Turbulence spectra and surface fluxes in the atmospheric surface layer over theLoess Plateau
Wei LI1, Tetsuya HIYAMA2, Nakako KOBAYASHI1, Atsuhiro TAKAHASHI3, Atsushi HIGUCHI4,Masanori NISHIKAWA1, and Yoshihiro FUKUSHIMA3
1Graduate School of Environmental Studies, Nagoya University, Japan

2

Hydrospheric Atmospheric Research Center, Nagoya University, Japan
3

Research Institute for Humanity and Nature, Japan

4

Center for Environmental Remote Sensing, Chiba University, Japan

1. Introduction
In recent years, several new theories about turbulence structures in the atmospheric surface layer (ASL)
have been proposed. These theories do not agree with Monin-Obukhov similarity theory, which was almost
universally accepted previously (Hunt and Morrison, 2000; McNaughton and Brunet, 2002; McNaughton,2004). Hunt and Morrison (2000) proposed a new theory (hereafter ‘top-down’ model) for near-neutral
boundary layers at high Reynolds number. Following their work, Högström et al. (2002) validated thistheory against atmospheric data and found predictions from the model agree well with the measurements ofASL variances and spectra. This ‘top-down’ model that dominate at high Reynolds number differs from the‘bottom-up’ instability mechanisms that dominate at low Reynolds number proposed by others.
McNaughton and Brunet (2002) challenged Townsend’s hypothesis (Townsend, 1961) and proposed thatinactive outer-layer scaling motions do interact with active inner-layer scaling turbulence near the surface
and therefore Monin-Obukhov similarity theory fails. However, all of the above discussions were for thesituation of near-neutral condition. In case of the unstable ASL, McNaughton (2004) provided a new way tounderstand turbulence processes in the surface layer by presenting a ‘bottom-up’ model, called TEAL(Theodorsen ejection amplifier-like) model.
The land surface is the important intermedia of the heat transfer between the earth and the atmosphere.
To some extent, the earth’s surface is always non-homogeneous. The vertical structure of the atmosphericboundary layer (ABL) is modified over heterogeneous surfaces compared to over homogeneous surfaces.
The Loess Plateau, as a semi-arid plateau, possesses a typical land surface heterogeneity and consequentlyinduces special processes of energy budget and fluxes transportations in the ABL.
In this study, spectra of wind velocity components from an experiment conducted on the Loess plateau

were presented. Turbulent fluxes were also calculated to investigate the ABL evolution and to offer a basis
for the regional fluxes determinations over such a heterogeneous landscape.

2. Data and Calculations
From May 2004, an ABL field observation was carried out in the middle south area of the Loess Plateau,located at N 35° 12’, E 107° 40’. The climate belongs to semi-arid land climate, with mean annual
precipitation of 584 mm and mean annual temperature of 9.1℃. Flux and radiation observation system(FROS) were installed at the station.
The FROS includes three ultra-sonic anemometer/thermometers and three open-path CO2/H2O gas
analyzers measuring heat fluxes and CO2 flux installed on 2 m, 12 m, and 32 m heights, as well asradiometers on 2 m. The data logger is CR5000.
Wind velocity power spectra were calculated using the complex Fast Fourier Transform (FFT) from theNational Center for Atmospheric Research (NCAR) software package. We chose 38 runs of 30 min withdominant wind direction (southeast) during June 2004. The data were recorded during each run at 10 Hz,
giving records of 18000 points for all measurements at 2 m, 12 m and 32 m.

3. Results
Seasonal changes in turbulent heat fluxes and CO2 flux were all calculated based on turbulent data.
Figure 1 shows the time series of sensible and latent heat fluxes as well as net radiation in June of 2004. It
is clearly shown that the sensible heat flux (denoted as H) is approximately close to or sometimes larger
than the latent heat flux (denoted as LE) in June. However H was always smaller than LE in September(figures not shown). This is due to the solar radiation decrease in autumn of this observational region
resulted in smaller sensible heat flux, and more precipitation from July to September induced larger latent
heat flux.
Figures 2 to 4 present the near-neutral power spectra, plotted on double logarithmic axes, for threecomponents of wind velocity at 2 m, 12 m and 32 m, compared with Kansas results (Kaimal et al., 1972).
The normalized power spectra have slope of –2/3 in the inertial subrange. For the horizontal wind velocity
spectra (seeing Figures 2 and 3), double spectral peaks appear in the low frequency range and much more

evident in the lateral wind velocity v spectrum. This phenomenon doesn’t consist with the classic
Monin-Obukhov similarity theory. This demonstrates a scale separation of the active turbulence within thesurface layer and the much larger inactive motions in the outer boundary layer.
McNaughton and Laubach (2000) have observed similar results from the Warrawidgee experimentconditioned by a stable surface layer with a deep convective boundary layer over the upwind region. In thepresent study, the selected near-neutral surface layer was also largely disturbed by the upwind convective
boundary layer. This is due to that, during the clear summer days on the plateau, the extremely droughty
surface conditions decided deep convective boundary layer was usually formed over the region.
Consequently, we had the surface layer with inactive and active turbulence’s interaction, which particularly
affected heat transport.
The spectra in this study show clear height dependency from 2 m up to 32 m (Figures 2 and 3). The
normalized peak frequency shifts to higher frequency with height increasing and the spectral gap becomes
more evident. Especially prominent on 32 m, the v spectrum (Figure 2) shows a deep and clear gap. Thisparticularly demonstrates the scale separation of the outer and inner scaling motions. The w curves(Figure 4) from these three levels also show height dependency, more noticeable in lower frequency.

References
Högström, U., Hunt, J. C. R., and Smedman, A.: 2002, ‘Theory and Measurements for Turbulence Spectra and Variances in theAtmospheric Neutral Surface Layer’, Boundary-Layer Meteorol. 103, 101–124.
Hunt, J. C. R. and Morrison, J. F.: 2000, ‘Eddy Structure in Turbulent Boundary Layers’, Euro J. Mech. B – Fluids 19, 673–694.
Kaimal, J. C., Wyngaard, J. C., Izumi, Y., and Coté, O. R.: 1972, ‘Spectral Characteristics of Surface-Layer Turbulence’, Quart. J.
Roy. Meteorol. Soc. 98, 563–589.
McNaughton, K. G.: 2004, ‘Turbulence structure of the unstable atmospheric surface layer and transition to the outer layer’,Bound.-Layer Meteor. 112, 199-221.
McNaughton, K. G. and Brunet, Y.: 2002, ‘Townsend’s Hypothesis, Coherent Structures and Monin–Obukhov Similarity’,Boundary-Layer Meteorol. 102, 161–175.
McNaughton, K. G. and Laubach, J.: 2000, ‘Power Spectra and Cospectra for Wind and Scalars in a Disturbed Surface Layer at theBase of an Advective Inversion’, Boundary-Layer Meteorol. 96, 143–185.

Figures2Flux Density (W/m )

800

800
HLERn600

600

400

400

200

200

00-200-200
1/6

11/6

6/6

21/6

16/6

26/6

Date of JuneFig. 1 Time series of sensible (H) and latent (LE) heat fluxes during June 2004 (based on the sensors installed on 12 mheight). Net radiation flux (Rn) is also drawn in the figure.

102m
12m
32m
Kansas
1f Su ( f )
2u*
0.1

0.01
1E-4

1E-3

0.01

0.1

1

10100fz / u

Fig 2 Normalized power spectra of u wind velocity under near-neutral condition on three heights.

102m
12m
32m
Kansas
1f Sv ( f )
2u*
0.1

0.01
1E-4

1E-3

0.01

0.1

110100fz / u

Fig 3 Normalized power spectra of v wind velocity under near-neutral condition on three heights.

10.1

f Sw ( f )
u*2

2m
12m
32m
Kansas

0.01

1E-3

1E-4
1E-4

1E-3

0.01

0.1

110100fz / u

Fig 4 Normalized power spectra of w wind velocity under near-neutral condition on three heights.