Boundary-Layer Meteorol (2007) 124:449–463 DOI 10.1007/s10546-007-9180-y O R I G I NA L PA P E R
Turbulence spectra in the near-neutral surface layer over the Loess Plateau in China Wei Li · Tetsuya Hiyama · Nakako Kobayashi
Received: 22 December 2005 / Accepted: 6 March 2007 / Published online: 13 June 2007 © Springer Science+Business Media B.V. 2007
Abstract We present the power spectra of wind velocity and the cospectra of momentum and heat fluxes observed for different wind directions over flat terrain and a large valley on the Loess Plateau. The power spectra of longitudinal (u) and lateral (v) wind speeds satisfy the −5/3 power law in the inertial subrange, but do not vary as observed in previous studies within the low frequency range. The u spectrum measured at 32 m height for flow from the valley shows a power deficit at intermediate frequencies, while the v spectrum at 32 m downwind of the valley reaches another peak in the low frequency range at the same frequency as the u spectrum. The corresponding peak wavelength is consistent with the observed length scale of the convective outer layer at the site. The v spectrum for flat terrain shows a spectral gap at mid frequencies while obeying inner layer scaling in its inertial subrange, suggesting two sources of turbulence in the surface layer. All the spectra and cospectra from the valley direction show a height dependency over the three levels. Keywords
Cospectra · Loess Plateau · Power spectra · Spectral gap · Topography
1 Introduction The Loess Plateau in China lies in the middle region of the Yellow River Basin, which is also a semi-arid region affected by the Asian monsoon system with clear seasonal variations. The interactions between the surface and the atmospheric boundary layer (ABL) over this region have significant climatic significance for all of the eastern Asia
W. Li (B) · N. Kobayashi Graduate School of Environmental Studies, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan e-mail:
[email protected] T. Hiyama Hydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Japan
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region. The topography of the plateau is flat tablelands dissected by numerous large and steep gullies. However, until now the role of these gullies in the structure of ABL turbulence over the Loess Plateau is still not clear. In recent years, several new theories about turbulence structure in the atmospheric surface layer (ASL) have been proposed (Hunt and Morrison 2000; Högström et al. 2002; Mc Naughton and Brunet 2002 ; McNaughton 2004b). These theories differ from Monin–Obukhov similarity theory, which was almost universally accepted previously. Monin-Obukhov similarity theory hypothesizes that the larger-scale motions in the boundary layer and the variables that characterize them have no significant influence on the flow near the ground. However, many observations, as well as largeeddy simulations, indicate that the theory is not always applicable. McNaughton and Brunet (2002) demonstrated that during the day in the ASL large-scale motions must somehow coexist with small-scale turbulence, and suggested that Monin–Obukhov similarity theory is completely successful only in the special situation of stable but fully turbulent nighttime conditions when the outer-layer motions are fully uncoupled. Hunt and Morrison (2000) and Hunt and Carlotti (2001) proposed a new theory for the near-neutral boundary layer at high Reynolds number. The dominant mechanism is that large-scale eddies in the middle layer impinge at the surface, being decelerated as they move along with the mean flow, and generate rapidly increasing shear stresses within internal shear layers. A downdraft moves toward the surface creating a cat’s paw, which generates an inner shear layer in the direction of the advected cat’s paw, and streamwise vortices are produced by blocking. If two streamwise vortices of opposite sign interact, an updraft is created and the eddy shear layer grows (Hunt and Morrison 2000). Högström et al. (2002) tested this theory against atmospheric observations and found that the model predictions agree well with measurements of ASL variances and spectra. It correctly predicted the variation of σw2 /u2∗ with height, the low frequency fall-off of the dimensionless spectrum for the vertical velocity, as well as the dimensionless longitudinal velocity spectrum in the surface layer. This ‘top–down’ model that dominates at high Reynolds number differs from the ‘bottom–up’ instability mechanisms that dominate at lower Reynolds number proposed by others. McNaughton and Brunet (2002) challenged Townsend’s hypothesis (Townsend, 1961) and proposed that inactive outer-layer scaling (OLS) motions do interact with active inner-layer scaling (ILS) turbulence near the surface and therefore Monin-Obukhov similarity theory fails. Following that, McNaughton (2004b) presented a ‘bottom–up’ model, called the TEAL (Theodorsen ejection amplifier-like) model, to understand turbulence processes in the unstable ASL, which is incompatible with Hunt and Morrison’s (2000) linearized ‘top–down’ model. This model is ‘bottom–up’ due to the mechanism that the initial instabilities form at the ground to produce attached eddies that grow upwards by a cascade process until the largest of them span the surface layer. The basic eddy in this model is the TEAL structure. When an oncoming flow meets an upward squirt of air, it lifts over and curls around this ejection creating a vortex with a hairpin-shaped core, therefore initiating the TEAL structure. This hairpin vortex creates another larger ejection from within its arc. Thus each TEAL structure is an ejection amplifier, leading to an upscale cascade of TEAL structures. Growing TEAL structures compete for space by distorting each other and only the best formed and most symmetrical at each stage produce ejections able to initiate a further cycle of the cascade (McNaughton, personal communication, 2005).
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Fig. 1 The topography of the experimental region. The digital elevation data were based on http://www2.jpl.nasa.gov/srtm/)
In this study, we attempt to better understand turbulence in the ASL over the heterogeneous surface on the Loess Plateau, the power spectra of wind velocity components as well as cospectra of momentum and heat fluxes from an experiment conducted over the plateau are calculated. The spectra will be compared with some previous spectra over more ideal surfaces. The differences in the behaviours of horizontal wind velocity spectra in lower frequency ranges, which are most prominent in the spectra at 32 m height, will be mainly discussed. The spectral properties and the ASL structure will be analyzed and explained from the topography influence on the plateau as well as the consideration of the ‘bottom–up’ mechanism.
2 Experiment 2.1 Site Description The experiment was carried out at a field site of the Changwu Agro-ecological Experimental Station, Institute of Soil and Water Conservation, Chinese Academy of Sciences, located in the middle southern area of the Loess Plateau in China, 35◦ 12 N, and 107◦ 40 E. The Loess Plateau has a semi-arid land climate, and lies within 100◦ – 115◦ E and 34◦ –40◦ N. The Loess Plateau consists generally of strongly dissected flat terrain and gullies, with typical depth of the order of 100 m and surface width of about 1 km (see Fig. 1). Its total area is 0.62 million km2 (35% tableland; 65% gully slopes). The annual precipitation ranges from 150 mm to 750 mm, 70% of which falls in summer. Because loess soil is susceptible to erosion, the Loess Plateau landscape includes numerous steep gullies. Approximately 90% of the soil deposited into and by the Yellow River each year originates from the Loess Plateau (Kimura et al. 2004a,b; Takayama et al., 2004). The land cover of the study site is heterogeneous, consisting of wheat, apple trees, and residences; the area is mainly flat, except for a large valley with the nearest edge
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about 500 m away from the observation tower to the south-east. The valley has the depth of order 100 m, a surface width of about 1 km, extending to the south-east, with the length of order 10 km. The dominant wind direction is from the south-east during summer and north-west during the other three seasons. The mean annual precipitation is 584 mm and the mean annual air temperature is 9.1◦ C. The long-term statistical data demonstrate that the precipitation over the experimental area occurs mainly from July to September, and that the maximum air temperature occurs in July. 2.2 Instrumentation Since May 2004, ABL field observations have been conducted. A flux and radiation observation system (FROS) was used to measure radiation components and turbulent fluxes in the ASL. The FROS included three ultra-sonic anemometer/thermometers (1210R3; Gill Instruments, Ltd., UK) installed at 2,12, and 32 m heights measuring turbulent wind and temperature fluctuating quantities, as well as shortwave radiometers (CM21; Kipp & Zonen, Inc., USA) at 2 m. The data logger was of the type CR5000, produced by Campbell Scientific, Inc., USA. The ABL height was observed by means of a Wind Profiler Radar (L-28) manufactured by Sumitomo Electric Industries, Ltd., Japan.
3 Method 3.1 Data Processing We used 30-min mean radiation, mean wind speed, and mean precipitation data to select clear days, then prepared raw turbulent data (recorded at 10 Hz) from the ultrasonic anemometer/thermometer to calculate the turbulence spectra on these days. Firstly we selected the wind direction data separately (south-east and north), and removed data if (1) the wind speed was lower than 1.5 m s−1 ; (2) momentum flux u w was positive; (3) |T∗ | was smaller than 0.01 K; (4) the nonstationarity ratio NR was larger than 2. Here NR was defined as NR ≡ σRbtw by Mahrt (1998), where σbtw E is the between-record standard deviation of the record-averaged flux, and RE is the random error. We divided the 30-min time series into six records and each record into five sub-record segments. Then σbtw and RE can be calculated. For flow over complex terrain, errors may arise when vector quantities are measured in a reference framework that is not consistent with that of the equations used to analyze them. To solve this problem, three mathematical transformations were applied here to transform the sampled velocity data from the instrument’s reference frame to the streamline reference frame according to Kaimal and Finnigan’s strategy (1994). We selected wind with direction within the range 125◦ –145◦ to include the upwind topography, the south-east valley, and wind from the north to represent wind flowing from the flat terrain. 3.2 Spectrum Calculation Wind velocity power spectra and flux cospectra were calculated using the complex fast Fourier transform (FFT) courtesy of the National Center for Atmospheric Research
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(NCAR) software package. We chose 30-min runs during one month (June 2004) for wind from the valley direction (south-east), and wind from the flat terrain direction (north). The data were recorded during each run at 10 Hz, giving records of 18,000 points for all measurements at 2 12 and 32 m. According to Kaimal and Finnigan (1994), before employing the FFT algorithm, the linear trends should first be removed from the time series. In addition, the data were also transformed by applying a tapered window (Hamming window adopted here) to reduce the discontinuity at the boundaries of the sampling period. For each 30-min run, the FFT algorithm produced a set of 9000 complex spectral coefficients. Here we combined their real parts and imaginary parts to yield the power spectra as well as the cospectra; the resulting spectra were then smoothed by a Hanning filter. The physical frequency was normalized by the measurement height and mean horizontal wind speed. The power spectra were normalized by u2∗ , the momentum flux cospectra by −u2∗ , and the heat flux cospectra by −u∗ T∗ , where u∗ and T∗ were calculated at the height corresponding to the spectra, 2 m, 12 m, or 32 m. u∗ was determined 1/2 , and T∗ from −w T /u∗ . To allow comparison of the spectral varifrom −u w ances for different atmospheric stabilities (z/L, where z is the measurement height and L the Obukhov length), the spectra were separated into z/L ranges between −0.5 and 0.5 in steps of 0.05. Ensemble averaging was applied for the spectrum series within every stability range to reduce the random errors. The data for −0.05 < z/L < 0 were selected to represent near-neutral conditions.
4 Results Due to similar spectral behaviour at lower frequencies, the analysis in this study relies on the scaling scheme of McNaughton and Laubach (2000), which was applied to describe spectra in the surface layer using ILS and OLS. ILS is appropriate to parts of the spectrum dominated by the effects of friction with the ground. The spectral forms were well defined by the Kansas experiment (Kaimal et al. 1972). In outer-layer scaling, the corresponding frequency scale depends on the turbulence length and velocity scales that characterize the motions in the outer layer. The outer layer is the Deardorff convective boundary layer (CBL); the length scale is the height of the CBL, zi , and the velocity scale is the convective velocity scale w∗ . The treatment of McNaughton and Laubach (2000) was based on measurements above flat terrain. However our situation comprises inhomogeneous topography with a large valley near the experimental site. We attempt to analyze the distinction between the wind spectra over a large valley surface and the wind spectra over a flat surface, while following their scaling regime. The power spectra and cospectra in near-neutral conditions will be presented and compared with the results of Kaimal et al. (1972) and with the results from the Tibetan Plateau of Hong et al. (2004), in which the surface was sparsely covered with short grass with a canopy height smaller than 0.05 m, and was flat and homogeneous with fetches of several km. All spectra in this study are plotted with double logarithmic axes. The spectra were normalized before averaging, indicated on the vertical axes of the plots. The individual spectra were averaged at matching normalized frequency fields with a step of 0.1.
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Figure 2 shows the variations of the turbulence statistic σw /u∗ with z/L at 2, 12 and 32 m; it can be seen that it remains nearly constant within the z/L range of −0.05 to 0.05. 4.1 The horizontal wind velocity power spectra Figures 3 and 6 present the near-neutral power spectra at 2, 12 and 32 m for the longitudinal and lateral components of wind for flow from the valley. The normalized spectra of the two horizontal wind components in this study have slopes of −2/3 in the inertial subranges. Both sets of horizontal wind velocity spectra (see Figs. 3 and 6) show some double spectral peaks in the whole frequency range. For the wind spectra for flow from the flat terrain direction, which is not the dominant wind direction, no data were selected at 2 m height, and for 12 m level, flow distortion existed due to the tower and the instrument mount. Thus only the spectra at 32 m are presented here. Figs. 4 and 5 show the comparison of the horizontal
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power spectra at 32 m for flow from the valley direction and from the flat direction respectively. 4.1.1 u Spectra Figures 3 and 4 show the u spectra of valley upwind and flat terrain upwind. In Fig. 4, the u spectra at 32 m from both directions are presented and are compared with the
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neutral Kansas u spectrum (Kaimal et al. 1972) and those observed at 3 m and 30 m over the Tibetan Plateau by Hong et al. (2004). The high frequency parts of the two u spectra from both flat and valley directions are mainly consistent and parallel to the Kansas curve in the inertial subrange. This means that these spectra obey ILS at these frequencies. In Fig. 4, the u spectrum at 32 m for the flat terrain shows a similar peak frequency as the Kansas spectrum, with higher peak power. In the low frequency part it is also enhanced. On this plot, the u spectrum at 32 m for the valley also shows large differences at intermediate and lower frequencies from the Kansas spectrum. It should be noted that the conditions in the present work differed in several ways from the ideal neutral conditions prevailing at the Kansas experiment. In the present terrain, the land surface was inhomogeneous at the farm scale over the flat topography, and the observation tower was 500 m downwind of the edge of the south-east valley. Thus the shapes of our wind power spectra will be significantly different to those obtained in ideal conditions. When south-east winds occurred at the experimental site, the air flowed upwards over the slopes of the valley and passed through the crest. Over the crest, an internal boundary layer started to develop downstream of the valley. For flow over escarpments (Bowen and Lindley 1977; Emeis et al. 1995), a wake region should be generated close to the ground, immediately behind the crest of the valley, and is a region of higher turbulence intensities and lower mean flow speeds. The high intensity turbulence dissipates quickly as the flow proceeds downstream and becomes insignificant after about 10 escarpment heights downstream. Bowen and Lindley (1977) investigated air flow over forward-facing escarpments in a simulated neutral-stable boundary layer in a wind tunnel. For our situation of a moderate slope, with the measurement height of 32 m, the valley height H of 100 m, and the measurement site 500 m downstream of the crest, the measurement height was therefore approximately 0.3H and the distance
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downstream of the crest was 5H. According to their modelled results, our measurement position was still within the wake region but practically the crest of the valley had insignificant modification to the turbulence in the flow. Compared to that from the flat terrain, the valley u spectrum at 32 m shows a power deficit at intermediate frequencies near the Kansas spectral peak (see Fig. 4), a feature that has been reported for spectra over complex terrain by, e.g. Gallagher et al. (1988), Panofsky et al. (1982), Founda et al. (1997). It was also observed to occur for the mountain site of Great Dun Fell in neutral-stable conditions (Gallagher et al. 1988), and explained as due to a combination of flow over a hill with enhanced small scales in local equilibrium, and damping of intermediate spectral scales by upper level stratification. Högström et al. (1982) introduced the terminology of ‘spectral lag’ for this spectral behaviour, and Panofsky et al. (1982) also found this at the White Sands site, where for certain wind directions for which the slopes were large, the spectral lag was present, but absent for other smoother directions. Founda et al. (1997) assessed the influence of the irregular topography at the summit of a hill in complex terrain, and also observed a power deficit at low frequencies for one constant wind direction under near-neutral stability. They found the largest scales involved in their experiment were about the same order as the scales of the topography and consequently should be subject to local equilibrium near the surface within the inner layer and rapid distortion above. In Fig. 4 the low frequency part of the valley u spectrum is largely enhanced. As discussed by McNaughton and Laubach (2000), this should be associated with the outer-layer scaling. In Fig. 3, the valley u spectra at 2 and 12 m heights do not show a clear spectral gap as the 32 m spectrum, and the u spectra at 3 and 30 m by Hong et al. (2004) were also enhanced at low frequencies, as in our spectra.
4.1.2 v Spectra The v spectra at 32 m for flat terrain and valley are coincident and parallel to the Kansas curve at high frequencies (see Fig. 5); this indicates that they obey ILS. The inner peak frequency of the flat terrain v spectrum at 32 m is lower than that of the Kansas spectrum, and within the decade 0.02–0.1 in the normalized frequency scale, it has a spectral gap. Thus the spectrum shows double spectral peaks in the whole frequency range. This phenomenon is inconsistent with the classic Monin-Obukhov similarity theory. McNaughton and Laubach (2000) observed similar results from the Warrawidgee experiment over a paddy field conditioned by a stable surface layer with a deep CBL upwind. They explained that such a spectral gap demonstrates a scale separation of the active turbulence within the inner surface layer and the much larger inactive turbulence in the outer boundary layer, and proposed the scaling scheme of the outer and inner layer turbulence. Based on this work, McNaughton and Brunet (2002) theorized how such outer and inner motions interact in the surface layer through a bottom–up instability mechanism. The valley v spectrum at 32 m reaches the inner peak in the high frequency range at a higher normalized frequency 0.3 than the flat v spectrum does at 0.1, but at the same position as the valley u spectrum at 32 m does (see Figs. 4 and 5). This indicates that the difference of topography between the valley and the flat terrain has an effect on the structure of the inner surface layer.
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The valley v spectrum at 32 m is largely enhanced at lower frequencies and reaches another peak at the same normalized frequency, 0.01, as that of the valley u spectrum, representing a 3,000-m peak wavelength. Such a length scale λm corresponds to our observed boundary-layer height zi , about 2,000 m for a south-east wind (Nishikawa, personal communication, 2006), with the relationship λm = 1.5zi in the convective outer layer. This indicates that the valley v spectrum at 32 m obeys OLS in the low frequency range. When south-east winds occurred and consequently the valley was upwind of the experimental site, the boundary layer was well developed. The flat v spectrum at 32 m reaches its lower frequency peak at the normalized frequency 0.02, referring to a peak wavelength λm of 1,500 m and a boundary-layer height zi of about 1,000 m. This height is coincident with the observed one (Nishikawa, personal communication, 2006), indicating that the spectrum obeys OLS. The properties of these spectra demonstrate that the surface layer formed both over the valley and over the flat terrain was influenced by the outer layer motions. The bottom–up model in surface layer (Hunt and Morrison 2000; McNaughton 2004a, b, c) is valid for our situation. However, the outer layer that interacted with the inner surface layer formed over the valley was at a significantly different length scale from the outer layer formed over the flat terrain. Compared to the u spectrum, the valley v spectrum at 32 m shows a more evident spectral gap. McNaughton and Brunet (2002) interpreted this as the OLS structures travel faster than the ILS structures in the u direction. The above analysis shows that the v spectrum at 32 m downwind of the valley is a combination of the topography function and the bottom–up mechanism in the surface layer. To some extent, our spectra provide experimental evidence to the bottom–up model over inhomogenous terrain. In addition, similar to the spectra of Hong et al. (2004), in Fig. 6 our v spectra at 2 and 12 m heights are also largely enhanced at low frequencies, although they do not show an obvious spectral gap. The v spectra in this study show a height dependency from 2 m up to 32 m (Fig 6). The inner normalized peak frequency shifts to be higher with height increasing. 4.2 The vertical wind velocity power spectra The w spectra at 32 m height for flow from the valley and from the flat surface (see Figure 7) are consistent with each other at most frequencies, obeying ILS. They agree with the Kansas w spectrum (Kaimal et al. 1972) in the inertial subrange and have similar peak frequency and peak power as it. The spectra decrease almost linearly on log–log scales within the low frequency region. Because large-scale motions are essentially horizontal near the ground, the w spectra have no prominent peak at lower frequencies. The w spectra downwind of the valley at 2, 12, and 32 m levels also show a height dependency, more noticeable in the lower frequency range (see Fig. 8). 4.3 The cospectra The cospectra of uw and wT always provide us valuable information needed for estimating momentum flux and heat flux. Fig. 9 shows the near-neutral uw cospectra at the three heights for wind from the valley direction, compared with the neutral Kansas uw cospectrum (Kaimal et al. 1972). All the cospectra in this study are plotted on logarithmic horizontal and linear vertical axes. In Fig. 9, the uw cospectra at 2 m and
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12 m show similar shapes as the Kansas curve, with the slight shift of the peak frequencies. The uw cospectrum at 32 m also shows the feature of double spectral peaks in the whole frequency range. One peak occurs at the higher normalized frequency of 0.3, and is associated with the behaviour of the corresponding u spectrum; the valley u spectrum at 32 m has its inner peak power at the same position in high frequency range.
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Figure 10 shows the comparison of the uw cospectra at 32 m for wind from the valley direction and from the flat direction respectively. Also plotted is the Kansas uw cospectrum (Kaimal et al. 1972). Compared to the valley uw cospectrum, the flat uw cospectrum is more dispersed in the middle frequencies, and has a larger peak than the valley uw cospectrum; the peak position is at the normalized frequency of around 0.03, which is also consistent with the feature of the flat u spectrum.
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Figure 11 shows the near-neutral wT cospectra at the three heights for flow from the valley, also compared with the neutral Kansas curve (Kaimal et al. 1972). The observed cospectrum at 2 m reaches about the same peak level as the Kansas cospectrum, shifting to the lower normalized frequency. The experimental wT cospectra become more scattered up to the 12 and 32 m levels. The valley wT cospectrum at 32 m again shows a spectral gap at the similar normalized frequencies as the corresponding uw cospectrum and u spectrum; even if the power spectra of temperature T are not shown in this study, this should still be associated with the topography function. Figure 12 is the comparison of the two wT cospectra at 32 m height for valley upwind and flat terrain upwind. The cospectra indicate that a larger sensible heat flux was produced over the flat terrain than that over the valley surface.
5 Conclusion The power spectra of turbulent wind velocity and cospectra of momentum flux and heat flux over the Loess Plateau during mid summer have been calculated and analyzed in this study. The measurements took place under near-neutral conditions at the experimental site where the northern terrain was flat, a large valley was about 500 m south-east to the observation tower, and the land cover was heterogeneous. The calculated horizontal velocity spectra for flow from both directions are consistent with each other in the high frequency range, obeying ILS (McNaughton and Laubach 2000); they do not decrease linearly on log-log scales within the lower frequency range as would be expected on the basis of the trends demonstrated by the Kansas spectra (Kaimal et al. 1972). The u spectrum measured at 32 m for wind from the valley shows a power deficit at intermediate frequencies. The v spectra at 32 m for both directions
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show a spectral gap at mid frequencies while the lower frequency part of the valley v spectrum is largely enhanced. The valley v spectrum at 32 m reaches its inner peak at higher normalized frequency than the flat v spectrum at 32 m, but the same as the valley u spectrum at 32 m. This indicates that the topography difference between the valley and the flat terrain has an effect on the inner surface-layer structure. The valley v spectrum at 32 m reaches another peak in the lower frequency range at the same normalized frequency as the valley u spectrum, referring to a peak wavelength of 3,000 m. This length scale is corresponding to the observed boundary-layer height when south-east winds occurred, with the relationship in the convective outer layer, λm = 1.5zi . The flat v spectrum at 32 m reaches its lower frequency peak at a frequency referring to a 1,500-m peak wavelength, which is also consistent with the observed boundary-layer height. These features indicate that the spectra obey OLS (McNaughton and Laubach 2000) at lower frequencies; the surface layers formed both over the valley and over the flat terrain were influenced by the outer layer motions. However, the outer layer formed over the valley was at a significantly different length scale from that formed over the flat terrain. The bottom–up model in the surface layer (Hunt and Morrison 2000; McNaughton 2004a, b, c) is valid for our situation. Thus the main feature of interest in the present work is that the valley dissecting the flat surface on the Loess Plateau causes the difference on the length scale of the outer layer interacting with the inner surface layer. The v spectrum at 32 m for flow from the valley is a combination of the topography action and the bottom–up mechanism in the surface layer. For some aspects, the present spectra provide experimental evidence to the proposed theory (Hunt and Morrison 2000; McNaughton 2004a, b, c) for the turbulence structure of the ASL, when applied to situations over inhomogenous terrain, involving a ‘bottom–up’ instability mechanism.
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Acknowledgements The Research Institute for Humanity and Nature of Japan supports this study. We give our special thanks to the reviewers of this paper for their many insightful comments on revising. We thank Mr. Nishikawa and other members in our experiment team, Prof. Fukushima, Dr. Higuchi, and Dr. Takahashi. We also give many thanks to Prof. W. Z. Liu, Mr. S. J. Li and other cooperative staffs in Institute of Soil and Water Conservation, Chinese Academy of Sciences (CAS).
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