dynamics of soil acidification: an economic analysis

Ecological Economics 31 (1999) 449–462

ANALYSIS

Dynamics of soil acidification: an economic analysis

Erik C. Schmieman *, Ekko C. van IerlandEn6ironmental Economics Group, Department of Economics and Management, Wageningen Uni6ersity, Hollandseweg 1, 6706 KN,

Wageningen, The Netherlands

Received 23 November 1998; received in revised form 14 June 1999; accepted 14 June 1999

Abstract

This paper studies the dynamic aspects related to the problem of acidification. It shows how accumulation ofacidification in ecosystems can be studied in economic modelling by incorporating dynamic aspects of soilacidification. In contrast to the often applied critical loads approach which only focuses on the final state of a soil,the dynamic approach applied in this study gives information about the temporal development of the quality of a soil.Using an economic optimal control model containing these dynamic aspects the paper compares abatement policiesbased on static critical loads to abatement policies based on a dynamic analysis. It shows that soil dynamics play anessential role in identifying optimal policies. Based on numerical simulations cost-effective abatement strategies forcombined reduction of sulphur dioxide (SO2) and nitrogen oxides (NOx) are determined. It is also shown thatabatement cost savings may be realised when intertemporal cost efficiency is taken into account. The results indicatethat current European policies which are based on a critical loads approach instead of dynamic analysis of soilquality, are non-optimal from both an ecological and an economic point of view. © 1999 Elsevier Science B.V. Allrights reserved.

Keywords: Acid rain; Critical loads; Dynamics of acidification; Soil acidification; Optimal control

www.elsevier.com/locate/ecolecon

1. Introduction

Acidification affects water, soil and ecosystems.Acidifying compounds such as sulphur dioxide(SO2) and nitrogen oxides (NOx) are often pro-duced together, most typically by the burning of

fossil fuels. Ammonia (NH3), causing acidificationand eutrofication, is usually emitted by agricul-tural activities. Currently, many ecosystems in theUnited States, Europe, and the emergingeconomies in Asia face acid deposition far inexcess of their specified critical loads.1 The excess

* Corresponding author. Tel.: +31-317-483809; fax: +31-317-484933.

E-mail addresses: [email protected] (E.C.Schmieman), [email protected] (E.C. van Ier-land)

1 A critical load is defined as a quantitative estimate ofexposure to one or more pollutants below which harmfuleffects, which are judged to be significant on specified elementsof the environment, do not occur according to present knowl-edge (Nilsson and Grennfelt, 1988).

0921-8009/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

PII: S 0921 -8009 (99 )00067 -1

E.C. Schmieman, E.C. 6an Ierland / Ecological Economics 31 (1999) 449–462450

acid depositions and their transboundary naturemake it necessary to reduce acidification on aninternational level.

By introducing the critical loads concept in the1980s an indicator was created that could be usedin policy plans aiming to reduce the problem ofacidification. The relative simplicity of the con-cept has led to many applications in the environ-mental economic literature. Many studies havecalculated cost-effective reduction of sulphurdioxide, nitrogen oxides and ammonia based ondeposition calculations and critical loads.2 Ini-tially the studies contained a limited number ofcritical loads. Later, however, after increasedknowledge of ecosystems and their response toacid deposition and detailed mapping of criticalloads, it became possible to develop models thatcalculate cost-effective reduction strategies basedon critical loads for various ecosystems and fordifferent pollutants.

Abatement policies for acidification presently inplace in the European Commission and theUnited Nations Economic Commission of Europe(UN-ECE) are founded on the use of criticalloads. In the resulting protocols under the con-vention on long-range air pollution, depositiontargets are formulated in ‘gap closure’ scenarios.The ‘gap’ is the difference between the actualdeposition and the critical load, and the target isto reduce this gap by a certain percentage at somepoint in time. However, in the period betweensigning the agreements and the time the targetswill be met, depositions are exceeding criticalloads, and soils will deteriorate. It is unknown towhat extent, and how long it will take for the soilto fully recover. Information about the temporaldevelopment of the soil quality (as being analysedin this study by explicitly modelling the basesaturation) can therefore be useful to redefinepolicy targets. This would avoid damage toecosystems in the period during which critical

loads are exceeded and would take into accountthe time it takes the soil to recover. We will showhow one can overcome the shortcomings of acritical load as an indicator to protect ecosystemsfrom acidification.

Natural scientists stress that it is not sufficientto focus solely on acid deposition and criticalloads: the dynamic aspects of acidification shouldbe taken into account as well. Rennings andWiggering (1997) point out that the critical loadconcept is only an initial indicator for the envi-ronmental quality of complex ecosystems. In astudy on critical loads and recovery of forestsoils, Hettelingh and Posch (1994) show the im-portance of knowing the time a soil or ecosystemneeds to recover from excess acid deposition.With knowledge of the recovery period, which canbe longer than 70 years (Hettelingh and Posch,1994), one can determine the rate at which emis-sion abatement should be implemented. The useof dynamic soil acidification models also canprovide important additional informationfor regional steady-state critical load calculations(Forsius et al. 1997). De Vries (1993) statesthat critical loads give information about theacceptable levels of acid deposition in the longterm. Dynamic soil acidification models can beused to predict the time period before a criticalion concentration or ion ratio will be reached.Other natural science studies stressing the impor-tance of analysing abatement policy options usingdynamic soil acidification models include Holm-berg (1989), De Vries and Kros (1991) and Bull(1995).

Important economic and political reasons alsoexist for incorporating these dynamic processesinto economic models. The timing of emissionreduction influences abatement costs, technologi-cal development and economic growth. Postpone-ment of emission reductions may be efficient if themarginal productivity of capital is positive. Fu-ture burdens are relatively cheaper because fewercurrent resources are set aside for future reduc-tion. In addition, the costs of reduction are ex-pected to decline over time (Wigley et al., 1996).Earlier reductions, however, may be efficient be-cause earlier emission reductions will stimulatelearning (Grubler and Messner, 1998) and emis-

2 See, for example, Maler (1989), the Regional AcidificationInformation and Simulation (RAINS) model, Alcamo et al.(1990), Van Ierland (1991), Amann et al. (1992). Other appli-cations are found in Altman et al. (1994), Amann andKlaassen (1995), Zylicz (1995), Amann et al. (1997) the Eu-ropean Commission (1997) and Amann et al. (1998a).

E.C. Schmieman, E.C. 6an Ierland / Ecological Economics 31 (1999) 449–462 451

sion reduction can prevent irreversible damage toecosystems and related economic costs. Despitethese reasons, dynamic aspects of acidificationreduction strategies are examined in only a fewenvironmental economic studies (the most impor-tant are Kaitala and Pohjola (1988), Kaitala et al.(1992), Maler (1994) and Maler and De Zeeuw(1994)).

Acidification as a transboundary air pollutionproblem has often been analysed in game theory(either static or dynamic) because acidificationaffects a common property resource in an asym-metric way, involves many countries, all withdifferent incentives, and the countries have notagreed upon a set of rules (Maler, 1989). In adynamic acid rain game, damage is determined notby annual depositions, but rather by accumulateddepositions (Maler, 1994). However, not beingable to incorporate accumulation of acid deposi-tions, Maler focuses on dynamics induced by anacid rain game that is played repeatedly in thefuture. Recently, Maler and De Zeeuw (1998)introduced in ‘the acid rain differential game’ away to account for accumulation of acidification.They assume that when critical loads are exceededthe buffer stock for acidification decreases, andwhen depositions are below critical loads thebuffer increases. However, the behaviour of thebuffer stock is not related to chemical processes inthe soil or to the quality of the soil in a way thatdescribes ‘real’ soil acidification. The studies havein common a focus on steady state outcomeswithin a game theory framework. Kaitala et al.(1992) include an equation that describes dynamicsoil acidification based on results from a dynamicsoil acidification model. This equation calculatesthe temporal development of a chemical soilparameter (the base saturation) that can be consid-ered to be a soil quality indicator. They relate thisindicator to reduced forest growth and hence toeconomic damages caused by acidification. Apply-ing game theory, Kaitala et al. (1992) derive bothco-operative and non co-operative solutions to anacid rain game between Finland and the USSR.

The aims of our paper are three-fold; first, toinvestigate how dynamic aspects of acidificationcan be included in economic modelling used tocalculate cost-effective time paths for reducing

acidifying pollutants; second, to show how gapclosure scenarios based on critical loads can func-tion in a model that accounts for dynamic pro-cesses in acidification; and third, to performintertemporal cost-effectiveness analysis.

Our study enhances the literature by integratingimproved ecological modelling that incorporatesdynamic aspects of acidification with economicmodelling, and by contrasting the results obtainedfrom a dynamic model with those of more tradi-tional comparative static models based on criticalloads. By doing so, this study presents a methodfor combining dynamic economic modelling withthe modelling of dynamic soil acidification pro-cesses. The study also provides insights into thetemporal development of soil quality and presentsintertemporal cost-effective3 strategies that takeinto account both environmental and economicfactors.

The structure of the paper is as follows, thesecond section identifies the dynamic behaviour ofthe quality of soils with respect to acidification.The third section develops a theoretical modelsuitable for analytical purposes by deriving opti-mal time paths for the reduction of SO2 and NOx.In the fourth section we illustrate mechanismsusing a numerical example, and the fifth sectiondeals with spatial and intertemporal cost-effective-ness. We draw conclusions in the last section.

2. Dynamic aspects of soil acidification

In this section we describe a simplified soilacidification model that includes the dynamics ofsoil acidification.4 Dynamic aspects of soil acidifi-cation can be indicated by the temporal develop-ment of the base saturation of a soil.5 The base

3 From an economic viewpoint it would be desirable toapply cost-benefit instead of cost-effectiveness analyses. How-ever, valuing damages is a difficult task (if not impossible). Toovercome these difficulties we apply cost-effectiveness analysis.

4 Acidification models with many equations describing indetail soil and water chemistry are too complex to integratewith economic models; therefore we use a simplified andcondensed model.

5 Other indicators that could be used are, among others, thepH of a soil or the aluminium concentration in a soil.


saturation is defined as the fraction of exchange-able base cations in the solid phase of a soil. It isa chemical soil parameter that can be consideredas a soil quality indicator for acidification. Thefraction of exchangeable base cation indicates theavailability of nutrients in the soil and thisavailability of nutrients influences growth offorests and other vegetation.

The base saturation at time t, B(t) is defined asthe stock quantity and is expressed as a fractionwith 0BB(t)51. The dynamic behaviour of thebase saturation in a soil can be described by thefollowing state equation (Eq. (1))6;

B: (t)=dB(t)

dt= −bB(t) lnB(t)−gD(t)B(t) (1)

with D(t) being a deposition function, and b\0and g\0 as coefficients which can be estimatedusing dynamic soil acidification models. By a statetransformation of f(t)= ln B(t) (and thus B(t)=ef(t)) the state equation transforms into (omittingsubscript t with respect to f):

f: = −bf−gD(t) (2)

Parameter b can be interpreted as a recoveryrate, while g identifies how fast a soil responds to(changes in) acid deposition. A lower base satura-tion will result in a more acidified and less fertilesoil. From Eq. (2) we can derive that the basesaturation recovers faster at lower levels (that is,the more a soil is degraded by acidification thefaster the soil recovers) and that the process ofacidification is always reversible. This is a suitabledescription of the behaviour of the base satura-tion (De Vries and Reinds, 1998). Below a certainvalue of the base saturation, what we call thecritical value, vegetation and ecosystems that de-pend on the soil are assumed to face increasing

risks of damage and harmful effects, due to long-term acidification (Posch, 1998).

The critical loads for acid deposition arederived from the critical base saturation (Bc), andare derived for steady state conditions that is forf: =0. Using Eq. (2) and Bc, which transforms tofc(fc= ln Bc), and, assuming an infinite timehorizon, we can derive the critical load (Dc) foracid deposition from the following expression:

Dc=−bfc

g(3)

If we solve Eq. (3) for the critical base satura-tion fc, it can be seen that fc is independent ofthe initial condition of the soil, and independentof depositions before the time period under con-sideration (before t=0), and the analysis does nothave to start before the process of acidificationbegan (before industrialisation). For our calcula-tions we set the parameter values at b=0.015,g=0.0001 and the critical limit for the base satu-ration at Bc=0.10. The values for b and g arechosen arbitrarily, but magnitudes are based onparameters estimated for a poor Finnish forestsoil as applied in Kaitala et al. (1992). Using soilscientific research, we know that a reasonablecritical limit for the base saturation is either 0.05or 0.10 (Posch, 1998).

Using Eq. (3) we can compute the critical load,Dc:345 acid equivalents per hectare per year(eq/ha per year). The resulting soil is quite sensi-tive to acidification since actual critical loadsrange from less then 200 acid eq/ha per year insome places in Scandinavia and Central Europe toover 1000 acid eq/ha per year in most of SouthernEurope. From Eq. (3) and Fig. 1 we also see thatfor a constant deposition below the critical load(Dcon=100 acid eq/ha per year), the base satura-tion will converge to B:0.51. For a constantdeposition higher than the critical load (Dcon=900 acid eq/ha per year), B will converge toB:0.002.7 See Fig. 1 for the temporal develop-

6 The only relation we could find in the literature thatdescribes soil acidification dynamics in one simple equation

reads B: (t)=dB(t)

dt=aB(t)−bB(t) lnB(t)−gD(t)B(t). The

equation is taken from Kaitala et al. (1992) and is derived bythese authors using a model developed by Holmberg (1990).To further simplify the equation we set a equal to zero byassuming that the term is captured by gD(t) as a type ofbackground deposition. Further, we express the base satura-tion as a fraction and not as a percentage.

7 Solving Eq. (3) for the ln-transformed base saturation

gives f=−Dcg

b. For known b and g and given constant

deposition Dc and by applying the exponential transformationthe base saturation Bc can be determined.


Fig. 1. The temporal development of the base saturation (as a fraction) for a constant high (900 eq/ha per year) and constant low(100 eq/ha per year) acid deposition for four different cases, Bc=0.10 and the critical load Dc:345 acid eq/ha per year.

ment of the base saturation for different initialconditions of the soil (B0) and different levels ofdeposition.

By formulating a model that incorporates soildynamics one can determine when the criticalbase saturation (Bc) will be reached given initialconditions of a soil and assuming a known depo-sition function (D(t)). By using critical loads only,as is being done in many studies, one cannotanalyse the temporal development of the condi-tion of a soil itself.

In the next section we develop an analyticalmodel that accounts for the dynamic behaviour ofsoils, and we derive optimal cost-efficient timepaths for emission reduction.

3. Dynamic cost-effective reduction ofacidification

In our model we want to reduce emissions ofpollutants that lead to acidification of soils. Un-abated emissions are represented by En,t

k andabatement is given by An,t

k for acidifying pollutantk, with n representing an emitting country for anytime t and both emission and abatement are ex-pressed in kilotons (1 kiloton is 1 000 000 kg). Theabatement cost functions are given by Ck(An,t

k )and are assumed to be twice differentiable, convexand increasing in An,t

k (that is C %n,k\0, C %%ni,k\0)at any time t. Total abatement cannot exceedtotal emissions (En,t

k ]An,tk Öt). For now we as


sume no technical progress, resulting in constantabatement cost functions over time. For reasons ofsimplicity we assume further that unabated emis-sions (E( n

k) are given and are constant over time.This can be explained be assuming no economicgrowth and no growth in energy consumption.Emissions in country n are transported to receptorcountries m by air, and depositions in receptorcountry m can be calculated using transport ma-trices Mk.8 The matrix Mk is assumed to be constantover time.

Total reduction costs (TC) are calculated as thesum of both the discounted reduction costs inperiod t to the time that the problem reaches theconstraint in the base saturation which we call theterminal time T, and, the discounted reductioncosts beyond time T to maintain reduction levelsthat avoid further decrease of the base saturation.

TC=%n

%k

�& T

0

e−rtCn,tk (An,t

k )dt

+&�

T

e−rtCn,tk (An,t

k )dt�

(4)

We can rewrite this expression resulting in Eq. (5)yielding a maximisation problem formulated asmaximising the negative costs, with V being thepresent or discounted value of the sum of totalabatement costs over the whole period, An,t

k beingthe variable to control, and u(fm

c ,AT,r,T) express-ing a scrap value function depending on the lowerbound of the base saturation, as well as theabatement level in period T(AT), the discount rate rand T. Accordingly, we want to find the abatementpath An,t

k that maximises (omitting subscript t)9:

MaxV=%n

%k

& T

0

−e−rtCnk(An

k)dt−u(fmc ,AT,r,T)

(5)

subject to the soil equations for every country m (weassume that every country consists of one homoge-neous soil):

f: m= −bmfm−gm%k

mmk (E( k−Ak) (6)

with bm\0, gm\0. Row vector mkm is the mth row

of matrix Mk. E( k and Ak are, respectively, theemission and abatement vectors of pollutant k.Further, abatement cannot exceed emissions (E( n

k−An

k]0). The ln-transformed base saturation isrequired to be greater than a critical value fm

c inany country m at any t(fm−fm

c ]0) and the initialcondition for a soil is given by the initial fm

0 valueand is assumed to be known (fm(0)=fm

0 ).The current value Lagrangian L reads as follows:

L=H=%n

%k

(−Cnk(An

k))

+%m

lm

�−bmfm−gm%

k

mmk (E( k−Ak)

�+%

n

mnk(E( n

k−Ank)+%

m

mm(fm−fmc ) (7)

This results in a control problem with m stateequations and k pollutants in every emitting coun-try. As long as the constraints are not binding (andhence the Kuhn Tucker multipliers mm and mn arezero) the optimal marginal costs of reduction aregiven by (the details of deriving Eq. (8) are given inthe Appendix).

C %nk=C %%nk A: n

k

r+bm

(8)

This indicates that the marginal abatement costof a pollutant k is equal to the change in themarginal cost multiplied by the change in abate-ment divided by the discount rate plus the recoveryrate bm. In other words, according to Hotelling’sefficiency rule, the relative change in marginalabatement costs should be equal to the sum of thediscount rate and the recovery rate

(C %%nkA: n

k

C %nk=r+bm). (9)

It should be noted that the relative change isindependent of both how the soil responds to aciddeposition (parameter gm) and the transport matrixMk. Both the discount and the recovery rate have

8 The transport matrices include a factor that translatedepositions in kton to acid equivalents per hectare per year, 1kg/ha sulfur is equivalent to 62.5 acid equivalents per hectareand 1 kg/ha nitrogen converts to 71.428 acid equivalents perhectare.

9 Using the concept of limits the second term of Eq. (4) canbe rewritten as follows:u(fm

c , AT, r, T)= �T e−rtC(At)dt limb��

bTe−rtC(At)dt

= limb��

�−C(At)e−rt

r

nT

b

=C(AT)e−rT

r


the same effect, a higher value shifts abatementeffort to the future and a lower value shifts theefforts to the present. The results are very similarto optimal paths of abatement of greenhouse gases(see, for example, Falk and Mendelsohn (1993)).The optimal time path of the base saturation canbe determined by substituting the optimal paths ofemission reduction in Eq. (6). Together with theinitial and transversality condition the abatementlevels at t=0 can be calculated. The optimal timepath of reduction is also determined by parametergm and transport matrix Mk. Moreover, the asym-metric transport matrix partially determines thelevel of the base saturation and may lead todifferent developments in different countries, evenif the soils are assumed to be identical. By usingproper functional forms of the cost functionstogether with the transversality conditions theoptimal path for the base saturation can be deter-mined (see Appendix).

From this section we conclude that a highdiscount rate r, a high recovery rate b as well ashigh marginal abatement cost C %(A) tend to post-pone emission reduction, though for different rea-sons. A high recovery rate has a volume effect andmakes it less necessary to abate because from anatural science point of view the soil can absorb agreater acid deposition. A high discount rate orhigh marginal costs have a price effect and lead topostponement of emission reduction because of ahigher present value of abatement costs. The slopeof the marginal abatement cost curve (C %%(A)) alsodetermines the distribution over time, a steepermarginal cost curve results in smaller changes inabatement over time. Each is an important factorfor obtaining cost-effective solutions.

4. Accumulation of acidification, critical loads anddamage delay time

To further investigate factors that influencecost-effective solutions we analyse the results of anumerical optimisation model that contains dy-namic aspects of soil acidification. Two abatementscenarios are of particular importance and wecompare them to show the main mechanisms.First, we examine the ‘optimal abatement’ sce-

nario in which the model calculates cost effectivereduction of SO2 and NOx given a minimumstandard for the quality of the soil (a lower boundon the base saturation). Second, we investigate‘the protocol implementation’ scenario in whichwe assume that emission reductions are imple-mented analogous to the current European poli-cies based on the sulphur and nitrogen oxidesprotocols (United Nations, 1985, 1988). In thisscenario it is assumed that no emission reductionis realised in the first period 1980–1984. In 1985the target reduction is minus 40% of 1980 emissionlevels to be realised in the year 2000 for both SO2

and NOx. Between 2001 and 2010 a further reduc-tion is implemented to minus 80% of 1980 levels,and beyond 2010 emission levels are assumed to beconstant. In addition, we assume that emissionreduction measures are linearly implemented be-tween the year that the target becomes effectiveand the year the target is to be met. The data usedin the numerical model are given in Table 1.

4.1. Accumulation of acidification and criticalloads

Fig. 2 shows the typical development of deposi-tion patterns for the cost effective abatement pathand the protocol implementation scenario. Emis-sions show similar patterns because they are lin-early transformed by the transport matrix to

Table 1The most important data used in the one country model runa

Value

Constant emissions (for all t beforeabatement)

1700SO2 (Kton/year)700NOx (Kton/year)

Deposition before abatement (acid eq/ha 1650per year)

Initial value base saturation, fm0 (fraction) 0.40

0.10 (0.05)Critical value base saturation, fmc (fraction)

345 (450)Critical load (acid eq/ha per year)4.8 (3.7)Initial exceedance of critical load (times

critical load)5 (2.8)Discount rate (%)

a Data are hypothetical but are selected according to Eu-ropean magnitude. Numbers between brackets are used insensitivity analysis.


Fig. 2. Typical deposition pattern according to implementation of the European sulphur dioxide and nitrogen oxides protocols andthe deposition patterns according to the cost effective abatement strategy.

depositions. The reduction is higher in the optimalreduction strategy relative to reduction in theprotocol scenario, due to the extra restriction thatwe impose, and the quality of the soil is not allowedto decrease under a certain level. Efficiency gainsare realised by a trade-off between SO2 and NOx

reduction depending on their marginal abatementcosts. This is comparable to the ‘ordinary’ costeffective solution in a multiple pollutant setting.Due to technical limitations, the maximum reduc-tion for both pollutants is assumed to be 90% ofthe unabated emission level. This explains the kinkin the optimal deposition path (at t=2002). At thatpoint sulphur reduction is limited to 90% andfurther reduction is realised by NOx abatementwith higher marginal costs. The discount rate andthe marginal abatement costs determine the distri-bution of abatement over time and hence thereduction time path. For a lower (higher) discountrate, the constraint on the soil quality becomesbinding later (earlier) in time.

Fig. 2 shows that the depositions reach thecritical load in both countries after the year 2010.With the deposition at 330 acid eq/ha per year andthe critical load at 345 acid eq/ha per year, depo-sitions are strictly below the critical load becausea uniform cut back of 80% for both NOx and SO2

is more than sufficient to reach the critical load. If

one were to compare the deposition to the criticalloads, one would conclude that ecosystems areprotected and will not encounter an increased riskof damage due to acidification after the year 2011.Although many studies draw this conclusion it isnot always correct (e.g. some cost-effective acidreduction scenarios calculated with the RAINSmodel that are based on a target of x%-percentecosystems protection (Amann et al., 1998b). Be-low we explain why.

4.2. Accumulation of acidification and the damagedelay time

Fig. 3 shows the development of the base satura-tion in both the optimal reduction strategy andthe protocol implementation scenario. Under theoptimal reduction strategy the lower bound on thebase saturation is reached at about t=2011 andthen remains constant.10 From Eq. (8) we have

10 It should be noted that different soils characterised bydifferent values for the parameters bm and gm respond differ-ently to excess acid loads. Therefore, for some soils a temporalexceedance of critical loads might not be a problem becausethe soils respond so slowly that they would never reach theircritical values. However, some soils may respond so quicklythat critical values are soon surpassed and the quality of thesoil will deteriorate even more then in the previous analysis. Inthat case, stringent reduction policies may be required.


already concluded that the recovery rate b andthe discount rate r both have the same effect. Anincreased time preference delays the time at whichabatement costs are incurred, causing the criticalvalue for the base saturation to be reached earlierin time.

Recalling Fig. 2, one would believe, that ac-cording to the deposition levels, ecosystems areprotected from increased risk of damage due toacidification in both scenarios after 2010. Fig. 3,however, leads to a different conclusion. In theprotocol implementation scenario, the quality ofthe soil in the country indicated by the basesaturation falls under the critical value in 1990and stays under for more than 90 years after thefull implementation of the protocols becomes ef-fective (provided that depositions remain constantafter 2010). Accordingly, the soil needs a longperiod to recover from the excess acid loads in thefirst three decades of the period under consider-ation. In this recovery period, also denoted asdamage time lag (DTL) (Hettelingh and Posch,1994), ecosystems face increased risk to acidifica-tion damage. This may result in reduced forestgrowth, a decrease in biodiversity, or other nega-tive effects. This mechanism shows exactly what

could happen when politicians agree on deposi-tion targets based solely on critical loads to bereached at some point in time. Damage mayoccur, because the critical loads approach doesnot take into account the extent that soils aredegraded and how long recovery may take. In-sights into the temporal development of the qual-ity of a soil can thus be useful for redefiningemission and deposition policy targets. It mayeven be the case that early reduction or morestringent policy targets at an earlier date may becost-efficient when the monetary value of damageis taken into account. Moreover, a cost benefitanalysis including dynamics of soil acidificationand potential damage caused by low soil qualitymay result in shifting emission reduction closer tothe present.

5. Spatial and intertemporal cost-effectiveness ina transboundary context

In this section we show how allowing for in-tertemporal cost-effectiveness can lead to betterco-operative cost-effective solutions relative tostatic cost-effective solutions. The model in this

Fig. 3. Typical development of the base saturation according to implementation of European sulphur dioxide and nitrogen oxidesprotocols and the development of the base saturation according to the cost effective abatement strategy.


Table 2The most important data used in the numerical model runsa

Country BCountry A

Constant emissions (for all tbefore abatement)

2000500SO2 (Kton/year)800NOx (Kton/year) 300

0.40 0.40Initial value base saturationfm

0 (fraction)Critical value base saturation 0.10 0.10

fmc (fraction)

Critical load (eq/ha per year) 345345Discount rate (%) 55

a Data are hypothetical but are selected according to Eu-ropean magnitude

To analyse potential cost savings of flexibletiming we follow the analyses of Manne andRichels (1995) with respect to greenhouse gasreduction. We distinguish three situations. InCase I, the time path of emission reduction isfixed and the countries both reduce a fixed per-centage of their unabated emissions. From this‘uniform cut back’ scenario (similar to implemen-tation of the European SO2 and NOx protocols)the model calculates depositions and the resultingquality of the soil indicated by the base saturation(a similar scenario has been investigated in theprior section).

In Case II we allow for spatial effectiveness,which in fact is comparable to the cost-effectivesolution that can be calculated with IIASA’sRAINS model (Alcamo et al., 1990). In this sce-nario we set maximum depositions equal to thecalculated depositions of Case I for each corre-sponding period. Therefore, Cases I and II haveidentical paths for depositions (see Fig. 4) and thebase saturations (see Fig. 5) in both countries.Results for Country A and Country B are com-parable, therefore, we only show the results forCountry B because its soil is binding.

Fixing maximum deposition loads is similar towhat is often called a ‘gap closure scenario’. Thedifference between a uniform cut back (Case I)and a scenario allowing for spatial cost-effective-ness (Case II) occurs in the allocation of therequired emission reduction between countries.Countries are co-operative in finding the cost-ef-fective solutions by reducing emissions in thecountry facing lowest marginal costs either forSO2 or NOx reduction.

Case III allows for intertemporal and spatialcost-effective considerations by setting a mini-mum level for the base saturation rather than byfixing emission or deposition levels. From Cases Iand II we know the lowest reached base satura-tion at any point in time (i.e. Bm

c =0.043), andtherefore we require that Bm(t)]Bm

c for all t. Tomake Case III comparable to Cases I and II weadd one more restriction. The base saturation inCase III should have at least the level of the basesaturation in Cases I and II for every correspond-ing year after 2020. The latter restriction impliesthat emission reduction cannot be postponed fur-ther into the future relative to Case I and II.

section and its assumptions are equal to the as-sumptions in the analytical model developed ear-lier with the following details. The numericalmodel contains two countries, both of which havea single soil for reasons of simplicity. The impactof acid deposition on the soils of the countries ismodelled using the relations developed in section2. To derive emission targets we focus on the basesaturation (Bj) of the soil. The countries facedifferent abatement cost curves for the pollutant,even though the discount factor (e−rt) is equal forboth countries. Using the model, we investigatepotential gains from international co-operationand from flexible timing in the two-country worldunder consideration. We provide more detailsabout the data in Table 2.

To gain familiarity with the model we performa base run to determine the cost-effective abate-ment paths for NOx and SO2 given the constraintsBm(t)]0.10Öt for both countries. Country B, thedown wind country, has the binding soil. Thatmeans that the optimal solution is driven by theconstraint imposed on the base saturation inCountry B. The critical limit for the base satura-tion is reached in 2011, and deposition is equal tothe critical load (345 eq/ha per year). For t]2011emissions and depositions remain constant. Thedeposition in country A is below the critical load(DA=203 eq/ha per year) resulting in a recoveryof the quality of the soil. The base saturationconverges to a steady state in which BA=0.26.


If we allow for spatial and intertemporal trade-offs (in the way described under Case III) we findthat emissions are lower (and abatement costs arehigher) for the first years compared to Cases I andII (see Fig. 4). The quality of the soil, indicated bythe base saturation, in Country B stays at least asgood over the whole period under consideration(see Fig. 5). In country A the base saturationdecreases below the level of Cases I and II after2010 and remains slightly below.

In this numerical illustration, international co-operation will lead to 26% cost saving comparedto a uniform emission reduction. If the countriesco-operate in their reduction strategies and if theyallow for intertemporal cost-effectiveness, thenthey can realise an additional 6% cost savingsrelative to a uniform emission reduction. Addi-tionally, the quality of the soil in Country B stayshigher for the first 33 years compared to Case Iand Case II (see Fig. 5). Different discountrates do not change the percentage cost savingsmuch.

From this analysis we can conclude that costsavings, along with the same or less acidified soil,are possible if countries were to distribute their

emission reductions cost-effectively over time,taking into account dynamic aspects of soilacidification.

6. Conclusions

We have performed a dynamic optimisation ofcost-effective abatement strategies for a combinedreduction of the major acidifying compounds SO2

and NOx. The study provides a way to analyseoptimal time paths of emission reduction for SO2

and NOx by showing how dynamic aspects of soilacidification can be incorporated into economicmodelling. Based on dynamic soil acidificationmodels we can conclude that the stock behaviourof acidification cannot be described empiricallyusing linear functional forms. Using a numericalmodel we show the main features of the model.The results indicate qualitatively that an analysisof acidification in a dynamic setting takes intoaccount hard ecological constraints better thanthe traditional critical loads approach.

We also show that intertemporal cost-effectivereduction strategies may lead to cost savings com-pared to spatial international co-operative cost-ef-

Fig. 4. Deposition path for Case I: Uniform emission reduction, Case II: Spatial cost-effective emission reduction, and Case III:Intertemporal and spatial cost-effective emission reduction. Case I and II result in the same line, and only the results for (binding)Country B are shown.


Fig. 5. The base saturation for Case I: Uniform emission reduction, Case II: Spatial cost-effectiveness emission reduction, and CaseIII: Intertemporal and spatial cost-effective emission reduction. Case I and II result in the same line and only the result for (binding)Country B are shown.

fective solutions. This can be explained by a morecost-effective distribution of emission reductionover time when intertemporal efficiency is allowedcompared to spatial efficiency only. By allowingintertemporal efficiency, reduction measures withlow marginal costs are implemented early in time,and measures with high marginal costs are imple-mented later in time. In addition, we show thatthese cost-savings can be combined with a bettersoil quality indicated by a higher base saturation.

Currently European acidification policies arefounded on the use of critical loads resulting inacid depositions temporally exceeding the criticalloads. Based on critical loads analysis it is un-known to what extent a soil recuperates, and howlong it will take for the soil to fully recover.Information about the temporal development ofthe soil quality by explicitly modelling the basesaturation as is being done in this study cantherefore be useful to redefine policy targets. Thisavoids damage to ecosystems in the period duringwhich critical loads are exceeded, and takes intoconsideration the time necessary for soil recovery.Therefore, the results indicate that current Eu-ropean policies which are based on a critical loads

approach instead of dynamic analysis of soil qual-ity, are non-optimal from both an ecological andan economic point of view.

Acknowledgements

We wish to thank Maximilian Posch from theNational Institute of Public Health and the Envi-ronment, Bilthoven, The Netherlands, for givinguseful suggestions for the formulation of soilacidification dynamics. We thank Erwin Bulte forexplaining optimal control theory, and we thankCorjan Brink, Leen Hordijk and Carolien Kroezefor their useful suggestions. We thank threeanonymous reviewers for providing useful sugges-tions to improve the manuscript.

Appendix A

The first order conditions and the necessaryconditions that can be derived from the Lagran-gian given in Eq. (7) are (Eqs. (A1), (A2) and(A3)):


(L(An

k= −C %nk+%m

lmgm %k

Mk−mnk=0Ök,n (A1)

l: m=rlm−(L(fm

=lm(r+bm)−%m

mmÖm (A2)

f: m=(L(lm

= −bmfm= −lm %k

mjk(E( k-Ak) (A3)

The Kuhn Tucker conditions are shown in Eq.(A4) and Eq. (A5):

(L(mn

=Enk−An

k]0, mn]0, mn(E( nk−An

k)=0Ök,n

(A4)

(L(mm

=fm−fmc]0, mm]0, mm(fm−fm

c )

=0 Öm (A5)

If the optimal path of abatement is denoted byAn

k* and the optimal terminal time by T* then thetransversality conditions are (with pm(t)=ertlm)Eq. (A6):

pm(T)−(u(fm

c ,T)(T

]0,fm(T)−fmc ]0,

�pm(T)−

(u(fmc ,T)(T

�(fm(T)−fm

c )=0 (A6)

L(Cnk(An

k*(T*)), Ank*(T*), fm* (T*), pm* (T*),

mn*(T*), mm* (T*))+(u(fm

k ,T*)(T

=0 (A7)

The problem is formulated using a currentvalue Hamiltonian, the shadow price is given bylm and the current value shadow price by pm=ertlm.

In economic interpretation, Eq. (A5) meansthat if the lower bound (fm

k ) for the base satura-tion level is not binding, namely, that the stock orbuffer capacity of the soil to neutralise acidifyingdepositions is not totally used up, then the priceof abatement must be zero. According to Eq.(A7), a marginal change in the value of the scrapterm due to a marginal change of the terminaltime T* will be equal to an opposite change of thevalue of the Hamiltonian. The terminal time Tdepends on the discount rate, the recovery ratebm, the sensitivity of the soil gm to deposition andthe initial quality of the soil fm

0 .

References

Alcamo, J., Shaw, R.W., Hordijk, L., 1990. The Rains Modelof Acidification: Science and Strategies in Europe. KluwerAcademic Publishers, Dordrecht.

Altman, A., Amann, M., Klaassen, G., Ruszczynski, A.,Schopp, W., 1994. Cost-effective sulfur emission reductionunder uncertainty. Working Paper 94–199. InternationalInstitute for Applied Systems Analysis, Laxenburg.

Amann, M., Klaassen, G., 1995. Cost-effective strategies forreducing nitrogen deposition in Europe. J. Environ.Manag. 43, 289–311.

Amann, M., Bertok, I., Cofala, J., Klaassen, G., Schopp, W.,1992. Strategies for reducing sulfur dioxide emissions inEurope. SR-92-008. International Institute for AppliedSystems Analysis, Laxenburg.

Amann, A., Bertok, I., Cofala, J., Gyarfas, F., Heyes, C.,Klimont, Z., Makowski, M., Shibayev, S., Schopp, W.,1997. Cost-effective control of acidification andgroundlevel ozone. Third Interim Report. InternationalInstitute for Applied Systems Analysis, Laxenburg.

Amann, M., Bertok, I., Cofala, J., Gyarfas, F., Heyes, C.,Klimont, Z., Kurz, R., Shibayev, S., Schopp, W., 1998a.Cost-effective control of acidification and ground-levelozone. part A: methodology and databases. Fifth InterimReport to the European Commission, DG-XI. Interna-tional Institute for Applied Systems Analysis, Laxenburg.

Amann, M., Bertok, I., Cofala, J., Gyarfas, F., Heyes, C.,Klimont, Z., Makowski, M., Schopp, W., Syri, S., 1998b.Cost-effective control of acidification and ground-levelozone. Part C: acidification and eutrophication scenarios.Interim Report prepared for the 21st Meeting of the UN/ECE Task Force on Integrated Assessment Modelling.International Institute for Applied Systems Analysis(IIASA), Laxenburg.

Bull, K.R., 1995. Critical loads-possibilities and constraints.Water Air and Soil Pollut. 85, 201–212.

De Vries, W., 1993. Average critical loads for nitrogen andsulfur and its use in acidification abatement policy in theNetherlands. Water Air Soil Pollut. 68, 399–434.

De Vries, W., Kros, J., 1991. Assessment of critical loads andthe impact of deposition scenarios by steady state anddynamic soil acidification model. Report 36. The WinandStaring Centre, Wageningen.

De Vries, W. Reinds, G.J., 1998. Personal Communication.European Commission, 1997. Elements of a cost-effective

emission reduction policy. Some insights from the Eu-ropean auto oil 1 programme using the Leuven model.II/022/97-EN. European Commission Directorate-Generalfor Economic and Financial Affairs, Economic Services,Evaluation Transport, Environment and Energy Policies(II-B4), Brussels.

Falk, I., Mendelsohn, R., 1993. The economics of controllingstock pollutants: an efficient strategy for greenhouse gases.J. Environ. Econ. Management 25, 76–88.

Forsius, M., Alveteg, M., Guardans, R., Holmberg, M.,Jenkins, A., Johansson, M., Kleemola, S., Rankinen, K.,


Renshaw, M., Sverdrup, H., Syri, S., 1997. Assessment ofthe effects of the EU acidification strategy: dynamic mod-elling on the integrated monitoring sites. Finnish Environ-ment Institute, Helsinki.

Grubler, A., Messner, S., 1998. Technological change and thetiming of mitigation measures. International Institute forApplied Systems Analysis, Laxenburg (unpubl.).

Hettelingh, J.P., Posch, M., 1994. Critical loads and dynamicassessment of ecosystem recovery. In: Grasman, J., VanStraaten, G. (Eds.), Predictability and Non-linear Mod-elling in Natural Sciences and Economics. Kluwer Aca-demic, Dordrecht, pp. 439–445.

Holmberg, M., 1989. Model of ion dynamics and acidificationof soil: simulating recovery of base saturation. In: Fen-hann, J., Mackenzie, G.A., Rasmussen, B. (Eds.), Environ-mental Models: Emissions and Consequences. Elsevier,Amsterdam, pp. 359–368.

Holmberg, M., 1990. Ion exchange dynamics and soil acidifi-cation: model development and testing (licentiate thesis).Department of Mathematics and Systems Analysis,Helsinki University of Technology, Helsinki.

Kaitala, V., Pohjola, M., 1988. Optimal recovery of a sharedresource stock: a differential game model with efficientmemory equilibria. Natural Res. Modelling 3, 91–119.

Kaitala, V., Pohjola, M., Tahvonen, O., 1992. Transboundaryair pollution and soil acidification: a dynamic analysis ofan acid rain game between Finland and the USSR. Envi-ron. Res. Econ. 2, 161–181.

Manne, A., Richels, R., 1995. The Berlin mandate: the cost ofmeeting post-2000 targets and timetables. Columbus, OhioUSA (unpubl.).

Maler, K.G., 1989. The acid rain game. In: Folmer, H., VanIerland, E.C. (Eds.), Valuation Methods and Policy Mak-ing in Environmental Economics. Elsevier Science, Amster-dam, pp. 231–252.

Maler, K.G., 1994. Acid rain in Europe: a dynamic perspectiveon the use of economic incentives. In: Van Ierland, E.C.

(Ed.), International Environmental Economics: Theories,Models and Applications to Climate Change, InternationalTrade and Acidification. Elsevier Science BV, Amsterdam,pp. 351–372.

Maler, K.G., De Zeeuw A.J., 1994. Critical loads in games oftransboundary pollution control, paper presented at a con-ference: the economics of atmospheric pollution. theoriesapplied models and implications for international policymaking, 16–19 November 1994, Wageningen.

Maler, K.G., De Zeeuw, A.J., 1998. The acid rain differentialgame. Environ. Res. Econ. 12, 167–184.

Nilsson, J., Grennfelt, P., 1988. Critical loads for sulphur andnitrogen. Report from a workshop held at Skokloster,Sweden March 19–24, 1988. Kobenhavn.

Posch, M., 1998. Personal Communication.Rennings, K., Wiggering, H., 1997. Steps towards indicators

of sustainable development: linking economic and ecologi-cal concepts. Ecol. Econ. 20, 25–36.

United Nations, 1985. Protocol to the 1979 convention onlong-range transboundary air pollution on the reduction ofsulphur or their transboundary fluxes by at least 30%.ECE/EB.AIR/12. United Nations, Geneva.

United Nations, 1988. 1988 Protocol to the 1979 Conventionon Long-range Transboundary Air Pollution Concerningthe Control of Emissions of Nitrogen Oxides and theirTransboundary Fluxes. ECE/EB.AIR/21. United Nations,Geneva.

Van Ierland, E.C., 1991. The economics of transboundary airpollution in Europe. Environ. Monitor. Assess. 17, 101–122.

Wigley, T.M.L., Richels, R., Edmonds, J.A., 1996. Eco-nomic and environmental choices in the stabilisationof atmospheric CO2 concentrations. Nature 379, 240–243.

Z& ylicz, T., 1995. Cost-effectiveness of air pollution abatementin Poland. Environ. Res. Econ. 5, 131–149.

.

dynamics of soil acidification: an economic analysis

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