USGS Publications Warehouse

Abstract

A hydrologic budget is a statement accounting for the water gains and losses for selected periods in an area. Weekly measurements of precipitation streamflow, surface-water storage, ground-water stage, and soil resistivity were made during a 2year period, April 1, 1950, to March 28, 1952, in the Beaverdam Creek basin, Wicomico County, Md. The hydrologic measurements are summarized in two budgets, a total budget and a ground-water budget, and in supporting tables and graphs. The results of the investigation have some potentially significant applications because they describe a method for determining the annual replenishment of the water supply of a basin and the ways of water disposal under natural conditions. The information helps to determine the 'safe' yield of water in diversion from natural to artificial discharge. The drainage basin of Beaverdam Creek was selected because it appeared to have fewer hydrologic variables than are generally found. However, the methods may prove applicable in many places under a variety of conditions. The measurements are expressed in inches of water over the area of the basin. The equation of the hydrologic cycle is the budget balance: P= R+E+ASW+ delta SW + delta SM + delta GW where P is precipitation; R is runoff; ET is evapotranspiration; delta SW is change in surface-water storage; delta SM is change in soil moisture; and delta GW is change in ground-water storage. In this report 'change' is the final quantity minus the initial quantity and thus is synonymous with 'increase.' Further, ,delta GW= delta H .x Yg, in which delta H is the change in ground-water stage and Yg is the gravity yield, or the specific yield of the sediments as measured during the short periods of declining ground-water levels characteristic of the area. The complex sum of the revised equation P ? R - delta SW ? ET - delta SM, which is equal to delta H. x Yg, has been named the 'infiltration residual'; it is equivalent to ground-water recharge. Two unmeasured, but not entirely unknown, quantities, evapotranspiration, (ET) and gravity yield, (Yg), are included in the equation. They are derived statistically by a method of convergent approximations, one of the contributions of this investigation. On the basis of laboratory analysis, well-field tests, and general information on rates of drainage from saturated sediments, a gravity yield of 14 percent was assumed as a first approximation. The equation was then solved, by weeks, for evapotranspiration, ET. The evapotranspiration losses were plotted against the calendar week. Using the time of year as a control, a smooth curve was fitted to the evapotranspiration data, and modified values of ET were read from the curve. These were used to compute weekly values of the infiltration residual which were plotted against ground-water stage. The slope of the line of best fit gave a closer approximation of gravity yield, Yg. The process was repeated. The approximations converged, so that a fourth and final approximation resulted in a close grouping of all the points along a line whose slope indicated a Yg of 11.0 percent, and a slightly asymmetric bell-shaped curve of total evapotranspiration by weeks was obtained that is considered representative of this area. Check calculations of gravity yield were made during periods of low evapotranspiration and high infiltration, which substantiate the computed average of 11.0 percent. Refinements in the method of deriving the ground-water budget were introduced to supplement the techniques developed by Meinzer and Stearns in the study of the Pomperaug River basin in Connecticut in 1913 and 1916. The hydrologic equation for the ground-water cycle may be written Gr=D + delta H. x Yg + ETg, in which Gr is ground-water recharge (infiltration); D is ground-water drainage; delta H is the change in mean ground-water stage (final stage minus initial stage); Yg is gravity yield (taken as 11.0 percent in computations here); and ETg is ground-water evapotranspiration. The ground-water recharge is derived from the hydrograph of mean water level of the 25 wells, plotted weekly. The ground-water decline during periods of no rain (no recharge) is called a recession curve, and has a characteristic shape. This curve is extrapolated during periods when water levels rise in response to rain, so that the difference between peak stage and extrapolated recessive stage may be determined. This difference, multiplied by the gravity yield, is the ground-water recharge, Gr. The ground-water drainage, D, is calculated from a base-flow rating curve obtained by plotting the average water level in the 25 wells against the base flow obtained from the stream hydrograph. From this curve a close approximation of true weekly base flow was obtained and plotted as ground-water runoff on the stream hydrograph. This method is a second contribution of this investigation to statistical hydrology. The difference between the mean ground-water stage of any two periods, delta H, multiplied by the gravity yield, Yg, gives the net change in ground-water storage. When the final stage is less than the initial stage the difference becomes?delta H. With these factors known, the ground-water equation was solved for ground-water evapotranspiration, ETg. Comparison of ETg and total evapotranspiration, ET was thus possible, for individual periods and on an annual basis. Abundant rainfall and high infiltration rates provide this portion of the Atlantic Coastal Plain with large quantities of ground water, which are discharged about equally by runoff and evapotranspiration. Recovery of water lost to nonbeneficial plants, or by unused streamflow, would permit large expansion of ground-water facilities such as wells, dug ponds, and collection galleries, for irrigation, industry, or municipal supply.