Design of network experiments for regional-scale atmospheric pollutant transport and transformation

DESIGN OF NETWORK EXPERIMENTS FOR REGIONAL-SCALE ATMOSPHERIC POLLUTANT TRANSPORT AND TRANSFORMATION* C.

A~osp~eric

M. SHEIH, G. D. HEX+and B. B. HICKS

Physics Section, Radiological and Environmental Research Division, Argonne National Laboratory, Argonne, IL 60439, U.S.A.

Abstract-Design criteria for the selection of regional-scale network sites, sampling times, and sampling intervals are investigated in terms of the verification requirements for various numerical models. Network experiments are classified into tracer experiments to test the physical and chemical mechanisms of atmospheric pollutant tra~formation and transport, and air quality experiments toevaluate the extent of air pollution. For the tracer ex~riments, two lines of five stations are r~ommend~. The spatial separation between the lines is about #km, and the distances between stations are 170 km for the upstream line and 200 km for the downstream line. For air quality measurements, more than 13 stations are needed to recover the annual pattern of the pollutant concentration.

1. INTRODUCTION The

prospect of increasing the number of coal-burning electrical power plants raises a number of important questions about the consequences to the environment and to public health. Although there have been many studies to assess the impact of pollution on a local scale, that is over a length-scale of a few tens of kilometers, the impact of ~llution on regional scales, i.e. covering hundreds to thousands of kilometers, is largely unknown. In order to provide the information required to assess the impact of increasing the number of coal-burning power plants, several extensive research efforts, such as the Sulfur Transformation And Transport Experiment (STATE), the Sulfur Regional Experiment (SURE) and the Multistate Atmospheric Power Production Pollution Study (MAP3S), are currently being planned. These studies will include field programs to examine the dominant physical and chemical mechanisms controlling sources, sinks, transport, and tr~formation of sulfur and otber compounds. In addition to field programs these studies will also include modeling programs to simulate the effect of the governing processes and thus to provide the basis of assessing the consequences of various planning strategies. The success of a regional-scale network experiment will depend to a large degree upon the coordination of the observational program with the modeling program. The modellers look to the observations to answer two questions : (a) How can complex subgrid* Work supported by U.S. Energy Research and Development Ad~n~tration.

scale processes such as dry deposition be parameter&d, and (b) Does the model give realistic results? The observer, on the other hand, can look to numerical simulations to provide necessary information for planning the sampling network. The programs are necessarily interde~~dent. Air pollution field experiments can be arbitrarily classified into two categories according to their purposes, namely m~surements of air quality for evaluating the extent of air pollution and measurements of atmospheric dynamic processes for studying the life cycle of pollutants. The ~as~emen~ to be conducted in STATE and SURE, for example, are primarily airquality measurements, whereas some of the experiments proposed for MAP3S would be tracer studies which allow the study of the physical and chemical governing mechanisms. It should be emphasized that, with so many unknown pollutant sources in a regional-scale area, the most reasonable approach for understanding the mechanisms of pollutant transport and chemical reaction in the atmosphere is through isotope tracer experiments of the particular pollutant of interest. The purpose of the present paper is to outline design criteria for the above two types of experiments. The approach that will be followed in order to design a tracer experiment is to examine the numerical models currently being developed by many investigators and then to deduce sampling criteria from theory and physical reasoning. For designing an air-quality sampling network, the main criteria for locating sampling sites will be based upon the results of numerical simulation for the northe~tern United States.

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C. M. SHEIH.

C.

D.

2. DESIGN OF TRACER EXPERIMENTS

(a) The short-term Gaussian plume model One of the most commonly used nuherical models is based on the assumption of a Gaussian plume. A typical Gaussian plume model being used to simulate long-range pollutant dispersion over northeastern United States is more or less similar to the equation given by Heffter and Ferbe (1973, i.e.

c=

Q 2ZU,“(2K1$U (z -

z,y--_~__ 2V,ti

4KJ

(nKJf

EPt

t

H

T,

(1)

where C is the pollutant concentration, Q is the pollutant source strength, oI is the standard deviation of the plume width in the horizontal direction y whose origin is the plume centerline, K, is the vertical eddy diffusivity, J is the mean wind speed, z, is a stack height, t is the time, V,, is the surface deposition velocity, E is the precipitation scavenging ratio, P is the precipitation rate, H is the thickness of the precipitation layer, and T, is the chemical decay time constant. This equation is the conventional Gaussian plume formula with additional terms for surface deposition, precipitation scavenging, and chemical decay. The center line of the plume is the trajectory of the simulated tracer advected by the observed mean wind velocities. The characteristic length scale of the turbulent eddies participating in the horizontal diffusion in (1) is of the order a,(t) and the corresponding time scale is

HESS and B. B. HICKS

standard deviation from its true value, which arises because of the finite sampling time. Since 2T, is the minimum time interval for obtaining independent samples (4) suggests that the number of the independent samples required is

(5) It should be stressed that the number of samples given in (5) refers to measurements under the same atmospheric conditions. Since a tracer experiment with a detailed wind fieki is not available for computing each of the parameters in (2) and (3), estimates of these parameters will be made, based on available observations and intuitive assumptions. For a regional-scale problem at 100 km downstream from a pollutant source, Heffter (1965) gives by = 10 km (see Fig. 1). If we assume that (u’*)f = 4 m s- 1 and L = 0.10, then the sampling interval, sampling time and number of samples are 2T, - 1.4 h T av N 280 h N-200. If the studies are to concentrate on convective conditions, between 1000 and 1600h say, only four samples can be taken per day and a total of at least 50 days are needed for the experiment. More specifically, if one is interested in the statistical distribution of pollutant concentration in a cross section of a plume at 100 km downstream from a source, an aircraft should

‘““’

T, = a@+ with 1 lag

Jo

I02

d’,(K)dK

t

where #,(K) is the spectrum of the horizontal wind speed component normal to the plume trajectory, K is the wave number, and p is the corresponding smallscale turbulent energy which is responsible for the diffusion of the plume. The time scale T, is of same order as the integral time scale, and thus the estimated time interval required to obtain an independent sample from aircraft measurements traversing the plume cross-section is equal to or greater than 2T, (Tennekes and LumIey, 1972). If one assumes that the diffusion in the horizontal plane is a Gaussian distribution, then the required sampling time for computing the standard deviation of the plume width can be written as 4T 4T, T., = F - cz

(see Lumley and Panofsky, 1964), where T is the integral time scale of the Lagrangian autocorrelation function of u’, and L is the error of the computed

++

+

4

Fig. 1. Long-distaacc horizontal standard deviation (a,) as (He&r, 1958). Symbols reprcaent observations by GiWd (#, Abrahamet al. ( ). Bad and Fuquay (e), Panquill a), Pack and Angel1 ( and *), Clasaitkd Project I (*), Sakagami (0). Angel1 function of travel dktancx from the source

(

), Richardson and Proctor (0).

U.S. Weather Bureau

1147

Design of network experiments traverse the plume cross section no more than once in one hour. Similarly, the cases of neutral and stable stratifications should be studied independently, during appropriate periods at other times of the day. Again it should be emphasized that the requirements for adequate data to verify the concentration distribution around the plume center line pertains to a mobile measuring station, moving with the plume. Furthermore, it should be noted that there is some practical difficulty in predicting the plume center line for a regional-scale area from available wind fields. The observed wind field generally being used is derived from data obtained from NOAA. These data are given at every 12 h and the average distance between observing stations is about 200 km, which corresponds to a temporal resolution of 6 h for a typical wind velocity of 10 m s - ‘. Since the trajectory of a plume is computed from the wind field interpolated both in time and space from these observational data, the wind velocity components with periods smaller than 12 h are filtered out in the process of interpolation. It should be pointed out that, no matter what scheme is used in computing the trajectory, one cannot improve with confidence the 12h resolution provided by the original data. The effect of this can be illustrated by making use of Fig. 2, which shows a typical horizontal wind velocity spectrum. The figure indicates that, with the above 12-h low-pass filtering operation, 30% of the total horizontal wind energy or 55% ofthe total r.m.s. value of the horizontal wind velocity is not accounted for in the computation of the trajectory. More specifically, for the example given earlier the r.m.s. error in predicting the plume center could be 55 km at 100 km downstream from the source. In practical applications the observation network for testing numerical predictions will probably be spatially fixed. For a fixed network the averaging time required for acquiring adequate data must be increased because large-scale turbulent motions (meandering of the plume) will mean that the plume will be overhead only intermittently. For the averaging period given in (6), the large-scale motions become much more important in dispersing the pollutant than the small-scale motions. This can be seen in Fig. 2 where the turbulent energy in the spectral band corresponding to periods longer than 1 h, the energy of the

II

to-’

I

Ill

10-6 lO"J

I

I

I

IO-4 10-3 10-2

n(Hz)

Fig.2. Energy density (nF(n)) of the horizontal velocity at

50 m near Munich (after Fiedkx, 1971X as a function of the cyclical frequency n.

meandering motions, is about 6 times larger than that of periods less than 1 h. This implies that data from spatially fixed observing stations cannot be used to test the predictions of small-scale turbulent diffusion models. This is because the effect of meandering motion will become important in the dispersion and can not be easily separated from that of small-scale turbulent diffusion long before adequate sampling duration, 220 h according to (6) is attained. It can, however, be used to test a long-term-average model, such as the statistical trajectory model to be discussed in the next section. In addition to the time scale for horizontal diffusion, other time scales enter into the physical and chemical processes of the plume. These are the scales for vertical duffusion, surface deposition, precipitation scavenging, and chemical transformation, the first three of which are given, respectively, from (1) as

(7) T_=$ where h is the height of the planetary boundary layer. For example, if an experiment is performed in conditions such that 1= 10 m s-‘, h = H = 2 km, K =30m’s-‘, Vd=0.02ms-‘, E=4 x 10’ and 1: = 7 x lo-‘m s-‘, then the appropriate constants and corresponding distance scales will be as listed below ; TV= 18h

L, = 648 km

Td= 16h

Ld = 576 km

T,=2h

L,=72km

T, = 27.8 h

Lc = 1OOOkm.

(8)

There is no simple functional relationship available for T,, but its value has been obtained from studies over Western Europe by Eliassen and Saltbones (1975). The characteristic time and length scales for vertical diffusion are the time and the distance downstream of a pollutant source beyond which the plume becomes well mixed in the planetary boundary layer. For t >>T, the parameterization of the pollutant concentration profile can be greatly simplified because the concentration can be taken to be uniform over most of the profile. The other temporal and spatial scales in (8) refer to the temporal and spatial separation required to sample significant long-term variations in pollutant concentration for each of the mechanisms, provided that the formulae used have properly parameter&d the variables involved. The above analysis indicates that aircraft measurements traversing the plume at distances T,d, (T, + T&i, and (T, + T,)ti downstream from the source should give adequate information to test various

1748

C. M.

SHEIH,

D. HESS and B. 9. HICKS

G.

mechanisms in the numerical model. The number of traverses and the minimum time interval between successive traverses is given in (6). Furthermore. if C,i, is the minimum concentration detectable by an instrument, then, at the center line of the plume, the required emission rate is

label for each trajectory. The mean coordinates are represented by an overbar and are computed from

(13)

Q > 27Xr,(2K,t)~ 1 C& where L is the total number of trajectories originated from each source, and the standard deviations are computed from

w

For the example given eariier, namely at 1OOkm downstream from the source, if CF,,= 10 km, I<, = 30 rn’s-l , ii = lOmsand Cmin= lpgmW3, the emission rate has to be larger than 1.7 T h-‘. (b) Long-term statistical

trajectory

model

The statistical trajectory model approximates the long-term average plume from each pollutant source by a series of Lagrangian puffs. This model was originally introduced by Durst ct al. (1959) and applied by 3olin and Persson (1975) over western Europe. Recently it has been used by Sheih (1977) to simulate the atmospheric pollution sulfur dioxide and sulfate over the northeastern United States. The concentration at a point of interest is computed from summing all the contributions of the puffs to that point, i.e.

(14)

O;(J?i) = (Yjl - $jj,”

The required sampling time for computing the standard deviations (7, and fly of the horizontal distribution function of concentration in (10) is found from the integral time scale defined by T, = Jo” R,(Qd[ where R,(i) for a = u and u refers to the autocorrelation functions of the wind velocity components, of each trajectory end point at the same time after release,

ml

R,U, n) =

C,(x,.Y,z) =

u’txjl + Xj(l+n)3Yjl + Yj(l+n))“‘(Xjf9 Y./l) --(16) Z!“(Xj$, Yjl)

t i=l

a$‘Xj) = ;s --.--

i

QijkPb(X

-

Xp

I’

-

.PjY’rk(~,

t)

(10)

j=l

where C, is the pollutant concentration, the subscripts sulfur dioxide and sulfate, respectively, Qiik is the pollutant source of the k-th specie in thej-th p&emitted from i-th source, M is the total number of sources, N is the total number of puffs, and P, and P,, are the horizontal and the vertical distributions of con~ntrations, respectively. The horizontal distribution function of both sulfur dioxide and sulfate concentrations is assumed to be Gaussian, i.e.

k = 1 and 2 represent

and n is a time tag in multiples of the time interval between the successive trajectories. The quantities with primes are fluctuations from mean values defined as

To illustrate the above analysis wind data for the month of April 1972, provided by the National Climatic Center, NOAA, were used. The autocorrelations R, and R, for the horizontal wind components were computed for a tracer originating in southern Illinois and the results are shown in Fig. 3. Assuming the conventional exponen~~ly decaying correlation function for the wind components, one can

To compute the parameters for the above equation, a simulated tracer particle is released twice a day from each source and its locations are computed at 3-h intervals, namely xjl = u(xu- lttt Y,j- t ~1”

(12)

Yjj = Gx,- 1)ttYe-‘& where At is the time interval; u and v are the velocity components in the x and Y directions, respectively ; j = 1, 2, ---, N are trajectory end points at times t = At, 2At, ---, NAt from the release; and I is the

10 12

14

t fhr) Fig. 3. Lagrangian autocorrelation functions, R, (0) and R, (A), computed from the wind velocities of the regional-scab trajectories of simulated tracer particies.

Design of network experiments

estimate that the integral time scales are about 5 and 11 h for R, and R,, respectively. According to (4) and (5), the sampling interval, the total sampling time and the total number of samples will be 2T,>22h Tpv - 184 days

(181

N-200. This analysis also gives the coordinates of the centers and the standard deviations of the puffs, as required in (11) and as shown in Fig. 4. The vertical distribution functions of sulfur dioxide and sulfate concentrations are computed by integrating the finite-difference form ofthe following equations - AP,, $6(Z - h,, t) (19)

where Pzk for k = 1 and 2 are the vertical distribution functions of the concentrations for sulfur dioxide and sulfate, respectively, and K, is eddy di~~ivity. The decay constants for sulfur dioxide and sulfate are assumed to be A = 10T5 s-l and B = 10e6 s-l, respectively. The Dirac delta function 6(z - h, t) gives a unit pollutant at the effective stack height h, to each puff. The last term in (20) represents the formation of sulfate from the conversion of sulfur dioxide. The eddy diffusivity follows the simple formulation used by Bolin and Persson (1975), i.e. kU*Z, K‘-

i a5ku, i0

for zg I z I 85 m 85mSzIh

(21)

zrh

Fig. 4. Mean coordinates of the statistical plumecenter line, dispersion cc&icients of the trajectories, and sulfur budgets at various times from release. * However, some recent experiments suggest substantially greater sulfate deposition velocities (e.g. Wesely et af., 19’77).

1749

where k is the von K&m&n constant, and the friction velocity u* and inversion height h are assumed to be 0.4ms-’ and 2 km, respectively. The frequently accepted values of deposition velocities, 1 cm s- ’ for sulfur dioxide and 0.1 cm s- ’ for sulfate, are used for illustration.* It should be noted that the parameters in (19}-(21) represent long-term average values, as also do those involved in defining the horizontal concentration distribution. The sulfur budgets (computed from integrating the vertical profiles of P,, and Pzz which are obtained from the numerical integration of (19) and (20)) in the form of sulfur dioxide, sulfate and surface deposition are also shown in Fig. 4. There are several possibilities of using the information provided in the figure for planning a sampling network. For example, if one is interested in measuring the transformation rate of sulfur dioxide to sulfate, Fig. 4 suggests that the sampling stations should be located within 30 h from release to see si~ifi~ant changes in the amount of sulfate. In order to parameterize the chemical transformation, measurements at least at two cross sections of the plume are necessary. If the sensitivity of the instrument requires that the difference in the amount of sulfur dioxide has to be at least 20”/, of the emission, then the two cross sections can be sent at 10 and 20h downstream from the source, i.e. at (x, p), = (530 km, 420 km) and (a, y)2 = (860 km, 700 km). Furthermore, since one has to identify the gross picture of the pollutant concentrations across the plume, several measuring stations, say 5 stations, are needed in each cross section, The sep~ations between these stations should be of the order of the standard deviation of the plume width at that site. If one uses 0.5 uY, the smaller component of the standard deviations, as the spatial interval, then the separations between the sampling stations at the upstream and the downstream cross sections will be 170 and 200 km, respectively. The proposed sampling stations centered around the center line of the Idng-term-average plume are shown in Fig. 5.

Fig. 5. The location of sampling stations for the statistical trajectory model. The symbols are the site of tracer release (q), upstream sampling stations (e) and downstream sampling stations (A).

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t ‘. M. SHEIH, G. D.

in order to test the vertical dispersion formulations of the models, e.g. ( 1Q-(2 1), vertical profiles ofP, I and Pzz will be required. Typical profiles obtained by use of the model presented here are shown in Fig. 6. Since the thickness of a plume increases as it travels downstream, the vertical extent to be covered by an experiment should be varied accordingly. if the vertical thickness of a plume to be covered by the expcriment is set at some height, for example, where the polhttant concentation is 107; of the peak concentration of the profile, then the figure shows that the heights should be about 1 km for 1 h, 1.6km for 3 h and 2 km (the assumed inversion height) for 10 h and longer from the time of release. The results also show that on the average the plume becomes fully developed throughout the inversion layer a day after the release, after which fewer data are required to define the vertical profiles and some simplifications can be justified in the analysis of the data. Ideally, one would take profile measurements for all plumes at the same time interval from the release; in this way, measurements of the same age could be averaged together for different trajectories. However. this would require more accurate estimation of the plume location than is permitted by contemporary methods, since wind data for computation of trajectories are only available twice a day. Obviously, accurate estimation of plume location is necessary for positioning sampling aircraft inside the plume and for identifying appropriate measurements made by the surface stations. With further development in the use of satellite pictures and in the computer simulation of the tracer trajectories, such experiments will become feasible for a regional-scale problem. The number of samples and the sampling time interval can be estimated with fZ)-(5) as discussed earlier. (c) The grid model The grid model offers another approach. In this model the variables in a finite difference equation

Fig. 6. The vertical con~ntration profiles of sulfur dioxide (dash&f and sulfate particulate (solid) in a puff at various times from release.

HESSand 3. B. ?b?KS represent average values over the grid volume surrounding the grid point and over the time increment, i.e.

The temporal average in (22) is not a dominating influence, since the Courant condition, Ax > uAf, which is necessary for computational stability implies that the spatial average across Ax is more important than across the equivalent spatial distance uAt of temporal resolution At. To derive the appropriate equation for the grid model consider the diffusion equation,

ac

ac

a2c

-4-Q-S ‘f*j”?xi=vdx~~j

(23)

where C is the pollutant concentration, U, is the wind velocity vector, v is the molecular diffusivity, Q is the source and S is the sink. The dependent variables in (23)can be represented by the sum of the large- and the small-scale component which in general can be written as b, = B + cb:

(24)

where the terms on the right hand side are the (Iargescale) did-volume-average and the sub~~-~e components. Substituting (24) for each of the variables in (23) and averaging the equation over the grid volume yields

de -p+==

af? SXj

a --y --g+

XI

t-Q-S,

(251

where the rno~cu~~ terms have been neglected. Since over the variables in the above equation are avera the grid volume, the subgrid-scaIe components appear only in the flux term. It should be noted that only in this way can (25) be transformed into a unite-different equation without introducing any a&sing effects (e.g. Blackman and Tukey, 1958). In other words, when observational data are used in initializing the variables for a finite-difference model, the data have to be averaged over the grid volume before they are used. For the region of interest for MAip3S, the nortbeastern United States, the horizontal dimensions shown in Fig. 5 are about 2ooO km east-west and 1500 km north-south. A reasonable horizontal grid array is 20 x 1.5,which will result in 100 km as the grid length for both horizontal directions. However, the meteoroIo& cal variables provided by NOAA have a horizontal spatial resolution of 200 km determined by the separation of the observation stations, which means that to compare the numerical results with observations no advantage is achieved by using a horizontal grid Iength less than 200 km u&as some an&ySis is aB&&Ie for improving the resolution of the data. The vertical dimension to be covered is the upper Iimit of the inversion height, @picaBy aboat 2 km. The vertical

1751

Design of network experiments

grid increments can beeither an expanding or constant length. Whichever grid increment is used, the first layer within the constant flux layer (z c 20 m) is generally treated by parameterixation, because no finitedifference scheme can properly resolve the small-scale transfer processes near the ground without using an unre~onably small vertical grid length. This suggests that an experiment for this layer should be designed to look for similarity profiles for all the variables involved in the same way as that of Monin-Obukhov similarity for momentum. For the iayers above the constant flux region, if a constant grid length is assumed and a typical grid number of 20 is used, the grid increment will be 100 m. Again, if the spatial resolution given by the NOAA data recorded at every 50 mb is considered, a better choice for the vertical grid length might be 5OOm. This suggests that for comparison with the numerical prediction, either a dense network ofsampling stations or remote-aping devices should be used to give averages, over volumes with dimensions of (Ax, Ay, AZ) = (200 km, 200 km, 5OOm) and (200 km, 200 km, 20m) for the region above and below the constant flux layer, respectively, for all quantities in (25). The par~ete~tion of the flux terms as defined in (24) and (25) should include all the scales smaller than the grid dimensions. The requirements eliminate many of the eddy-diffusivity formulae, This is because the averaging operation for obtaining, mean variables for these formulae is performed in time over measurements taken at a fixed point whereas the overbar values in (25) represent spatial averages over the m~urements taken at the same time throu~out the entire grid volume. To assure that a representative grid volume average can be taken, the observational sites should be as uniform QSpossibk and away fromlarge s~gr~-scafe po~lufu~ sources. More s~cifically, if the dimension of a pollutant cloud is smaller than the grid dimension, the average pollutant concentration in the grid volume will depend strongly upon the grid dimension. Therefore, the sampling sites should be sufficiently far away from the pollutant source that the cloud has developed to a size comparable with the grid dimension. For the horizontal grid dimension of 200 km in the present example, the horizontal standard deviation of a plume width will reach this dimension at about 2000 km downstream from the source according to the observations shown in Fig 1. Furthermore, since a plume takes less time in dispers-

ing across the vertical grid dimension, as is shown in Table 1, the dominating factor for selecting the site for a box-budget experiment addressing a plume from an isolated source has to be the horizontal length scale (> 2OOOkm). The temporal resolution of a numerical model is the time increment used in the numerical inte~ation. The precise value of the time increment depends upon the numerical scheme and can be obtained from a numerical stability analysis. For the present discussion, general requirements encountered in the analysis will be used, i.e. At
(26)

and

(27) where K, is the eddy difIusivity of the subgrid-scaIe pollutant diffusion. Typical values of these variables in the atmosphere are shown in Table 1; the eddy diffusivity in the horizontal direction has been estimated from the data reported by Heffter (1965) and the vertical mean velocity is assumed to be 0.01 m s- ‘. The results show that the upper limit of the time increment is 5.6 h for horizontal integration and ranges from 0.14 to 13.9 h for vertical integration under unstable to stable atmospheric conditions, respectively. These time increments are the averaging times for the observational data for a ‘real time’ #mp~son with the numerical prediction. However, other factors such as the temporal resolution of the available meteorological data also have to be considered. For example, if the NOAA wind data taken at every 12 h are used as input to the numerical model, the model is expected to resolve pollutant concentrations with periods of variation larger than 12 h. Consequently, 12-h or longer average values of pollutant concentration have to be addressed in the comparison of the observations and the predictions. 3. DESIGNOF AIRQUALITYSAPPING NEXWORKIS FOR SULFUR POLLUTION The contours of SO2 concentration to be used in the present discussion of locating sampling sites are shown in Fig. 7. The contours are computed by Sheih (1977)

Table 1. Time increment for the numerical integration

DirectiOnS

(m)

2 x 105

Horizontal Vertical

Typical values for the parameters u A% 4

stable unstable

5 x 10’ 5 x 16

(m s-l)

10 0.01 I

(m2 s-l)

Maximum time increment

for numericalintegration A%h

@I

10s

5.6

0.1 102

13.9 0.14

@+2/(2K,)

(h)_ 56 350 0.35

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C. M.

SHEIH.

G. D. Hess and B. B. HICKS

Fig. 7. Contours of sulfur-dioxide concentration (pg m- 3, at 2 m above the ground and locations of suitable air-quality sampling stations (A).

with the long-term statistical trajectory model for the month of April, 1972. Since the period of the simulation is not long enough to give statistically true average values for the contours, the network resulting from consideration of these contours should be regarded as an illustration of the technique and apphcable only to the period being considered. Contours of SOi- are also available from the model but the requirements for measuring these contours will not be as stringent as that of SO, because the spatial variability of SOi- is smaller. Therefore, only SO, will be considered in discussing the sampling network. Simulations of the short-term or hourly variations of the pollutant concentrations are not considered here because they can not be predicted from the available pollutant emission inventory which is given in terms of annual total values and the regional-scale meteorological variables given at 12-h intervals. Since the main anthropogenic source of sulfur in the atmosphere in the northeastern United States is believed to be from the coal-fired power plants, the emission of sulfur dioxide from the 53 major power plants in the area of interest of the MAP3S program is used in the simulation. An obvious consideration in the design of a sampling network is the need to arrange the sampling stations such that the observations will be able to reproduce as closely as possible the overall pattern of pollutant concentration. This requires (1) The number of stations should be sufficiently large to detect the general pattern. (2) The network should be capable of detecting the maximum pollutant concentration. (3) The network should be capable of giving the background pollutant concentration. (4) The separation between the sampling stations should be proportional to the distance between the successive contours of pollutant concentration in the neighborhood of the stations (i.e. station separation should be determined by the local horizontal gradient of pollutant concentration).

(5) The network should provide at least an array of stations in the direction along the general prevailing wind for assessing the effects of chemical transformation. It should be noted that measurements of SO: _ is also required to study the chemical transformation and that the stations should be kept away from local sources to ensure obtaining representative values for the regional-scale problem. (6) The network should have at least an array of stations in the direction perpendicular to the general mean wind for evaluating the effects of horizontal turbulent diffusion. In the area of the present interest, the general wind direction is WSW. In order to illustrate the use of the above requirements, the SO, concentration map in Fig. 7 is used as a basis for determining a sampling network. To determine the location of the sampling stations, a pair of orthogonal axes which are parallel and perpendicular to the mean wind direction, respectively, are drawn through both locations of maximum pollutant concentrations over the Indiana-Kentucky border and the Pittsburgh area. The sampling stations are then located at the selected intersections of these axes and the contours, where the selections are made with the intent of keeping as few stations as possible yet still being able to detect the main features of the pollution pattern from those stations. The stations are indicated by solid triangles in the figure. Additional stations are located at the areas of maximum pollutant concentrations and in central Kansas, a location remote from the polluted area suitable for measuring background pollutant concentrations. The required number of samples, sampling time intervals and total sampling time for each station are 200 samples, 22 h and 184 days as discussed earlier in Section 2(b).

4. CONCLUSION

network experiments can be Regional-scale classified as tracer experiments for studying the mechanisms of pollutant transport and transformation, or air quality measurements for evaluating the extent of air pollution. Tracer experiments can be designed using the requirements implied by the numerical models currently available or being developed. In this way, suitable observational data can be obtained for parameterizing the variables in the models and for examining their accuracy. For a short-term Gaussian plume model, mobile stations traversing two cross sections, separated by approximately 1000 km, are required to quantify the transformation of sulfur dioxide to sulfate particles. The sampling intervals are of the order of one hour for obtaining independent samples, and 200 samples are needed for COtI’VUting t’ average concentration to within 10% of the true value. The requirements on the number of samples are the same for all the models discussed. For the longterm statistical trajectory model, two arcs of fixed

1753

Design of network experiments

stations are recommended. In order to see 20% change in the sulfur dioxide budget, a separation of about 400 km between the two arcs is required. The separations between stations in the same cross sections of the long-term plume are 170 and 200 km for the upstream

and downstream

arcs, respectively.

For the

grid model, a box-budget experiment with the box dimensions (Ax, Ay, AZ) = (2OOkm, 2OOkm, 5OOm) and (200 km, 200 km, 20m) for regions above and below the constant flux layer, respectively, are recommended. The sampling intervals are 5.6 h for variables in the hor~ontal direction, and 0.35 h in unstable and 14 h in stable stratification for variables in the vertical direction. The selection of the sampling sites for air quality measurements for the region of the interest of MAP3S is based upon the concentration map produced by a numerical simulation. The results show that about 13 stations enable the general features of the pollutant concentration to be recovered.

Aekno~fe~~eme~s

- Thanks are due to M. L. Wesley and J. D. Shannon of Argonne National Laboratory and to M. C. MacCracken of Lawrence Livermore Laboratory for reviewing the manuscript and to J. M. Hales of Pacific Northwest Laboratories for encouraging this study of sampling network design.

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