GROUNDWATER SAFE YIELD USING
LOW FLOW FREQUENCY ANALYSIS
Katherine A. Popko
Young S. Yoon
Boyle Engineering Corporation
Presented at the
1983 ASCE National Specialty Conference
March 14-16, 1983
National Water Well Association Western Regional Conference
San Diego, California
October 24-26, 1983
GROUNDWATER SAFE YIELD USING
LOW-FLOW FREQUENCY ANALYSIS
Katherine Ann Popkoi and Young Sub Yoon2
This analysis method was developed for a groundwater availability study in a
rural San Diego County, California, water district. Majestic Pines is a water
district governed by the San Diego County Board of Supervisors. The district
serves Kentwood-in-the-Pines and Whispering Pines, quiet mountain communities
located approximately one mile east of Julian. The customers served by the
district are completely dependent upon groundwater for their water supply.
Lengthy droughts common to most of Southern California occur in this area. If
the basin were pumped at a rate based on standard methods of estimating safe
yield, the groundwater supply could be severely depleted under drought
conditions. Subsequently, groundwater levels could decline below economic
pumping depths. Therefore, a low-flow frequency analysis method was developed
to estimate annual pumpage that would not result in excessive water level
declines during selected droughts. This paper addresses five questions:
What is safe yield?
How is it usually estimated?
Why use low-flow frequency analysis?
How is this method applied?
-- Who should use. this analysis?
IAssociate Civil Engineer, Boyle Engineering Corporation
San Diego, California
2Director of Hydrologic Services, Boyle Engineering Corporation
Safe yield is the quantity of naturally occurring groundwater that can be
withdrawn over the long term without causing undesirable effects on a basin.
These effects are the direct result of lowered groundwater levels caused by
depleting groundwater in storage. Impacts to be avoided can be economic, such
as higher pumping costs and the need to deepen wells or replace pumps. They
can be legal or political, for example, interference with existing water
rights or modification of the groundwater regime in a neighboring basin. And
they can be environmental, such as sinkhole formation, baseflow depletion,
land subsidence, and salt water intrusion.
The term safe yield is currently falling into disfavor because "a never-
changing quantity of available water depending solely on natural water sources
and a specified configuration of wells is essentially meaningless from a
hydrologic standpoint" (Todd, 1980). In other words, there is no number that
will always prevent depletion of groundwater in storage, since hydrologic
conditions and basin management practices continually change. "Safe yield"
recently has been replaced by terms such as "perennial yield," "potential
sustained yield," and "maximum basin yield." But whatever the term, the
concept of a maximum withdrawal allowable without causing undesirable effects
remains the same.
There are many ways to estimate safe yield, but most require a substantial
amount of data. Estimates of safe yield are often based on long-term average
annual recharge if data necessary for other methods are not available.
Recharge can be computed using stream baseflow when suitable records exist.
Where precipitation is the principal source, recharge can be calculated by
considering the natural processes that divert the rainfall before it reaches
the aquifer system. The most important of these are soil moisture retention,
surface runoff, and evapotranspiration. This is a common method of computing
recharge in San Diego County, where few streams are perennial, few streamflow
records are lengthy, and relatively little hydrologic data on individual
basins are available.
When estimating recharge, it must be remembered that all of the water
recharging a basin is not available for pumping. Before it can be tapped by
wells, some groundwater will leave the basin. It will be consumed by
phreatophytes, seep to a river, or flow downgradient to another groundwater
basin. However, in the typical long-term average annual recharge method of
computing safe yield, these losses are not considered. Furthermore, the
effects of drought conditions are not accounted for in this safe yield
analysis method. But drought effects can be significant, because when
recharge becomes negligible, pumpage at rates equivalent to average annual
recharge can severely deplete a basin. Our modified method of estimating safe
yield using low-flow frequency analysis was developed to overcome these
deficiencies in the average annual recharge method.
The first step in this analysis was to calculate recharge expected during
droughts with various return periods and durations. In our study, annual
recharge was calculated for each water year with historical precipitation
records (1906 to 1980). This time span included a lengthy dry period (1959 to
1977) when average annual precipitation was 21 inches, and a wet period (1978
to 1980) when average annual precipitation exceeded 41 inches. Monthly
infiltration was calculated by subtracting monthly runoff and evapotran-
spiration from the sum of monthly precipitation and antecedent soil moisture.
If the infiltration was greater than the soil's water holding capacity,
recharge was calculated as infiltration minus water holding capacity. If
infiltration was less than water holding capacity, recharge was assumed to be
zero. A value of maximum probable monthly recharge was used so recharge would
not be overestimated when rainfall was very high. This value was based on
aquifer effective porosity and maximum probable monthly change in groundwater
levels. Annual recharge for each water year was computed as the sum of
recharge from October to September. A graphical low-flow frequency analysis
method described by Hudson and Roberts (1955) was then applied, using recharge
instead of streamflow. The return period for each value of annual recharge
was calculated using the Weibull formula:
T (n + 1)
T return period (years)
n number of years of record
m order number of events with the lowest event
in the array being order number 1.
Historical extreme values were plotted on extreme probability paper with
recharge on the logarithmic scale, and a straight line was drawn through the
points. As Figure 1 shows, in our results, cumulative groundwater recharge
during the 100-year drought would be about 10 inches for a drought lasting 10
years, and 44 inches for a drought lasting 20 years.
The next step of the analysis was to estimate groundwater level declines that
would occur during selected droughts if given quantities of water were
GROUNaATER RECHARGE FREQUENCY CURVES
FOR DROUGHT PERIODS
2 3 4 5
10 25 50
RETURN PERIOD (YEARS)
withdrawn from the basin. The amount withdrawn could be current pumpage plus
natural outflow, long-term average annual recharge, or some future pumpage
plus natural outflow. In our case, the withdrawal quantity tested was a long-
term average annual recharge of 4.3 inches/year. The 100-year drought was
selected for our return period. A mass curve of recharge versus drought
duration was plotted. The points for that drought were obtained from the
recharge frequency curve. Cumulative withdrawals were then plotted as a
straight line on the mass curve. Figure 2 illustrates our results. The
greatest distance between the line and the curve represents the maximum water
deficiency in inches. This was converted to a groundwater level decline using
effective porosity of the aquifer. As shown in Figure 2, the maximum
groundwater deficiency was 41 inches. This is equivalent to a groundwater
level decline of 230 feet, using an effective porosity of 0.015.
The last step in this analysis was to evaluate the significance of the
resulting groundwater level decline. Of the undesirable economic, legal, and
environmental effects discussed previously, economic considerations were the
most significant in our relatively small and isolated inland basin. We found
a 230-foot decline would be excessive, considering power costs and existing
well depths. After testing other values, a safe yield of 550-acre-feet per
year was determined. This would result in a water level decline of approxi-
mately 120 feet for the 100-year drought. This safe yield was approximately
50Z less than long-term average annual recharge derived from 75 years of
The large difference in safe yield calculated with the average annual recharge
method versus low-flow frequency analysis illustrates the significant impact
MASS CURVE OF GROUNDWATER RECHARGE
OCCURRING ONCE IN 100 YEARS
0 41 1
Z 40 --
5 10 15 20 25
DURATION OF LOW RECHARGE (YEARS)
of drought conditions. Therefore, the low-flow frequency analysis method
should be considered for any basin subject to droughts. This method also has
a flexibility lacking in the average annual recharge method. Many withdrawal
rates can be evaluated quickly, so the impact of varying management practices
can be tested. Also, the hydrologist is not limited to one basin yield that
will supposedly avoid problems. Instead, a range of alternative withdrawal
rates that produce a range of groundwater level declines under a given set of
circumstances can be presented. Then the various members of a management team
can evaluate the impacts and decide on the best policy.
1. Hudson, H.E., Jr., and W.J. Roberts, 1955. 1952-1955 Illinois Drought
with Special Reference to Impounding Reservoir Design. Illinois State
Water Survey Bulletin 43, pp. 25-31.
2. Todd, D.K., 1980. Groundwater Hydrology. John Wiley & Sons, New York,
New York, p. 363.
woLile Enqlneewrn Corporatwon
1501 Quail Street consulting enaUneers I architects
P.O. Box 7350 714/476-3400
- ~Mmpet PasakONA 92658-7350 TeAlx 65561
June 7, 1988
Deborah A. Locklair
*Blain & Cone, P.A.
202 Madison St.
Tampa, FL 33602
Dear Ms. Locklair:
In response to your letter of May 31, enclosed are reprints of the following
Agricultural Master Planning and Water Quality
Cypress Wetlands for Tertiary Treatment
Evaluation of Agricultura Irrigation Projects Using Reclaimed
Modeling for Land Application of Wastewater
Water Conserv II Innovative Solution to Effluent Disposal by
Orlando and Orange County
Water Hyacinths for Wastewater Treatment
Water Resource Management in Orlando, Florida
9 Conjunctive Use of Surface and Ground Waters The California
e Financing of Water Projects
e Groundwater Safe Yield Using Low Flow Frequency Analysis
e Need for a Hydrogeologist During Well Construction
Regional Water Supply and Distribution Planning for Orange County
e Water Availability The Ultimate Development Limitation
It is our intent to offer pertinent technical article reprints in each issue
of Boyle's newsletter. New articles will be offered throughout the year, so
review the reprint list carefully.
Further information on the above subjects is available by contacting Boyle's
Orlando office. Thank you for your interest.
/ YLE E ERING CORPORATION
KathyO s s
cc: K. L. Prime, Boyle/OR