Spectral Structure of Turbulent Fluxes in the Atmospheric Boundary Layerover a Thermally Non-Homogeneous Land Surface‐ with a small summary of GAME related ABL studies –* Tetsuya HIYAMA1, Mikhail A. STRUNIN 2, Michiaki SUGITA3, and Joon KIM4
(1: HyARC, Nagoya University, Japan, 2: Central Aerological Observatory, Russia,
3: University of Tsukuba, Japan, 4: Yonsei University, Korea)* HyARC, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japane-mail: hiyama@hyarc.nagoya-u.ac.jp
Abstract
This presentation consists of two parts. As a first step in the presentation, a statistical result on the recent research
topics in the atmospheric boundary layer (ABL) community is shown. The number of research papers focusing on ABL
and turbulent structures over several non-homogeneous land surfaces is increasing and published recently.
Next we introduce one of the important research results on the ABL and turbulent structures over a non-homogeneous
land surface, obtained from GAME related sub-project. Data obtained during aircraft observations in convective
boundary layer (CBL), developed over thermally well-marked patch with mesoscale size on a land surface, were thebasis for the spectral analysis of airflow. Research was conducted at a Lena River site near Yakutsk City from April toJune 2000, as part of GAME-Siberia experiments. Analysis of wavelet cospectra and spectra allowed separating fluxes
and some other variables into turbulent (with the scales less than depth of CBL or approximately 2 km) and mesoscale(up to 20 km) to explore them independently. Analyses showed that vertical distributions of turbulent and mesoscaleportions of the fluxes (sensible heat, water vapour, momentum and carbon dioxide fluxes) and other variables (windspeed and air temperature fluctuations) obeyed different laws. Turbulent vertical scaling profiles of all fluxes followed
an almost hyperbolic decay, which differed from generally accepted similarity models for the CBL. Mesoscale verticalprofiles of all fluxes and other variables clearly showed sharp inflections at the same relative height of 0.55 in the CBL.
Our findings suggest that conventional similarity models for sensible heat fluxes describe both turbulent and mesoscale
flows. The peculiarities of vertical profiles supported the suggestion that different kinds of mesoscale motions existed in
the mixed layer. The results indicate that the motion that expanded up to the relative (with respect to the depth of theCBL) level of 0.55 could have been initiated by thermal surface heterogeneity. Entrainment processes between theupper part of the CBL and the free atmosphere may have caused the other mesoscale motion.
Keyword: Aircraft observation, Non-homogeneous land surface, Turbulent and mesoscale characteristics, Wavelet
transform

1. Introduction
1.1.
Overview of recent ABL studies
The number of ABL-related papers was statisticallyreviewed. We selected four major international journals
mainly dealing with ABL studies e.g., “Boundary-LayerMeteorology (BLM)”, “Journal of Applied Meteorology(JAM)”, “Journal of Geophysical Research (D-series;Atmosphere) (JGR)”, and “Agricultural and ForestMeteorology (AFM)”. As a result, research papers
focusing on ABL and turbulent structures over several
non-homogeneous land surfaces, including urban canopy,
land-sea interfacial region, and thermally heterogeneous
land surface, are published frequently. The number ofpapers focusing on cloud-topped boundary layer (CTBL),
and those on formations of ABL in some mesoscalemeteorological conditions using data set of aircraft
observations and Large-Eddy Simulations (LESs) is also
increasing recently.

1.2.

ABL studies in GAME-Siberia based onaircraft observation

From the statistical reviews described above, we
recognized that ABL structures over heterogeneous
surface or CTBL are important issues to be studied
recently. We introduce one of the important research
results on the ABL and turbulent structures over a
non-homogeneous land surface, obtained from GAME
related sub-project.

The study was conducted as part of GAME-Siberia
aircraft observations made during the so-called IntensiveObservation Period from April to June 2000 (IOP2000),in the vicinity of Yakutsk City, Eastern Siberia. Previousanalyses determined the development of a mesoscale
thermal internal boundary layer (MTIBL) inside the CBLover the Lena River and its banks (Strunin et al., 2004).
The present paper examines the wavelet spectral analysesof fluxes and discusses how different-sized eddies havecontributed to energy, water vapour, and carbon dioxidethroughout the CBL.

2. Observation site and flight schemes
Details of aircraft observations during the IOP2000 in
the vicinity of Yakutsk City were provided in Hiyama etal. (2003). We used data from research flights undertaken
at approximately one-week intervals (depending onweather conditions) on May 1, 9, 12, and 20 and on June
1, 5, 9, and 19, 2000.
The sampling site near Yakutsk consisted of tworiverbanks of the Lena River. Long flight paths between
the banks crossed the Lena River lowlands
approximately perpendicular to the main channel of theriver. These flights were termed as “regional” samplinglegs or paths. Regional flight paths of about 90 km in theeast-west direction were made at five different levels
above the highest point of the underlying terrain.
Measurements on the regional flight paths were taken

from around 1200 to 1330 local solar time (i.e., in the
middle of the day, when temporal variations in surface
fluxes should not be large).
The surface under the flight paths can be characterized
as non-homogeneous. The surface state and the state of
the Lena varied with the seasons. Both the size of theheterogeneous underlying surface, and the temperature
contrast between the river lowland and the surrounding
terrace, changed with the season.
Total depth of CBL zi is applied as a vertical scale
above surface layer. Changing of zi was apparent in a
local decrease of the upper CBL boundary over the Lena
River and its lowlands. Thus, a local depth of the CBLδ(x) was defined as a function on the distance along theregional flight path x as;
L1 max(1)
δi =δ ( x )dx
Lmax ∫0where Lmax is the total distance of the regional flight path.
Values ofδi were used in scaling equations instead ofthe main depth of the CBL zi, and all scaling profiles
were built up versus the normalised (or relative) height z/
δi (z is the height above the underlying surface).

3. Wavelet analysis
A wavelet transform was applied for spectral analysisof the turbulent variables f(t) or g(t) and turbulent fluxes
in the CBL. A detailed description and investigation ofthis method is presented in Strunin and Hiyama (2004).
Turbulence characteristics derived from aircraft
turbulence data are usually calculated using length a andwave number k. According to Taylor’s hypothesis, time t
was converted to distance b as b=Ut, and frequency ξ
was converted to wave number k as k=ξ/U. The wavelet
transform was applied to a spatial-scale function f(x) as
follows:+∞1x−b(2)Wf (a , b ) =f ( x )Ψ ()dx1∫a 2 −∞awhere a=1/k is the spatial scale of the turbulent eddy, andb is the distance along the flight path (or location).
The wavelet spectrum was calculated as follows(Hudgins et al., 1993);+∞

S f ( a ) = CΨ−1 ∫ Wf ( a , b ) db
2(3)

−∞

where CΨ is the normalising coefficient (CΨ=1.0636). Awavelet cross-spectrum (Hudgins et al., 1993) was also
calculated as follows.
+∞

S fg ( a ) = CΨ−1 ∫ Wf ( a , b )Wg ( a , b )db

(4)

−∞

Investigations have shown the reliability of thewavelet method using the present data set (Strunin andHiyama, 2004). Good coincidence of the Morlet wavelet
with the Fourier spectra for small-scale turbulent eddies
has been shown. Comparison of the Morlet and Haar
wavelet spectra has also shown good results for thelarge-scale part of the spectra.

4. Results
Wavelet cospectra between vertical wind speed
fluctuations and potential temperature fluctuations,humidity fluctuations, carbon dioxide fluctuations werecalculated according to equation (4). As well known,
wavelet transform executes strong smoothing cospectra
at small wave numbers. This is one of important featuresof the wavelet method, which made it the most suitable
for the spectral analysis of atmospheric turbulence. In
order to smooth curves at long wavelengths cospectra
were smoothed with a five-points moving average filter.
Then cospectra were normalised based on maximum
absolute values of correspondent line-averaged fluxes.

4.1.

Separation of cospectra into turbulent
and mesoscale parts

Normalised wavelet cospectra versus the normalised(non-dimensional) wave number kz for flight
experiments from 1 May to 19 June were plotted. As theresults, almost all obtained cospectra had two clearly
expressed peaks, indicating the existence of exchangemechanisms with two prevailing scales. We suggest thatthe smaller-scale peak characterises turbulent motion andthe larger-scale peak corresponds to mesoscale flow.
Clearly expressed peaks in the cospectra indicated that
two types of motion induced fluxes of substances in theCBL. The first type consisted of turbulent eddies withscales less than the reduced depth of the CBLδi. Peaks
in this part of the cospectra were most evident fornormalised cospectra in sensible heat and carbon dioxide
fluxes. The second type consisted of mesoscale flowswith a scale ranging fromδi (about 2 km) up to 20 km.
We assumed that these distributions could be
decomposed into two Gaussian curves. Figure 1 shows
the procedure for separating cospectra into turbulent andmesoscale parts. The wave number axis is presented in alogarithmic scale.
We considered four typical situations. The curve of thecalculated cospectrum is presented as dependent on the
wave number by a logarithmic scale, and is shown by thesolid black line. The dotted grey line shows the turbulent
part, and the grey solid line marks the mesoscale part ofthe cospectrum. In the clearest case, when mesoscale andturbulent peaks of the cospectrum are far from each other(scales differ by 5 – 10 times), the minimum of thecospectrum can be chosen as the boundary between theparts (Figure 1a, boundary shown with the line A - B).
This situation was typical for numerous cospectra. If
mesoscale and turbulent peaks had opposite directions,the point of the change in the cospectra sign was treatedas the boundary between the two types of motion. If
there were close peaks (Figure 1b) or distant peaks(Figure 1c), the difference was not considered essential.
These situations were most typical for carbon dioxide
cospectra. If cospectra peaks were close to one another(scales differed by less than five times, as illustrated in
Figure 1d), we applied other separation techniques. Solidand dotted grey lines in this panel demonstrate themesoscale and turbulent distributions of fluxes. To findthe point of separation, we constructed a tangent line in
the bend of the curve between peaks. The 45o inclinationof the tangent line corresponded to the crossing point ofadditive Gaussian distributions, which we treated as theseparation point between the mesoscale and turbulent
parts of the fluxes. This situation was typical for watervapour cospectra.
Thus, all cospectra (solid black curves) can be treatedas a combination of two independent distributions: theright-hand one (dashed grey curves) corresponds to theturbulent part, and the left-hand one (solid grey curves)
corresponds to the mesoscale part. Turbulent andmesoscale fluxes are shown by squares under the dashedand solid grey curves, respectively (Figure 1a).
Thus, we presented cospectra as superposition of two
kinds of motion, which could be explored separately.
This allowed deriving the different relations for “pure”
turbulent and mesoscale portions of fluxes.

Figure 1. Scheme of separating the mesoscale andturbulent parts of cospectra for their differentcombinations. Lines A – B in panels show the scaleboundaries between mesoscale and turbulent parts ofcospectra.

4.2.

Scaling of turbulent and mesoscale fluxes

Decomposition of cospectra allowed the separating
and independent scaling of the “pure” turbulent andmesoscale portions of sensible heat, water vapour,momentum, and carbon dioxide fluxes. Turbulent andmesoscale parts of the fluxes were calculated throughintegrating cospectra at corresponding scale ranges. As
mentioned above, cospectrum estimated through thecospectra showed practically full coincidence with flux
calculated by the eddy correlation method (Strunin andHiyama, 2004). Boundaries between turbulent andmesoscale parts were defined separately for eachsampling path, but they were the same for different kindsof fluxes.
Results of flux scaling based on data obtained for all
regional sampling paths (experiments from May 1 toJune 19, 2000) are presented in Figure 2. Height was
normalised on corresponding reduced depths of the CBL
δ i. Typical values of 95% confidential intervals,
estimated based on random error are also shown in thefigure. As Figure 2 clearly shows, turbulent andmesoscale flux profiles behaved differently for all kindsof fluxes. Turbulent sensible heat fluxes decreased withheight and became negligibly small near the upperboundary of the CBL. Scattering of points is very small,suggesting hyperbolic dependence on height. Scatteringof the normalised momentum and water vapour turbulent
fluxes was larger, but these fluxes also decreased withheight and became small at the top of the CBL. In any
case scattering of the profile points did not exceed 95%
confidential intervals. Depending on surface conditions,turbulent carbon dioxide flux can be upward ordownward and its average value (which used as shift inscaling the fluxes) changes in wide limits. Presence ofsinks and sources on underlying surface prevents thevanishing of the fluxes to the upper part of CBL.
Nevertheless, the shape of the scaled flux profile wassimilar to those for other turbulent fluxes. Thus, it ispossible to say that turbulent carbon dioxide flux
behaved analogously to other turbulent fluxes, but withrespect to some reference (non-zero) value of the flux.
Vertical profiles of the mesoscale parts of all fluxes(right-hand side panels in Figure 2) are essentiallydifferent from corresponding turbulent fluxes. All profiles
had peculiarity (a strong inflection) at the same
normalised height of approximately z/δi = 0.55 (markedby dashed lines in the right-hand side panels of Figure 2).
This inflexion exceeds 95% confidential interval, thus it
can be treated as reliable. Sensible heat fluxes werealmost constant up to this height and had values of 0.2 –0.4 of the total fluxes. However, at the highest levels, or at
normalised heights more than 0.55 the fluxes decreased
rapidly and became negative (downward flux) at a
normalised height range of 0.7 – 0.8. Profile of mesoscale
fluxes of water vapour also has strong inflection at thenormalised height of 0.55. The behaviour of carbon
dioxide mesoscale profile is similar to the mesoscaleparts of other fluxes.
Hyperbolic decay of the turbulent sensible heat fluxes
contradicts generally accepted similarity models of theCBL (see, for example, Kaimal and Finnigan, 1994;Sorbjan, 1991). As it seen from Figure 2, total sensible
heat flux profiles could be created by summarising theturbulent and mesoscale portions of the fluxes. The
resulting profile has a shape that is close to that of theconventional similarity model. Flux decreased with theheight and became zero at a normalised height z/δi ofapproximately 0.7 – 0.8. Downward fluxes werestrongest at the top of the CBL. This behaviour is typicalof the flux profile of a CBL over a homogeneous land
surface. More detailed consideration shows that sensible
heat flux profile does not strictly obey general acceptedmodel. The profile bends at the normalised height ofaround 0.1 – 0.2 (due to the large values of turbulentfluxes), and again at a height of approximately 0.5 – 0.6(due to the strong blending of mesoscale flux profiles). It
is important to note that Albertson and Parlange (1999)
predicted this shape of the flux profile over an arid
heterogeneous patched surface based on a large eddy
simulation (LES) technique (see Fig. 2 in Albertson andParlange, 1999). The quality coincidence of theoreticaland experimental results validates the reliability andefficiency of the applied separation approach.
Mesoscale flows in the upper and lower parts of theCBL had different natures. The role of mesoscale motion
increased with height and maximised in the middle partof the mixed layer. Mesoscale exchanges then sharply
decreased, and increased again at the higher level. In ouropinion, the presence of two peaks in the profiles
indicates that there were two mechanisms of mesoscale
exchange in the non-homogeneous CBL. One wascaused by the influence of a thermally heterogeneous
land surface. This influence extended up to the middle ofthe CBL (z/ δ i = 0.55). Another mechanism wasconstituted by the entrainment process between the CBL
and the free atmosphere or, in the case of MTIBL
development, the entrainment process between the upper
part of the layer and zones above that layer. Thus, wesuggest that the influence of surface-level thermal
mesoscale heterogeneity extended only up to thenormalised height of z/δi = 0.55, where these motions
then died out. The next loop of the vertical profile wasdetermined by entrainment from the free atmosphere (ina case without MTIBL development) or the zone above
the MTIBL. The space above the zone of MTIBL
development cannot be treated as free atmosphere, butrather as a vast area of entrainment (Strunin et al., 2004).

potentiality to investigate spectral characteristics of
non-homogeneous variables and overlap practically
full-scale range of airflow in the CBL. This techniquealso allowed correctly separating flows in the CBL into
turbulent (with the scale length less than the depth of theCBL, i.e., approximately 1 – 2 km) and mesoscale
motions to a maximum scale of 20 km. Clearly expressedpeaks in wavelet cospectra and spectra suggested theway of separating data into mesoscale and turbulent
variables independently. This approach allowed
constructing similarity models of fluxes and othervariables for thermodynamic and surface conditions,which considered as unfit for previous scaling.
Obtained vertical profiles of turbulent and mesoscalevariables (variances and fluxes) demonstrated different
behaviour. Turbulent profiles of the fluxes decreased
with the height almost hyperbolic decay. All of theprofiles had sharp inflections in the middle part of theCBL. This allowed us to suggest that there were twokinds of mesoscale motions in the CBL over the
non-homogeneous land surface. It was supposed thatmesoscale motions developed from two directions, one
caused by the effect of the thermally heterogeneous
surface, the influence of which extended from the surface
to the middle of the CBL, and the other reflecting
entrainment of the CBL with the free atmosphere or thezone above the MTIBL.

References

Figure 2. Scaling of mesoscale and turbulent parts ofsensible heat H, momentum M, water vapour E andcarbon dioxide Q fluxes based on correspondent absolutemaximum fluxes.

5. Conclusions
Wavelet transform was applied for the aircraft dataobtained over the land surface with thermally-mesoscale
size of path surfaces. The wavelet transform gave

Albertson, J.D. and M.B. Parlange, Natural integrationof scalar fluxes from complex terrain.
Advances in Water Resour., 23, 239 – 252,
1999.
Hiyama, T., M.A. Strunin, R. Suzuki, J. Asanuma, M.Y.
Mezrin, N.A. Bezrukova, and T. Ohata, Aircraft
observations of the atmospheric boundary layerover a heterogeneous surface in Eastern Siberia.
Hydrol. Proc., 17, 2885 – 2911, 2003.
Hudgins, L.H., M.E. Mayer, C.A. Frieche, Fourier andwavelet analysis of atmospheric turbulence, in“Progress in Wavelet Analysis and Applications,
Meyer Y. and S. Roques (eds.)”, Editions
Frontiers, 491 – 498, 1993.
Kaimal J.C. and J.J. Finnigan, Atmospheric Boundary
Layer
Flows,TheirStructureandMeasurements. Oxford Univ. Press, New York,
Oxford, 289 pp, 1994.
Sorbjan, Z., Evaluation of local similarity functions in
the convective boundary layer, Boundary-Layer
Meteorol., 30, 1565 – 1583, 1991.
Strunin, M.A., T. Hiyama, J. Asanuma, and T. Ohata,
Aircraft observations of the development ofthermal internal boundary layers and scaling of
the convective boundary layer over nonhomogeneous land surfaces. Boundary-Layer
Meteorol., 111, 491 – 522, 2004.
Strunin, M.A. and T. Hiyama, Applying wavelet
transforms to analyze aircraft-measured
turbulence and turbulent fluxes in theatmospheric boundary layer over Eastern
Siberia. Hydrol. Proc., 2004 (in press).