Estimation of Surface Heat Flux and Inversion Height with a Doppler Acoustic Sounder

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 measurements, 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 2/w:Wt * = 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. The zero and one-reliability factors are dependent on the return of more than 25 % of transmitted sound pulses as acceptable echoes. The data correspond to a sampling interval of one hour.

4.1 Mixing heights

Analysis for onset (May and June) and active (July and August) phases of monsoon is presented separately. Figures l(a and b) show the time plot of back-scattered sound 294 L K Sadani and B S Murthy

Figure l(c). Acousticecho return as a functionof height and time on 9th July 1990. intensity (echogram) versus height. It shows the march of convective activity of ABL for morning hours from 0600 to 1200 hr IST. The rise of the temperature inversion layer capping the CBL is a recognizable atmospheric feature on the plots. From this feature, the height of the inversion layer was obtained for the above period and compared with computed heights from the reflectivity profile and a3w/Z profile. Underneath this capping layer, the start of convective activity is visible at 0700 hr IST in the form of rising thermal plumes. After 1100 hr, the capping inversion layer, having lifted up to more than 1000 m, becomes undetectable by sodar echogram and cannot be seen on the facsimile recorder because the upper maximum limit on the recorder is up to 1000 m and is therefore not seen in the figures. Figures l(a and b) are facsimile records of convective activity of ABL during the morning hours on 28th May and 7th June respectively. The synoptic condition of the atmosphere over Kharagpur on the four days of analysis, shown in table 1, indicates that 28th May falls in the pre-monsoon period whereas 7th June falls in the monsoon onset phase. A weekly (Ist-7th June) cumulative rainfall of 50 mm was reported at Alipore (Calcutta) Observatory (MOCC 1990) during the onset phase. Figures 1(c and d) show the thermal structure of the ABL during the morning hours on 9th July and 24th August respectively. On 9th July, the inversion height remained stationary at around 200 m during 0500-0800 hr IST and increased suddenly during 0900-1000 hr IST. On 9th July, the capping inversion layer dissipated after l l00hr IST. On 24th August, the capping inversion layer (figure I d) remained stationary at Surface heat flux and inversion height 295

Figure l(d). Acoustic echo return as a function of height and time on 24th August 1990. around 300m during 0500-0900 hr IST and dissipated after 1100 hr IST causing the ABL to grow beyond the detectable range of sodar facsimile (1000 m). The echogram is noisy because of the background noise, during the period 0930-1100hr IST, making the inversion layer hardly detectable.

5. Discussion and results

5.1 Vertical reflectivity (back-scatter) analysis

The thermal structure detected by sodar provides a reliable estimation of Z~. The figures 2(a, b) and 3(a, b) show the graphs of reflectivity vs. height for the days i.e., 28th May, 7th June, 9th July and 24th August during the morning hours i.e., 0600-1000 hr IST respectively for the Kharagpur site. Each profile is averaged over an hour of observation period. The peak in each profile coincides with the bottom of the elevated inversion layer on facsimile record (figures la, b, c and d). In accordance with the results of Kaimal et al (1976), our acoustic sounder reflectivity profile results show mean minimum reflectivity height between 0.4 Z~ and 0.6 Z~ while from 0900 hr IST onward, the profile shows mean minimum reflectivity height of approximately 0.7 Z i. 296 L K Sadani and B S Murthy

Table 1. Synoptic condition of the atmosphere over Kharagpur on the four representative days during MONTBLEX 1990.

Weekly cumulative Date Synoptic state rainfall (mm)

28th May Pre-monsoon (Not available) 7th June Monsoon onset phase (lst-7th June) 50 9th July Intense convective clouds and (6th-12th July) 235 trough fluctuation 24th August Period of monsoon depression/ (24th-30th August) 65 Low pressure systems

Figure 2(a). Reflectivityprofiles on 28th May 1990.

Figure 2(b). Reflectivityprofiles on 7th June 1990.

The inversion heights are given in column 3 of tables 2-5. The data here show that the increase in the inversion height is associated with an increase in the surface heat flux. This is obvious, because the thermals that originate at the surface traverse larger distances vertically if the surface heat flux is higher and cause more mixing. Surface heat flux and inversion height 297

Figure 3(a). Reflectivltyprofiles on 9th July 1990.

Figure 3(b). Reflectivityprofiles on 24th August 1990.

5.2 Heat flux profile and~inversion heights

Using sonic anemometer data and sodar measured inversion heights, the computed mixed layer velocity scale w, for 28th May and 7th June is found to be around 1.15 m/s between 0900 and 1100 hr. Since sonic data are not available for 9th July and 24th August, the w,, computed using sodar derived heat flux values, are 0-87m/s and 1-16 m/s respectively between 0900 and 1100 hr IST. This shows that the layer below the capping inversion was well mixed by thermals. So we have used equations (5) and (8) which are applicable to a well-mixed layer for the computation of surface heat flux. The linear profiles of a~/Z during the morning hours i.e., from 0600 to 1000 hr IST, are shown in figures 4-7 for 28th May, 7th June, 9th July and 24th August respectively. The linear fit is not always good, because - dw' O'/dZ is not constant in the mixed layer, which is an ideal condition. Each profile is an average over an hour's duration. The ordinate intercept is taken as the inversion height and the abscissa intercept (a3w/Z)o is used for computation of surface heat flux for that hour. Using equation 5, the computed heat flux values and inversion heights are given in columns 7 and 2 respectively of 298 L K Sadani and B S Murthy

Table 2. Comparison of surface heat flux and inversion height on 28th May 1990.

Surface heat flux H Inversion height Zi(m) a~/Z at (W/m 2) Surface surface Time From From reflec- temperature x 103 By By Sky IST profile tivity profile ~ (m 2 s-3) eq. (8) eq. (5) condition

0600-0700 260 210 27"54 1'2 51'79 25-03 clear 0700-0800 390 330 28'37 2'5 54'00 52-28 -do- 0800--0900 325 330 29'08 2"8 99-85 58-69 -do- 0900--1000 390 420 29-96 3-6 90-09 75"68 -do- 1000-1100 410 480 31-48 3"5 86"42 73"95 -do-

Table 3. Comparison of surface heat flux and inversion height on 7th June 1990.

Surface heat flux H Inversion height Z,(m) a~/Z at (W/m 2) Surface surface Time From From reflec- temperature x 103 By By Sky IST profile tivity profile ~ (m 2 s - s) eq. (8) eq. (5) condition

0600-0700 310 180 27"2 0-8 33-55 16"66 7/8 octa 0700-0800 290 270 28"6 3-0 77-92 62"78 -do- 0800-0900 215 300 29"8 4"0 78"22 84.04 -do- 0900-1000 -- 480 31.0 -- 79'10 clear 1000--1100 560 570 32-8 3-6 101-12 76-39 -do-

Table 4. Comparison of surface heat flux and inversion height on 9th July 1990.

Surface heat flux H Inversion height Z,(m) a~/Z at (W/m2) Surface surface Time From From reflec- temperature x 103 By By Sky IST profile tivity profile ~ (m 2 s-3) eq. (8) eq. (5) condition

0600-0700 240 180 26"70 0"38 33"50 7.90 over cast 0700-0800 305 180 27-40 0-26 17-90 5.42 -do- 0800-0900 610 330 28"20 0"75 63.67 15"63 -do- 0900-1000 570 600 28.40 1-40 45-27 29.28 -do- 1000-1100 630 700 28-50 1.35 40.77 28.24 -do-

tables 2-5. For 7th June, it is not possible to compute surface heat flux at 0900 hr using equation (5) as unambiguous linearity was not observed in the ~/Z profile (figure 5). A comparison of inversion height Z~ as estimated above with values obtained by the reflectivity method is shown in columns 2 and 3 of tables 2-5. The comparison shows Surface heat flux and inversion height 299

Table 5. Comparison of surface heat flux and inversion height on 24th August 1990.

Surface heat flux H Inversion height Zi(m) a~/Z at (W/m2) Surface surface Time From From reflec- temperature x 103 By By Sky IST profile tivityprofile ~ (m2 s- 3) eq. (8) eq. (5) condition

0600-0700 160 270 27.8 ff75 24-28 15.65 5/8 octa 0700-0800 350 270 28.7 1.15 66"08 24.08 -do- 08130--0900 450 330 29.4 1"1 44-50 23'08 -do- 0900-1000 550 ~ 500 30'4 2.40 37"95 50"53 3/8 octa 1000-1100 550 ~ 600 31"6 5-00 85-07 105"68 -do-

that the two estimates of Z i are in good agreement, especially during the two time periods between 0900 and ll00hr IST on 28th May. We have computed the surface heat flux (column 6) using the inversion height (column 3) and equation (8) and the values are also shown in the same tables. The sodar model 2000 measures wind speeds in every 30 m layer of air beginning from 60 to 1500 m or to maximum elevation. The 30 m air layer is nothing but one gate resolution. Hence estimated inversion heights can differ by 30 m and subsequently the surface heat flux obtained from equation (8), which incorporates the Z i term, varies by 20% between 0600 and 0700 hr IST and by 12% between 0800 and 1000 hr IST; during this time the layer underneath is well mixed. The surface heat flux computed by equation (5) also depends on the number of points exhibiting linearity in the well-mixed layer, depending upon the ideal condition stated above. Therefore more points on the linear fit indicate the amount of mixing in the layer (figures 4-7). Bandyopadhyay et al (1991) have computed the surface heat flux at the same site by the profile method and the Van Uldan and Holstag method (1985). Their computed heat flux differs from the present values by 36 W/m 2 at 0900 hr IST and by 33 W/m 2 at 1000 hr IST, because the present values are volume averages over the site. Compared with the observed values (Bandyopadhyay et al 1991) at the same site, our sodar overestimates the surface heat flux between 0600 and 0800 hr and underestimates it between 0800 and 1000 hr on 28th May and 7th June. Melas (1990) has also reported that sodar derived surface heat flux H (equation 8) overestimates the measured surface heat flux obtained with the direct technique at low values, and underestimates it at high values. However our computed heat flux values and those measured at the site (Bandyopadhyay et al 1991) are of the same order. Surface heat flux has been computed using equations (5) and (8) on 9th July and 24th August from 0600,to 1000hr IST. As is evident from tables 4 and 5, equation (8) overestimates the surface heat flux compared to that by equation (5). Table 1 shows that 6th-12th July is characterized by intense convective clouds and trough fluctuations. A cumulative weekly rainfall (6th-12th July) of 235 mm was reported. The decrease of surface heat flux from 7th June to 9th July can be attributed to the intensification of the monsoon and increased precipitation over the station (Kharagpur). The surface heat flux on 24th August is nearly of the same magnitude as that observed on 9th July. 400 400~, 400 MAY 28 th 0600 hr "~ MAY 28 th 0700 hr MAY 28 th 0800 hr

300 i1 ~300 1 *"~ ..300

~200 g~ (3 oo1\ \ ~:200 ILl "1- .,,,, g~ s 1oo loo ~2 ...... "\ r~ 0 0 ...... i ...... i ...... i 0.00 1.00 2.00 3.00 0.00 1.00 2.00 3.00 0.00 2.00 4.00 6.00 8.00 "w ~.3/z "* I 0 3 ~.3/z ".10 3 ~.3/z "*I 0 3

600 800 MAY 28 th 0900 hr MAY 28 th 1000 hr

-'-',400"5

I-- "l- . ~

IJJ "1-200 T200

0 ., ...... , ...... , 0 i,' ...... , ...... , ...... i o.oq 2.oo ,.00 e.oo 8.00 0.00 2.oo ,.oo ,.oo 3.oo 1o.oo ~.~/z ".I0 3 ~'-~//Z "'10 3

Figure 4. a~lZprofiles on 28th May 1990. 400 600 600 JUNE 7 th 0600 hr JUNE 7 th 0800 hr *

300 JUNE 7 th 0700 hr ~',400 J DE ~',400 t~ v v T~200 i I t.,I -I- Ld "r2o 0 "I-20 o tOO * =a.

0 o , ...... , ...... i ...... t ...... i 0 0.00 0.50 l.~o J.5o o.oo 1.oo 2.o0 3.o0 4.00 0.00 2.00 4.00 8.00 8.00 10.00 ~.3/z "* 10 ~ ~3/z ".10 ~ o-,3/z "* 10 ~

800 800 JUNE 7 t~ 1000 hr

w JUNE 7 th 0900 hr 600 6OO

DE v

~400 ~400

"-r 1 $ 2OO 20O

0 ...... , ...... 1 ...... , 0 ...... j -i ...... ~ 0.00 2.00 4.00 8.00 0.00 2.00 4.00 6.00 O%a/z "* 10 3 o",~/z ",1o ~ Figure 5. a~/Z profiles on 7th June 1990. t~ 300 JULY 9 TH 0600 hr 350 =$ JULY g TH 0700 hr 650- JULY 9 TH 0800 hr d,

~50 lk ~,250, ~---,5o ~,~200 r.~ I..- I.- "1- "1'- (3 (3 _=. ~150 bJ "r" -r- 150 "r" 25 0

100 :#

50 ...... ~ ...... ~ ...... 5 0 "-t 0.00 0.10 0.20 0.30 0.40 0.50 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.00 0.50 1.00 1.50 2.00 ~/z "* 10 3 ~3/z .10 3 ~3/z ".10 ~ JULY 9 TH 1000 hr JULY 9 TH 0900 hr u

850 850 =k'=k

"5650 ~eso I,- I ** I-- "1- -r ~ 450 ** ,,~ 8 450 "7" I

250 250

50 '50 ,,., ...... h,~ ...... ~, ..... 0.00 0.50 1.00 1.50 0.00 0.50 1.00 1.50 2.00 2.50 ~/Z ".10 3 Figure 6. a~/Zprofiles on 9th July 1990. 3o0 3. * AUGUST 24 1t"1 0600 hr 24 TH 0700 hr 450 * AUGUST 24 TH 0800 hr 350

~E ~ 250 I.- _0250 **•T hJ "I- \ I50 ,oo1\ . t50 \\, * N\ , 6o 1 ...... ~ ...... * ...... 5O ...... i ...... i ...... i,, 50 ...... i ...... i ...... J,, 0.00 0.50 t.O0 1.60 2.00 2.50 0.00 0.50 1.00 1.50 0.00 0.50 1.00 1.50 r ".10 3 ~,,3/z *10 3 ~.3/z "'10 3 r ;:P

AUOUST 24 TH 0900 hr AUGUST24 TH 1000 hr 850 I ~ * * 850 :1 =k "~ 650 -] * . ~85o I *s

"1- .

60 1 ...... ~ ...... ~'""t ...... 50 .... ~ ..... 0.00 1.00 2.00 3.00 4.00 5.00 0.00 2.00 4.00 8.00 ~,~/z ".I0 ~ ~,.3/z '~ I 0 3

Figure 7. ~/Z profiles on 24th August 1990. 304 L K Sadani and B S Murthy

28 th MAY 1990 7 th JUNE 1990 1.0 1. 0 ~ ~:~-~** 0600 hr ~=~: 0600 hr ::::: 0700 t 1 ~ I :::::0700 0.8 -:::~0800 O. a I t 1 I ..... 08OO I 1 I ~ :::::.OgO0 1000 I000 0.6 0.0

N +-q 0.4 0.4

0.2

0.0 0. 0 ...... ,...... ,...... ,...... ,...... , 0.00 0.20 0.40 0.80 0.00 0.00 0.20 0.40 0.00 0.80 t.O0

a~(m 2 s- z)

Figure 8(a). Profiles of vertical velocity variance (a~) on 28.5.90 and 7.6.90.

9 th JULY 1990 24 th AUGUST 1990 1.0 1.0 ~ 0600 hr *~*=~ 0600 hr :r162 ~ 0700 6. a O. 8 ::=:: 0800 :=:::(~00 ;:;:-: OgO0 :::=::: 1000 .to. s 0.8

i,4 0.4 0.4

0.2 0.2

O. 0 ...... , ...... ,..:..~., o. o ...... , ...... i ...... , ...... , ...... , 0.00 0.I0 (I.20 0,30 0.60 0.50 ,5.60 0.oo o.2o o.4o 0.60 0.8o t.~

o~(m2s -2) o~.(m ~ s- '1

FigureS(b). Profiles of vertical velocity variance (a,~)2 on 9.7.90 and 24.8.90.

The inversion height during the late morning hours, i.e., 0900-1100 hr IST, is more during the active monsoon period (July and August) compared to that during the pre-monsoon period (May). The growth rate of the ABL from 0900 to 1000 hr is 270 m/hr during the active phase (24th August) whereas it is 180 m/hr during the onset phase and 170m/hr during the relatively weak phase of the monsoon.

5.3 Vertical velocity variance profiles

The graphs of vertical velocity variance profiles for 28th May and 7th June (figure 8a) from 0600 to 1000 hr IST correspond to the rise of the temperature inversion layer with the increasing convective activity. Figure 8(a) presents five variance profiles, each being calculated for an hour's period beginning from 0600 hr IST. The altitude is normalized by the height of the inversion evaluated from the reflectivity profile. It should be Surface heat flux and inversion height 305

Table 6. Hourly averaged normalized heights of maximum variance and their range.

Z/Z, range of Time Z/Z, corresponding to constant maximum Date IST maximumvariance (a~) variance(a~)

28.5.90 0600 0"57 -- 0700 0"36 0.36-0'45 0800 0"36 0'36-0-37 0900 0"27 0-27-0"63 1000 0'19 0"19-0'63 07.06.90 0600 0"67 -- 0700 0-33 0"33-0-55 0800 0'30 0.30-0.40 0900 0"38 0.38-0.44 1000 0'26 0"3-0"68

Table 7. Hourly averaged normalized heights of maximum variance and their range.

z/z, range of Time Z/Z~ corresponding to constant maximum Date IST maximum variance (a~) variance(~r~)

9.7.90 0600 0.32 -- 0700 0.32 -- 0800 0.36 -- 0900 0.54 0.54-0.60 1000 if30 0.30-0.60 24.8.90 0600 0.22 -- 0700 0.56 -- 0800 0-20 -- 0900 0-24 0.24-0.50 1000 0-26 0.26-0-56

emphasized that the vertical velocity variance is not constant in the mixed layer. The measured value aw2 (figures 8a and b) is small near the surface and increases to a maximum in the middle of the ABL and then decreases with height (Caughey 1982). From table 6 we see that Z/Zi corresponding to maximum variance (a~) decreases while the range of constant maximum variance increases from 0600 to 1000hr as convective activity increases. o-w2 averaged in the height interval 0.19 Zi < Z < 0"63 Z~ is approximately equal to 0.49 at 1000hr IST on 28th May and 0"66 at 1000hr IST on 7th June. Figure 8(b) presents variance profiles from 0600-1000hr IST on 9th July and 24th August. The magnitude of variance (a~) on 24th August is relatively high compared to that on the other three days. On 9th July, a w2 in the mixed layer (0.1Z~-0.7Z~) has fluctuated much during 0900-1100 hr (figure 8b) whereas it has remained constant on 24th August. As shown in table 7, the ABL below the capping inversion gets well mixed by 0900 hr and remains constant in the height interval 0"2Z~-0"7Z v 306 L K Sadani and B S Murthy

6. Conclusion

In this paper, we have described the measurement of surface heat flux in the CBL using two different methods proposed by Caughey and Readings (1974) and Wyngaard (1986) respectively. These methods are applicable to a well-mixed layer when the capping inversion is underneath the detection range of the sodar. Surface heat fluxes computed by these methods are on the same order of magnitude as those measured by the tower. The peak in the reflectivity profile coincides well with the base of inversion on the echogram. The inversion heights computed from linear extrapolation of a~/Z vs Z profile agree well with those obtained from the reflectivity profiles. The maximum value of the vertical velocity variance a~ is reached at a rather low level of 0"2Z~. It remains constant in the height interval 0"2Zi-0"65Z i on the four days during 0900-1100 hr. The height of the ABL in the late morning hours (0900-1 I00 hr) is greater during the active phase of the monsoon (July-August) than during the pre-monsoon (May) and onset (June) phases, inspite of a decrease in the surface heat flux from May to August. But on each individual day, the ABL height is directly proportional to the surface heat flux. This shows that the interaction between the monsoon and the ABL over the trough region is quite complex and requires the understanding of the physical processes involved. Doppler sodar measured vertical velocity variance can be used to make reliable estimates of the ABL height and surface heat flux in the convective boundary layer.

Acknowledgements

The authors would like to thank their colleagues of the boundary layer group of the Instrumental and Observational Techniques Division for the co-operation they extended during the period of observation of MONTBLEX 1990. The MONTBLEX-90 was sPonsored and supported by the Department of Science and Technology, Government of India. The authors wish to express their thanks to the DST.

References

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