Proc. Indian Acad. Sci. (Earth Planet. Sci.), Vol. 105, No. 3, September 1996, pp. 289-307. Printed in India. Estimation of surface heat flux and inversion height with a Doppler acoustic sounder L K SADANI and B S MURTHY Indian Institute of Tropical Meteorology, Pune 411008, India Abstract. In this paper, acoustic sounder (sodar) derived vertical velocity variance (a2~) and inversion height (Z,) are used to compute the surface heat flux during the convective activity in the morning hours. The surface heat flux computed by these methods is found to be of the same order of magnitude as that obtained from tower measurements. Inversion heights derived from sodar reflectivity profiles averaged for an hour are compared with those obtained from the a~/Z profile. Variation of a2~ in the mixed layer is discussed. The data were collected during the Monsoon Trough Boundary Layer Experiment 1990 at Kharagpur. The analysis is made for four days which represent the pre-monsoon, onset, active and relatively weak phases of the summer monsoon 1990. The interaction of the ABL with the monsoon activity is studied in terms of the variation of inversion height, vertical velocity variance and surface heat flux as monsoon progresses from June to August. Keywords. Sodar; vertical velocity variance; inversion height; surface sensible heat flux. 1. Introduction Sodar is now widely used to study the thermal as well as the wind structure of the Atmospheric Boundary Layer (ABL). Sodar derived vertical velocity variance (a 2) is of utmost importance in the computation of surface sensible heat flux in the Convective Boundary Layer (CBL). The sodar back-scattered intensity record (echogram) is used to see the erosion of night time ground-based inversion and its uplifting by thermal plumes that originate at the surface during the day time. Sodar estimates of ABL parameters can be even more representative than direct measure- ments, since they are volume averages which are therefore less sensitive to local conditions (Melas 1990). According to Wyngaard (1986), the accuracy of indirect estimates of ABL parameters can be comparable to that of the underlying similarity relationship. In the present study we have computed surface sensible heat flux by two different similarity methods proposed by Caughey and Readings (1974); McBean and McPherson (1976); and Wyngaard (1986). The analyzed data were taken with a three-axis monostatic Doppler sodar model 2000, manufactured by M/s Aeroviron- ment Inc., USA. 289 290 L K Sadani and B S Murthy 2. Method of computation 2.1 Variance method Using the similarity theory, McBean and McPherson (1976) and Yokogama et al (1977) have shown that vertical velocity variance can be expressed as 2 I- / --7-s,d [7 g ----;-~,) ] (7 w -- A Lzt,-,, ,,, a2 , (1) where A = universal constant, -u'w'dU/dZ = local mechanical production of turbulence, dU/dZ = mean wind shear, o/O.w% = local buoyancy production of turbulence, Z = height, g = acceleration due to gravity, o" = virtual potential temperature fluctuation, U' = longitudinal velocity fluctuation, W' = vertical velocity fluctuation. In a well-mixed layer, the mechanical production is negligible and equation (1) can be simplified to a z ~- a(Z'9/O'w'O'v) 2/3, (2) where ~ = A62/3 ~-1.4 (see Caughey and Readings 1974; McBean and McPherson 1976). Accordingly, a plot of a~/Z versus Z gives the local heat flux: 3 tr___~= a3/2.0/0" w' 0'~. (3) Z Therefore, the local heat flux profile can be determined by using the vertical velocity variance given by sodar (for details see Weill et al 1980). In the well-mixed layer, dOUdZ = 0 and dOo/dt = -dw'O'JdZ = constant and the heat flux decreases linearly with height. Therefore, 3 -~O"w = o~3/2.o/O.Qo(1 - Z/h.), (4) where Qo = (w'O;) at Z = 0 is the temperature flux at the surface and h. is the height at which temperature flux vanishes by linear extrapolation. The buoyancy flux at the surface (w'O'o)o is related to the temperature flux (w'O')o by the equation (see Garratt 1992) (w'O'o)o=(w'O')o[1 + 0"61ff~1, where fl is known as the Bowen ratio and 7 = Cp/2 is called the psychrometer constant. The humidity correction term A = 1 + 0"6107/fl changes from 1-10 for moist air (fl = ff75) Surface heat .flux and inversion height 291 to 1.0l for very dry air (fl = 10). At the surface 0 = T, so Surface heat flux H = (a3w/Z)o (T/y) ~- 3/2 p Cp, (5) where p is the density of air and Cp is the specific heat at constant pressure. (a3w/Z)o can be obtained by extrapolating the linear part of the profile to the surface. Therefore the surface heat flux can be computed from the vertical velocity variance profile. By this method we get surface heat flux in moist convective conditions whose value is 10% more than the heat flux measured in dry convective conditions (Garratt 1992). 2.2 Inversion height method Wyngaard 11986) suggested that for the middle-mixed layer, a Wt2/w: * = b, (6) where b is a constant proposed to be 0.4, w. is the mixed-layer velocity scale given by [Z,Hg] ~/3, w, = L~J (7) and Z, = height of the inversion base in CBL. Melas (1990) estimated that b = 0-45 in the height interval 0.1 Z~ to 0-7 Z~. We have computed b from sonic anemometer and sodar data and found it to be approximately equal to 0.45-0.5 in the same height range 0"1 ZrO'7Z ~. From equations (6) and (7), we can write surface heat flux, H = b- 3/2 (g/O)- i p C, ~3/Zi. (8) Therefore with Z i (the height of ABL) known from reflectivity profiles and trw averaged in the above height interval, the surface heat flux H can be computed. The H so computed by equations (5) and (8) has been compared with that computed from the tower data by the profile method. The temperature structure of ABL as inferred from the sodar echogram provides a reliable estimate of mixed layer depth (Zi) in the convective boundary layer (CBL). The peak in the echo-intensity profile coincides with the bottom of the capping inversion layer on the echogram. Kaimal et al (1982) have shown that sodars are able to locate the inversion base with very good accuracy. Melas (1990) has reported that sodar estimates of Z~ are in very good agreement with rawinsonde measurements. In the present analysis, we have used back-scattered intensity profiles averaged over a one- hour period to estimate Z,. These values are compared with those obtained by linear extrapolation of a3./Z vs Z profile. 3. Site and its general features A monostatic three-axis Doppler sodar, model 2000 manufactured by M/s Aeroviron- ment Inc., USA, was installed by the authors at Kharagpur (22 ~ 25'N, 87 ~ 18'E) in the 292 L K Sadani and B S Murthy month of April 1990 for MONTBLEX. The three antennae were configured in an L pattern, one pointing towards geographic East and the second pointing towards geographic North. Both antennae are inclined at 30 ~from the vertical. At the centre the third antenna points exactly vertically up. Tilted antennae are pointed against the prevailing surface wind direction so that the sound pulse reaches a maximum height (1500 m) and gives wind speeds at high levels. The sodar site enjoys an uninterrupted fetch of more than 500 m towards south, the direction of the summ6r monsoon wind. The site beingga flat fairly open terrain, the influence of topography on wind characteristics is expected to be small. The mean seasonal weather pattern at this site is determined by the presence of the monsoon trough during the Indian summer monsoon season, i.e., from June to August. Upon the onset of monsoon the dry convection changes over to deep moist convection. One of the objectives of MONTBLEX is to study the diurnal variation of ABL under the monsoon trough. In this paper we attempt to verify whether the similarity methods can be used to compute surface heat flux during the disturbed conditions of ABL. 4. Observed data The sodar measures vertical velocity W(m/s) until the end of the sampling interval and evaluates the standard deviation by standard software. The manufacturer specified Figure l(a). Acoustic echo return as a function of height and time on 28th May 1990. Surface heat flux and inversion height 293 Figure l(b). Acoustmecho return as a functionof height and time on 7th June 1990. range for W and a w is 0-3.7 m/s and 0-1.9 m/s respectively. The vertical velocity accuracy and aw resolution are 0.1 m/s. The sodar-observed vertical wind data (from May to August 1990) d~aring the onset and active phases of the monsoon were studied. Our measured value of W lies between 0-16 and 0-48 m/s. Analysis has been done for four representative days of the different phases of monsoon, i.e., 28th May, 7th June, 9th July and 24th August 1990. On these days the CBL had a well-defined capping inversion with rising thermal plumes below (see figures la, b, c and d). Heat fluxes and inversion heights have been computed for these four days. The sodar uses a standard electronic filtering process for the good quality of data. The data with zero reliability factor (R) were used for the present study. The data with reliability factors of 0 and 1 are considered best according to the filtering procedure adopted for the data acquired with this instrument.