SEQUENCING WATERSHED CONSERVATION AND GROUNDWATER MANAGEMENT REFORMS

Transcription

1 SEQUENCING WATERSHED CONSERVATION AND GROUNDWATER MANAGEMENT REFORMS Bashara A. Piafi, * Souhern Illinois Universiy, Carbondale James A. Roumasse, Universiy of Hawaii a Manoa ABSTRACT: Conserving he waershed can help o preserve groundwaer recharge. Prevening overuse of available waer hrough pricing reforms can also subsanially increase he value of an aquifer. Inasmuch as users are accusomed o low prices, efficiency pricing may be poliically infeasible, and waershed conservaion may be considered as an alernaive. We esimae and compare welfare gains from pricing reform and waershed conservaion for a waer managemen disric in Oahu ha obains is waer supply from he Pearl Harbor Aquifer. We find ha pricing reform is welfare superior o waershed conservaion unless he laer is able o preven very large recharge losses. If waershed conservaion prevens only small recharge losses, is ne benefi may be negaive. If adopion of waershed conservaion delays implemenaion of pricing reform, he benefis of he laer are significanly reduced. KEYWORDS: Efficiency, Groundwaer Managemen, Waershed conservaion * Deparmen of Economics, Souhern Illinois Universiy, 1000 Faner Drive, MC 4515, Carbondale, IL 62901, Tel: ; Fax: ; piafi@siu.edu. 1

2 INTRODUCTION Waershed degradaion can lead o reduced recharge of groundwaer aquifers. Conserving he waershed can help o preserve he groundwaer supplies by avoiding his loss of recharge. This is an especially valuable benefi in places such as Oahu, HI, where waer sources are geographically consrained. Prevening overuse of available waer hrough pricing reforms can also subsanially increase benefis from groundwaer sock. One example of overuse is he curren policy on Oahu of pricing waer a average exracion and disribuion cos ha ignores he user cos, or he scarciy value of waer. Correcing his overuse by adoping efficiency pricing can avoid he unimely depleion of groundwaer supplies and yield large welfare gains. Thus, waershed conservaion and efficien pricing can each help o augmen he groundwaer aquifer. However, since efficiency prices are generally higher han he inefficien, saus quo prices, pricing reform may be poliically infeasible and waershed conservaion may be considered as an alernaive. We compare wo pricing scenarios (efficiency and saus quo pricing) and hree waershed conservaion scenarios: no conservaion, conservaion ha prevens a 1 % loss of recharge, and conservaion ha prevens a 10 % loss of recharge. The opimizing model exends previous models of groundwaer managemen o allow for groundwaer recharge o vary according o waershed conservaion. We allow for growing waer demand and a sandard hydrological specificaion of a coasal aquifer, using he Pearl Harbor waer disric on Oahu as an example. We show ha welfare gains from waershed conservaion are small compared wih hose from pricing reform, unless waershed conservaion can provide proecion agains large recharge losses. If waershed 2

3 conservaion is relaively ineffecive, is benefis may be less han he cos. The benefis of conservaion increase subsanially in he presence of price reform. Finally, if waershed conservaion is adoped and leads o delays in adoping pricing reform, subsanial poenial gains are los. The presenaion of he model follows immediaely below. We hen apply and numerically solve he model for he case of he Pearl Harbor aquifer, and examine welfare effecs of efficiency pricing and waershed conservaion. In he final secion, we summarize he resuls and conclude. THE MODEL To solve for he efficien rajecories of groundwaer exracion and shadow values, we envision a social planner maximizing he presen value of consumer benefis ne of exracion and disribuion coss. As groundwaer is exraced, he efficiency price changes over ime wih he changes in exracion cos and waer scarciy. Desalinaion of seawaer is available as a backsop resource. When he full marginal cos of groundwaer, including he marginal user cos, has risen o he uni cos of desalinaion, he backsop is used o supplemen seady sae groundwaer recharge. We se up a regional hydrologic-economic model o opimize groundwaer use, along he lines of Krulce e al. (1997). Waer is exraced from a coasal groundwaer aquifer ha is recharge from a waershed and leaks ino he ocean from is ocean boundary depending on he aquifer head level, h. As he head level rises, underground waer pressure from waershed decreases and he rae of recharge decreases. Also, leakage surface area and ocean-ward waer pressure increase and he rae of leakage 3

4 increases. Thus, we model ne recharge, l, (recharge ne of leakage) as a posiive, decreasing, concave funcion of head, i.e., lh ( ) 0, l ( h) < 0, l 0. The aquifer head level, h, changes over ime depending on he ne aquifer recharge, l, and he quaniy exraced, q. The rae of change of head level is given by: γ h = l( h ) q where γ is a facor of conversion from volume of waer in gallons (on he R.H.S.) o head level in fee. In he remainder of his secion, however, we subsume his facor, i.e., h is considered o be in volume, no fee. Thus, we use h = l( h) q as he relevan equaion of head moion. If he aquifer is no uilized (i.e., quaniy exraced is zero), he head level will rise o he highes level h, where leakage exacly equal balances inflow, lh ( ) = 0 As he head canno rise above his level, we have lh ( ) > 0 whenever he aquifer is being exploied. The uni cos of exracion is a funcion of he verical disance waer has o be lifed, f = e h, where e is he elevaion of he well locaion. A lower head levels, i is more expensive o exrac waer because he waer mus be lifed over longer disance agains graviy, and he effec of graviy becomes more pronounced as he lif, f, increases. The exracion cos is, herefore, a posiive, increasing, convex funcion of he lif, c( f) 0, where c ( f) > 0, c ( f) 0. Since he well locaion is fixed, we can redefine he uni exracion cos as a funcion of he head level: c ( ) 0 q h, where c ( h) < 0, c ( h) 0, lim c ( h) =. The oal cos of exracing waer from he aquifer a q q q h 0 he rae q given head level h is cq(h).q. The average uni cos of disribuion from wells o users is c d. The uni cos of he backsop (desalinaion) is represened by c b and he quaniy of he backsop used is b. The demand funcion is D(p, ), where p is he price 4

5 a ime, and he second argumen,, allows for any exogenous growh in demand (e.g., due o income or populaion growh). A hypoheical social planner chooses he exracion and backsop quaniies over ime o maximize he presen value (wih r as he discoun rae) of ne social surplus. q + b r 1 Max e D ( x, ) dx [ cq( h) + cd] q [ cb + cd] b d q, b 0 0.(1) Subjec o: h = l( h) q.(2) The curren value Hamilonian for his opimal conrol problem is: q + b 1 H = D (,) x dx [ cd+ cq( h)] q [ cd+ cb] b + λ l( h) q 0 ( ).(3) Applying Ponryagin s Maximum Principle leads o he following necessary condiion for an opimal soluion (defining p D 1 ( q + b, ) ). p 1 = c ( h q ) + c d + q( ). ( ) r l ( h ) p + c h l h Exracion and disribuion cos Marginal User Cos.(4) Here, p is he reail price of he waer delivered o users and, herefore, includes he disribuion cos, which would be excluded in compuing he wholesale price, or he price before disribuion. Equaion (4) implies ha a he margin, he benefi of exracing waer mus equal acual physical coss (exracion and disribuion) plus marginal user cos (decrease in he presen value of he waer sock due o he exracion of an addiional uni). Thus if waer is priced a physical coss alone, as is common in many areas, overuse will occur. Equaion (4) also implies ha he reail (consumer) price is equal o he disribuion cos plus he wholesale price (i.e., he price before disribuion). Re-arranging (4), we ge an equaion of price moion: 5

6 p = [ r l ( h)] [ p c ( h) c ] + l( h ) c ( h ).(5) q d q The firs erm on he R.H.S. is posiive and he second is negaive. Their relaive magniudes deermine wheher he price is increasing or decreasing a any ime. However, if he ne recharge is large and he exracion cos is sensiive o he head level, he second erm is large and may dominae by he firs erm, making he price fall. The soluion o he opimal conrol problem is governed by he sysem of differenial equaions (2) and (5). When desalinaion is used, he price mus exacly equal he cos of he desaled waer, and we can use p = c + c p = 0 in (4) o ge: b d c = c ( h ) b q ( l( h )) c ( h ) q r l ( h ).(6) Since he derivaive of he R.H.S. wih respec o h is negaive, he h ha solves equaion (6) is unique. We denoe i as h *. Whenever desalinaion is being used, he aquifer head is mainained a his opimal level, herefore, he quaniy exraced from he aquifer equals he ne inflow o he aquifer. Tha is, demanded is supplied by desalinaion. q = l(*) h. Excess of quaniy A compuer algorihm has been designed using Mahemaica sofware o firs solve equaion (6) o obain final period head level and hen use i as a boundary condiion o numerically solve equaions (2) and (5) simulaneously for he ime pahs of efficiency price and head level. Welfare is compued as he area under he demand curve minus exracion and disribuion cos (objecive funcion (1)). As in many jurisdicions, acual pricing by he Honolulu Board of Waer Supply is based on hisorical cos recovery. To represen his saus quo pricing scenario, assume ha price is se equal o only he long run average cos of exracion and disribuion. 6

7 Inasmuch as his formulaion overlooks he opporuniy cos of waer, i resuls in faser wihdrawal and premaure desalinaion, compared wih he efficiency-pricing scenario. Once desalinaion sars, he saus-quo price is defined as he volume-weighed average cos of waer from he wo sources. For examining he effecs of saus quo pricing, we calculae he ime pah of exracion rae, q, dicaed by he quaniy demanded a average cos pricing, i.e., price equal o he cos of exracion and disribuion (bu no he user cos). When he head level reaches he poin where ne recharge is equal o exracion, he rae of exracion is frozen a ha level, q max, so ha he head level does no fall any furher. Any excess demand is me from he desalinaion backsop. The saus quo (average cos) price, p sq, will, herefore, be a volume-weighed average cos of waer from he wo sources (desalinaion and underground aquifer): ( ) sq p = cq( h) qmax + cb q q max / q + c d.(6) APPLICATION This secion applies he above model o he Pearl Harbor waer disric and he Ko olau waershed on Oahu, and compues efficien price pahs and welfare effecs of efficien pricing wih and wihou waershed conservaion. Calibraion Mos coasal aquifers in Hawai'i exhibi some form of a basal or Ghyben- Herzberg lens (see Mink, 1980). The volume of waer sored in he aquifer depends on he head level, he aquifer boundaries, lens geomery, and rock porosiy. Alhough he 7

8 freshwaer lens is a paraboloid, he upper and lower surfaces of he aquifers are nearly fla. Thus, he volume of aquifer sorage is modeled as linearly relaed o he head level. Using GIS aquifer dimensions and effecive rock porosiy of 10%, Pearl Harbor aquifer has billion gallons of waer sored per foo of head. This value is used o calculae a conversion facor from head level in fee o volume in billion gallons. Exracing 1 billion gallons of waer from he aquifer would lower he head approximaely by 1/78 or fee, giving us γ = f/million gallons (mg). Economerically esimaed ne recharge, l, as a funcion of he head level, h, yields he ne recharge funcion: 2 lh ( ( )) = h ( ) h ( ), where l is measured in million gallons per day (mgd). The cos is a funcion of elevaion (and, herefore, he head level), specified as: 0 n ( ) ( 0), where c 0 is he iniial exracion cos when he head level ch ( ( )) = c e h ( ) e h h() is a he curren level, h 0 = 15 fee. There are many wells from which freshwaer is exraced and, using a volume-weighed average cos, we have separaely esimaed he iniial average exracion cos in Pearl Harbor a $0.407 per housand gallon (g) of waer. e is he average elevaion of hese wells and is esimaed a 50 fee, and n is an adjusable parameer ha conrols he rae of cos growh as head falls. We assume n = 2. (Sensiiviy analyses for n = 1 and n = 3 did no change he conclusions of his aricle. Since head level does no change much relaive o he elevaion, he value of n does no affec he resuls appreciably.) The uni cos ( c b ) of desaled waer has also been separaely esimaed a $7/g. This includes a cos of desaling ($6.79/g) and addiional cos of ransporing he 8

9 desaled waer from he seaside ino he exising freshwaer disribuion nework ha we assume o be $0.21/g. We use a demand funcion of he form: D(p, )=A e g (p ) -µ, where A is a consan, g is he demand growh rae, p is he price a ime, and µ is he price elasiciy of demand. The demand growh rae, g, is assumed o be 1% (based on projecions in DBEDT, 2005). The consan of he demand funcion, A (= mgd) is chosen o normalize he demand o acual price and quaniy daa. Following Krulce e al. (1997), we use η = 0.3 (also see Moncur, 1987). We calculae he disribuion cos, c d = $1.363/g, from he waer uiliy daa (Honolulu Board of Waer Supply, 2002). Resuls Below we repor he calculaed ime pahs of prices and head levels for wo scenarios: coninuaion of he saus quo pricing policy, 2) swiching o efficiency pricing. Dollars Price Years Fee Head Level Years (a) Saus Quo Price (b) Saus Quo Head Level Fig.1: Saus Quo Scenario 9

10 Saus Quo As shown in Fig. 1, he saus quo price begins a $1.77/g, falls slighly as he head level increases, and hen increases slowly as he head level falls. Afer 59 years, he head level reaches he seady sae a abou 8 fee and aferward, exracion mus no exceed ne recharge. Thus, in year 60, consumpion is parly supplied from he backsop source (desalinaion) and parly from he groundwaer source. The (saus quo) price is herefore a volume-weighed average of he cos of he backsop and he cos of he groundwaer. This resuls in a jump in price from $1.93 o $3.76/g in year 60. Aferward, as consumpion coninues o grow, more and more of i is supplied from he backsop source and he price (as a volume-weighed average cos) coninues o increase oward he backsop price (plus disribuion cos). Dollars Opimal Price and Cos Price Fee Head Level Cos Years Years (a) Efficiency Price (b) Head level a Efficiency Price Fig. 2: Efficiency Scenario Efficiency As shown in Fig. 2, he efficiency price begins a $2.11/g, falls very slighly as he head level increases (Fig. 4), and hen increases slowly as he head level falls. Afer 10

11 90 years, he head level reaches he seady sae a abou 8 fee and aferward, exracion mus no exceed ne recharge. Thus, in year 91, consumpion is parly supplied from he backsop source (desalinaion) and parly from he groundwaer source, wih he resul ha he efficiency price is equal o ha of he backsop plus disribuion cos. Aferward, he price remains he same as consumpion coninues o grow and more and more of i is supplied from he backsop source. Normal Recharge (281 mgd) 1% Less Recharge Saus Quo Scenario C: Saus Quo and Waershed Conservaion Conservaion 42.9 Scenario A: Saus Quo bu No Waershed Conservaion Reform Reform Efficiency Scenario D: Efficiency and Waershed Conservaion Conservaion 71.9 Scenario B: Efficiency bu No Waershed Conservaion Figure 3: Presen Value of Welfare Gain ($ million) from Reform and Waershed Conservaion (Prevening Loss of 1% Recharge) Welfare Fig. 3 repors welfare under four differen scenarios. In scenario A, saus quo pricing is coninued and lack of waershed conservaion causes a 1% recharge loss. (In realiy, he loss may be greaer or smaller, may occur in he fuure raher han immediae, and/or may happen once or muliple imes. Here, we assume ha he ne effec of all he losses from lack of waershed conservaion is equal o ha of one percen immediae loss of recharge. Analysis wih 10% loss is also repored laer in his secion.) In scenario B, efficiency pricing is underaken bu again lack of waershed conservaion causes a 1% 11

12 recharge loss. In scenario C, saus quo pricing is coninued bu waershed conservaion prevens recharge loss. In scenario D, efficiency pricing is underaken and again waershed conservaion prevens recharge loss. Saring from scenario A, he gains from pricing reform (moving o scenario B) are abou $878 million. In comparison, he gains from waershed conservaion (moving o scenario C) are abou $43 million. In addiion, since saus quo pricing involves over-use and wasage, a uni of recharge is more valuable a efficiency prices han a saus quo prices. To see his, noe ha if we are in scenario A, and move o scenario C (adop waershed conservaion ha prevens he loss of recharge), he welfare gain is abou $43 million. Insead, if we are in scenario B, and move o scenario D (adop waershed conservaion), he welfare gain is abou $72 million. Waershed conservaion is, herefore, more valuable under efficiency pricing han under saus quo pricing. If he presen value of conservaion coss is greaer han $43 million, bu less han $72 million, hen conservaion would be warraned if and only if pricing reform were done firs. This may indeed be he case. In a recen survey (Kaiser, 2004) of conservaion expers in Hawaii, 30% of expers indicaed ha conservaion expendiures of $3 million/year for five years followed by annual expendiures of $300,000/year would be needed o avoid deerioraion of he Ko olau waershed ha recharges he Pearl Harbor aquifer. The presen value of hese expendiures is $43.2 million, a 1% discoun rae. The difference beween he benefis of pricing reform and waershed conservaion depends on he amoun of recharge loss ha is being saved by waershed conservaion. Figure 4 examines he welfare effecs if lack of waershed conservaion would cause a 10 12

13 % loss of recharge. Once again, waershed conservaion underaken afer pricing reform is more valuable han before he reform. Normal Recharge (281 mgd) 10% Less Recharge Saus Quo Scenario C: Saus Quo and Waershed Conservaion Conservaion Scenario A: Saus Quo bu No Waershed Conservaion Reform Reform Efficiency Scenario D: Efficiency and Waershed Conservaion Conservaion Scenario B: Efficiency bu No Waershed Conservaion Figure 4: Presen Value of Welfare Gain ($ million) from Reform and Waershed Conservaion (Prevening Loss of 10% Recharge) However, his ime, he gain from pricing reform alone (B A) is almos he same as he gain from waershed conservaion (C A). This is because waershed conservaion is now providing a bigger service (prevening a 10% recharge loss). For even larger recharge losses prevened, gains from waershed conservaion will be higher han he gains from pricing reform. Finally, delay in adoping pricing reform can subsanially affec he resuling gains, as shown in Figure 5. Waershed conservaion: Adop now Efficiency pricing: Adop now Waershed conservaion: Adop now Efficiency pricing: Adop afer 10 years Waershed conservaion: Adop now Efficiency pricing: Adop afer 20 years Coninue wih saus quo pricing and no conservaion Figure 5: Welfare gains from waer managemen reforms ($ million) 13

14 CONCLUSION This paper compares he effecs of adoping efficiency pricing and waershed conservaion policies. If saus quo pricing policy is coninued in he sudy area, he use of expensive desalinaion echnology would be required in abou 60 years; under efficiency pricing i would be required i afer 90 years. The swich o efficiency pricing, herefore, yields a welfare gain of abou $900 million in presen value. The pricing reform is welfare-superior o waershed conservaion ha prevens a recharge loss of 10% or less. Simulaing he wo pricing scenarios wih differen recharge condiions brough abou by waershed conservaion or lack hereof, we find ha waershed conservaion is much more beneficial if i is underaken afer pricing reforms. Thus, if he cos of conservaion is sufficienly high, i may no be beneficial o pursue i wihou pricing reform. 14

15 REFERENCES DBEDT, Populaion and Economic Projecions for he Sae of Hawaii o 2030 (DBEDT 2030 Series): Repors of Resuls and Mehodology. Honolulu: Hawaii Deparmen of Business, Economic Developmen, and Tourism. Honolulu Board of Waer Supply, Annual repor and Saisical Summary: July 1, 2000 June 30, Honolulu, HI. Kaiser, B., Survey of Waershed Expers on Risks o Ko'olaus from Invasives and oher hreas. Available a hp:// U= Accessed on Sepember 27, Krulce, D. L., J. A. Roumasse, and T. Wilson, Opimal Managemen of a Renewable and Replaceable Resource: The Case of Coasal Groundwaer. American Journal of Agriculural Economics 79 (4): Mink, John F., Sae of he Groundwaer Resources of Souhern Oahu. Honolulu, HI: Board of Waer Supply, Ciy and Couny of Honolulu. Moncur, J. E. T., Urban Waer and Drough Managemen. Waer Resources Research 23 (3):