Regional Source Quantification model for sulphur oxides in Europe

0304-6981/80/@901 1027$02.00/O

Atmospheric Endronment, Vol. 14. pp. lO27-IOS4. 0 PergamonPressLtd. 1980.Printedin Great Britain.

REGIONAL

MODEL SOURCE QUANTIFICATION SULP~UR OXIDES IN EUROPE L. P.

PRAHM,

K. CONRADSEN*

FOR

and L. B. NIELSEN*

Danish Air Pollution Laboratory, National Agency for Environmental Protection, Risyi National Laboratory, 4000 Roskilde, Denmark (First received 9 November 1979 and received for pubficution 7 February 19X0) Abstract-An air quality model for estimation of emissions on a regional scale is developed. The model uses measured air con~trations and air trajectory transport maculations to determine the emissions. The optimal emission strength is obtained by a least square approximation between measured and estimated air concentrations of potlutants. The Regional Source Quantification (RSQ) model is used on the European Long-Range Transport data base for sulphur oxides collected by the Norwegian Institute for Air Research. The data base consists ofabout 60,000 SO, and SO4 air quality samples and four times as many 48-h back trajectories. The estimated emission strengths based on about 7500 samples are shown to agree fairly well with the national emission

strengths estimated previously from population and industrial density as well as consumption offuel and raw materials. This is taken as a verification of the RSQ model. Use of the RSQ model in future studies for estimating emissions of other micropollutants is discussed. Optimal location of monitoring stations and emission fields as well as the duration of the study period are retated to the standard deviations on the emission strengths. The RSQ model is used not only for emission estimation but also for estimation of optimal decay and oxidation parameters to be used in the air trajectory model. We find the decay parameter for SO, to be 1.3 x 10-5s-1, and for SO, to be 1.6 x 10m6s-r. The emission plus initial oxidation to Sod, is found to contain about 12% of the total sulphur emission. while the succeeding oxidation defined in the air trajectory model is found to be insignificant.

1. INTRODUC~ON

Air quality studies can be based on receptor or source oriented meteorological air quality models. Receptor oriented models give estimates on air quality without information on emissions. The source oriented models, which are those most frequently used, relate the estimated air quality to emissions. This is preferable because control of the air quality can be enforced by suitable regulation of the emittents. Emission inventories are required for the source oriented models. The emission survey is usually conducted by estimation of the consumption of raw materials, especially fossil fuel, in different geographical areas. Obtaining accurate emission inventories is obviously of great importance, and possible alternative procedures for conducting and controlling emission inventories are of interest. This is especially the case for micropollutants where the primary sources might be unknown. During the OECD study, “Long-Range Transport of Atmospheric Pollutants” (LRTAP), regional transport of sulphur oxides has been demonstrated and quantified. See for example Ehassen (19?8}, Ottar (1978) and Prahm et al. (1976). These studies are based on emission inventories produced mainly by each * Affiliation : Department of Mathematical Statistics and Operations Research, Technical University of Denmark, 2800 Lyngby, Denmark.

participating country, air trajectories and measured SO, and SO, concentrations. Application of the emission inventory in Eulerian models was demonstrated e.g. by Prahm and Christensen (1977). Regional transport modelling is reviewed by Eliassen (1980). In the present study, we develop a Regional Source Quantification (RSQ) model for quantification of emission strength on a regional scale by use of air quality measurements and air trajectories. Using the data base from LRTAP, the European suiphur emissions are quantified. Comparison with the national emission inventories reported by LRTAP gives agreement within the estimated accuracy for most areas. This is considered as a verification of the model. In addition, we discuss the disagreements between the LRTAP emission information and the estimated fields which might either be caused by model assumptions, errors in measured concentrations and/or errors in the original emission inventories. Causes of deviations are identified. Possible application of the RSQ model for planning of future monitoring networks, e.g. for alternative micropollutants, is discussed. The RSQ model is also used for optimization of SOZ and SO, oxidation and decay parameters by requiring minimum deviation between measured and estimated concentrations. Source finding studies have been reported earlier for small scales, i.e. up to about 20-30 km, where the advecting wind can be assumed to connect sources

1027

L. P. Piwtbt, K. CONRADSEN and L. B. NIEIsf k

102X

with receptors by straight lines. Breuer (1965) presented a method which can be used to establish information on contributions from various point sources to the receptors in a limited urban or rural area. His method is based on short term averages of measured concentrations. Hogstrom (1975) discussed a procedure for assessing the relative contribution of local point sources to the air pollution observed in a community based on 3-12 measurement stations. His procedure is like Breuer’s but based on 24-h averages instead of short-term averages. On an even smaller scale, Yamartino and Lamich (1979) presented a source-ending algorithm based on the least square principle like the present study. They used their algorithm on the data base from an airport and found that only the largest sources could be localized. In the present study, we use the regional European data base and study the relations between number of measured samples, the location of stations, number of emission fields and size of emission fields which are required to obtain reliable emission estimates. A preliminary presentation of the results has recently been published (Prahm et ul.. 1979). 2. METEQROLOGICAL

TRAJECTORY

emissions (per area and time unit) from the ennss~ou fields are then estimated by a regression analysis with the measured SO, and SO, concentrations as dopendent variables and the emissions as independent variables. The model estimates of SO, and SO, for each day and each station are obtained by averaging the concentration estimates from 5 trajectories. The au samples are collected from 6 GMT to 6 GMT the next day, and the backward trajectories are computed four times a day from 0 GMT with 6 h intervals. Therefore, 5 trajectories are used for each sample and the averaging is done with the weights l/S, 2/8,2/g, 2;8 and l/S respectively. The concentration estimates for each trajectory are obtained by equations similar to those given by Eliassen and Saltbones (1975) Go, dt

_

-k,Cso, + (1 - @-

d&o _= -k,C,, dt with the solutions &o,(r) = Cso,,sr,,,exp( +

MODEL

e

+ :jk,C,,, \

b,$

(1.1)

+ $,.

(I.21

-k,rrAr)

(1 - c( - @exp( -k,CjAt + tO))QjAt/h,

(1.3)

j-0

The connection between the air quality measurements and the emission fields which are to be estimated is obtained by an air trajectory mode1 similar to the one used in the OECD, LRTAP project (Eliassen, 1978). The trajectory mode1 treats horizontal transport and oxidation of SO, together with transport and production of SO4 in the atmospheric boundary layer, which is assumed to have a constant depth of 1000 m. All parameters, i.e. decay, production and transport terms, in the model are assumed to be constant in the whole depth of the atmospheric boundary layer. The trajectory model is used to define sets of linear ~uations for estimated SO* and SO4 concentrations with the emission fields as unknowns and with coefficients determined by the trajectory model. The

GO,@)

=

CSO~.S~~IU

ew(-4nA.t)

xc so,.START[exP(-k2~Af)-exp( -k~Wl

-exp(

- k,fjAt

f Co))]QjAr/h

+ g ,$ /3exp( - k,CjAt + t,))QjAt,,%. 1-o

_~__.

h ; At 1, n

(1.4)

The symbols used are defined in Table 1: see also Eliassen (1978). The yearly emissions are assumed to consist of a _I____... _~.~_

_._-._-.__

Model parameters

k, k, k,

$$) I2

Table 1. Parameters in the used meteorological dispersion model

Qj

+

Sulphur dioxide concentration Sulphate concentration Sulphur dioxide concentration at the trajectory starting point Sulphate concentration at the trajectory starting point Sulphur emission per area, and time unit for trajectory point SOz decay constant SO4 decay constant SO, -+ SO, transformation constant Mixing height Local SO, deposition Local SO, - SO, oxidation Trajectory time step Time shift Number of time steps

(pugmm3)

bgmw3) (pgm-2/h-*) 1 X 10-5(s-‘) 4 X 10-6(s-‘f 3.5 X IO-b(s- 1) loo0 (m) isq; 7% 2h lh 24

Regional source quantification model for sulphur oxides in Europe time-independent part of 65% and a time-dependent part of 35%. The time-dependent part is taken to vary as a cosine through one year with maximum in January and minimum in July. A slight modification of the original model causes introduction of four new parameters. In order to obtain a reasonable average decay time for the emissions considered in each integration step t, is included. This modification of the original model is of numerical nature and exerts only minor influence on the results. CSOI.sTARTand CSo4,sTARTare the concentrations at the trajectory starting points, later referred to as the background concentrations. The additive terms which depend on Cso2.sTARI.and in (1.3) and (1.4) are called the background Cso4.sTART contributions, i.e. the contributions to the receptor point concentrations originating from CSOl,sTART and Cso4,sTART. The integration procedure used in (1.3) and (1.4) is illustrated in Fig. 1. The meteorological air quality model described in this section is a crude approximation of reality, and a , discussion of its shortcomings is presented in Section 6.

3. DESCRlPTlON OF AIR QUALITY DATA AND METEOROLOGICAL DATA

The data base for this project was collected by the Norwegian Institute for Air Research during the OECD project, LRTAP, (OECD, 1977 ; Ottar, 1978) TRAJECTORY

and consists of air quality measurements and calculated air trajectories. The measurements are precipitation data and SO2 and SO4 concentrations from diurnal sampling obtained at 45 measuring stations located in 10 European countries as shown in Fig. 2. For each station, back trajectories are calculated 4 times a day by a method proposed by Petterssen (1956). The trajectories are based on observed 850 mb winds which are supplemented by quasi-geostrophic winds in areas with few observations. The period considered is 1 January 1973 to 31 March 1975, in which period the monitoring system was most active. According to the LRTAP report (OECD, 1977, pp. 3.8-3.9 and 7.42), some of the SO, and SO, data were of low quality. For this reason, Danish SOz data for the whole period, German SO4 data for the whole period and Swedish SO2 data from 1 January to 31 October 1973 are excluded from the analysis. To avoid some of the uncertainty caused by incloud and subcloud scavenging, data from a measurement station are excluded from the analysis if the recorded diurnal precipitation is larger than 0.1 mm at the station. This does not assure that there has been no precipitation along the trajectory, but the probability of precipitation occurrence is reduced. The given time resolution for the trajectories is not sufficient to achieve an appropriate space resolution for changing synoptic weather patterns. For this reason, a trajectory criteria in addition to the precipitation criteria has been used. The longest distance

TRACK

J

:m+l

JX,

tlmez-mht,

jz2,

Arernge

aye

IS

At + t,

Fig.

1.

Qm

time:-Zht,

02

(hoursj.

J-1,

/ Emission 0, during the time points J:O and jzl. Average age 1s to=1 hour.

1029

At !a-tuern

tlmr:-lht,

01

the

RECEPTOR

POINT

POSITION

OF MEASUREMENT

Schematic explanation of the integration procedure

STATION

used in (1.3) and (1.4).

I<. P.

k.WM, K. CoNH41)st v and L. B. Nrt LSFL

Fig. 2. ~ographi~al map with iso-contour lines showing the number of SO, samples with an allocated trajectory passing through squares of 127 x 127 km*. (a) all monitoring stations, and (b) selected stations. The stations are shown on the mans with small circles.

Regional source quantification model for sulphur oxides in Europe

SO4

DATA

MAXDST

(127 km)

Fig. 3. Histogram showing the distribution of maximal distauce (MAXDST) between trajectory origins for trajectories allocated to each SO, sample. Mere is used ah the data which passed the precipitation criteria.

---

DATA

WITHOUT

(ORDINATE -

MAXDST

L

Trajectory

SCALE

CRITERIA

IS DIVIDED

BY

3)

6

20 DISTANCE

25 (127 km)

Fig. 4. Histogram showing the distributian of the distance between gravity center of trajectory origins for trajectories allocated to each SO., sample and the air quality measurement statious. The dotted line represents all data passing the precipitation criteria. The ordinate scale is for this curve divided with a factor of 3. The s&d fine gives the data passing the critereriaof MAXDST c 6 (standard data set),

i I’ 1’~\lfhl. K. CO’UKAW+V and 1. H. Ntt t st 2

AIR

QUALITY

MEASURING

STATIONS

Fig. 5. Histogram showing the selected number of samples from the air quality measurement stations. The code for the stations is from OECD (1977). Each country has its own letter code. The lowest black bar represents 1973 data, the open bar 1974 data and the upper black bar 1975 data. Total number of samples is 3771 for SO, data and 4123 for SO, data. (a) SO, data, and (b) SO, data.

Regional source quantification model for sulphur oxides in Europe between the starting points of the 5 trajectories allocated to the same air quality sample is calculated. The frequency distribution of this measure (MAXDST) is shown in Fig. 3 for the SO0 samples fulfilling the precipitation criteria. A detailed study of single trajectories and the desired spatial resolution of emission fields lead to the trajectory criteria that samples with MAXDST 2 6 (unit: 127 km) are excluded from the analysis. The question arose whether this trajectory criteria favoured weather conditions giving short trajectories, For this reason, Fig. 4 was produced. The figure shows that the criteria do favour short trajectories but not in a critical way. The total data base of about 2 x 30,ooO samples is reduced to about 2 x 15,000 by the precipitation criteria and further by the trajectory criteria to about 2 x 3800 samples. The contribution of samples from each measurement station for each year is shown in Fig. 5. Most of the samples are from 1973 and 1974. Exclusion of Danish, German and Swedish data is seen from the figure. This reduced data base is referred to as the standard data base. The distribution of the SO2 and SO, concentrations used in the analysis is shown in Fig. 6. For both SO2 and SOL, there are far more values at O-l pg me3 than one would expect in comparison with reported clean air Atlantic background measurements (Prahm et al., 1976) which give values of about 0.8 pg rnF3 for SO, and about 0.2 fig mm3 for SO,. Keeping this in mind, one can see from Fig. 6 that the high probabiIity of low concentrations indicate that the instruments used have a detection limit or uncertainty for SO, at 2-3 pg m-3. Similarly, the relatively large number of SO, samples below 0.8 /Ig m- 3 seen from Fig. 6(c) must be considered erroneous. The observed errors must be due to shortcomings in sampling procedure, chemical analysis and data handling. A detailed study of the frequency distributions from single stations reveals both larger and smaller uncertainties or detection limits. From English stations, SO_, concentrations were given as integer values of pg mm3 and this caused the peaks for positive integer values in the distribution shown in Fig. 6(c). The RSQ model gives estimates of emissions and, as discussed in the following sections, also an uncertainty estimate. If a large number of trajectories cross an emission field, the uncertainty is smaller than if only a few trajectories cross. It is therefore important to know the number of trajectory crossings which are actual for each emission field. A geographical measure of trajectory density has been defined as the number of air quality samples which has at least one of its allocated trajectories passing through a grid square (unit area of 127 x 127 km2). The spatial distribution of this trajectory density measure is given in Fig. 2 for the used Sod. samples. It is seen that the high density appears close to the positions of the measurement stations. The predominant westerly winds for most of the region are also observed as a higher trajectory density

1033

west of the stations than east of them. In Fig. 2(b), only nine measurement stations are used. It is clearly observed that the high density occurs as islands around the selected stations, fn Section 8, a direct relation between (trajectory density) x (emission field size) and uncertainty relevant for future planning of monitoring networks and emission field areas is given. 4. EMISSION FIELDS

The source terms Qj (see Equations (1.3) and (1.4)) used in the air trajectory model are dependent on the geographical position. Figure 7 shows a map of the considered European region and the considered air quality measurement stations. The OECD, LRTAP study (Ottar, 1978) was based on emission surveys giving emission strength as tons sulphur per year per 127 x 127 km’ area, and the European region was divided in 37 x 31 emission fields with the same area. Thus, although the emission within each field (127 x 127 km* square) might be highly variable in space, an average constant emission is used all over each field. In order to obtain small uncertainties in the RSQ model estimates, a large number of trajectories have to cross each emission field as discussed in Section 8. In addition, the dimensions of the emission fields must not be small compared to the uncertainty of the calculated trajectory positions. Therefore, the European area is divided into a small number of emission fields. The contours of the emission fields follow the grid system used in the OECD project, and each field contains a finite number of the 127 x 127 km2 fields. Two approaches to the spatial definition ofemission fields are presented. The 23 emission fields in Fig. 7 are defined on the basis of land contours, national boundaries and population density. These fields are used in most of the computations described. Figure 8 shows an alternative approach giving 37 emission fields, based on a geometrical procedure using small fields close to the measurement stations and larger fields in remote areas. Future studies could be made on alternative compounds, with different positions of measurement stations, different sampling periods and perhaps in a different geographical area. The emission fields, especially the size of each field, should then be defined with regard to desired uncertainty in the RSQ model estimates, using the relations between uncertainty and number of trajectory crossings specified in Sections 3 and 8. 5. THE STATISTICAL MODEL We now consider the meteorological model from a statistical point of view. As mentioned earlier, the 24-h means are found by averaging five values of Cso2 from Equation (1.3) or Cso, from Equation (1.4) over the five trajectories computed every 24 h for every measuring site. This gives two simple linear relations for every day and location :

cl

0

5

15

20

25

30

35

40 ‘N.,

45 : ~:q”:’ !

50

Regional source quantification model for sulphur oxides in Europe

2

3

4

5

i

Fig. 6. Distribution function of measured concentrations from the selected samples. (a) SO2 data, (b) SO4 data and (c) SO., data with a finer resolution than in (b).

3 1

Fig. 7. Map showing. the European region covered in thestudy. The small circles are positions ofair quality sampling stations. The 23 numbered areas are the 23 emission fields.

1035

3

Fig. 8. Map showing

37 emission

fields used as alternative

where the as and bs are known constants given by the trajectory equations, and QI, . , , QN are the emission constants corresponding to the chosen division of Europe into emission fields. The summation over VEI corresponds to contributions from every time step for the five trajectories. Clearly, the model will not give values that exactly equal the observed ones, even if we had perfect information on the emissions and the meteorology. This is due to a lot of factors : the approximate nature of the model and the non-representativity of the emission constants, the trajectories and the measured values, etc. Therefore, we add an error term to the right hand side of the equations. Now, we consider n observations Yt, . . , , Y, of either SO2 or SO4 corresponding to different locations and times. Then, we can reformulate the models as follows: “j

to the 23 fields of Fig. 2

Yi represents the observation corresponding to a specific time--location combination. The coefficients uij are computed by means of the model if the trajectory corresponding to Yi is passing through emission fieldj, and they are made equal to 0 if not. Finally, ci is the ith error term or residual. We assume that the I:iS have means zero, and that they are uncorrelated with the same variance cr2.The first assumption is not crucial, whereas the second and third could be more doubtful. However, analyses of the observed residuals did not reveal strong violations to the assumptions, and as a first approximation to reality, we use the model in the described form. lfwe use matrix notation, we can bring the model on the form Y=AQ+E,

where Y is a n x 1 vector of observed concentrations, A is a n x N matrix of known constants, Q is a N x I vector of the unknown emission constants, and E is a II x 1 vector of random residuals with expectation and dispersion E(c) = 0

N I’, = C anjQj + I:,. j=l

D(E) = dI.

Here, I is the n-dimensional unity matrix. The Q’s can be estimated by least squares, which

1037

Regional source quantification model for sulphur oxides in Europe according to the Gauss-Markov theorem give the minimum variance unbiased estimators among all linear estimates, cf. Rao (1965). The solution is obtained by solving the normal equations (A’A)Q = A’Y, giving 8 = (A’&-

IA’Y,

where A’ denotes the transpose of A. As mentioned

above, 0 is unbiased, i.e. E(b) = QThe variance C’ is estimated by $2

1

=

-(Y n - P(A)

-

A@(Y

- A@,

where p(A) is the rank of A. The uncertainty estimated by

6. RSQ MODEL VERIFICATION

on Q is

ri(Q) = 2fA’A)-“. ffe is assumed to be normally distributed, then 0 will a normal distribution N(Q,c?(A’A)- ‘) and ri2 wiI1follow a a2X2/fdistribution with n - p(A) degrees of freedom. The least square solution presented in this paper was obtained by computer programs from the SAS library described by Barr et af. (1976). Though a great number of equations have to be combined for each solution, no numerical troubles occur as Iong as the emission fiefds are chosen in such a way that B(Q) contains reasonable values, i.e. the &‘s are of the same magnitude. If we discard these criteria, spurious emission estimates with deviations from the “best” estimates of both stochastic and numeric nature might accur. By “best” estimates, we mean the best obtainable estimate using the data base and the meteorological dispersion model. After having form~ated the model Y = AQ + E with E(s) = 0 and D(r) = a21, the question arises whether the parameter estimates r& and the standard deviations fli give a good description of the actual emissions and the fluctuations around those. This will depend on two questions at least. The first is whether the model is satisfactory from .a purely probabilistic point of view, i.e. whether the deviation between the observations and the mode1 values can be considered as purely random. This matter is discussed in Section 7 where it is shown that with a few exceptions the residuals fulfill that condition, Secondly, even if these conditions are met, the estimates pi are not necessarily reliable guesses of the true emissions. Whether they are true or not wili depend on questions like whether the model is of a descriptive nature or whether it real& gives a satisFactory explanation of the chemical, physical and meteorological processes which determine the impact of the emission of SO2 on the air concentrations observed. This cannot he decided decisively within the limits of the present study. Among other things, very precise information on true emission

follow

values would be required. On the other hand, we must emphasize that the model is based on chemical/physical/meteorological considerations, and, as will be seen below, there is a reasonable agreement between what is believed ta be the more reliable of the OECD emission values and the estimates & On the whole, we therefore conclude that the estimates resulting from studies following the lines given in the present paper can be considered as reasonable estimates of emission values and the UP certainties involved in the estimations. This, of course, does not imply that the air quality model cannot be refined and improved to give even more reliable results.

The Regional Source Quantification model is based on the air trajectory model and the statistical model, An air trajectory model is only a crude imitation of reality. The most important causes of errors and uncertainties resulting in deviations from the true conceniraiions and in difTerences between measured concentrations and model estimates ofconcentrations are hereby listed: (1) Space resolution in measurement and trajectory model estimate A measurement represents average concentration in one estimate is an average over a emission, dispersion and decay neglected in the model.

information on time point, while a model volume_ AB details in within this voiume are

(2) Measured concentration (a) Lacking representativity of and errors in sampting equipment, procedure for transport and storage. (b) Lacking representativity and errors in the chemical analyses and data handling. (cc) Influences from local sources, e.g. from nearby houses or traffic. This causes the measurements to be not necessarily representative for the regional background, which is the aim. (3) Emissions (a) Uncertainty on the GECD (1977) emission estimate. (b) Uncertainty on the yearly variation in the emission as well as the variation during day and week. (c) Uncertainty on the effective emission height, which causes various proportions of the emissions to be deposited locally. (4) Trajectory model (a) Horizontai space and time resolution are hmited. The 6-h interval between trajectory arrivals should ideally be much shorter in order to represent emission contributions from all relevant emission areas. (b) Horizontal diffusion is neglected.

L. P. PRAHM, K. CO”~RADSFN and L. R. NIFIS~Y

-50

-40

-30

-20

-io

0

io

20 SO2

30

40

RESIDUALS

+3/m3)

20

40

50

0

-so

-40

-30

-20

-io

.o

io

SO4

30 RESIDUALS

50

(pg/m’)

Fig. 9. Histogram of residuals (difference between measured and RSQ-model concentrations). background concentrations included. (a) SO2 data, and (b) SO., data.

No

Regional source quantification model for sulphur oxides in Europe (c) Limited trajectory length of 48 h causes influence from concentrations at trajectory starting points. (d) Trajectory track includes uncertainty on wind speed and velocity measurement. It is uncertain which height gives the most representative transport wind. (e) Assumption of constant mixing depth is not correct. in reality, it varies as well geographically as in time, dependent on weather and surface conditions. (f) The model does not represent vertical diffusion. (g) Dispersion caused by wind velocity and directional sheer is not accounted for. (h) Lacking time and space resolution on precipitation information. Uncertainty on incloud and subcioud scavenging representation. (i) Uncertainty on dry deposition decay parameters for SO2 and SO,+ as well as on oxidation rate. These parameters should be varying in space and time as functions of weather, chemical environment, surface conditions, gaseous and aerosol characteristics. (j) Assumption of a linear relation between concentrations, emission and decay. Despite these deficiencies, the air trajectory model and measurements have been used by Eliassen (1978) with applicable results. We now present a careful study of the statistics of the deviations between trajectory model estimates and measurements on a large number of samples in order to find out how serious the mentioned uncertainties and errors are for the RSQ model and thereby suggest improvements on the modei. It will generally not be possible to see the influences of these deficiencies on the residuals from the model. On the whole, these errors will be averaged out and thus just result in a coarser model, i.e. a model with a larger standard deviation. In other words: The influence of all the relationships which we do not account for are transferred to the error term in the model. The more emission fields included in the model, the smaller will be the standard deviation of the error term. If, however, we want to use the model for predictive purposes or generally to make inferences, it is important that the error terms are randomly distributed with approximately the same symmetric distribution, preferably a normal distribution, (As long as the error terms have a unimodel, symmetric distribution, the statistical analyses are fairly efficient.) In order to test whether those conditions are fulfilled, we examine the empirical residuals for systematic patterns. If such a pattern is found, it is investigated whether it can be explained by the above mentioned deficiencies. If such a connection is found, terms can be incorporated in the model which attempt to take these relations into account. In Fig. 9, the frequency distributions of the residuals from the models are shown. They are fairly symmetric except for a few large, positive outliers. Thus, cases are found where the observed values are much larger than the ones calculated from the model. This could easily be explained by factors (2a), (2b), (2~) or (4e). If we

1039

exclude those outliers, the residuals are still not quite normal, but a comparison against the very skewed raw distributions shows that the model essentially has explained a systematic variation in the data. Table 2 shows the means and standard deviations for the residuals for given length and origin of the trajectories, and for given monitoring stations. 2(a) and 2(b) give the values for the SO2 residuals, but the values for SO, look much the same except for one thing, namely that the means of the residuals for longer trajectories are negative, and for shorter trajectories positive, i.e. the model overestimates the SO, content if the trajectory is long and underestimates it if the trajectory is short. The same pattern is not seen on the SO, values. This might indicate that the decay and oxidation parameters for SO* are erroneous as mentioned under 4(i) of Section 6 and further discussed in Section 9, or it could be caused by uncertainty on scavenging as put forth under 4(h). If systematic errors occurred on some remore monitors (cf. the remarks below), it might contribute to the negative residuals for sulphate. An evaluation of the data quality from each air quality measurement station is obtained from a study of the variance reduction VR given in Table 2(c) and defined as VR=l-

variance of residuals of concentration variance of measured concentration

*

The RSQ model estimates and measured concentration values are in complete agreement if VR = 1, while a small or even negative value shows no correspondence between measured and RSQ concentrations. The correlation R is a similar expression, also shown in Table 2(c) in order to obtain comparability with other studies. The general pattern is that measurement stations in remote areas with low average measured concentrations are connected with poor variance reduction and correlation. This is the case for both SO2 and SO, at the Norwegian stations (N) and some Swedish (S) and Finnish (SF) stations. Most significant examples are SF 5 in northern Finland and DK 1 at the Faroe Islands. The explanation might be that the average concentration level is too close to the detection limit and certainty for sampling and analysis. The French station F4 is an example of a poor variance reduction in an area ofrelatively high average concentration level. The poor variance reduction might here be caused by influence from local sources. However, the special siting in the height of 1300m should also be noted. The values of the residuals for all five Finnish monitoring stations show that the SO, residuals are (on the average) negative. This could be due to systematic underestimation of SO, by the Finnish monitors, or it could be due to a ‘remoteness effect’ as described above. Another reason could be underestimation of dry deposition in the area considered.

1040

1,

P

PRAfih1,

K.

C‘I)\RAI)Sf

I\

and L. H. iVIf-fsf

\

Table 2(a1

Origin of trajectories (emission field No.) 1 1 ; 4 5 6 7 X 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23

Residuals on SOz-data STD

Mean

(pgrn-“) - 0.2 - 0.9 0.7 - 0.6 -2.3 0.‘)

I .o -0.8 -2.7 - 1.1 - 1.2 - 1.1 -37 - 3.0 - 2.6 2.X I.6 -- 0.9 I.1 1.X 0.9 - 1.1 I.1

deviation (uf! m 3, 9.1 6.5 14.9 6.X 5.5 19.4 15.1 10.1 12.X 16.3 19.7 19.0 I I.8 13.0

1x.0 11.6 16.3 175 lb.4

13.9 5h 7’./ 19.4

In Table 3, the correlations between emission field estimates are tabulated. The given values are small which means that the stochastic deviation for one emission field estimate does not affect the stochastic deviation for another emission field estimate, from a practical point of view. The correlation matrices for SOz data and SO4 data, respectively, are very much alike, refiecting physical conditions between the geometrical shape of the emission fields and the predominant trajectories. Neighboring emission fields are negative correlated. As the systematic deviations are rather small, we will conclude that the model, from a statistical point of view, is fairly satisfactory, and that the deviations between measured values and model estimates can be described sufficiently by e random variable with mean 0 and standard deviations as given in Section 7. Further verification of the mode1 is obtained by comparison between RSQ estimates from the model with the LRTAP estimates, Semb (1978), discussed in the following section. 7. EMISSION ESTIMATES

Emission estimates are obtained by use of the RSQ model, consisting of the meteorological air trajectory model described in Section 2, the data base described in Section 3. and the statistical model from Section 5.

Length of trajectories (I27 km)

Residuals on SO,-data STD Mean deviation (pgm ‘1 (pg m i) ~~I .7

._2.I 1.5 0.4 - I .o -- I.7

6

0

10 II 11 I:, 14 15 16 I7 1X IY 20 21 22 23 24

0.: -0 X I.1 I.1 m-o.7 --0 I -- 0.4 - 0.1) -7.2 -- 0 6 - 0.7 _ 3.0 -- 4.Y 45 0.h _ 2.3 -94 - 22.6 7.3

6.4 10.2 16.6 14.7 10.0 10.3 12.4 13.1 16.1 13.4 10 7 9.x 11.4 X.5 64 10.6 10.3 Y.6 X.X 16.1 10.X 4.6 23.1

The emission estimates from the RSQ model are compared with LRTAP, OECD estimates (Semb, 1978) in the scatter diagrams, Figs 10 and 11. The corresponding results, including uncertainty, are presented in Table 4. The results referred to here are based on the 23 emission fields given in Fig. 7. RSQ estimates by use of the 37 emission fields from Fig. 8 are tabulated in Table 5. One should note that even a perfect RSQ mode1 would not give emission estimates identical with the LRTAP, OECD estimates. Thus, the deviation between emissions estimated by the two different procedures can be caused by errors in both procedures. A good agreement between the two independent estimates, however, is a strong indication of the adequacy of the RSQ procedure and the LRTAP estimate for the country considered. (a) Background

contributions

The concentrations at trajectory starting points, called background concentrations, are used in the model given in (1.3) and (1.4). Different methods for estimation of the background for SOa and SO, data are discussed in the following. The trajectory starting point for each air quality sample is determined as the center of gravity for the five trajectory starting points allocated to the considered sample, and each trajectory starting point is allocated to the emission field where it is situated. The

1041

Regional source quantification model for sulphur oxides in Europe Table 2(c).

Measurement (ngm? Al

A2 CH2 Dl D2 D3 :: DK1 DK2 DK3 DK4 DK5 DK6 Fl FZ F3 F4 F5 F6 Ni N3 N9 N 23 NLl NL2 NL? NL4 Sl 52 s3 s4 S5 S6 S7 S8 S9 s 15 SF1 SF2 SF3 SF4 SF5 UK1 UK2

SO,-data

SC&-data

Station

15.3 13.1 10.1 17.3 25.2 11.1 25.5 22.3

28.7 5.3 3.4 9.7 9.3 7.7 5.4 4.0 3.3 4.0 17.7 13.5 7.5 35.1 5.7 7.2 5.9 5.1 4.1 2.1 3.8 5.6 8.4 1.3 7.2 6.3 7.8 3.4 2.6 21.5 10.X

Mean of residuals (ngm-?

R

Variance reduction VR

-4.1 -4.5 - 3.2 6.1 4.5 -8.8 5.4 2.6

0.42 0.53 5.37 0.4% 0.66 5.33 5.56 5.25

5.18 0.25 0.07 5.22 0.32 -5.5 5.2% 5.05

15.5 1.5 -4.5 -2.3 - 5.3 -5.9 1.5 0.3 - 0.6 0.0 -5.5 - 1s -5.6 7.7 - l.% 1.5 0.7 0.3 0.3 -2.8 -5.5 - 1.5 3.6 - 1.9 1.5 - 2.4 - 1.5 -2.2 -0.4 4.1 2.5

0.54 5.46 5.54 0.09

0.60 0.44 0.18 0.24 0.12 0.31 0.74 5.61 5.55 5.4% 5.11 0.24 0.44 0.23 0.18 -0.41 0.1% 5.45 5.69 0.59 5.3% 0.45 0.54 0.52 5.12 5.51 OS5

0.21 5.25 5.07 -0.24 0.36 5.15 -0.0% -0.12 - 5.29 -0.02 5.37 0.37 5.29 5.16 -1.00 -0.06 5.1% 5.05 -5.04 -0.1% -0.0% 0.16 5.32 0.35 5.13 0.15 0.17 5.24 -0.03 0.23 5.31

Me~u~meut (pg me3) 11.0 11.4 13.5

0.6 3.1 4.8 4.4 6.4 6.5 18.9 4.2 7.3 4.5 9.9 11.6 2.9 2.1 3.2 2.3 11.4 9.3 6.4 14.5 4.8 3.8 3.8 3.1 2.1 4.5 2.5 4.8 3.7 2.2 2.7 21 2.4 1.8 5.9 7.1 4.8

Mean of residuals (pgmm3) 5.9 0.5 0.2

-t.7 0.5

5.6 0.0 0.8 0.8 8.0 -2.1 -1.1 -7.3 2.7 -5.6 -0.1 -0.7 0.1 -5.6 1.7 1.5 -5.5 0.8 - 5.5 -0.4 0.4 5.5 -0.3 5.9 -0.1 -0.2 1s 5.3 -5.5 -0.8 -5.5 -5.5 -0.7 -5.1 5.3

R

Variance reduction VR

0.30 0.25

0.19 0.08 0.05

0.27 0.64 0.69 0.46 5.63 0.60 0.62 5.46 0.49 0.24 5.62 0.38 0.29 0.16 0.15 0.52 0.69 5.56 5.61 5.81 0.58 5.26 5.58 0.32 0.45 5.28 5.53 0.80 5.57 0.24 0.45 5.45 0.59 0.62 0.18 0.70 5.5%

-5.54 0.45 0.46 0.13 5.38 0.35 0.31 -0.09 0.24 -5.58 0.37 0.15 5.56 - 0.04 -0.07 0.27 0.48 5.28 5.25 5.66 0.2% -0.17 0.33 0.05 -0.11 0.57 0.26 0.64 0.27 0.07 5.16 5.00 0.34 0.39 - 1.64 5.44 5.29

5.44

Table 2. Statistics on residuals derived from RSQ calculations for SOz without background estimation and with background ~timation for SO+ The different groupings are: (a) Origin of trajectories (emission fields from Fig. 7). (b) Length of trajectories. (c) Monit~~ng stations. fields are then given unknown background contributions in the equations for SOz and SO* (1.3) and (1.4). The statistical model is used with these additional unknown variables, i.e. for each field, there is an unknown emission strength, an unknown background contribution for SOz, and an ~known background cont~bution for SO+ The background contribution for a sample originates from the emission field which includes the gravity of the trajectory starting points, and is the contribution from the trajectory starting point to the concentration at the receptor point. This procedure emission

resulted in background contributions for SO4 ranging from 0.4 to 1Opg me3 of SO*, as shown jn Table 6. About 50% of the SO0 background concentration remains as sulphate contribution at the receptor point, and 1 lug mm3 SO, background concentration gives 0.28 pg me3 SO, concentration at the receptor point. The correiation between the emission estimate and corresponding background contribution is high, From -0.4 to -0.9, which should be expected. The estimated background contributions should not be confused with clear air background concentrations but interpreted according to the definition given here.

lu42

L. 6’. PRAHM,

K. CCJNRALXEN

and L. 3. N~.srv

Table 3. Correlation matrix for RSQ results without background concentration. Values multiplied by IO. ‘These matrices correspond to the results shown in Figs 10(a) and It(a). (a) SOL data, (b) SO, data

W ____,_____._.________.~_~~_._x_---_

__-l_.l-

___--..“““--..~ .-.-.__._~

-....

“XI-

i

1

i

1

2 3 4

5 6 7 8 9 10 11 12 13 14

2 0

3

-.--

o-3 0

4

5

6

0 O-1-2 0 0 -2

7 8 9 10 11 12 13 ____.____~__~_~~_.._~_-..~.___~-

0

0 0

o-1 1

o-1 0 0

0 -2 0 -1

-3 -2

0 -2

0 0 0 0 0 -1 -2

0 0 0 0 0 o-3 cl 0 0 0 0 0 O-1-f 0 0 -2 0 -3

15

16

0 0 0

0 0 0

0

0

0

0

0

0 0 0 0 0 0 0 0 -4

0 0 0 a 0

a 0 0 0 0 1 -1 -1 0 0

0 0 0 0 0 u 0 0 0 0

0 0 0 0 0 0 0 0 0

-2 -2

1 0

-2

19 20 21 22

t7 18 19 20 ..._._ _.“_.__.I..-_____-__

0 0

-1

15 $6 17 IX

23 ..__P

O-3-1 0 0 a 0 I 0 u 0 0 0 0 0 0 0 1 0 -3 0 0

14

0 0 -1

0 0 0

0 0 0

-

21

22

23

- _-..“ll. . -

1

0

0

0

0 0

0 0

0 0

0 0

0

0

0

0

0

0 0 it 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

I) 0 0 0 it t) 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0

0 0 0 if f

0 0 0 0 0 1) ti tf Gi 0 3 -3

-I t 0 0 -3 f -f -1 -3 a - 1 o-3

0

-2

0

0

-2

-2

1 -3

_---__

The values for emission fieIds 22 and 23 are uncertain because of the low number of trajectory crclssings, as seen in Fig. 2(a); however, &heAtlantic contribution is low and the contributions from central parts of Europe are high, as expected. The effect of the background contribution on the estimated emissions is clearly seen

__^_____I,^_~.,_,_._.

..__.____r..._ .~ ..--.

--..1..1-

in the scatter diagrams, Figs Xi@) and El(b), where RSQ estimates are Iarger than the LRTAP estimates when the background contribution is neglected in calculations with SO4 data. The procedure for background estimation discussed here, however, did not give reasonable results for SO2

1043

Regional source quantification model for sulphur oxides in Europe SO2

I

0

DATA

WITHOUT

I

I

25

50

I

-I5

OECD

SOa

0

25

DATA

ANNUAL

WITH

I

1

I

125

60

EMISSIONS

15 ANNUAL

ESTIMATION

too

BACKGROUND

50 OECD

BACKGROUND

(IO3

TONS

I

1

175 S /

127

x

200 127

km2)

ESTIMATION

100

125

EMISSIONS

(10

60 TONS

S /

q-f5 127

x

200 127

km2)

EMISSION

FIFI..Db

Fig. 10. RSQ, annual emissions with SO2 data. OECD (1977) emission estimate is shown with 0. (a) Scatter plot. No background concentrations included. (b) The same as (a), but estimated background concentrations included. (c) Emission from each field and the corresponding uncertainty (twice standard deviation). Background concentrations are included.

(4

*- f-

SO4

I

DATA

WITHOUT

BACKGROUND

ESTIMATION

L

P’

I

0

I 25

I 50 OECD

I 75 ANNUAL

1 100 EMISSIONS

I 125 (lo3

I 60

1 r?s

1 200

TONS S / 127 x 127 km’)

I

-20

I

0

RSQ

20

ANNUAL

$0 60 I_,J”_I

80

100 I

EMlSSlONS

i

ICI3

120

4% I

TrlN5

160 I

f? /

x

(80 I

127

200

127

km2

) 220

Table 4. RSQ results for emission fields&awn in Fig. 7. RSQ results which differ more than two standard deviations rrctm the LRTAP resufts are marked with x Unit $0” ton S!127 x 127 km’

_.

..__..

RSQ with combined SO,-

RSQ with SO1-data ~~~CUi~~~~~ EEli$SiO!l

fields

with background

^ I _-... ,/.... -.__. _.

..~.._., --

RSQ with SO,-data

und SC&data

(~~~IC~~~~i~n

Standard deviation

_

with background

__... ~_.

Standard deviation

,l_ll_ _.___._I_.

~alc~lati[~l~ with SO, background ..-

Standard OECD deviation estimates _...,.. __.,^

6> I\ 44 fir t8 x

2 4 9 3 3

1 7 5Fi 3 7

4

x

8 3 15

4 7

--

.-....-__ -.

..,---_..__

31 12

data. This is probably caused by the weak influence at some areas, the accuracy might be even less satisfacthe SO1 receptor concentration from the SO, con- tory. The accuracy on the RSQ estimates appears as centrations at the trajectory starting points. Only 157”J, twice the standard deviation defined in Section 4. For a it means that only about S% ofthe of the background concentration ofS@ remains at the normaldistribution, receptor point, which gives a small con~~bution values should be beyond this &ervaL One may thus compared with the detection timit and uncertainty of expect that at least one of the estimated regional emission fields for each computation will have an even the sampling and chemical analysis procedureof about 3 fig m - 3 as discussed in Section 3. Therefore, the SQz greater stochastic error than 2 times the standard deviation. The results obtained are shown in Figs 10 ~a~k~ound is estimated by an atternative procedure. The measured and computed yearly average SO:! and 11 and in T&es 4 and 5. The statistical method crmcentrations from Europe (Fig. 9.3, OECD, 1977) used does not prevent the emission fields being given are used as SQz background concentrations. The used negative vaiues. This does not mean, however, that values are given in Table 6. A similar procedure has not they are physical sinks. The emission fields shown in Figs IO and If and Tab& 5 all have a positive been used in est~maiing SO, baGk~ound contribution, because this ~un~~bution depends on both SO> and possibility for being greater than zero, Thus a negative estimated value may be interpreted in the way that SQa background concentrations. the emission field is source free, The effect between The RSQ model results for SO* show insi~n~fi~~t differences when the background concentrations are estimates for geographically neighboring emission included and when they are excluded. This may be a fields is small as long as the correlations between estimated emission are low. This is the case as seen result of the weak influence from the background concentrations, compared with u~~r~~nties dis- from Table 3. RSQ gives the uncertainty in terms of absotute values which means that the relative uncussed in Section 6. certainty is Large for weak sources and small for strong sources, while the LRTAP absotute uncertainties are Available information on the emissions, such as small for weak sources and large for strong sources. between population density and fuel consumption, are used to With this in mrnd, significant deviator estimates from LRTAP and RSQ methodsappears for construct the LRTAP emission estimates. However, emission fields 6, 11, 12, 14 and 18 in Pig. 11. One these estimates cannot be taken as true emission reason for the deviation knight be different data strengths. UECD (1977) reports that the LRTAP estimates are only accurate at best to l&25%. For &e&ion, since the Danish SO2 measurements and the

1047

Regionai source quantification model for sulphur oxides in Europe

Table 5. RSQ results for emission fields shown in Fig. 8. RSQ results which differ more than two standard deviations from the LRTAP results are marked with x

Emission fields

2.

CakuIation STD with SO,-data deviation (lo3 ton S/127 x 127 km*)

2 3 4 5 4

6 -9 -1 34 34

8 4 6 12 19 18

;i 9 10 I1 12 13 14 $5 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

60x 30 17 26 6 3 20 26x 64 12 23 21 16 12 45 130x 113x 103 x 21x 95X 184x 63 -89x t52 167x 25 x 55 -1 12 4I 27

1: 7 7 8 13 11 7 7 8 6 6 8 10 9 1.5 12 10 12 7 8 8 25 10 9 6 12 17 8 13 9

11X

Calculation with SC&data witb simuftaneous estimation STD of background deviation contribution (iO3 ton S/127 x 127 km2)

SO, measurements are excluded from the analysis. Figures 10 and 11 show that emission fields 6, 11, 15 and 18 do not have overlapping uncertainty intervals using SO1 and SO4 data. It might also be caused by various deficiencies in the comparability of the sampling and chemicat analysis procedure among the different countries, as well as model deficiencies. RSQ model runs with some measurement stations excluded show, as might be expected, that single stations have a strong intluence on the estimated emission strength close to the station and only weak influence on distant emission fields. Thus, systematic errors at single stations do have a large effect at nearby emission &Ids. There is a clear trend, however_ indicating RSQ estimates which are significantly lower than the LRTAP estimate for DDR and some parts of Poland and Czechoslovakia. A number of RSQ model runs which exclude some measur~ent stations reveal the same trend. The reason for this difference is not at all clear, but it could be that the sulphur emission German

: -2 7 -5 -37x 31 13x -1 23 -‘: 6 13 19X 13 1.5 27 19 is 30 24x 61 x 61 x 46 104X

127 37 19 106X

152 89 19x 83 -3 -2 10

UECD estimates (lo3 ton S/ 127 x 127 km’)

6 4 5 I1 19 t7

0 0 1 6 2 t7

12 9 7 6 10 12 10 8 9 8 7 7 8 8 10 15 15 12 If IO 13 13 19 14 11 10 15 15 10 17 12

47 44 12 21 1 3 2 9 53 3 16 13 24 2 40 233 206 82 48 169 112 49 18 145 141 46 63 10 8 42 22

factors used for burning of brown coal are overestimated in the LRTAP study. One has to distinguish between the wet and dry weight of the fuel and take into account the sulphur bound in the ash. The observed feature could also be caused by a relatively farge toeal deposition caused by low effective emission height and/or emission of relatively large particles, which are affected by gravitational settling. Finally, some investigations (Newman et al., 1975 ; Forrest and Neck, 1977) reveal a different in oxidation rates and the ratio between SOz and SO, at short distances from coal-fired and oil-fired power plants. This would influence the SO4 levels from areas with mainly coal or oii combustion. The relativety large eo~umption of cod in some East European countries might thus influence the emission estimates systematically with a tendency to underestimation. In Table 5, emission field 29 for SO2 calculations and field 6 for SO, calculations are estimated severely negative. The reason for this is thought to be stochastic

104X

1.. P. PKAHM,K.

CONKADS~N

and L. 8. Nux.s~~

‘Table6. Results of background estimation. Used in thecalculations with SO, data and derived from the calculations with SO, data Emission fields shown in Fig. 7

so, background contribution estimated simultaneously with emission estimation lllgm-3

_.....

Standard deviation jfrgm-31

correlation coef%cients between estimated background contributions and corresponding estimated emissions

_._“_.

1.6

0.4

1.x 3.8 311 1.7 ?.I 2.4 1.x 1M 3.7 7.4

0.7 1.3 0.6 0.7 0.9 0.7 0.8 1,I 1,4

I .o

- 0.6

3.0

1.1 0.9

-0.5 -0.4 - 0.4 - 0.6 -M -0.x

0.4 2.1 3.t h.J 9.x 2.0

i .o I.0 1.2 I.8

8.8

1.a I.8

2.5 4.0 7.6 9.6

1.0 I.2 2.8 1.7

- 0.9 -. 0.8 - if.8 -0.6 - Cf.6 -11.5 -0,s -0.6 - 0.4 - 0.4

- 0.6 -0.7 -0.6 -0.8 -03 -0.8

Estimated SC& background concentrations

(iigrne31 0 h

6

6

12 1’‘. 24 24 12 24 24 12 1’i 12 I? 6

as discussed above. For f&M 6, it shouId afso be noted between the Q’es and Cmcasuredwill he limited. as we that Ttafy is separated from the measuring stations by roughly have the Alps causing less reliable results. The results with 37 emission fields confirm the results found with 23 emission fields for most areas in Europe. Therefore, a considerable u~c~tainty on the measured values wilt make it impossible to predict me6zs~& The squared multiple correlation coe~c~ent bevalues. This result is also intuitively quite reasonable. tween the daily SO, and SU, values estimated on the The uncertainty in the trajectory cafcuiations combasis of different emission fields and the measnrem~ots pared with the grid net used for spatial emissiofi are presented in Table 7, In general, the corre~~t~~ns resolution may cause the R2-value for SO, data to be are low. This, however, does not necessarily indicate improved when we average the LRTAP emissions over that the RSQ and LRTAP models are rough approxithe 23 em&on fields instead of using the (127 x mations to reality. It just tells us that the models are I27)km’ LRTAP emission grid net, This is not the case not well-suits for prediction ofmeasur~ values on a for SUa because of the strong near field influence for specific monitorzr. The reason for this coutd be the S02. The correfation with SO, decreases because the considerabIe uncertainty on the sampling and the detailed near field information decreases. chemical analyses. The v&es obtained by the monitor For SO, data, the correlation improves when could be influenced by tocal sources, etc. In brief, we additional “~ttjn~ parameters” are inchzded, i.e. the consider a simple model for concentrations : background values, while the correlation decreases for ctrue SC& because the fixed background values estimated (6.1) = C,,,,,(Q) f 812 ~nde~dent of the actual c#n~n~atjo~ and trajeccnteasllrcd ffa tories are not fitting ~arnete~~ = Giie + ?a The cafcufations 513 the ~o~r~thms of the conwhere E$is the residual. due to randomde~ations from the model, and z1 is the error on the measured value. If centrations have no direct physical ~~t~pretation~ we suppose that q and i:2 are independent with They are used in order to reveal w~et~~r,the high& skewed originaX data should be tran~~~~rn~ to imvariances 0: and ai, we have prove the predictive performance of the model and to sqc mcsrurcd)= a: +- 4, improve the randomness of the residuals. As this turned out not to be the case, we of course prefer the where ~f~@&,~~,,~~)is the variance of the measured model which allowed a physic& interpretat~oo. coucentrati~ns and the squared multipIe correlation

1049

Regional source quantification model for sulphur oxides in Europe

SO,

DATA

1-3

OECD

A a

MAXDST MAXDST

WITH

BACKGROUND

ESTIMATION

c)

ESTIMATES RSQ

c 4 A 5

ESTIMATES

m

1

$2223

2

524

I

III

720

I I I 817(3(61810

I

I

II 9

6

I I II 31912~514~1 EMiSSION

Fig.

1

I

FiELDS

12. RSQ,

annual emissions hased on different subset of the selected SO, data. ~tirnat~ values less than - 20 units are represented in the figure as - 20. Background concentrations are included.

8. MONITORING NETWORK AND SAMPLING PERfOD With respect to planning of future studies, it is important to achieve some insight about the size of the data base which is required to reduce the ~~ertainty on the RSQ model estimates to a desired level. Information ofthis kind from SO2 and SO4 data might also be used for planning of studies of emissions of alternative airborne chemical compounds, if these compounds have similar dispersion and deposition characteristics. The crucial questions are how many monitoring stations should be used, how close they should be placed, and for how long a period the network should operate. From comparisons between RSQ estimates on different data bases and LRTAP emission estimates, we have reason to assume that the un~rtainty range given by the RSQ model will include the true emission

value in most cases. The uncertainty range is here defined as twice the standard deviation from the RSQ model. Figure 12 illustrates these considerations. The RSQ model is used on 1973 and 1974 data separately. Runs are also performed with a more strict trajectory selection criteria than used on the standard data base, The effect of a reduced number of measurement stations is of special interest. Nine stations are selected, preferably one in each of the West European countries which participated in the LRTAP study. Figure 2(b) shows the density of trajectory points for this data subset for the whole period. Figure 13 shows RSQ estimates including un~rtainty for a RSQ cai~u~ation with reduced number of stations and period (onfy 1974). The results should be compared with Fig. IO(c). It is observed that the uncertainty increases with decreasing number of samples.

Table 7. Comparison between LRTAP and RSQ estimates. The LRTAP emission estimates are based on Fig. 2.4, OECD (1977). The table shows the squared correlation, RZ, between daily concentration measur~ents and model estimates using LRTAP and RSQ emissions Method

Component

Number of samples

SO, so4

3771 4123

RSQ

RSQ

LRTAP

LRTAP 23 emission fields

excl. background

incl. background

0.33 0.25

0.30 0.28

0.32 0.37

0.29 0.39

RSQ

with log of measurements _~ 0.29 0.39

E~IISSION

FIELDS

Fig. 13. RSQ, annual emissions with SO2 data from 1374 from 9 selected stations shown in Fig. 2[b). Uncertainty is given as twice the standard deviations. OECD (i877) emission is shown with 0. No background concentrations included.

In order to establish a relation between RSQ model estimate of uncertainty and size of data base, a number of RSQ model estimates have been computed on the bases of different subsets of the standard data base. The size of the data base is defined by the trajectory density inside an emission field. This density is of course dependent on different conditions such as size of emission field and distance to the monitoring stations. Figure 2 shows the trajectory density distributed over Europe when all 23 measurement stations are included and when a subset of only 9 stations is used. These maps can be used to estimate the trajectory density wittin emission fields around a rnon~to~~g station. In Fig. 14, the obtained refation between trajectory density within an emission geld and RSQ model estimate of uncertainty is shown. The large number of points in Fig. 14 originate from computation on the subsets of data mentioned in the figure legend. The straight tine is the expected regression line with slope - -0.5, if the uncertainty is of stochastic nature. The good agreement between this fine and the model rat&s suggests a procedure for future planning of studies of emission quantification for compounds with atmospheric dispersion characteristics and geog raphical source distribution like SO1 and SO4 through the following steps : (a) The desired uncertainty is determined. (b) The required trajectory density in the emission fields is found from Fig. 14 where the ordinate is

scaled with the ratio between the total yearly emission of the considered campound and the total yearly emission of S02. The size of emission fields and position of measured station are now found using information on the trajectory density given in Fig. 2. Alternative location of monitoring stations is studied by trajectory density computations like those given in Fig. 2 and alternative emission field arrays are studied in connection with the trajectory density. Since the uncertainties are determined by shortcomings in both modei formu~~on and measurements, it is not possible to predict the reduction in estimated uncertainty caused by improvements in either mode! or measurements, If improvements are achieved, uncertainties obtained from Fig. 14 can be regarded as upper limits, 9. DECAY AND OXIDATION PADAMETER OPTIMIZATION

The RSQ ealcufations presented in Sections 7 and 8 are based on the air trajectory model with the decay and transformation parameters given in Table 2.1. These parameters have been taken from the previous regional studies of Eliassen (1978). The decay parameters were previously examined by comparison between measured and estimated concentration using l/i0 of the present data base and with fixed strengths of emission f%eIds(Ehassen and Saltbones, 1975).

Regional source q~~ti~~ation

model for sulphur oxides in Europe

fO51

Equation (1.4) is now rewritten by use of two The RSQ model and the standard data base can now factious, fi and fi: be used for optimization of a number of different parameters. We will here, however, restrict ourseives GO4 = CSOl.baclclroundFon*ribulion to a study of decay and oxidation parameters. The optimization is based on minimjzation of the residual i- k,0 -a - Blf;fM + B.&W (9.1) sum of squares (RSS), determined from the difference between measured concentration values and model fr andfi are determined from the trajectory model for fixed k2 and the other parameters are determined by estimates. The decay parameter for SO*, kr, is seen to cause a regression analysis, k, is then found from the steepest minimum RSS for kr = 1.3 x 10n5 smi in Fig. 15. descent method for the RSS values. Table 8 shows results from the regression analysis. For k2 I 4 x Equation (1.3) is used for this optimization. From the ordinate scale in the figure, we observe that the RSS low6 s-t, the term k,(l - u - 8) is not significant at a 5% level and this term is thus excluded from the value is only weakly dependent on the k, value, and the previous recommended value k, = lOis s-* used in analysis. k3 is estimated to be less than 4 x IO-’ s- I. Sections 8 and 9 is thus consistent with the data base. The regression analysis is redone revealing the results Variation of k, in the considered range does not affect given in Table 9. An optimal value for k2 is found to be 1.6 x 10e6 s-l with the background contribution at the estimated emission fields significantly. 2.4 pg m- 3 and fl at 12%. A background contribution For estimation of sulphate production and decay, of 2.4 pg m-3 is not in disagreement with measured we use (1.4). The third and fourth terms in (1.4)contain the products QJ x k, and Qj x p, which means that Qj SO, and SO4 concentrations in Europe (OECD, 1977, Figs 9.3 and 9.4). cannot be determined independently of k3 and @from The k2 value does not deviate si~ifi~a~tly from the (1.4) because we also have Cs04sfARTand C’s,,,,,, as value in Table 2.1 although it is somewhat lower. It is independent variables to be estimated; we use, thereinteresting that k3 isestimated to about zero with a fore, fixed Qj values from the OECD (1977) estimate. relatively large initial oxidation of SO* to SO,,. This This estimate was shown not to deviate significantly result might be caused by the fact that the oxidation from RSQ estimates (Section 8).

SO2

DATA

I

tw.

I

moo.

I

a3w. TRAJECTORY

@LJowo. COUNTS

Fig, 14. Standard deviation of RSQ resufts for each emission field as function of number of trajectories passing the emission field. This number of trajectories, trajectory counts, iscomputedas the sum of trajectory densities from each 127 x 127 km2 grid square inside the emission fief&sgiven in Figs. 7 and 8. The trajectory density is defined in Section 3. Overlay plot of values from 7 different RSQ calculations with 7 cases of the standard data base. The solid line is the linear regression line with the (expected) slope 01= -0.5. Empirical slope is u = 0.56. The cases are: (1) Standard data base and 23 emission fields. (2) The same as (1) and year = 1973. (3) The same as (I) and year = 1974. (4) The same as (If and MAXDST < 4. (5) The same as (1) and MAXDST -z 5. (6) The same as (1) and selected stations. (7) Standard data base and 37 emission fields.

Table 8. Estimation of CSOr.bacltgroundcon(Fibulion, k3( 1 - a - 8) and /? from (9.1.) by a regression analysrs for different values ofkl. (a) Main results, (b) corresponding correlation matrix (a)

.._-.. _._. k, (IO-“s-‘1 _

ll^--l--_l__ 1 2 4

5

._-_ _,.l_ll_.-

CSO&b.WkgP2”*d STD STD STD Cnntribulion deviation deviation fl deviation R2 RSS k,(f -*-B) (lO-?s-“] (gg m-“f (l’,,) -. ___. ...-.. - _..1 .___ __.________” __^_I____.. .I-_. .,_______.(Bgm~‘t._. 2.4 -4.2 2.3 1 0.1 13 0.2616 184371 2.4 - I.5 2.3 13 1 0.1 0.2612 184491 2.4 2.4 13 1 0.1 3.9 0.2602 184744 2.5 1 0.1 6.6 2.4 I? 0.2596 184876

I__---......--I ox.

. .------I____ __--

.-,- .._.-..- -. _...--

.--._-..--

_-

__._“._._

(b)

CSOe.bsctgmund

w B

-

conrtibution - r - P)

1

0.1

-0.3

I

- 0.9

1

._~. .__-_.__.__________.__~_~

rateat larger distances from the source could be ofthe same order of magnitude as the loss of sutphate above the mixing layer of 1000 m. We do not include this loss in the model which might be the reason that the net sulphate production is obtained by a k, value ofzero. The initial oxidation rate fi = 12% is about twice as large as the previous estimate (Eliassen, 1978) but not in disagr~meut with general information from pfume studies by Newman et al. (1975). The very low oxidation rate at some distance from the source is

consistent with a very low average rate discussed by Wilson and Gillani (1979). It is also interesting to note the plume oxidation measurements from coal-fired power plants by Forrest and Newman (19771 which show no systematic increase in the Y; of sulphur dioxide converted to sulphate over distances from 3 to 200 km. It is reported that: “Most of the oxidation occurs during the early history of the plume with virtually no further conversion taking place downwind”. Maximum conversion of SOz to SOI seldom

k

(10-5i-‘)

Fig. 15. Optimization of decay rate for SO2 by rn~n~ng the residual square sum during RSQ computations with standard data base. No background included.

1053

Regional saurce quantification model for sulphur oxides in Europe Table 9. Estimation of

and fl from (9.1.) by a regression analysis for different values of k,, ks f; 0 is assumed

CSOL,krcksmundEonfribution

CSOa.back!$mmd chntributioa%

kz


1 1.5 *1.6 1.7 2 3

STD deviation

@

R2

CL)

@fs mm31

2.5 2.5 2.4 2.4 2.4 2.4 2.4

STD deviation

0.i 0.1 0.1 0.1 0.1

11 11 12 12 12 12 14

_..-

0.3 If.3 0.3 0.3 0.3 0.3 0.3

0.2608 0.2610 0.2611 0.2611 0.2611 0.2611 0.26Q6

RSS @$ m-6)

184573 184520 184499 184499 184500 184510 184626

* Best statistical fit.

exceeded 5% in coal-fired plumes, while it reached 20% in oil-fired plumes (Newman et al., 1375). Repeated RSQ studies, with separate initial oxidation parameters for coal- and ail-fired sources, are thus of interest.

Location and emission strength of sulphur oxide sources in Europe are estimated by a meteorological air quality model. The model is based on air quality me~urem~ts and air trajectories ~rodu~ for the OECD project, LRTAP. The data base used consists of 24-h SO2 and SO, measurements from about 45 stations in Europe d~~~~g the period from 1973 to 1975, and of air trajectories arriving 4 times a day at each station. By use of an air trajectory air quahty model, a large number of linear equations are produced estimating SO2 and SO, values with emission fields as unknowns. Relating the rn~sur~ and estimated SO, and SO, values to each other by a ieast square method gives an estimate of the emission iieids. About 75cO samples and IS,W trajectories were used. The estimated fields are compared with ~nfo~~t~ou on emissions estimated in the OECD project, LRTAP. Agreement between the LRTAP estimate and the mode1 result is found for most of the emission areas. The emission in some European areas, however, is found to be both overestimated and uuder~timat~ compared with LRTAP, Possibte reasons for this disagreement are discussed. The Regional Source Quantj~catio~ (RSQ) model presented here is demonstrated to be applicable for source estimation on a regional scale. The RSQ model is also suggested for optimal siting of monitoring stations. The decay and oxidation parameters in the air trajectory model are determined by the RSQ model. These estimated parameters are “optimal” when the trajectory mode! is used, but care should be taken in interpretat~ou of the result for other apphcations. The decay parameter values agree fairly well with previous estimates, while the oxidation parameters estimated by the RSQ model were found to correspond with a greater initial oxidation than most

commonly used, and an insignificant oxidation during transportation, ~c~~w~e~g~~e~~s- The data base, consisting of measured air ~~~en~~~~~~s, pr~~~it~~~o~,and computed trajectory points, used in this study was kindly made available in computer compatible form by Anton Eliassen, Norwegian Meteorological Institute. We would also like to thank him for valuable discussions during the study. This source finding study was suggested by Brynjulf Ottar, Norwegian institute for Air Research, and it was economically supported by the Council of Scandinavian Ministers. REFEREWES Barr A. Ay ~ood~~bt

J. I-I.,Sal1J. P. and Helwig J. T. (1976) A Users G&& ro SAS-76. SAS Institute, Inc.. Raleigh, North Carolina, W.S.A. Breuer W. (1965) Die Atrssagekrafr ~~nr~~~er~~c~er Immissionsmessungen. IWL, Institut fur Gewerbliche Wasserwirtschaft und Luftreinhaltung E.V. Forum 65. Baud 3. Eliaesen A. (1978) The OECD study of long-range transpo~ of air pollutants : Long tr&ns~rt modelling. ~r~os~~e~~~ ~~v~o~~e~r 12,4?9-487. Eliassen A. (f980) A review of long-range transport modeiling. J. Appt 1M&.I9 (in press). Eliassen A. and faftbones-l. (1975) ISecay and tr~~sformatioo rates of SO,, as estimated from emission data, trajectories and measured air concentrations. Atmospheric Enuirorlment9,425-429. Forrest J. and Newman L, (1977) Further studies on the oxidation of suiphur dioxide in coal-fired power plant plumes. ~rmo~~~r~c ~~~~r~~rne~~t&465-474. Hiigstrom IL fI975) Con&-ming the locat sources of observed air pollution in communities. Atmospherk Environment 9, 929. Newman L., Forrest J. and Manowitz 8. (1975) The application of an isotope ratio technique to a study of tbe atmospheric oxidation of sulphur dioxide in the plume

from an oil-fired power plant. Atmospheric Environment 9, 959-968; and The application ofan isotopic ratio technique to a study of atmospheric oxidation of sulphur dioxide in the plume from a coal-fired power plant. ,&mo@rerfc ~~U~O~~~~ 9* 969-977. OECD ft977) The OECD Program on ~Q~g-R~~ge Transport of Air ~u~~~r~~r~.Measurements and Fj~~~~ff~,Urgani-

zation for Economic Cooperation and Development, Paris, France. Ottar B. (1978) An assessment ofthe OECD study on longrange transport of air pollutants (LRTAP). Atmospheric Endvnment

Pettersen

12, 445-454.

S. (1956) Weaf~er Anulysis and Forecasr~~.

1054

L. P. PRAHM, K. CONRADSEN and L. B. NIF.I_SE~

McGraw-Hill, New York. Prahm L. P. and Christensen 0. (1977) Long-range transmission of pollutants simulated by a two-dimensional pseudospectral dispersion model. J. Appl. Met. 16, 896.-9 10. Prahm L. P., Conradsen K., Nielsen L. B. and Eliassen A. (1979) Regional source quantification model for sulphur oxides in Europe. Proc. WMO Symp. on the Long-range Tronsport of Pollutants and its Relation to General Circulation Including Stratospheric/Tropospheric Exchange Processes. Sofia, Bulgaria, l-5 October 1979. WMO report, No. 538. Prahm L. P., Torp U. and Stern R. M. (1976) Deposition and transformation rates of sulphur oxides during atmospheric transport over the Atlantic. Tellus 28, 355- 372.

Rao CC. R. (1965) Linear Srutisticul Infirence Ed I[\ Applications. Wiley, New York. Semb A. (1978) The OECD study of long-range transport ol air pollutants. Source inventory. Armospheric Enrironmenr 12, 455-460. Wilson W. E. and Gillani N. V. (1979)Transformatlon during transport: a state of the art survey of the converslon from SO2 to sulphate. Proc. WMG Symp. on the Long-range Transport of‘Pol1utant.s and its Relation to General Circulation Including Stratospheric/Tropospheric Exchanye Prw cesses. Sofia, Bulgaria. 1 5 October 1979. WMO report, No. 538. Yamartino R. J. and Lamich D. F. (1979) The formulation of a source finding algorithm. Preprint volume, 4th Symp. on Turbulence, D@iision and Air Pollution. 15-18 January 1979, Reno. American Meteorological Society, Boston.