Transactions on Ecology and the Environment vol 13, 1997 WIT Press, ISSN

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$A Study of the Evolution of the Nocturnal Boundary-Layer Height at the Central Nuclear de Almaraz (Spain): Diagnostic Relationships Jose A Garcia*, M L Cancillo', J L Cano\ G Maqueda^, L Cana^, C$

1 A Study of the Evolution of the Nocturnal Boundary-Layer Height at the Central Nuclear de Almaraz (Spain): Diagnostic Relationships Jose A Garcia*, M L Cancillo', J L Cano\ G Maqueda^, L Cana^, C Yagiie^ *Dto. de Fisica, Universidad de Extremadura, Badajoz, Spain ^Dto. de Ciencias Atmosfericas, Universidad Complutense, Madrid, Spain *Institute Nacional de Meteorogia, Madrid, Spain Abstract Because of the importance of the planetary boundary height in determining pollutant concentrations near the surface, a study of the nocturnal boundary layer was carried out at the Central Nuclear de Almaraz (Spain). During the night there is a distinction between the turbulent or mixing layer (ML) height and the nocturnal cooling layer or nocturnal stable layer (NSL) height. A number of scales that measure the height of both layers were studied, finding that while the NSL height increases as the night progresses, the ML height does not show any trend. Also a number of secondary length scales, used for diagnostic purposes, were analyzed. These secondary scales show a high variability. A correlation analysis of different diagnostic relationships shows that only in a few cases are the correlation coefficients significant. 1 Introduction Knowledge of the Planetary Boundary-Layer Height (PBLH) and its evolution is of the greatest interest for the study of pollutant dispersal, boundary layer modeling and its parameterization. It is also required as a scaling parameter in similarity theories. During the day, the PBLH is usually identified with the base of an elevated inversion or stable layer capping a well-mixed convectively driven boundary layer. During the night or in the case of a surface-based stable boundary layer, the PBLH is not so well defined. In this case one must differentiate between the Turbulent Nocturnal Planetary Boundary Layer (TNPBL), which could be identified with the Mixing Layer (ML), and the Nocturnal Planetary Boundary Layer (NPBL), which could be identified with the Nocturnal Stable Layer (NSL). During the night, buoyancy forces are opposed to the effects of mechanical turbulence, weakening the mixing processes. However, near the ground, where the shear can be high, there subsists a certain level of turbulence, great

132 Measurements and Modelling in Environmental Pollution enough to keep this layer well mixed, transferring heat from above to the cooled ground and extending this cooling upward, at the same time

2 132 Measurements and Modelling in Environmental Pollution enough to keep this layer well mixed, transferring heat from above to the cooled ground and extending this cooling upward, at the same time as mixing pollutants emitted near the ground level. Surface cooling is also transmitted to the atmosphere through radiative transfer, so that the depth of the NPBL, defined as the height up to which cooling of the atmosphere due to the presence of the ground is important, could be much greater than the TNPBL depth. Thus, during the night the planetary boundary layer could be considered as multilayer, with a turbulent layer near the ground and a non-turbulent layer above but still undergoing significant cooling. In this simplified picture of the nocturnal planetary boundary layer, we are neglecting effects such as horizontal advection, katabatic winds, high-level turbulence associated with the low-level wind maximum (Low Level Jet), discontinuous turbulence, etc. Because of the importance of the ML height for dispersion models, the purpose of the present study is to evaluate the different definitions of the ML/NSL heights for a particular site, in this case the vicinity of the Central Nuclear de Almaraz and to develop diagnostic relationships which parameterize ML/NSL depth as a function of parameters measured at the surface. 2 Depth Scale Definitions 2.1 Primary Length Scale Definitions Compared with the daytime convective boundary layer, the depths of both the ML and the NSL are much more difficult to define and estimate from data. A variety of definitions can be constructed, based on different physical properties and methods of computation from data. These different definitions of length scales could be divided into two groups, primary length scales and secondary length scales [12]. A primary length scale is the height of some physically recognizable feature of the Boundary Layer directly accessible to observation which unambiguously identifies the vertical extent of the turbulent or thermal effects of the surface. A secondary length scale is a scale derived from a thermodynamic or dynamic conservation equation. Examples of secondary length scales are the Obukhov length L, the Ekman layer depth, etc. In this section some of the primary length scales are introduced, leaving for the next section the secondary length scale definitions. As was noted above, during the night, two different layers, the ML layer and the NSL layer may be distinguished. The top of the ML is usually defined as the height at which turbulence, measured through the heat flux or the momentum flux, decreases to a small fraction, say 5%, of its surface value. High resolution profiles of turbulence parameters covering the range 50 to 500 m are needed for this definition to be used. Such measurements are only possible at very selected sites or during special boundary layer experiments. An easier way to estimate the turbulence level is through the gradient Richardson number Ri as this only requires knowing the temperature and speed profiles. Theoretically, when this number is less than or greater than some critical value (usually between 0.25 and 1), the atmospheric flow becomes turbulent or laminar respectively. Unfortunately its proper evaluation requires a high degree of accuracy in the

Measurements and Modelling in Environmental Pollution 133 measurements of the wind speed because its gradient appears squared in at the denominator of the definition of Ri.

3 Measurements and Modelling in Environmental Pollution 133 measurements of the wind speed because its gradient appears squared in at the denominator of the definition of Ri. A similar number but which does not suffer from this problem is the bulk Richardson number Rib. Different definitions can be found in the literature. Here we shall use that of Andrd and Mahrt [1] where [/max is the maximum wind speed in the layer (0,z), A0 is the difference of the potential temperature between the first point of the sounding (normally less than 5 m) and height z and % the potential temperature of thefirstpoint of the sounding. The height of the ML is defined as Rib(h^) = Ribcr (2) where Ribcr is a critical bulk Richardson number. There is no a consensus in the literature about the value to take for this number. Here, we shall use a value of 0.5, which is typical of the critical Richardson numbers given in papers surveyed by Mahrt [9j. With reference to the nocturnal boundary layer (NSL) depth, there are several definitions in the literature, among which can be cited The surface inversion height h<, proposed by Yu [15] and defined as the height where the temperature gradient reaches its dry adiabatic value. The problem with this definition is that it does not include the thicker layer of significantly stratified air situated above. The height h< to which significant cooling has extended, as judged from the time evolution of the potential temperature profile (Melgarejo and Deardorff) [10]. We modified Melgarejo and DeardorfTs definition by taking the potencial temperature profile at 1800UTC as a reference, and then calculating the cooling at the height z at time t as the difference between the potential temperatures measured at height z at time t and at time 1800UTC. The height he is calculated as the height where the cooling has fallen to l/e of the surface value. The height hp where the potential temperature gradient ff exceeds 3.5 x 1Q~*K m~*, the low-level value of the standard atmosphere (Andre and Mahrt) [1]. 2.2 Secondary Length Scale Definitions. Diagnostic Relations As we noted above, a secondary length scale is a scale derived from a thermodynamic or dynamic conservation equation. Among the most frequently used secondary length scales, can be cited the following: In a series of papers, Zilitinkevich ([16], [17]), from similarity and dimensional analysis considerations, suggest taking for the height of the Nocturnal Boundary Layer the expression

4 134 Measurements and Modelling in Environmental Pollution where d is a constant, L the Monin-Obukhov length, %* the friction velocity and / the Corioli parameter. A number of model calculations (e.g, Businger and Aria [6]) have confirmed this expression. DeardorfF [8] proposes the following empirical formula: Clarke [7] speculates that, based on similarity theory, the height of the stable boundary layer may be determined by hm = k j. (5) Arya [3] proposes that ha = L could be more appropriate for strongly stratified conditions encountered at night. Based on a heat balance equation, Stull [12] proposes the heat-flux-history length scale hg defined as where the nocturnal integral operator / is denned by t being the time since evening transition and r a dummy variable of the integration. QH is the surface sensible heat flux expressed in kinematic units (i.e. Kms~*) and A0, is the cooling just above the earth's surface. Assuming a balance between inertia forces and buoyancy forces, Brost and Wingaard [5] propose as a length scale /i6 = ^ (7) w& ^ ' where a^ is the standard deviation of the vertical speed and w& is the Brunt-Vaisala frequency. Much of the research about the parameterization of the NBL depth has been into the relationship between the primary and the secondary length scales, in order to construct diagnostic relationships between the two kinds of scales. This is what we propose to do in this present paper, to parameterize the inversion height as a function of parameters measured at ground level. 3 Data Data were gathered between 24 and 29 September 1995 at the Central Nuclear de Almaraz, Spain (39 45'N, 5 40'W, 225 m MSL) with an AIR, USA, tethersonde system and a 15 m meteorological mast with a sonic thermometer-anemometer

5 Measurements and Modelling in Environmental Pollution 135 ATIALJSIS CM SUPCRFICJC a 12 h (TMQ) Dia...27/09/1995^_ Figure 1: Synoptic situation at surface, 27 September at 12UTC (Kaijo Denki DAT300) and a fast response thermometer (AIR, FT1 AT) mounted on its top. Following the eddy-correlation method, the friction velocity it*, the sensible heatflux,h and the Monin-Obukhov length L were determined each half hour. The tethersonde system provides profiles of temperature, pressure, mixing ratio, wind speed, wind direction and height above the ground up to a maximum height of m. Measurements were taken, when possible, hourly from 06 to 24 UTC. Each ascent takes about 20 minutes. All times indicated in the diagrams and in the text are UTC and show the beginning of each sounding. Sunrise and sunset took place at about 0615UTC and 1815UTC. During the observational period the weather was sunny with low to moderate wind speed. The Azores High (A) extended well over the Iberian Peninsula with a north-easterly to eastnortheasterly flow. The frontal systems remained quite far away from Almaraz. Figure 1 represents a typical synoptic situation of the observational period. From 25 September evening to 26 September afternoon soundings were suspended due to the high winds present in the zone. 4 Time evolution of the scale depths 4.1 Primary scale depths The heights /i», /i<., and hg were obtained from the temperature and potential temperature profiles (the virtual potential temperature profile 0* was not obtained because of failure of the humidity probe). Also the bulk Richardson number profile was obtained from the wind and the potential temperature profile. As noted above, the level at which this number reaches its critical level may be considered the mixing layer depth 7i^/. Figure 2 shows the time evolution of the primary scale depths for each day (as was mentioned above, there are no observa-

6 136 Measurements and Modelling in Environmental Pollution tions for the night 0925/0926). The following conclusions can be drawn from an analysis of the figure. During the night, the scales that measure the NSL height 800 ~ 600 f 400 I 200 Night 0924/ Night 0926/0927; ~ 600 f 400 X Night 0928/ Figure 2: Time evolution of the primary length scales for the four days under study hi, h^ and hg grow, while the scale that measures the ML height hmi remains nearly constant. The maximum ML height occurs at 18 UTC, probably due to the fact that at this time of the day there persists some of the diurnal convective turbulence keeping the layer well mixed. It may be seen that the gradient height hg definition of the NSL it is greater than the inversion height In definition. This is because the inversion height does not take into account the layer of air with significant stratification that lies above the inversion layer. However, their time evolution is quite similar. A linear regression line of hi versus hg was found to be hi = -9(±66) +0.69(±0.17)ha (8) with a determination coefficient R* of This means that the inversion height hi is on average some 31% lower than the stable height hg. Except for the night 0924/0925 both are greater than the cooling height /%<.. This has no physical significance because there is a high degree of arbitrariness in the he definition. 4.2 Secondary length scales Four of the six secondary scales defined in section 2.2, {& /%, Ji^ and &*} are based on the Monin-Obukhov length L and the friction velocity %*. Because L and %* are highly correlated (a good deal of the L variation is dominated by %* variation) a correlation analysis of these four scales was carried out. The results

7 Measurements and Modelling in Environmental Pollution 137 show that they are strongly correlated, with coefficients from 0.77 (ha/hm) to 0.99 (hd/hz). Thus, because of its simplicity, only hm will be used in the subsequent analysis. Figure 3 shows the time evolution of the scales {/im, /% and A*} for the four nights under study. As may be seen, there is no longer any increase of the scales during the course of the night. The high variability shown by these scales is probably because during the night long periods are needed for the averaging in order to obtain significant results. 500 Night 0924/ ^ 300 -f 200 I boo hj Nigrit 0927/0928 V < 300 Nigh( 0926/0927 [jh." f Oi " X boo Nighjt 0928/0929 ~ hi" * n Figure 3: Time evolution of the secondary length scales for the four days under study; hm has been divided by ten and /%& multiplied by ten ^ 4.3 Diagnostic Relationships As was mentioned above one of the purposes of developing secondary scales is to construct diagnostic relationships between secondary and primary scales. A cross-correlation analysis between the two groups of scales, {/im, ht>, h*} and {hi, hg, he, Rib}, revealed that only the scales hg and hi show significant correlation coefficients with the scales h\> and /%*%, so that we limit our study to these scales. The best-fit regression lines are of the form and the resulting estimates are listed in table 1. Figure 4 shows a scatter plot of hg and hi versus /%& and hm. As may be seen from the table, the results are quite satisfactory, mainly in the hg, hi versus /% relationships. However there is a high variability as is reflected by the estimated variance and the scatter of the points in figure 4. This variability would be reduced if the regression fit were

$138 Measurements and Modelling in Environmental Pollution Table 1: Coefficients of the log-linear regression line of the NSL heights {&,,, /%} versus the secondary length scales /% and h^: a, 6 are$

8 138 Measurements and Modelling in Environmental Pollution Table 1: Coefficients of the log-linear regression line of the NSL heights {&,,, /%} versus the secondary length scales /% and h^: a, 6 are the regression coefficients, P? is the determination coefficient and a* the estimated variance of the regression. The standard errors of the coefficients are given in parenthesis, - a b R- a b R' h, (0.38) (0.08) (0.35) (0.08) hi a = 8.81 (0.55) b =-0.84 (0.11) R' 0.70 or 0.58 a = 6.37 (0.59) b =-0.39 (0.13) R done for each night. As pointed out by Andr< [2], the variation from night to night of the nocturnal boundary-layer depth could be as large as the variation within a particular night. For each individual night the estimated variance of the regression a* would be much lower. Unfortunately we do not have enough soundings per night to obtain significant regression coefficients. The sign of the estimated slope b shows that there is an inverse relationship between the NSL depth measured by kg or /% and the secondary length scales b& and hm- This is probably because when the NSL is forming at sunset and thus is thinner, there persists some of the diurnal convective turbulence. As the night proceeds the NSL height begins to rise as the level of the turbulence falls. 5 Summary and Conclusions As a summary of the present study the following conclusions can be drawn: The NSL height as measured by hgjii and he rises with time as the night advances. On the other hand, the mixing layer depth as measured by /w, has a great variability but shows no growing trend as the night proceeds. In all the cases studied the NSL depth is much greater than the ML depth, which means that the heat is transported by other processes in addition to turbulence, probably by radiation, advection or drainage of chilled air. The secondary scales analyzed also show a great variability. Of the six scales reviewed, four {/% /%, hm and A*} are highly correlated, so that only one of them hm was used in the subsequent analysis. Only four of the set of the diagnostic relationships studied were found to be significant, those between /i,/i6 and /%<,,/%. Acknowledgments We would like to thank Dr. V. L. Mateos for help during the measurement period. Thanks are also due to the Central Nuclear de Almaraz for its financial support.

9 Measurements and Modelling in Environmental Pollution 139 Scatter Plot of h,vs. h«scatter Plot of h, vs. h. # * h. Scatter Plot of h,vs. h» COOO h» Scatter Plot of h, vs. h> h Figure 4: Scatter plot of the NSL scales km (top) and h\> (bottom) heights kg and hi versus the secondary length References [Ij Andre, J.C. and L. Mahrt, The Nocturnal Surface Inversion and the Influence of Clear-Air Radiative Cooling, J. Atmos. Sci, 1982, 39, [2] Andre*, J.C., On the Variability of the Nocturnal Boundary-Layer Height, J. Atmos. Sci, 1983, 39, [3] Arya, S. P. S., Parameterizing the Height of the Stable Atmospheric Boundary Layer, J. AppL Meteor., 1981, 20, [4] Benkley, C. W. and L. L. Shulman, Estimating ly Mixing Depths from Historical Meteorological Data, J. AppL Meteor., 1979, 18, [5] Brost, R. A. and J. C. Wyngaard, A model Study of the Stably Stratified Planetary Boundary Layer, J. Atmos. Sci., 1978, 35, [6] Businger, J.A, and S. P. S. Aria, Height of the Mixed Layer in the Stably Stratified Planetary Boundary Layer, Advances in Geophysics, Vol 18A, Academic Press, 462 pp, [7] Clarke, R. H., Observational Studies in the Atmospheric Boundary Layer, Quart. J. Roy. Mcttor. Soc., 1970, 96, [8] Deardorlf, J. W., Parameterization of the Planetary Boundary Layer for Use in General Circulation Models, Mon. Wea. Rev., 1972,,

10 140 Measurements and Modelling in Environmental Pollution [9] Mahrt, L.,Modelling the Depth of the Stable Boundary Layer, Bound.-Layer Meteor., 1981, 21, [10] Melgarejo, J. W. and J. W. DeardorfF, Stability Functions for the Boundary- Layer Resistance Laws Base upon Observed Boundary-Layer Heights, J. Atmos. Sci., 1974, 31, [11] Smeda, M., Incorporation of the Planetary Boundary-layer Processes into Numerical Forecasting Models, Bound.-Layer Meteor., 1979, 16, [12] Stull, R. B., Integral Scales for the Nocturnal Boundary-Layer. Part 1: Empirical Depth Relationship, J. Climate and Appl Meteor., 1983, 22, [13] Wetzel, J. P., Toward Parameterization of the Stable Boundary Layer, J. Climate and Appl Meteor., 1982, 21, [14] Yamada, T., Prediction of the Nocturnal Surface Inversion, J. Appl Meteor., 1979, 18, [15] Yu, T. W., Determining the Height of the Nocturnal Boundary-Layer, J. Appl Meteor., 1978, 17, [16] Zilitinkevich, S. S., On the Determination of the Height of the Ekman Boundary Layer Bound.-Layer Meteor., 1972, 3, [17] Zilitinkevich, S. S., Resistance Laws and Prediction Equations for the Depth of the Planetary Boundary Layer, J. Atmos. Sci., 1975, 32,

An observational study of the planetary boundary layer height at the central nuclear

An observational study of the planetary boundary layer height at the central nuclear de Almaraz, Spain J.A. Garcia", M.L. Cancillo", J.L. Cano\ C. Vague* Dto. de Fisica, Universidad de Extremadura, 06071