PREDICTING BASE FLOW USING HYDROGEOLOGIC PARAMETERS

WATER RESOURCES BULLETIN VOL. 14, NO. 3 AMERICAN WATER RESOURCES ASSOCIATION JUNE 1978

PREDICTING BASE FLOW USING HYDROGEOLOGIC PARAMETERS'

James W . Naney, Donn G. DeCoursey, Bill B. Barnes, and Gene A. Gander'

ABSTRACT: A method is presented for predicting base flow using easily measured, or estimated, hydrogeologic parameters. A mathematical model based upon the theory of subsurface flow to parallel drains is applied to a small watershed in Oklahoma. An example of model application is presented for a five-year period of record from this small watershed. Three years of data are used to calibrate the model, and two years of data are used for model validation. Hydrographs of observed and predicted base flow are presented for the five-year period of record.

We concluded from this limited application of the model, on a small watershed, that the modeling techniques discussed herein were valid and should be tested for longer time periods on a larger watershed to determine their general applicability. (KEY TERMS: base flow; groundwater; hydrogeologic; model; soil moisture; watershed; parallel drains; transmissivity ; specific yield.)

INTRODUCTION

In most areas of the Great Plains, the climate and geology cause base stream flow regimes, where groundwater depletion provides the entire streamflow for several months each year. Bjorklund and Brown (1957) reported that streamflow of the South Platte River in Colorado and Nebraska was entirely from base flow several months of each year. The Cimarron (Could, 1905) and Washita (Schoof, 1971) Rivers in Oklahoma are maintained by groundwater discharge during low flow periods. Surface water records at 116 low flow measuring stations in Texas and 35 in Oklahoma indicated that many stream flows in the South Central United States are maintained, at least for parts of each year, by the release of groundwater storage.

Groundwater levels reported by the U.S. Geological Survey for the South Central States (Sayre, 1957) showed a general pattern of groundwater flow towards streams in

'Paper No. 77144 of the Wafer Resources Bulletin. Discussions are open until February 1, 1979. Contribution from the Southern Region, Oklahoma-Texas Area, Agricultural Research Service, USDA, Chickasha, Oklahoma, in cooperation with the Oklahoma Agricultural Experiment Station, Stillwater, Oklahoma.

'Naney, Barnes, and Gander, respectively, Geologist, Computer Specialist, and Mathematician, Agricultural Research Service, Chickasha, Oklahoma; DeCoursey, Hydraulic Engineer, USDA Sedi- mentation Laboratory, Oxford, Mississippi.

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Naney, DeCoursey, Barnes, and Gander

the area. Water level data from the South Platte River basin in Colorado and Nebraska also indicated a general effluent stream condition (Bjorkland and Brown, 1957).

Because so many streams in the Great Plains have only groundwater discharge for several months of the year, reasonable prediction of seasonal and total streamflow re- quires a good estimate of this flow. The prediction of groundwater discharge apart from surface flow is also desirable because of differences in their water quality characteristics.

In this paper, models using hydrogeologic parameters were used to predict base flow rates and compare them to those observed on a small agricultural watershed in Oklahoma (Figure 1). Data from existing geologic and topographic maps were used to estimate parameters for the model. Groundwater flow characteristics within the watershed are similar to those discussed above in the Great Plains States; i.e., effluent streams with groundwater profiles similar to subdued topographic profiles.

Figure 1. Location Map of Watershed No. 5142.

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Predicting Base Flow Using Hydrogeologic Parameters

MODEL DEVELOPMENT A model for predicting base flow contribution to stream flow was developed for a

watershed in Pennsylvania (Aron and Borelli, 1973). The model was based on an analogy between seepage toward a stream and drainage toward tile lines using the Dupuit- Forchheimer assumptions, as described by Glover (1 966).

The theoretical basis for the model is illustrated in Figure 2 where h is the drainable fluid depth; H is an initial uniform drainable depth, D is the distance of the drain above the impermeable layer; 2L is the distance between drains; D, is an average depth of saturation; x is the horizontal distance along the flow direction; and hc is the height of drainable fluid midway between the drains. Thus, the model relates the water level h, both temporally, t , and spatially, x, along average flow path lengths, L, the distance from the groundwater divide to the channel, to soil transmissivity, T, Specific yield, Sy, and original groundwater level, H, by the equation:

h(x,t) = - 4 H 5 1 exp [ -‘2n2:t] s i n [ y ]

SY (2L) n n=l,3,5 n

where h(x,t) is the height of the saturated zone at a distance, x, from the channel, at a time, t, after drainage begins.

Aron and Borelli (1 973) showed that by integrating Equation (1) from x = 0 to x = 2L, differentiating the resultant equation for storage with respect to time, and dividing by the original storage, S o , the equation could be expressed as a discharge, q(t), per unit volume placed in storage at time, t = 0.

00

q(t) = 2R2 n=1,3,5 2 exp [-‘2n:R2t]

where

Therefore, flow expressed by Equation (2) is analogous to a unit response of groundwater released from storage to the channel.

They used the expression in this form and obtained a value of R by fitting the expression to a flow record from a 28-day dry weather period on a stream in Pennsylvania. To use the expression in this form an estimate of the amount and timing of recharge to storage must be made. Aron and Borelli, in demonstrating the use of Equation (2), used a hydrograph-separation technique to estimate the volume going into storage and assumed all groundwater entered groundwater storage at midday on those days when storm peaks occurred.

Because we wanted a model that could be used on ungaged watersheds, we needed to (1) eliminate the need for fitting the watershed parameter, R, and (2) find a means of estimating the amount of timing of recharge. The need to fit R was eliminated by using

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L L

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measured or estimated values of L, T , and Sy to relate R directly to watershed characteristics. Values of T and Sy can be obtained from available pump tests or estimated from well drillers’ measurements of well capacity, drawdown, and static water level. Values of L are obtained from topographic maps and observed groundwater levels. The amounts and timing of recharge to the groundwater were calculated by assuming that recharge would take place at a constant rate when soil moisture in the upper four feet of the soil profile exceeds field capacity.

MODEL APPLICATION The technique is best described using an example. Therefore, a small watershed

(Watershed No. 5142 on Spring Creek, a tributary to East Bitter Creek, which is itself a tributary to the Washita River in southwestern Oklahoma) (Figure 1) was selected to calibrate and test the model. Streamflow records for the station are available from 1967 to 1972. The watershed area is 0.569 square miles, with very little alluvium, and the drainage system is characterized by deeply incised channels. Water levels observed in drill holes and observation wells indicated that groundwater levels at the divide were 10 to 15 feet above the water surface in the open channels. At the point where the groundwater table intersects the channels, groundwater flow becomes open channel flow.

First, characteristics of the watershed for estimating the parameter R were obtained. Observed groundwater elevations in the watershed showed the groundwater divide coin- cides with the topographic divide. Therefore, a topographic map of the watershed was used to measure the length of the groundwater flow paths from the boundary of the watershed divide to the channel. The length of each groundwater flow path (L) is shown in Figure 3. Each flow path was assumed to reach halfway to the adjoining flow paths, as shown by the cross hatched area in Figure 3.

The 16 flow paths assumed for Watershed No. 5142 and indicated in Figure 3 were grouped by length into four categories, and an average length was chosen to represent each category. Lengths of the four categories were 350, 1,100, 2,100, and 2,500 feet. Widths represented by the four lengths are segments 1 through 4, respectively (Figure 4). The sum of the products of the length and the respective widths is equal to the drainage area.

The specific yield (Sy) and transmissivity (T) were estimated from a classification of permeability values, by grain-size distribution (Kent, et aL, 1973), and available pump test data (Levings, 1971) along with data available from local well drillers’ logs. Estimated values of 0.002 for Sy, and 12.4 ft2/day for T, were used for the watershed. A unit discharge, q(t), that amount of water contributed from groundwater storage of a 1-inch recharge event over the watershed area was determined for Watershed No. 5142 using Equation (2) for each of the four length categories. A total unit hydrograph for base flow from the watershed, obtained by summing the unit discharges from the four areas, is shown in Figure 5.

To calculate the release from storage using this groundwater unit hydrograph, estimates of the volumes and times of groundwater recharge are needed. These were obtained from a soil-moisture accounting system in which rainfall, evapotranspiration, and deep seepage were balanced. We developed a soil moisture model to determine this balance, following calibration with in si tu data.

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SYALE IN FE5T

0 2000

WATERSHED NO. 5142 EXPLANATION

GROUND- WATER FLOW PATH

ASSIGNED FLOW PATH WIDTH - SURFACE FLOW

- Figure 3. Flow Path Distribution.

W IN THOUSANDS OF FEET

Figure 4. Histogram of Drainage Area at Watershed No. 5142.

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I 10

10 O

10' I

10-2

10-3

K r 4

10-5

10'6

I O - ~

10-8 I 1 I

100 200 300

TIME (DAYS)

Figure 5 . Unit Hydrograph for Watershed No. 5142.

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The model computes a value of soil moisture for each day for two different zones, an upper zone of 6 inches and a lower zone of 42 inches. Each zone's moisture is calculated using a budgeting equation. For the upper zone, the form of the equation is:

where USMitl is the updated soil moisture; USMi is the soil moisture value for the previous day, (P - @At is precipitation minus runoff which occurred since the previous prediction, and CF is capillary movement between zones calculated as a function of the dif- ference in moisture content. CF is either positive or negative, thus indicating direction as well as volume of flow.

The form of the equation is:

CFAt = b(LSMi - USMi) (4)

where LSM is lower zone soil moisture adjusted to inches of water per six inches of soil, USM is upper zone soil moisture adjusted to inches of water per six inches of soil, and the coefficient b is fitted.

Evapotraspiration, ET, is water removed from the soil profile by plant use and direct soil evaporation. An optimum ET demand was determined by fitting the model t o available soil-moisture data. Fifty percent of the total water available for ET was extracted from each of the two zones, based on this criteria. The ET was calculated from the following relation, developed from three years of climatic and soil moisture data:

where TA is mean daily air temperature; Tmin is the minimum temperature at which the plants transpire; Tma, is the maximum temperature, which is likely to occur in the cli- matological record; SR is daily solar radiation in langleys; S b a x is largest SR reading likely to occur; SM is soil moisture from both zones; WP is soil moisture at wilting point; FC is soil moisutre at field capacity; and ETma, is the maximum possible daily ET ab- struction, assuming optimum ET conditions.

We assumed gravitational flow, GF, occurs at moisture values, which exceed field capacity. This yields the flow decay relation:

GF = a(SMi - FC) (6)

where FC is field capacity, and the coefficient, a, is a fitted coefficient, which relates to permeability. The lower zone is budgeted similarly to the upper zone where

LSMitl = LSMi t CF - ET t GFl - GF2 (7)

where GF1 is accretion to the lower zone from upper zone gravity flow, and GF2 is loss from the lower zone due to gravity flow. Then CF2 hecomes the input to groundwater.

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The linearity between recharge to groundwater storage and release from that storage to open channel flow was used as a basis for convolving recharge events with the baseflow-unit hydrograph. These recharge events correspond to gravitational flow from the top four feet of the soil profile and are not at the groundwater surface. However, the vertical distance the water must move (about 90 feet maximum) to intersect the groundwater table is relatively short as compared with the horizontal distance that the water in the saturated zone must travel (over 2,000 feet in many places) to reach the stream channel.

Therefore, water drained from the top four feet of the soil profile by the soil moisture model was considered an instantaneous recharge event at the water table. The mathematical model presented in this study was calibrated using data from the three-year period, January 1968 to December 1970. Initial parameter estimates were generated using 1967 data.

RESULTS The model was validated using two years of record, January 1971 to December 1972.

The calibration, necessary in this study, was to obtain estimates of the two soil moisture model parameters, GF1 and GF2, that determine the rate and timing of groundwater recharge, respectively. The routing of this water through the saturated zone to the channel did not require calibration since the parameters, Sy, T , and L, were obtained from field data.

The base flow hydrograph for the entire period of record far Watershed No. 5142, with the three-year calibration and two-year validation periods used to develop and test the model indicated, is shown in Figure 6. Base flow for the period of record was separated from the total flow hydrograph for Watershed No. 5 142, using a simple hydrograph separation technique (Linsley , Kohler, and Paulhus, 1949). Data collection from Watershed No. 5142 was terminated in January 1973.

LITERATURE CITED

Aron, Gert and John Borrelli, 1973. Stream Baseflow Prediction by Convolution of Antecedent Rain- fall Effects. Water Resources Bulletin 9(2):360-365.

Bjorklund, L. J. and R. F. Brown, 1957. Geology and Water Resources of the Lower Platte River Valley Between Harding, Colorado, and Paxton, Nebraska. U.S. Geological Survey, Water Supply Paper 1378, p. 60.

Glover, Robert E., 1966. Use of Mathematical Models in Drainage Design. Transactions of American Society of Agricultural Engineers, pp. 210-212.

Gould, Charles N., 1905. Geology and Water Resources of Oklahoma. U.S. Geological Survey, Water Supply Paper 148, pp. 90-100.

Kent, D. C., James W. Naney, and Bill B. Barnes, 1973. An Approach to Hydrogeologic Investigations of River Alluvium by the Use of Computerized Data Processing Techniques. Groundwater, ll(4): 3041.

Levings, Gary L., 1971. A Groundwater Reconnaissance Study of the Upper Sugar Creek Watershed, Caddo County, Oklahoma. M. S. Thesis, Oklahoma State University, pp. 24-60.

Linsley, R. K., Jr., M. A. Kohler, and J. L. H. Paulhus, 1949. Applied Hydrology. McGraw-Hill, pp. 398404.

Schoof, R. R., 1971. Southern Great Plains Research Watershed, Annual Reports, 1961-1973. Sayre, A. N., 1957. Water Levels and Artesian Pressures in Observation Wells in the United States,

1955. U.S. Geological Survey, Water Supply Paper 1405, p. 284.

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Sayre, A. N., 1973. Water Resources Data for Oklahoma. U.S. Department of the Interior, Geological

Sayre, A. N., 1973. Water Resources Data for Texas. U.S. Department of the Interior, Geological Survey, Pt. 1 , Surface Water Records, pp. 189-191.

Survey, Pt. 1 , Surface Water Records, pp. 588-600.

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PREDICTING BASE FLOW USING HYDROGEOLOGIC PARAMETERS