E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 3 3 7 – 3 4 7

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ANALYSIS

Adaptation and mitigation strategies for controlling stochasticwater pollution: An application to the Baltic Sea

Ing-Marie GrenDepartment of Economics, SLU, Box 7013, S-750 07, Uppsala, Sweden

A R T I C L E I N F O

E-mail address: Ing-Marie.Gren@ekon.slu.s

0921-8009/$ – see front matter © 2007 Elsevidoi:10.1016/j.ecolecon.2007.09.010

A B S T R A C T

Article history:Received 17 April 2007Received in revised form21 August 2007Accepted 11 September 2007Available online 10 October 2007

The purpose of this paper is to analyse and compare the costs of two strategies againsttransboundary water pollution, mitigation and adaptation measures, which are linked withrespect to risk. Chance constraint programming is applied, and the analytical resultsindicate that total costs for given probabilistic targets are higher (lower) than the costswithout risk linkage for negative (positive) covariance between the two classes of measures.A comparison of two international policies—cooperation and national uniform standards—indicates that cleaning under non-cooperative uniform national standards can be increasedwhen considering stochastic pollution and linkage in risk between mitigation andadaptation measures. The empirical application to the Baltic Sea shows that the risklinkage can increase or decrease minimum costs for a given probabilistic target undercooperative solutions by 17 or 13%, and decrease the cost under national uniform policy for agiven overall probabilistic target by approximately 10%.

© 2007 Elsevier B.V. All rights reserved.

Keywords:Stochastic water pollutionMitigationAdaptationCost effectivenessStochastic programmingCovariance

Jel Classification:Q53; R14; H23; G11

1. Introduction

Difficulties of managing stochastic pollution of waters consti-tute an important cause of aggravation of several types ofwater quality problems in spite of societies' relatively earlyperception of the environmental problem. One prominentexample is damages from eutrophication caused by nutrientenrichment in several parts of the world, such as the BalticSea, Black Sea, Mississippi delta, Chesapeake Bay, and theMediterranean (see e.g. Turner et al., 1999; NRC, 2000;Bodungen and Turner, 2001). Damages from nutrient enrich-ment occur from the oxygen depletion that takes place due tobiological growth of certain algal species. Huang et al. (1997),Söderqvist (1998), and Markowska and Zylicz (1999) show thatpeople are willing to pay a significant amount of money for

e.

er B.V. All rights reserved

reducing damages from nutrient enriched bays. However,pollutant emission sources are spatially spread in drainagebasins where pollutant transports to the water recipientsfollow one or several different paths: air, soil, subsurface- andgroundwater streams (e.g. Destouni et al., 2006). Therefore, thefinal impact on the recipient is predicted only under condi-tions of risk and uncertainty. This uncertainty is one reasonfor the EU water directive's recommendation of expressingwater quality targets in precautionary termswhere the targetsshould be obtained with high reliability (EU, 2000). Thepurpose of this paper is to analyse the impact of risk linkagesbetweenmitigation and adaptationmeasures on cost effectivesolutions to given pollution targets under conditions ofstochastic loads to water recipients. An empirical applicationis made on the Baltic Sea, which has been suffering from

.

338 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 3 3 7 – 3 4 7

damages of eutrophication during a period of 30 years (e.g.Wulff et al., 2001).

In principle, as for many other environmental problems,decision makers can respond to water pollution in two ways,by mitigation and/or adaptation measures (e.g. Fankhauseret al., 1999; Kane and Shogren, 2000; Mendelsohn, 2003; Tol,2005; Perrings, 2005; IPCC, 2007; Zehaie, 2007). Except forPerrings (2005), who analyses optimal mitigation and adapta-tion measures for prevention of alien species invasion, allstudies are applied to climate change policies, where mitiga-tion strategies usually refer to measures reducing carboncontent in the atmosphere and adaptation measures toadjustment to climate change effects such as flood protection.Following Perrings (2005), mitigation measures are heredefined as all measures that reduce pollutants from theemission sources, such as changed land use practices inagriculture and increased cleaning at sewage treatmentplants. All measures responding to the pollutant load changesat the water recipient are defined as adaptation measures.These measures do not change the emissions from the sourcebut instead reduce the impact of these emissions on the waterrecipient. Examples of adaptation measures are creation ofwetlands at rivermouths, and cultivation ofmussels or alga inshallow coastal waters. All these types ofmeasures reduce theload entering the water recipient or reduce the concentrationratio of pollution in the water.

Disregarding risk, the choice between mitigation andadaptation measures is determined by their marginal costs ofachieving the target. Interdependency between the two typesof measures can be revealed by the marginal cost increasingimpact on adaptationmeasures frommitigationmeasures dueto the dependence of the adaptation measures' effectivenesson pollutant load entering the water recipient (e.g. Byström,1998; Hart, 2003). When considering risk, the choice ofmeasures is also determined by their relative predictabilitywith respect to effects on the water recipient. This has beenanalysed in Kane and Shogren (2000) who use a model ofendogenous risk and find that the interdependency betweenmitigation and adaptation measures can either increase ordecrease total cost depending on abatement technology. Thispaper makes an extension by a further analysis of theabatement technology, which includes mitigation and adap-tation measures for reducing the mean and variance of waterpollution. It is shown that interdependency between the twoclasses ofmeasures increases or reduces total costs for a givenreliability target depending on the covariation in risk.

This study analyses and calculates the optimal allocationofmitigation and adaptationmeasures bymeans of stochasticprogramming, where the decision problem includes minimi-zation of costs for pre-specified target(s) of maximum loadsunder probabilistic constraints (see e.g. Birge and Louveaux,1997). This method has been applied in other studiescomparing policies for water pollution (e.g. McSweeny andShortle, 1990; Shortle, 1990; Byström et al., 2000; Gren et al.,2002; Elofsson, 2003). As shown in these studies, the solutiongives an optimal portfolio allocation of emissions amongsources, which is determined by their mean and varianceimpact on load to the water recipient. The variance is, in turn,dependent on the choice of measures and spatial scales. Inseveral studies (McSweeny and Shortle, 1990; Shortle, 1990;

Byström et al., 2000) only one spatial scale, a drainage basin, isconsidered. Gren et al. (2002) and Elofsson (2003) account forthe possibility of locatingmeasures in different heterogeneousregions, but disregard interdependency in risk betweenmeasures. The main contribution of this paper is the explicittreatment of this interdependency in risk between adaptationand mitigation measures at different spatial scales. Further-more, the role of covariance in load among sovereigncountries for costs of national and coordinated internationalpolicies are calculated and compared.

A fewcaveats are inorder. Due to the focuson the abatementportfolio aspects, the dynamics of water pollution is notincluded. As discussed inmore detail in the chapter presentingthe empirical application on the Baltic Sea, this neglect isparticularly serious for phosphorous pollution due to the longtime adjustments in the sea to changes in load. As shown inHart (2003) consideration of dynamics may have significantimpacts on the choice of mitigation or adaptation measures forwater pollution. However, nitrogen is a more mobile substanceand responses in the sea can take placewithin the same seasonas the change innitrogen load. The static stochasticmodel usedis therefore justified for management of nitrogen loads, whichcause damages from eutrophication in many marine waters.

This paper is organized as follows. First, the theoreticalmodel for assessing mitigation and adaptation measuresunder stochastic water pollution is presented. Next, theconditions for optimal use of the measures are derived foroverall cost effective solutions and for uniform nationalpolicies. The model is then applied to cost effective nitrogenabatement of the nutrient enriched, or eutrophicated, BalticSea in Northern Europe. The paper ends with a brief summaryand discussion of the results.

2. The model

Consider a drainage basin, such as that of the Baltic Sea, withseveral smaller basins, h=1,…n, and countries, g=1,..,j, whereeach country containsmgbn drainage basins. All countries anddrainage basins have coastal zones to the marine sea, whichimply that there are no external relations in loads amongregions in the catchment but only in the marine sea, which isdemonstrated in the following. Two main strategies areavailable for each drainage basin; mitigation measures, whichimply decreases in upstream emissions in drainage basin h incountry g, Mghi with i=1,..,m different measures, or adaptationmeasures, such as construction of nitrogen sequestration at therecipient, Aghk, with k=1,..,p different abatement options.Examples of mitigation measures are changes in farming orforestry land use practice and improved cleaning at sewagetreatment plants and industry. Adaptation measures implyincreased pollutant sequestration from pollutant assimilationby plants or from transformation of nitrogen into harmless gas,such as buffer strips and wetlands. For simplicity and withoutloss of generality, only one adaptation measure, wetlandconstruction, is considered at river mouths in the coastal zonein each basin, and Agh then refers to the area of wetlands.Wetland creation is regarded as a particularly promisingtechnology for the cleaning ofnutrients for downstreamaquaticecosystems (see e.g. Mitsch et al., 1988; Mitsch and Gosselink,

339E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 3 3 7 – 3 4 7

1993). Part of the nutrients that enter a wetland is transformedinto harmless gas, sedimented at the stream bottoms, orassimilated by water plants. Therefore, by strategic locationsof wetlands, at river mouths in the coastal zone with largepollution concentration, upstream emissions can be reduced bythe wetland before entering the marine sea.

Upstream emission from a drainage basin h in country g isassumed to be stochastic due to variable climatic conditionsaccording to

Egh ¼ PEgh �

XiMghi þ egh; ð1Þ

where E―gh is the unregulated emission level,Mghi with i=1,..,mdifferent mitigation measures, and ɛgh the error term. Adap-tive pollutant abatement in a basin, Sgh, is dependent onpollutant entering the site, Egh, area of the wetland, Agh, andstochastic factors such as precipitation and temperature(Mitsch and Gosselink, 1993). Consequently, adaptive abate-ment, Sgh, is defined as a function of upstream load to thewetland and wetland size, which is written as

Sgh ¼ Sgh Egh;Agh; eghA� �

; ð2Þ

where ɛghA is the error term, and Sgh is increasing in Egh andAgh. Total pollutant load to the marine sea from all countries gand drainage basins h is then

T ¼X

g

Xh

Egh � Sgh� �

ð3Þ

Stochastic programming is applied where it is assumed thatthe objective of the policymaker is tominimize total abatementcosts for achieving a probabilistic target on maximum T, socalled chance constraint programming (see e.g. Charnes andCooper, 1964; Birge and Louveaux, 1997). The pollution target,T⁎,is then required to be obtained with a minimum level of achosen probability α ∈ (0,1), which is written as

Pr TV T4½ �z a ð4Þ

There exist a number of studies where this method hasbeen used to include probabilistic constraints in models, forexample Paris and Easter (1985), Milon (1987), McSweeny andShortle (1990), Shortle (1990), Byström et al. (2000), Gren et al.(2002), Elofsson (2003). The technique is to standardize thevariables of the probabilistic constraint in Eq. (4) and utilizethe properties of the standard distribution to obtain adeterministic abatement requirement corresponding to theprobabilistic formulation in Eq. (4). The deterministic equiv-alent to the pollution constraint in Eq. (4) is written as:

E T½ � þ /aVar Tð Þ1=2 V T4; ð5Þ

where

Var Tð Þ ¼X

g

XhVar Tgh

� �þX

h

Xj p h

Cov Tgh;Tgj� �� �

þX

g

Xkpg

Cov Tg;Tk� �

; ð6Þ

Var Tgh� �

¼ Var Egh� �

þ Var Sgh� �

� 2Cov Egh; Sgh� �

; ð7Þ

E is the expectation operator, and ϕα is a standard numbersuch that

R /a

�l f uð Þdu ¼ a; φ is the standardized distribution of

T and f(φ) is the probability density function for φ. In order toavoid positive probabilities for negative loads to the marineseawe assume a lognormal distribution in the total load to thesea, T, but no assumptions are imposed on the probabilitydistributions for Tgh,, due to the difficulties of then assessingthe probability distribution of T (see discussion in e.g. Kampasand Adamidis, 2005; Destouni and Gren, 2005). For givenexpected loads, probability, and coefficient of variation for T,the standard number for this distribution can then be obtainedfrom statistical tables for the standard normal by a suitabletransformation (see Gren et al., 2002).

The expression for the variance in total load to the recipient,Var(T), is of specific interest in this paper. This can be dividedinto three main components: variances within and amongcountries, the first and second term respectively at the righthand side of Eq. (6), within and among drainage basins in acountry, i.e. the expressionwithinparentheses at the right handside of Eq. (6), andbetweenmitigation andadaptationmeasuresin a drainage basin as shown by Eq. (7). The variance for eachdrainage basin, Var(Tgh), has an interesting interpretation. Thetwo first variables at the right hand side of Eq. (7) reflect the ownvariances of upstream pollutant load and adaptationmeasures.When independence is assumed between Egh and Sgh, Var(Tgh) ispositive and contains only these variances as in Gren et al.(2002). However,whether or not this is the correct expression forVar(Tgh) when considering stochastic interdependence dependson the signs andmagnitudes of the covariance term at the righthand side. If this term is positive, Var(Tgh) is reduced ascompared to when Cov(Egh,Sgh)≤0. This, in turn implies thatthe restriction in Eq. (5) becomes less tight, and, hence, the totalcosts for achieving the probabilistic target are reduced.

Cost functions for mitigation and adaptation measures,Cghi(Mghi) and Cgh(Agh) respectively, are assumed to be increas-ing and convex.

3. Optimal allocation of measures

From the probabilistic restriction (Eq. (5)) it is seen thatminimum costs for a probabilistic constraint are alwayshigher then for the deterministic case when the variance inT is disregarded, which has been shown theoretically inseveral studies and demonstrated empirically in some (e.g.McSweeny and Shortle, 1990; Shortle, 1990; Gren et al., 2002;Elofsson, 2003). However, the role of stochastic pollution foroptimal allocation of abatement measures have been lessinvestigated, and in particular the role of the covariance inpollutant loads among measures and countries.

A marine sea like the Baltic Sea is shared by severalsovereign countries. Therefore, optimal mitigation and adap-tation measures are here derived under two types ofinstitutional designs for achieving an agreed target ofmaximum load, T⁎, at the minimum probability α. One iswhere all countries cooperate on an overall cost effectivesolution and the other is an agreement of a policy withuniform proportional load reductions with the same reliabilitytarget as under the cooperative policy. Uniform policies havebeen common for nitrogen reductions to the Baltic Sea, wherecountries have agreed to reduce their loads by a certainproportion in relation to the initial loads (Hjort, 1992).

340 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 3 3 7 – 3 4 7

Under an overall cost effective solution, total costs from alldrainage basins are minimized with respect to the chanceconstrained target, which is written as

MinMghi ;Agh

Xg

Xh

XiCghi Mghi

� �þ Cgh Agh

� �� �� �s: t: Eq: 5ð Þ

ð8Þ

The first-order conditions for optimal allocation of abate-ment measures are

ACghi

AMghi ¼ k wAVar Tð ÞAMghi

� �þ E AEgh

� �AMghi � E ASgh

� �AMghi

!ð9Þ

ACgh

AAgh ¼ k wAVar Tð ÞAAgh

� �� E ASgh

� �AAgh

!ð10Þ

where

w ¼ /aVar Tð Þ�1

2;

AVar Tð ÞAMghi ¼ AVar Egh

� AMghi þ AVar Sgh

� AMghi � 2ACov Egh;Sgh

� AMghi

þX

jph

ACov Tgh;Tgj� AMghi þ

Xlpg

ACov Tg;Tl�

AMghi ;

ð11Þ

and

AVar Tð ÞAAgh ¼ AVar Sgh

� AAgh � 2ACov Egh;Sgh

� AAgh

þX

j p h

ACov Tgh;Tgj� AAgh þ

Xl p g

ACov Tg;Tl� AAgh

ð12Þ

The left hand sides of Eqs. (9) and (10) show the marginalcosts of the two types of measures, and the right hand sidespresent the marginal impacts on the target T⁎. The latterconsists of two main parts for both types of measures, themarginal impact on expected load and on variance in load.The condition for optimal ACghi

AMghi contains an additional compo-nent, the third term within parentheses at the right hand sideof Eq. (9), which is the impact of reductions in up streams loadon adaptive abatement. The reduction in load implies lessabatement for a given level of adaptation measures, and isthus reducing the total marginal impact ofMghi. This marginalcost increasing impact of mitigation measures for waterpollution on downstream abatement measures has beenshown in several other studies (e.g. Byström, 1998; Hart, 2003).

For AVar Tð ÞAMghi b0 and AVar Tð Þ

AAgh b0, the marginal impacts are in-creased and, for a given T⁎, total minimum costs are decreasedas compared to when the marginal impacts on variances arenon-negative.However,whetherornot themarginal impactsonthe variances are negative depends on the probability distribu-tions and the functional relation between load and themeasures. In the empirical application in Section 4, constantcorrelation coefficients are assumed among drainage basins,and linear functionsareassumedfor the impactof themeasureson load to the Baltic Sea. Themarginal impacts on the variancesfrom themeasures are then negative. Total minimum costs arealso reduced for a positive Cov(Egh, Sgh) as compared to anegative, which can be seen from the coefficient ψ, which isincreasing in Cov(Egh, Sgh). Furthermore, marginal impacts on

the target decrease when the derivatives of Cov(Egh, Sgh) withrespect toMghi and Agh are positive.

The cost effective location of measures among countries isfurther determined by the sumof covariance terms over all thecountries and drainage basins. Regions with positive covari-ance in load then have cost advantages since a decrease inload from these regions reduce overall variance more than ifthe same measure is implemented in regions with zero ornegative covariances. However, the spill-over of covarianceamong countries is not accounted for under the assumeduniform policy, and the difference in total cost under nationalregimes as compared to the coordinated solution depends onthe sign of the sum of covariance terms. In order to show this,first-order conditions under national abatement is derived byassuming that the national targets are formulated as equalproportional targets of unregulated loads, which is derivedfrom the international target T⁎=νT′, where νb1 is the targetedshare of unregulated pollution T′. The target for each countryg is then Tg⁎=νTg′, where Tg′ is unregulated load. It is furtherassumed that the reliability requirement, ϕα, is the same forall countries. Each country contains mgbn drainage basins.The decision problem for country g is thus formulated as

MinMghi ;Agh

Xmg

h

XiCghi Mghi

� �þ Cgh Agh

� �� �s: tXmg

hE Eghh i

� E Sghh i

þ /aVar Tgð Þ1=2V Tg⁎ð13Þ

Associated first-order conditions are

ACghi

AMghi ¼ kg wg AVar Tgð ÞAMghi

� �þ E AEgh� �AMghi � E ASgh

� �AMghi

!ð14Þ

ACgh

AAgh ¼ kg wg AVar Tgð ÞAAgh

� �� E ASgh� �AAgh

!ð15Þ

where

wg ¼ /a Var Tgð Þ�1

2;

AVar Tgð ÞAMghi ¼ AVar Egh

� AMghi þ AVar Sgh

� AMghi

�2ACov Egh;Sgh�

AMghi þX

jph

A Cov Tgh;Tgj�

AMghi

ð16Þ

AVar Tgð ÞAAgh ¼ AVar Sgh

� AAgh � 2ACov Egh;Sgh

� AAgh þ

Xjph

ACov Tgh;Tgj� AAgh

ð17Þ

By comparing the first-order conditions (Eq. (14)) and(Eq. (15)) with those under the coordinated solutions, i.e. Eqs.(9) and (10), it can be seen that the single country solutions donot include the impacts of its cleaning on total variancethrough the sum of effects on all covariance terms. Thisimplies that total abatement under uniform national probabi-listic targets will be higher (lower) than the overall targetedload for positive (negative) sum of marginal impacts on thecovariance terms among countries. However, the interdepen-dency between the mitigation and adaptation measures as

341E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 3 3 7 – 3 4 7

revealed by the covariance term can either counteract orenforce this effect depending on the sign of the covarianceterm. The empirical demonstration to the Baltic Sea indicatesthat this effect is non-negligible.

Table 1 – Nitrogen loads, own variances, sum ofcovariances, and shares of total variance for year 2000

Countries Nitrogenload,

Ownvariance

Sum ofcovariances

Share oftotal

4. An application to the Baltic Sea

Like many seas and lakes, the use of the Baltic Sea as apollutant sink has been an important reason for the ecologicaldamages from eutrophication (e.g. Elmgren, 2001). Thisproblem was recognised already in 1974, but a ministerialdeclaration of nitrogen reductions, which at this time wasregarded as the limiting nutrient for biological growth,was nottaken until 1988 (e.g. Hjort, 1992). It was then agreed to reducethe total load to the Baltic Sea by 50%. However, in the year of1995, the target of the 1988 declaration had not yet beenmet. Itis presumed that approximately 10–15% nitrogen reductionhas been reached (Elofsson and Gren, 2004). Calculations ofminimum cost solutions under alternative internationalpolicy systems are therefore made for reductions up to 40%.Before presenting the results, a brief presentation of calculat-ed nitrogen transports, variances in load, and costs of differentmitigation and adaptation measures is provided, which isbased on Gren (2001) and Elofsson (2003).

Admittedly, reductions of only nitrogen will not solve theeutrophication problem of the Baltic Sea, which includes seabottoms with oxygen depletion, increased frequency of toxicblue green alga, and degradation of fish stock reproduction(e.g. Elmgren, 2001; Wulff et al., 2001). These damages arecaused by both fast and slow driven processes in nutrientloads, and differ for different areas of the Baltic Sea. Generally,it is regarded that Baltic Sea responses are slowwith respect tochanges in phosphorous loads, partly due to the long-termbinding of phosphorus in the sediments (e.g. Boesch et al.,2006). Nitrogen is a more mobile substance, and biologicalreactions in the coastal zones can occur within the sameseason as the change in load. This is one reason for imple-mentation of measures such as storing of manure duringwintertime, which aim at decreasing the leaching of nitrogenduring spring and thereby reducing the availability of nutrientfor algae growth in subsequent summer time. The need forprecision in nitrogen load reductions in order to avoiddamages in the near future can thus be regarded as ajustification for reliability constraints on the reduction target.

thousandton N

variance

Denmark 86 459 1324 0.136Finland 75 233 523 0.057Germany 36 53 529 0.044Poland 257 4136 1175 0.401Sweden 138 724 1489 0.168Estonia 59 113 74 0.014Latvia 131 689 −572 0.009Lithuania 60 93 734 0.063Russia 110 342 968 0.108Total 952 6842 6311 1.00

Sources: Nitrogen load data from Gren (2001) and drainage basincoefficients of variation and correlation coefficients from Elofsson(2003).

4.1. Brief presentation of nitrogen transports, mitigationand adaptation measures

In order to match data on nutrient drainage basin transportswith estimates of abatement costs, the entire Baltic Sea watercatchment of approximately 1,745,000 km2 is divided into 23drainage basins, which are shown in Fig. A1 in the Appendix.For each of these regions nutrient emissions originate fromthree types of sources: agriculture, sewage from householdsand industry, and air deposition. The calculations of nitrogenloads to the coastal waters of the Baltic Sea from theseemission sources are divided into two steps. First, all emissionsources are identified and quantified. Next, these emissions

are transformed into loads to the Baltic Sea by means of dataon leaching from the root zone into waters stream in thedrainage basins, retention of nutrient during the transport tothe sea, and air transports of nitrogen oxides and ammonia.Calculated loads are calibrated to nutrient loads measured atriver mouths along the coastal waters in 2000 due to theavailability of load data for this year (see Elofsson (2003) forfurther description).

Variance and covariance terms are estimated by means ofconstant correlation coefficients of nitrogen load for the 23drainage basins (Elofsson, 2003). These are, in turn, based onthe measurements of nutrient concentration at all rivermouths along the Baltic Sea coastal lines. It is assumed thatthe variation in load is caused by all emission sources notlocated at the coast. Table 1 presents data on nitrogen loads tothe coastal waters, own variances, and sum of covarianceterms with other countries.

Poland is the country with the largest share of total load,followed by Sweden and Latvia. We also see from Table 1 thatthe covariance among countries are significant and accountfor almost half of the total variance. However, in spite of therelatively large sum of total variance, the coefficient ofcorrelation (standard deviation divided by mean load) oftotal load is approximately 0.12, which, together with thereliability requirement, determine the impact of the probabi-listic part on the load constraint in Eq. (5).

Mitigation measures are implemented at all emissionsources with leaching or discharges into the waters of thedrainage basin. This study includes mitigation measures forchanges in agricultural practices, increased cleaning capacityat sewage treatment plants, and reductions in nitrogen oxideemissions from traffic and industry. More precisely, themeasures included in this empirical analysis are: increasednutrient cleaning capacity at sewage treatment plants,catalysts in cars and ships, flue gas cleaning in stationarycombustion sources, and reductions in the agriculturaldeposition of fertilizers and manure. Included land usemeasures are: change in spreading time of manure fromautumn to spring, cultivation of so called catch crops, energyforests, ley grass, and creation of wetlands. A change of

0

5000

10000

15000

20000

0 10 20 30 40Nitrogen reduction in %

Mill

ions

of

SEK

in 2

005

pric

es

Corr.=-1 Corr.=-0.5 Corr.=0

Corr.=0.5 Corr.=1

Fig. 1 –Minimum cost solutions for correlation coefficients of−1, −0.5, 0, 0.5 and1betweenwetlandabatement andupstreamnitrogen load for different nitrogen reductions at the reliabilityconstraint α=0.975. (1 Euro=9.34 SEK, August 20, 2007).

342 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 3 3 7 – 3 4 7

spreading time from autumn to spring implies less leachingsince, in spring, there is a growing crop which utilises thenutrients. Catch crops refer to certain grass crops, which aredrilled at the same time as the ordinary spring crop but thegrowth, and thereby the use of remaining nutrients in the soil,is concentrated to the period subsequent to the ordinary cropharvest.

Cost estimates of all mitigation measures are obtainedfrom Gren (2001) and Elofsson (2003). Abatement cost esti-mates for sewage treatment plants, fertiliser reductions,reduction in nitrogen oxides from reduced use of fossil fuelare based on econometric estimates of panel data. Estimatesof abatement costs for sewage treatment plants are based onpanel data for Sweden and Poland, the estimates of which aretransferred to other countries. Swedish estimates are trans-ferred to Finland, Denmark and Germany, and the Polishestimates to Estonia, Latvia, Lithuania and Russia. Costs forfertiliser reductions are calculated as losses in producersurplus, which, in turn, are calculated from estimates offertiliser demand functions in Sweden, Denmark, Finland, andGermany. Abatement costs of all other measures are obtainedfrom enterprise budgets in each country. Marginal costestimates indicate that improved cleaning at sewage treat-ment cost is the least costly option, and installation ofcatalysts in cars the most expensive measure, see Table A1in the Appendix. The reason for the high cost of catalysts is thelow impact from reductions in emissions of nitrogen oxides onthe Baltic Sea.

Since early 1990's there are several studies of wetlandcreation cost and pollutant abatement. The earliest study,Gren (1995), applies simple linear approximation of cost andabatement functions, while later studies such as Byström (1998)make econometric estimates of both cost and abatementfunctions. Cost functions for Swedish wetland creation arealso estimated by econometric methods in Scharin (2003) andSöderqvist (2002). However, none of these two latter studiesestimate wetland abatement functions. This study thereforeuses the cost andabatement functions fromByström (1998). Thecost per unit wetland area, which includes opportunity cost ofland and maintenance cost, estimated in Byström is approxi-mately 20% higher than in the other two studies (in 2003 prices).The estimates are transferred to other countries based on thevalue of land as opportunity cost for wetland creation.

Unfortunately, there exist no data on variance andcovariance in load for emission sources and wetlandabatement. We therefore make the simplifying assumptionthat the variations in loadings as reported in Table 1originate from all upstream located emission sources in therespective drainage basin. It is further assumed that thecoefficient of variation for wetland abatement is 0.7 (Byströmet al., 2000), and that the correlation coefficients of nitrogenamong all drainage basins and countries as reported inElofsson (2003) are constant. The ranges of correlationcoefficients for each country are reported in Table A1 in theAppendix.

4.2. Results

Based on the above assumptions and data, we obtain costeffective solutions for different levels of nitrogen reduction

up to a 40% reduction level. In order to calculate impacts oflinkages in risk between mitigation and adaptation mea-sures, minimum costs solutions are calculated and com-pared for five values of the correlation coefficient betweenupstream emission and wetland abatement, ρ, where ρ=1,ρ=0.5, ρ=0, ρ=−0.5 or ρ=−1. For ρ=0 there is no linkages inrisk, and when ρ=1, ρ=0.5 and ρ=−0.5, ρ=−1 there is apositive and negative relation respectively. The standard ϕα

is derived for α=0.975 with assumption of lognormaldistribution of total load to the Baltic Sea (see Gren et al.,2002 for transformation of normal to lognormal standard).This assumption is made to avoid small but positiveprobabilities for negative nitrogen load to the Baltic Sea.The algorithm applied for all calculations is GAMS (Brookeet al., 1998). Results are presented in Fig. 1.

Fig. 1 indicates negligible differences in minimum costsolutions for different assumptions on the risk linkagebetween upstream emission and wetland abatement forreduction levels below 20%. At the most, the minimum costsolutions for positive or negative linkages in risk diverge by1.5% from the solution where ρ=0 (see Table A2 in theAppendix). However, at higher reduction levels the costs caneither decrease by 13%, or 1830mill SEK, or increase by 17%, or2484 mill SEK, as compared to when it is assumed that ρ=0.

Themarginal cost at different reduction levels, fromwhichcost effective charges/subsidies at emission source can becalculated according to Eqs. (9) and (10), are also unaffected bythe choice of ρ at reductions less than 20% (see Table A2 inAppendix). At the 40% reduction level, the marginal cost isapproximately 60% higher or 35% lower than themarginal costfor ρ=0. The linkage in risk between the two types ofmeasurescan therefore have considerable effects on incomes for firmspaying charges or receiving incomes from compensationpayments.

Although positive or negative linkages in risk betweenupstream emission and wetland abatement have a minorimpact on total minimum costs and marginal costs atrelatively low nitrogen reduction levels, they can havelarge impacts under uniform national policies. In Table 2,

Table 2 – Costs in millions of SEKa for international and national uniform N reductions of 20% with α=0.975

Countries Correlation=0 Correlation=1 Correlation=−1

Coord. b National Coord. b National Coord. b National

Unadj. c Adj. d Unadj. c Adj. d Unadj. c Adj. d

Denmark 518 3491 2978 518 1219 1015 518 7315 6290Finland 185 890 839 136 865 748 185 865 840Germany 279 568 539 279 490 435 279 625 578Poland 1020 2652 2534 1020 2246 1981 1020 3018 2860Sweden 579 1443 1377 564 1414 1223 641 1414 1377Estonia 70 26 25 70 25 22 70 26 25Latvia 85 41 40 143 40 37 85 41 40Lithuania 343 143 140 294 133 124 332 143 140Russia 332 289 268 332 271 238 332 289 268Total cost 3409 9543 8640 3355 6703 5823 3460 13,724 12,356Reduction in % 20 21 20 20 23 20 20 21 20

a 1 Euro=SEK 9.34 (August 20, 2007);b Coordinated solution where overall costs are minimised;c National solutions where countries disregards impacts on total covariance with unadjusted target;d National solutions where the target is adjusted so as to achieve 20% nitrogen reduction.

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results from national probabilistic targets are presented for anitrogen reduction of 20%. This level is chosen since athigher reduction requirements, there is at least one countrythat cannot achieve the target due to limited abatementcapacities. For each correlation coefficient results are pre-sented for coordinated solutions and for uniform nationalpolicies, where the latter two are more fully described below.

As demonstrated in several studies, total costs underuniform national policies are higher than the coordinatedoverall minimum cost solutions (e.g. Baumol and Oates, 1988).The results in Table 2 show that the efficiency losses fromuniform systems are significantly affected by the assumptionof the correlation coefficient. They are smallest when ρ=1,being approximately 50% lower than when ρ=−1. This ispartly explained by the significant decrease in abatementcosts for Denmark when ρ=1, which has relatively highabatement costs due to the large variance in nitrogen loadand limited low cost options with impacts on expected andvariance in load.

Table 2 also shows the impact on total overall reductionwhen each country meet its own probabilistic constraint.Since countries are assumed not to consider covariance withother countries, total nitrogen load reduction differs from thetarget. These reductions are shown in the columns Non-adj.for all three levels of the correlation coefficient. Theovershooting impact of national probabilistic targets fromthe neglect of covariance with other countries is strongestwhen ρ=1. Although some countries are not affected at all—Estonia, Latvia, Lithuania, and Russia—since wetland con-struction is not part of their cost effective program at 20%nitrogen reduction, all other countries abate more whichimplies that, in total, an overall reduction of 23% is achievedinstead of the targeted 20%. If this is accounted for by relaxingthe overall nitrogen reduction target, as shown by thecolumns Adj., in Table 2, total costs could be reduced by 10–13% depending on the sign of the correlation coefficient. Loadreduction costs for Denmark are reduced considerably,

approximately 15–17%, from considering the overshootingof the overall probabilistic target under uniform nationalpolicy.

Given the noteworthy impact on costs of the sign of thecorrelation coefficient between wetland abatement andupstream emission, it is of interest to further investigateplausible sign. There exist no measurement of the covari-ance, but it is known that, for a given nitrogen deposition,leaching from land is relatively large under seasons with lowgrowth of plants and when there is much precipitation,which in turn is dependent on the temperature (e.g. Arheimeret al., 2005). Nitrogen abatement by wetlands can, inprinciple, take place by growing plants, sedimentation atthe water stream bottoms, and by denitrification wherenitrogen is transformed into harmless nitrogen gas (e.g.Mitsch and Gosselink, 1993). Abatement by plant assimilationdepends on the temperature, being high for warm climatewhen there also is relatively little leaching which wouldindicate a negative covariance in emission and abatement.Sedimentation by plants depends on currents and biologicalconditions on the bottoms, which may not be muchcorrelated with nitrogen emissions from land. However, alarge part of nitrogen abatement takes place by denitrifica-tion, which mainly depends on the water turnover in thewetland. When this is low, denitrification occurs at highloads of nitrogen, which would indicate a positive covariancein nitrogen upstream leaching and abatement by wetlands(Poe et al., 2003). Thus, the sign of the covariance depends onwhich abatement technology is most important for thewetland. If denitrification is important, the impact on totalcosts of a correlation coefficient of 0.5 might then berelatively realistic, which reveals that total costs at highreduction levels can be reduced by approximately 6% and themarginal cost at the same reduction level by 17%. A policyconclusion from this study is thus to consider variability inupstream load and in abatement when designingwetlands asnitrogen sinks.

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5. Summary and discussion

The purpose of this paper has been to analyse and comparemitigation and adaptation strategies against stochastic waterpollution with a focus on the role of linkages in risk betweenthe two strategies. Stochastic programming was applied andlinkage in risk was defined as the covariance betweenremaining pollutants after mitigation measures and adapta-tion measures, such as construction of wetlands. The analyt-ical results then showed that positive covariance decrease andnegative increase total risk, which, in turn, implies that totalcosts for a given probabilistic target decrease or increase.Measures with positive marginal impact on the covariancethen have a cost advantage as compared to measures withnon-positive marginal effect.

It was also shown, that, in an international perspective, thecovariance in load between countries entail a public good orpublic bad aspect depending on whether the covariance ispositive or negative. When country targets are derived on thebasis of common proportional reductions and reliabilityconstraints, total abatement may exceed that of a commoninternational target. The reason for the larger abatement inthis study is that countries are assumed not to considerreductions in the covariance with other countries, but onlytheir own variances.When there is a positive relation betweenabatement and the covariance, more abatement is carried outunder national uniform policies than under the coordinatedsolution. However, if marginal abatement decreases thecovariance, too little abatement is undertaken by each countryso the overall probabilistic target is not met. This over- orundershooting effect of uniform national probabilistic targetsis enforced or counteracted by the linkage in risk betweenmitigation and adaptation measures depending on theircovariance.

The application to the Baltic Sea demonstrated nosignificant differences in total costs at low reduction levelsfor a positive or negative covariance between pollutant loadand adaptive abatement, but at higher reduction levels totalcost can diverge by approximately 17% from the case whenthere is no linkage in risk. The range of marginal costs islarger, and can either exceed the no linkage case by 60% or be35% lower for negative and positive covariance respectively.However, although the impact of linkage in risk is small ontotal costs for relatively low nitrogen reduction levels, therecan be considerable difference for countries under a systemwith uniform probabilistic targets. Furthermore, the over-shooting effect can imply a total cost increase by approxi-mately 15% for a positive covariance and by 10% for a non-positive covariance.

Thus, policies not considering the risk and linkages in riskbetween mitigation and adaptation measures can result inhigher costs than necessary for achieving given probabilistictargets. However, the design of efficient policies under riskand risk linkages can be difficult in practice due to the need ofdifferentiating instruments with respect to the impact onaverage and variable pollutant load from each emissionsource and adaptation measure (see e.g. Shortle, 1990;Byström et al., 2000). Furthermore, the existence of asymmet-ric information among policy makers and firms undertaking

the mitigation and adaptation measures may give rise tomoral hazard (e.g. Laffont and Tirole, 1993). Both these factorscreate transaction costs, which should also be consideredwhen designing policies accounting for risk. The results in thispaper indicate that efficiency losses of uniform policysystems, which most often entail relatively low transactioncosts since all firms face the same requirement, may in fact bereducedwhen considering linkages in risk betweenmitigationand adaptation measures.

In the analysis in Section 3 and empirical application inSection 4 it has been assumed that the countries do notconsider the impact on its own variance from load reductionsin other countries. If this assumption is relaxed, and Nashsolutions are found where each country acts given othercountries choices, the nitrogen load reduction would besmaller and, hence, the overshooting impact would bereduced (see e.g. Barrett, 2005). The empirical results pre-sented in Section 4 can then be considered as upper and lowerlimits of the cost from deviating from the overall probabilistictarget. It is, however, quite likely that these costs increase forhigher reduction and/or reliability requirements.

From the theoretical analysis and the empirical demon-stration on the Baltic Sea we can conclude that considerationof linkages in risk between mitigation and adaptationmeasures, measured as covariance in pollutants after mitiga-tion measures and adaptation measures, can either increaseor decrease overall risk in total pollution to the water recipientand thereby total and marginal cost for a given probabilisticconstraint. However, due to the relatively recent interestamong researchers for the variability of pollution emissions,existing data are rather incomplete. Although pollution loadsto the Baltic Sea are relatively well documented, the empiricalconclusions of this paper therefore partly rest on assump-tions, in particular with respect to covariance among abate-ment measures.

The problemof lack of data is aggravatedwhen consideringalso regulation of phosphorous loads, since this would requirequantified dynamic relation between the two nutrients forcreation of eutrophication in stochastic terms. Elofsson (2006)demonstrates that total costs and associated allocation ofmeasures differ significantly depending on assumed function-al relation between nitrogen and phosphorous in producingeutrophication in the Baltic Sea in a static and deterministicsetting. Hart (2003) shows how total costs depend on targetsetting and water ecosystem responses to pollutant loads in adynamic setting. The current study shows that considerationof allocation of risk among mitigation and adaptation mea-sures also has considerable impacts on total costs underreliability constraints. Future research incorporating slow andfast processes in the dynamics of nitrogen and phosphorousrespectively under probabilistic constraints can therefore befruitful also under assumed quantified relations betweensdifferent nutrients and abatement measures.

Acknowledgements

I am much indebted to two anonymous referees for their veryvaluable comments and to the Swedish Research CouncilFormas for financial support. The usual disclaimer applies.

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Appendix A

Table A1 – Expected marginal costs for mitigation and adaptation measures, SEK/kg N reduction, coefficient of variation ofnational load, and correlation coefficients with other countries

Countries Mitigation: Adaptation: wetlands Coefficient of variation Correlation coefficients

Agriculturea Sewage Air emm.b

Denmark 25–220 48–144 180–805 15–180 0.25 −0.08–0.74Finland 34–250 48–244 515–3700 60–750 0.21–0.25 −0.36–0.65Germany 22–140 20–61 453–3000 25–350 0.20 −0.35–0.68Poland 33–240 9–45 420–2800 10–120 0.18–0.29 −0.31–0.76Sweden 22–850 48–244 150–1780 60–750 0.17–0.35 −0.51–0.85Estonia 60–670 9–45 130–650 12–160 0.18 −0.51–0.60Latvia 80–420 9–45 160–1100 12–160 0.20 −0.45–0.59Lithuania 78–610 9–45 220–1500 12–160 0.16 0.15–0.71Russia 31–350 9–50 160–1900 10–120 0.17–0.39 −0.19–0.70

Sources: Gren (2001), Elofsson (2003);a Livestock reductions (pigs, chicken, and cattle), land use changes (catch crop, energy forests, ley grass), spreading of manure in spring, andfertilizer reductions;b Installation of catalysts in cars, and flue gas cleaning at stationary combustion sources.

Table A2 – Total minimum costs, TC in mill SEK/year, and marginal cost, MC in SEK/kg N reduction, at different nitrogenreductions in per cent and assumptions of correlation coefficients between upstream nitrogen emission and wetlandabatement

% N reduction Corr.=−1 Corr.=−0.5 Corr.=0 Corr.=0.5 Corr.=1

TC MC TC MC TC MC TC MC TC MC

10 1630 12 1630 12 1628 12 1627 12 1627 1220 3460 27 3427 27 3409 26 3376 25 3355 2530 7483 50 7287 48 7077 48 6858 46 6579 4140 16,683 289 15,733 268 14,235 178 13,390 148 12,407 116

346 E C O L O G I C A L E C O N O M I C S 6 6 ( 2 0 0 8 ) 3 3 7 – 3 4 7

Fig. A1

Fig. A1 –The Baltic Sea drainage basin (Elofsson, 2003).

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