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The Economics of Water Management to Reduce Waterlogging
Copyright © IFAC, Water and Related Land Resource Systems Cleveland, Ohio 1980
THE ECONOMICS OF WATER MANAGEMENT TO REDUCE W ATERLOGGING WATERLOGGING IIIl1 s. H. Johnson, 111 Ford Foundation, P. 0, O. Box 11-1096, Nana Post Ojj';ce, Office, Bangkok 11, Thaz'land Thailand
Abstract. Drainage, groundwater withdrawals and altered irrigation practices are among the techniques for reducing waterlogging problems resulting from inefficient water use. However, these corrective measures are often not adopted since the private costs incurred by the individual operator quite often exceed the private benefits. Net social benefits are likely to be positive, so collective action may be appropriate. The overall objective of this paper is to develop devel op an integrated approach combining both economic and physical considerations in order to evaluate possible collective alternative approaches to relieving waterlogging problems. Using survey data from the San Luis Valley, this thi s paper presents a recursive linear programming model that includes both uncertainty and capital constraints. This model incorporates a weekly short-run water allocation model and a simplified water balance model of the groundwater to form a complete simulation model. The model was run using 20 years of historical climatological data to represent the longrun effects of policies which might be undertaken by the water users or by the Colorado State state Engineer. Policy alternatives modeled include: investment in canal lining lining,, total conversion to sprinkler irrigation irrigation,, various restri ctions on groundwater pumpage, and a modified quota-market system. A restrictions comparison of the economic and physical results of these simulated alternatives is made and policy recommendations are suggested. Keywords. Economics; water resources; waterlogging; irrigation; drainage; simulation model; conjunctive use.
IINTRODUCTION NTRODUCTION In areas where irrigated agriculture provides the agrarian base of society, soc i ety , the blessing ble ssing caries with it i t grave responsibilities. On one hand, control of water resources re sources permits the establishment of highly productive agricultural practices and the consequent expansoc i ety in regions where natusion of human society ral rainfall provides either either an inadequate or or an unreliable moisture supply. suppl y . On the other hand, the operation of a complex irrigation system demands certain technological technol ogical and soso cial imperatives which, which , if ignored, may lead to disaster. A high degree of technical and administrative expertise is necessary to operate and maintain a sophisticated water resource system. Where this expertise is i s not available waterlogging--the saturation of soils due to the water table rising into the crop root zone--and salinizat salinization--the i on --the buildup of salts in the soil--is a very real threat that hangs over nearly every irrigated area in the arid parts of the world.
~ormerly at the Department of Economics, ~ormerlY Colorado state State University, Fort Collins, Colorado.
This circumstance c ircumstance has prompted socio-agriculturalists to raise the question of whether irrigated agriculture is in fact a permanent (Gulhati enterprise (G ulhati and Smith, 1967). While historical data may seem to present arguments to the contrary ((Luthin, Luthin, 1957), 1957 ) , there can only be a single answer to the above question. The nation and the world are heavily dependent on irrigated agriculture and, with the current status of world food supplies relative to a growing population, will become more, not less, dependent in the future. Therefore to protect this vital segment of the world's productive capacity, proper drainage works must be provided and a favorable salt balance maintained (Moore, 1972). In the arid west it is usually not too difficult to find an irrigated area that shows symptoms of waterlogging and salt accumulation in the soil. In the state of Colorado alone these symptoms are found in parts of the Grand Valley, the Arkansas Valley, the San Luis· Luis Valley and in sections of the Platte River Valley. For this study the San Luis Valley was selected as the research area, but it should be emphasized that the research methodology applies equally well to any arid area with similar problems.
s.
236
H. Johnson, III
The overall objective of this paper is to present an interdisciplinary simulation model (incorporating engineering, agronomy and resource economics) to the optimal management of irrigation water in order to minimize waterlogging and salinization and to improve water-use efficiency (Johnson, 1975). 1975 ) . The farmers in the San Luis Valley are aware of the dangers of these problems but to date have not had the data or the analytical tools to analyze the economic implications of alternative solutions. The model developed here provides the analytical tool to simulate many different strategies and the results of these simulation runs provide the local planners ner s both economic and physical data with which to measure the tradeoffs between different alternatives. CONDITIONS LEADING TO MARKET FAILURE The San Luis Valley is a large, relatively flat area located in the highlands of south central Colorado. The climate is that of a high mountain desert with an average annual precipitation of approximately 200 millimeterse ter s . The desert climate and the short growing season of 90-120 days makes irrigation essential for agricultural production. The area of the San Luis Valley Valley selected for this lie s within a closed basin which is research lies north of the Rio Grande River and is separated from the Rio Grande drainage by a low alluvial divide. This closed basin covers an 7 ,6 15 square sQuare kilometers. area of about 7,615 Gr oundwater in the Closed Basin occurs in two Groundwater aquifers--confined aQuifers--confined and unconfined. The unaQuifer is relatively shallow (less confined aquifer than 61 meters) and occurs nearly everywhere in the Closed Basin. The confined or artesian aquifer aQuifer is quite Quite deep (up to 3,048 meters ) and occurs under nearly one-half of meters) Valley . The aquifers aQuifers are sepathe San Luis Valley. rated r ated by a clay layer layer or or an upper layer of volcanic rock r ock (Emery, (Emery , Snipes and Dumeyer, 1972) . Following Foll owi ng the completion of the major irrigation canals in the later 1880's, 1880 's, farmers of north European stock came to settle in the San Luis Valley especially especiall y the area north of the Rio Grande River. T. T . C. Henry sought to repeat the successes with with wheat that he had had in Kansas. Kansas . Beginning operation in the spring of 1884, 1884 , he planted great fields. His North Farm located l ocated ten kilometers north of Monte Vista contained 2,833 2 , 833 hectares. His neighbors nei ghbors soon followed. Spring wheat and oats became the crops of the northern valley (Smiley, (Smiley , 1913). To irrigate their fields the farmers developed a unique uniQue system of irrig,irrig~ tion known as sub-irrigation. This involved bringing the groundwater table within 500750 millimeters of the ground surface by massive applications of surface water during the spring runoff and by maintaining the groundwater water by small flows in sub-ditches (Hafen,
1948). However, while good, this method soon logged lower lands and of many farms (Tipton, (Tipton , of
the early results were. were ~ resulted in watereventual abandonment 1939) . 1939).
Drainage by community effort started but, while relieving local problems, these systems contributed to down gradient waterlogging and simply served to pass problems on to other a areas. A number of proposals for a main outlet drain to Closed t o carry water from the Cl osed Basin to the river have been discussed with w the latest project proposed by the U. S. S. Bureau of Reclamation being a series of well w fields directly in the sump area of the (U .S . House of Representatives, Closed Basin (U.S. 1970 ) . These wells would pump the t he poor quaQua1970). lity groundwater and then gravity flow it into a mixing lake where once the Quality quality was acceptable it would be released into the Rio Grande River as part of Colorado's Colorado 's Rio Grande reQuirement (Radosevich (Radose vi ch and Hamburg, Compact requirement 1971) . Since the U.S. Bureau proposal is not acceptable to all farmers and it is not at all certain to be funded, the farmers in the valley alternatives. are exploring other al ternatives . The large scale diversions from the Rio Grande River into a hydrologically closed basin combined with the use of sub-irrigation as well as the large scale development of deep artesian wells have created the waterlogged conditions. Local drainage projects and the recent expansion of shallow wells have served to reduce the problem in some areas but the valley still is lacking a systematic approach to an overall solution. solution . The recent introduction of center pivot sprinklers pumping out of the shallow aquifer aQuifer creates a situation situati on where a few operators are overdrafting the aQuifer while the majority are over-irrigaaquifer ting and contributing to the waterlogging conditions in the valley. These problems ve themselves within the conwill not resol resolve text of an unregulated enterprise system and therefore require reQuire some collective action (Eckstein, (Eckstei n , 1958). 1958) . Economic arguments that pure competition leads to an optimal opti mal allocation of resources are contigent upon no external effects (Baumol, 1969). 1969) . Where these externalities exist, particularly 'technolo' technological' externalities (Viner, 1932) as in the case of individual farms using a 'common' common pool', individual decisions do not account for all the effects of the decision (Bower, 1963) . Hirshleifer, De Haven and Milliman Milliman (1969) ( 1969) have developed an excellent analysis of alternative economic solutions to this 'commonpool' problem. Three solutions that assure decisions made will meet the criteria cri teria of allocative efficiency are: (1) ( 1) centralized decision making; (2) assignment of ~ ~ production rights or Quotas; quotas; and (3) imposii mposition of use taxes. The interested reader should refer to their discussion for the relative merits of these three alternatives,
The Economics of Water Management
but primarily due to the relative ease of administration of a quota system a modified form of groundwater pumping quotas and aquifer management was selected. This solution goes to the heart of the commonality problem; it replaces common rights with specificity of shares. The present value of net economic return is used as the criterion for comparing a variety of quota and mixed systems.
BASIC f-l0DEL HODEL The analytic tool used in the allocation models is linear programming (LP) but in order to provide an algorithm that captures the multi-stage aspects of the irrigation season, the model uses sequential linear programming (SLP). SLP is defined by de Lucia (1969) as a series of linked LP models where the LP coefficient matrix for each decision review period of the growing year depends on the solution of the LP problem of the preceding period and exogenous inputs. However, before the SLP model can begin its optimization runs it is necessary to establish an initial planted area for each farm for each year of the twenty-year simulation period. This is accomplished by using separate LP planning models. The model used is based on Shackle's (1955) concept of focus-loss focusgain which is similar to the idea of safetyfirst constraints proposed by Roy (1952). The essence of this concept is the assumption that the decision-maker wishes to maximize his expected gain as long as the probability or possibility of obtaining some critically low value of total gross margin is so small it can be ignored. Shackle, while further elaborating his focus-loss focus-gain concept
237
in a series of essays, did not really attempt to develop this concept into a practical tool. However, Boussard (1971) and Boussard and Petit (1967) have developed a method of taking uncertainty into account when representing farmers' production decisions. Their methodological approach is based on the assumption that farmers choose, among various possible actions, the one which will maximize the expected gain, provided the possibility of ruin is so small that it can be neglected. This decision criterion requires that the term 'a negligible possibility of ruin' be definable in a practical and a mathematical sense. Boussard and Petit (1967) and Kennedy and Francisco (1974) have defined ruin in terms of minimum income required to cover all unavailable expenses. Where Pi is a focus of loss for each of n crops, (LOSS) is total permitted loss, (MINI) is income indispensable for consumption and (STBO) is short-term borrowing, the focus-loss constraint equations can be written as:
< 0 (i=l, 2, ... , n) where P.X. - l/n (LOSS) -~ J. J. 1
1
LOSS < ~E C.X. - MINI - STBO (i=l, 2, ... , n) --
i lJ. l J. i
or rearranging ~ E
C.X. - LOSS - STBO = MINI (i=l, 2, ... , n)
i i lJ. lJ.
Using the focus-loss concept as a constraint it is thus possible to formulate the decision making process under uncertainty in a linear programming ' context. A schematic represenprogramming'context. tation of one of the planning models is shown in Table 1.
TABLE 1 Representative Matrix for Planning Model
Constraint Types
Crop Activities Xl·········· .X .Xn n
Maximum Acreage Available
1.0
Water Balance
a1 1*
... ,. I. 1.0 ....... ........ aann
Maximum Ditch Water
Water Activity (Ditch) (Di tch) (Well) (Well ) X + X Xn+l Xn+2 n 1 n +2
-1.0 1.0
Capital (FUND (FUND))
Objective Function (max.)
-1.0
P 1** · Pt*·
-l/n p P
Constraints
Minimum Income (MINI)
LOSS X Xn+4 n +4
1.0
Maximum Well Water Focus-Loss
STBO X Xn+J n +3
-l/n
n
b n
b *** 1 c *** 1
c
e *** n
e
n
-dn+l**** -dn +2
n
-dn + 1
-dn +2
-1.0 -1.0 -h
*Water is in units of acre feet. **Focus-loss is in units of dollars per acre. ***Capital, income and objective function are in units of dollars per acre. ****Water prices are in dollars per acre foot.
-1.0
s. S.
238
H. Johnson, III
lation losses, rainfall recharge, upward leakages from the confined aquifer and mountain runoff. The water leaves the aquifer by groundwater pumping and beneficial and non·beneficial evapotranspiration. The sum of the water moving into the unconfined aquifer and the water moving out of the unconfined aquifer is recorded for each season and used to calculate the change in the aggregate water table level over the Closed Basin. Johnson (1975), Appendix E, provides the mathematical relationships and the assumptions upon which this model is based.
Once the planning model for each area has been optimized based on the 'estimated' annual water available for that area, the solution values (i.e., planted acreage for each crop) are passed to the water allocation initial acreage constraints for model as the 1nitial that year. Due to the fact that the productivity of any crop varies throughout the growing season and depends, in large part, on the irrigation regime followed (Flinn and Musgrave, 1967), it was also necessary to incorporate into the SLP algorithm a method of relating moisture stress to plant yield (Martin and Young, 1967). The technique used is a simplified version of the 'stress day index' developed Hller and Clark (1971) and thus is quite by Hiler similar to models used by Anderson and Maass (1971) and by Young and Bredehoeft (1972) in that it assumes the crop yield to be diminished by a specific percent if the crop requires water but is not irrigated during that time period.
usa usd
SIMULATION OF ALTERNATIVE STRATEGIES
alloca-coare, The planning models are linked to the alloca-coarec tion models as well as to the hydrologic mo- moondel representing the groundwater to form a complete simulation tool. The planted areas alloc, alloc, from the planning model are passed as conccstraints to the allocation model which is run-h ru in a sequential manner to optimally allocate alloc the available surface and groundwater to the a to crops for each two-week period during the ste~ irrigation season. Table 3 provides a step step chart of the simulation model.
The percentage of decrement in yield as a result of water deficit is indicated by the crop susceptibility factor (CS) which is both a function of the plant species and the stage of growth of the plant. Table 2 presents the CS values used in the allocation model.
thsen The simulation model was used to represent theen the economic and hydrologic effects for the admit selanj entire Closed Basin over a 20-year planning selani period of activities taken either by the the agricultural water users or policies adminis~nin~ adminis~nin@ tered by the Colorado State Engineer. Acti-the vities that were modeled to represent self- Acticontrol actions by the water users include: self(1) status ~ under 1974 conditions; (2) (3) normal increase of sprinkler irrigation; (3) 3) selective canal lining; (4) conversion to (3) almost total sprinkler irrigation; and (5) axquasi-market quota system which allows ex-
The final model represents the unconfined aquifer. Eventually the water management model will be combined with a sophisticated hydrologic (mathematical) model developed on a grid point system in order to pinpoint changes in water table depth, but the present simplified hydrologic model treats the unconfined aquifer as a single reservoir and keeps track of the water entering and leaving this aquifer. The water enters the aquifer as leakage from canals and streams, deep perco-
TABLE 2 Crop CroE Susceptibility SusceEtibilitl Values Used in the Model (Percentage Yield Reduction in Different Time Periods) . -JI..-
Dates
Apr. 1-15
Apr. May 16-30 1-15
Barley One Stress Two Stress Three Stress Four Stress S-tress Potatoes One Stress Two Stress Three Stress Four Stress Alfalfa One Stress Grass Hay One Stress
.10
May June 16-31 1-15
June July 16-30 1-15
July Aug. 16-31 1-15
Aug. Sept. Sept. 16-311-15 16-31 1-15 16-30
.03
.07 .02
.10 .02 .08 .02
.25 .07 .07 .02
.22 .07 .04 .02
.20 .06
.05
.05
.06 .02
.10 .04
.15 .04 .04 .02
.15 .05 .05 .03
.23 .08 .07 .03
.23 .08 ,07 .03
.23 .08 .07 .03
.20 .07 .07 .02
.06 .04
.10
.15
.15
.20
.25
.25
.25
.20
.20
.10
.10
.10
.15
.20
.25
.25
.25
.20
.10
.10
Sept. 16-30
.10
.10
The Economics of Water Management
TABLE)
CA] [A]
steps for Simulation Model
Read all objective function values, water application rates, parameters for planning models.
[BJ Read 'estimated' hydrologic data for [B] determining planting acreage in each subarea.
[CJ
Compute crop acreages for subarea i.
[DJ [DJ
Check to see that planted acreage for all subareas has been calculated; if [CJ until all have been not, return to [C] calculated.
[E] [EJ
Read hydrologic data for all 1) allocation periods.
[FJ
Read groundwater level; determine which application rate to follow.
[GJ
Compare crop water demand to total of available water.
[HJ
If sum of supply exceeds demand, irrigate all crops and record water used.
[IJ
If demand exceeds supply, call allocation model to maximize net returns with available water; record water used.
[J] Check to see if all irrigation activities for all subareas for 1) time periods have been calculated; if not complete, return to [F] [FJ until complete.
[KJ [K]
Compute the gross margin for each area.
[LJ
Record the gross margin and water used for all subareas.
[MJ
Check to see if 20 years have been completed; if not, return to [B] [BJ until complete.
[NJ ~J
Discount the returns for each year to present value; record present values.
[oJ
Secord ~ecord water used for 20 years.
[p] [pJ
Determine change in water table depth as a result of 20 years of operation.
change of surplus water. Activities modeled poliCies implemented by the to represent policies Colorado State Engineer include: (1) restrictions on number of days per week water users can pump their wells and (2) the implementation of a strict quota (one acre-foot per acre) on groundwater pumping. The results of the simulation runs are summarized in Table 4. These results consistently indicate that policies which could be implemented by the water users themselves in conjunction with a groundwater augmentation organization as compared to the policy op-
239
tions open to the State Engineer would not only significantly increase economic returns to the water users but would also reduce the waterlogging and salinity problems. This results from the increased water use efficiency of the sprinklers which significantly reduce the water returning to the aquifer as a result of deep percolation losses or canal leakage losses. The sprinklers also provide an excellent method for leaching the salts out of the root zone and hence reclaiming salinized land. POLICY IMPLICATIONS The simulated economic benefits associated with scenarios based on private initiative and self-discipline by the water users are, in every case, superior to rules and regulations implemented and enforced by the Colorado State Engineer. It is thus in the best interests of the Closed Basin water users to develop their own water management system in a manner that allows them to manage the unconfined aquifer such that in wet years the aquifer is recharged by nature and in dry years the aquifer would be artificially recharged. Any excess river water (Closed Basin Rio Grande River water rights) would be leased out in the valley or traded to the State of Colorado for augmentation. In dry years the water should be used to maintain the aquifer level. The Colorado State Engineer is vested with statutory authority for the administration of the water resources of the State. As long as the private policies of the Closed Basin water users do not conflict with the statutory obligations of the State Engineer, the water users are not affected by the powers of the State. Since a policy that permits a loosely controlled system for the management of the water resources of the Closed Basin is superior to a structured system of rules and regulations, it is in the interest of the water users to cooperate with the state State Engineer to avoid legal conflict between public and private interests. An aquifer management plan plus a restriction on development of new irrigated land in the Closed Basin will provide sufficient excess water so that the Closed Basin water users will not be in conflict with the State Engineer but will even be in a position to help other water users or reduce the compact debt. The relationship between the Rio Grande River and the underground storage system directly connects the private actions of the groundwater users to other water users in the San Luis Valley and along the entire northern Rio Grande River. Thus the effects of private economic decisions become public policy and hence the Closed Basin water users must work directly with the state State Engineer and other Rio Grande River water users to insure maximum benefits for all.
240
S. H. Johnson, Johnson , III
TABLE 4
Summary of the Seven Simulation Runs, Runs I Closed Basin Valley , Colorado Color ado 1974-1994 San Luis Valley,
Si mulati on Run Simulation Characteri sti cs Characteristics
Present Pr esent Value of Economic a Returns
II
Status quo (1974) conditions condi tions
$182,432,489 $182 , 432 , 489
7536
11 II
Change to sprinklers spr inkl er s followi ng past trend t r end following
$187 , 742 ,677 $187,742,677
7202
+ 0.24
III 111
s prinkler s and Change to sprinklers sel ected canals line selected
$186,177,421 $186 , 177 , 421
6548
+ 0.94 0 . 94
IV IV
totall y to Change almost totally s prinkl er s sprinklers
$215 , 887 , 694 $215,887,694
6321
2 .53 - 2.53 3 . 04 - 3.04
V V
Simulate r estricti ons on Si mulate restrictions gr oundwater pumping pumpi ng CC groundwater
$185,348,064 $185 , 348 , 064 $177 , 39 1, 196 $177,391,196 $169 , 812 , 794 $169,812,794 $151 , 023 , 764 $151,023,764
6766 6139 5380 4231
+ 0.58 0 .58 + 0.91 1 . 37 + 1.37 2 . 07 + 2.07
$133,002,764 $133 , 002 , 764
3080
+ 1.92
d $177 , 774 , 140 140d $177,774,
6556
0 .61 + 0.61
Case
- It
-,~
. ~1.
VI
Ope~te O pe~te under under strict
Total Groundwater Pumped (million cubic meters)
Water Change in Water Table Level (meters)b
pumping quota
VII VII
Quota but can purchase addi t i onal water water additional
~conomic ~ conomi c return r eturn over over a twenty year time period per iod discounted to present value at
8%. 8% .
bC hange in i n water water table tabl e level l evel is based on change in head between the confined and bChange unconfi ned aquifers. aquifer s . Plus Pl us (+) indicates an upward rise r ise in water table level. level . unconfined ( - ) indicates i ndicates a downward drop in water water table level. level . Mi nus (-) Minus pumpi ng limit, limit , respectively. r espectively . 4 , 3, 3 , and 2 day per per week pumping c 5 , 4,
~conomic returns ~conomic r eturns for fo r case VII includes i ncl udes $1,943,569 $1 , 943 , 569 rebate to water users for gr oundwater not pumped. pumped . groundwater REFERENCES
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The Economics of Water Management
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(Ed . ) (1957). (1957) . Drainage Dr ainage of Luthin, J.N. (Ed.) No . 7. 7. Agricultural Land, Monograph No. American Society of Agronomy, Agronomy , Madison. Madison . Martin , W. and R.A. R. A. Young (1967). (1967) . Modeling Martin, production response relations for irrigation water: water : review and implications. implications . Mimeographed paper presented to the WesWes tern Agricultural Economics Research Council , December 1967. 1967 . University of Council, Arizona, Arizona , Tuscon. Tuscon . Moore, Moor e , C.V. C. V. (1972). (1972) . On the necessary and sufficient conditions for a long-term Water Resources irrigated agriculture agriculture.. Water Bull. , 8, 802-812. 802-812 . Bull., Radosevich,-G.E. and D.H. Hamburg (1971). (1971) . Laws , Compacts, Compacts , Treaties Tr eaties Colorado Water Laws,
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Shackle, (1955).. Uncertainty in Shackle , G.L.S. G.L. S . (1955) Economics, Economi cs , and Other Other Reflections. Ref lections . Cambridge bri dge University Univer s ity Press, Pr ess , Cambridge. Smiley , J.C. J.C . (1913). (1913) . Semi-Centennial HisSmiley, tory of the State of Colorado, Col orado , Vol. Vol . 1. Lewis Publishing Publi shi ng Company, Company , New York. Yor k . Tipton , R.J. R. J . (1939). (1939) . San Luis Valley ProPr oTipton, ject: Wagon Wheel Gap Reservoir, Reser voir , Platoro Plator o Reservoir, Mogote Reservoir, Re ser voir, Closed Basin Drain, Drain , Vol. 1. 1 . Colorado Col orado Water Conservation Board, Denver. U.S. U.S . House of Representatives Repr esentati ves (1970). ( 1970) . Closed Basin Division, Division , San Luis Valley Pro~ Pro~ Colorado, 91-369. Col or ado , House Document No. No . 91 -369 . U.S. U.S . Government Gover nment Printing Office, Washington, D.C. Viner, J. J . ((1932). 1932) . Cost curves and supply curves. curves . Zeit. Zeit . Nationalokonomie. Nati onal okonomie. Young , R.A. and J.D. J .D. Bredehoeft Bredehoeft (1972). ( 1972) . Young, Digital Di gital computer simulation simUlation for solving pr oblems of conjunctive management problems groundwater gr oundwater and surface water systems. systems . Water Res. , ~, ~ , 533-556. Water Resources Res.,
THE ECONOMICS OF WATER MANAGEMENT TO REDUCE W ATERLOGGING WATERLOGGING IIIl1 s. H. Johnson, 111 Ford Foundation, P. 0, O. Box 11-1096, Nana Post Ojj';ce, Office, Bangkok 11, Thaz'land Thailand
Abstract. Drainage, groundwater withdrawals and altered irrigation practices are among the techniques for reducing waterlogging problems resulting from inefficient water use. However, these corrective measures are often not adopted since the private costs incurred by the individual operator quite often exceed the private benefits. Net social benefits are likely to be positive, so collective action may be appropriate. The overall objective of this paper is to develop devel op an integrated approach combining both economic and physical considerations in order to evaluate possible collective alternative approaches to relieving waterlogging problems. Using survey data from the San Luis Valley, this thi s paper presents a recursive linear programming model that includes both uncertainty and capital constraints. This model incorporates a weekly short-run water allocation model and a simplified water balance model of the groundwater to form a complete simulation model. The model was run using 20 years of historical climatological data to represent the longrun effects of policies which might be undertaken by the water users or by the Colorado State state Engineer. Policy alternatives modeled include: investment in canal lining lining,, total conversion to sprinkler irrigation irrigation,, various restri ctions on groundwater pumpage, and a modified quota-market system. A restrictions comparison of the economic and physical results of these simulated alternatives is made and policy recommendations are suggested. Keywords. Economics; water resources; waterlogging; irrigation; drainage; simulation model; conjunctive use.
IINTRODUCTION NTRODUCTION In areas where irrigated agriculture provides the agrarian base of society, soc i ety , the blessing ble ssing caries with it i t grave responsibilities. On one hand, control of water resources re sources permits the establishment of highly productive agricultural practices and the consequent expansoc i ety in regions where natusion of human society ral rainfall provides either either an inadequate or or an unreliable moisture supply. suppl y . On the other hand, the operation of a complex irrigation system demands certain technological technol ogical and soso cial imperatives which, which , if ignored, may lead to disaster. A high degree of technical and administrative expertise is necessary to operate and maintain a sophisticated water resource system. Where this expertise is i s not available waterlogging--the saturation of soils due to the water table rising into the crop root zone--and salinizat salinization--the i on --the buildup of salts in the soil--is a very real threat that hangs over nearly every irrigated area in the arid parts of the world.
~ormerly at the Department of Economics, ~ormerlY Colorado state State University, Fort Collins, Colorado.
This circumstance c ircumstance has prompted socio-agriculturalists to raise the question of whether irrigated agriculture is in fact a permanent (Gulhati enterprise (G ulhati and Smith, 1967). While historical data may seem to present arguments to the contrary ((Luthin, Luthin, 1957), 1957 ) , there can only be a single answer to the above question. The nation and the world are heavily dependent on irrigated agriculture and, with the current status of world food supplies relative to a growing population, will become more, not less, dependent in the future. Therefore to protect this vital segment of the world's productive capacity, proper drainage works must be provided and a favorable salt balance maintained (Moore, 1972). In the arid west it is usually not too difficult to find an irrigated area that shows symptoms of waterlogging and salt accumulation in the soil. In the state of Colorado alone these symptoms are found in parts of the Grand Valley, the Arkansas Valley, the San Luis· Luis Valley and in sections of the Platte River Valley. For this study the San Luis Valley was selected as the research area, but it should be emphasized that the research methodology applies equally well to any arid area with similar problems.
s.
236
H. Johnson, III
The overall objective of this paper is to present an interdisciplinary simulation model (incorporating engineering, agronomy and resource economics) to the optimal management of irrigation water in order to minimize waterlogging and salinization and to improve water-use efficiency (Johnson, 1975). 1975 ) . The farmers in the San Luis Valley are aware of the dangers of these problems but to date have not had the data or the analytical tools to analyze the economic implications of alternative solutions. The model developed here provides the analytical tool to simulate many different strategies and the results of these simulation runs provide the local planners ner s both economic and physical data with which to measure the tradeoffs between different alternatives. CONDITIONS LEADING TO MARKET FAILURE The San Luis Valley is a large, relatively flat area located in the highlands of south central Colorado. The climate is that of a high mountain desert with an average annual precipitation of approximately 200 millimeterse ter s . The desert climate and the short growing season of 90-120 days makes irrigation essential for agricultural production. The area of the San Luis Valley Valley selected for this lie s within a closed basin which is research lies north of the Rio Grande River and is separated from the Rio Grande drainage by a low alluvial divide. This closed basin covers an 7 ,6 15 square sQuare kilometers. area of about 7,615 Gr oundwater in the Closed Basin occurs in two Groundwater aquifers--confined aQuifers--confined and unconfined. The unaQuifer is relatively shallow (less confined aquifer than 61 meters) and occurs nearly everywhere in the Closed Basin. The confined or artesian aquifer aQuifer is quite Quite deep (up to 3,048 meters ) and occurs under nearly one-half of meters) Valley . The aquifers aQuifers are sepathe San Luis Valley. rated r ated by a clay layer layer or or an upper layer of volcanic rock r ock (Emery, (Emery , Snipes and Dumeyer, 1972) . Following Foll owi ng the completion of the major irrigation canals in the later 1880's, 1880 's, farmers of north European stock came to settle in the San Luis Valley especially especiall y the area north of the Rio Grande River. T. T . C. Henry sought to repeat the successes with with wheat that he had had in Kansas. Kansas . Beginning operation in the spring of 1884, 1884 , he planted great fields. His North Farm located l ocated ten kilometers north of Monte Vista contained 2,833 2 , 833 hectares. His neighbors nei ghbors soon followed. Spring wheat and oats became the crops of the northern valley (Smiley, (Smiley , 1913). To irrigate their fields the farmers developed a unique uniQue system of irrig,irrig~ tion known as sub-irrigation. This involved bringing the groundwater table within 500750 millimeters of the ground surface by massive applications of surface water during the spring runoff and by maintaining the groundwater water by small flows in sub-ditches (Hafen,
1948). However, while good, this method soon logged lower lands and of many farms (Tipton, (Tipton , of
the early results were. were ~ resulted in watereventual abandonment 1939) . 1939).
Drainage by community effort started but, while relieving local problems, these systems contributed to down gradient waterlogging and simply served to pass problems on to other a areas. A number of proposals for a main outlet drain to Closed t o carry water from the Cl osed Basin to the river have been discussed with w the latest project proposed by the U. S. S. Bureau of Reclamation being a series of well w fields directly in the sump area of the (U .S . House of Representatives, Closed Basin (U.S. 1970 ) . These wells would pump the t he poor quaQua1970). lity groundwater and then gravity flow it into a mixing lake where once the Quality quality was acceptable it would be released into the Rio Grande River as part of Colorado's Colorado 's Rio Grande reQuirement (Radosevich (Radose vi ch and Hamburg, Compact requirement 1971) . Since the U.S. Bureau proposal is not acceptable to all farmers and it is not at all certain to be funded, the farmers in the valley alternatives. are exploring other al ternatives . The large scale diversions from the Rio Grande River into a hydrologically closed basin combined with the use of sub-irrigation as well as the large scale development of deep artesian wells have created the waterlogged conditions. Local drainage projects and the recent expansion of shallow wells have served to reduce the problem in some areas but the valley still is lacking a systematic approach to an overall solution. solution . The recent introduction of center pivot sprinklers pumping out of the shallow aquifer aQuifer creates a situation situati on where a few operators are overdrafting the aQuifer while the majority are over-irrigaaquifer ting and contributing to the waterlogging conditions in the valley. These problems ve themselves within the conwill not resol resolve text of an unregulated enterprise system and therefore require reQuire some collective action (Eckstein, (Eckstei n , 1958). 1958) . Economic arguments that pure competition leads to an optimal opti mal allocation of resources are contigent upon no external effects (Baumol, 1969). 1969) . Where these externalities exist, particularly 'technolo' technological' externalities (Viner, 1932) as in the case of individual farms using a 'common' common pool', individual decisions do not account for all the effects of the decision (Bower, 1963) . Hirshleifer, De Haven and Milliman Milliman (1969) ( 1969) have developed an excellent analysis of alternative economic solutions to this 'commonpool' problem. Three solutions that assure decisions made will meet the criteria cri teria of allocative efficiency are: (1) ( 1) centralized decision making; (2) assignment of ~ ~ production rights or Quotas; quotas; and (3) imposii mposition of use taxes. The interested reader should refer to their discussion for the relative merits of these three alternatives,
The Economics of Water Management
but primarily due to the relative ease of administration of a quota system a modified form of groundwater pumping quotas and aquifer management was selected. This solution goes to the heart of the commonality problem; it replaces common rights with specificity of shares. The present value of net economic return is used as the criterion for comparing a variety of quota and mixed systems.
BASIC f-l0DEL HODEL The analytic tool used in the allocation models is linear programming (LP) but in order to provide an algorithm that captures the multi-stage aspects of the irrigation season, the model uses sequential linear programming (SLP). SLP is defined by de Lucia (1969) as a series of linked LP models where the LP coefficient matrix for each decision review period of the growing year depends on the solution of the LP problem of the preceding period and exogenous inputs. However, before the SLP model can begin its optimization runs it is necessary to establish an initial planted area for each farm for each year of the twenty-year simulation period. This is accomplished by using separate LP planning models. The model used is based on Shackle's (1955) concept of focus-loss focusgain which is similar to the idea of safetyfirst constraints proposed by Roy (1952). The essence of this concept is the assumption that the decision-maker wishes to maximize his expected gain as long as the probability or possibility of obtaining some critically low value of total gross margin is so small it can be ignored. Shackle, while further elaborating his focus-loss focus-gain concept
237
in a series of essays, did not really attempt to develop this concept into a practical tool. However, Boussard (1971) and Boussard and Petit (1967) have developed a method of taking uncertainty into account when representing farmers' production decisions. Their methodological approach is based on the assumption that farmers choose, among various possible actions, the one which will maximize the expected gain, provided the possibility of ruin is so small that it can be neglected. This decision criterion requires that the term 'a negligible possibility of ruin' be definable in a practical and a mathematical sense. Boussard and Petit (1967) and Kennedy and Francisco (1974) have defined ruin in terms of minimum income required to cover all unavailable expenses. Where Pi is a focus of loss for each of n crops, (LOSS) is total permitted loss, (MINI) is income indispensable for consumption and (STBO) is short-term borrowing, the focus-loss constraint equations can be written as:
< 0 (i=l, 2, ... , n) where P.X. - l/n (LOSS) -~ J. J. 1
1
LOSS < ~E C.X. - MINI - STBO (i=l, 2, ... , n) --
i lJ. l J. i
or rearranging ~ E
C.X. - LOSS - STBO = MINI (i=l, 2, ... , n)
i i lJ. lJ.
Using the focus-loss concept as a constraint it is thus possible to formulate the decision making process under uncertainty in a linear programming ' context. A schematic represenprogramming'context. tation of one of the planning models is shown in Table 1.
TABLE 1 Representative Matrix for Planning Model
Constraint Types
Crop Activities Xl·········· .X .Xn n
Maximum Acreage Available
1.0
Water Balance
a1 1*
... ,. I. 1.0 ....... ........ aann
Maximum Ditch Water
Water Activity (Ditch) (Di tch) (Well) (Well ) X + X Xn+l Xn+2 n 1 n +2
-1.0 1.0
Capital (FUND (FUND))
Objective Function (max.)
-1.0
P 1** · Pt*·
-l/n p P
Constraints
Minimum Income (MINI)
LOSS X Xn+4 n +4
1.0
Maximum Well Water Focus-Loss
STBO X Xn+J n +3
-l/n
n
b n
b *** 1 c *** 1
c
e *** n
e
n
-dn+l**** -dn +2
n
-dn + 1
-dn +2
-1.0 -1.0 -h
*Water is in units of acre feet. **Focus-loss is in units of dollars per acre. ***Capital, income and objective function are in units of dollars per acre. ****Water prices are in dollars per acre foot.
-1.0
s. S.
238
H. Johnson, III
lation losses, rainfall recharge, upward leakages from the confined aquifer and mountain runoff. The water leaves the aquifer by groundwater pumping and beneficial and non·beneficial evapotranspiration. The sum of the water moving into the unconfined aquifer and the water moving out of the unconfined aquifer is recorded for each season and used to calculate the change in the aggregate water table level over the Closed Basin. Johnson (1975), Appendix E, provides the mathematical relationships and the assumptions upon which this model is based.
Once the planning model for each area has been optimized based on the 'estimated' annual water available for that area, the solution values (i.e., planted acreage for each crop) are passed to the water allocation initial acreage constraints for model as the 1nitial that year. Due to the fact that the productivity of any crop varies throughout the growing season and depends, in large part, on the irrigation regime followed (Flinn and Musgrave, 1967), it was also necessary to incorporate into the SLP algorithm a method of relating moisture stress to plant yield (Martin and Young, 1967). The technique used is a simplified version of the 'stress day index' developed Hller and Clark (1971) and thus is quite by Hiler similar to models used by Anderson and Maass (1971) and by Young and Bredehoeft (1972) in that it assumes the crop yield to be diminished by a specific percent if the crop requires water but is not irrigated during that time period.
usa usd
SIMULATION OF ALTERNATIVE STRATEGIES
alloca-coare, The planning models are linked to the alloca-coarec tion models as well as to the hydrologic mo- moondel representing the groundwater to form a complete simulation tool. The planted areas alloc, alloc, from the planning model are passed as conccstraints to the allocation model which is run-h ru in a sequential manner to optimally allocate alloc the available surface and groundwater to the a to crops for each two-week period during the ste~ irrigation season. Table 3 provides a step step chart of the simulation model.
The percentage of decrement in yield as a result of water deficit is indicated by the crop susceptibility factor (CS) which is both a function of the plant species and the stage of growth of the plant. Table 2 presents the CS values used in the allocation model.
thsen The simulation model was used to represent theen the economic and hydrologic effects for the admit selanj entire Closed Basin over a 20-year planning selani period of activities taken either by the the agricultural water users or policies adminis~nin~ adminis~nin@ tered by the Colorado State Engineer. Acti-the vities that were modeled to represent self- Acticontrol actions by the water users include: self(1) status ~ under 1974 conditions; (2) (3) normal increase of sprinkler irrigation; (3) 3) selective canal lining; (4) conversion to (3) almost total sprinkler irrigation; and (5) axquasi-market quota system which allows ex-
The final model represents the unconfined aquifer. Eventually the water management model will be combined with a sophisticated hydrologic (mathematical) model developed on a grid point system in order to pinpoint changes in water table depth, but the present simplified hydrologic model treats the unconfined aquifer as a single reservoir and keeps track of the water entering and leaving this aquifer. The water enters the aquifer as leakage from canals and streams, deep perco-
TABLE 2 Crop CroE Susceptibility SusceEtibilitl Values Used in the Model (Percentage Yield Reduction in Different Time Periods) . -JI..-
Dates
Apr. 1-15
Apr. May 16-30 1-15
Barley One Stress Two Stress Three Stress Four Stress S-tress Potatoes One Stress Two Stress Three Stress Four Stress Alfalfa One Stress Grass Hay One Stress
.10
May June 16-31 1-15
June July 16-30 1-15
July Aug. 16-31 1-15
Aug. Sept. Sept. 16-311-15 16-31 1-15 16-30
.03
.07 .02
.10 .02 .08 .02
.25 .07 .07 .02
.22 .07 .04 .02
.20 .06
.05
.05
.06 .02
.10 .04
.15 .04 .04 .02
.15 .05 .05 .03
.23 .08 .07 .03
.23 .08 ,07 .03
.23 .08 .07 .03
.20 .07 .07 .02
.06 .04
.10
.15
.15
.20
.25
.25
.25
.20
.20
.10
.10
.10
.15
.20
.25
.25
.25
.20
.10
.10
Sept. 16-30
.10
.10
The Economics of Water Management
TABLE)
CA] [A]
steps for Simulation Model
Read all objective function values, water application rates, parameters for planning models.
[BJ Read 'estimated' hydrologic data for [B] determining planting acreage in each subarea.
[CJ
Compute crop acreages for subarea i.
[DJ [DJ
Check to see that planted acreage for all subareas has been calculated; if [CJ until all have been not, return to [C] calculated.
[E] [EJ
Read hydrologic data for all 1) allocation periods.
[FJ
Read groundwater level; determine which application rate to follow.
[GJ
Compare crop water demand to total of available water.
[HJ
If sum of supply exceeds demand, irrigate all crops and record water used.
[IJ
If demand exceeds supply, call allocation model to maximize net returns with available water; record water used.
[J] Check to see if all irrigation activities for all subareas for 1) time periods have been calculated; if not complete, return to [F] [FJ until complete.
[KJ [K]
Compute the gross margin for each area.
[LJ
Record the gross margin and water used for all subareas.
[MJ
Check to see if 20 years have been completed; if not, return to [B] [BJ until complete.
[NJ ~J
Discount the returns for each year to present value; record present values.
[oJ
Secord ~ecord water used for 20 years.
[p] [pJ
Determine change in water table depth as a result of 20 years of operation.
change of surplus water. Activities modeled poliCies implemented by the to represent policies Colorado State Engineer include: (1) restrictions on number of days per week water users can pump their wells and (2) the implementation of a strict quota (one acre-foot per acre) on groundwater pumping. The results of the simulation runs are summarized in Table 4. These results consistently indicate that policies which could be implemented by the water users themselves in conjunction with a groundwater augmentation organization as compared to the policy op-
239
tions open to the State Engineer would not only significantly increase economic returns to the water users but would also reduce the waterlogging and salinity problems. This results from the increased water use efficiency of the sprinklers which significantly reduce the water returning to the aquifer as a result of deep percolation losses or canal leakage losses. The sprinklers also provide an excellent method for leaching the salts out of the root zone and hence reclaiming salinized land. POLICY IMPLICATIONS The simulated economic benefits associated with scenarios based on private initiative and self-discipline by the water users are, in every case, superior to rules and regulations implemented and enforced by the Colorado State Engineer. It is thus in the best interests of the Closed Basin water users to develop their own water management system in a manner that allows them to manage the unconfined aquifer such that in wet years the aquifer is recharged by nature and in dry years the aquifer would be artificially recharged. Any excess river water (Closed Basin Rio Grande River water rights) would be leased out in the valley or traded to the State of Colorado for augmentation. In dry years the water should be used to maintain the aquifer level. The Colorado State Engineer is vested with statutory authority for the administration of the water resources of the State. As long as the private policies of the Closed Basin water users do not conflict with the statutory obligations of the State Engineer, the water users are not affected by the powers of the State. Since a policy that permits a loosely controlled system for the management of the water resources of the Closed Basin is superior to a structured system of rules and regulations, it is in the interest of the water users to cooperate with the state State Engineer to avoid legal conflict between public and private interests. An aquifer management plan plus a restriction on development of new irrigated land in the Closed Basin will provide sufficient excess water so that the Closed Basin water users will not be in conflict with the State Engineer but will even be in a position to help other water users or reduce the compact debt. The relationship between the Rio Grande River and the underground storage system directly connects the private actions of the groundwater users to other water users in the San Luis Valley and along the entire northern Rio Grande River. Thus the effects of private economic decisions become public policy and hence the Closed Basin water users must work directly with the state State Engineer and other Rio Grande River water users to insure maximum benefits for all.
240
S. H. Johnson, Johnson , III
TABLE 4
Summary of the Seven Simulation Runs, Runs I Closed Basin Valley , Colorado Color ado 1974-1994 San Luis Valley,
Si mulati on Run Simulation Characteri sti cs Characteristics
Present Pr esent Value of Economic a Returns
II
Status quo (1974) conditions condi tions
$182,432,489 $182 , 432 , 489
7536
11 II
Change to sprinklers spr inkl er s followi ng past trend t r end following
$187 , 742 ,677 $187,742,677
7202
+ 0.24
III 111
s prinkler s and Change to sprinklers sel ected canals line selected
$186,177,421 $186 , 177 , 421
6548
+ 0.94 0 . 94
IV IV
totall y to Change almost totally s prinkl er s sprinklers
$215 , 887 , 694 $215,887,694
6321
2 .53 - 2.53 3 . 04 - 3.04
V V
Simulate r estricti ons on Si mulate restrictions gr oundwater pumping pumpi ng CC groundwater
$185,348,064 $185 , 348 , 064 $177 , 39 1, 196 $177,391,196 $169 , 812 , 794 $169,812,794 $151 , 023 , 764 $151,023,764
6766 6139 5380 4231
+ 0.58 0 .58 + 0.91 1 . 37 + 1.37 2 . 07 + 2.07
$133,002,764 $133 , 002 , 764
3080
+ 1.92
d $177 , 774 , 140 140d $177,774,
6556
0 .61 + 0.61
Case
- It
-,~
. ~1.
VI
Ope~te O pe~te under under strict
Total Groundwater Pumped (million cubic meters)
Water Change in Water Table Level (meters)b
pumping quota
VII VII
Quota but can purchase addi t i onal water water additional
~conomic ~ conomi c return r eturn over over a twenty year time period per iod discounted to present value at
8%. 8% .
bC hange in i n water water table tabl e level l evel is based on change in head between the confined and bChange unconfi ned aquifers. aquifer s . Plus Pl us (+) indicates an upward rise r ise in water table level. level . unconfined ( - ) indicates i ndicates a downward drop in water water table level. level . Mi nus (-) Minus pumpi ng limit, limit , respectively. r espectively . 4 , 3, 3 , and 2 day per per week pumping c 5 , 4,
~conomic returns ~conomic r eturns for fo r case VII includes i ncl udes $1,943,569 $1 , 943 , 569 rebate to water users for gr oundwater not pumped. pumped . groundwater REFERENCES
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The Economics of Water Management
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(Ed . ) (1957). (1957) . Drainage Dr ainage of Luthin, J.N. (Ed.) No . 7. 7. Agricultural Land, Monograph No. American Society of Agronomy, Agronomy , Madison. Madison . Martin , W. and R.A. R. A. Young (1967). (1967) . Modeling Martin, production response relations for irrigation water: water : review and implications. implications . Mimeographed paper presented to the WesWes tern Agricultural Economics Research Council , December 1967. 1967 . University of Council, Arizona, Arizona , Tuscon. Tuscon . Moore, Moor e , C.V. C. V. (1972). (1972) . On the necessary and sufficient conditions for a long-term Water Resources irrigated agriculture agriculture.. Water Bull. , 8, 802-812. 802-812 . Bull., Radosevich,-G.E. and D.H. Hamburg (1971). (1971) . Laws , Compacts, Compacts , Treaties Tr eaties Colorado Water Laws,
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