Aircraft turbulence measurements to estimate surface heat fluxes from themixed layer variance methods over semi-arid grassland
Ayumi Kotani and Michiaki Sugita
Graduate School of Life and Environmental Sciences, University of Tsukuba

ABSTRACT
Turbulence data obtained by aircraft observations in convective boundary layer (CBL) were analyzed toestimate the regional surface heat fluxes by means of the variance methods. The observation was carried out
from June to October of 2003 as part of RAISE (Rangelands Atmosphere-Hydrosphere-Biosphere Interaction
Study Experiment) project. The flight paths covered the experimental area of Kherlen river basin in
Mongolia, and several heights within and above CBL (the height of CBL is estimated to be 700 - 1200m foreach flight) were flown repeatedly above the ground based observation sites in relatively homogeneoussemi-arid grassland. Within the area, two flux stations and four automatic weather stations (AWS) were in
operation during the flights to produce reference values.
The vertical profiles of the second order moments, i.e., the variance, of temperature followed in general
the functional curves proposed by previous studies based on CBL observations or numerical modeling,although, similar to those studies, at higher level of CBL (higher than 80% from the surface), the scatter ofdata became larger. These variance statistics were applied to the variance formulations to estimate surface
heat fluxes. The equations have some experimentally determined constants and these constants werecalibrated with the current data set. The resulting rms error of the estimated sensible heat flux was improved
from about 80 Wm-2 (before calibration) to 40W m-2 (after calibration). Finally, these equations with locallycalibrated coefficients were applied to the data over the other areas with the AWS, where surface fluxes havebeen obtained by the bulk similarity method. Although the rms error increased, it was probably because oflarger uncertainty of the ground-based fluxes derived by the bulk method.
1.Introduction

studies are available on this topic with examples of

The aircraft observation has an advantage in

Asanuma (1996) from aircraft and Sugita and Kawakubo

deriving area-averaged values and detecting the spatial(2003) from tower observation of the lower half of thevariability, although it requires careful instrument

convective boundary layer.

settings and data processing especially in case of using

In this study, investigation of the mixed layer

wind data in eddy correlation method to evaluate fluxes

variance methods by means of airborne data is presented.

(e.g., Lenschow, 1986).

The variance methods toestimate surface fluxes from the associated variances

2. Datameasurements in the surface or mixed layer on the other

Aircraft observation

hand are appealing in this context because it is possible

The temperature turbulence data were obtained by

to derive surface fluxes without observing wind velocity.

aircraft observation carried out from June to October ofThe variance methods have been applied to surface layer

2003 as a part of the field observation of RAISE

and produced satisfied results (e.g., Wesely, 1988). On(Rangelands

the contrary, convective boundary layer, where theInteraction Study Experiment in Northeastern Asia). The

flux-variance relationship is not fully understood andRAISE study area covers the Kherlen river basin, theestablished yet. Until now, only a limited number ofarid to semi-arid region in northeastern Mongolia, with a

Atmosphere-Hydrosphere-Biosphereboreal forest in northern and upper watershed andgrassland (Steppe) area towards the southern anddownstream part.

3.Results
In the convective boundary layer (CBL), turbulence

The instruments were installed to a wing of an

statistics were found to follow the convective (oraircraft, AN2 to measure scalar variables of the airmixed-layer) scaling. The aircraft observed temperaturetemperature and humidity with a fine thermocouple

variance σθ scaled with T* (= θv w'θ 'v0(CC-type) and a Kripton hygrometer (KH20, Campbel

virtual potential temperature and w'θ ' 0 v is surface

Scientific Inc.). The data were sampled at 10Hz. Also

temperature flux, and hi is boundary layer height) plotted

positioning information was obtained by a GPS receiver.

against ξ = zhi-1, where z is sensor height in Figure1 withThe flight path covered the experimental area and several

some formulation proposed in previous studies. The

heights of 100, 200, 500 and 1000m were flown

boundary layer height hi was estimated by the method

repeatedly above the ground observation site (see below).

proposed by Liu and Ohtaki (1997) with spectral data ofAlthough each path length is different depending on thehorizontal velocity observed at one of the flux stations.

weather condition, those with flight paths longer than 5

The height of CBL is around 700 – 1200 m. Thekm, which is equivalent to 100 s of averaging time, andobserved values follow the functional forms in generalwith the standard deviation of the flight level within 30

except for the upper part of CBL, where the scatter ism have been selected for analysis. For each path, the data

relatively larger probably because of the entrainment flux

have been processed to remove a trend by a linear

dominating near the inversion layer. Thus, those data

regression method before the analysis.

were not used for variance methods.

[(1.5aircraft
surface station) (gh ) ] ,θv is
2

−1

1/ 3i

Kaimal et al.(1976)
Moeng and Wyngaard(1984)

Ground based observation
automatic weather stations (AWSs) were in operation
during the flights. At the flux stations, the surface fluxesof sensible heat and water vapor were directly measured
by the eddy correlation method every 30 minutes (Li etal., unpublished). Since the eddy correlation flux data

1z hi-1

Within the area, two flux stations and four

0.5

00.1

1σθv2 T*-2

10100Figure1 Vertical profile of normalized variance of θ

showed the energy imbalance, the energy shortage has
been distributed into the turbulence energy flux bykeeping Bowen ratio (Twine et al., 2000) for thisanalysis.
The surface fluxes of AWS sites were estimated by

Kaimal et al. (1976) obtained with observation datafor 0.1≤zhi-1≤0.5,

σ θ 2T* −2 ≈ 1.8ξ −2 / 3(1)Others have included the whole boundary layer diffusion

applying the bulk similarity method, with meteorologicalprocess with the top-down and bottom-up

data such as air temperature, humidity, wind speed andmodel (Moeng and Wyngaard, 1984), which separates

radiation. The bulk transfer coefficients have been

the source of the boundary layer diffusion process into

evaluated based on the data sets obtained through a fluxthe surface and the inversion origins, and can be written

measurement carried out for a few days at each of thein general form by Asanuma (1996),

AWS sites during the field campaign (Kojima, 2004).

(TDBU)

22⎛ w'θ 'h ⎞⎛ w'θ 'h w'θ '0 ⎞⎛ w'θ '0 ⎞⎟ f t (ξ ) + 2⎜
⎟ f tb (ξ ) + ⎜⎟⎟⎜ v⎟⎜ v ⎟ f b (ξ )vv
0
⎝ h ⎠
⎝ h⎠
⎝ 0 ⎠

σ θ 2 = ⎜⎜of the sensible heat flux was improved to about 35 Wm-2(2)with the calibration.

In the case of the convective

where vh and v0 are the velocity scale at the inversion

scaling for lower half of ABL (Figure2, left), the original

base and at the surface, respectively. These scales should

constants (Kaimal et al., 1976) produced the same level

include the effect of surface shear and the convectiveof difference with the calibrated constant, which might(buoyant) forcing. Therefore available selection can bereveal that the convective scaling of the lower boundary

the friction velocity u*, convective velocity w* and theirlayer is rigid for various surface types. For thecombination such as v* =(w*3+8u*3)1/3 (Driedonks, 1982),TDBU-basedfor example. Since velocity was not observed in thevelocity scale gave little difference in the results, which

present study, u* was estimated with the Rossby-number

agreed with previous studies (Asanuma, 1996). Thesesimilarity which gives relation between the surface stressresults with the calibration are comparable to thoseand the geostrophic wind. The geostrophic wind speed

obtained by the tower based data of Sugita andcan be evaluated with the horizontal wind of the six

Kawakubo (2003).

hourly NCEP/NCAR reanalysis data (Kalney et al.
follows,, f tb = a 3 (1 − ξ ) 4 ξ a ,a5f b = a 6 ξ a7 (3)where a1 to a7 are the constants to be determined
experimentally.
By changing the combination of the velocity scalerms difference (Wm-2)*1

Combination of v0, vhAircraft

Tower*2(1)40.5 → 37.2

41.0(2a) v0 = vh = w*

82.0 → 34.1

60.9 → 40.3

(2b) v0 = v*, vh = w*

106.3→ 34.4

136.0→ 44.1

*2 Sugita and Kawakubo (2003)

under various conditions are possible. Here, two

The variance equations with these calibrated

combinations shown in Table 1 have been tested.

coefficients were applied to the AWS site, where fluxes

Equation (1) and (2) were rewritten to obtain surface flux

have been derived by the bulk similarity method with thew' θ ' 0 by following Sugita and Kawakubo (2003). As

meteorological data. The sensible heat flux by variancementioned, the constants in equation (3) are still not wellmethod and the bulk method at three AWS sites isAs such in thecompared in Fig.3. The rms difference between thesepresent analysis, first those constants previously

fluxes is 68 Wm-2, which is rather large since it might

proposed were applied and then they were calibrated

contain the error of referenced surface fluxes and thus

with the current data sets.

require further studies.

The local calibration was performed in the same

300

Hs (W m-2)

coefficients were changed at a small step until the root300
original constantcalibrated constantmanner as Sugita and Kawakubo(2003), where powers a2,a4, a5 and a7 in equation (3) are retained and the otherof*1 original constant → calibrated constantand the entrainment model, several selections of the test

established and need further studies.

combinations

Equation number

200

Hs (W m-2)

athoseTable 1. Result of variance method

1996 ). The universal function ft, ftb and fb are written as
f t = a1 (1 − ξ ) 2

formulation,

100

200

100

mean square (rms) difference between the estimated flux
and reference flux became the smallest.
The result before and after the local calibration isshown in Fig.2 and Table 1. As shown, the rms difference

000100200-2

H (W m )3000100200300

H (W m-2)

Figure2 Comparison of estimated H and measured Hsat flux site (left: eq.(1), right: eq.(2a))

the Growth of the Atmospheric Boundary Layer.
500

Boundary-Layer Meteorol.,85, 497-504.

HAWS (W m-2)

400

Kaimal, J. C., Wyngaard, J. C., Haugan, D. A., Cote, O.

● AWS-B■ AWS-U▲ AWS-D

300200R. and Izumi, Y. (1976): Turbulence Structure in theConvective Boundary Layer. J. Atmos. Sci., 33,637-662.

100

Kalney, E. and coauthors (1996): The NCEP/NCAR

00100

200 300
H (W m-2)

40050040-year reanalysis project, Bull. Amer. Meteor. Soc.,

Figure3 Comparison of estimated H and measured

74, 789-799,
Kojima, T. (2004): The investigation of the factors which

HAWS at AWS site (eq.(2a))

govern evapotranspirarion of Kherlen river basin in

4.Conclusion

Mongolia. MSc Thesis, University of Tsukuba,85p.

Turbulence data obtained by aircraft observations in

Lenschow, D.H. (1986): Aircraft Measurements in theCBL were analyzed to estimate the surface fluxes byPlanetary

BoundaryLayer.

Inmeans of variance methods. Observed temperature

Atmospheric Boundary Layer, 5-18 pp. Am.

variances followed in general the CBL scaling andMeteorol. Soc., Boston.

Probing

theproduced the surface heat fluxes with about 80Wm-2 ofLi, S.-G., Asanuma, J., Kotani, A., Eugster, W. and Sugita,

rms difference against ground based eddy correlation

M. Net ecosystem carbon dioxide exchange overfluxes. The calibration of the experimentally determinedgrazed steppe in central Mongolia, unpublished.

coefficients within the equations reduced the difference

Liu,X., and Ohtaki,E.(1997): An Independent Method toto 40Wm-2. This rather large error relative to reference

Determine the Height of the Mixed Layer,

value is partly due to uncertainty of other parameters

Boundary-Layer Meteorol.,85, 497-504.

ThisMoeng, C.-H. and Wyngaard, J.C. (1984): A Comparison

degree of error, however, is comparable to tower basedof Shear- and Buoyancy-Driven Planetary Boundary

measurement.

Layer Flow. J. Atmos. Sci., 41, 3161-3169.

such as CBL height or regional friction velocity.

Finally, these equations with the locally calibrated

Sugita, M. and N. Kawakubo(2003): Surface andcoefficients were applied to the data over the other areas

Mixed-layer Variance Methods to Estimate Regionalwith the AWSs, where surface fluxes have been obtained

Sensible Heat Flux at the Surface. Boundary-Layerby the bulk similarity method. Although the differenceMeteorol.,106,117-145.

increased, it was probably because of the larger

Twine, T.E., Kustas, W. P., Norman, J. M., Cook, D. R.,

uncertainty of the ground based fluxes derived indirectly.

Houser, P. R., Meyers, T. P., Prueger,, J. H., Starks, P.
J.

andWesely,M.

flux

L.(2000):

Correcting

underestimates

overReference

eddy-covariance

Asanuma, J. (1996): Turbulence Variance Characteristics

grassland. Agric. For. Meteorol., 103, 279-300.

ain the Unstable Atmospheric Boundary Layer above

Wesely, M. (1988): Use of Variance Techniques to

Flat Pine Forest, Ph.D. Thesis, Cornell University,

Measure Dry Air-surface Exchange Rates. J. Atmos.

118 pp.

Sci., 44, 13-31.

Driedonks, A.G. M. (1982): Models and Observation of