Convective boundary layer height evaluations R. Stlibi, Ph. Tercier, Ch. Haberli Environmental Meteorology, Swiss Meteorological Institute, CH-1530Payerne, Switzerland Abstract The convective boundary layer (CBL) depth is an important parameter for air pollution problems because it controls the vertical extension of the volume of dispersion. Conventional methods to evaluate CBL height are based on ground meteorological measurements recorded by automatic networks. Another continuous source of informations regarding the structure of the atmosphere are given by the operational aerological soundings launched daily at 0 UTC and 12 UTC. Advanced meteorological pre-processor gather informations from both sources to better characterize the CBL structure in order to evaluate its depth. An alternate approach is the analysis of the soundings introduced by Betts. Based on conserved thermodynamic variables, his examination of temperature, pressure and humidity profiles permits to detect transitions between layers of different nature. In particular, CBL features, like the capping inversion layer and the well mixed layer below it, can be differentiated by this method. These two approaches have been applied to a summer smog study data set (POLLUMET, Switzerland 90-93). A comparison of the results are presented in these pages which show a good agreement for the selection of clear days of the campaigns. The sensitivity of the CBL height evaluation regarding two different parametrisation schemes for the sensible heat flux is given. The complementarity of the informations given by the meteorological pre-processor for the lower part of the CBL and by the soundings analysis for the upper part is shown. Finally, a long term statistics of the CBL height evaluation is presented to put back the POLLUMET campaigns results in an extended time perspective. 1 Introduction From the late fifties, short range atmospheric dispersion models have assumed Gaussian dispersion processes and relied on meteorological measurements recorded near the ground. Progresses in the understanding of the structure of the
252 Air Pollution Engineering and Management atmospheric boundary layer and its dispersion capacities, but also the evolution of the computer technology, recommend that the models have to be adapted to the actual knowledge. This implies that the meteorological input must also be improved. Regarding the CBL height parameter, this means that the traditional simple method like Holtzworth [1] have to be replaced. Two advanced methods are presented here: thefirstone is a direct analysis of the profiles provided by the soundings while the second rely on the Tennekes [2] equations for a one dimension slab model. 2 Belt's method The method used here to analyse the sounding has been developed by Betts & Bruce [3]. The aerological soundings provide with wind & PTU informations on a column of the boundary layer close to the launching site. In particular they permit to calculate conserved variables profiles related to temperature and humidity, which define the thermodynamic state of the atmosphere. In figure 1, an example of a typical clear summer day sounding is shown. At theright,we findfirstthe humidity and wind profiles. At the centre, the temperature related profiles are given while the pressure appear on the left. The potential temperature 0(z) is a conserved variable with respect to the pressure changes while the equivalent potential temperature 0g(z) is additionally conserved towards humidity changes. The equivalent potential temperature at saturation 8^(z) refer to saturated air. As discussed by Betts, the profiles 0^(z), 0^(z) and p*(z) are indicative of the vertical thermodynamic state of the atmosphere. In particular, the conjunction of a local maximum of p* and a local minimum of G^z) can be interpreted as the base of an inversion (-2400 asl). The top of the CBL is marked by a minimum of p* and a maximum of O^z) (-3000 asl). Betts has developed these criteria on the basis of averaged smooth profiles. In this study, [hpa] -200-100 0 [m/s] 0 20 40 r(z) (z)» : V(i, z) - 0.005.010.015 [K] [kg/kg] Figure 1 Typical summer day sounding where r is the mixing ratio, u is the wind speed, T is the temperature, 0 is the potential temperature, 0^ is the equivalent potential temperature, 0^ is the equivalent potential temperature at saturation and p* is the difference between the actual pressure and the corresponding pressure of saturated air.
Air Pollution Engineering and Management 253 the individual profiles are used and a refinement of the criteria as well as a critical review of the time sequence were necessary. We have used this analysis of the sounding in order to have a reference point at launching time (0 UTC and 12 UTC) to compare with models evaluation of the CBL height 3 Advanced meteorological preprocessor (OML) The dispersion model OML has been developed at the "Air Pollution Laboratory" at Ris0 (Denmark) [4 & 5]. Its meteorological pre-processor is based on the Tennekes equations which yield the time evolution of the parameters h(t) and A6(t) of the modelled 6(z,t) profile (seefig.2): (2) where Ag and A^ are constants, g the gravitation, (9'w')<, the sensible heat flux at the ground, u* the wind speed scaling variable and f the Coriolis parameter. The parameter y(z>h) = d6/dz, which characterizes the free atmosphere above the CBL, is evaluated using the aerological sounding data [4]. A numerical 10 12 Hours 14 16 Figure 2 On the left, the one dimension slab model profile of 6(z) is sketched. The three lines are the time evolution of the model's parameters as calculated by the OML for the 7 July 1993: h(t) the CBL height, A6(t) the jump of the potential temperature profile at h and 8h/8t(t) the rate of increase of h(t).
254 Air Pollution Engineering and Management solution for equs (1) & (2) is found while the initial conditions for the integration are given by the midnight soundings [4]. The assumption of a dry, homogeneous air mass is made. The sensible heat flux is estimated using a parametrisation of the surface meteorological observations. Among those parametrisations, two are frequently cited in the literature: the Berkowicz & Prahm [6] (BP) scheme and the Van Ulden & Holtslag [7 & 8] (VUH) scheme. A comparison of the results using those two schemes is presented in the next paragraph. Figure 2 illustrates the result of the calculation for the 7 July 1993. We can see that even if h(t) presents a smooth increase during the course of the day, significant changes are found in the evolution of A0(t) and dh(t)/dt. They are explained by the changes of y(z=h(t)) as a function of the calculated CBL height. 4 POLLUMET results The POLLUMET project (summer smog study 1990-1993) was a project which has collected an adequate set of data over the Swiss Plateau allowing the validation and the comparison of CBL height determinations [9]. Figure 3 shows the result of the comparison for the 1990 POLLUMET campaign. The two lines, resulting from the Betts's analysis, represent the limits of the capping inversion, also called entrainmerit zone [10], between the CBL and the free atmosphere. 4 -,3 - OML(VUH) OML(BP) 2-1 - net>1 0 6 6 3 4 2 1 0 0 0 0 1 3 1 2 7 6 0 0 0 1 0 - prec I I""" I I" IMIIIIIIII TTjrrr 24 12 25 ^ 26 ^ 27 July 90 mpmtttllll IN inn I ill M 28 12 29 12 30 Figure 3 Results of the analysis of the POLLUMET campaign 1990 for the site of Pay erne (Alt: 500 m asl). "b" and "o"-lines are for lower and upper limits of the temperature inversion capping the CBL. The OML results are presented for two parametrisations of the sensible heat flux: BP and VUH (see text). At the bottom of the figure, indications of the nebulosity and precipitations are given as well as the position of the surface inversion at night noted by "i".
Air Pollution Engineering and Management 255 The result of the OML model is given for the two parametrisations of the sensible heat flux introduced earlier. The differences in the calculated CBL heights induced by the use of VUH and BP schemes are significant for this 1990 episode. Usually the results are much closer. This episode were preceded by a particularly long dry and hot period which is presumably responsible for the observed differences. In this case and by reference to the Betts's analysis, the use of the BP scheme causes an overestimation of the CBL height. Concentrating on the calculation with the VUH scheme, we see a good agreement with Betts's methods evaluations of the CBL height. For the 26 July, Betts's analysis find a more significant change of the conserved variables at high altitude, probably because of the presence of a more humid or a cloud layer. For the last day of that period, the synoptic situation has changed and bad weather came in. The OML routines detect the weather change by analysis of the sounding temperature profile which prevents to fulfil the homogeneity hypothesis. In this case, a simpler relation is used (h~u*/f) to evaluate the CBL height. This relation is also used in the model for the night-time with an arbitrary lower bound at 150 m agl. At night, Betts's approach gives the "residual layer" height instead of the depth of the surface inversion layer. In that sense, the two methods complete each other at night-time and during the periods where convection is not established. In summary, it appears that both methods coincide well over the analysed episodes. This justifies their use for statistical evaluations of the CBL depth in order to place the results of the short POLLUMET campaign within a larger time perspective. 5 Statistical analysis OML Model For the period 1989-1993, isolines of constant CBL height have been calculated on the basis of monthly averages of the daily variation. They are presented on figure 4 where the two line types are for the different parametrisations BP and VUH. As an illustration for the July case, the CBL growth starts at about 7h30 reaching 1400 m asl by noon (point A) and culminates at roughly 2000m asl at the end of the afternoon (point B). There is a substantial variability around those mean values. The standard deviation grows up and levels off at noon at the typical value of 350 m. Regarding the effect of the schemes used for the sensible heat flux, a systematic offset in time appears on the growth of the CBL height (the two types of line are nearly parallel). In the OML program, the beginning and the end of the day are defined by the sign reversals of the sensible heat flux. In the morning, the beginning of the convection in VUH scheme starts nearly half an hour later than for the PB scheme. In the evening, the VUH scheme tends to overestimate the heat flux since the extremities of the isolines correspond approximately to the end of the day. But the maximum of CBL height for the two schemes in the late afternoon are within -150 m. For the summer period, we can estimate a mean growth rate of the CBL depth of -200 m/h between 8 and 12 o'clock which slowly decreases to -60 m/h later on.
256 Air Pollution Engineering and Management o ffi Month 10 12 Figure 4 Contour plot of constant CBL height [m asl] calculated with the OML model for the site of Payerne (altitude 500m asl). The x-axis is the month of the year while the y-axis is the hour of the day. The two line types refer to the VUH ( ), resp. BP ( ), schemes. Betts's Method A group of soundings have been selected on the criteria of a low daily cloudiness (<2/8) and a maximum hourly ozone concentration larger than 120 jug/m^ in the rural area on the Swiss Plateau. Over the summer periods of the years 1990-1994, thirty-six days fulfil the criteria. The noon (12 UTC), respectively midnight (0 UTC), subgroups have been treated separately and the result of the Betts's analysis is given on figure 5. More than one layer were detected in most of the soundings. The characteristics of the lowest layer are given on the left of the figure and those of the second layer on the right. We see that, at noon, thefirstlayer is well defined with a base around 1000 m asl and a depth between 150 m and 600 m. At midnight, the base and depth of the (residual) capping inversion is still fairly well confined for those days. The second layer characteristics are not so well defined, and there is no clear separation between the two subgroups. This fact is expected since this second layer is much less connected to the CBL daily cycle than to the synoptic system. For comparison with the model values, it is recommended to take as a characteristic CBL height the base altitude increased by half of the depth of the layer [10]. Using this definition, we get an average value of 1400 m asl for the noon subgroup, resp. 2100 m asl for the midnight: subgroup. Betts's analysis of the 12 UTC soundings for the three 1990, 1991 and 1993 POLLUMET cam-
Air Pollution Engineering and Management 257 Lower layer Upper layer o : noon sounding x : midnight sounding 3 e 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Depth [km] o : noon sounding x : midnight sounding 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Depth [km] Figure 5 Results of the Betts's analysis on a selection of clear summer days. The base altitude as a function of the depth of thefirsttwo layers are shown. The noon subgroup appears with a "o" symbol and the midnight subgroup with a "x" symbol paigns gives the mean CBL height of 1500, 1600 and 2100 m asl respectively. The conclusion is that the 1990 and 1991 episodes where representative of the typical summer conditions of the Swiss Plateau (see also point A on fig. 4) but the 1993 episode is not. For the 0 UTC soundings, we reach the same conclusions. 6 Conclusions Two approaches have been presented which both allow a convective mixing height estimate. The first one is based on an analysis of the profiles of conserved thermodynamic variables (Bett's method) calculated using the aerological sounding informations on temperature, humidity and pressure. The second is based on a one dimension slab model of the boundary layer with a numerical solution of the Tennekes's equations (OML model). Both methods use the aerological soundings and ground measurements which make them very useful for having statistical informations on the mixing height based on long term series. They are also adequate methods to characterize the evolution of vertical development of the convective boundary layer. The data set of the POLLUMET Swiss project is used because of its denser set of soundings than the usual "twice a day" frequency. Both methods
258 Air Pollution Engineering and Management have been evaluated and compared over three campaigns. Adjustments of the Bett's analysis were necessary because of its application on individual soundings. The OML model were used with two different parametrisations of the sensible heat flux to characterize the effect of this critical meteorological input. Finally, both methods were used to determine statistical values representative of the Swiss Plateau conditions. Compared to these reference values, the 1990 and 1991 POLLUMET episodes present a good agreement while the 1993 episode is significantly different. Acknowledgments The authors thank Dr. Olesen for providing the model OML as well as Dr. Beljaars for providing a library of routines to calculate the surface fluxes. References 1. Holtzworth C.G., 1967: Mixing depths, wind speeds and air pollution potential for selected locations in the United States. J. AppL Meteorol. 6, 1039-1044. 2. Tennekes H., 1973: A Model for the Dynamics of the Inversion Above a Convective Boundary Layer. J. ofatm. Sciences, vol. 30, pp. 558. 3. Betts, A.K., Bruce A.A., 1987: Conserved Variable Analysis of the Convective Boundary Layer. Thermodynamic Structure over Tropical Oceans. J. of Atm.Sci.,44, 1,83-99. 4. Olesen H.R., Brown N., 1992: The OML Meteorological Preprocessor. National Environmental Research Institute, Air Pollution Laboratory, MST LUFT-A122, Denmark. 5. Olesen H.R., Jensen A.B., Brown N., 1992: An operational procedure for mixing height estimation. National Environmental Research Institute, Air Pollution Laboratory, MST LUFT-A96, Denmark. 6. Berkowicz R., Prahm L.P, 1982: Sensible heat flux estimated from routine meteorological data by the resistance method. /. of Applied Meteorology, vo!21,no 12, pp. 1845. 7. Van Ulden A.P., Holtslag A.A.M., 1985: Estimation of atmospheric boundary layer parameters for diffusion applications. J. of Climate and Applied Meteorology, vol 24, pp. 1196. 8. Beljaars A.C.M., Holtslag A.A.M., Van Westrhenen R.M., 1989: Description of a software library for the calculation of surface fluxes. Royal Netherlands Meteorological Institute, Technical reports: TR-112. 9. Tercier Ph., Stu'bi R., Haberli Ch., 1995. Evaluation de la hauteur de la couche de melange dans le cadre du projet POLLUMET. Internal report of the Swiss Meteorological Institute. 10. Stull R.B., 1989: An Introduction to Boundary Layer Meteorology. Atmospheric Sciences Library. Kluwer Academic Publishers, 666 p.