCHER
422
[Trans. AGU, V. 28 - 3]
been made by months for water years of 12 months' duration. In this study a water year, subsequently termed a hydrologic year, is determined by the occurrence of a major storm at the end of
the dormant season. The period thus defined will be of only approximately 12 months' duration.
In addition to the use of a major storm in the spring to determine the beginning and end of the
hydrologic year, levels in ground-water wells were used to check and define more accurately
those times. In every case the dates chosen coincided with the most significant rises and peaks
in the well levels. At these times the soil moisture is at field capacity, retention storage opportunity is at a minimum and for practical purposes may be considered to be zero; and the ground
water stored is at the maximum for that particular hydrologic year. It is felt that because of
these factors the hydrologic status of the watershed at such a period of the year is more qualitatively constant from year to year than at any other time. In addition soil moisture is quantitatively constant from year to year at these times. It may further be said that the period is the divide
between accretion and depletion of total watershed storage.
Other workers [HOYT and others, 1936; HOUK, 1921; VERMULE, 1894] have described water
years divided into various monthly durations based on periods of vegetation growth, soil moisture
accretion, and ground-water storage, but in all cases the year has been of arbitrary 12 months'
duration. PARKER [1932, p. 183] stated "if the period at which the water stored up in the ground
is at a maximum could be definitely observed, the relations of the rainfall to runoff for the intervals between these maxima would be more constant than for any other period." HOYT and others
[1936] in their study of the Skunk River Basin in Iowa used September as the beginning of the accretion, and the tabulated data and computations indicate that April is generally the dividing month
between accretion and depletion. PARKER [1932] also stated that "the difficulty lies in the fact
that these maxima are, so far as present information exists, somewhat more irregular in time
than the minima in stream flows and are less easily observed." He also agrees ' that the date of
maximum storage of ground water has theoretical advantages" and, thus, it appears evident that
the difficulty he mentions is one that stems from a lack of hydrologic data and which, in the present
study, is overcome by the availability of such data. Adequate well records have made possible the
observation of the "period at which the water stored up in the ground is at a maximum."
In the humid, high-rainfall area of the southern Appalachians-, it'also appears that there is
actually more regularity in the periodicity of maximum total watershed storage than there is in
the time of minimum stream flows. This may be attributed to the seasonal distribution of rainfall,
the influence of vegetation, temperature, and in
case of this particular watershed, to the nature
of the soil profile. Since the vegetation demand
remains essentially the same from year to year
and the monthly distribution of rainfall is fairly
uniform and there is no change in the soil surface
or profile, it follows that the opportunity for watershed storage is constant from year to year and
that maximum watershed storage will be reached
with comparative regularity each hydrologic year.
A VATERSMZD MO. Ifl
1036-1*45
Rainfall and runoff of the drainage basin under study have also been discussed in other papers [HOOVER, 1944]. The relationship between
rainfall and runoff corrected for increments to,
or decrements from, ground-water storage for
the hydrologic yearly periods is of interest. The
correction for ground-water storage is simply an
integration of the area under the composite depletion curve of ground-water flow or can be
made more directly by use. of a storage curve after SNYDER [1939]. The result of the regression
analysis made is shown in Figure 1. The x-intercept of the linear equation is noted to be 38.69. In
statement form, it is construed that 38.69 inches
of precipitation represents what is commonly
known to hydrologists as rainfall losses to runoff
for a mean hydrologic year.
Fig. 1--Relation of runoff corrected for storage
Table 2 is a balance sheet of the water cycle
to precipitation for nine hydrologic years
components on watershed 18 for the nine hydro-
BALANCED WATER CYCLE ON WATERSHEDS
423
logic years of record. P is precipitation, RO is runoff, Q is average rate of runoff during the
last day of the hydrologic year, S is storage, and E is evaporation. The dates are the beginning
and end of the hydrologic year. The closing dates are 48 hours after the cessation of the major
storm and are further specified by ground-water well level observations as previously indicated.
Columns 1 and 2 are the total amounts of precipitation and runoff respectively for the periods
noted. Column 3 is the mean dally discharge in cubic feet per second per square mile for the
year-end day, and Column 4 is the change in ground-water storage from one hydrologic year to the
next. Decreases are noted by minus signs. The actual amount of ground water in storage is not
known, and 0.5 csm is used as thfe zero base for the storage curve.
In expanding the primary equation inflow = outflow + storage so as to have more intimate
knowledge of the various factors making up the water cycle,, the form of equation P = RO + S +
E + T + R is commonly used. In keeping running accounts or accounts over a definite period of
time P, RO, E, and T (transpiration) are kept as summations or totals for the period, and S and R
are changes in ground-water storage and retention storage, respectively, from the beginning to the
end of the period. By choosing the hydrologic year as described, the R factor is eliminated since
the soil moisture is at field capacity at the beginning and end of the year. Assuming a yearly T of
17 inches, as has been estimated by HOOVER [1944] based on actual removal of forest vegetation
on an adjacent experimental watershed, E (Column 6) may then be determined being the only unknown remaining in the expanded equation.
Table 2--Balance sheet of nine hvdrologic years. Coweeta watershed 18
Year
(dates inclusive)
Apr. 1,
Mar. 10,
Mar. 25,
Mar. 15,
Apr. 26,
Mar. 26,
Mar. 30,
Mar. 26,
Mar. 11,
1936-Mar. 9, 1937
1937-Mar. 24, 1938
1938 -Mar. 14, 1939
1939-Apr. 25, 1940
1940-Mar. 25, 1941
1941 -Mar. 29, 1942
1942-Mar. 25, 1943
194 3 -Mar. 10, 1944
1944-Mar. 1, 1945
Averages
P
(D
RO
(2)
Q
(3)
S
(4)
RO+S
(5)
E
(6)
in
78.02
64.65
84.52
59.71
51.91
64.12
74.78
68.39
66.36
in
44.33
26.58
47.41
27.60
20.96
24.32
39.61
33.61
33.25
csm
3.99
4.08
8.21
4.31
2.07
5.45
6.72
6.11
3.77
in
0.60
0.16
5.03
-4.66
-3.97
5.70
1.64
-0.74
-3.52
in
44.93
26.74
52.44
22.94
16.99
30.02
41.25
32.87
29.73
in
16.09
20.91
15.08
19.77
17.92
17.10
16.53
18.52
19.63
68.05
33.07
33.10
17.95
Based on field observations, it is known that there are periods during the year other than those
discussed here at which soil moisture reaches field capacity. This is particularly the case when
high rainfall originating from tropical hurricanes occurs during the summer months. Balances
for these periods may be carried in the same manner using that portion of T which occurs in the
period.
At present on the Coweeta Experimental Forest the continuous measurement of soil moisture
for the entire soil profile is being taken at weekly intervals. This may be extended to include
more frequent measurements immediately following storm periods. The lack of such measurements in the past has constituted a serious deficiency in hydrologic data required in the field of
land-use hydrology. Since soil moisture is the basic source of E and T, with the addition of these
now missing data it will be possible to keep more accurate balances for the water cycle components for any period, and the accuracy of stream flow forecasts will be considerably improved.
With this outlook in view, it is evident that this paper is intended as a step towards tightening up
present water balance techniques, and at the same time is in the nature of a status and progress
report of such techniques.
References
HOOVER, M. D., Effect of removal of forest vegetation upon water yields, Trans. Amer. Geophys.
Union, v. 25, pp. 969-977, 1944.
HOUK, I. E., Rainfall and runoff in the Miami Valley, Miami Conservancy District Tech. Rep.,
pt. 8, pp. 134-176, 1921.
424
LIEBERMAN and FLETCHER
[Trans. AGU, V. 28 - 3]
HOYT, W. G., and others, Studies of relations of rainfall and runoff In the United States, Water
Supply Paper 772, U. S. Geol. Surv., pp. 245-255, 1936.
HURSH, C. R., HOOVER, M. D., and FLETCHER, P. W., Studies in the balanced water economy of
experimental drainage areas, Trans. Amer. Geophys. Union, v. 23, pp. 509-517, 1942.
PARKER, P. A. M., The control of water, Geo. Routledge and Sons, Ltd., London, pp. 183-193,
1932.
SNYDER, F. F., A conception of runoff phenomena, Trans. Amer. Geophys. Union, v. 20, pp. 725738 1939
VERMULE, C. C., New Jersey Geol. Surv., v. 3, pp. 11-108, 1894.
Appalachian Forest Experiment Station,
Asheville, North Carolina.
(Manuscript received June 27, 1946; presented at the Twenty-Seventh Annual Meeting,
Washington, D. C., May 29, 1946; open for formal discussion until
November 1, 1947.)