Recent observational data (turbulence variables by sonic anemometers and three-dimensional flow pattern by Doppler lidar), obtained during the Cooperative Atmosphere Surface Exchange Study field campaign in October 1999 (CASES-99), show evidence of a layered structure of the near-neutral surface layer: (i) the eddy surface layer (ESL), which is the lower sublayer where blocking of impinging eddies is the dominating mechanism; and (ii) the shear surface layer (SSL), which is an intermediate sublayer, where shear affects the isotropy of turbulence. The origin of the eddies impinging from aloft (probably from the SSL) down to the ESL is preliminarily addressed in this study, since the Doppler lidar data show evidence of linearly organized eddies embedded in the surface layer (i.e., about 100-m vertical extent) and horizontally spaced by about 300 m. This is consistent with theories predicting that the primary mechanism of eddy motion in high Reynolds number wall layers is “top-down.”
The layered structure of the surface layer also has a visible effect on vertical profiles of vertical velocity variance (w2) and momentum transport. In the ESL, w2 scales as z2/3 while it is constant or slightly decreases within the SSL. Concerning momentum transport, ejections contribute identically to the momentum flux as do sweeps in the ESL, whereas in the SSL, ejections give about 50% higher relative contribution.
a. Scientific motivation
The analysis of turbulence structure and its spectral characteristics in the neutral surface layer (SL) has been the subject of considerable theoretical, numerical, and experimental effort for the last decades, since turbulence is one major process controlling momentum, sensible and latent heat and matter exchanges between the surface and the planetary boundary layer (PBL).
At present, most of the effort is focused on (i) understanding the dynamical processes that contribute to the turbulent surface fluxes, and particularly the role of turbulent eddies; and (ii) derivation of reliable and accurate parameterization of surface turbulence. Indeed, in atmospheric modeling, most of the turbulent processes occur at subgrid scale and are thus not explicitly resolved by numerical models. The resolved scales are assumed to contain most of the energy of turbulent motion while on subgrid scales, motions are less energetic. This approach works well far from regions of large gradients (in the mid-PBL for instance), whereas subgrid contribution may become larger than the resolved part near the surface. Consequently, model results become more sensitive to the subgrid scheme in this region.
b. State of knowledge in near-surface dynamical processes
The large amount of near-surface data collected to the present show clear evidence that turbulence characteristics can be described by Monin–Obukhov similarity theory (Monin and Obukhov 1954) over a large range of frequencies in the SL (e.g., Busch 1973 for a review). This similarity theory provides a framework relating the turbulence properties and the characteristic SL parameters such as the height above the ground z and the Monin–Obukhov length LMO. These analytical relationships are essential for subgrid-scale parameterization of turbulence in numerical models.
Similarity theory agrees best with experimental results in unstable stratification, whereas more discrepancies are reported in near-neutral and strongly stable conditions. Busch and Panofsky (1968) used a large amount of data collected over a wide variety of terrain characteristics (rough or smooth, inhomogeneous or homogenous, land or sea) and heights to derive analytic expressions for the longitudinal [E11(k1)] and vertical [E33(k1)] velocity spectra (k1 is the longitudinal wavenumber, which is related to the frequency f by Taylor's hypothesis, k1 = 2πf/U, where U is the mean wind). They show that k1Eii(k1) (i being 1, 2, or 3) follow a −2/3 power law on the high-frequency side (inertial subrange) and a +1 power law on the low-frequency side with a pronounced spectral peak at an intermediate frequency varying with height above the surface. Davenport (1961) published measurements of k1E11(k1), which show evidence of a plateau at intermediate-frequency range meaning that E11(k1) follows a −1 power law revealing turbulence anisotropy in the SL. Similarly, Sitaraman (1970) reports that k1E11(k1) shows a less well-defined peak than k1E33(k1). Deviation from expected isotropy very close to the ground (below 20 m) is pointed out by Kaimal et al. (1969). Kaimal et al. (1972) investigate the onset of isotropy by computing the ratio E33/E11 (which should equal 4/3 in isotropic conditions) as a function of frequency f for various stability conditions. The ratio E33/E11 < 4/3 at large scale (i.e., for small f or k1) and increases rapidly in the decade prior to attaining its isotropic value (4/3), moving systematically to higher values of k1 with increasing stability.
More recent theoretical and numerical studies (e.g., Hunt and Carlotti 2001; Carlotti 2002) as well as experimental results (Richards et al. 1997; Lauren et al. 1999; Högström et al. 2002) show that (i) at low-frequency range, k1E11(k1) ∝ k1; (ii) at intermediate-frequency range, k1E11(k1) is constant (i.e., equivalent to a −1 slope for E11) and; (iii) at high-frequency, k1E11(k1) ∝ k−2/31 (inertial subrange). This results are consistent with the results of Kader and Yaglom (1989) and Yaglom (1991).
Concerning the vertical velocity spectra E33, the results are more difficult to interpret. Kader and Yaglom (1989) and Yaglom (1991) use dimensional analysis to show that E11 and E33 should display the same spectral shape, and give some experimental results supporting this theory. On the other hand, Hunt and Carlotti (2001) use rapid distortion theory (RDT) to predict that in the intermediate-frequency range where k1E11(k1) is constant, it is necessary that E33(k1) be independent of k1. This result applies very close to the ground (below about 15 m where RDT may be applied). This result does not mean that turbulence displays some sort of isotropy very close to the ground. It implies that vertical fluctuations on large scales (i.e., small k1) are more damped than horizontal fluctuations on the same scale, since for a given k1 in the range where this result applies, E33(k1) is much smaller than E11(k1). These predictions are in agreement with the experimental results from Busch and Panofsky (1968), Richards et al. (1997), Lauren et al. (1999), Högström et al. (2002).
The two different predictions for the behavior of E33 are both supported by experimental results and may appear as contradictory. In the present paper, we show that there is no contradiction between these results and we propose a unified theory.
In terms of energetics in the SL, the existence of a −1 range in E11 and/or E33 means that dissipation is enhanced since the −1 slope is less steep than the −5/3 slope. The traditional eddy-to-eddy energy cascade is shortcut by a direct transfer of energy to the small scales (Hunt and Carlotti 2001). A key issue is thus to understand the relation between the spectrum shape and the dynamics of the turbulent eddies in the SL. Hunt and Morrison (2000) suggested that large eddies impinge onto the ground (top-down mechanism for eddy motion at high Reynolds number) where they generate internal boundary layers due to blocking (i.e., zero tangential velocity at the ground) in which smaller eddies develop and where a k−11 self-similar range is observed for horizontal velocity fluctuations. The existence of these smaller eddies is supported by the experimental work of Hommema and Adrian (2003) in the neutral PBL even though Adrian et al. (2000) disagree with Hunt and Morrison (2000) on the mechanism responsible for these substructures (they propose a bottom-up mechanism for eddy motion). Hunt and Carlotti (2001) called the region close to the ground where the smaller eddies are generated the eddy surface layer (ESL). They suggest that its depth is about zi/100, where zi is the PBL depth.
The large eddies may be the structures identified as “streaks” by Drobinski and Foster (2003) in large eddy simulations (LES) or as “very large scale motions” by Kim and Adrian (1999) in pipe flow. LES of PBL flows with neutral stratification display near-surface streaks with average spacing of hundreds of meters (Deardorff 1972; Moeng and Sullivan 1994; Lin et al. 1996, 1997; Drobinski and Foster 2003). Using LES, Lin et al. (1997) derive a relationship between the streak spacing (λ) and the distance from the ground z and the PBL depth zi. Streaks form, evolve, and decay over relatively short lifetimes after which they rapidly regenerate. The estimation of a typical time scale for streaks has been made by Foster (1997) using a linear model and by Lin et al. (1996) and Drobinski and Foster (2003) by following in time and space the evolution of streaks in LES. They found a typical time scale of several minutes.
The smaller eddies may be the “cat's-paws” observed on water surfaces and interpreted by Hunt and Morrison (2000) as the signature of these surface eddies. Wilczak and Tillman (1980), using a network of in situ temperature and velocity sensors, showed that under slightly unstable, high wind speed conditions, near-surface plumes are distinctly elongated in the mean wind direction with typical longitudinal and lateral dimensions of several hundred and several tens of meters, respectively (i.e., an order of magnitude smaller than the large eddies). Shaw and Businger (1985) find that plume-scale (10–100 m) intermittency can occur in the nearly neutral SL and employ conditional sampling to describe their relationship to the turbulent transfer. The typical lifetime of these smaller eddies detected close to the ground by microfronts identification (Mahrt and Howell 1994) ranges between a few seconds (Finnigan 1979; Kikuchi and Chiba 1985) and several tens of seconds (Khalsa and Businger 1977; Antonia et al. 1983; Bergström and Högström 1989; Chen 1990).
The existence of this −1 range in the horizontal spectra and of the organized eddies raises several questions. What is the link between the two? What is the origin of the −1 range in the spectra and of the organized eddies? What are their practical consequences as far as parameterization is concerned?
In the field of low Reynolds number turbulence, it was shown by Hunt and Carruthers (1990) using pure shear RDT that streaks and a k−21 horizontal spectrum are two aspects of the distortion of a weakly turbulent velocity field by a strong shear, answering the first two questions. Unfortunately, there is no such theoretical result for high Reynolds number fully developed turbulence.
In order to explain the origin of the −1 range in the horizontal spectra at high Reynolds number, Tchen (1953) developed a theory based on the presence of an intense shear alone. The only role of the ground is to create the shear. This theory is based on the use of a closure assumption. It was developed at a time when the visualization of coherent structures was not possible, and therefore does not address the key issues raised by the existence of coherent structures.
On the other hand, Hunt (2001), using the phenomenological ideas of Hunt and Morrison (2000), developed a theory where the −1 subrange in E11 can be explained by a specific distribution of the small eddies near the surface in the ESL.
As it has been demonstrated that organized eddy motions are responsible for much of the heat and momentum transfer in PBL (see Raupach et al. 1991 for a review), parameterizations may need to explicitly account for the effects of near-surface organized eddies as they, for instance, must also account for PBL rolls (Brown and Foster 1994; Foster and Brown 1994). However, following Townsend (1976), this −1 range could be associated with “inactive motion,” that is, a turbulent motion which participates in the turbulent kinetic energy but not in the vertical transport of momentum and heat [it is worth noticing that Townsend's (1976) idea originated in experiments by Grant (1958) of long-range correlations in a boundary layer, which are now understood as being similar to a −1 range in the spectrum].
Inspired by this idea, Redelsperger et al. (2001) showed how the energy deficit of turbulence very close to the ground due to enhanced dissipation (the −1 slope being less steep than the −5/3 slope) affects the coefficients to be used in subgrid schemes, while being consistent with Monin–Obukhov similarity theory. They accordingly developed a new subgrid-scale parameterization, which takes into account the −1 range for the spectrum and suitable both for SL and freestream turbulence, and gives physical reasons to discard the choice of the Prandtl mixing length κz for the subgrid mixing length (where κ is the von Kármán constant and z the height) (see also Carlotti and Drobinski 2004, manuscript submitted to J. Fluid Mech.). This parameterization reproduces very well the mean profiles issued from the Monin–Obukhov similarity theory.
c. Objectives of this study
The present work uses some of the very many data collected during the Cooperative Atmosphere Surface Exchange Study field campaign of October 1999 (CASES-99; Poulos et al. 2002) to make a critical review of the literature and to suggest a new understanding of some of the features of atmospheric turbulence in the SL, trying to fill in the gap between the morphological approach (based on the analysis of the structures present in the flow) and the statistical approach (also called “energetical approach,” based on the statistical analysis of the turbulent motion).
For this study, we make use of the data from rawinsondes, sonic anemometers, and a Doppler lidar, which proved to be a uniquely suited instrument to study turbulent eddies in the PBL [e.g., PBL rolls, see Drobinski et al. (1998); or surface streaks, we are only aware of a single published direct observation by Weckwerth et al. (1997)].
After the introduction in section 1, the instrument setup and the meteorological environment are described in section 2. In section 3, a new layering concept of the SL is proposed. In section 4, the eddy generation in the SL is discussed, and in section 5, the effect of the layered structure of the SL on the vertical profile of turbulent kinetic energy in the SL is addressed. Conclusions and suggestions for future works and prospects are given in section 6.
a. CASES-99 experiment
The CASES-99 experiment was designed to be a nighttime experiment to study the stable boundary layer and to study physical processes associated with the morning and evening transition periods (Poulos et al. 2002). The experimental period was from 1 to 31 October 1999 near Leon, which is 50 km east of Wichita, Kansas. Figure 1 shows the CASES-99 main site and the location of a selected set of instruments. A large number of instruments was deployed in this general area.
The current study uses data collected on 13 October 1999 from six 10-m and one 60-m meteorological towers, radiosonde releases, and the high-resolution Doppler lidar (HRDL) developed by National Oceanic and Atmospheric Administration/Environmental Technology Laboratory (NOAA/ETL) in cooperation with the National Center for Atmospheric Research Atmospheric Technology Division (NCAR/ATD) and the Army Research Office (ARO).
The topography of the CASES-99 site is flat with shallow gullies and very gentle slopes covered with prairie grass about 0.5 m tall. These slopes can affect or generate flows at night, but they are not a factor for this afternoon study.
1) High-Resolution Doppler Lidar
HRDL measures range-resolved profiles of aerosol backscatter and radial velocity, that is, the component of wind velocity parallel to the beam. It operates in the near infrared (2.02 μm), so the scattering targets are predominantly aerosol particles. HRDL is well suited for surface layer studies because of its good range resolution (30 m), velocity accuracy (0.1 m s−1), and narrow beam (see Grund et al. 2001 for further details). HRDL's beam can be scanned through the entire upper hemisphere with a scanner resolution of 0.01°. During the CASES-99 experiment, the strategy was to employ a variety of routine survey scans interspersed with higher angular resolution scans to probe features of interest. Routine survey scans generally consisted of a mix of azimuth and elevation scans. Azimuth scans, performed by varying the azimuth angle of the lidar beam while maintaining a fixed elevation angle [so-called plan position indicator (PPI) scans], are useful for surveying the horizontal structure and variability of the velocity field. Alternatively, the elevation or vertical-slice scan [so-called range–height indicator (RHI) scans] is performed by varying the elevation angle of the lidar beam while maintaining a fixed azimuth angle. Vertical-slice scans are useful for analyzing the structure of the velocity field in a 2D vertical cross section of the planetary boundary layer.
In CASES-99, HRDL has been used to study properties of the low-level jet that forms after sunset (Banta et al. 2002) and properties of a shear-instability wave event (Newsom and Banta 2003). However, during CASES-99 we also obtained data during the afternoon to study the convective boundary layers on several occasions, including the afternoon of 13 October 1999.
2) Tower in situ sensors
In situ sensors operated by NCAR and mounted on a 60-m tower and six nearby 10-m towers provided basic meteorological information as well as high-rate wind and temperature data. These sensors operated more or less continuously during the entire monthlong CASES-99 field program.
Wind measurements were made at 5-m intervals on the 60-m tower (hereafter called main tower). Eight sonic anemometers were positioned at heights of 1.5, 5, 10, 20, 30, 40, 50, and 55 m. The sonic anemometers provided three-component wind and temperature data at a sampling rate of 20 Hz. Additionally, four slower-response prop-vane anemometers were positioned at heights of 15, 25, 35, and 45 m.
Thermocouples were installed at 32 levels on the main tower at an average vertical spacing of 1.8 m and on two adjacent 10-m towers.
During intensive observing periods (IOPs), radiosondes were released every 2 h from the main site (Fig. 1) and a triangle of other nearby locations. During non-IOP periods releases occurred 3 times daily. The sonde sampled atmospheric pressure, ambient temperature, and relative humidity at 1 Hz during ascent and transmitted these data to the ground with navigational aid signals from a global positioning system (GPS). Wind measurements at low levels, however, were subject to substantial error due to difficulties in establishing GPS lock.
b. Mean atmospheric conditions
Figure 2 displays the strength and direction of wind as well as the potential temperature from the 1300 central standard time (CST; 1900 UTC) sounding of 13 October 1999. The potential temperature measured by the rawinsonde shows a well mixed layer (ML) capped by a large temperature inversion of 8 K across 350 m at about 750-m height, which defines the PBL top height zi. The potential temperature is constant and equal to 294 K in the ML and the wind blows from the northeast up to 1.7-km height and backs toward the west above. In the first 150 m, the wind varies between 5 near the ground to 10 m s−1, so the near-surface vertical shear of horizontal wind is ≃3.3 10−2 s−1. The SL is characterized by a logarithmic surface wind profile with no veering up to about 150 m, which we define as the top of the SL (Figs. 2 and 3).
A second weaker inversion is visible in the free troposphere (FT) at 1.7-km height, which coincides with the backing of the wind direction, indicating large-scale cold advection through this layer.
With a rather high solar insolation during the day, and significant cooling at night, a significant diurnal cycle drives the stratification in the PBL. We calculate a local stratification parameter using in situ sensors on the instrumented mast. Following Deardorff (1972), the stratification in the PBL can be expressed as zi/LMO, where LMO is the Monin–Obukhov length given by
The variables u∗ and w∗ are the friction velocity and the convective velocity scale, respectively, defined by
where T is the temperature, κ the von Kármán constant (κ ≃ 0.4), g the gravity acceleration, w the turbulent vertical velocity (the mean vertical velocity is considered equal to 0 m s−1), θυ the turbulent potential temperature, and u′ the turbulent longitudinal velocity component. To derive u′, we choose to rotate the coordinate system with the downstream direction x′ along and the cross-stream direction y′ perpendicular to the streak axes (Lin et al. 1996; Foster 1997; Drobinski and Foster 2003), so that
with u and υ the turbulent horizontal velocity components and α the mean wind direction. The turbulent fluxes u′w and wθυ are directly computed from the sonic anemometer measurements in the SL. The surface momentum and heat fluxes are equal to ρu2∗ and −ρcpu∗θ∗, respectively (Fig. 4), where ρ is the air density, cp the specific heat at constant pressure, and θ∗ the scaling temperature given by
The PBL stability is given by the ratio zi/LMO: zi/LMO < 0 (zi/LMO > 0) indicates thermal instability (stability).
Between 1200 and 1330 CST, LMO ≃ −100 with large momentum and heat fluxes (≃0.5 m2 s−2 and ≃250 W m−2, respectively). As the momentum flux drops from ≃0.5 to ≃0.25 m2 s−2, LMO increases to ≃−50, indicating higher instability. Between 1600 and 1715 CST (shaded area), the heat flux decreases to nearly zero due to a large temperature drop (2.5 K h−1) and the momentum flux is halved due to a weaker wind (drop of 1.5 m s−1 h−1). After 1715 CST, both the momentum and heat fluxes are nearly zero. Between 1600 and 1715 CST, zi/LMO ranges between −7 and +3, which corresponds to quasi-neutral stratification (modeling studies suggest that low-level linear streaks occur in shear-dominated PBL flow when zi/LMO = 0). In the following, we will thus focus on the 1600–1715 CST time period.
As u∗ = (where τ is the shear stress, τsfc the shear stress at the surface, and ρ the air density) is a relevant scaling variable for neutral PBL flows, Fig. 5 displays the variation of as a function of height when averaged over the half-hour period. The fluctuations are small and a constant value of 0.4 corresponding to the value of the linear fit in z = 0 will be taken for u∗. In Fig. 3, the mean surface wind is approximated by
(dashed line), where Φm = (1 − 15z/LMO)−1/4 is the empirical stability function for SL (Businger et al. 1971) and z0 is the roughness length. For comparison, the typical logarithmic wind speed profile for strict neutral stability U ≃ (u∗/κ) ln(z/z0) is plotted in a solid line with z0 ≃ 4 cm. It is very close to the measured wind speed at all levels suggesting that the assumption of near neutrality between 1600 and 1715 CST is met.
3. Layered structure of the surface layer
The aim of this section is to explore the vertical structure of the SL to (i) find out the depth of the region within the SL where turbulence anisotropy exists and (ii) validate the shape of E11 and E33 as a function of height.
This issue could have been addressed by using the numerous spectra published in the literature, but the difficulties encountered to do so are mainly due to the fact that (i) the measurements were made with different types of instrument, some of which, in particular in the past, were of questionable technical quality; (ii) some spectra were deliberately strongly high-pass filtered, so that their low-frequency range was severely distorted [this is the reason why the Kansas spectra of Kaimal et al. (1972) do not show a constant range in f E11(f)]; (iii) the atmospheric stability is sometimes not measured but just inferred (e.g., the paper by Lauren et al. (1999), which uses “balloon soundings from a nearby meteorological station” to estimate the vertical temperature gradient); and (iv) topographical features; this is particularly relevant for measurements taken at great heights (order 100 m), where the “flux footprint” may be several kilometers upstream.
In this study, the fluctuations of longitudinal and vertical velocity measured at the eight levels of the 60-m tower are used to compute E11 and E33 as a function of height and in strictly identical atmospheric conditions.
a. Longitudinal velocity spectra
Figures 6 and 7 display the normalized spectra of longitudinal (or streamwise) and vertical velocity plotted against frequency f (which can be converted to k1 using Taylor's hypothesis by k1 = 2πf/U with U being the mean wind) at 1.5, 5, and 10 m AGL (Fig. 6) and 20, 30, and 55 m AGL (Fig. 7). The normalized spectrum of longitudinal velocity E11 evidences three spectral regimes: a very low frequency range where fE11(f)/u2∗ ∝ f (only visible at 1.5 and 5 m in Fig. 6), an intermediate-frequency range where fE11(f)/u2∗ is constant (i.e., −1 power law for E11), and at high frequency the inertial subrange is visible (i.e., for f > f11m where f11m is the lower limit of the −5/3 subrange).
We compare these observations to the rapid distortion theory calculations of Hunt and Carlotti (2001) of streamwise spectra. For an altitude less than a few tens of meters, RDT predicts a broad self-similar −1 range in E11, starting at a very large scale down to the scale given by the height of the measurement. Previous atmospheric measurements have shown evidence of this in various conditions (Kader and Yaglom 1989; Yaglom 1991; Fuehrer and Friehe 1999; Richards et al. 1997; Högström et al. 2002).
The inertial subrange is the range of frequencies where the turbulence is nearly isotropic and the energy transfer across each wavenumber from larger eddies to smaller eddies is almost constant. The intermediate-frequency subrange (−1 power law) encompasses turbulent eddies that are significantly anisotropic due to interaction with the ground, and this is also the frequency band where the local turbulence is generated. Figures 6 and 7 show that the lower limit f11m of the −5/3 subrange for E11 decreases with height.
The vertical profile of f11m is displayed in Fig. 8a. A good fit is obtained between the observations and the equation f11m ≃ 0.125U/z (U being the mean flow at height z). This agrees with the theoretical predictions by Högström et al. (2002), who suggest a proportionality relationship between f11m and U/z. The fit lies between the empirical results of Kaimal et al. (1972), who find f11mz/U ≃ 0.08–0.1 and f11mz/U = 1/(2π) (i.e., k11m = 2πf11m/U = 1/z) suggested by Hunt and Carlotti (2001; their Fig. 2). Hoxey and Richards (1992) show that the −1 intermediate subrange gradually disappears with height (their Fig. 7).
RDT suggests that the surface blocking and shear, which are at the origin of turbulence anisotropy through distortion mechanism, become negligible when height increases and wind weakens. At the low-frequency subrange, there is very little local generation of turbulence at low heights and most of the turbulence is the result of energy being diffused from structures generated at higher altitude. In the inertial subrange, any shearing of structures that might create a contribution to the Reynolds stress is rapidly destroyed by the rest of the turbulence. The intermediate subrange thus must be carefully accounted for in turbulence parameterization, as it contributes to most of the turbulence, thereby playing an essential role in energy and matter transport.
b. Vertical velocity spectra
At 1.5 and 5 m AGL, normalized spectra of vertical velocity E33 display a range where fE33(f)/u2∗ ∝ f (low-frequency range) and the inertial range (high-frequency range) (Figs. 6b,d). This agrees with Perry et al. (1986) and RDT, which show that E33 possesses a 0 range (i.e., are flat) at the same frequency range where a −1 range is expected for the longitudinal velocity spectrum E11 and the transverse velocity spectrum E22. Carlotti (2002) shows that near the surface and at low frequency, the expression of spectra is given by RDT, whereas at high frequency, corresponding to very small structures not affected by the surface, Kolmogorov scaling is relevant (i.e., −5/3 power law).
On the other hand, arguing that at intermediate frequency the horizontal and vertical spectra should not depend on z and using an overlap argument, Kader and Yaglom (1989) and Yaglom (1991) claim that one should get E33 ∝ f−1. The observations contradict this at very low levels, but this prediction is in agreement with the observations made above 30 m (Figs. 7d,f). We suspect that Kader and Yaglom (1989) and Yaglom (1991) made their measurements at about 40-m height, which is higher than the general measurement heights used for SL turbulence studies, and is consistent with our results. One can note the “smooth” transition between the 0 power-law intermediate range and the −1 power-law intermediate range between 10 and 30 m (Figs. 6d and 7b).
As for E11, the lower limit f33m of the −5/3 subrange for E33 decreases with height. The vertical profile of f33m is displayed in Fig. 8b. A good fit is obtained between the observations and the equation f33m ≃ 0.43U/z. Kaimal et al. (1972) show that f33m ≃ 0.5U/z and that f33m/f11m ≃ 5. Our results do not differ too much from their empirical results even though our data give f33m/f11m ≃ 3.6, which is slightly lower.
c. Concept of layered structure
In classical theories, the SL is defined as the lower part of the PBL where the mean velocity profile is logarithmic and the fluxes close to their surface values. It is generally assumed that the spectrum decays as f−5/3. It was suggested by Yaglom (1991) that in the lower part of the SL, the spectra E11, E22, and E33 decay actually as f−1. On the other hand, Hunt and Carlotti (2001) showed with RDT that very close to the ground, in a layer they called “eddy surface layer,” if E11 decays as f−1, then E33 must be constant.
The lower sublayer where blocking is the dominating mechanism, as analyzed in Hunt and Carlotti (2001); following their terminology, we suggest calling this sublayer the eddy surface layer (ESL).
An intermediate sublayer, where shear affects the isotropy of turbulence and the physics is the one described by Yaglom (1991) as the “forced convection sublayer”; we suggest calling this sublayer the shear surface layer (SSL).
The existence of an upper surface layer (USL) at the upper part of the SL (i.e., at the transition with the ML) is suggested by Yaglom (1991). In this sublayer, also referred to as the mixed convection sublayer or free convection sublayer, the mean velocity profile is logarithmic and the horizontal and vertical spectra decays as k−5/31. There is no experimental result on this layer in the data we analyzed, and therefore its study is left for the future.
As discussed above, the vertical velocity spectra between 10 and 30 m reveal a smooth transition between the ESL and SSL. In the SSL, turbulence is created locally by shear and, following Yaglom (1991), the relevant scales are determined by friction. Therefore, on dimensional argument, one must have
at intermediate wavenumbers. Following Tchen (1953), the same −1 range can be found by dynamical arguments and not only on dimensional ground. He suggested a closure distinguishing resonant and nonresonant eddy interaction in a sheared layer that gives results very similar to the present spectra.
The process in the ESL is quite different: eddies created above, that is, in the SSL, impinge onto the ground through the ESL, in a top-down process. Indeed, eddies in the SSL have a motion relative to the mean flow (as any eddy defined as a packet of closed vorticity lines), and a proportion of them will go down. These eddies are distorted by the ground in the way described by RDT (Carlotti 2001). Therefore in the ESL, at intermediate-frequency range,
In Hunt and Carlotti (2001), it was argued that the −1 range in the spectra was created locally in the ESL due to local effects of friction. It was shown in Carlotti (2001) that it is not necessarily so, and that the −1 range may exist prior to the distortion by the ground. The present work goes in the direction of a −1 range created above the ESL in the SSL. This layered structure is schematically represented in Fig. 9.
The reason that shear is not the dominant mechanism in the ESL even though it is very strong is that, as showed by RDT, blocking is (ideally) an infinitely fast mechanism (mathematically, it is controlled by an “elliptical” equation, see Durbin 1993), while shear is a relatively slow phenomenon (controlled by an hyperbolic equation). Hence, the dynamics of eddies impinging onto the ground in the ESL is dominating by blocking.
The dependence of the spectrum shape with measurement heights has been investigated recently by Richards et al. (1999) who discuss the dependence of the spectral models as functions of friction (through u∗ and z0) and height from their observations in Silsoe, Bedford, United Kingdom. They derive empirical spectral models in the intermediate subrange. This empirical approach leads to a gradual variation of the power-law exponent (the exponent decreases with height). They suggest that at high frequency E11(f) ∝ f−5/3, whereas at low frequency E11(f) ∝ f−[0.55+0.12ln(z/z0)] (for z0 = 0.01 m, the slope of the spectrum is −0.83, −1.05, −1.4 for z = 0.115, 1.01, and 10 m, respectively. These values were obtained also experimentally by Richards et al. 1997). It is satisfying from a modeling and parameterization point of view but less satisfying in terms of a layering concept, which links each sublayer in the SL to physical processes. Richards et al.'s (1999) results also suggest that the ESL depth increases with increasing roughness length. In Hunt and Carlotti (2001), an evaluation of the thickness of the ESL was suggested, based on the idea of a modified dissipation process in the ESL and on the decomposition of the turbulent flow between turbulence of scale less than the thickness of the ESL and large eddies. This evaluation of the thickness of the ESL predicts that it increases with roughness with values ranging between 2 m over agricultural fields and 30 m in suburban areas. However, the ESL depth prediction is not fully satisfactory because very crude approximations were made, and because the existence of the SSL that is proposed here was not accounted for. Using the same two main ideas as in the evaluation of Hunt and Carlotti (2001), further exploration should be made taking into account the existence of the SSL and checking all approximations made previously, but we believe it is out of the scope of the present paper.
4. Eddy generation in the surface layer
A key issue is the link between E11 and E33 and the nature of the eddies impinging onto the ground. In the previous section, we suggest that these eddies originate from the SSL through wind shear instabilities, part of these eddies are carried down to the ground through the ESL. As suggested in the introduction, the impinging eddies may be the near-surface streaks described by Foster (1997) and Drobinski and Foster (2003) since they reside in the high-shear surface region. Scratching on the ground, they may generate smaller eddies such as Hunt and Morrison's (2000) cat's paw. The top-down mechanism is consistent with Hunt and Morrison (2000) and Drobinski and Foster (2003) who found evidence for occasional downward-propagating waves from the ML (or/and USL) into the surface region that may enhance streak growth (see also Lin 2000). In terms of the energy budget, this means that there is no local balance between shear production and dissipation. Högström et al. (2002) also suggest that the excess energy is brought down to the surface by a pressure transport term.
In the following, we focus the analysis on the Doppler lidar data that clearly show evidence of streamwise elongated eddies, and we compute momentum fluxes from the 60-m tower to quantify momentum transport by the near-surface eddies and to analyze the correlation between the vertical structure of the SL on the momentum transport efficiency.
a. Near-surface eddies
Up to now, most of the organized structures have been investigated using time series of in situ wind, temperature, and humidity measurements. Remote sensing allows us to visualize the flow. For instance, Fig. 10 shows one scan of radial velocities nearly parallel to the surface from HRDL measurements on 13 October 1999 between 1601 and 1604 CST. Figure 10 shows the elongated structures in the streamwise direction close to the ground with organized regions of alternating high- and low-speed fluid. The structures are what were called streaks by Drobinski and Foster (2003). These streaks of stronger velocity are oriented parallel to the surface wind direction with a horizontal spacing of about 300 m, which is comparable to what is seen in large eddy simulation (LES) studies (e.g., Deardorff 1972; Moeng and Sullivan 1994) and Weckwerth et al.'s (1997) Doppler lidar observations.
The vertical structure in the cross-wind direction of the streaks noted in Fig. 10 is shown in Fig. 11, which consists of six panels taken at about 21-s intervals (except for the first ones) on 13 October 1999 at about 1610 CST. The variation of radial velocities in the vertical is not due to wind direction variation, since it is nearly constant up to 2 km MSL (Figs. 2 and 3). The scans show that the finescale streaks occur in the SL below about 50 m, and that individual streak patterns are short-lived. The near-surface convergence–divergence patterns are consistent with the helical circulations found in larger roll vortices, which occupy the entire PBL and which have been observed by lidar and radar (e.g., Drobinski et al. 1998). These properties are consistent with those found in Drobinski and Foster (2003). The sequence of cross sections also suggest a similar behavior to that proposed by Drobinski and Foster (2003) who found that the streaks are tilted at the beginning of their life cycle; then the streaks strengthen, extend vertically, and are more vertically oriented; finally they reduce their vertical extent before vanishing. However, a more thorough analysis would be needed to determine if the observations agree with the development phases described in Drobinski and Foster (2003). A rough estimate of the time duration of this event from its onset until its breakdown is about 2 min, which is slightly shorter than found by Lin et al. (1996) (about 5 min) and Drobinski and Foster (2003) (about 10 min).
We further analyzed the cross-wind and along-wind vertical-slice scans by computing transverse and longitudinal wavenumber (k2 and k1) spectra (Fig. 12) (Drobinski et al. 2000; Newsom and Banta 2003). The spectra were computed by first interpolating individual sweeps to a rectangular x–z grid (where x is the range from the lidar), and the horizontal velocity was estimated by dividing the radial velocity by the cosine of the elevation angle. This is a valid assumption as along as the elevation angle remains small. The wavenumber spectrum of the horizontal radial velocity as a function x was computed at each z level. A Hanning window was used to minimize spectral leakage effects. Power spectra were averaged over all sweeps in each of the scan sequences (about 20–25 sweeps). This procedure follows the analysis described in Newsom and Banta (2003). One-dimensional power spectra for four vertical levels are shown in Fig. 12.
The spectra show several peaks at the lowest levels (Fig. 12a), including the highest peak corresponding to the 300-m streak scale and one corresponding to the lower wavenumber variations evident in the cross sections of Fig. 10. This is consistent with the appearance of the cross sections in Fig. 11, which show both lower and higher wavenumber structures in addition to the 300-m streaks. The spectra from the higher levels show that the 300-m fluctuations die quickly with height above 50 m, but the lower wavenumber variations are present through deeper layers. This suggest the existence of multiscale structures very close to the surface, whereas higher above only the larger structures are present. The features seen in the transverse spectrum near the ground reinforce the existence of streaks of 300-m dimension in the cross-wind direction. These streaks diminish with height and are not visible in the longitudinal spectra, which indicate primarily lower wavenumber activity. Using LES, Lin et al. (1997) derived a relationship between relationship between the streak spacing (λ) and the distance from the ground z and the PBL depth zi:
where a = −0.24, b = 0.564, σa = 2.387 × 10−2, and σb = 3.383 × 10−2. The standard deviations of a and b are σa and σb. At about z = 10 m above ground with zi ≃ 750 m, Eq. (8) gives λ = 336 m, which is in good agreement with the observed streak spacing.
Horizontal mean and variance profiles were also calculated from the vertical-slice scans using the procedure outlined in Banta et al. (2002). Scan data were binned into horizontal bins at 10-m vertical intervals, and for each 10-m vertical interval we calculated a horizontal mean and variance. The mean wind and velocity variance profiles for the cross-wind and along-wind vertical-slice scans are shown in Fig. 13. The profiles of the wind speed and direction and the longitudinal velocity variance obtained with HRDL are compared with the same profiles obtained from the sonic anemometer measurements collected between 1600 and 1625 CST, which is about the same time interval as for HRDL measurements. The agreement is very good. The mean flow shows little variation with height, but the variance decreases significantly above 80 m (top of the SSL or USL), especially in the cross-wind direction. This is consistent with the streaks being the major source of variation and existing at low levels in the SL. The vertical profiles of the transverse velocity variance υ′2 obtained from HRDL and the 60-m tower are not comparable because with HRDL, υ′2 is computed in the cross-wind direction whereas with the sonic anemometers, it is computed in the along-wind direction.
b. Momentum transport
As the streaks most often occur in updraft–downdraft pairs (Moeng and Sullivan 1994; Lin et al. 1996), this mechanism can impact on the shear production in the SL through the momentum fluxes. Following Lin et al. (1996), the total momentum flux u′w can be divided into four contributions (quadrant analysis): , , , and , where the superscript sign indicates the sign of the velocity fluctuation component. The momentum fluxes are computed from the sonic anemometer measurements between 1600 and 1715 CST.
The results are shown in Fig. 14. They indicate (i) bursts and ejections dominate and vary relatively slowly with height with a mean value of about 30% for both bursts and sweeps in agreement with Högström and Bergström (1996) observations (Fig. 14a); and (ii) a dominance of negative momentum fluxes as ≃ −0.5, which is in agreement with LES studies by Moeng and Sullivan (1994) and Lin et al. (1996) (Fig. 14b). This means that generally, regions of downward (upward) vertical velocity coincide with regions of positive (negative) u′ velocity fluctuations.
Now looking in detail, Fig. 14 shows that the relative contribution of ejections to total momentum flux compared to the relative contribution of sweeps increases significantly with height. In the ESL (up to 10 m, i.e., z/zi = 0.014), ejections contribute identically to the momentum flux as do sweeps. In the SSL (above 10 m), ejections give about 50% higher relative contribution, which is in agreement with Högström and Bergström (1996) even though a little higher. In the SSL, sweeps events u′+w− occur most often (≃35%), while the absolute magnitude of ejections u′−w+ is the strongest (≃2.5u2∗), similarly to Lin et al. (1996).
The dominant contribution of ejections in a top-down process may appear contradictory. This may be a matter of terminology. Indeed, let us consider for example a streak with associated overturning flow. Near the surface the effect of the convergent flow beneath the updraft region will produce a downward momentum flux that looks like an ejection in that the perturbation velocity is upward. The converse contribution to the downward momentum flux in the downdraft region will look like a sweep. However, in this case the coherent eddy inducing this contribution to the momentum flux may not be moving up or downward itself.
Högström and Bergström (1996) stressed the ambiguity in distinguishing between really significant coherent structures of relatively long duration and short ejections and sweeps embedded in these bigger structures. It is a key issue for future prospects to understand better the dynamics in the ESL and in the SSL that would explain the different behaviors within these two layers, as described above. Högström and Bergström (1996) point out that the bursts and sweeps are together almost entirely responsible for the momentum flux and that more than three-quarters of this flux is due to organized motion within these structures.
5. Turbulent kinetic energy in the surface layer
The turbulent kinetic energy (TKE) is one of the most important variables since it measures the intensity of turbulence. It is directly related to the momentum, heat, and moisture transport from the surface through the PBL. It is also sometimes used as a starting point for approximations of turbulent diffusion. The governing equation for the TKE, e′ = (u′2 + υ′2 + w2)/2, is
where the left-hand side term is the energy growth (EG), the first term on the right-hand side is the shear production (SP), the second is buoyancy production (BP), the third is the turbulent transport (TT), the fourth is the pressure transport (PT), and the fifth is the dissipation term (D). The different terms of the TKE budget [Eq. (9)] are computed by averaging between 1600 and 1715 CST. Only the terms EG, SP, BP, and TT can be computed from the sonic anemometer measurements. Local storage EG ≃ 0 m2 s−3.
The TKE budget is primarily dominated by SP and BP is nearly zero confirming the near-neutrality of the SL (Fig. 15a). Figure 15b shows good agreement between the shear production S and the parameterization u3∗(1 − z/zi)Φm/κz (Lenschow 1974; Moeng and Sullivan 1994). The TKE flux we′ is about 0.5u3∗ in the near-neutral SL (Fig. 15c), which is in good agreement with the studies by Shaw and Businger (1985), Grant (1992), and Moeng and Sullivan (1994), for instance.
The contributions from the downstream (u′2) and overturning (υ′2 and w2) to near-surface total TKE e′ are displayed in Fig. 16a, which shows the variances normalized by u2∗, as a function of height. In this quasi-neutral flow, u′2/u2∗, υ′2/u2∗, and w2/u2∗ increase between the ground and 0.015zi (i.e., 10 m) where they reach a maximum, then u′2/u2∗ and υ′2/u2∗ decrease with height while w2/u2∗ is roughly constant above up to 0.08zi of the order of 1.5u2∗. The variances u′2/u2∗, υ′2/u2∗, and w2/u2∗ are about 5–6, 3, and 1–2, respectively, as also found by Panofsky (1974). The ratios of υ′2/u′2 and w2/υ′2 are about 0.5, which is in good agreement with LES studies (Moeng and Sullivan 1994) and observations (Nicholls and Readings 1979; Grant 1986, 1992).
It is generally stated that w2 is constant with height in the lower atmosphere (Panofsky 1974; Yaglom 1991) and this was found in the Kansas experiments. Kader and Yaglom (1989) and Yaglom (1991) also show that a −1 intermediate subrange in E11 and E33 (i.e., in the SSL) leads to variances or spectra independent of height. This agrees with the data analyzed in the present paper, where w2 ≈ 0.24 m2 s−2 (1.5u2∗) above 10 m in the SSL. For the ESL, Carlotti (2001) proposed a pure blocking RDT model adapted for sheared neutral boundary layers and taking into account a −1 intermediate subrange in E11 only. This model shows
where the constants cij are of order one, Λ is the length scale characterizing the lower limit of the −1 range in the spectrum [Λ ≃ ziU/u∗, see Hunt and Morrison (2000)], and β13 an unknown shear parameter. Equation (10) for w2 shows that the theory predicts a constant variance of the vertical velocity in the ESL. In our case, Fig. 16b displays w2 as a function of height (circles) with statistical uncertainty at 1 − σ. The variance w2 increases throughout the ESL (up to 10 m) (even though one could admit that a constant variance is not a bad approximation).
In the 1972 Minnesota experiments, w2 increased by 13% between 4 and 16 m. These latter observations are consistent with wind-tunnel boundary layer data over smooth and rough walls (e.g., Mulhearn and Finnigan 1978). Högström (1990) measured an increase of w2/u2∗ from about u2∗ to about 1.5u2∗ for heights up to 0.04 × 0.3fc/u∗, where fc is the Coriolis parameter and 0.3u∗/fc is an estimation of the height of the PBL. In the present case, fc = 8.88 × 10−5 s−1, u∗ ≃ 0.4 m s−1 so the estimated PBL depth is 1350 m. This is not a very good estimate of the height of the PBL, which is measured to be about 750 m. Several authors used RDT to model w2/u2∗. In a convective case, Hunt (1984) showed that
where ue is the typical velocity of the eddies and Le an eddy length scale. From this, a qualitative argument based on the decomposition of the flow into two separate motions, the blocked motion supposed to follow a convective behavior and the sheared motion supposed to be unaffected by the ground, Hunt and Carlotti (2001) were able to explain the increase of vertical velocity variances and to propose a possible scaling for this evolution, namely,
with CS being close to 1.7 following Townsend (1976). This result was found to be fully consistent with the measurements of Högström (1990) (Högström et al. 2002). In our case, the measurements up to 10-m height are fit with the equation 0.16 + 0.017z2/3 (Fig. 16b). The fitted equation differs from Eq. (12), which gives 0.27 + 0.05z2/3 for Le = 10 m and u2e = w2(z = Le) (Hunt and Carlotti 2001). The analyzed data suggest CS being close to 1.
Moeng and Sullivan (1994) simulation predicts a rapid decrease of w2/u2∗ from 0.5u2∗ to 0.25u2∗ between the surface and 0.1zi. A possible explanation of the discrepancy between the results from Moeng and Sullivan (1994), Högström et al. (2002), and the present experiment is that the LES of Moeng and Sullivan (1994) has coarse resolution near the ground and is therefore very subgrid-model-dependent. Thus, they found (their Fig. 9) that the very sharp decrease of w2 with increasing heights very close to the ground could be an artifact of the subgrid model.
So, for a neutral atmosphere similar to the one studied here, in Richards et al. (1997) and in Högström et al. (2002), the height of the ESL is roughly 10 m, as discussed in Hunt and Carlotti (2001). The height of the SSL is about 80–100 m. This study allows us to reconsider the “problem of the variance of the vertical velocity” in the following way: w2 increases throughout the ESL (see also Högström et al. 2002) and appears constant (or slightly decreases) above in the SSL [even in the USL and MSL as shown in Shaw and Businger (1985) in their Fig. 12c] (see Fig. 16).
One major result of the present study is the determination of a layered structure of the surface layer (SL) in the near-neutral planetary boundary layer (PBL). Indeed, the surface layer can be divided into two sublayers: (i) the eddy surface layer (ESL), which is the lower sublayer where blocking of impinging eddies is the dominating mechanism (Hunt and Carlotti 2001); and (ii) the shear surface layer (SSL), which is an intermediate sublayer, where shear affects the isotropy of turbulence (Kader and Yaglom 1989; Yaglom 1991). The existence of an upper surface layer (USL) at the upper part of the surface layer is suggested by Yaglom (1991), where the mean velocity profile is logarithmic and the horizontal and vertical spectra decays as k−5/31. There is no experimental result on this layer in the data we analyzed, and therefore its study is left for the future.
The present paper also relates for the first time experimentally the presence of near-surface organized eddies with anistropic turbulence characteristics in quasi-neutrally stratified PBL. It also attempts to determine the origin in the SSL of the eddies impinging on the surface (in the ESL). Nevertheless, these are first results that need a more thorough analysis using further high quality field experiments and numerical modeling (e.g., large eddy simulations).
In the future, the effort will be focused on (i) the processes that drive the depths of the ESL, SSL, and USL; (ii) the impact of buoyancy on the existence of anisotropy of near-surface turbulence [which has already been reported in stable situations, Drobinski et al. (2002) and in slightly unstable conditions in this paper] and on the morphological aspects of near-surface eddies (as recently discussed in Kim and Park 2003); and (iii) the improvement of Redelsperger et al. (2001) subgrid model by including the vertical structure of the SL (particularly the ESL, SSL).
The authors would like to thank the anonymous referees that helped to improve the manuscript significantly; P. Naveau and J. C. R. Hunt for fruitful discussions on statistical analysis of turbulence measurements and near-surface structures; and M. C. Lanceau for help in collecting the referenced papers. The work was conducted at the Service d'Aéronomie and Laboratoire de Météorologie Dynamique of Institut Pierre Simon Laplace (IPSL).
Funding for analysis and field measurements was provided by the Army Research Office under Proposals 40065-EV and 43711-EV, and the Center for Geosciences/Atmospheric Research at Colorado State University. The National Science Foundation [Grant ATM-9908453 (HRDL)] also provided funding for the field measurements and analysis. This research has also been funded by the Centre National de Recherche Scientifique (CNRS) and the Institut des Sciences de l'Univers et de l'Environnement (INSUE) through the Programme Atmosphère Océan à Multi-échelle (PATOM).
Corresponding author address: Dr. Philippe Drobinski, Institut Pierre Simon Laplace/Laboratoire de Météorologie Dynamique, Ecole Polytechnique, 91128 Palaiseau Cédex, France. Email: firstname.lastname@example.org