Influential Receptors in Targetted Emission Control Strategies
S t u a r t Batterman
August 1987 WP-87-079
Working Papers are interim reports on work of the International Institute f o r Applied Systems Analysis and have received only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute or of its National Member Organizations.
INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS A-2361 Laxenburg, Austria
Preface
The Regional Acidification INformation and Simulation (RAINS) model w a s ori- ginally developed to simulate effects of control s t r a t e g i e s of acid deposition. Re- cently, w e s t a r t e d t o extend RAINS with a n optimization m o d e which allows a u s e r of t h e m o d e l t o investigate receptor-oriented r a t h e r than source-oriented poli- cies. Applied t o Europe which in RAINS is subdivided in about 600 a r e a s , a n optim- ization demands l a r g e computer resources. In o r d e r t o be able to perform t h e op- timization on a personal computer, t h e problem size should b e reduced consider- ably.
S t u a r t Batterman from Texas A&M University (USA) who joined t h e Acid Rain P r o j e c t f o r s h o r t periods in 1986 and 1987 h a s found a n ingenious way t o cope with t h e problem size. In t h i s p a p e r h e r e p o r t s on his method and shows several exam- ples of use of t h e method of "influential receptors".
Leen Hordi jk
Leader, Acid Rain P r o j e c t
Abstract
Emission abatement s t r a t e g i e s which are t a r g e t t e d on environmental goals may provide cost-effective a l t e r n a t i v e s to flat-rate, source-oriented policies. I t i s not a trivial m a t t e r , however, t o develop t a r g e t t e d s t r a t e g i e s . Such s t r a t e g i e s may r e q u i r e t h e numerical optimization involving l a r g e numbers of variables and constraints. These problems demand l a r g e computer r e s o u r c e s . Moreover, t h e op- timization p r o c e s s itself i s likely t o be o b s c u r e f o r all but t h e most technically competent decision-makers.
In t h i s p a p e r , s e v e r a l techniques a r e p r e s e n t e d which identify t h e r e c e p t o r s locations which influence t h e outcome of t a r g e t t e d emission abatement s t r a t e g i e s . A s only such "influential" r e c e p t o r s are needed in optimization problems, t h e i r identification may permit a dramatic reduction in t h e computational burden. These r e c e p t o r s a l s o allow a more d i r e c t i n t e r p r e t a t i o n of t h e optimization problem.
A f t e r developing t h e s e f i l t e r s , influential r e c e p t o r s a r e identified f o r s e v e r a l pol- icies r e l a t e d t o t h e reduction of sulfur deposition in Europe.
Acknowledgements
The author i s indebted t o Markus Amann f o r his suggestions and review of this paper. Leen Hordijk encouraged the development of the simple ideas presented.
Wolfgang Schopp provided much assistance in the implementation of these ideas.
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vii-
T a b l e o f C o n t e n t s
1. Introduction 2. Rackground
2.1 Targetted emission abatement s t r a t e g i e s 2.2 Limitations of t a r g e t t e d s t r a t e g i e s 2.3 Influential r e c e p t o r s
2.4 Examples of influential r e c e p t o r s 3. Receptor f i l t e r s
3.1 Mathematical definition of inf luential r e c e p t o r s
3.2 Filter 1: Identifying r e c e p t o r s which cannot exceed t a r g e t s 3.3 Filter 2: Identifying influential r e c e p t o r s
3.4 Filter 3: Identifying t h e feasibility of t a r g e t loadings 3.5 Example problem
3.6 Spatially varying r e c e p t o r sensitivity 3.7 Policy constraints
4. Examples of influential r e c e p t o r s in Europe 4 . 1 Peak sulfur deposition
4.2 Peak SO2 concentrations 4.3 Flat r a t e deposition reductions 5. Summary and conclusion
References Figures
Influential Receptors in Targetted Ehksion Control Strategies
S t u a r t Battennan
1. INTRODUCTION
This p a p e r d e s c r i b e s a n a p p r o a c h to identify r e c e p t o r locations which influ- e n c e t h e outcome of t a r g e t t e d emission abatement s t r a t e g i e s aimed at controlling acidic deposition. These "influential" r e c e p t o r s define t h e smallest, but e n t i r e l y sufficient set of r e c e p t o r s r e q u i r e d f o r consideration in optimization problems.
By using only influential r e c e p t o r s , t h e number of r e c e p t o r s modeled in t a r g e t t e d emission control policies may b e g r e a t l y reduced, t h u s enabling a commensurate d e c r e a s e in t h e computational burden. The identification of t h e s e r e c e p t o r s a l s o provides insight into t h e f a c t o r s which influence t h e solution of t h e optimization problem. These f i l t e r s have been incorporated into t h e optimization module of t h e Regional Acidification INformation and Simulation Model (RAINS) (Alcamo et d., 1987).
Chapter 2 provides some background f o r t a r g e t t e d control policies. Chapter 3 p r e s e n t s t h e mathematical definition of t h e problem of identifying influential re- c e p t o r s , suggests a solution a p p r o a c h , and extends t h i s technique t o encompass spatially varying r e c e p t o r sensitivity and policy constraints. In C h a p t e r 4, t h e in- fluential r e c e p t o r s in E u r o p e are found using t h e EMEP m o d e l and s e v e r a l t a r g e t s f o r sulfur deposition. C h a p t e r 5 discusses t h e application of t h e s e results.
2. BACKGROUND
Environmental impacts f i r s t a t t r i b u t e d to long r a n g e t r a n s p o r t of a i r pollu- t a n t s o c c u r r e d in relatively few and w e l l defined a r e a s , such as t h e Black Forest, s o u t h e r n Finland and Sweden in Europe, and t h e Adirondacks in North America.
L a t e r r e s e a r c h indicates t h a t transboundary a i r pollutants may cause increased acidity and environmental impacts o v e r a much b r o a d e r , continental scale. Im- p a c t s of c o n c e r n include l a k e acidity, f o r e s t damage, accumulation and release of toxic metals in soil and drinking water, and materials damage in t h e constructed environment.
In recognition of t h e a d v e r s e e f f e c t s of acidic deposition, national and inter- national e f f o r t s t o r e d u c e emissions of p r e c u r s o r pollutants have begun. In Eu- r o p e , t h e Protocol t o t h e Convention on Long-Range Transboundary Air Pollutants (1986) s t a t e s a goal of reducting s u l f u r emissions by at l e a s t 30% from 1980 levels.
These reductions are t o b e achieved by 1993. This uniform o r "flat-rate" reduc- tion constitutes a "source-oriented" emission abatement strategies.
2.1. Targetted emission abatement strategies
In c o n t r a s t t o source-oriented s t r a t e g i e s , "receptor-oriented" o r "targetted"
emission abatement s t r a t e g i e s are focussed d i r e c t l y on environmental goals. These s t r a t e g i e s may achieve environmental t a r g e t s efficiently by coordinating emission reductions among t h e major emittors of pollutants. By linking mathematical models of pollutant emissions, abatement control costs, atmospheric t r a n s p o r t and en- vironmental impacts, c o n t r o l s t r a t e g i e s may be designed which are both more economical and more environmentally beneficial t h a n source-oriented s t r a t e g i e s . This a p p r o a c h h a s been used f o r North America by Ellis et aL. (1985), Fortin and McBean (1983) and Morrison and Rubin (1985), and f o r Europe by Batterman et aL.
(1986), Hordijk (1986), and Amann et aL. (1987). Similar policies have been suggest- ed f o r minimizing c o n t r o l c o s t s of emission abatement on a local s c a l e (Kohn, 1982).
Batterman et aL. (1986) and Amann et aL. (1987) have evaluated t h e c o s t s of s e v e r a l receptor-oriented policies in Europe. In some situations, i t i s possible t o achieve low deposition levels at environmentally sensitive r e c e p t o r s at a f r a c t i o n of t h e c o s t of f l a t - r a t e reductions. These initial studies indicate t h a t t a r g e t t e d s t r a t e g i e s may be advantageous, and f u r t h e r investigation seems warranted.
2.2. Limitations of targetted strategies
The usefulness and a c c e p t a n c e of t a r g e t t e d s t r a t e g i e s may b e impeded by a number of f a c t o r s . F i r s t , acidification i s a multifacetted problem. Targetted stra- tegies must be multiobjective, and t h u s solutions will b e subjective and depend on t h e decision-maker. The mathematical formulation of t h e decision problem as a n optimization problem might be highly simplified, considering only one o r two sub- objectives, f o r example. In addition, models usually have a s t r o n g bias towards ex- pected o r a v e r a g e results. P o o r o r even c a t a s t r o p h i c outcomes, to which decision makers may b e especially a v e r s e , may not b e modeled due t o t h e i r presumed low probability.
A second f a c t o r impeding t h e a c c e p t a n c e of t a r g e t t e d s t r a t e g i e s i s t h e high d e g r e e of political cooperation r e q u i r e d f o r implementation. Environmental im- p a c t s often o c c u r hundreds of kilometers from pollutant s o u r c e s and p e r h a p s in a d i f f e r e n t country, and t h u s cause-eff e c t relationships may a p p e a r tenuous. Cost sharing o r c o s t shifting mechanisms may b e useful t o equalize t h e c o s t s and in- c r e a s e t h e benefits of controlling transboundary pollutants.
A t h i r d f a c t o r concerns t h e mathematical models used t o formulate and evalu- a t e s t r a t e g i e s . These models have various e r r o r s , both known and unknown. If t h e e r r o r s a r e l a r g e , i t may not b e possible t o design t a r g e t t e d abatement s t r a t e g i e s . I t i s difficult t o reliably quantify s o u r c e - r e c e p t o r relationships which indicate t h e contributions of d i f f e r e n t pollutant sources. While atmospheric dispersion models may produce reasonably a c c u r a t e long-term (e.g., annual a v e r a g e ) predictions, t h e s e predictions are t h e sum of contributions from many countries, and model biases regarding contributions from one country may b e compensated by biases in t h e opposite direction from o t h e r countries. In t a r g e t t e d s t r a t e g i e s , however, g r e a t e r demands are placed on t h e a c c u r a c y of individual s o u r c e - r e c e p t o r r e l a - tionships; e r r o r s concerning costs, depositions and t h e overall c o n t r o l s t r a t e g y may b e compounded if s o u r c e - r e c e p t o r relationships a r e inaccurate. Similar con- clusions may hold f o r c o s t and emission models.
Because of model uncertainty, decision-makers may tend t o d i s r e g a r d model results. This possibility may o c c u r whether t h e models are used in a n optimization framework, o r in t h e more conventional "scenario analysis" mode.
A f o u r t h f a c t o r is r e l a t e d t o environmental t a r g e t s . T a r g e t s may b e r e l a t e d t o any of t h e d i v e r s e impacts caused by acidic deposition. T a r g e t s may u s e e i t h e r direct indicators of environmental impacts, e.g., f o r e s t impacts o r l a k e acidity, o r i n d i r e c t indicators, e.g., s u l f u r concentration and deposition levels. I t is ex- tremely difficult t o define i n d i r e c t indicators which will p r o t e c t f o r e s t s and l a k e s , f o r instance, from damage due t o acidification. T h e r e are l a r g e g a p s in t h e knowledge concerning t h e environmental consequences of transboundary pollu- t a n t s , and much of t h e d a t a n e c e s s a r y to use t h e s e models o n a l a r g e s c a l e is una- vailable. Additional difficulties are caused by dynamic ecosystem changes, limita- tions of c u r r e n t knowledge, and unanticipated developments in both p r e c u r s o r em- issions (e.g., from changed e n e r g y use p a t t e r n s ) and world climate.
One a p p r o a c h for specifying environmental t a r g e t s uses c r i t i c a l loadings f o r s u l f u r deposition (Nilsson, 1986). These c r i t i c a l loadings r e p r e s e n t maximum depo- sition levels below which no significant environmental impacts are believed to oc- c u r in t h e ecosystem. Such loadings may v a r y according t o t h e sensitivity of t h e t e r r e s t r i a l and aquatic environments.
A fifth factor r e l a t e d to t a r g e t t e d schemes, and t h e o n e a d d r e s s e d in t h i s pa- p e r , r e l a t e s t o t h e complexity of t a r g e t t e d schemes. In t h e mathematical specifi- cation of t h e optimization problem, environmental t a r g e t s f o r m c o n s t r a i n t s at some or a l l locations or " r e c e p t o r s " in t h e modeled domain. For transboundary a i r pol- lutants, t h e modeled domain is often v e r y l a r g e , covering E u r o p e or n o r t h e r n North America, f o r instance. Few areas c a n b e excluded as having no significant environmental impacts f r o m acidic deposition. Thus, t h e number of environmental c o n s t r a i n t s may b e v e r y l a r g e and involve hundreds of s o u r c e s and r e c e p t o r loca- tions. The corresponding optimization problem i s complex numerically and compu- tationally.
A complete discussion of t h e limitations of t a r g e t t e d s t r a t e g i e s i s beyond t h e s c o p e of t h i s work. H e r e , t a r g e t t e d s t r a t e g i e s are viewed as a l t e r n a t i v e s t o "flat r a t e " reduction schemes which may merit f u r t h e r discussion and analysis. A s t h e analysis of t a r g e t t e d s t r a t e g i e s r e q u i r e s models which i n t e g r a t e many a s p e c t s of t h e problem, t h i s a p p r o a c h p e r h a p s has t h e g r e a t e s t usefulness in a pedagogical sense: t h e models used r e p r e s e n t t h e c u r r e n t state of knowledge and c a n help focus discussion on t h e most c r i t i c a l a s p e c t s of t h e problem. Of c o u r s e , decision- makers and model u s e r s should b e aware of t h e assumptions and uncertainties of t h e models. The model d e v e l o p e r s should provide a f r a n k assessment of t h e s t r e n g t h s a n d weaknesses of t h e i r model.
2.3. Influential receptors
Both t a r g e t t e d emission c o n t r o l s t r a t e g i e s and more conventional s c e n a r i o analysis mode of m o s t i n t e g r a t e d models s h a r e t h e need to evaluate environmental impacts o v e r a l a r g e domain. This i s done by calculating ambient concentrations and depositions of s u l f u r at hundreds of locations, called r e c e p t o r s . Environmen- t a l impacts t h e n may b e estimated at t h e s e locations using ecological models.
The primary t a s k a d d r e s s e d h e r e is t h e identification of t h e r e c e p t o r s which influence t a r g e t t e d emission c o n t r o l s t r a t e g i e s . Such r e c e p t o r s a r e called "in- fluential" r e c e p t o r s . If environmental t a r g e t s are achieved at t h e influential re- c e p t o r s , t h e y also will b e satisfied at all r e c e p t o r s . A l l o t h e r so-called "inactive"
r e c e p t o r s may b e omitted in t h e formulation and solution of t a r g e t t e d c o n t r o l poli- cies. The influence of t a r g e t t e d s t r a t e g i e s t o only a few r e c e p t o r s and s o u r c e re- gions h a s been noted by s e v e r a l r e s e a r c h e r s , e.g., Ellis et al. (1985). In g e n e r a l , just a f e w r e c e p t o r s and "driving airsheds" were found t o limit t h e available a b a t e - ment options.
In t h i s p a p e r , s e v e r a l "filters" are developed t o identify influential r e c e p - tors. The f i l t e r s c a n b e used t o select a s u b s e t of r e c e p t o r s which are r e p r e s e n - t a t i v e and which provide "early warning" of a d v e r s e e f f e c t s . These r e c e p t o r s may b e used in both modeling and field studies (to help verify models).
The principal motivation for t h e p r e s e n t work i s t h e u s e of t h e s e f i l t e r s in t a r g e t t e d emission c o n t r o l s t r a t e g i e s . Environmental t a r g e t s at influential r e c e p - t o r s will form t h e c r i t i c a l or binding c o n s t r a i n t s which a f f e c t solutions to t h e op- timization problem. O t h e r r e c e p t o r s c a n b e ignored, at least f o r t h e p u r p o s e of op- timizing. Influential r e c e p t o r s are identified b e f o r e a n y optimization of emissions, costs o r environmental benefits. The f i l t e r s g r e a t l y r e d u c e t h e number of d e p ~ s i - tion c o n s t r a i n t s in optimization problems. F o r example, t h e European s c a l e RAINS model contains a b o u t 600 land-based r e c e p t o r s (Alcamo et al., 1987). In most op- timization problems, however, t h e r e are only s e v e r a l dozen influential r e c e p t o r s . This smaller problem i s solved much f a s t e r . Microcomputer implementations, which have s t r i c t limits on t h e number of constraints, t h u s become p r a c t i c a b l e .
2.4. Examples of influential receptors
The i n t e r p r e t a t i o n of influential r e c e p t o r s depends o n t h e formulation of t h e optimization problem. T h r e e examples shown below use t h e same t h e objective function, namely, t h e minimization of total costs, however t h e environmental tar- g e t s vary.
1. With maximum deposition limits, e.g., ~ ~ / m ' - ~ e a r , influential r e c e p t o r s are lo- cations which may e x p e r i e n c e t h e peak deposition u n d e r some set of emis- sions.
2. With limits on ecological impacts, e.g., f o r e s t damage as indicated by needle loss, influential r e c e p t o r s are locations which may e x p e r i e n c e t h e most s e v e r e ecological impacts under some emission condition.
3. With deposition limits based on a specified p a t t e r n , e.g., t h a t achieved by a 50% c u t in 1980 emissions, t h e deposition at influential r e c e p t o r s may b e closest or equal to t h e specified limits under some emission conditions.
A d i f f e r e n t set of influential r e c e p t o r s may b e g e n e r a t e d f o r each combina- tion of environmental goals and emission constraints. For example, s o u t h e r n Scan- dinavia may contain many of t h e influential r e c e p t o r s f o r l a k e acidification, while c e n t r a l E u r o p e may contain t h e influential r e c e p t o r s f o r forest damage. Different sets of influential r e c e p t o r s may o c c u r with different pollutants as well. If d e s i r e d , t h e s e p a r a t e l i s t s of influential r e c e p t o r s resulting from e a c h indicator
may b e combined, a n d o n e f u r t h e r level of f i l t e r i n g c a n b e used t o identify a s u p e r - s e t of influential r e c e p t o r s which includes s e v e r a l i n d i c a t o r s .
3. RECEPTOR FILTERS
This s e c t i o n p r e s e n t s t h r e e f i l t e r s which h e l p t o identify influential r e c e p - tors, defined as locations at which c o n c e n t r a t i o n , deposition or environmental tar- g e t s become binding c o n s t r a i n t s in t a r g e t t e d emission c o n t r o l s t r a t e g i e s . The t h r e e f i l t e r s are used r e s p e c t i v e l y to (1) identify r e c e p t o r s which c a n n e v e r e x c e e d environmental t a r g e t s ; (2) identify influential r e c e p t o r s ; a n d (3) test t h e feasibility of t h e environmental t a r g e t s . The a p p r o a c h a p p l i e s in a g e n e r a l way to optimization problems which h a v e few binding o r a c t i v e c o n s t r a i n t s in comparison t o t h e number of s l a c k c o n s t r a i n t s . B e f o r e d e s c r i b i n g t h e f i l t e r s , t h e mathemati- c a l definition of influential r e c e p t o r s is given. The c h a p t e r a l s o includes a simple example showing pair-wise comparisons used t o identify influential r e c e p t o r s . The f i l t e r s are t h e n e x t e n d e d t o handle spatially varying r e c e p t o r sensitivity a n d poli- c y c o n s t r a i n t s .
3.1. Mathematical definition of influential receptors
F o r simplicity, t h e following discussion u s e s s u l f u r deposition as t h e environ- mental indicator. In t h i s c a s e , influential r e c e p t o r s are locations which may pro- d u c e l o c a l maxima in deposition f o r some set of emissions. The r e s t r i c t i o n s in t h e example are r e l a x e d l a t e r when t h e vulnerability or sensitivity of r e c e p t o r s , t h e cumulative e f f e c t s of pollution, a n d policy c o n s t r a i n t s are i n c o r p o r a t e d .
F i r s t , d e f i n e f e a s i b l e emissions Si as emissions f o r c o u n t r y or r e g i o n i between s p e c i f i e d u p p e r a n d lower bounds:
These bounds should r e f l e c t t h e e x p e c t e d r a n g e of emissions, e.g., from totally u n a b a t e d t o completely c o n t r o l l e d . In t h e E u r o p e a n c o n t e x t , v e c t o r
Sf
c o n t a i n s emissions S1 from 27 E u r o p e a n c o u n t r i e s , a l l satisfying t h e bounds given in Equa- t i o n (1).Any v e c t o r
Sf
t h a t s a t i s f i e s t h e c o n s t r a i n t s in Equation (1) belongs to t h e f e a s i b l e emission s p a c e , c a l l e d S, s u c h t h a tSf
E S.R e c e p t o r s are g e o g r a p h i c a l l o c a t i o n s at which pollutant c o n c e n t r a t i o n s a n d depositions are computed. The deposition at r e c e p t o r k ,
Dk,
i s c a l c u l a t e d assuming a d d i t i v e e f f e c t s from e a c h pollutant s o u r c e region:where Ti, r e p r e s e n t s t h e dispersion, chemical transformation and deposition of s u l f u r emissions from country i to r e c e p t o r k , and B k i s "background" or deposi- tion at r e c e p t o r k which i s uncontrollable o r unattributed t o specific emission s o u r c e s . Using matrix notation, depositions are calculated at a l l r e c e p t o r s in vec- t o r D using t h e v e c t o r s of emissions
S
and background levelsB
a n d t h e t r a n s p o r t matrix T:(Individual r e c e p t o r s c o r r e s p o n d t o r o w s of t h e t r a n s p o r t matrix.)
R e c e p t o r j i s a n influential r e c e p t o r if t h e highest deposition among a l l re- c e p t o r s o c c u r s at t h e jth location f o r s o m e feasible v e c t o r of emissions
%
satisfy-ing Equation (1):
(D, ( q )
>
(Dk ( q ) f o r some%
E S; f o r all j # k (5) Influential r e c e p t o r s may b e viewed as locations of local maximum f o r a l l possible samples of emissions in t h e feasible emission space. (This problem is d i f f e r e n t from simply determining t h e single s i t e a t which t h e maximum deposition o c c u r s , which i s t h e r e c e p t o r with t h e highest deposition when all emissions are at t h e u p p e r bounds.) In g e n e r a l , t h e r e may b e s e v e r a l o r many influential r e c e p t o r s , depending on t h e t r a n s p o r t matrix T and t h e feasible emission space. These r e c e p - tors may be identified using t h e f i l t e r s described below.3.2. Filter 1: Identifying receptors w K c h cannot exceed targets
The f i r s t and extremely simple f i l t e r identifies a n d eliminates r e c e p t o r s at which t h e deposition calculated using t h e maximum feasible emissions, e.g., the unabated situation, i s below a specified t a r g e t , Dtar,,:
if (Xi Ti, Si,max
+
Bk) G Dtar,, t h e n eliminate r e c e p t o r kEliminating r e c e p t o r s using Equation (6) does not establish whether t h e remaining r e c e p t o r s are influential. I t helps to r e d u c e t h e computational work r e q u i r e d in t h e n e x t s t e p , however.
3.3. Filter 2: Identifying influential receptors
The second f i l t e r identifies influential r e c e p t o r s and may b e used after t h e application of Equation (6). The logic i s as follows. R e c e p t o r s fall into one of t w o c l a s s e s , i.e., influential a n d "inactive" (uninfluential) r e c e p t o r s . Pair-wise com- parisons are used t o identify some or all of t h e inactive r e c e p t o r s . By exclusion, t h e remaining r e c e p t o r s constitute influential r e c e p t o r s .
Substituting Equation (3) into Equation (5), r e c e p t o r k i s inactive if:
(Tj
Sf +
Bj) 2 (TkSf +
Bk) f o r s o m e j # k ; f o r a l lSf
E S (7) Thus r e c e p t o r k i s inactive if i t s deposition i s always smaller than or equal t o deposition at s o m e o t h e r r e c e p t o r j. Collecting terms, r e c e p t o r k is inactive if:(T,
-
Tk) Sf+
Bj-
Bk 2 0 f o r s o m e j # k ; f o r a l l % E S ( 8 ) The inactivity of r e c e p t o r k may b e established by finding t h e smallest d i f f e r e n c e between deposition a t r e c e p t o r s k and j, called djk:djk
=
min [(Tj-
Tk) + BJ- Bkl
S
If t h e "worst case" d i f f e r e n c e i s still positive, t h e n r e c e p t o r k i s a n inactive re- c e p t o r . The minimum i s found by observing t h a t e x t r e m a in t h i s l i n e a r problem oc- cur at edges or c o r n e r s of t h e h y p e r c u b e formed by t h e feasible emission space.
Equation (9) may b e evaluated by selecting e a c h S , such t h a t :
Si i s indeterminate and i r r e l e v a n t if Tij
=
Tik. I t should b e noted t h a t d J k h a s no re- lationship to dkj. Both values must b e computed.The p r o c e s s d e s c r i b e d above identifies a s u b s e t of t h e inactive r e c e p t o r s s i n c e Equation (9) eliminates r e c e p t o r s which are inactive with r e s p e c t to only s i n g l e r e c e p t o r s . I t d o e s not eliminate r e c e p t o r s which are inactive as esta- blished by t w o or m o r e r e c e p t o r s . For example, r e c e p t o r m may have g r e a t e r deposition t h a n r e c e p t o r k in one portion of t h e feasible emission s p a c e ; r e c e p t o r n a l s o may have g r e a t e r deposition t h a n r e c e p t o r k in t h e remaining emission space. R e c e p t o r k would not b e eliminated using Equation (7) although i t s deposi- tion is always l e s s than or equal t o depositions at one of t h e o t h e r r e c e p t o r s . A s defined by Equation (5), r e c e p t o r k i s inactive as i t n e v e r produces t h e maximum deposition. This situation i s analogous to elements of a c o r r e l a t i o n matrix: e a c h element indicates a single dependency between p a i r s of variables, b u t not t h e dependencies involving t h r e e or more variables, i.e., multiple colinearity. Howev- e r , even t h e s u b s e t provides a g r e a t reduction in t h e number of r e c e p t o r s con- sidered.
Tolerance
An optional s t e p may b e used to f u r t h e r r e d u c e t h e number of r e c e p t o r s in- cluded in t h e influential set. For p r a c t i c a l purposes, influential r e c e p t o r s which obtain just slightly h i g h e r depositions t h a n o t h e r r e c e p t o r s may b e eliminated. A t o l e r a n c e level, DtOl, may b e specified t o define t h e cutoff point. The t o l e r a n c e
may b e specified as a f r a c t i o n (e.g., 1 % ) of t h e maximum deposition.
With a tolerance, r e c e p t o r k i s inactive if:
(T,
-
T,)S, +
B,-
B,+
DL,,=
0 f o r some j # k; f o r allSf
E S (11) To use a t o l e r a n c e , Equation (11) r e p l a c e s Equation (8); DLol i s a l s o added t o t h e r i g h t hand side of Equation (9). This s t e p d e s t r o y s some p r o p e r t i e s (including uniqueness) of t h e set of influential r e c e p t o r s . However, t h e remaining subset of influential r e c e p t o r s may b e much smaller and entirely satisfactory.To implement f i l t e r 2, pair-wise comparisons between a l l r e c e p t o r s a r e re- quired. With s e v e r a l hundred o r thousands of r e c e p t o r s , this is a l a r g e number of comparisons. However, once a r e c e p t o r is determined a s inactive, i t may b e elim- inated from f u r t h e r consideration. A solution s t r a t e g y w a s designed t o exploit t h i s f a c t and speed computation. Initially, a r e c e p t o r is selected which is expected t o b e influential, e.g., one with a high deposition. This r e c e p t o r is compared t o a l l o t h e r r e c e p t o r s , many of which a r e likely t o b e inactive and thus eliminated. In subsequent iterations, r e c e p t o r s a r e selected in t h e same manner. This p r o c e d u r e w a s found t o be extremely efficient with r e s p e c t t o maximum deposition.
3.4. Filter 3s Identifying the feasibility of target loadings
The final f i l t e r is used simply t o determine if t h e t a r g e t c a n b e attained in t h e feasible emission space. If t h e t a r g e t c a n b e achieved a t minimum emissions, t h a t is:
c a n b e satisfied f o r e a c h r e c e p t o r , t h e optimization problem is feasible and a solu- tion exists. If t h i s equation cannot b e satisfied a t some r e c e p t o r s , t h e n no solution c a n b e obtained, and t h e t a r g e t s and/or t h e minimum emission v e c t o r must b e modi- fied. This f i l t e r is used only t o avoid t h e time consuming optimization p r o c e s s f o r a problem which h a s no feasible solution.
3.5. Example problem
A simple example using 4 r e c e p t o r s (A,B,C,D) and 2 emittors (1.2) i s used t o demonstrate t h e pair-wise comparisons described in t h e previous section. The r a n g e of feasible emissions and t r a n s p o r t matrix are given below. For simplicity, no background concentrations a r e assumed.
Emission ranges: 4 S S1 S 1 0 2 S S, S 5
Transport matrix: r e c e p t o r country 1 country 2
A 15 30
B 1 0 25
C 40 1 0
D 5 30
First, r e c e p t o r s A and B are examined. Equations (10) and (11) a r e used t o com- pute t h e minimum difference between t h e s e r e c e p t o r s , dAB:
Since d A B X , r e c e p t o r B is a n inactive r e c e p t o r . Of course, this may b e determined by inspection in this example since r e c e p t o r B has smaller coefficients f o r both countries than r e c e p t o r A, and thus always has a lower concentration. Next, re- c e p t o r s A and C are compared:
Receptor C cannot b e eliminated as dAcsO. Comparing r e c e p t o r s A and D:
Since dAD>O, re c e p t o r D may b e eliminated. A s only two r e c e p t o r remain, w e only need t o compute dCA:
Receptor A c a n b e eliminated since dAcsO. Thus, of t h e f o u r r e c e p t o r s , only re- c e p t o r C is influential. It is sufficient t o use only this r e c e p t o r in optimizations with t h e objective of reducing t h e maximum deposition at t h e f o u r r e c e p t o r s .
9.6. Spatially varying receptor sensitivity
Different soil types, hydrological domains, f l o r a and fauna may have different responses t o t h e same level of pollutant deposition o r ambient concentration.
Thus, t h e sensitivity o r vulnerability t o pollution varies spatially o v e r t h e recep- t o r s . If t h e relative sensitivity or environmental impact can b e expressed as a linear function of deposition o r concentration, t h e f i l t e r described in Section 3.3 may b e used t o identify influential r e c e p t o r s . The linearity requirement may not b e too r e s t r i c t i v e as threshold effects are satisfactorily represented, and lineari- zation may b e adequate for many purposes. Further flexibility is gained by t h e specification of only relative, not absolute, response functions. For example, i t is adequate t o specify t h a t a n area is 50% more sensitive than another, o r has a threshold effect 2 g/m2-yr lower.
The sensitivity of r e c e p t o r j is defined t o b e Linear if t h e environmental indi- c a t o r o r response, given by function R, is a linear and/or threshold function of
deposition or concentration D j:
where b(Dj
-
koj) i s z e r o if concentration Dj is lower t h a n threshold koj and unity otherwise; kl, and k2, are t h e i n t e r c e p t s and s l o p e of t h e indicator function.These t h r e e parameters are site-specific. While Equation (13) implies s t r i c t l y l i n e a r dose-response functions, in t h e c o n t e x t of finding influential r e c e p t o r s , i t i s a f a i r l y flexible formulation. Equation (13) may r e p r e s e n t (1) "proportionally"
varying sensitivity, (2) t h r e s h o l d e f f e c t s , and (3) cumulative dosages or p a s t en- vironmental "strain,
"
as shown below.P r o p o r t i o n a l e f f e c t s are modeled by kpj. For example, a doubling of k2j (with kl,=O) r e p r e s e n t s a n area which i s "twice a s sensitive" t o t h e s a m e amount of deposition.
Some models of environmental r e s p o n s e use concentration or deposition thresholds, below which n o a d v e r s e e f f e c t s are assumed to o c c u r . In t h i s case, k l j i s set to t h e negative of t h e t h r e s h o l d concentration.
Cumulative or historical e f f e c t s of pollutant e x p o s u r e may b e modeled using Equation (13) by calculating t h e "environmental s t r a i n " at r e c e p t o r j, f j , as
where t h e r e s p o n s e i s a function of deposition from time tl to time t2. The s t r a i n i s added to t h e i n t e r c e p t t e r m klj. Note t h a t t h e long t e r m (historical) r e s p o n s e function i s not limited to l i n e a r forms ( t h e s h o r t t e r m dose-response relationship s t i l l must b e linear.) The historical s t r a i n may b e calculated as a n c u r r e n t equiuaLent d e p o s i t i o n DBj:
This technique i s e x a c t if a l i n e a r r e s p o n s e m o d e l (where impact is a function of cumulative total dosage (where dosage
=
pollutant level x e x p o s u r e time) is used.Spatially varying functions may b e i n c o r p o r a t e d into t h e formulation by modifying t h e threshold concentration Dthres, t h e v e c t o r of background concentrations B, and t r a n s p o r t matrix T to DBthres, BBj and TBij, respectively. f o r all r e c e p t o r s :
3.7. Policy constraints
A s mentioned e a r l i e r , i t is difficult and controversial to define deposition o r concentration objectives on t h e basis of environmental impacts. A s a n a l t e r n a t i v e t o such receptor-based goals, deposition constraints may b e formulated on t h e basis of emission goals in a source-based s t r a t e g y . A s a n example, a number of countries have a g r e e d t o r e d u c e emissions from 1980 levels by at least 30% by 1993. The deposition p a t t e r n resulting from t h e s e emission reductions, o r some o t h e r emission p a t t e r n , might s e r v e as constraints in t a r g e t t e d emission reduction s t r a t e g i e s t o minimize a g g r e g a t e European costs. In t h e c a s e of 30% uniform reductions f o r a l l emitters, t h e deposition at e a c h r e c e p t o r , Dj, must satisfy t h e following constraint:
where Si,lg80 i s t h e 1980 emissions from country i. Receptor k will b e inactive if i t s deposition constraint is satisfied w h e n e v e r t h e deposition constraint on some o t h e r r e c e p t o r , say r e c e p t o r j, i s satisfied f o r a l l feasible emission v e c t o r s
%
:(Dkl%)SGk if ( D j J % ) S G j f o r all
%
E S ; f o r some jfk ( 1 8 ) Equation ( 1 8 ) may b e written as:(Gk-Dkl%)20 if ( G j - D j l S f ) W f o r a l l
%
E S; f o r s o m e j f k (19) T h e r e i s a subtle difference between Equations (19) and (5) used t o define a n in- fluential r e c e p t o r in t h e c a s e of meeting a single deposition limit. Unlike Equation (5). Equation ( 1 9 ) permits no comparison between levels at r e c e p t o r s j and k. How- e v e r , r e c e p t o r s are always inactive if they have equal o r g r e a t e r "slack" o r m a r - gin in meeting deposition goals than o t h e r r e c e p t o r s . Thus, inactive r e c e p t o r k would meet deposition t a r g e t s by a n amount equal t o o r l a r g e r t h a n those at in- fluential r e c e p t o r j:(Gk-Dk(Sp) 2 (Gj-DjlSp) 2 0 f o r all
Sp
E S ; f o r some j f k ( 2 0 ) This i s more r e s t r i c t i v e than by Equation ( 1 9 ) , i.e., fewer r e c e p t o r s would satisfy Equation (20). However, because t h e t r a n s p o r t matrix T contains only positive elements, Equations (19) and ( 2 0 ) produce equivalent results. Thus, Equation (20) may b e t r e a t e d like Equation (9); r e c e p t o r k is inactive if t h e r e e x i s t s a r e c e p t o r j such t h a t(Gk-Dkl Sf) 2 (G,-Dj(%) f o r a l l
Sf
E S; f o r some j f k (21) Multiplying through by negative one, w e obtain a form similar t o Equation (9):(Dkl%-Gk) S (Gj-Dj(%) f o r all
%
E S ; f o r some j f kThe p r o c e d u r e given by Equation (16b) is used t o account f o r deposition goals by adjusting t h e constant o r background t e r m :
B,,
=
B,-
G, (23)4. EXAMPLES OF INFLUENTIAL RECEPTORS
IN
EUROPEThis c h a p t e r p r e s e n t s s e v e r a l examples of influential r e c e p t o r s in Europe, in- cluding:
-
Reducing t h e highest sulfur deposition in Europe;-
Reducing t h e highest r u r a l SO2 concentrations in Europe; and-
Maintaining t h e deposition p a t t e r n resulting from a 50% reduction in 1980 SO2 emissions.Because of d a t a and modeling limitations, information concerning r e c e p t o r sensi- tivity
-
t h a t is, d i r e c t environmental indicators-
w a s not used. Only indirect indi- c a t o r s , SO2 and s u l f u r deposition are used. Thus, t h e influential r e c e p t o r s in t h e s e examples may not correspond t o areas which s u f f e r t h e most s e v e r e environmental impacts. However, t h e examples i l l u s t r a t e t h e utility of t h e r e c e p t o r f i l t e r s .The examples u s e t r a n s p o r t coefficients obtained from t h e EMEP-1 atmospher- i c t r a n s p o r t model. The EMEP model g e n e r a t e s SO2 concentrations and sulfur deposition (both w e t and d r y ) in a grid (of dimension 27 X 31) covering Europe, western Asia, and n o r t h e r n Africa. A somewhat smaller a r e a , laying between l Z O W and 42" E, and 35" N and 72.5" N i s considered in t h i s p a p e r . The locations of t h e 650 r e c e p t o r s contained in t h i s area are shown in Figure 1. The t r a n s p o r t coeffi- cients are developed by simulating f o u r y e a r s of meteorology (fall, 1978 t o sum- m e r , 1982) is used. (The model i s described by Eliassen and Saltbones, 1983; and WMO, 1984.)
Emissions f o r t h e t h r e e cases are based on historical (1980) emission data. (A description of t h e s e emissions may b e found in Batterman et aL., 1986). Emissions from 27 countries are considered. S e v e r a l sets of emission c o n s t r a i n t s are used a s t h e a c t u a l emission reduction potential i s unknown. In addition, t h e different constraints i l l u s t r a t e t h e sensitivity of t h e number and location of influential re- c e p t o r s t o t h e feasible emission s p a c e .
4.1. P e a k sulfur deposition
Figure 2 shows t h e locations of t h e influential r e c e p t o r s f o r t h e f i r s t case in which t h e maximum s u l f u r deposition i s reduced. In e a c h figure, t h e maximum emis- sions of e a c h country Si,,,, are t h e 1980 emissions. The minimum emissions Si,min a r e 33 and 10% of 1980 emissions in t h e figures, respectively. These limits apply t o e a c h of t h e 27 countries modeled. Thus, t h e two figures representatively r e p r e s e n t a t h r e e and ten-fold r a n g e in emissions.
With t h e three-fold r a n g e in emissions, t h e r e are only 4 influential r e c e p t o r s . The number of influential r e c e p t o r s i n c r e a s e s rapidly as g r e a t e r variation in i s permitted in emissions. In all c a s e s , t h e number of influential r e c e p t o r s h a s been greatly r e d u c t e d from t h e 650 originally considered.
4.2. Peak S% concentrations
Figure 3 shows locations of t h e influential r e c e p t o r s with r e s p e c t t o maximum SOz concentrations using t h e s a m e emission r a n g e s as in t h e previous section. The p a t t e r n f o r SOz is similar t o r e s u l t s obtained f o r sulfur deposition, although i t is shifted somewhat t o t h e south. Also, t h e r e a r e more influential r e c e p t o r s f o r SOz than f o r sulfur deposition. These differences r e s u l t from t h e d i f f e r e n t t r a n s p o r t matrices: maximum SOz levels o c c u r relatively close t o emission s o u r c e s , while significant sulfur deposition r e q u i r e s longer distances. Prevailing n o r t h e r l y winds have g r e a t e r influence on sulfur deposition. In addition, sulfur deposition pat- t e r n s tend t o b e smoother and more diffuse, resulting in f e w e r "peaks" and t h u s f e w e r influential r e c e p t o r s f o r t h e problem considered.
4.3. Flat rate deposition reductions
The f l a t rate o r uniform emission reductions c u r r e n t l y considered would r e s u l t in a "flat r a t e " deposition reduction (neglecting t h e background term). For example, a 50% flat rate emission reduction would lead t o a similar change in sulfur deposition. (Model assumptions concerning linearity, i.e., t h e invariance of t h e t r a n s p o r t coefficients t o emissions, cannot b e discussed h e r e . ) In t h i s section, t h e s e deposition levels are used as deposition t a r g e t s .
Figure 4 shows t h e location of influential r e c e p t o r s f o r sulfur deposition based on a 50% f l a t rate reduction in emissions. In t h i s c a s e , a t o l e r a n c e of O . l g / m z - y r w a s used. For t h i s indicator, t h e f i l t e r s are much l e s s effective in el- iminating r e c e p t o r s .
5. DISCUSSION AND CONCLUSION
This p a p e r h a s p r e s e n t e d a n a p p r o a c h t o finding t h e r e c e p t o r s which may in- fluence t h e outcome of t a r g e t t e d emission s t r a t e g i e s . Any constraints t h a t a r e a linear function of emissions c a n b e handled similarly. The method i s quite general and applicable t o many optimization problems.
In t h e examples r e l a t e d t o peak concentrations or depositions, t h e r e are re- latively f e w influential r e c e p t o r s . This a r i s e s due t o t h e similarity (colinearity) of t r a n s p o r t coefficients f o r n e a r b y r e c e p t o r s , and t h e relatively f e w v e r y s t r o n g
"peaks". Only about half t h e r e c e p t o r s in t h e f l a t rate reduction case w e r e omit- ted. Most likely, many additional r e c e p t o r s would b e eliminated if t h e f i l t e r w a s a b l e t o determine dominance with r e s p e c t t o two o r more r e c e p t o r s simultaneously.
Only influential r e c e p t o r s need be modeled to determine optimization r e s u l t s a n d / o r worst-case environmental impacts using a scenario-analysis model. Thus, identifying influential r e c e p t o r s simplifies t h e generation and evaluation of emis- sion abatement s t r a t e g i e s . A s relatively f e w r e c e p t o r s remain after application of t h e f i l t e r s , microcomputer based implementations of optimization and s c e n a r i o analysis models become f a r m o r e practical.
Currently, simple l i n e a r optimization models have been used to g e n e r a t e op- timal emission s t r a t e g i e s . Modeling of nonlinear environmental indicators, howev- e r , will r e q u i r e m o r e effort. In this case, t h e identification of influential r e c e p - tors will b e m o s t beneficial.
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Alcamo, J., M. Amann, J.-P. Hettelingh, M. Holmberg, L. Hordijk, J . Kamari, L.
Kauppi, P. Kauppi, G. Kornai, and A. Makela (1987). Acidification in Europe: a simulation model f o r evaluating control s t r a t e g i e s . Ambio, 6 (in print).
Amann, M., S. Batterman, and J.-P. Hettelingh (1987). Sulfur abatement s t r a t e g i e s subject t o regional deposition t a r g e t s in Europe. IIASA Working P a p e r (in p r e s s ) .
Batterman, S., M. Amann, J.-P. Hettelingh, L. Hordijk, and G. Kornai (1986). Op- timal SO2 abatement policies in Europe: some examples. ILASA Working P a p e r WP-8642, International Institute f o r Applied Systems Analysis, Laxenburg, Austria.
Eliassen, A. and J. Saltbones (1983). Modeling of long r a n g e t r a n s p o r t sulfur o v e r Europe: a two y e a r model r u n and some model experiments. Atmos. E n v . , 17, 1457-1473.
Ellis, J.H., E.A. McBean, and G. J. F a r q u h a r (1985). Deterministic l i n e a r program- ming model f o r acid r a i n abatement. J. E n v . Engg., 111, 119-139.
Fortin, M. and E.A. McBean (1983). A management model f o r acid r a i n abatement.
Atmos. E n v . , 17, 2331-2336.
Hordijk, L. (1986). Towards a t a r g e t t e d emission reduction in Europe. Atmos.
E n v . . 20. 2053-2058.
Kohn, R.E. (1982). A L i n e a r P r o g r a m m i n g Model f i r A i r P o l l u t i o n C o n t r o l . MIT P r e s s , London, England.
Morrison, M.B. and E.S. Rubin (1985). A linear programming model f o r acid r a i n policy analysis. J. A i r P o l l u t i o n Control A s s o c i a t i o n , 35, 1137-1148.
Nilsson, J. (ed.) (1986). C r i t i c a l L o a d s for S u l p h u r a n d Nitrogen. Nordic Coun- cil of Ministers, Environment Report 1986-11.
World Meteorological Organization (1984). f i n a l Report of t h e E x p e r t Meeting o n t h e Assessment of t h e Meteorological Aspects of t h e 2 n d P h a s e of E W . WMO/TD-11 WMO, Geneva.
EMEP Receptors
in Europe
10 Longitude
f i g u r e 1. Locations of EMEP receptors. Squares indicate receptor locations.
Influential Receptors for S Deposition
3 foM rawe in 1980 emissions
1 0 3 0
Longitude
F i g u r e 2a. Locations of influential receptors for sulfur deposition f o r 3-fold range of feasible emissions. Squares indicate receptor locations.
Influential Receptors for S Deposition
10 fold range in 1980 emissions
10 Longitude
figure 2b. Locations of influential receptors f o r sulfur deposition f o r 10-fold range of feasible emissions. Squares indicate receptor locations.
Influential Receptors f o r SO2
3 fo!d range in 1980 emissions 70
F i g u r e 3a. Locations of influential receptors f o r SO2 concentrations for 3-fold range of feasible emissions. Squares indicate receptor locations.
Influential Receptors for SO2
10 fold range in 1980 emissions
10 Longitude
F i g u r e 3 b . Locations of influential receptors f o r SO2 concentrations f o r 10-fold range of feasible emissions. Squares indicate receptor locations.
lnflueniial Receptors for S Deposition
Usinq Year 2000 Emission Bounds
1 0 Lonqi tude
f i g u r e 4. L o c a t i o n s of inflliential r e c e p t o r s t o a c h i e v e a 50% r e d u c t i o n in 1980 d e p o s i t i o n . S q u a r e s i n d i c a t e r e c e p t . o r l o c a t i o n s .
