Optimal sustained-yield pumping strategies were developed for the irrigated and industrialized eastern shore of the Great Salt Lake. The combined optimization and simulation model, in which steady-state, finite difference, quasi-three-dimensional ground water flow equations were embedded as constraints, computes the optima,! distribution for sustainable annual ground water pumping rates for alternative scenarios. 1. The model deals with management of a large, multilayer, confined/unconfined (linear/nonlinear) aquifer system. 2. The research can help manage water in the study area where· the demand for water of sufficient quality and quantity is increasing due to urbanization

Peralta, Richard C.

Takahashi, Shu

English

DigitalCommons@USU

\1 ~ GROUND WATER · · IN THE PACIFIC RIM COUNTRIES Proceedings of the Symposium Sponsored by the Irrigation and Drainage Division of the American Society of Civil Engineers Edited by Helen J. Peters Honolulu, Hawaii July 23-25, 1991 ~ Published by the American Society of Civil Engineers 345 East 47th Street New York, New York 10017-2398 ~ ~ () -..1 Optimal Aquifer Planning with Salt Water Boundary Shu ~akahashi1 and Richard C. Peralta2 Abstract Optimal sustained-yield pumping strategies were develOped for the irrigated and industrialized eastern shore of the Great Salt Lake. The combined optimization and simulation inodel, in which steady-state, finite-difference, quasi-three-dimensional ground water flow equations were embedded as constraints, computes the optima,! distribution for sustainable annual ground water pumping rates for alternative scenarios. 1. The model deals with management of a large, mUltilayer, confined/unconfined (linear/nonlinear) aquifer sy~tem. 2. The research can help manage water in the study area where· the demand for water of sufficient quality and quantity is increasing due to urbanization. Tntrodqrt;ioo The East Shore Area is bounded by the Great Salt Lake on the West and the Wasatch Front mountains on the East. It extends from Willard on the north to Farmington on the south. The population of the East Shore Area has tripled with the growth of agriculture, industry, and business during the last 40 years (Price, 1985) . Potentiometric heads in the East Shore Area have declined· for more _than 40 years. The decline ranges from 20 feet on agricultural lands along the shore of the Great Salt Lake to 50 feet in the vicinity of Hill Air Force Base, :where large pumping wells are installed. The decline ~~qa~sed by increasing pumping for M&I use and decreasing -~--~----------------1 Gtad.uate student, Dept. of Agric. and Irrigation Eng., . Utah· Sta·te univ., Logan UT 84322-4105 2 ' A:Ssoc. Prof., Dept. of Agric. and Irrigation Eng., Utah State Univ., Logan UT 84322-4105, (801)750-2785 64 OPTIMAL AQUIFER PLANNING 65 subsurface recharge from lower precipitation along the Wasatch Front. Near the shore of the Great Salt Lake, the potentiometric heads of the aquifer are above the ground surface. On agricultural lands, small-diameter flowing wells installed at relatively shallow depths are used for irrigation, stock, and domestic use. In the urban area along the Wasatch Front, large-diameter pumping wells are installed at greater depths for M&I use (Belke and Waddle, 1972) . The ground water reservoir, consisting of one unconfined and two partially confined aquifers, is expected to be able to meet the increasing demand for water in the East Shore Area (Fig. 1). However, if the ground water is not managed properly, the following problems may result from the declines in potentiometric heads: 1. Pumping costs may increase. 2. Many flowing wells on agricultural lands may not produce the required discharge. 3, Salt or brackish water may intrude from the Great Salt Lake. In this study, an optimization model that simulates the ground water flow was used to develop sustained-yield, ground water management strategies for the area. MpdeJ f'qrmqlatjon This modified version of the USU ground water management model (Gharbi et.al, 1990) consists of: 1. Objective function which maximizes total ground water extraction. where, 9i N maximize z = jt g1 l•l ground-water pumping in a cell i, (L3/T); total number of cells with pumped wells; (1) In the model, discharge, i.e. ground water pumping, is a negative value, and recharge is a positive value. 2. Constraints and bounds to describe the physical system and management desires. The steady-state finite-difference form of the quasi-three-dimensional ground-water flow equation (McDonald and Harbaugh, 1984) is involved in the model as a constraint. CR1, i, j+l/2 (hl, L j+1-h1, !, j) +CR1, i, j-1/2 (hl. i, j-1-h1. i, j) +CC1, !+1/2, :l Ch1, i+l, :~-hl, 1, j) +CC1, 1-112, j (h1, i-i, :l-h1, i,:!) +CV1+1/2, i, j (hl+l,i, j-h1, i, :l) +CV1-112, i, :1 (hl-1.!, :l-h1, i, :1) =g1, ·i, j +qf 1, !, j +qr1, i, j +q91, L j +qd 1, i, j +qc1, i, j +qrd 1, i, j ( 2) GROUND WATER IN THE PACIFIC RIM where, j j j j CRl.i, :l+l/2 "" Zdx:l (T 1, i, :1 T 1, i,j+l) / (T 1, i, :ldy i+l +T 1, !, :1+1 dy i) 1 i i + i ccl,i+l/2,:1 = 2dyi(Tl,i.:ITl,i+l,:ll/(Tl,i,jdx:l+l Tl,i+l,jdx:l) CVl+l/2,!, j""dX:JdYi/ { (dzl/2Kzl,i, :1) + (dzl+1/2Kzl+l,i, j)} 1, i, j =layer, row, and column indices of a finite-difference cell; hl, i, :1 T1, .i, :1 =potentiometric head, (L); =transmissivity of a cell, (L2/T); The transmissivity of unconfined layer 1 is a function of head. Transmissivities of layers 2 and 3 are assumed constant. dz,dy,dx=cell sizes in layer 1, row i, and column j, (L); Kz1, i, j gl,.i, :1 qfl, i,'j =vertical hydraulic conductivity, (L2/T); =pumping rate in a cell, (L3/T); =discharge from flowing wells in a cell, (L3/Tl: = -nfl.i,j (hl,i.:l-hgsl,i,jl for h1,i,j ~ h95 l,i,j "" 0 for h1,i,j < hgsl,i,j where, IJf =coefficient describing reduction in discharge rate of the flowing wells per 1 foot head decline, (L2/T); 'hgs=ground surface, (L); qr1 ,.i, j =known recharge in a cell in the recharge area along the Wasatch Front, including bedrock recharge, unsaturated seepage from the Weber River and Ogden River, canal seepage, precipitation and irrigation seepage, (L3/T); q91, 1,:1 =saturated flow between the aquifer and general boundary head ceils, that is used for estimating diffuse seepage from the aquifer to the Great Salt Lake, (LJ/T); = D<J1,i,:l (hl,.i,:I-Mbl,i.:!l where, m =hydraulic conductance between the aquifer and the general boundary head cell, (L2/T); h<Jb=water level of the Great Salt Lake, (L); qd 1, 1 , :1 =saturated flow leaving the aquifer in a cell with. ,drains, (L3/T); = Od 1, .i,:! {hl, 1, :1 -Bdl, 1,:1) ~ 0 where, Od =hydraulic conductance and drains, (L2/T); for h1,L :1 ~ hdl,i,:l for h 1, 1,:1 < hd1, 1,:1 between the aquifer Bd =Bottom elevation of the drains, (L); ~ ~ ~ . ' OPTIMAL AQUIFER PLANNING 67 qel,i, :1 =distributed discharge from evapotranspiration in a cell, (L3/T); Eo dx;~dYi for h 1 , 1,:1 ~ hs1, 1,j =Eo dXjdydhl,i,j-(h3 1,1,j-del,id) )/del,i,j for h 3 l,Lj-dl,i,j ~ h1.1,:1 < h 3 1,i,j -o for h1,1,j < hsl,i,:l-dl,.i,:l where, Eo =potential evapotranspiration, (L/T); hs =potentiometric surface elevation below which evapotranspiration decreases, (L); de =extinction depth, (L) ; qrd 1 , 1 ,;~:areduction of vertical flow between layer 2 and layer 3 due to partial desaturation of the cell in layer 3, (L3/T); =CV2 ,1. j (EtopJ, 1, :1 -hJ, i, j) ~o (qrd 2, 1, :1=-qrd 3, i, j) for for hJ,i,j 5. hJ, i, j > Etop 3 ,l, j EtopJ, L j where, EtoP3= elevation of the top of layer 3, (L); Bounds on pumping and head are: gLl,i,j ~ gl,i,j ~ gul,i,j and hL1,1,:1 5. h1,1,:1 where, L,U =notations of upper and lower bounds hL1,1, :1= bottom elevation of layer 1 For the confined/unconfined aquifer (linear/nonlinear system), the model has to be rerun (cycled) until variables (heads) do not change with cycle (Gharbi et.al, 1990). The predictive simulation of the USGS (Clark, et al., 1990) used the 1970-1984 average annual recharge rate of 10,700 acre-ft (normal climatic condition) and the 1980-1984 average annual pumping rate of 23,400 acre-ft. Those geohydrologic and pumping data were included in the combined model. Description of scenarios The results of alternative future scenarios were compared. Due to the rapid urbanization in the area over the last 20 years, the demand for M&I water has increased markedly, but demand for irrigation water, which is mainly obtained from the Weber River, has not increased as much as expected. Those trends are expected to continue. For all scenarios, it was assumed to be more important to extract water for M&I than to have flowing wells for agricultural use. Scenario 1 is the no-management option. Optimal sustainable annual ground water pumping rates were computed using the modified USU model for scenarios 2, 3, and 4. Those scenarios were developed using different sets of bounds on withdrawal rate from existing pumping wells . GROUND WATER IN THE PACIFIC RIM Scenario 1: A steady-state predictive simulation estimated the additional water-level declines that would ultimately result from continuing current withdrawals from flowing wells and pumping wells. scenario 2: The ;l.qwer bound on pumping was the current withdrawal rate for all existing pumping wells. For most cells, the upper bound on pumping was twice the current withdrawal rate for existing pumping wells in those cells. In the nine cells that contained u.s. Bureau of Reclamation (USBR) wells, well capacity was the upper bound on pumping. Scenar.io 3: The upper bound on pumping was twice that of scenario 2, except for cells with USBR wells. Other bounds were the same as scenario 2. Scenario 4: The lower bound on pumping was the current wi th<;ir~J.Wal rate for all existing pumping wells. For most cells, the upper bound on pumping was 1.114 cfs (500 gpm) larger t:han in scenarios 2 and 3. In the 13 cells that contained·uSBR and Hill Air Force Base wells, well capacity was the upper bound on pumping. BeSJJJtS Sod Dj SCJJSSion Computed steady-state water budgets of the aquifer are summarized in Table 1. For scenarios 2, 3, and 4, optimal sustainable ground water pumping rates were 126%, 137%, and 193% of the current pumping rate, respectively. Discharges of the flowing wells are 75%, 71%, and 50% of the unmanaged discha-rge rate. Clearly, an increase in pumping in the urban area along the Wasatch~ Front decreases water from flowing wells th~t. is available for agriculture. Table 1 Computed steady-state water budgets of the aquifer Items Scenario 1 Scenario 2 Scenario 3 Scenario 4 Ids) fcf:q lcf:sl !cf:sl A. Recharo:e to the aqidfer 148 148 148 148 B. Di:spharge from the amd fer Pumped wells 32 40 44 62 Flowing wells 42 31 30 21 Evapotranspiration a a a 8 Drain d!'scharge 46 4a 46 40 pi ffnsed 'ili:epage .2..Q. 2..l 2..Q. ll Total HB 148 148 148 ~ ~ ~· OPTIMAL AQUIFER PLANNING L.y.t 1 (tippet l•y.r) ~ .. d ...... i ..._ .... ...,,.._.._........,. ,_ Actloo<OIIwlthorllln....r-r.n Actlft<OII"''~-""""''""""""' Lay.r Z (Middle llyer) m Layer 3 (lower layelj logond _,. ~ .......... -~ ..... ...., .......... ---··---- ... ~_ ..... ""' -.. -...... .-....... -..... ~ Figure 1. Discretization of the East Shore Area 69 GROUND WATER IN THE PAOFIC RIM Summary This paper illustrates the utility of the embedding method in. optimizing sustained-yield planning. Using a modified 'version of the USU management model, optimal sustained-yield strategies were computed for a large, three-layer C!-qul:fer system. Solved problems have about 12,000 single equations & single variables, and about 47,000 non-zero elements. References 1. Belke, K.L., and Waddell K.M., "Groundwater conditions in the East Shore Area, Box Elder, Davis, and Weber counties, Utah, 1960-1969," Technical Publication No. 35,· State of Utah, Department of Natural Resources, Salt ·Lake City, Utah, 1972. 2. Clark, D.w., Appel, C.L., Lambert, P.M., and Puryear R.L., "Ground-water resources and simulated effects of withdrawals in thE East Shore Area of Great Salt Lake, Utah,'' Technical Publication No. 93, State of Utah and United States Geological Survey, Salt Lake City, Utah, 1990. 3. Gharbi, A., Peralta, R.C., and Waddell, K.M., "Modelling for potentiometric surface management of multilayer aquifer systems," International Summer MeBting, Columbus, Ohio, American Society of Agricultural· Engineers, Paper No.90-2060, 1990. 4. McDonald, M.G., and Harbaugh, A. w., 11 A three-dimensional finite difference groundwater model, 11 U.S. Geological Survey. Open File Report 83-875, 1984. 5. Price D., 11 Ground water in utah's densely populated Wasatch Front area- The challenge and the choices," USGS Water-Supply paper 2232, U.S.Geological Survey, Salt Lake City, Utah, 1985. Acknowledgement The authors are grateful to Ali Gharbi for his support and to Andrea Wilson for graphical support. We appreciate the financial support of the Dept. of Agricultural and Irrigation Engineering and Agricultural Experiment Station (approved as paper no. 4125), Utah State University, Logan, UT 84322~4810 and of Nippon Koei, Co.,Ltd. Cooyersjoo t~ 1 cfs = 724.0 acre-ft/yr 1 acre-ft/yr = 1233.4 m3 r. ~ ~ 0. 02832 m'/s Abstract Chloride Sources in a California Coastal Aquifer by John A. Izbicki1 The Oxnard Plain, about 60 miles nonhwest of Los Angeles, is underlain by a complex system of five aquifers that are used for water supply. These aquifers have a total thickness of more than 1,000 feet. On the basis of previous studies, it had been estimated that more than 23 square miles of the Oxnard aquifer (shallowest of the five major aquifers) is intruded by seawater that entered primarily through outcrop areas in submarine canyons near the coast. Water-quality data, including stable-isotope analyses, from more than 40 wells installed as part of this study show that the area affected by seawater intrusion is less than originally believed. The source of elevated chloride concentration, in at least some wells, is leakage of seawater through failed well casings or through abandoned irrigation wells perforated in more than one aquifer. In other wells, irrigation return may be the cause of elevated chloride concentrations. In addition, seawater has intruded deeper aquifers near Hueneme submarine canyon and a brine other than seawater may have invaded deeper aquifers near Point Mugu. Introduction Agencies responsible for management of seawater intrusion on the Oxnard Plain presently use 100 mg/L (milligrams per liter) chloride as the criterion to determine the position of the seawater front. (Chloride concentration in native ground water typically is about40 mg!L.) On the basis of this criterion, iL had been estimated that in 1989 more than 23 square miles of the Oxnard aquifer was intruded by seawater (County of Ventura Public Works Agency, 1990). However, several sources of poor-quality (high chloride concentration) water, other than lateral movement of seawater, contribute chloride at concentrations greater than 100 mg/L to wells. These sources include: irrigation-return water, seawater in overlying contaminated aquifers, and poQr-quality water from deposits that surround and underlie much of the ground-water basin. This paper identifies potential sources of chloride in aquifers of the Oxnard Plain. It is based on preliminary work that is part of tho U.S. Geological Survey's Southern California Regional Aquifer-Systems Analysis. Hydrogeology The Oxnard Plain is about 60 miles northwest of Los Angeles. The 130-square-mile area contains a complex: system of five aquifers that are used for water supply. These aquifers have a total thickness of more than 1,000 feet. The aquifer system is underlain by consolidated marine sediments and volcanic rocks similar to those exposed along the south-east margin of the Oxnard Plain. A shallow unconfined aquifer, which contains relatively 1Hydrologist, U.S. Geological Smvey, 5735 Kearny Villa Road, Suite 0, San Diego, CA 92I23 71 

Optimal Aquifer Planning with Salt Water Boundary

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Optimal Aquifer Planning with Salt Water Boundary

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