Boundary Layer Parametrization for Atmospheric Diffusion Models by Meteorological Measurements at Ground Level.

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1 IL NUOVO CIMENTO VOL. 17 C, N. 2 Marzo-Aprile 1994 Boundary Layer Parametrization for Atmospheric Diffusion Models by Meteorological Measurements at Ground Level. R. BELLASIO('), G. LANZANI('), M. TAMPONI(2) and T. TIRABASSI(~) (1) Dipartimento di Fisica dell'universit5 - Milano, Italia (2) PMIP, 4 a UO, Fisica e Tutela dell'ambiente - Milano, Italia (3) FISBAT-CNR -Bologna, Italia (ricevuto il 28 Gennaio 1993; approvato il 25 Ottobre 1993) Summary. - Over recent years several theoretical and experimental works have made it possible to evaluate the basic parameters describing the atmospheric boundary layer by means of elementary meteorological measurements in proximity to the ground. This has opened up the possibility of utilizing atmospheric pollutant dispersion models able to use direct evaluations of atmospheric turbulence through friction velocity and the Monin-Obukhov length. The present paper provides an application of these new techniques in the Milan area. PACS Sz - Air quality and air pollution Introduction. It is widely recognized today that air quality is a crucial factor influencing public health. While air quality depends on the quantity of pollutants emitted into the atmosphere, a significant role is also played by meteorological variables. For example, in most cases the pollutant threshold is exceeded in Milan, one encounters strong atmospheric stability, a condition in which pollutants are less dispersed and therefore less diluted. This poses the necessity of describing the low levels of the atmosphere, most of the principal dispersion processes take place. Up to now, in the practical models for air quality control and forecast (eg. those of the U.S. EPA (United States Environmental Protection Agency)), the description of the low layers of the atmosphere is based on semi-empirical categories, such as those proposed by Pasquill-Gifford. However, in recent years, following the works of Holtslag and Van Ulden [1], Weil and Brower [2], Van Ulden and Holtslag [3] and Hanna and Paine [4], it turns out that the fundamental parameters for describing the characteristics of the 163

164: R. BELLASIO, G. LANZANI, M. TAMPONI and T. TIRABASSI atmospheric surface and boundary layers can be evaluated by means of measurements at ground level.

2 164: R. BELLASIO, G. LANZANI, M. TAMPONI and T. TIRABASSI atmospheric surface and boundary layers can be evaluated by means of measurements at ground level. This has allowed the development of models that describe pollutant diffusion on the basis of an input of ground-level meteorological data (acquired by means of an automatic network), but which are able to directly evaluate atmospheric turbulence using the values of the Monin-Obukhov length and friction velocity, instead of applying empirical classes such as those proposed by Pasquill-Gifford. The said models are not yet among those offered by the U.S. EPA, as they are still undergoing study to facilitate their utilization. The European scientific community involved in the study and development of atmospheric-diffusion models aims at a unitary choice of a coherent group of models to constitute the basis of future decisions and investigations (in analogy with the work performed by the EPA in the United States). In this context, models that make direct evaluations of atmospheric turbulence have been proposed. This is what emerged at a recent conference (Objective for Next Generations of Practical Short-Range Atmospheric Dispersion Models), held in Denmark in May 1992, which was organized precisely to obtain a harmonization of European models and to establish their basic scientific principles. This work presents an application of the new techniques in the characterization of the atmospheric boundary layer in the area of Milan Mgorithms and procedures for the determination of L and u.. To determine the wind and temperature profiles and all the other parameters useful for a characterization of the PBL (Planetary Boundary Layer) it is necessary to evaluate the friction velocity u, and the Monin-Obukhov length L. During the day, in unstable conditions, one is able to determine u. and L if the sensible heat flux, the horizontal wind speed, the air temperature and the roughness are known by means of the Holstlag-Van Ulden method. This method permits the calculation of the friction velocity u. and the Monin-Obukhov length L, in the case of an unstable boundary layer, by means of the following equation: (1) u, = ku~ [ln (z/zo) -- ~m (z/l) + ~m (zo/l )] -1, (2) L = pcptu3, kgqh ' k is the von Karman constant (k = 0.4), z0 the surface roughness length, u~ the wind speed at height z, T is the air temperature, g the acceleration of gravity, p the density of air, Cp the specific heat at constant pressure, Qh the sensible heat flux and ~bm a stability function defined as (3) ~r = 21n(0.5(1 + r -FIn (0.5 (1 -F ~bme)) - 2 arctg(~bm 1) + u/2, and (4) Cm = ( z/L) -1/4 From (1) and (2), u. and L can be solved by iteration, when T, Qh, z0 and uz are known. The computation starts with an estimate of u. according to (1), with the

3 BOUNDARY LAYER PARAMETRIZATION FOR ATMOSPHERIC DIFFUSION ETC. 165 initial condition 1/L = O. Then, with (2), an estimate for L is obtained which is used in a new computation of u, by way of (1). All subsequent calculations improve the estimate of u,. We followed the iterative process until we achieved an accuracy of 1% in the successive values of L. As the sensible heat flux Qh was not directly available among the input data, this value was estimated from the measurements of the net radiation. Thus, the surface radiation budget can be written as (5) Q,+A=Qh+LE+G, Q, is the net radiation (W/m2), A Qh LE G is the heat flux of anthropogenic origin (W/m2), is the sensible heat flux (W/m2), is the latent heat flux (W/m2), is the soil heat flux (W/m2). The heat flux of anthropogenic origin can be neglected in practice, since it is small compared to the other terms [5]. The relation between LE, Q,, Qh and G can be established following the approach of Penman-Monteith [6], but this requires many input parameters. Therefore, it is convenient to follow the simplified version of this approach proposed by De Bruin and Holtslag [7]. In this way, we obtain (6) LE = (Q, - G) + fla, 1 + (V/s) ~qs (7) s -- ST' qs being the saturation specific humidity and cp (8) v = T' Cp being the specific heat of air at constant pressure and 2 the latent heat of water vaporization; a and fl are empirical constants. Table I shows the values of ~/s proposed by Holtslag and Van Ulden[1], while table II gives the values of a suggested by Hanna and Chang [8]. It is assumed [8] that fl = 20 W/m 2. G is linked to Q, by a simple relation [1]: G=cQ,, c for rural areas rises from 0.05 to 0.25, while assuming in urban areas a value of roughly 0.3 [9].

4 166 ~ BELLASIO, G. LANZANI, M. TAMPONI and T. TIRABASSl TABLE I. -- ~/S as a function of T as proposed by Holtslag and Van Ulden [1]. T(~ ~/s l TABLE II. - Values of ~ proposed by Hanna e Chang[8]. Conditions 0.0-4) desert arid rural areas rural areas without rain for several days urban areas wet rural areas oceans and lakes at more than 10 km from the coast Thus, Qh can be determined. The approach can be utilized also in cases the measurement of net radiation is not available: instead, it can be calculated on the basis of solar elevation and percentage of clouds present in the sky, according the scheme proposed by Holtslag and Van Ulden [1]. One obtains (9) Q. = (1 - r) RC + RE + RU, r is the surface albedo, assumed to be equal to 0.12 for urban areas [10], RC RE RU is the incoming short-wave radiation from the atmosphere, is the incoming long-wave radiation from the atmosphere, is the outgoing long-wave radiation from the surface. This gives (10) (1 -- r) RC + C1T ~ -- at 4 + C2N 1 +C3

5 BOUNDARY LAYER PARAMETRIZATION FOR ATMOSPttERIC DIFFUSION ETC. 167 and (11) RC = (a~ sin ~b + a2)(1 + b~n~), T is the air temperature (~ a N is the Stefan-Boltzmann constant, is the cloud cover, 4) is the solar elevation, ai, as, b~, b2, C~-Ca are empirical constants [1]: a~ W/m s, a2 =--30 W/m 2, b I , b , Cl = W/(m 2 K6), C W/m s, Ca ((1 -- a) T/s + 1) (?/s + 1), ~,? and s assume the values mentioned above. During the night, in stable conditions, the Weil-Brower method [2] can be utilized for the direct determination of both u, and L. In this case, we use the scale temperature 0,, defined by: 0, ---- Qh pcp u, " The method is based on an observation reported by Van Ulden and Holtslag [3], which shows that 0, is proportional to (u,) 2 for small values of u,, more or less constant for medium values of u,, and proportional to 1/u, for very large values of U,. One can determine 0, (in Kelvin degrees) in two ways. The first is empirical, valid for medium values of u, [1]: (12) 0,, = 0.09 ( NS), N is the fraction of cloud cover. A second estimate of 0,, valid for small values of u,, is TCDN U 2 (13) 0, b~,zg b m = 4.7, Cos = 0.4/ln (Z/Zo).

$Thus, having the measurement of u at height Zm, according to the analytical solution of Weil and Brower [2], one obtains.u0 (14) u, -- 2 -- \C~)/2u(z~] ] ]' Uo = (4.7zmgO,/T) l/z, CDs = 0.4/In (Z/Zo).$

6 168 R. BELLASIO, GI LANZANI, MI TAMPONI and T. TIRABASSI Bearing in mind the above considerations, the smallest value between 0,, and 0,2 is chosen as 0,. Thus, having the measurement of u at height Zm, according to the analytical solution of Weil and Brower [2], one obtains.u0 (14) u, \C~)/2u(z~] ] ]' Uo = (4.7zmgO,/T) l/z, CDs = 0.4/In (Z/Zo). With u, known, L can be immediately calculated, obtaining Qh from the definition of 0, Application of the methods in the Milan area. The techniques described in the preceding section were applied in the area of Milan. Two typical days were chosen, characterized by different meteorological conditions, one in summer, I:20/07/90 and one in winter, II:15/12/90. Day II was representative of a condition of prevalent winter time stability, occurring in coincidence with a situation of high pressure, clear sky and weak wind. Day I represents a typical summer condition with high atmospheric turbulence during the day in coincidence with the good level of solar radiation and nocturnal stability due to ground cooling in the absence of cloud and weak wind. Both days were chosen attempting to avoid perturbed conditions in which the algorithms described here are not immediately applicable due to the ensuing spatial alteration of the profiles of micrometeorological variables. In particular, the two days were characterized by temperature profiles at 6.00 a.m. and a.m., which differ greatly in the first 500 m of PBL (planetary boundary layer), showing prevalently stable conditions for the winter day (fig. 1). Moreover, the temperature values are much higher on the summer day compared to the winter day: for example, slightly less than 30 ~ was recorded at ground level at midday in summer while less than 5 ~ was found in winter (fig. 2). The thermal profiles reported in fig. 1 were measured by the Military Airforce at Milan Linate airport, situated in a rural area just outside Milan, while the groundtemperature trends in fig. 2 were recorded at the Rodano station of the Milan air quality control network, close to the airport. The hourly trends of net radiation confirm the results of the thermal-profile analysis (fig. 2). In particular, the negative nocturnal values of --7 mw/cm 2 confirm the absence of cloud during the night for both days. However during the diurnal period of the summer day, a peak value of approximately 50 mw/cm 2 was recorded, indicating the presence of strong convective motions giving rise to high instability. Conversely, the winter day had a peak value of less than 10 mw/cm 2. The wind speed measured at 10 m height at the Rodano station (fig. 3) shows

7 BOUNDARY LAYER PARAMETRIZATION FOR ATMOSPHERIC DIFFUSION ETC OO g 29O 280i 270 q 260 1, z (m) Fig. 1.- Temperature profiles at 6.00 and a.m. on the days 20/7/90 ( a.m., -A a.m.) and 15/12/90 (II) (O a.m., -El a.m.). (I) ( hour Fig Daily evolution of net radiation (Q,) and temperature (T) on the days 20/7/90 (I) (41- Q,, -r T) and 15/12/90 (II) (-~- Q,, -f5- T). modest values (less than approximately 2 m/s) through the entire period of both days. It should be mentioned that, while the temperature measurements were recorded at rural sites, the same cannot be said for the net radiation measurements, which were performed at the city centre station of Milan, via Juvara, since there were no sensors available at other sites. Figure 4 shows the hourly trends of the mixing layer thickness (H) calculated in unstable conditions using the method of Panofsky and Dutton [10]: T(t) -- T O (15) //(t) -, F-A

8 170 R. BELLASIO, G. LANZANI, M. TAMPONI and T. TIRABASSI ~ , 89, i r ' 6 ' 8 '1'0'1'2~14 '1'6' I~8'2(} '22'24 hour Fig Daily evolution of the wind speed at the ground on the days 20/7/90 (1) (~-) and 15/12/90 (II) (-~) O0 600 ~500 aoo 3OO 2OO IO hour Fig Daily trend of the mixing layer height (H) on the days 20/7/90 (I) (-i) and 15/12/90 (II) (-~-). T = ~ represents the adiabatic temperature gradient in dry air and A- 0T 0z is the temperature gradient, calculated at dawn, To is the temperature at dawn, and T(t) is the temperature at time t for which the value of H is to be found.

9 BOUNDARY LAYER PARAMETRIZATION FOR ATMOSPHERIC DIFFUSION ETC. 171 In stable conditions, we used the Zilitinkevich method[ill (16) H _~ 0.37 /u,_.l ~]f' f is the Coriolis parameter?_..._ (17) f= 292 sin r ~ is the angular velocity of the Earth and r the latitude. This formula gives results that are affected by large errors due to the high wind speed arising from the very high value of L in this case. In such situations h is limited by its value in the neutral case [3]. In neutral conditions it is possible to use the following formula: (18) H --~ 0.3 u--2-*. ]fl If there is an inversion at height H~,the height of PBL is the minimum between H and H~. It should be noted that on day II the mixing-layer depth remains very low throughout the entire 24-hour period, presenting a weak maximum at 2.00 p.m., that is a few hours after the maximum solar radiation. On day I during stable conditions, similar mixing-layer height values were found to those of day II, while during the unstable conditions a gradual and sustained evolution was observed until 7.00 p.m. During the period of instability the PBL height went from 200 m up to a maximum of approximately 850 m height. From 7.00 p.m. to 8.00 p.m. a sharp drop was noted, caused by a sudden passage from unstable to stable conditions. Figure 5 shows the trend of 1/L calculated for the two days. Day I reveals I ~ -o ' 1'2' 14 1'6 ~1'8 ' 20 '12 ' 24 hour Fig Daily trend of the inverse of the Monin-Obukhov length (l/l) on the days 20/7/90 (I) (-D) and 15/12/90 (II) (-4~-).

10 172 R. BELLASIO, G. LANZANI, M. TAMPONI and T. TIRABASSI a maximum convectivity in coincidence with the day time minimum of mechanical turbulence (fig. 3 and 6) at a.m. On day II, 1/L remains more or less constant throughout the 24-hour period, a behaviour that was expected in relation to the algorithms used for the determination of L as described above. Figure 6 reports the trends calculated for the friction velocity u, for the two days. Itcan be seen that the values of u, reflect the trends of wind speed at the ground (fig. 3). In fact, u, is lower on average on day II compared to day I and presents peak values in coincidence with those of wind velocity at the ground. Figure 7 shows the vertical profiles of the eddy diffusivity coefficients, the momentum and heat coefficients being calculated for the surface layer between ~ hour Fig Daily trend of the friction velocity (u,) on the days 20/7/90 (I) (41-) and 15/12/90 ~II) (-~) O ) '0 height (m) 80 Fig Profiles of momentum (kin) (-O-) and heat (kh) (-l) diffusion coefficients on 20/7/90 between a.m. and 1.00 p.m.

11 BOUNDARY LAYER PARAMETRIZATION FOR ATMOSPHERIC DIFFUSION ETC a.m. and 1.00 p.m. on the summer day. These were obtained using the relations (19) Km -- ku. z ~bm ' ku. z (20) gh -- --, Ch ~bh and Cm are for the various stability conditions: - stable Z (21) Ch=~bm L, - neutral (22) ~bh = ~bm = 1 (23) (24) - unstable t L/- 1/2 ~bh = ) The heat diffusion coefficient was found to be very pronounced. In fact, while the mechanical turbulence behaved in much the same way with regard to both momentum and heat transport, convective turbulence more strongly affects heat transport than momentum transport Conclusions. The present work presents methods for calculating the parameters characterizing the PBL used in pollutant diffusion models, by means of elementary ground-level measurements, such as air temperature, wind speed and net radiation or, unavailable, cloud cover. These measurements, based on the data simply recorded by air quality control networks, permit the development of a new generation of diffusion models which are capable of making a theoretically more correct evaluation of atmospheric turbulence than that obtained through empirical classes, like those of Pasquill- Gifford. Moreover, the present work sets out to provide some examples of how the proposed algorithms can be applied in an area studies with diffusion models have previously been performed. This was done with the intention of utilizing in the future the new generation of models.

12 174 R. BELLASIO, G. I~d~IZANI, M. TAMPONI and T. TIRABASSI The authors wish to thank Provincia di Milano, USSL 75/III of Milan and the Italian Military Airforce for providing the data used. This work was partially financed by the Strategic Project of the Italian Research Council,Aree Metropolitane e Ambiente,. REFERENCES [1] A. A. [2] J. C. [3] A. P. [4] S. [5] T. [6] J. [7] H. [8] S. [9] W. [lol H. [111 s. M. HOLTSLAG and A. P. VAN ULDEN: J. Clim. Appl. Meteor., 22, 517 (1983). WEre and R. P. BROWER: JAPCA, 34, 818 (1984). VAN ULDEN and A. A. M. HOLTSLAG: J. Clim. Appl. Meteor., 24, 1196 (1985). R. HANNA and R. J. PAINE: J. Clim. Appl. Meteor., 28, 206 (1989). R. OKE: Boundary Layer Climates (John Wiley & Sons, New York, N. Y., 1978). L. MONTEITH: Q. J. R. Meteor. Soc., 107, 1 (1981). A. R. DE BRUIN and A. A. M. HOLTSLAG: J. Appl. Meteor., 21, 1610 (1982). R. HANNA and J. C. CHANG: Boundary Layer Meteor., 58, 229 (1992). R. OKE: Q. J. R. Meteor. Soc., 108, 1 (1982). A. PANOFSKY and J. A. DuvroN: Atmospheric Turbulence (J. Wiley & Sons, 1983). S. ZILITINKEVICH: Boundary Layer Meteor., 3, 141 (1972).

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