A Lidar study of the limits to buoyant plume rise in a well-mixed boundary layer

Pergamon

Atmospheric EnvironmentVol. 29, No. 17, pp. 2275-2288, 1995 Copyright © !995 El~vier Science Ltd Printed in Great Britain. All fights r ~ r v e d 1352-2310/95 $9.50 + 0.00

1352-2310(95) 00092-5

A LIDAR STUDY OF THE LIMITS TO BUOYANT PLUME RISE IN A WELL-MIXED BOUNDARY LAYER M. B E N N E T T Environraental Technology Centre, Department of Chemical Engineering, UMIST, P.O. Box 88, Manchester M60 1QD, U.K. (First received 17 June 1994 and in final form 16 February 1995)

Abstract--A series of 69 x 15 rain trajectories of the plume from a direct-cooled, 360 MW(e) power station have been measured with a rapid-scanning Lidar to downwind distances of 3 km; the measurements were made in August and September 1993 in eastern England. The results indicate that, in sunny conditions, buoyant rise is halted when plume dements start to impinge on the top of the boundary layer. By contrast, the Briggs "break-up" model, according to which plume rise ceases when the plume is broken up by ambient turbulence, tidied to predict the distribution of observed final plume heights. It is concluded that in U.K. conditions buoyant rise is likely to be limited by the depth of the boundary layer. Several methods of estimating the depth of the boundary layer from Lidar measurements are discussed. The initial plume rise at Staythorpe was similar to the plume rise at other inland power stations. Key word imlex: Lidar, plume rise, remote sensing, boundary-layer depth, plume height.

1. INTRODUCTION When assessing the near-field environmental impact of a source of pollutant to the atmosphere, it is usually ground-level concentrations which are of most interest. These depend not merely on the magnitude of the source, on the wind speed and on the rapidity of vertical and lateral dilution, but also, crucially, on the effective source height. Simple dimensional considerations show that, when the instantaneous lateral and vertical dispersion rates are proportional to each other, the maximum ground-level concentration is proportional to the inverse square of the plume height, h. For time-averaged concentrations and moderate travel times, however, the lateral spread is proportional to the travel time, t, while the vertical dispersion may be modelled by Fickian diffusion to give a spread proportional to x/~. In this case the maximum ground-level concentration is proportional to the inverse cube of the plume height. Whatever the model chosen, ground-level concentrations are very sensitively dependent on the effective source height. In general, this is not the same as the height of the stack, hs. If the flue is well designed, aerodynamic effects around the source (stack-tip downwash, building wake entrainment, etc.) should be small. A substantial emission, however, will in general contain significant momentum and buoyancy: these ensure that the plume rises away from the emission point even after it has been bent over by the wind. For most emissions, it is essential that this buoyant

rise be taken into account when estimating the ground-level impact of the source. The standard theory of the buoyant rise of a bentover plume (Briggs, 1984; Bennett et al., 1992) predicts that in a neutral atmosphere the rise of the plume and its instantaneous spread should be proportional to Br(Fb, x, u) =

1 + t)

x2/3/u

(1)

where Fb is the buoyancy flux, u the wind speed at plume height and x the distance downwind from the source. The cross-over timescale, z, is twice the ratio of momentum flux to buoyancy flux: for t < ~, the rise is dominated by the initial momentum of the emission while for t > z the rise is dominated by the buoyancy of the emission. The rise of the plume centreline relative to the surrounding air is given by h(x) - hs = C1 Br(Fb, x, u)

(2)

while the instantaneous, shear-generated, lateral and vertical spreads are given by ay(x, 0 ) = f l y Br(Fb, x, u)

(3)

trz(x, 0) = r/z Br(Fb, x, u).

(4)

and

The second arguments of zero in the expressions for try and az denote that they are intended to apply for zero averaging time. Best estimates for the coefficients

2275

2276

M. BENNETT

little more than a best guess, albeit an extremely wellinformed one. Various other less physically well-based criteria have been used to terminate the rise in an unstratified boundary tayer. Moore and Lee (1982), for example, terminated the rise at a travel distance of 2 km, this being further than the then existing measurements of plume rise. One criterion which is not valid is to terminate the rise when the velocity of plume rise falls below the mean velocities of ambient turbulence. As stressed by Briggs, it is the lengthscale which is critical: if the scale of the thermals is much larger than that of the plume, the plume will continue to rise relative to the surrounding updrafts or downdrafts. In this case the plume may loop strongly, but it will still rise in the mean. In practice, of course, neutral stratification does not extend upwards indefinitely. A strongly buoyant plume in a weakly turbulent boundary layer should rise to the top of the layer, where it may or may not be trapped by a capping inversion. Studies of such situations have been made in stratified water tanks (e.g. Manins, 1979). In practical applications, however, it is not clear whether the plume may have broken up before it reaches the capping inversion. In summary, ground-level concentrations are extremely sensitive to buoyant plume rise, but the physical mechanisms limiting this rise are unclear. To clarify these mechanisms, we therefore undertook a measurement campaign with the UMIST Rapidscanning Lidar (Bennett et al., 1992) at a mediumsized power station. Our intention was to identify limits to the plume rise predicted by equations (1) and (2) and to put these limits into a theoretical context. The power station chosen for the study was Staythorpe near Newark-on-Trent, Notts (Fig. 1). By modern standards this was rather a small, coalburning, power station with a capacity less than one-tenth that of Drax, where we had unde~aken our most extensive previous studies (Bennett et al., 1992). This smaller source size should have allowed the plume to reach its limiting rise within the measurement range of the Lidar. The power station is on the left bank of the Trent, gHo which is 100 m wide at this point, and was directH . ----- (5) paCpTa cooled. Although some hills rise to a height of 56 m AOD, 3 km to the NW of the station, all our measurewhere Ho is the surface sensible heat flux and the ments were taken when the plume was being carried other symbols have their usual meanings. Briggs' best over the plain of the Trent at an elevation of between estimates of the various constants of proportionality 11 and 15 m AOD. The base of the stack is at 13 m suggested that the rise at break-up should be approx- AOD. Topographic effects should therefore be negliimately gible. The countryside around the plant is mostly rural, with large fields divided by hedges and occa~- 3 (Fb'~3/SH - 2/5 sional woods and villages. The built-up area of Zb It~'-~U) , • (6) Newark commences 2.5 km to the W of the site. A further advantage of Staythorpe was its relative This formula is commonly used by atmospheric dis- proximity to the Belmont TV mast. This has a height persion modellers for the final rise in a convective of 388 m and is located on the top of the Lincolnshire boundary layer. In applying such models, it should Wolds at a height of 125 m AOD, 55 km to the NE of be remembered that the coefficient in equation (6) is Staythorpe. We thus had access to wind and temper-

C1, rb and r/~ were sought by Bennett et al. (1992) and it was recommended that C1 = 1.35 for direct-cooled, coastal power stations (Fawley, Littlebrook), while C1 = 1.64 for indirect-cooled, inland power stations (Drax, Didcot): it was not clear whether it was the presence of cooling towers or of a coast which gave rise to this difference. The plume spread parameters were ~b = 0.51 and r/z = 0.43 for either type of station. The difficulty in applying equations (1) and (2) when estimating a maximum ground-level concentration is that these equations predict that in neutral stratification the plume rises indefinitely. Fickian diffusion (or random walk) arguments require that for travel times greater than TL, the Lagrangian integral timescale, the vertical plume spread should be proportional to x/~, while equations (1) and (2) predict that the rise should be proportional to t z/3. For a sufficient stack height, ground-level concentrations should therefore be zero at all distances! For travel times less than TL, the plume spread is proportional to the travel time. In this case, the time-averaged plume does reach the ground at some travel distance and Briggs (1984), having defined the final effective plume height as the mean plume centreline height at this distance, was able to derive a formula for this height. A problem with this "touch-down" model is that it is only valid for small travel times. Hanna (1981) measured TL in the convective boundary layer and found values of typically only 80 s. This would imply that the touch-down model is strictly applicable only to plumes which might disperse to the ground within a few hundred metres, i.e. relatively small sources. Briggs also suggested a plume "break-up" model for terminating the rise within a convective boundary layer. In this model, the plume rises, its diameter grows and its internal velocities decay until these are comparable with the scales of length and velocity of the ambient turbulence. Once this point is reached, the plume breaks up rapidly. Within the inertial subrange, the turbulent energy at a given lengthscale is determined by the turbulence dissipation rate, which is in turn proportional to the dimensionless buoyancy flUX,

Lidar study of the limits to buoyant plume rise

/ \

2277

5 0 km

N

Ft. T r e n t

× Belmont

Staythorpe

Fig. 1. Map of locations mentioned in text.

ature profiles up to a substantial fraction of the b o u n d a r y - l a y e r depth, t h o u g h care must be t a k e n in their i n t e r p r e t a t i o n since the site is subject to coastal influences (Bennett, 1992). T h e m e a s u r e m e n t s were m a d e between July a n d S e p t e m b e r 1993. S t a y t h o r p e was c o n s t r a i n e d to be o n load for m o s t of this period because of limitations to the local 400 k V grid. The power station was closed in M a r c h 1994 after a new switching station h a d been commissioned.

2. EXPERIMENTAL ARRANGEMENTS UMIST's Rapid-scanning Lidar has already been described in Bennett et al. (1992). The Lidar is mobile, being mounted in a 6 T commercial vehicle, and is able to obtain essentially instantaneous cross-sections of backscatter in the atmosphere with a range resolution of 2.5 or 5 m. Repeat cross-sections may be obtained every 4 s. The Lidar operates at a single wavelength, 532 nm, and so is unable to make any estimate of the sizes of particle producing the scattering. In our earlier studies of buoyant plume rise, we obtained lateral cross-sections of the plume at various distances downwind by parking the Lidar ~ 1 km from the stack and scanning the laser beam laterally through the plume in turn at 2 or 3 distances downwind. Over the course of 30 rain, 400 scans could then be obtained. This was a robust procedure for capturing the plume at travel distances of up to 1.5 kin.

For the purposes of this survey, however, we wished to be able to capture the plume after up to 3 km travel. If we had simply increased the distance of the Lidar from the stack to 2 km and attempted to obtain lateral cross-sections, there would have been a considerable risk that modest changes in wind direction could have taken the plume out of the measurement window of the Lidar: there would then have been a considerable delay ( > 1½h) while the Lidar was moved to a new site and set up again. For the purposes of this survey, therefore, we adopted the procedure of parking the Lidar as close to the stack as possible and attempting to scan downwind in a vertical plane through the plume. Again, the plume would be lost if the wind changed direction in the course of a series of scans, but in this case a simple software command could redirect the Lidar to a new direction for the next series. The plume at Staythorpe was not normally visible downwind against a clear sky (the electrostatic precipitators had been somewhat overspecified): we therefore had to seek the plume with the Lidar. Our procedure was to run a series of trial scans at 5° intervals until the plume could be identified on an oscilloscope trace. A series of live scans in the optimal direction would then be recorded for 15 rain; this could amount to up to 240 scans. At the end of the series, the computer would take 10 rain to download the data to file. The search for an optimal downwind direction could then recommence. Obviously, searching for an invisible plume in light and variable winds could be a particularly frustrating task but, ultimately, 78 such series were obtained (Table 1). The backscatter signal is measured by two photomultiplier tubes in the Lidar and these may be set to different sensitivities to log over different range windows. For the purposes of this survey, these windows were normally set to

M. BENNETT

2278

Table 1. Summary of 15 min Lidar runs containing usable measurements of plume height. There were 78 runs made in all No. of cloud-free runs

Range of Z i (m)

090893 100893 120893 130893 160893 170893 180893 190893 140993 150993 230993 240993

0 3 3 9 5 3 9 11 0 0 7 3

-1235- > 1270 535-620 1160- > 1270 525- > 1270 1235- > 1270 650-1195 1015-1275 --675-880 590-750

Total

53

--

Date

No. of cloudy runs

Range of Zo (m)

Range of wind speed (m s - l )

2 6 0 0 1 1 0 0 1 4 1 0

760-900 780-1220 --1245 1300 --325 250-650 750 --

6.3-9.2 6.6-13.1 5.8-7.6 2.9-5.2 5.4-8.9 1.7-6.8 1.5-5.5 4.8-8.2 9.8 6.6-9.8 1.3--4.2 3.2-3.6

16

--

--

Note: "Cloud-free" denotes cloud-base > 1300 m.

Table 2. Source characteristics of Staythorpe power station 360 121.9 (i.e. 400') 6.2 (i.e. 20'3")

Nominal capacity (MWe) Stack height (m) Stack ID at exit (m) (single flue at exit) Exit velocity (m s- 1) Exit temperature (°C) Excess 0 2 at exit (%) Fb/QM(m4 s - 3 M W - 1 (F b =

Z/Fb (s" m - ' )

ranges of 500-1720 and 1250-2470 m, gwing some overlap between the two transducers and allowing measurement of the plume out to a travel distance of about 2.5 kin. The range resolution was set at 5 m. For some of the measurements in September 1993, the maximum range was increased to 3 kin. Each scan comprised 60 shots between elevations of 1.5 and 31 ° (ground clutter permitting). The vertical resolution thus varied between 4 and 22 m. A selection of meteorological measurements is also made at the Lidar, namely 10 m wind speed and direction, temperature and humidity and surface insolation. These are logged every 10 s. In this application, the wind measurements were not usually of much value because of obstruction by the boiler house. As discussed below, the Lidar measurements themselves could be used to estimate boundary-layer depth and wind speed at plume height. Source data (Table 2) were provided by the power station staff. Fuel calorific values and mean thermal efficiency were provided on a weekly basis and were used to calculate the range of FJQu ratios quoted in the table. Electrical load fisures, Qu, in MW were provided on a x2h basis and were matched with the Lidar sampling periods to provide an estimate of Fb for each period. Since the power station had a single flue, the exit velocity depended upon the load; the ratio z/Fb, however, should remain approximately constant and is quoted in the table. (The momentum component of the rise is insignificant but has been includedfor completeness.) The buoyancy flux varied between 599 and 1699 m4s -3 during the course of the experiments.

18.1 (at full load) 135-140 7 4.64-4.77 1700 m4s -3 on full load) 0.007413 (z = 12.6 s on full load)

3. ESTIMATION OF PLUME PARAMETERS AND WIND SPEED

Typical p l u m e cross-sections are s h o w n in Figs 2 a n d 3. These display b a c k s c a t t e r as a function of height a n d range from the Lidar. T h e legend along the t o p of the g r a p h denotes the b a c k s c a t t e r intensity in digitizer bits. This has been corrected for the 1/r 2 signal variation, using a n o m i n a l range of 1000 m, a n d also to a n o m i n a l m i n i m u m laser energy. N o allowance has been m a d e for changes in the optical gain of the system (e.g. m a n u a l v a r i a t i o n of a p e r t u r e sizes). A m e a n b a c k s e a t t e r of 1 unit at 2400 m (Fig. 2a) thus corresponds to a measured signal of (2-4)-2 bits o n the digitizer, amplified by h o w e v e r m u c h the laser energy o n each shot exceeded its n o m i n a l m i n i m u m . The absolute signal zero is a p p r o x i m a t e l y correct, being the m e a n sky-light intensity seen b y the p h o t o m u l t i plier tubes immediately before each shot. It is clear, however, t h a t further c a l i b r a t i o n would be necessary to interpret the m e a s u r e d b a c k s e a t t e r intensities as concentrations. T h e p l u m e in Fig. 2a was m e a s u r e d in the early a f t e r n o o n with active c o n v e c t i o n a n d a deep b o u n d -

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Fi s. 2. (a) Sinsle Lidar scan of the Staythorl~ plume in convective conditions. Date: 18/8/93; ~me 14:30:24 (BST); scan direction: 42.0 °. Co) 15 rain average (i.e. 2.50 scans) of the plume shown in Fig. 2& The streaks ar~c :from the shadows of power lines. Source and metcorolo~cal parameters over this period were: buoyancy flux, 1026 m ' s - 3 ; boundary layer depth, 1120 m; wind speed, 5.5 m s - 1; insolation, 425 W m - 2

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Lidar study of the limits to buoyant plume rise

2281

tance, x, were calculated by constructing the cumulative backscatter profile over a given height range (say, 50-800 m) which was presumed to include the plume but not ground clutter (e.g. power lines) or low cloud. The instantaneous plume height, h(x), was then taken as the median of the cumulative backscatter, while the vertical plume standard deviation, ¢,(x, 0) was taken as half the distance between the 15.87 and 84.13 percentiles. This gives a robust estimate of the two parameters, not unduly influenced by noisy outliers. With a small amount of geometry, appropriate Lidar ranges could be calculated for downwind distances in increments of 250-500 m. For each scan, rangecorrected plume backscatter, plume height and instantaneous vertical plume spread were all calculated at these increments of x. From the whole 15 min series, backscatter-weighted means and variances of these parameters were then calculated. It is these time-mean trajectories of plume height which should demonstrate the buoyant plume rise. Time-mean backscatter cross-sections of the form of Figs 2b and 3b were plotted for all the 15 min runs. Plume parameters at a given distance were rejected if the plume was visibly clipped at the highest angle of elevation: this was never a problem at the greatest range since the scans here extended up to 1270 ml On the basis of the plotted backscatter cross-section, a complete run on 17/8/93 was also rejected since the cross-section did not appear to be that of a single plume. Our previous work with lateral plume cross-sections (Bennett et al., 1992) showed that it is possible to estimate the mean wind speed at plume height by applying a lag correlation technique to time series of plume height or lateral plume displacement at two (a) The boundary layer is normally deeper than different distances downwind; comparisons with mast 400 m; the ambient aerosol density should therefore measurements (Sutton and Bennett, 1994) showed that the wind speed could be estimated to an accuracy be uniform up to this height. (b) The algorithm accounts for the decay in back- of a few percent using this technique. Although not as scatter intensity with distance arising from the total reliable, it is possible to apply the same technique to the longitudinal profiles obtained in the present study, scattering loss from the beam. (c) The instantaneous plume elements would only using lag correlation between time series of plume rarely occupy more: than half the atmosphere up to height or of total backscatter at 500 m increments this height (cf. Figs 2a and 3a). It would not be so easy downwind. Comparing Lidar wind speeds with hourto distinguish between plume and ambient for a time- ly wind speeds measured at 388 m at Belmont gave a correlation coefficient of r = 0.8, with a tendency for averaged profile. the wind speed at Belmont to be greater by ~ 1 m s- 1. Clearly, the algorithm will break down if the plume The main problem with the technique in the present escapes from the boundary layer and rises into a layer application is that the plane of the Lidar scan tends to of different aerosol density. We do not believe that be imperfectly aligned with the wind direction. Puffs this happened in the course of this campaign. which are detected in the Lidar plane at one distance If there is low cloud, a different problem arises, for will not therefore necessarily be recaptured 500 m there may be condensation in the plume. It is then further downwind. The criterion for the successful impossible to distinguish between backscatter from identification of a correlation was therefore relaxed aerosol and that from condensed water. For this rea- from a peak correlation coefficient of r = 0.3 to son, cloud-free and cloudy runs have been distin- r = 0.2. If analysis using 500 m increments failed to guished in Table 1. find a correlation, the analysis was repeated at 250 m Having subtracted the ambient aerosol and ob- increments. Even with the smaller increment, it was tained instantaneous cross-sections of the plume not possible to estimate the wind speed on all occaalone, plume parameters at a given downwind dis- sions: of the runs listed in Table 1, the procedure failed

ary layer. Its looping structure may clearly be seen. Conversely, by the early evening, active turbulence had ceased and the much more coherent plume of Fig. 3a can be seen. 'The sequences of images including Figs 2a and 3a can be stored in PCX format and recalled in rapid succession to give an impression of the plume advecting across the screen at about 10 x real time. As expected, the loops are seen to move downwind as they gradually break up. When low cloud is present, features like wind shear may also be distinguished. The time-averaged backscatter cross-sections over the full series of which Figs 2a and 3a are members are shown in Figs 2b and 3b. It may be seen that the time-averaged profiles are starting to approximate to a Gaussian shape, especially in the slightly stable case of Fig. 3b. The blank streaks across the time-averaged cross-sections are the shadows of power lines; these obscured the view :from the only usable site for SW winds. We do not believe that they significantly affected estimates of mean plume height. Before backscatter cross-sections of the type shown in Figs 2 and 3 can be used to calculate parameters of the dispersing plume, it is necessary to subtract an offset corresponding to the backscatter at a given distance arising from the ambient aerosol. For the purposes of this study, we define the background at a given range on a given scan as the median of the backscatter intensities observed by shots up to a height of 400 m. This background level is then smoothed with a running average over seven range bins before being subtracted from the raw backscatter signal. This algorithm gives a robust distinction between plume and ambient because:

2282

M. BENNETT Plume rise at Staythorpe, 1993 600Z ee •

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Fig. 4. Trajectories of plume rise measured at Staythorpe in cloud-free conditions plotted against the buoyant plume rise parameter, Br(Fb, x, u). The dashed line shows the predicted rise for C1 = 1.64.

for one cloud-free run on 10/8/93 and for four cloudfree runs on 13/8/93. Given the wind speed and the emission parameters, the measured plume trajectories (on cloud-free runs) could be compared with the predictions of equations (1) and (2), This is done in Fig. 4. It may be seen that, given the uncertainties associated with longitudinal profiles, an initially acceptable agreement between theory and measurement breaks down for Br > 300m. Our previous studies only measured plume rise for Br less than this value. As may be seen from the figure, a range 3 times as great has now been sampled and limits to plume rise have apparently been observed. In the earlier studies we had used model aircraft to measure temperature profiles up to 500 m. For inland sites by day in summer, these usually showed a neutral stratification; we do not believe the initial rise at Staythorpe to have been significantly affected by stability. The mean observed value of C1 for Br < 300 m in Fig. 4 is 1.70 _ 0.10 (n = 121, 95% confidence limits). This strongly suggests that the plume from Staythorpe behaves in the same way as those from the indirect-cooled, inland power stations of our earlier studies. By implication, it was the presence of a coastline which led to a decreased value of C1 at Fawley and Littlebrook. In our subsequent analysis, we shall assume that the "inland" value of Ct = 1.64 is appropriate at Staythorpe: the predicted rise for this value of C1 has been marked with a dashed line in Fig. 4.

4. ESTIMATION OF BOUNDARY-LAYER DEPTH

As discussed in the introduction, the capping inversion atthe top of the boundary layer may on occasion limit the final rise of the plume. We suspected that this may have occurred for some of the trajectories with very large Br shown in Fig. 4. We were therefore anxious to obtain a realistic estimate of the boundary-layer depth to associate with each plume trajectory: we were well placed to do this, having a Lidar at our disposal. The use of Lidar to estimate boundary-layer depths is not original (cf. e.g. Giebel, 1981) and is straightforward so long as the aerosol content of the boundary layer differs substantially from that of the atmosphere above. The point may be illustrated in Figs 5 and 6. These graphs show the 15 rain backscatter intensities observed at the highest elevation of each scan plotted against range from the Lidar. Each range bin thus corresponds to an increment in height of 5 x sin(31.5 °) = 2.6m. The backscatter is plotted as logl0(range 2 x intensity), so that the plotted variable should depend only on the aerosol concentration and be roughly independent of range. For comparability with Figs 2 and 3, the intensity has been normalized with respect to laser energy and unit range has been taken as 1000 m. Figure 5 demonstrates clearly the presence of low cloud. The boundary layer in this case is much clearer than the air above. We have taken the cloud base to be the height where the mean backscatter starts to rise

Lidar study of the limits to buoyant plume rise :-'

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Fig. 5. 15 min mean Lidar backscatter intensity as a function of range for a shot elevation of 31 ° and a range window of 500-1720 m in the presence of a low cloud base. The cloud base was estimated to be at a height of 1475 x sin (31°) = 760 m. "Mean end level" and "noise level" refer to the statistics of the last 30 bins of the profile. "Shot energy" refers to the mean laser power. The Lidar scans upwards so, out of these scans of 60 shots, the 60th has the greatest elevation.

f

. . . . . . . . . . . . . . . . .

1.~

---

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I

171~: I~:~:,,

)

:ll,O=s

~T"2

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i

~

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a"l.- .i . . .

[:

I

"~[I~.

I:

)

"1..

":llS.O7

1~o93.~,,o4 .,.ou ~

L.KUgL:

LS~L: ~ v :

8 . 9 3 o,

Z.l.,.z 1o22.9

~Iln,g~Tl~ :

31.5

11 ~x~m:

~.o

[8HOT 68 OUT OF

68

0.77

-.

19

lllll~h~ll, m

Fig. 6. 15 n'~.n mean Lidar back~atter return for a shot elevation of 31.5° and a range window of 1250-2470 m through a hazy boundary layer with no cloud. The boundary-layer depth was estimated to be 2290 x sin (31.5 °) = 1195 m. very quickly, which m a y here be t a k e n to be at a range of 1475 m a n d a height of Zc ffi 760 m. Figure 6 d e m o n s t r a t e s the converse, with a hazy b o u n d a r y layer a n d clear air above. In this case, the signal falls off very sharply at ranges greater t h a n 2200 m. W e have here t a k e n the t o p of the b o u n d a r y layer to be at a range of 2290 m a n d a height of AE 29:17oE

Z i - - 1195 m. O n occasions w h e n the d e p t h of the b o u n d a r y layer was apparently greater t h a n the height s p a n n e d by the Lidar, a n o m i n a l value of Zi = 1300 m was archived. Identification of the t o p of the b o u n d a r y layer is m u c h m o r e difficult if there is little difference in aerosol c o n t e n t between the b o u n d a r y layer a n d the free

2284

M. BENNETT 1.00

F I L E : 1EdW93. b~4 15:00:33 UINDOU 8 2 RECS. t~A~.IiAGED: 253 END ~ : 7.383 NOISE LEUEL : 1.'~o0 SI]OT D I m i t Y : 1GSG.9 ELEX~T ION: 1.5 letZII~JYH: 19~i.B

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.

.

.

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.

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FILE: ~ . y 0 4 15:00:35 U INDOW #Z IiCCS. ~gQIR~JW: 2 5 3 ~ LEUID.: 5.345 N O l ~ I,EUEL: 2.599 SHOT II,ERGY : 1558.9 ELIP~T lOB: 31. B ~ZIHUlq4: 198.8 SHOT 6 8 OUT OF 6 8

_

I I I I

1.00

0.64]

(b)

125°

1750

RANGE, m

Fig. 7. (a) 15 rain mean Lidar backscatter return for a shot elevation of 1.5° and a range window of 1250-2470 m through a clear boundary layer. (b) 15 rain mean Lidar backscatter return as for preceding figure but at an elevation of 31°. The boundary-layer depth was estimated to be 2095 x sin (31°) = 1080 m.

atmosphere. Such an occasion may be seen in Figs 7a and b, where the backscatter profiles: at ele~'ations of 1.5 and 31 ° are compared. The decay of intensity with range at the lower elevation is probably due to the gradual loss in beam energy as a result of total scattering. F o r a constant aerosol concentration, this should give a straight-line decay, as is observed. At the greater elevation, the signal falls off more quickly with range. This presumably arises from the atmospheric aerosol concentration declining with height, but there is no clear discontinuity to mark the top of the mixed

layer. Careful inspection of Figs 7a and b, however, shows that the bin-to-bin variation in the backscatter is markedly greater at the higher elevation, particularly at the greater ranges. We may view this as a change in the mixing properties of the atmosphere with height~ Close to the ground, the atmosphere is well mixed and backscatter varies little with range. Outside the boundary layer, however, quite sharp changes in aerosol content may occur over short distances. Stall (1988, p. 413), for example, notes that changes in wind direction with height in the stable

Lidar study of the limits to buoyant plume rise layer can lead to a "layer-cake" appearance to the backscatter profile. Following the relative variances of backseatter as a function of range at the two elevations should therefore give an estimate of the boundary-layer depth. In the case shown, the variance at the greater elevation was considered to be significantly larger than that at the lower one for ranges greater than 2095 m, implying a boundary-layer depth of 1080 m. These procedures for estimating a boundary-layer depth are clearly somewhat qualitative. As will be seen later, however, so long as a realistic value is chosen, a good estimate of plume height can be made.

5. CORRECTION O F T H E MEASURED P L U M E RISE FOR DISPERSION

In principle, the: plume trajectories plotted in Fig. 4 may now be compared with the available boundarylayer depths. One further correction is necessary, however, before this can be done accurately. Equations (1) and (2) predict the mean height of the plume centreline in an unlimited neutral atmosphere. If a capping inversion is present, turbulent eddies cannot carry the plume upwards through the inversion but, once the plume has reached the inversion, may only disperse it downwards. The conventional way of treating this mathematically is to add a reflected plume with a centreline height of 2Z~ - h to the primary plume. Thus, for a Gaussian plume of concentration X and source strength Q,

x(x, y, z)

=

-

Q

e-f/2¢,z {e -0'-z)z/2¢~

2nuorox "~ e - (2z,- h - z)

212¢~}

(7)

for z < Z~ and, naturally, X = 0 for z > Z~. A simple calculation shows that the mean plume height

ZI :=

Zt

Izx(z) dz/ I z(z ) dz

0

0

(8)

must be less than the plume centreline height by an amount

hoorr=h-~.---t_

-- ~ e - ~ / 2 d~}

(9)

where ¢ = (Zi - h)/oz. From the discussion in Section 3, it should be evident that the trajectories in Fig. 4 are of mean plume height rather than plume centreline height (they are time means, weighted by backscatter intensity). They must therefore be corrected according to equation (9) before they can be directly compared with equations (1) and (2). Clearly, we require estimates for a~ in order to apply equation (9). We cannot use the measured value of a, since this is itself affected by the proximity of the capping inversion. For simplicity, we have instead

2285

used the Langevin-type equation

2 T L~X trz(x, T) z =~z(x, 0)2 + 2 ~ w [ u - TL[1 -- e_X/{UTL)]} (10) (Tennekes, 1979). We used Hanna's (1981) value of TL ffi 80 s for the Lagrangian integral timescale in the above expression and a regression from turbulence measurements on the Belmont TV mast (Bennett, 1991) for the turbulence intensity aloft, namely

~2 = 0.00364(UEo)2/3

(11)

where u is the wind speed at 207 m in m s- 1 and Eo is the insolation in W m -2. This regression predicted hourly means of aw between frequencies of 1/900 Hz and 2 Hz with a residual standard deviation of 31%; it is considered that the countryside at Staythorpe is sufficiently similar to that around Belmont for it to remain valid. Equation (4) was used to estimate the instantaneous plume spread in equation (9) with the proviso that the instantaneous plume should stop spreading once its top has reached the capping inversion, i.e. h, + C1 Br + t/z Br ~ Zi.

(12)

Thus, the maximum value of Br to use when calculating the plume spread should be

Zi.~ h$

Brm. = -C1- +. ~/g

(13)

This limit was also used in the calculation of centreline plume height for equation (9). Having calculated hcorr (which could be as great as 100 m) it is possible to plot the corrected value of the measured plume height against the predictions of equations (1) and (2) for unconstrained rise. This is shown in Fig. 8. In order to normalize the trajectories, both measured and predicted values have been divided by the available boundary-layer depth, Zt - h,. In plotting these trajectories, only cloud-free conditions with insolation greater than 100Win -2 have been included. Conditions may therefore be considered to be more or less convective. Apart from two labelled exceptions, all trajectories now cluster along the measured = predicted line, with the plume rise apparently petering out for a measured rise of about Zi - h,. The exceptions were both re-examined: (a) The estimate of the wind speed (u = 1.9 m s-1) for run Y02 on 18/8/93 only intermittently exceeded the correlation threshold. The wind speed measured at 388 m at Belmont for the corresponding hour was 3.5 m s- 1. The wind direction at the time was southerly at both locations, so it was thought unlikely that Belmont should be in the sea-breeze flow; though there may have been differences in boundary-layer depth between the Vale of Trent and the ridge of the Wolds. The trajectory was deemed unreliable.

2286

M. BENNETT Plume rise at Staythorpe, 1993 1.5-

sJ sS se •s

1.o-

~ • ' "

180893.y02

o.5-

•s

0

I

0.5

I

1.0 Predicted rise h(Zi-Hs)

I

1.5

I

2.0

Fig. 8. Trajectories of measured and predicted plume rise at Staythorpe in cloud-free conditions with the rise sealed by the available boundary-layer depth and the measured rise corrected for dispersion near the top of the layer. The dashed line denotes measured = predicted rise.

(b) The estimate of wind speed (u = 1.5 m s- 1 ) for run Y01 on 18/8/93 significantly exceeded the correlation threshold. Again, the wind speed at Belmont was greater than that measured by the Lidar, being 3.7 m s- 1. Given the strength of the correlation signal, we considered that we had observed an occasion on which the plume had risen to the top of a moderately deep (Z~ = 695 m) boundary layer in a light wind. This was consistent with the observed plume profile.

6. COMPARISONOF MODELS After discounting the unreliable trajectory noted above, it would appear that Fig. 8 supports the view that the plume centreline continues to rise according to equations (1) and (2) until condition (12) has been met. Some caution should be exercised here, however, since Br(Fb, x, u) has been used in calculating both the predicted rise and the correction to the measured rise. A spurious correlation might thus have been produced. This may also have arisen from normalizing both coordinates with Zi - hs. This potential problem was checked by comparing measured values of the final plume rise with predicted values based on independently measured variables. "Final" plume rises were deemed to have been observed when the trajectories shown in Fig. 4 had an ultimate slope of less than 0.3. This gave a set of 16

observations. For each observation, the expected plume rise was then calculated using equations (1) and (2), subject to a value for Brmaxgiven by equation (13) and the dispersion correction given by equation (9). Measured and predicted values of the plume rise are displayed as a scatter diagram in Fig. 9 with statistics in Table 3. As may be seen, the correlation is highly significant. Paradoxically, there is only a weak correlation between the final plume rise and the measured depth of the boundary layer. This may be seen from the second line in Table 3, where the final rise has been correlated with Zi - hs. What seems to be happening is that in a shallow boundary layer the plume rises directly to the capping inversion; a deep boundary layer, however, is often associated with active turbulence so the plume can be dispersed significantly downwards while it is rising towards the top of the layer. (The plume also has a much longer travel time during which to disperse.) The net statistical effect of the layer being deep or shallow is therefore rather small, though it may be important on individual occasions. ' The third line in Table 3 reports the statistical comparison between the measured final plume rise and the predictions of the plume break-up model, equation (6). A scatter plot of the comparison is shown in Fig. 10. As in the calculations leading to Fig, 9, insolation rather than surface-sensible heat flux

Lidar study of the limits to buoyant plume rise

2287

Table 3. Statistics of final plume rise prediction using plume reflection and plume break-up models, n ffi 16 Model for limiting plume rise

Residual standard deviation (m)

Ratio measured/predicted

Reflection BL depth Break-up

67.5 91.3 93.5

1.01 + 0.10 0.49 -t- 0.09 1.42 + 0.30

jo /, S

0

o ,P"

"i:::

¢,, 0 0¢~

8400 _=

s

0

s 'O 0 /,

.=

Y

200 --

/0

a qo

/,

/, s

/

S

I 2OO Predicted

0

I

I

400

600

I

800

M a x i m u m plume heights at Staythorpe, 1993 ¢

-

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/

oo /o

0

s

0

0

o 0

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tS

0.11% n.s. n.s.

/

I 200

7. CONCLUSIONS

final plume rise (m)

Fig. 9. Scatter plot of the measured final rise against its predicted value taking reflection at the top of the boundary layer into account. The dashed line shows the mean value of measured/predicted.

l

0.692 0.217 - 0.011

/

¢/

u

p (one-sided)

the weak theoretical dependence of Zb on H . , some positive correlation should be expected if the model was appropriate for the situation. We surmise that, for the relatively shallow boundary layers experienced in the U.K., the plume breakup model is a poor guide to final plume height: before they can be broken up through the mechanism modelled by equation (6), plumes from moderate or large thermal sources will usually have risen to the capping inversion.

M a x i m u m plume heights at Staythorpe, 1993 60O

r

I

i

400 600 Predicted final plume rise (m)

I

8OO

Fig. 10. As Fig. 9 but using equation (6) for the predicted rise. The dashed line shows the mean value of measured/predicted.

had to be used in equation (6): besides scatter, this will lead to the dimensionless buoyancy flux being consistently overestimated and hence the predicted final plume height underestimated. The reported ratio of measured to predicted heights in Table 3 is in fact rather large. What is of more interest, however, is that there is no case-by-case correlation between measured and predicted plume heights by this method. Given

The main conclusion that we draw from our fullscale measurements of a buoyant plume in a range of meteorological conditions is that a moderate or large thermal emission (20 M W or larger) will usually be enough to allow elements of the plume to reach the top of the boundary layer before buoyant rise becomes negligible. The final mean plume height, bowever, may be substantially less than the boundary layer depth, since dispersion causes a mean downward flux once the plume has approached the impenetrable barrier of the capping inversion. We recommend, therefore, that the standard equations for the rise of the centreline of a buoyant plume, equations (1) and (2), be limited by equation (13) as the plume approaches a capping inversion. It is this centreline height which would be used in the Gaussian plume formula, equation (7). For smaller sources, or more active convection, a touch-down model might be more appropriate; in such a model the maximum ground-level concentrations occur when elements of the plume are carried directly to the ground by downdrafts (cf. Fig. 2a). Willis and Deardorff (1978) noted this effect in their water tank simulations of non-buoyant emissions into a convective boundary layer. This mechanism would normally require that the ground-level maximum occurs for a travel time less than the Lagrangian integral timescale. The initial plume rise that we observed at Staythorpe was similar in magnitude to that from other inland power stations at Didcot and Drax (Bennett et aL, 1992) for which we recommended a plume rise parameter of C1 = 1.64. We now believe that the smaller value of C1 = 1.35 observed at Fawley

2288

M. BENNETT

and Littlebrook was due to the nearby presence of a large body of water. Measurement of the depth of the boundary layer with a Lidar is straightforward when the aerosol content of the boundary layer differs significantly from that of the free atmosphere. We have suggested a method of estimating this depth when aerosol differences are slight. Further measurements to validate the method would be most valuable. Acknowledgements--We are grateful to the Natural Environment Research Council for providing a grant to enable us to carry out this work; to National Power for permission to take measurements at Staythorpe; to the management and staff at the power station for their generous and willing assistance; to Mr S. Sutton and Mr D. Doocey for technical help; and to Prof. R. F. Griffiths for advice and encouragement.

REFERENCES

Bennett M. (1991) Turbulence climatology on a 389 m TV mast. National Power Research Report TEC/L/0492/R91. Bennett M. (1992) Wind statistics from the Belmont TV mast, 1983-89. Weather 47, 114-122. Bennett M., Sutton S. and Gardiner D. R. C. (1992) An analysis of Lidar measurements of buoyant plume rise and

dispersion at five power stations. Atmospheric Environmerit 26A, 3249-3263. Briggs G. A. (1984) Plume rise and buoyancy effects. In Atmospheric Science and Power Production (edited by Randerson D.), pp. 327-366. U.S. Dept. of Energy, DOE/TIC-27601. Giebel J. (1981) Verhaltan and Eigenschaften atmosph~rischer Sperrschichten. Landesanstalt ffir Immissionsschutz des Landes Nordrhein-Westfalen, Essen, LIS Report no. 12. Hanna S. R. (1981) Lagrangian and Eulerian time-scale relations in the daytime boundary layer. J. appl. Met. 20, 242-249. Manins P. C. (1979) Partial penetration of an elevated inversion layer by chimney plumes. Atmospheric Environment 13, 733-741. Moore D. J. and Lee B. Y. (1982) An asymmetrical Gaussian plume model. Report no. RD/L/2224NS1, Central Electricity Generating Board. Stull R. B. (1988) An introduction to boundary layer meterology. In Atmospheric Sciences Library. Kluwer Academic Publishers, Dordrecht. Sutton S. and Bennett M. (1994) Measurement of wind speed using a rapid-scanning Lidar. Int. J. Remote Sens. 15, 375-380. Tennekes H. (1979) The exponential Lagrangian correlation function and turbulent diffusion in the inertial sub-range. Atmospheric Environment 13, 1565-1568. Willis G. E. and DeardorffJ. W. (1978) A laboratory study of dispersion from an elevated source within a modeled convective planetary boundary layer. Atmospheric Environment 12, 1305-1311.