- Email: [email protected]
Estimating vertical diffusion from routine meteorological tower measurements
Atmospheric Enuirunment Vol. 13. Pp. lSS9-lS64. 0 Pcrgsmon Press Ltd. 1979 Printed in Glut Britain.
CKW-6981/79/1101-IS59
So2.00~
ESTIMATING VERTICAL DIFFUSION FROM ROUTINE METEOROLOGICAL TOWER MEASUREMENTS ROLAND R. DRAXLER
Air Resources Laboratories, National Oceanic and Atmospheric Administration, Silver Spring, MD 20910, U.S.A. (First received 3 April 1979 and injvalform
15 May 1979)
Abstract - Data from an instrumented meteorological tower are used to calculate vertical dispersion coefficients and vertical diffusivities using surface layer concepts. The tower instrumentation is similar to that at many power plant sites and only a temperature gradient and wind speed are required for the calculations. The calculated vertical turbulence compares well with bivane data collected on the tower. Calculations of vertical dispersion also compare well with dispersion data collected at other sites.
1. INTRODUCTION
The purpose of this study is to determine if routine meteorological measurements made from a tower not equipped with high-resolution turbulence quality instrumentation can be used to make estimates of vertical dispersion using surface-layer concepts. Hourly values of wind speed and temperature from a meteorological tower located in Georgia near the Savannah River are used to calculate the bulk Richardson number from which Monin-Obukhov length and friction velocity are estimated following the method used by Golder (1972). From these parameters, vertical wind fluctuation and vertical diffusivity are calculated through semi-empirical functions consistent with surface-layer theory, the layer in which the fluxes of heat and momentum are assumed to be relatively constant with height. The hourly calculated values of vertical wind direction fluctuation (a+) are compared with measured bivane data from the Georgia tower. Estimates of nz, the standard deviation of the vertical concentration profile are made from the calculated a, values using the functions given by Draxler (1976). These calculated u, values are segregated by stability, averaged, and compared with u, data collected from experiments at Jiilich (Vogt and Geis, 1974), a site in Germany of similar roughness. Also, the calculated vertical diffusivities are averaged, and compared with average diffusivities obtained from pollutant Flux measurements made at a site in Pennsylvania (Shaffer, 1973). The calculated diffusivities are summarized as annual average vertical profiles of K, by stability category. Stability categories, computed from nomograms provided by Golder (1972) using on-site data, were compared with stability categories computed following the method of Turner (1964) using data from a nearby airport. 2. CALCULATION METHOD Most methods for estimating dispersion
either o,, the standard deviation of the vertical concentration profile, or K,, the vertical diffusivity. Recent investigations have determined a more precise relationship between the vertical wind fluctuation (u+) and corresponding u, values (see Draxler, 1976; Irwin, 1979). Vertical wind fluctuation measurements are not usually taken, except during special micrometeorological turbulence experiments. From these experiments, relationships between vertical wind fluctuation, vertical ditfusivity and more common tower meteorological observations have been derived within the surface layer. Panofsky (1973) presents the most recent overview of the relevant theory.
2.1 Vertical windJluctuotion The standard deviation of the vertical wind direction is approximated by Q* % a,/li,
(1)
where uw is the standard deviation of the vertical wind velocity and U is the mean horizontal wind speed during the period u, is computed. Since ii is measured, only u, need be determined. Panofsky et al. (1977) showed that during unstable conditions (Z/L < 0), (I, = 1.3u*(l-3Z/L)“3,
(2)
where u* is the surface friction velocity (a measure of mechanical turbulence), Z is the computation height, and L is the Monin-Obukhov length (a measure of stability). Panofsky (1973) showed that during neutral and stable conditions (Z/L 2 0), (I, = 1.3u*.
(3)
Pasquill(l974, p. 77) summarizes many different experiments and confirms Equation (3) during neutral conditions. Since Cis observed, only ut and L are required to calculate 01. 2.2 Vertical diffiusivily We will assume that the vertical diffusivity of a passive pollutant is similar to that of heat where K, = bZ#;‘,
(4)
where k is a constant equal to 0.35, and $r is the normalized temperature profile. Businger et al. (1971) suggest that when Z/L < 0, Qh = 0.74(1-92/L)-“*,
usually require 1559
(5)
1560
ROLAND
R.
and when Z/i. 5 0
&,,, the friction velocity is given by
i$h = 0.74 + 52/L.
2.3 Friction velocity and ~onin-Ob~kkov
length
The two required parameters, u* and L, can be determined from an estimate of the roughness length and a measurement of temperature gradient and wind speed on a tower following the procedure given by Golder (1972). The method wilf be outlined briefly here, but see Golder’s article for a more detailed discussion with all relevant references. First, the bulk Richardson number.
is computed from the tower observation. Here, @ is the acceleration of gravity, F is the ambient temperature (K) and A0 is the potential temperature gradient in “Km-i which can be approximated by AT+ S,,,where fi4,the dry adiabatic lapse rate, is about 1K per 100 m. The wind speed ii, and r, are determined at the computation height Z which is defined as the geometric height through which the temperature gradient is measured. _ The Richardson number is related to the observed bulk Richardson number [Equation (7)] through
L
cpln
-I
(fu
where 2, is the roughness length, Cp, is the dimensionless wind shear and &,, is the integral of d,,, from Z, to Z/L. Both #, and I&, will be defined later by an empirical approximation. Because #, and JI, are both functions of R,, Equation 181is iterated to solve for R, until the riaht side is within 10e4 ofS from Equation (7). computation gf R, with Equation (8) is preferable over computation from tower wind speed gradients due to the possible error in squaring the difference of two large numbers. The dimensionless wind shear, $,,, and its integral JI,,,used in Equation (8) for stable conditions (B 2 0)are those used by Golder (1972) where #, = (1 - 5Rf)-‘, and
(9) &II- -5R,(l - SR,)- ‘.
During unstable conditions (B c 0) we use
JI,=]n&pJo-
u2 = kti(ln Z/Z, - &_,)- ‘.
16)
The calculation of K, is similar to the vertical wind fluctuation calculation in that only uL and L need to be determined.
Cp, = (l-
DRAXLER
15R,)-‘“,
Ci[~-ll[c*+ll> In
Er+'lEr.-'1
+ 2(tan-‘{ - tan-‘C,) and
, (IO) 1 J
[ = (I - 15R,)“4, (11)
(, = (I - 1SRI&/Z)‘“,
which follows Nickerson and Smiley (1975) [a modification of Equation (10) for I&,,has been proposed by Benoit, 19773. With R, calculated from Equation (8) the MoninObukhov length t can be determined from the reiations Z/L = R,
(R, < 0).
(12)
i?/L = R,(l--5R,)-’
(R, z 0).
(13)
The calculation procedure can be simplified because Richardson number can be eliminated from Equations (8-l 1) and thereby L can be obtained directly from B. With
(14)
The friction velocity is independent of height in the surface layer hence Equations (1) and (4) describe a+ and X, as a function of height through Equations (2). (5) and (6). Surfacelayer theory is usually considered to apply only very near the surface. Golder’s (1972) analysis consisted of data from six different sites, four had upper measurement levels at or below 16 m. One site had data levels similar to the Georgia tower. At this site, one. much smoother than the Georgia location, the roughness length was found to increase when the heights of the anemometers were increased. Golder (1972) obtained the best results with an effective 2, of O&m. Hence the calculations for the Georgia site used the largest 2, provided for in Golder nomograms, 0.50 m. Panofsky (1973) suggested that surface layer concepts may be applicable to heights of as much as 150 m. Testing these concepts with data from routine meteorological tower m~urements could provide a basis for utilizing more current theory in dispersion estimates from meteorological data available to a broad segment of the power industry. 3.
METEOROLOGICAL
DATA
The meteorological data required for this analysis were obtained from a tower used by the Georgia Power Company to estimate the impact of a future power plant site. The tower is located approx 9 km north of Girard, Georgia and 2 km south of the Savannah River. This tower was selected because of its proximity to the Savannah River Plant (SRP) and the potential usefulness of any results to a dispersion experiment conducted at SRP (Telegadas er al., 1978). The terrain near the tower is fairly uniform and vegetation consists mostly of scrub pines lo-15 m in height. The area surrounding the tower has been cleared of vegetation and was part of the construction site for the data period used in this paper. The tower is similar to others required by the US. Nuclear Regulatory Commission. It is instrumented at three levels, 12,30 and 46 m for temperatures and at the lower and upper Jevets for horizontal winds. Dew point, solar radiation and rainfall are available on the lowest level. In addition, a bivane, not usually required, provided data for a limited period (April-December 1977) on the 30-m level. This provided an opportunity to compare calculated vertical turbulence values with actual observations. The met~roIogi~1 data for the period of bivane operation were recorded on magnetic tape. Calculations were made with the 30-12m temperature gradient, wind speed at 12 and 46 m and the ambient temperature at 12m, all averaged for f-h periods centered on each hour. Wind speeds required at heights between 12 and 46m were geometrically interpolated. Approximately 4800 h, equally divided between day and night were avaifable. The bivane data were recorded as the range of vertical wind direction observed during each 4-h period. The observed range was divided by six to approximate the actual Q+ for comparison with calculated values ofa,. This approximation has been tested for horizontal standard deviations by Markee (1963) but its use for a, is subject
Estimating vertical diffusion
1561
I 2
5 OBSERVED
U@
(VERTICAL
20
10 (deg)
RANGE)
Fig. 1. Calculated standard deviation of the vertical wind direction vs the vertical range (divided by six) of the 30-m level bivane.
to considerable uncertainty. However, if the distribution of wind directions within the observed range is normal, then 6 u+ should represent about 99% of the observations within the range. 4. RESULTS
Calculations as described in section 2 were performed each hour during the data period to determine e6 and K,. 4.1 Vertical wind jluctuation
When the 4800 calculated hourly values of a, were compared with the observed Us (vertical range of the bivane divided by 6) 82% of the points were within a factor of two and 32% were within 2004, however, underprediction occurred in 65% of the cases. Twenty percent of thecases (every 5th hour) are shown in Fig. 1 and the correlation coefficient is 0.46. As stated before, dividing the range by six may be a poor estimate of the actual standard deviation, and therefore, it is difficult to determine if the underprediction actually exists or to what magnitude. However, the results shown in Fig. 1 do at least suggest that some confidence can be placed in the calculations. The calculated u+ values can also be used to obtain the vertical dispersion coefficient u,. One method given by Draxler (1976), for elevated releases within the surface layer, 6, = u,X[ 1 + 0.90(t/500)0~s0] - 1,
(15)
when ZJL I 0 and 0, = UdX[l + 0.95(t/1tM)0.*‘]- 1,
when Z/L > 0 and where X is the downwind distance and t, the travel time (s) is given by X/U. The calculated u+ values and observed wind speeds were segregated by Pasquill-Turner stability category (Turner, 1964) from the calculated l/L and Z, through the conversion nomograms given by Golder (1972) and averaged for the entire data period. The average values of Us and Uare shown in Table 1. These values were used in Equations (15) and (16) to predict u, for the different stability categories and the results are shown in Fig. 2 as the solid lines. The dashed lines are the average vertical dispersion values Vogt and Geis (1974) determined for Jiilich, a location comparable to the Georgia site but with larger surface roughness. Except for the D stability curve, the curves are similar at distances of less than 1 km. The reason the Jiilich curves are higher at the further distances is uncertain. The difference in the D stability curve may be attributed to the larger roughness of the Jiilich site. Vogt and Geis found the vertical dispersion was always much greater during neutral stability at Jiilich than would be predicted assuming smooth terrain. These differences were less apparent during either stable or unstable conditions. The results from the vertical wind fluctuation calcuTable 1. Average values of calculated u, and observed I for the 30-m tower level Stability category %,e) i(m
(16)
s-‘)
ABCDEFG
23.2
12.7
8.8
6.6
6.0
4.5
2.1
2.1
2.9
3.6
3.6
3.2
2.5
1.7
1562
ROLAND
R.
5
DRAXLER
----
JiiLlCH
-
CALCULATED
t 2 t 1 100
_._I
I
1
I
I
200
500
1000
2000
DOWNWIND
DISTANCE
5000
(m)
Fig. 2. Calculated vertical dispersion coefficients at the Georgia tower location and vertical dispersion observed at Jiilich. Categories A and C were omitted to simplify the illustration;
however, they show
relationships similar to the other categories. suggest reasonable predictions of Q, that account for the roughness of the site can be obtained from a meteorological tower observation of only temperature gradient and wind speed.
lations
4.2 Vertical
d@ivity
Although the K-theory approach to vertical diffusion is most applicable for ground-level sources or elevated sources when the vertical extent of the plume 100
I
-
__
I
is much larger than the release height, many numerical dispersion models still utilize some form of a diffusivity profile. The results from the tower calculations can be used to obtain K, profiles in the surface layer directly or to develop climatological mean values. One of the assumptions to be tested is the suggestion that the diffusivity of heat is similar to that of a passive pollutant. Shaffer (1973) analyzed flux profiles of radon from hourly concentration measurements on a
III
SHAFFER
II
11 -
(1973)
”
CALCULATED
50
20
10
5
2
1
0.5 0
2
4
6
8
10 LOCAL
12
14
TIME
(hr)
16
18
20
22
24
Fig. 3. Time dependence of the annual average K, at 61 and 176 m observed from fluxes of radon (Shaffer, 1973) and from calculated values at the Georgia tower.
1563
Estimating vertical diffusion
results of Table 2, the annual average K, values were computed at several heights up to 2OOm and these profiles by stability category are shown in Fig. 4. As mentioned earlier, surface-layer concepts are not ap plicable above the surface layer, hence the profiles were not extended. Other researchers have found K, profiles to reach some peak value just above the surface layer (Pasquill, 1974, p. 345). During unstable conditions when K, increases rapidly with height, Panofsky (1975) suggests that above the surface layer and up to the mixing depth the exact numerical value of K, is unim~rtant since the pollutant con~ntrations become uniform with height. During stable conditions the K, profile above the surface layer may also be unimportant for ground sources, since little material should mix that far upward. The K, profiles suggest that a simple power law may be applied in the surface layer to represent the variation of K, with height with only at most a 50% variation from linear during the stable cases. When a straight line is passed through the approximate midrange-heights of the 2 and 1OOm K, values for each stability category, the coeficients a and b for
Table 2. Average values of the vertical diffusivity (m* s-‘) calculated at 100 m Stability
Annual
CilICgOry
average
A B c D E F G
161 101 67 I5 5.0 1.5 0.13
Spring* Summett 167 109 72 19 4.5 1.4 0.16
164 103 68 14 4.4 1.4 0.11
Fall:
Winters
140 81 60 I5 5.3 1.5 0.11
123 91 65 17 5.4 1.6 0.14
* Spring - April, May. t Summer - June, July, August. $ Fall - September, October, November. 5 Winter - December.
200-m tower near Philadelphia, Pennsylvania. From the time- and height-dependent flux values, he determined the diffusivity. He segregated his results by local time of day and month. His annual average values of K, as a function of time at 61 and 174 m are shown in Fig. 3 with the average K, values calculated from Equations (4-6). Generally, the agreement between a passive pollutant K, and the calcufated heat flux K, is excellent at both heights and therefore the surface-layer concepts used in the calculations may be applied to heights of at least 174 m. The differences in the early-morning values suggest a dependence on the thermal and roughness characteristics of the site. However, the differences are smaI1, a factor of two or less, when compared to the MO-fold diurnal range of Kz, When the calculated K, values are segregated by Pasquill-Turner Stability (Golder’s nomograms) and averaged (Table 2), they seem to be relatively independent of season. The standard deviation about the annual average is about 50% in each stability category. The seasonal values all fall within this range. The absence of seasonal dependence of K, in each stability category suggests that annual average values may be sufficient for use in diffusion models if the hourly stability values are available. To extend the
G 200
K,(m2 s-‘) = aZ(my
are given in Table 3 for each stability category. The roughness length (0.5 m) used in the calculations should be generally applicable over the coastal plain of the eastern U.S. 4.3 Stub~~itycategories
The Pasquill-Turner stability categories computed each hour following the the method ofTurner (1964) at the Augusta airport, about 20 km from the tower site, were compared to the hourly stability categories calculated at the tower with Golder’s (1972) nomogram. The analysis showed 65% more stabie (E/F/G) cases occurring at the tower than at the airport (61 vs 37% of 4800 h). Further, when stable conditions existed at the tower, the stability was most frequently neutral at the airport. During these times the wind speeds were 20-30% greater at the airport than on the
F
CBA
D
E
-
‘tit
1 0.01
I’* 0.1 VERTICAL
1’S
$‘* 1.0
MIXING
(171
(0 COEFFICIENT
100 (m2/sec)
Fig. 4. Annual average calculated vertical diffusivity profiles.
’
ROLAND R. DWAXLEH
I564
Table 3. Power-law coefficients for vertical diffusivity as a function of height between 2 and 100 m StabiliIy ctttegory u b
A
B
C
0
E
F
G
0.210 1.44
0.191 1.35
0.200
0.217 0.920
0.204 0.695
0.157 0.491
0.0422 0.244
1.26
10-m level of the tower. The stability classification method used at the airport calculates less stable categories with higher wind speeds. The different stability categories dete~in~ at the tower site may reflect real differences in thedispersion environment as
well as differences in the techniques. 5. CONCLUDING REMARKS An instrumented meteorological tower, typical of some used by the power industry in the United States, provided data to calculate vertical dispersion parameters from surface layer theory. When segregated by a Pasquill-Turner stability and averaged over a long period the vertical dispersion values showed consistence with dispersion datacollected at different sites. However, the hour-to-hour turbulence may be highly site dependent. That is, the degree of dispersion indicated by a Pasquill-Turner stability cagetory at an airport, where routine meteorological data are available, will most likely be different than what would be indicated by going through the calculations outlined in this paper for some power plant location a few kilometers away. The indicated differences are probably real considering the different micrometeorological climate of an airport. These results suggest two conclusions : (1) on-site meteorological data should be superior to off-site data for dispersion calculations, and (2) differences in meteorological data sites could lead to unrepresentative results when dispersion calculations are made with off-site data. Ack~wledgeme~s
- This work was supported by the Office of Health and Environmental Research of the Department of
Energy.
6.
REFERENCES
Benoit R. (1977) On the integral of the surface layer profilegradient functions. .I. appl. Mer. 16, 859-860. Businger J. A., Wyngaard J. C., Izumi Y. and Bradley E. F. (1971)Flux-profilereiationshipsin theatmosphericsurface iayer. J. atmos. Sci. tB, 181- 189. Draxler R. (1976) Determination of atmospheric diffusion parameters. Atmospheric Enoironment 10, 99-105. Golder D. (1972) Relationsamong stability parameters in the surface layer. Boundary Layer Met. 3,47-X Irwin J. S. (1979) Estimating plume dispersion - a recommended generalized scheme. Preprint volume of the Fourth Symp. on Turbulence. Dijiision and Air Fo~i~r~~ January 1979, pp. 62-69. American Meteorologi~l Society, Boston, MA. Markee E. H., Jr. (1963) On the relationship of range to standard deviation of wind fluctuations. Mon. Weath. Rea. 91, 83-87. Nickerson E. C. and Smiley V. E. (1975) Surface layer and energy budget parameterizations for mesoscale models. .I. appl. Met. 14, 297-300.
Panofsky H. A. (1975) A model for vertical diffusion coefficients on a growing urban boundary layer. Boundary Layer Met. 9,235-244.
Panofsky
H. A. (1973) Tower
blip
on ~~r~~~eoral~y,
micrometeorology,
In
(Edited by Haugen D.
A.), pp. I Sl- 176. American Meteorological Society, Boston, MA. Panofsky H. A., Tennekes H., Lenschow D. H. and Wyngaard J. C. (1977) The characteristics of turbulent velocity components in the surfaee layer under convective conditions. Boundary Layer Met. 11, 355-359. Pasquill F. (1974) Atmospheric Difusion, 2nd Ed. Halsted Press, New York. ShafferW. A. (1973) Atmospheric diffusion ofradon in a timeheight regime. Ph.D. Thesis, Drexel Univ., June, 109p., University MicrofiIms. Ann Arbor, MI. Telegadas K., Ferber G.. J., He5ter J L. and Draxler R. R. (1978) Caiculated and observed seasonal and annual Krypton-85 concentrations at 30-15Okm from a point source. Atmospheric Enuiranment 12, 1769- 1775. Turner D. B. (1964) A diffusion model for an urban area. J. appl. Met. 3, 83-91. Vogt K. J. and Geis H. (1974) Tracer experiments on the dispersion of plumes over terrain of major surface rougbness, J&l 131-ST. Central Division for Radiation Protection, Kernforschungsanlage, Jiilich GmbH, Jiilich, Federal Republic of Germany.
CKW-6981/79/1101-IS59
So2.00~
ESTIMATING VERTICAL DIFFUSION FROM ROUTINE METEOROLOGICAL TOWER MEASUREMENTS ROLAND R. DRAXLER
Air Resources Laboratories, National Oceanic and Atmospheric Administration, Silver Spring, MD 20910, U.S.A. (First received 3 April 1979 and injvalform
15 May 1979)
Abstract - Data from an instrumented meteorological tower are used to calculate vertical dispersion coefficients and vertical diffusivities using surface layer concepts. The tower instrumentation is similar to that at many power plant sites and only a temperature gradient and wind speed are required for the calculations. The calculated vertical turbulence compares well with bivane data collected on the tower. Calculations of vertical dispersion also compare well with dispersion data collected at other sites.
1. INTRODUCTION
The purpose of this study is to determine if routine meteorological measurements made from a tower not equipped with high-resolution turbulence quality instrumentation can be used to make estimates of vertical dispersion using surface-layer concepts. Hourly values of wind speed and temperature from a meteorological tower located in Georgia near the Savannah River are used to calculate the bulk Richardson number from which Monin-Obukhov length and friction velocity are estimated following the method used by Golder (1972). From these parameters, vertical wind fluctuation and vertical diffusivity are calculated through semi-empirical functions consistent with surface-layer theory, the layer in which the fluxes of heat and momentum are assumed to be relatively constant with height. The hourly calculated values of vertical wind direction fluctuation (a+) are compared with measured bivane data from the Georgia tower. Estimates of nz, the standard deviation of the vertical concentration profile are made from the calculated a, values using the functions given by Draxler (1976). These calculated u, values are segregated by stability, averaged, and compared with u, data collected from experiments at Jiilich (Vogt and Geis, 1974), a site in Germany of similar roughness. Also, the calculated vertical diffusivities are averaged, and compared with average diffusivities obtained from pollutant Flux measurements made at a site in Pennsylvania (Shaffer, 1973). The calculated diffusivities are summarized as annual average vertical profiles of K, by stability category. Stability categories, computed from nomograms provided by Golder (1972) using on-site data, were compared with stability categories computed following the method of Turner (1964) using data from a nearby airport. 2. CALCULATION METHOD Most methods for estimating dispersion
either o,, the standard deviation of the vertical concentration profile, or K,, the vertical diffusivity. Recent investigations have determined a more precise relationship between the vertical wind fluctuation (u+) and corresponding u, values (see Draxler, 1976; Irwin, 1979). Vertical wind fluctuation measurements are not usually taken, except during special micrometeorological turbulence experiments. From these experiments, relationships between vertical wind fluctuation, vertical ditfusivity and more common tower meteorological observations have been derived within the surface layer. Panofsky (1973) presents the most recent overview of the relevant theory.
2.1 Vertical windJluctuotion The standard deviation of the vertical wind direction is approximated by Q* % a,/li,
(1)
where uw is the standard deviation of the vertical wind velocity and U is the mean horizontal wind speed during the period u, is computed. Since ii is measured, only u, need be determined. Panofsky et al. (1977) showed that during unstable conditions (Z/L < 0), (I, = 1.3u*(l-3Z/L)“3,
(2)
where u* is the surface friction velocity (a measure of mechanical turbulence), Z is the computation height, and L is the Monin-Obukhov length (a measure of stability). Panofsky (1973) showed that during neutral and stable conditions (Z/L 2 0), (I, = 1.3u*.
(3)
Pasquill(l974, p. 77) summarizes many different experiments and confirms Equation (3) during neutral conditions. Since Cis observed, only ut and L are required to calculate 01. 2.2 Vertical diffiusivily We will assume that the vertical diffusivity of a passive pollutant is similar to that of heat where K, = bZ#;‘,
(4)
where k is a constant equal to 0.35, and $r is the normalized temperature profile. Businger et al. (1971) suggest that when Z/L < 0, Qh = 0.74(1-92/L)-“*,
usually require 1559
(5)
1560
ROLAND
R.
and when Z/i. 5 0
&,,, the friction velocity is given by
i$h = 0.74 + 52/L.
2.3 Friction velocity and ~onin-Ob~kkov
length
The two required parameters, u* and L, can be determined from an estimate of the roughness length and a measurement of temperature gradient and wind speed on a tower following the procedure given by Golder (1972). The method wilf be outlined briefly here, but see Golder’s article for a more detailed discussion with all relevant references. First, the bulk Richardson number.
is computed from the tower observation. Here, @ is the acceleration of gravity, F is the ambient temperature (K) and A0 is the potential temperature gradient in “Km-i which can be approximated by AT+ S,,,where fi4,the dry adiabatic lapse rate, is about 1K per 100 m. The wind speed ii, and r, are determined at the computation height Z which is defined as the geometric height through which the temperature gradient is measured. _ The Richardson number is related to the observed bulk Richardson number [Equation (7)] through
L
cpln
-I
(fu
where 2, is the roughness length, Cp, is the dimensionless wind shear and &,, is the integral of d,,, from Z, to Z/L. Both #, and I&, will be defined later by an empirical approximation. Because #, and JI, are both functions of R,, Equation 181is iterated to solve for R, until the riaht side is within 10e4 ofS from Equation (7). computation gf R, with Equation (8) is preferable over computation from tower wind speed gradients due to the possible error in squaring the difference of two large numbers. The dimensionless wind shear, $,,, and its integral JI,,,used in Equation (8) for stable conditions (B 2 0)are those used by Golder (1972) where #, = (1 - 5Rf)-‘, and
(9) &II- -5R,(l - SR,)- ‘.
During unstable conditions (B c 0) we use
JI,=]n&pJo-
u2 = kti(ln Z/Z, - &_,)- ‘.
16)
The calculation of K, is similar to the vertical wind fluctuation calculation in that only uL and L need to be determined.
Cp, = (l-
DRAXLER
15R,)-‘“,
Ci[~-ll[c*+ll> In
Er+'lEr.-'1
+ 2(tan-‘{ - tan-‘C,) and
, (IO) 1 J
[ = (I - 15R,)“4, (11)
(, = (I - 1SRI&/Z)‘“,
which follows Nickerson and Smiley (1975) [a modification of Equation (10) for I&,,has been proposed by Benoit, 19773. With R, calculated from Equation (8) the MoninObukhov length t can be determined from the reiations Z/L = R,
(R, < 0).
(12)
i?/L = R,(l--5R,)-’
(R, z 0).
(13)
The calculation procedure can be simplified because Richardson number can be eliminated from Equations (8-l 1) and thereby L can be obtained directly from B. With
(14)
The friction velocity is independent of height in the surface layer hence Equations (1) and (4) describe a+ and X, as a function of height through Equations (2). (5) and (6). Surfacelayer theory is usually considered to apply only very near the surface. Golder’s (1972) analysis consisted of data from six different sites, four had upper measurement levels at or below 16 m. One site had data levels similar to the Georgia tower. At this site, one. much smoother than the Georgia location, the roughness length was found to increase when the heights of the anemometers were increased. Golder (1972) obtained the best results with an effective 2, of O&m. Hence the calculations for the Georgia site used the largest 2, provided for in Golder nomograms, 0.50 m. Panofsky (1973) suggested that surface layer concepts may be applicable to heights of as much as 150 m. Testing these concepts with data from routine meteorological tower m~urements could provide a basis for utilizing more current theory in dispersion estimates from meteorological data available to a broad segment of the power industry. 3.
METEOROLOGICAL
DATA
The meteorological data required for this analysis were obtained from a tower used by the Georgia Power Company to estimate the impact of a future power plant site. The tower is located approx 9 km north of Girard, Georgia and 2 km south of the Savannah River. This tower was selected because of its proximity to the Savannah River Plant (SRP) and the potential usefulness of any results to a dispersion experiment conducted at SRP (Telegadas er al., 1978). The terrain near the tower is fairly uniform and vegetation consists mostly of scrub pines lo-15 m in height. The area surrounding the tower has been cleared of vegetation and was part of the construction site for the data period used in this paper. The tower is similar to others required by the US. Nuclear Regulatory Commission. It is instrumented at three levels, 12,30 and 46 m for temperatures and at the lower and upper Jevets for horizontal winds. Dew point, solar radiation and rainfall are available on the lowest level. In addition, a bivane, not usually required, provided data for a limited period (April-December 1977) on the 30-m level. This provided an opportunity to compare calculated vertical turbulence values with actual observations. The met~roIogi~1 data for the period of bivane operation were recorded on magnetic tape. Calculations were made with the 30-12m temperature gradient, wind speed at 12 and 46 m and the ambient temperature at 12m, all averaged for f-h periods centered on each hour. Wind speeds required at heights between 12 and 46m were geometrically interpolated. Approximately 4800 h, equally divided between day and night were avaifable. The bivane data were recorded as the range of vertical wind direction observed during each 4-h period. The observed range was divided by six to approximate the actual Q+ for comparison with calculated values ofa,. This approximation has been tested for horizontal standard deviations by Markee (1963) but its use for a, is subject
Estimating vertical diffusion
1561
I 2
5 OBSERVED
U@
(VERTICAL
20
10 (deg)
RANGE)
Fig. 1. Calculated standard deviation of the vertical wind direction vs the vertical range (divided by six) of the 30-m level bivane.
to considerable uncertainty. However, if the distribution of wind directions within the observed range is normal, then 6 u+ should represent about 99% of the observations within the range. 4. RESULTS
Calculations as described in section 2 were performed each hour during the data period to determine e6 and K,. 4.1 Vertical wind jluctuation
When the 4800 calculated hourly values of a, were compared with the observed Us (vertical range of the bivane divided by 6) 82% of the points were within a factor of two and 32% were within 2004, however, underprediction occurred in 65% of the cases. Twenty percent of thecases (every 5th hour) are shown in Fig. 1 and the correlation coefficient is 0.46. As stated before, dividing the range by six may be a poor estimate of the actual standard deviation, and therefore, it is difficult to determine if the underprediction actually exists or to what magnitude. However, the results shown in Fig. 1 do at least suggest that some confidence can be placed in the calculations. The calculated u+ values can also be used to obtain the vertical dispersion coefficient u,. One method given by Draxler (1976), for elevated releases within the surface layer, 6, = u,X[ 1 + 0.90(t/500)0~s0] - 1,
(15)
when ZJL I 0 and 0, = UdX[l + 0.95(t/1tM)0.*‘]- 1,
when Z/L > 0 and where X is the downwind distance and t, the travel time (s) is given by X/U. The calculated u+ values and observed wind speeds were segregated by Pasquill-Turner stability category (Turner, 1964) from the calculated l/L and Z, through the conversion nomograms given by Golder (1972) and averaged for the entire data period. The average values of Us and Uare shown in Table 1. These values were used in Equations (15) and (16) to predict u, for the different stability categories and the results are shown in Fig. 2 as the solid lines. The dashed lines are the average vertical dispersion values Vogt and Geis (1974) determined for Jiilich, a location comparable to the Georgia site but with larger surface roughness. Except for the D stability curve, the curves are similar at distances of less than 1 km. The reason the Jiilich curves are higher at the further distances is uncertain. The difference in the D stability curve may be attributed to the larger roughness of the Jiilich site. Vogt and Geis found the vertical dispersion was always much greater during neutral stability at Jiilich than would be predicted assuming smooth terrain. These differences were less apparent during either stable or unstable conditions. The results from the vertical wind fluctuation calcuTable 1. Average values of calculated u, and observed I for the 30-m tower level Stability category %,e) i(m
(16)
s-‘)
ABCDEFG
23.2
12.7
8.8
6.6
6.0
4.5
2.1
2.1
2.9
3.6
3.6
3.2
2.5
1.7
1562
ROLAND
R.
5
DRAXLER
----
JiiLlCH
-
CALCULATED
t 2 t 1 100
_._I
I
1
I
I
200
500
1000
2000
DOWNWIND
DISTANCE
5000
(m)
Fig. 2. Calculated vertical dispersion coefficients at the Georgia tower location and vertical dispersion observed at Jiilich. Categories A and C were omitted to simplify the illustration;
however, they show
relationships similar to the other categories. suggest reasonable predictions of Q, that account for the roughness of the site can be obtained from a meteorological tower observation of only temperature gradient and wind speed.
lations
4.2 Vertical
d@ivity
Although the K-theory approach to vertical diffusion is most applicable for ground-level sources or elevated sources when the vertical extent of the plume 100
I
-
__
I
is much larger than the release height, many numerical dispersion models still utilize some form of a diffusivity profile. The results from the tower calculations can be used to obtain K, profiles in the surface layer directly or to develop climatological mean values. One of the assumptions to be tested is the suggestion that the diffusivity of heat is similar to that of a passive pollutant. Shaffer (1973) analyzed flux profiles of radon from hourly concentration measurements on a
III
SHAFFER
II
11 -
(1973)
”
CALCULATED
50
20
10
5
2
1
0.5 0
2
4
6
8
10 LOCAL
12
14
TIME
(hr)
16
18
20
22
24
Fig. 3. Time dependence of the annual average K, at 61 and 176 m observed from fluxes of radon (Shaffer, 1973) and from calculated values at the Georgia tower.
1563
Estimating vertical diffusion
results of Table 2, the annual average K, values were computed at several heights up to 2OOm and these profiles by stability category are shown in Fig. 4. As mentioned earlier, surface-layer concepts are not ap plicable above the surface layer, hence the profiles were not extended. Other researchers have found K, profiles to reach some peak value just above the surface layer (Pasquill, 1974, p. 345). During unstable conditions when K, increases rapidly with height, Panofsky (1975) suggests that above the surface layer and up to the mixing depth the exact numerical value of K, is unim~rtant since the pollutant con~ntrations become uniform with height. During stable conditions the K, profile above the surface layer may also be unimportant for ground sources, since little material should mix that far upward. The K, profiles suggest that a simple power law may be applied in the surface layer to represent the variation of K, with height with only at most a 50% variation from linear during the stable cases. When a straight line is passed through the approximate midrange-heights of the 2 and 1OOm K, values for each stability category, the coeficients a and b for
Table 2. Average values of the vertical diffusivity (m* s-‘) calculated at 100 m Stability
Annual
CilICgOry
average
A B c D E F G
161 101 67 I5 5.0 1.5 0.13
Spring* Summett 167 109 72 19 4.5 1.4 0.16
164 103 68 14 4.4 1.4 0.11
Fall:
Winters
140 81 60 I5 5.3 1.5 0.11
123 91 65 17 5.4 1.6 0.14
* Spring - April, May. t Summer - June, July, August. $ Fall - September, October, November. 5 Winter - December.
200-m tower near Philadelphia, Pennsylvania. From the time- and height-dependent flux values, he determined the diffusivity. He segregated his results by local time of day and month. His annual average values of K, as a function of time at 61 and 174 m are shown in Fig. 3 with the average K, values calculated from Equations (4-6). Generally, the agreement between a passive pollutant K, and the calcufated heat flux K, is excellent at both heights and therefore the surface-layer concepts used in the calculations may be applied to heights of at least 174 m. The differences in the early-morning values suggest a dependence on the thermal and roughness characteristics of the site. However, the differences are smaI1, a factor of two or less, when compared to the MO-fold diurnal range of Kz, When the calculated K, values are segregated by Pasquill-Turner Stability (Golder’s nomograms) and averaged (Table 2), they seem to be relatively independent of season. The standard deviation about the annual average is about 50% in each stability category. The seasonal values all fall within this range. The absence of seasonal dependence of K, in each stability category suggests that annual average values may be sufficient for use in diffusion models if the hourly stability values are available. To extend the
G 200
K,(m2 s-‘) = aZ(my
are given in Table 3 for each stability category. The roughness length (0.5 m) used in the calculations should be generally applicable over the coastal plain of the eastern U.S. 4.3 Stub~~itycategories
The Pasquill-Turner stability categories computed each hour following the the method ofTurner (1964) at the Augusta airport, about 20 km from the tower site, were compared to the hourly stability categories calculated at the tower with Golder’s (1972) nomogram. The analysis showed 65% more stabie (E/F/G) cases occurring at the tower than at the airport (61 vs 37% of 4800 h). Further, when stable conditions existed at the tower, the stability was most frequently neutral at the airport. During these times the wind speeds were 20-30% greater at the airport than on the
F
CBA
D
E
-
‘tit
1 0.01
I’* 0.1 VERTICAL
1’S
$‘* 1.0
MIXING
(171
(0 COEFFICIENT
100 (m2/sec)
Fig. 4. Annual average calculated vertical diffusivity profiles.
’
ROLAND R. DWAXLEH
I564
Table 3. Power-law coefficients for vertical diffusivity as a function of height between 2 and 100 m StabiliIy ctttegory u b
A
B
C
0
E
F
G
0.210 1.44
0.191 1.35
0.200
0.217 0.920
0.204 0.695
0.157 0.491
0.0422 0.244
1.26
10-m level of the tower. The stability classification method used at the airport calculates less stable categories with higher wind speeds. The different stability categories dete~in~ at the tower site may reflect real differences in thedispersion environment as
well as differences in the techniques. 5. CONCLUDING REMARKS An instrumented meteorological tower, typical of some used by the power industry in the United States, provided data to calculate vertical dispersion parameters from surface layer theory. When segregated by a Pasquill-Turner stability and averaged over a long period the vertical dispersion values showed consistence with dispersion datacollected at different sites. However, the hour-to-hour turbulence may be highly site dependent. That is, the degree of dispersion indicated by a Pasquill-Turner stability cagetory at an airport, where routine meteorological data are available, will most likely be different than what would be indicated by going through the calculations outlined in this paper for some power plant location a few kilometers away. The indicated differences are probably real considering the different micrometeorological climate of an airport. These results suggest two conclusions : (1) on-site meteorological data should be superior to off-site data for dispersion calculations, and (2) differences in meteorological data sites could lead to unrepresentative results when dispersion calculations are made with off-site data. Ack~wledgeme~s
- This work was supported by the Office of Health and Environmental Research of the Department of
Energy.
6.
REFERENCES
Benoit R. (1977) On the integral of the surface layer profilegradient functions. .I. appl. Mer. 16, 859-860. Businger J. A., Wyngaard J. C., Izumi Y. and Bradley E. F. (1971)Flux-profilereiationshipsin theatmosphericsurface iayer. J. atmos. Sci. tB, 181- 189. Draxler R. (1976) Determination of atmospheric diffusion parameters. Atmospheric Enoironment 10, 99-105. Golder D. (1972) Relationsamong stability parameters in the surface layer. Boundary Layer Met. 3,47-X Irwin J. S. (1979) Estimating plume dispersion - a recommended generalized scheme. Preprint volume of the Fourth Symp. on Turbulence. Dijiision and Air Fo~i~r~~ January 1979, pp. 62-69. American Meteorologi~l Society, Boston, MA. Markee E. H., Jr. (1963) On the relationship of range to standard deviation of wind fluctuations. Mon. Weath. Rea. 91, 83-87. Nickerson E. C. and Smiley V. E. (1975) Surface layer and energy budget parameterizations for mesoscale models. .I. appl. Met. 14, 297-300.
Panofsky H. A. (1975) A model for vertical diffusion coefficients on a growing urban boundary layer. Boundary Layer Met. 9,235-244.
Panofsky
H. A. (1973) Tower
blip
on ~~r~~~eoral~y,
micrometeorology,
In
(Edited by Haugen D.
A.), pp. I Sl- 176. American Meteorological Society, Boston, MA. Panofsky H. A., Tennekes H., Lenschow D. H. and Wyngaard J. C. (1977) The characteristics of turbulent velocity components in the surfaee layer under convective conditions. Boundary Layer Met. 11, 355-359. Pasquill F. (1974) Atmospheric Difusion, 2nd Ed. Halsted Press, New York. ShafferW. A. (1973) Atmospheric diffusion ofradon in a timeheight regime. Ph.D. Thesis, Drexel Univ., June, 109p., University MicrofiIms. Ann Arbor, MI. Telegadas K., Ferber G.. J., He5ter J L. and Draxler R. R. (1978) Caiculated and observed seasonal and annual Krypton-85 concentrations at 30-15Okm from a point source. Atmospheric Enuiranment 12, 1769- 1775. Turner D. B. (1964) A diffusion model for an urban area. J. appl. Met. 3, 83-91. Vogt K. J. and Geis H. (1974) Tracer experiments on the dispersion of plumes over terrain of major surface rougbness, J&l 131-ST. Central Division for Radiation Protection, Kernforschungsanlage, Jiilich GmbH, Jiilich, Federal Republic of Germany.