the analysis of abatement costs means that wet- lands’ effect on the total variability of emissions
influences the optimal allocation of abatement between point and nonpoint emissions. This is
clearly displayed in Fig. 2 where the optimal area of wetlands varies, depending on the prevailing
situation. Knowledge of how the use of wetlands affects uncertainty may therefore be crucial for
identifying to what extent wetlands are beneficial to use for nitrogen abatement. Moreover, if the
criteria of economic relevance are fulfilled, it can be shown that a stricter reliability require-
ment implies that the pollution constraint shown in Fig. 2b becomes more convex McSweeny and
Shortle, 1990. Consequently, an extended use of wetlands is suggested the stricter the reliability
constraint. This result is a consequence of wet- lands, in this paper, being the only means by
which the uncertainty of total emissions can be reduced.
The second implication of the criteria above is perhaps more subtle. If the criteria are fulfilled,
the use of wetlands reduces the uncertainty of nonpoint emissions. In addition, parts of the
upstream nonpoint emissions are gathered in wetlands and the net emissions can be measured
at the downstream exit of a wetland. Thus, construction of wetlands may in fact contribute
to changing some of the characteristics of the nonpoint emissions in the watershed. Nonpoint
emissions are characterized by their uncertainty and the difficulty by which they can be measured
and monitored Malik et al. 1993; Shortle and Dunn, 1986. Wetlands reduce uncertainty and
provide a natural point at which the upstream pollution can be measured. In this respect we
can
therefore conclude
that wetlands
are ‘pointifiers’ of nonpoint emissions, i.e. an abate-
ment measure that makes nonpoint emissions assume the characteristics of point source emis-
sions. Since some of the upstream pollution can be measured as the outflow from the downstream
exit of a wetland, construction of wetlands implies that a portion of the upstream nonpoint
emissions can be measured and monitored as point sources.
4. Example
To illustrate the implications of the criteria established above, this section provides an exam-
ple of a stylized watershed using empirical data from southwestern Sweden. This is a region with
relatively high leakage of nitrogen due to intensive agriculture and sandy soils Johnsson and Hoff-
mann, 1997. Although the watershed is rather simplified, we use empirical data concerning costs,
agricultural yields, and nitrogen leakage. The out- line of this model follows the schematic illustra-
tion in Fig. 1. It is assumed that there is one representative farm in a watershed that emits
nitrogen through agricultural run-off or leakage, and that wetlands is the only measure by which
the nitrogen load to the sea from leakage can be reduced. Finally, there is one WWTP that emits
nitrogen directly into the coastal zone. The objec- tive of the policy maker is to maximize economic
return in the area, subject to a probabilistic pollu- tion constraint. The abatement target that is used
in this paper is a 30 reduction of the nitrogen load to the sea. The problem is formulated as
maximizing 4, subject to 6, and additional constraints regulating the maximum area of wet-
lands
and the
minimum level
of WWTP
emissions.
4
.
1
. Data and assumptions The representative farm is assumed to consist of
200 hectares of agricultural land that is used either for cultivation of winter wheat or as wet-
lands for nitrogen abatement. It is assumed that wetlands can cover at most 5 of the agricultural
land in the area Jansson et al., 1994; Leonar- dsson, 1994. Winter wheat is a common crop in
southwestern Sweden SLU, 1995. While there are other crops that yield higher profits on certain
soil types, such as sugar beets or potatoes, these crops require very specific contractual arrange-
ments and are therefore not included in this exam- ple. The opportunity cost of land, as calculated in
this paper, may therefore be considered as a somewhat conservative estimate. It is further as-
sumed that all agricultural land within the water- shed is homogenous.
Table 2 Characteristics of the hypothetical watershed
a
Wetlands Agricultural land
Waste water treatment plant 6600
– Initial emissions kg year
− 1
7000 –
10 Maximum area ha
200 0.76
Variance coefficient 0.35
– –
Variable profit SEK
b
ha
− 1
year
− 1
2242 –
12518 ha
− 1
44 kgN
− 1
Costs SEK
b
year
− 1
Initial marg. abatem cost SEK kgN
− 1
year
− 1
44 54
–
a
Sources: Bystro¨m 1998, Gren et al. 1997, Vatn et al. 1996, Johnsson and Hoffmann 1997, and SLU 1995.
b
SEK, 0.12 USD January 2000. Table 3
Results for three different levels of reliability of the optimal solution when emissions are reduced by 30 Reliability level a Profit 1000
Wetlands St. dev of total
Abatement share of Variance
Expected coefficient
emissions ha
abatement SEK
a
wetlands 50
0.26 269
0.0 30
2470 75
0.29 193
1.2 5
42 2320
0.22 144
1660 30
46 90
8.1
a
SEK, 0.12 USD January 2000.
Data to characterize the watershed are obtained from various sources. The costs for construction
of wetlands, together with the abatement capacity and the uncertainty of nitrogen abatement in wet-
lands, are obtained from Bystro¨m 1998.
4
Data for yield and profitability of crop cultivation are
obtained from SLU 1995, and the costs of in- creased nitrogen abatement in WWTPs are ob-
tained from Gren et al. 1997. Finally, data concerning leakage of nitrogen from agricultural
land are obtained from Johnsson and Hoffmann 1997. Estimates of the variability of leakage
from cultivation of wheat are not available for Swedish soils. Therefore data from a Norwegian
study is used and it is assumed that the variance coefficient for nitrogen leakage is the same in
Sweden as for the soils in the Norwegian study Vatn et al., 1996. Using these data and assump-
tions, the background information used to model the watershed is summarized in Table 2.
5
4
.
2
. Results To show how reliability constraints influence
the pollution constraints, and the array of feasible solutions, the model is solved for three different
levels of reliability. First the model is solved de- terministically, such that the variance of total
emissions does not influence the solution a = 0.5. Second, the model is solved for two levels of
reliability such that the variance receives different weight in the pollution constraint a = 0.75, and
a =
0.9. As mentioned above, the required level of reliability affects the restrictiveness and the
convexity of the pollution constraint as defined by Eq. 6. The results for each of the reliability
levels imposed are displayed in Table 3.
The optimal allocation between abatement in wetlands and emission reductions in the WWTP
varies depending on the level of reliability spe- cified. Table 3 shows that the level of required
4
It is perhaps noteworthy that in this paper we use Bystro¨m’s linear model of denitrification see Eq. 2, since it
is easier to calculate the uncertainty and the covariance be- tween agricultural land and wetlands if a linear model is used.
The parameter values of Eq. 2 used for this example are a = 167.5, and b = 0.079 Bystro¨m, 1998.
5
All data , calculations, and other background information that are used to characterize the watershed can be obtained
from the authors upon request.
certainty has a substantial impact on the optimal solution. As a increases, monitoring the uncer-
tainty of emissions becomes increasingly impor- tant. Therefore the optimal use of wetlands
increases with increased reliability requirements. The abatement efforts are now ‘switched’ from
point to nonpoint abatement due to the capacity wetlands have to reduce the uncertainty of non-
point emissions. Table 3 also shows that imposing reliability requirements is costly. Profits are re-
duced by approximately 50 when a reliability level of 90 is required, compared to the case
when only the expected nitrogen load is relevant to the problem.
The example is based on empirical values that are more or less uncertain. To analyze the sensi-
tivity of the solution to changes, the parameter values that are relevant to the economic criteria
established were changed. Table 4 displays the optimal area of wetlands when the cost, abate-
ment capacity, and variance parameters are changed.
It is clear from Table 4 that the optimal solu- tion is sensitive to changes in all the parameters
evaluated, regardless of reliability level. A de- crease in costs or an increase in wetlands’ abate-
ment capacity increases the optimal area of wetlands quite substantially. The correlation co-
efficient between the nitrogen abatement in wet- lands and runoff from agricultural land affects the
covariance between wetlands and agricultural land COVQ,R. In this paper it is assumed that
the correlation is 0.7. Reducing this parameter to 0.5 − 25 makes wetlands less attractive to use
in the solution. Due to the sensitivity to changes in the parameters, it is difficult to draw any
decisive conclusions from the empirical model regarding the economic relevance of wetlands un-
der uncertainty. However, all of the parameter changes that are displayed in Table 4 are con-
nected to the economic criteria established in the theoretical section of this paper. Therefore the
empirical results suggest that the established crite- ria captures the main determinants of whether
wetlands are economically rational to use for nitrogen abatement. Consequently, the established
criteria are of importance for determining whether or not wetlands should be restored in a particular
region.
5. Conclusions
