Directory UMM :Data Elmu:jurnal:A:Advances In Water Resources:Vol23.Issue4.2000:

Advances in Water Resources 23 (2000) 339±348

Surface heat ¯ux estimation with wind-pro®ler/RASS and radiosonde
observations
Jennifer M. Jacobs a,*, Richard L. Coulter b, Wilfried Brutsaert c
a

Department of Civil Engineering, The University of Florida, Gainesville, FL 32611, USA
Environmental Research Division, Argonne National Laboratory, Argonne IL 60439, USA
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA

b
c

Received 20 August 1998; received in revised form 28 June 1999; accepted 7 July 1999

Abstract
A bulk ABL similarity approach was used to make regional estimates of the sensible heat ¯ux by combining surface temperature
measurements with mixed layer temperature and wind speed pro®les. The mixed layer pro®les were measured by a 915 MHz Pro®ler/
Radio Acoustic Sounding System and by radiosondes in north-central Oklahoma at the ARM Southern Great Plains CART Central
Facility. A comparison of calculated sensible heat ¯ux values with regional mean values measured at two ground stations showed

good agreement with r ˆ 0:88 and r ˆ 0:76 for the 915 MHz pro®ler and the radiosonde data sets, respectively. Estimates of friction
velocity u by means of radiosonde wind pro®les gave good results when compared to values measured by an surface eddy correlation system with a correlation coecient r ˆ 0:77. However, u values obtained from wind pro®les measured by the 915 MHz
pro®ler were underestimated, because these velocity measurements were systematically too small. The results also show that the
915 MHz Pro®ler/Radio Acoustic Sounding System is capable of providing the needed temperature measurements to make reasonable regional estimates of sensible heat ¯ux. Ó 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction
Surface ¯uxes can be estimated by using atmospheric
boundary layer (ABL) similarity. Monin-Obukhov
similarity (MOS) relates surface ¯uxes to surface variables and variables in the atmospheric surface layer
(ASL). Bulk ABL similarity (BAS) relates surface ¯uxes
to surface variables and mixed layer atmospheric variables. An advantage of the BAS approach is that the
horizontal scale of the surface ¯ux estimates can be up
to two orders of magnitude larger than that for ASL
similarity. A disadvantage of BAS is that the mixed
layer structure is depends on more variables than that of
the ASL. These additional variables, such as possibly
the Coriolis e€ect and entrainment, in¯uence transport
processes in the outer region of the ABL. The various
forms of the bulk similarity functions for di€erent atmospheric conditions were reviewed elsewhere (e.g.,
[3,5]). Previous research has mostly investigated the

dependency of the BAS functions on the dimensionless
variable l ˆ hi =L where hi is the inversion height and L
the Obukhov length ([9,5]). The research of Sugita and

*

Fax: +1-352-392-3394.

Brutsaert [18] over hilly prairie at FIFE and Brutsaert
and Parlange [4] over ¯at forest at HAPEX-Mobilhy
showed that di€erent regions with similar roughness
characteristics have nearly identical optimal bulk similarity functions.
The bulk similarity approach for surface momentum
¯ux calculations requires knowledge of the mixed layer
average wind speed and the atmospheric stability. Sensible heat ¯ux calculations normally require knowledge
of the average potential temperature in the mixed layer,
the surface potential temperature, the surface ¯ux of
momentum, and the atmospheric stability. Temperature
di€erences between the surface temperature and the
mixed layer temperature control the rate at which heat is

exchanged between the surface and the atmosphere. As
these temperature di€erences are on the order of 5±10 C,
relatively small temperature measurement di€erences
may result in signi®cantly di€erent estimates of sensible
heat ¯ux.
In past applications of BAS, radiosondes have been
the primary source for necessary measurements of wind
speed, temperature, and humidity in the ABL. Such
measurements can be assumed to re¯ect the surface
conditions upwind from the radiosonde release point.
However, the brief measurement period as it traverses

0309-1708/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved.
PII: S 0 3 0 9 - 1 7 0 8 ( 9 9 ) 0 0 0 2 8 - 7

340

J.M. Jacobs et al. / Advances in Water Resources 23 (2000) 339±348

the ABL, may limit the radiosonde's ability to capture

representative averages. The recently developed active
radar pro®lers with radio acoustic sounding systems
(RASS) do not su€er from this temporal sampling
problem. Indeed, these ground-based remote sensing
instruments are able to monitor the atmospheric boundary layer continuously, and they can provide wind
speed and temperature measurements for most reasonable time periods of interest.
Previously, several studies have compared horizontal
wind and temperature estimates between pro®ler/RASS
and radiosonde data. For example, May et al. [12] found
the mean di€erence between RASS virtual temperature
measurements and radiosonde virtual temperature
measurements was only a few tenths of a degree. Weber
and Wuertz [21] compared 17,799 measurements of the u
(east) and the v (north) horizontal wind components.
The u-component had an average di€erence (radiosonde minus pro®ler) of 0.49 m sÿ1 and a regression
relationship of the form urs ˆ 0:81 ‡ 0:97uprofiler ; for the
v- component these results were 0.82 m sÿ1 and
vrs ˆ 0:77 ‡ 0:97vprofiler . They attributed the bias to instrument error and sampling di€erences. Martner et al.
[11] concluded that for 3361 pairs of wind velocity
measurements, the average di€erence (radiosonde minus

pro®ler) was 0.99 and 0.21 m sÿ1 for the u- and v-components, respectively. For the 745 temperature measurements, the average di€erence was ÿ0.07 C. Coulter
and Lesht [7] found that the average wind speed di€erence (radiosonde minus pro®ler) was 0.69 m sÿ1 and the
temperature di€erence was 0.04 K at the SGP CART
Central Facility. Angevine et al. [2] compared temperature and wind speed measurements from a 915 MHz
pro®ler/RASS system to those measured by cup and
sonic anemometers and a thermometer/hygrometer
mounted on a tower at 396 m above ground level. They
also found the pro®ler on average underestimated the
wind speeds. However, after removing data points which
they interpretted to be a€ected by ground clutter, it was
found that the average wind speed di€erence (pro®ler
minus anemometer) was 0.40 m sÿ1 and that the RASS
temperature was greater on average than the thermometer and the sonic anemometer by 1.12 and 0.98 K, respectively.
In summary, from these previous comparisons it appears that wind speeds measured by radar pro®lers tend
to be systematically smaller than those obtained by radiosondes by about 0.5±1.0 m sÿ1 . While it could be
argued in the case of wind speed that a systematic bias
of 0.5±1.0 m sÿ1 is relatively small, nothing is known
about its importance in the context of similarity formulations. In the case of RASS and radiosonde temperatures the di€erences are very small in most studies
and there is no clear bias one way or the other. For
temperature, even such small di€erences may be important as sensible heat ¯ux estimates can be sensitive to

relatively small variations in temperature measurements.
Clearly, a direct comparison between surface ¯uxes is
important to determine what, if any, impact the measurement di€erences for the two instruments have on
surface ¯ux estimates. The purpose of the present paper
is to examine the suitability of the pro®ler/RASS instrument for estimating surface ¯uxes routinely by
means of the same methods previously applied with
episodic radiosonde data. The data used were obtained
in an experiment that was conducted at an uncalibrated
site with the identical site and instrumentation already
analyzed in Coulter and Lesht [7]. The study region
consisted of harvested wheat ®elds (stubble) over level
terrain surrounding the Atmospheric Radiation Measurement (ARM) Cloud and Radiation Testbed
(CART) site in north-central Oklahoma. The 0.15 m
surface roughness at this site [10] was almost an order of
magnitude smaller than the 1.05 m roughness at the
FIFE site [17] or 1.2 m roughness at HAPEX-Mobilhy
[13], two sites where BAS was calibrated.

2. Experimental data

The data for this research were acquired in June and
July of 1995 at the Central Facility (CF) of the US
Southern Great Plains CART ®eld research site which is
operated by the US Department of Energy within its
ARM Program. A detailed description of the ARM
Program and the CART sites is provided by Stokes and
Schwartz [16]. The CF is a 160-acre complex located in
north-central Oklahoma between Lamont and Billings,
Oklahoma (7 300 W, 36 370 N). A map of the CF is
shown in Fig. 1. The topography of the area is ¯at with
only small changes in relief; small tree stands, at distances on the order of 1.5 km, dot the landscape. During
the experiment, stubble ®elds covered 80% of the region
and pasture and range land the remainder.
2.1. Atmospheric boundary layer pro®les
A 915 MHz Doppler radar wind pro®ler with RASS
(LAPTM -3000, Radian Corporation, Inc. 1) was operated at the CF's southern end. The radar wind pro®ler
provided measurements of wind velocity as a function of
height up to 6 km AGL by detecting scattered radio
waves from temperature and moisture ¯uctuations
moving with the mean wind [8,6]. The total wind vector

was estimated by determining the Doppler shift in the
transmitted frequency in the vertical direction and in at
least two tilted planes. The system had beams along ®ve
directions: 1 vertical and 4 each tilted 14 from vertical
1
Use of this name does not imply approval or recognition of the
product to the exclusion of others.

J.M. Jacobs et al. / Advances in Water Resources 23 (2000) 339±348

341

sulted in a vertical resolution of 105 m. Maximum
measurement heights ranged from 500 to 800 m depending on the atmospheric turbulence conditions and
wind speed during this study. It should be noted that
during the experiment, the 915 pro®ler/RASS was periodically only operated in the vertical mode and the
correction for the vertical velocity was not included. In
the vertical mode, temperature measurements can be
derived and are available for analysis, but horizontal
wind speeds cannot be derived.

2.2. Surface ¯ux measurements

Fig. 1. A map of the CART Central Facility in the Southern Great
Plains (adapted from [16]). The stars mark the eddy correlation (EC)
and the energy balance Bowen ratio (EBBR) surface ¯ux stations. The
solid squares mark the radiosonde release location and the 915 MHz
RASS/pro®ler. The dotted line marks the surface temperature (Ts )
transect route.

in the North, East, South, and West vertical planes. The
pro®ler operated in a single direction for approximately
30±45 s (dwell time) and then rotated to the next direction. The pro®ler cycled through the ®ve beams at
low power (low-level observations) and then again
through the ®ve beams at a higher power/longer pulse
length (high-level observations) setting. A 50 min average wind speed for each power was produced every hour
by averaging values from 11 or 12 cycles. The center of
the lowest range gate was 138 and 320 m for the low and
high power settings, respectively. The present study used
the low power 915 pro®ler wind speed observations.
In its RASS mode, the microwave radar pro®ler

vertical beam was concurrently operated with continously, randomly varying in frequency, sound waves
and provided virtual temperature measurements up to
1.5 km [8]. Virtual temperature is de®ned by
Tv ˆ …1 ‡ 0:61q†T ;

…1†

where q ˆ qv =q is the speci®c humidity, q the density of
air, and qv the density of water vapor. The RASS essentially measures the Doppler shift of the acoustic energy as it propagates vertically in the atmosphere,
providing a scattering source for microwave energy. The
virtual temperature is determined from the measured
speed of sound Ca and the measured vertical wind speed
w by
…Ca ÿ w†2
ÿ 237:16:
…2†
401:92
A 10 min average virtual temperature was obtained
hourly for range gates separated by 105 m which re-

Tv ˆ

Eddy correlation ¯ux measurements were made using
a sonic anemometer/thermometer and krypton
hygrometer (Applied Technologies, Inc.) mounted on a
3 m tower located immediately adjacent to a harvested
wheat ®eld; it was surrounded by wheat stubble to the
south and west and pasture to the north and east.
The system was located approximately 300 m north of
the 915 MHz pro®ler. The system produced half-hour
averages of the turbulent ¯uxes of sensible heat H, latent
heat LE, and momentum u .
In addition, measurements were made with an energy
balance Bowen ratio (EBBR) system (Radiation and
Energy Balance Systems, Inc.) which was located in a
nearby (200 m) green pasture. The EBBR was located
approximately 300 m NNE of the 915 MHz pro®ler. The
EBBR system measured air temperature T and vapor
pressure e at 0.96 and 1.96 m above the vegetation, in
addition to net radiation Rn and soil heat ¯ux G. Using
these measurements, the system calculated half-hour
average values of sensible heat and latent heat.
For the present analyses, the locally measured sensible and latent heat ¯uxes were ``regionalized'' by taking
the averages of the measurements from the EBBR station and the eddy correlation station weighted according
to the regional vegetation distribution of harvested
wheat and pasture, namely Hs ˆ 0:8Hec ‡ 0:2Hebbr .
2.3. Surface temperature measurements
Two infrared thermometers (IRTs) were used to
make surface temperature measurements over a 750 m
transect at the CF. The IRTs (Model 4000.2L, Everest
Interscience, Inc.) had a 4 ®eld of view and a 5 Hz
sampling frequency and they were mounted on a portable yoke and carried by a porter in the manner described by Slater et al. [15]. Both IRTs viewed about the
same 10 cm diameter sampling area, one from a nadir
viewing angle and the other from 50 o€-nadir. The o€nadir temperatures produced better surface ¯ux estimates than the nadir temperatures; thus only the results
from the o€-nadir view angle measurements are presented.

342

J.M. Jacobs et al. / Advances in Water Resources 23 (2000) 339±348

The surface temperature was measured between
0800 CDT and 1600 CDT during hourly walks along
the transect. Additional measurements were made on
the half-hour as necessary to match the atmospheric
pro®ler. The transect consisted of a 600 m harvested
wheat portion followed by a 150 m pasture portion and
the traverse lasted approximately 12 min as shown in
Fig. 1. The regional surface temperature was estimated
from the average of measurements during a single
transect.

3. Methodology
In the BAS approach, the surface ¯uxes can be estimated by the following equations for momentum ¯ux u
and sensible heat ¯ux H:

 

hi ÿ d
…3†
ÿ Bw ;
u ˆ jVa
ln
zo
 


hi ÿ d
ÿC ;
…4†
ln
H ˆ …hs ÿ ha †ju qcp
zoh
where j ˆ 0:4 is the Von Karman's constant, Va the
average mixed layer scalar wind Va2 ˆ u2a ‡ v2a , ua and va
the average wind speeds in the x- and y-directions, respectively, hi the inversion height, zo the momentum
roughness length, hs the potential temperature at the
surface, ha the average mixed layer potential temperature, cp the speci®c heat at constant pressure, zoh the
scalar roughness for sensible heat, and Bw and C the
bulk similarity functions for momentum and sensible
heat, respectively. Based on an analysis of surface layer
pro®les by Monin±Obukhov similarity, it was estimated
that the regional (i.e., mesogamma scale) surface
roughness for the ARM CART Central Facility can be
taken as zo ˆ 0:15 m, the displacement height d is negligible, and the scalar roughness is zoh ˆ 0:0038 m for
measurements from the o€-nadir viewing IRT [10].
Previous studies showed that zoh may be a function of
solar elevation or u [14,19,20]. However, Jacobs and
Brutsaert [10] found no relationship between zoh and
either solar angle or u . Therefore, a constant zoh value is
used in this study. As d is negligible, it is omitted from
the formulations in what follows. The surface roughnesses were derived at the local scale using wind speed
measurements at 10 m. Independent regional ¯ux estimates made radiosonde surface layer pro®les and these
roughness values were compared to eddy correlation
measurements. The sensible heat ¯uxes were in excellent
agreement (r ˆ 0:92). Moderate agreement was found
for momentum ¯uxes (r ˆ 0:66).
A variety of forms of the bulk similarity functions
have been proposed for stable, neutral, and unstable
atmospheric conditions. Previous research on these has
mostly dealt with their dependency on the dimensionless

variable l ˆ hi =L (e.g., [9,5]). L, the Obukhov length, is
de®ned by
Lˆ

ÿu3 q
;
jg…H =Ta cp ‡ 0:61E†

…5†

where g is the acceleration of gravity, E the surface ¯ux
of water vapor, and Ta the air temperature near the
ground.
Sugita and Brutsaert [18], Brutsaert and Parlange [4]
tested several Bw functions. Among those, the Bw formulations that were used to calculate u in this analysis,
are:
Bw ˆ a;
Bw ˆ a ln‰ÿ…hi =L†Š ‡ b;

…6†
…7†

where a and b are empirical constants. The FIFE experiment, which provided data for Sugita and Brutsaert
[18], was conducted over hilly prairie terrain in Kansas
where the roughness characteristics for the region are
zo ˆ 1:05 m and d ˆ 26:9 m. The measurements at
HAPEX-Mobilhy (H-M), used by Brutsaert and Parlange [4], were made above the Landes forest in France
and zo ˆ 1:2 m and d ˆ 6:0 m. Both of these experiments used mixed layer radiosonde wind measurements.
With the FIFE data, the constants were found to be
a ˆ 0:500 and b ˆ 1:72 for Eq. (7). With the H-M wind
pro®le data, the constants were found to be a ˆ 3:362
for (6), and a ˆ 0:374 and b ˆ 2:408 for (7). Because the
FIFE and the H-M functions for (7) give very similar Bw
values, it was decided to use their averages, namely
a ˆ 0:437 and b ˆ 2:064.
The formulations of Sugita and Brutsaert [18] for C
were used to calculate H in the present analysis; they
are:
C ˆ a;

…8†

C ˆ a ln‰ÿ…hi =L†Š ‡ b;

…9†

where a and b are constants. With the FIFE data, the
constants were found to be a ˆ 0:739 and b ˆ 2:95 for
(9).

4. Analysis and discussion
4.1. Comparison of mean values in the mixed layer
In this section, the wind speed and the virtual temperature measurements made in the mixed layer by the
radiosonde and by the 915 MHz pro®ler/RASS are
compared. For the radiosonde, virtual temperature
pro®les were determined by combining the radiosonde
pro®les of temperature and relative humidity using (1).
The speci®c humidity was determined from relative
humidity r (r ˆ e=e where e is the vapor pressure and e

J.M. Jacobs et al. / Advances in Water Resources 23 (2000) 339±348

the saturated vapor pressure) and the equations of state
for dry air and water vapor.
For each pro®le, the measurements made between the
bottom and top of the mixed layer were averaged. The
top of the mixed layer was taken as the boundary layer
inversion height hi ; this was initially determined for
each radiosonde pro®le as the height at which
dh=dp > 4 C/100 mb where h is the potential temperature and p the pressure. The results were con®rmed by
inspection. The inversion heights for the 915 MHz pro®ler/RASS measurements were determined by interpolating between the inversion heights of the nearest two
radiosonde pro®les; the bottom of the mixed layer was
taken as 0:10hi . Most wind speed pro®les had 10±20
measurements in the mixed layer with both instruments.
The RASS temperature pro®les also had 10±20 measurements in the mixed layer, where as the radiosonde
temperature pro®les usually had 50±100. Examples of
typical virtual temperature and wind pro®les obtained by
the pro®ler and the radiosonde are shown in Fig. 2; the
solid lines show the pro®le obtained by the radiosonde
launched within a few hundred meters of the pro®ler.
A pair of measurements was compared when the radiosonde launch occurred within the averaging interval
of the pro®ler. Fig. 3 shows 12 comparisons of wind
speed measurements from the radiosonde and from the
915 MHz pro®ler. These wind speeds have an excellent
correlation (r ˆ 0:95). For the 12 wind speeds, the average di€erence (Vrs ÿV915 ) is 0.45 m sÿ1 , the standard
deviation of the di€erences is 0.85 m sÿ1 , and the regression relationship V915 ˆ ÿ0:63 ‡ 1:03 Vrs . A T -test
with a ˆ 0:05 indicated that the 915 MHz pro®ler gives
signi®cantly lower mixed layer wind speed measurements than the radiosonde (p ˆ 0.047). The negative bias
of the pro®ler wind speed is consistent with the previous
comparisons discussed in Section 1. This bias could also
be due the di€erence in sampling methodology between
the pro®ler and the radiosonde. The pro®ler position is
stationary (Eulerian) while the balloon is transported
with the mean horizontal wind (Langrangian).
The temperature pro®les were compared when they
were made within a half-hour of each other. The 56 pairs
of mean radiosonde and RASS virtual temperature
mixed layer averages are shown in Fig. 4. For these
temperature measurement pairs, the maximum temperature di€erence is approximately 2 C, the average difference (Tv;915 ÿTv;rs ) 0.46 C and the standard deviation
of the di€erences 1.16 C. The temperatures are well
correlated (r ˆ 0:96), but their di€erence is statistically
signi®cant (p ˆ 0.0044). This di€erence is somewhat
larger than the results of [12,11,7]. This study only analyzes daytime measurements while the earlier studies
used both measurements made during the day and the
night. During the daytime, temperature ¯uctuations are
usually large, thus the di€erence between the radiosonde
and RASS measurements would be expected to vary

343

Fig. 2. Pro®les of (a) wind speed and (b) virtual temperature observations from the 915 MHz pro®ler (hollow symbols) and radiosondes
(solid line) on day 182 at 0930 (hollow diamonds), 1230 (hollow triangles), and 1530 (hollow squares). Individual radiosonde wind speed
observations are marked by the solid symbols. The boundary layer
inversion height is indicated by an arrow. Wind speed measurements
are o€set by 10 m sÿ1 and 20 m sÿ1 for the 1230 and the 1530 pro®les,
respectively. Temperature measurements are o€set by 5 and 10 K for
the 1230 and the 1530 pro®les, respectively.

more in this study than in the previous studies. Nevertheless, the present result is consistent with recent
studies by Angevine and Ecklund [1] and Angevine et al.
[2], who also found a positive bias (RASS reads high) in
comparisons between the RASS and other instruments
and who attributed the bias to range error, wind and
turbulence error, and approximations made to convert
the measured acoustic velocity to virtual temperature.

344

J.M. Jacobs et al. / Advances in Water Resources 23 (2000) 339±348

Fig. 3. Comparison of the mean wind speed averaged over the mixed
layer measured by the radiosondes and by the 915 MHz pro®ler. The
pro®les were made within a half-hour of each other. The solid line is
1:1. The correlation coecient is r ˆ 0:95.

Fig. 4. Comparison of the mean virtual temperature over the mixed
layer measured by the radiosondes and by the RASS. The pro®les were
made within a half-hour of each other. The solid line is 1:1. The correlation coecient is r ˆ 0:96.

4.2. Sensible heat ¯ux analyses
Coincident wind speed and temperature pro®les were
used to calculate u and H. The analyzed pro®les consisted of those measured (i) under unstable conditions
that were identi®ed with the criteria that the Obukhov
length was negative (L < 0) and (ii) under clear sky or

fully overcast conditions (to avoid sampling uncertainty
of surface temperature under partially sunlit conditions). The selection resulted in 13 915 MHz pro®les and
21 radiosonde wind pro®les listed in Table 1 that could
be used in the ¯ux analysis. The radiosonde and the
915 MHz pro®les were analyzed separately.
Eq. (1) was ®rst inverted to determine the RASS
mixed layer temperature from the RASS virtual temperature measurements and the radiosonde measurements of q. The surface ¯uxes H and u were then
calculated by iteratively solving (3)±(5) for each pro®le
in Table 1. Because the e€ect of evaporation on stability
is usually small, the values of E necessary to determine L
were simply taken from the surface measurements. The
logarithmic Bw function (7) was used in (3), with
a ˆ 0:437 and b ˆ 2:064. The FIFE C function (9) was
used in (4), with a ˆ 0:739 and b ˆ 2:95. Mean values of
H and Hs and the ratio of the means hHs i=hH i were
calculated for the data set. The relationship
H ˆ b0 ‡ b1 Hs and the correlation coecient r were
determined with an ordinary least squares regression.
The results are shown in Table 2. The 915 MHz dataset
yielded somewhat better results than the radiosonde
dataset. However, both regression relationships are
skewed and both datasets overestimate Hs on average.
New best ®t constants a and b for C were determined
for these datasets in an attempt to improve the H estimates. For each pair of constants, the surface ¯uxes H
and u were recalculated for each pro®le by iteratively
solving (3)±(5). The following criteria after Sugita and
Brutsaert [18] were used by trial and error to identify
these constants. The ratio of the average value of the
calculated surface ¯uxes to the average value of
the measured surface ¯uxes is as close as to 1 as possible;
the regression relationship (e.g., H ˆ b0 ‡ b1 Hs ) shall
have b1 close to 1, b0 close to 0, and the correlation
coecient r close to 1. This approach seeks to identify
the constants that on average produce unbiased surface
¯ux estimates of the measured surface ¯uxes. The
overall results of this procedure are given in Table 2 and
the individual ¯ux results for each pro®le are given in
Table 3. Fig. 5 shows the H values calculated by (4), (3),
and (5) with the optimized C functions as compared to
the measured Hs values. For the 915 MHz dataset, the
resulting best ®t was a constant C ˆ 5:9. For the radiosonde dataset, C was given by (9) where a ˆ 1:53 and
b ˆ ÿ1:90. Each dataset had a regression intercept close
to 0, a regression slope close to 1, and good correlation.
The FIFE C function and the optimized C functions
are shown in Fig. 6 along with the hi =L and C values
determined for the 13 915 MHz and the 21 radiosonde
wind pro®les when calculated by inverting (4) and substituting the measured regional value Hs for H and the
measured u values. This ®gure shows some scatter,
particularly for values of hi =L that are close to zero. The
C values appear to be slightly dependent on hi =L.

345

J.M. Jacobs et al. / Advances in Water Resources 23 (2000) 339±348
Table 1
Data for each pro®le
Day of
year

Time
(CDT)

Va
(m sÿ1 )

hs
(K)

ha
(K)

hi
(m)

L
(m)

Ta
( C)

q
(g kgÿ1 )

P
(hPa)

2.6
1.8
3.1
5.8
3.2
2.7
4.8
4.6
11.3
7.8
4.4
4.7
4.4
12.2
14.7
16.2
9.4
11.7
5.8
10.3
10.5

304.4
309.8
317.7
317.4
304.1
308.2
313.3
301.4
300.7
300.6
296.6
308.3
308.7
301.6
311.5
314.1
306.0
312.7
312.7
302.6
312.8

300.7
302.1
304.3
305.7
302.3
302.4
306.0
297.3
295.4
298.0
294.5
297.5
299.1
298.9
304.9
308.8
303.5
306.3
306.8
298.5
305.4

152
474
1509
2027
698
607
1747
589
286
1555
380
1383
1537
200
1309
1823
1100
1170
1498
227
2848

ÿ27
ÿ5
ÿ6
ÿ23
ÿ45
ÿ12
ÿ26
ÿ52
ÿ295
ÿ164
ÿ82
ÿ18
ÿ16
ÿ696
ÿ281
ÿ383
ÿ300
ÿ184
ÿ45
ÿ331
ÿ108

21.6
24.2
29.1
31.2
26.4
27.7
30.9
21.1
19.9
23.4
17.1
23.1
25.0
21.4
27.6
31.9
26.7
30.0
30.8
20.7
28.3

11.9
12.0
10.8
11.5
15.9
16.1
15.1
16.2
0.0
0.0
9.4
7.9
8.2
13.9
14.7
15.6
16.4
11.7
12.1
10.8
9.3

975.7
975.5
976.4
974.9
975.7
975.4
974.2
978.3
982.7
983.6
983.6
983.1
981.3
968.3
965.8
963.1
962.1
962.7
964.7
975.1
975.2

915 MHz pro®ler/RASS data
178
083629
4.0
178
093627
1.8
179
143628
5.5
179
152614
4.9
182
093637
2.8
182
103635
2.8
182
113634
2.0
182
123632
3.3
182
133631
3.5
182
143630
3.5
182
153630
3.0
182
163630
2.8
184
093620
8.0

300.1
307.0
317.4
313.7
299.6
302.5
306.6
308.1
308.6
309.1
308.6
308.3
302.0

298.8
300.8
304.7
306.5
295.1
296.2
296.8
298.2
299.2
299.7
299.9
301.0
300.4

152
205
1368
1727
406
744
1081
1388
1439
1491
1537
1537
239

ÿ77
ÿ6
ÿ18
ÿ24
ÿ13
ÿ10
ÿ4
ÿ9
ÿ10
ÿ10
ÿ8
ÿ8
ÿ210

18.7
22.1
29.8
30.9
17.3
20.6
22.3
23.2
24.0
24.5
25.1
25.2
21.6

11.5
11.9
16.2
15.2
9.4
8.6
8.2
7.9
8.3
8.3
8.3
8.2
13.9

975.8
975.7
974.7
974.3
983.6
983.6
983.2
983.1
982.6
981.8
981.3
980.8
968.3

Radiosonde data
178
093000
178
101000
178
122800
178
152900
179
123000
179
125100
179
152900
180
123300
181
092900
181
123000
182
093200
182
123000
182
153000
184
092800
184
122900
184
152900
185
092900
185
123700
185
153800
186
092900
186
122900

Table 2
Comparisons between the average measured Hs values and the average H values calculated using Eq. (3) for the radiosonde and the RASS pro®lesa
Pro®ler

Eqs.

a

b

hH i
(W mÿ2 )

hH i
(W mÿ2 )

hHs i=hH i

r

Intercept (b0 )
(W mÿ2 )

Slope (b1 )

RS
915 MHz
RS
915 MHz

(9)
(9)
(9)
(8)

0.739
0.739
1.53
5.90

2.95
2.95
ÿ1.90
ÿ

182.83
154.28
132.76
145.10

132.86
144.86
132.86
144.86

0.727
0.939
1.001
0.998

0.763
0.876
0.851
0.819

ÿ28.78
ÿ33.95
ÿ3.83
ÿ6.56

1.16
1.30
1.03
1.05

a

The ®rst two comparisons use the FIFE values of a and b in the C function. The second two comparisons use optimized values of a and b.

However, for the 915 MHz dataset ignoring this depedence produced the best estimates of H. There is no
systematic di€erence between the 13 915 MHz values
and the 21 radiosonde values.
4.3. Estimation of u
The u estimates obtained in Section 4.2 were compared to those measured by the eddy correlation system.
For the 13 915 MHz pro®les and 21 radiosonde wind

pro®les, the u results are summarized in Table 4.
Overall, the agreement is quite good. This result shows
that the average of the FIFE and the HAPEX- Mobilhy
Bw functions gives reasonable u results at an uncalibrated site. However, the u;s values were underestimated by the 915 MHz pro®ler wind speed
measurements and overestimated by the radiosonde
measurements; modi®cations of the C function did not
signi®cantly change this discrepancy. The analysis
described in Section 4.2 was also carried out using a

346

J.M. Jacobs et al. / Advances in Water Resources 23 (2000) 339±348

Table 3
The calculated and measured surface ¯ux values for each pro®lea
Day of year

Time (CDT)

Calculated

Measured

u
(m sÿ1 )

H
(W mÿ2 )

u;s
(m sÿ1 )

Hs
(W mÿ2 )

LEs
(W mÿ2 )

Radiosonde data
178
093000
178
101000
178
122800
178
152900
179
123000
179
125100
179
152900
180
123300
181
092900
181
123000
182
093200
182
123000
182
153000
184
092800
184
122900
184
152900
185
092900
185
123700
185
153800
186
092900
186
122900

0.25
0.18
0.26
0.42
0.25
0.23
0.35
0.36
0.82
0.50
0.34
0.37
0.34
0.86
0.92
0.97
0.60
0.77
0.41
0.76
0.66

45.0
96.6
252.8
269.2
21.1
78.1
136.3
69.0
154.2
53.4
30.0
229.6
194.8
72.4
224.7
183.7
52.8
189.5
115.1
108.0
212.4

0.28
0.16
0.35
0.40
0.17
0.20
0.26
0.34
0.45
0.37
0.34
0.25
0.33
0.62
0.72
0.82
0.80
0.60
0.60
0.34
0.44

53.4
109.8
292.2
240.2
72.0
105.9
141.7
53.7
54.8
64.6
99.0
167.4
165.4
115.6
221.1
188.3
98.6
179.0
121.5
98.9
147.1

92.5
112.5
204.6
171.5
127.4
168.0
156.5
128.6
157.5
197.7
172.5
268.5
296.0
90.4
246.1
297.5
132.8
301.1
282.8
112.6
279.8

915 MHz pro®ler/RASS data
178
083629
178
093627
179
143628
179
152614
182
093637
182
103635
182
113634
182
123632
182
133631
182
143630
182
153630
182
163630
184
093620

0.35
0.20
0.42
0.37
0.25
0.25
0.18
0.27
0.28
0.28
0.25
0.23
0.61

45.2
114.4
351.7
164.6
95.6
115.7
127.4
180.6
179.2
177.9
140.9
108.1
86.4

0.34
0.27
0.35
0.25
0.33
0.34
0.28
0.28
0.40
0.36
0.32
0.35
0.62

32.1
57.0
254.5
144.7
108.5
123.0
182.0
176.6
171.4
182.6
162.9
168.3
119.5

55.8
101.2
173.7
156.8
175.2
190.6
262.4
274.6
306.5
312.8
295.3
258.3
95.0

a

Values were calculated using Eqs. (1)±(3) with the optimized C parameters shown in Table 2.

constant Bw function (Bw ˆ 3:8 and Bw ˆ 3:1 for the
pro®ler and radiosonde data sets, respectively) with both
the FIFE C function and the optimized C functions.
However, in both cases, the results were either not
substantially di€erent or somewhat worse.
The eddy correlation system, mounted at a height of
2 m measures u values at the local scale, with wind
speeds that are a€ected mainly by the local roughness
zo ˆ 0:08 m, approximately. In contrast, mixed layer
wind speeds are a€ected by a more regional roughness,
in the present case approximately zo ˆ 0:15 m or perhaps even larger. Therefore, in principle at least, one
can expect that the regional u values captured by the
pro®ler and radiosonde should be at least as large and
likely larger than those measured by the eddy correlation system. In this sense, the radiosonde u results
which exceed those from the eddy correlation system,
are reasonable. However, the pro®ler underpredicts the

u values. This result is likely due to the fact that the
pro®ler measurements systematically underestimate the
wind speed values by approximately 0.5±1.0 m sÿ1 , as
discussed in Sections 1 and 4.1. To test the e€ect of the
wind speed underestimates on u calculations, the 915
pro®ler dataset (see Table 1) was reanalyzed with the
pro®ler wind speeds increased by 0.5 m sÿ1 . For a 0.5 m
sÿ1 increase, the calculated u values were more consistent with surface measurements (hu i ˆ hu;s i ˆ 0:35
m sÿ1 ). This increase is probably insucient, and larger
wind speed corrections would further increase the calculated u values. Further research is necessary into the
pro®ler algorithm and other factors (possibly ground
clutter) to improve the present understanding of this
systematic di€erence between the pro®ler and radiosonde wind speed measurements. Until this phenomenon is better understood, the pro®ler wind speed
measurements should probably be increased by a value

347

J.M. Jacobs et al. / Advances in Water Resources 23 (2000) 339±348

Fig. 5. Comparison between Hs and H calculated from (3), (4), and (5)
with the optimized C functions. The individual pro®les for the 915
MHz pro®ler dataset and the radiosonde dataset are crosses and diamonds, respectively. The solid line is 1:1.

on the order of 0.5 m sÿ1 prior to estimating surface
¯uxes.

5. Summary
An analysis of the bulk ABL similarity approach was
conducted with the mixed layer pro®les measured by a
915 MHz Pro®ler/RASS and by radiosondes at the
ARM CART Central Facility in Oklahoma. Simultaneous pro®les showed that the wind speed and the
temperature measurements by the pro®ler and the radiosondes were signi®cantly di€erent. Both instruments
were able to provide good estimates of H, and the
915 MHz pro®ler/RASS gave as good or better results
than the radiosondes. This result is encouraging as the
915 MHz pro®ler/RASS may be operated continuously
with little manual intervention. However, the 915 MHz
pro®ler underpredicted the u values because the mea-

Fig. 6. The bulk similarity function C values versus stability (hi =L).
The dotted line is the FIFE C ˆ 0:739ln‰hi =LŠ ‡ 2:95 curve, the solid
line is C ˆ 5:9 as optimized for the 915 MHz dataset, and the dashed
line is C ˆ 1:53ln‰hi =LŠ ÿ 1:90 as optimized for the radiosonde dataset.
The individual C values were calculated using Hs for each pro®le. The
C values for the 915 MHz pro®ler dataset and the radiosonde dataset
are crosses and diamonds, respectively.

sured V values were underestimated on average. Until
the matter is better understood, it may be advisable to
correct the 915 MHz pro®ler wind speeds by 0.5 m sÿ1 or
perhaps larger prior to estimating surface ¯uxes.
Clearly, additional ®eld tests to study the bulk similarity
function using simultaneous 915 MHz Pro®ler/RASS
and radiosondes pro®les are desirable.

Acknowledgements
Part of this work was supported through National
Aeronautics and Space Administration (NGT-51211 of
the Graduate Student Researcher Program, NAS531723 and NAG8-1518), Argonne National Laboratory
(No. 970632401) and the National Science Foundation

Table 4
Comparisons between the average measured u;s values and the average u values calculated using Eq. (2) for the radiosonde and the RASS pro®lesa
Pro®ler

Eqs.

hu i
(m sÿ1 )

hu;s i
(m sÿ1 )

hu;s i=hu i

r

Intercept (b0 )
(m sÿ1 )

Slope (b1 )

FIFE C Functions
RS
915 MHz

(9)
(9)

0.52
0.30

0.42
0.35

0.812
1.146

0.780
0.758

0.09
ÿ0.01

1.03
0.90

Optimized C Function
RS
(9)
915 MHz
(8)

0.51
0.30

0.42
0.35

0.830
1.142

0.784
0.766

0.08
ÿ0.03

1.01
0.95

a

The ®rst two comparisons were conducted using the FIFE parameters a ˆ 0:739 and b ˆ 2:95 for C. The second two comparisons use optimized C
functions where a ˆ 1:53 and b ˆ ÿ1:90 for the radiosonde pro®les and a ˆ 5:90 and b ˆ 0 for the 915 pro®ler.

348

J.M. Jacobs et al. / Advances in Water Resources 23 (2000) 339±348

(ATM-9708622). The authors also appreciate the opportunity to take necessary measurements at the US
Department of Energy ARM CART Central Facility.
Data were obtained from the Atmospheric Radiation
Measurement (ARM) Program sponsored by the US
Department of Energy, Oce of Energy Research, Of®ce of Health and Environmental Research, Environmental Sciences Division.
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