A New Sensitivity Analysis and Solution Method for Scintillometer Measurements of Area-Averaged Turbulent Fluxes

Scintillometer measurements of the turbulence inner-scale length $l_\mathrm{o }$ l o and refractive index structure function $C_n^2$ C n 2 allow for the retrieval of large-scale area-averaged turbulent fluxes in the atmospheric surface layer. This retrieval involves the solution of the non-linear set of equations defined by the Monin–Obukhov similarity hypothesis. A new method that uses an analytic solution to the set of equations is presented, which leads to a stable and efficient numerical method of computation that has the potential of eliminating computational error. Mathematical expressions are derived that map out the sensitivity of the turbulent flux measurements to uncertainties in source measurements such as $l_\mathrm{o }$ l o . These sensitivity functions differ from results in the previous literature; the reasons for the differences are explored.     

Scalar Flux–Gradient Relationships Under Unstable Conditions over Water in Coastal Regions

The scalar flux–gradient relationships of temperature ( $\phi _{T}$ ? T ) and specific humidity ( $\phi _{q}$ ? q ) under unstable conditions are investigated using eddy-covariance measurements of air–sea turbulent fluxes and vertical profiles of temperature and specific humidity collected from a marine meteorological platform. The gradients of temperature and specific humidity are obtained from measurements at five heights above the sea surface using the log-square fitting method and the simpler first-order approximation method. The two methods yield similar results. The proposed flux–gradient relationships $\phi _{T}$ ? T and $\phi _{q}$ ? q covers a wide range of instability: the stability parameter $\zeta $ ζ ranges from $-$ ? 0.1 to $-$ ? 50. The functional form of the proposed flux–gradient relationships is an interpolation between the Businger–Dyer relation and the free convection relation, which includes the “ $-$ ? 1/2” and “ $-$ ? 1/3” scaling laws at two different stability regimes. The widely used COARE 3.0 algorithm, which is an interpolation between the integrals of the Businger–Dyer and the free convection relations, is also evaluated and compared. The analysis and comparisons show that both schemes generate reasonable values of $\phi _{q}$ ? q in the whole unstable regime. The COARE 3.0 algorithm, however, overestimates $\phi _{T}$ ? T values under very unstable conditions. The errors in the flux–gradient relationships induced by the random errors in the turbulence measurements are assessed. When the random errors are taken into account, the observations agree with predictions of various schemes fairly well, implying that the dominant transport mechanism is adequately captured by the Monin–Obukhov similarity theory. The study also shows that $\phi _{q}$ ? q is significantly ${>}\phi _{T}$ > ? T under unstable conditions and that the ratio $\phi _{q}/\phi _{T}$ ? q / ? T increases with $-\zeta $ ? ζ . The ratio of $\phi _{q}$ ? q to $\phi _{T}$ ? T and the ratio of turbulent transport efficiencies of heat and water vapour ( $R_{wT}/R_{wq}$ R wT / R wq ) suggest that heat is transported more efficiently than water vapour under unstable conditions.     

Investigation of the Stable Atmospheric Boundary Layer at Halley Antarctica

Boundary-layer measurements from the Brunt Ice Shelf, Antarctica are analyzed to determine flux–profile relationships. Dimensionless quantities are derived in the standard approach from estimates of wind shear, potential temperature gradient, Richardson number, eddy diffusivities for momentum and heat, Prandtl number, mixing length and turbulent kinetic energy. Nieuwstadt local scaling theory for the stable atmospheric boundary-layer appears to work well departing only slightly from expressions found in mid-latitudes. An $E$ E – $l_{\mathrm{m}}$ l m single-column model of the stable boundary layer is implemented based on local scaling arguments. Simulations based on the first GEWEX Atmospheric Boundary-Layer Study case study are validated against ensemble-averaged profiles for various stability classes. A stability-dependent function of the dimensionless turbulent kinetic energy allows a better fit to the ensemble profiles.     

Towards Reconciling the Large-Scale Structure of Turbulent Boundary Layers in the Atmosphere and Laboratory

A collaborative experimental effort employing the minimally perturbed atmospheric surface-layer flow over the salt playa of western Utah has enabled us to map coherence in turbulent boundary layers at very high Reynolds numbers, \({Re_{\tau}\sim\mathcal{O}(10^6)}\) . It is found that the large-scale coherence noted in the logarithmic region of laboratory-scale boundary layers are also present in the very high Reynolds number atmospheric surface layer (ASL). In the ASL these features tend to scale on outer variables (approaching the kilometre scale in the streamwise direction for the present study). The mean statistics and two-point correlation map show that the surface layer under neutrally buoyant conditions behaves similarly to the canonical boundary layer. Linear stochastic estimation of the three-dimensional correlation map indicates that the low momentum fluid in the streamwise direction is accompanied by counter-rotating roll modes across the span of the flow. Instantaneous flow fields confirm the inferences made from the linear stochastic estimations. It is further shown that vortical structures aligned in the streamwise direction are present in the surface layer, and bear attributes that resemble the hairpin vortex features found in laboratory flows. Ramp-like high shear zones that contribute significantly to the Reynolds shear-stress are also present in the ASL in a form nearly identical to that found in laboratory flows. Overall, the present findings serve to draw useful connections between the vast number of observations made in the laboratory and in the atmosphere.     

Scaling of Wall-Normal Turbulence Intensity and Vertical Eddy Structures in the Atmospheric Surface Layer

Adequate high-quality data on three-dimensional velocities in the atmospheric surface layer (height \(\delta \)) were acquired in the field at the Qingtu Lake Observation Array. The measurement range occupies nearly the entire logarithmic layer from approximately \(0.006\delta \)–\(0.2\delta \). The turbulence intensity and eddy structures of the velocity fluctuations in the logarithmic region were primarily analyzed, and their variations in the z (wall-normal) direction were revealed. The primary finding was that the turbulent intensity of wall-normal velocity fluctuations exhibits a sharp upswing in the logarithmic region, which differs from classic scaling law and laboratory results. The upswing of the wall-normal turbulence intensity in the logarithmic region is deemed to be linear based on an ensemble of 20 sets of data. In addition, the wall-normal extent of the correlated structures and wall-normal spectra were compared to low Reynolds number results in the laboratory.     

Statistics of Turbulence in the Stable Boundary Layer Affected by Gravity Waves

In order to investigate effects of interactions between turbulence and gravity waves in the stable boundary layer on similarity theory relationships, we re-examined a dataset, collected during three April nights in 1978 and in 1980 on the 300-m tower of the Boulder Atmospheric Observatory (BAO). The BAO site, located in Erie, Colorado, USA, 30 km east of the foothills of the Rocky Mountains, has been known for the frequent detection of wave activities. The considered profiles of turbulent fluxes and variances were normalized by two local, gradient-based scaling systems, and subsequently compared with similarity functions of the Richardson number, obtained based on data with no influence of gravity currents and topographical factors. The first scaling system was based on local values of the vertical velocity variance $\sigma _\mathrm{w}$ and the Brunt–Väisäla frequency $ N,$ while the second one was based on the temperature variance $\sigma _{\theta }$ and $N.$ Analysis showed some departures from the similarity functions (obtained for data with virtually no influence of mesoscale motions); nonetheless the overall dependency of dimensionless moments on the Richardson number was maintained.     

On the Nature of the Transition Between Roll and Cellular Organization in the Convective Boundary Layer

Both observational and numerical studies of the convective boundary layer (CBL) have demonstrated that when surface heat fluxes are small and mean wind shear is strong, convective updrafts tend to organize into horizontal rolls aligned within 10–20\(^\circ \) of the geostrophic wind direction. However, under large surface heat fluxes and weak to negligible shear, convection tends to organize into open cells, similar to turbulent Rayleigh-Bénard convection. Using a suite of 14 large-eddy simulations (LES) spanning a range of \(-z_i/L\) between zero (neutral) and 1041 (highly convective), where \(z_i\) is the CBL depth and L is the Obukhov length, the transition between roll- and cellular-type convection is investigated systematically for the first time using LES. Mean vertical profiles including velocity variances and turbulent transport efficiencies, as well the “roll factor,” which characterizes the rotational symmetry of the vertical velocity field, indicate the transition occurs gradually over a range of \(-z_i/L\); however, the most significant changes in vertical profiles and CBL organization occur from near-neutral conditions up to about \(-z_i/L \approx \) 15–20. Turbulent transport efficiencies and quadrant analysis are used to characterize the turbulent transport of momentum and heat with increasing \(-z_i/L\). It is found that turbulence transports heat efficiently from weakly to highly convective conditions; however, turbulent momentum transport becomes increasingly inefficient as \(-z_i/L\) increases.     

Variability of the Structure Parameters of Temperature and Humidity Observed in the Atmospheric Surface Layer Under Unstable Conditions

The structure parameters of temperature and humidity are important in scintillometry as they determine the structure parameter of the refractive index of air, the primary atmospheric variable obtained with scintillometers. In this study, we investigate the variability of the logarithm of the Monin-Obukhov-scaled structure parameters (denoted as $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ ) of temperature and humidity. We use observations from eddy-covariance systems operated at three heights (2.5, 50, and 90 m) within the atmospheric surface layer under unstable conditions. The variability of $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ depends on instability and on the size of the averaging window over which $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ is calculated. If instability increases, differences in $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ between upward motions (large $C_{s}^2$ ) and downward motions (small $C_{s}^2$ ) increase. The differences are, however, not sufficiently large to result in a bimodal probability density function. If the averaging window size increases, the variances of $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ decrease. A linear regression of the variances of $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ versus the averaging window size for various stability classes shows an increase of both the offset and slope (in absolute sense) with increasing instability. For temperature, data from the three heights show comparable results. For humidity, in contrast, the offset and slope are larger at 50 and 90 m than at 2.5 m. In the end we discuss how these findings could be used to assess whether observed differences in $C_{s}^2$ along a scintillometer path or aircraft flight leg are just within the range of local variability in $C_{s}^2$ or could be attributed to surface heterogeneity. This is important for the interpretation of data measured above a heterogeneous surface.     

Laboratory Experiments on Convective Entrainment Using a Saline Water Tank

Entrainment fluxes in a shear-free convective boundary layer have been measured with a saline water tank set-up. The experiments were targeted towards measuring the entrainment behaviour for medium to high Richardson numbers and use a two-layer design, i.e. two stacked non-stratified (neutral) layers with different densities. With laser induced fluorescence (LIF), the entrainment flux of a fluorescent dye is measured for bulk Richardson numbers in the range 30–260. It is proposed that a carefully chosen combination of top-down and bottom-up processes improves the accuracy of LIF-based entrainment observations. The observed entrainment fluxes are about an order of magnitude lower than reported for thermal water tanks: the derived buoyancy entrainment ratio, $A$ , is found to be $A \approx 0.02$ , which is to be compared with $A\approx 0.25$ for a thermal convection tank (Deardorff et al., J Fluid Mech 100:41–64, 1980). An extensive discussion is devoted to the influence of the Reynolds and Prandtl numbers in laboratory experiments on entrainment.     

Improving a Two-Equation Turbulence Model for Canopy Flows Using Large-Eddy Simulation

Large-eddy simulations of the neutrally-stratified flow over an extended homogeneous forest were used to calibrate a canopy model for the Reynolds-averaged Navier–Stokes (RaNS) method with the $k-\varepsilon $ k - ε turbulence model. It was found that, when modelling the forest as a porous medium, the canopy drag dissipates the turbulent kinetic energy (acts as a sink term). The proposed model was then tested in more complex flows: a finite length forest and a forested hill. In the finite length forest, the destruction of the turbulent kinetic energy by the canopy was overestimated near the edge, for a length approximately twice the tree height. In the forested hill, the model was less accurate inside the recirculation zone and overestimated the turbulent kinetic energy, due to an incorrect prediction of the production term. Nevertheless, the canopy model presented here provided consistent results in both a priori and a posteriori tests and improved the accuracy of RaNS simulations with the $k-\varepsilon $ k - ε model.     

Investigation of the Flow Structure in Step-Up Street Canyons—Mean Flow and Turbulence Statistics

A step-up street canyon is a characteristic urban element composed of two buildings in which the height of the upwind building ( $H_\mathrm{u}$ ) is less than the height of the downwind building ( $H_\mathrm{d}$ ). Here, the effect of canyon geometry on the flow structure in isolated step-up street canyons is investigated through isothermal wind-tunnel measurements. The measurements were acquired along the vertical symmetry plane of model buildings using two-dimensional particle image velocimetry (PIV) for normal approach flow. The building-height ratios considered were: $H_\mathrm{d}/ H_\mathrm{u} \approx 3$ , and $H_\mathrm{d}/ H_\mathrm{u} \approx 1.67$ . For each building-height ratio, the along-wind lengths (L) of the upwind and downwind buildings, and the street-canyon width (S) were kept constant, with $L \approx S$ . The cross-wind widths (W) of the upwind and downwind buildings were varied uniformly from $W/S \approx 1$ through $W/S \approx 4$ , in increments of $W/S \approx 1$ . The objective of the work was to characterize the changes in the flow structure in step-up canyons as a function of W/S, for fixed L, S, and $H_\mathrm{d}/H_\mathrm{u}$ values. The results indicate that the in-canyon flow structure does not vary significantly for $H_\mathrm{d}/H_\mathrm{u} \approx 3$ for the W/S values considered. Qualitatively, for $H_\mathrm{d}/H_\mathrm{u} \approx 3$ , the upwind building behaves as an obstacle in the upwind cavity of the downwind building. In contrast, the flow patterns observed for the $H_\mathrm{d}/H_\mathrm{u} \approx 1.67$ configurations are unique and counter-intuitive, and depend strongly on building width (W/S). For $W/S \approx 1$ and $W/S \approx 2$ , the effect of lateral flow into the canyon is so prominent that even the mean flow patterns are highly ambiguous. For $W/S \approx 3$ and 4, the flow along the vertical symmetry plane is more shielded from the lateral flow, and hence a stable counter-rotating vortex pair is observed in the canyon. In addition to these qualitative features, a quantitative analysis of the mean flow field and turbulence stress field is presented.     

Characterization of Oscillatory Motions in the Stable Atmosphere of a Deep Valley

In a valley sheltered from strong synoptic effects, the dynamics of the valley atmosphere at night is dominated by katabatic winds. In a stably stratified atmosphere, these winds undergo temporal oscillations, whose frequency is given by $N \sin {\alpha }$ N sin α for an infinitely long slope of constant slope angle $\alpha $ α , $N$ N being the buoyancy frequency. Such an unsteady flow in a stably stratified atmosphere may also generate internal gravity waves (IGWs). The numerical study by Chemel et al. (Meteorol Atmos Phys 203:187–194, 2009) showed that, in the stable atmosphere of a deep valley, the oscillatory motions associated with the IGWs generated by katabatic winds are distinct from those of the katabatic winds. The IGW frequency was found to be independent of $\alpha $ α and about $0.8N$ 0.8 N . Their study did not consider the effects of the background stratification and valley geometry on these results. The present work extends this study by investigating those effects for a wide range of stratifications and slope angles, through numerical simulations for a deep valley. The two oscillatory systems are reproduced in the simulations. The frequency of the oscillations of the katabatic winds is found to be equal to $N$ N times the sine of the maximum slope angle. Remarkably, the IGW frequency is found to also vary as $C_\mathrm{w}N$ C w N , with $C_\mathrm{w}$ C w in the range $0.7$ 0.7 – $0.95$ 0.95 . These values for $C_\mathrm{w}$ C w are similar to those reported for IGWs radiated by any turbulent field with no dominant frequency component. Results suggest that the IGW wavelength is controlled by the valley depth.     

Similarity Scaling Over a Steep Alpine Slope

In this study, we investigate the validity of similarity scaling over a steep mountain slope (30–41 $^\circ $ ). The results are based on eddy-covariance data collected during the Slope Experiment near La Fouly (SELF-2010); a field campaign conducted in a narrow valley of the Swiss Alps during summer 2010. The turbulent fluxes of heat and momentum are found to vary significantly with height in the first few metres above the inclined surface. These variations exceed by an order of magnitude the well-accepted maximum 10 % required for the applicability of Monin–Obukhov similarity theory in the surface layer. This could be due to a surface layer that is too thin to be detected or to the presence of advective fluxes. It is shown that local scaling can be a useful tool in these cases when surface-layer theory breaks down. Under convective conditions and after removing the effects of self-correlation, the normalized standard deviations of slope-normal wind velocity, temperature and humidity scale relatively well with $z/\varLambda $ , where $z$ is the measurement height and $\varLambda (z)$ the local Obukhov length. However, the horizontal velocity fluctuations are not correlated with $z/\varLambda $ under all stability regimes. The non-dimensional gradients of wind velocity and temperature are also investigated. For those, the local scaling appears inappropriate, particularly at night when shallow drainage flows prevail and lead to negative wind-speed gradients close to the surface.     

Bulk Mixing and Decoupling of the Nocturnal Stable Boundary Layer Characterized Using a Ubiquitous Natural Tracer

Vertical mixing of the nocturnal stable boundary layer (SBL) over a complex land surface is investigated for a range of stabilities, using a decoupling index ( $0 < D_{rb} < 1$ ) based on the 2–50 m bulk gradient of the ubiquitous natural trace gas radon-222. The relationship between $D_{rb}$ and the bulk Richardson number ( $R_{ib}$ ) exhibits three broad regions: (1) a well-mixed region ( $D_{rb} \approx 0.05$ ) in weakly stable conditions ( $R_{ib} < 0.03$ ); (2) a steeply increasing region ( $0.05 < D_{rb} < 0.9$ ) for “transitional” stabilities ( $0.03 < R_{ib} < 1$ ); and (3) a decoupled region ( $D_{rb} \approx 0.9$ –1.0) in very stable conditions ( $R_{ib} > 1$ ). $D_{rb}$ exhibits a large variability within individual $R_{ib}$ bins, however, due to a range of competing processes influencing bulk mixing under different conditions. To explore these processes in $R_{ib}$ – $D_{rb}$ space, we perform a bivariate analysis of the bulk thermodynamic gradients, various indicators of external influences, and key turbulence quantities at 10 and 50 m. Strong and consistent patterns are found, and five distinct regions in $R_{ib}$ – $D_{rb}$ space are identified and associated with archetypal stable boundary-layer regimes. Results demonstrate that the introduction of a scalar decoupling index yields valuable information about turbulent mixing in the SBL that cannot be gained directly from a single bulk thermodynamic stability parameter. A significant part of the high variability observed in turbulence statistics during very stable conditions is attributable to changes in the degree of decoupling of the SBL from the residual layer above. When examined in $R_{ib}$ – $D_{rb}$ space, it is seen that very different turbulence regimes can occur for the same value of $R_{ib}$ , depending on the particular combination of values for the bulk temperature gradient and wind shear, together with external factors. Extremely low turbulent variances and fluxes are found at 50 m height when $R_{ib} > 1$ and $D_{rb} \approx 1$ (fully decoupled). These “quiescent” cases tend to occur when geostrophic forcing is very weak and subsidence is present, but are not associated with the largest bulk temperature gradients. Humidity and net radiation data indicate the presence of low cloud, patchy fog or dew, any of which may aid decoupling in these cases by preventing temperature gradients from increasing sufficiently to favour gravity wave activity. The largest temperature gradients in our dataset are actually associated with smaller values of the decoupling index ( $D_{rb} < 0.7$ ), indicating the presence of mixing. Strong evidence is seen from enhanced turbulence levels, fluxes and submeso activity at 50 m, as well as high temperature variances and heat flux intermittencies at 10 m, suggesting this region of the $R_{ib}$ – $D_{rb}$ distribution can be identified as a top-down mixing regime. This may indicate an important role for gravity waves and other wave-like phenomena in providing the energy required for sporadic mixing at this complex terrain site.     

Some Statistics of the Temperature Structure Parameter in the Convective Boundary Layer Observed by Sodar

The characteristics of the temporal and height variations of the temperature structure parameter $C_\mathrm{T}^{2}$ in strongly convective situations derived from the sodar echo-signal intensity measurements were analyzed for the first 100 m. It was corroborated that the probability density function (pdf) of the logarithm of $C_\mathrm{T}^{2}$ in the lower convective boundary layer is markedly non-Gaussian, whereas turbulence theory predicts it to be normal. It was also corroborated that the sum of two weighted Gaussians, which characterize the statistics of $C_\mathrm{T}^{2}$ within convective plumes and in their environment and the probability of plume occurrence, well approximates the observed pdfs. It was shown that the height behaviour of the arithmetic mean of $ C_\mathrm{T}^{2}$ (both total and within plumes) follows well a power law $C_\mathrm{T}^{2} (z) \sim z^{-q}$ with the exponent $q$ close to the theoretically predicted value of 4/3. But for the geometrical means of $C_\mathrm{T}^{2}$ (both total and within the plumes), $q$ is close to 1. The difference between arithmetically and geometrically averaged $C_\mathrm{T}^{2}$ profiles was analyzed. The vertical profiles of the standard deviation, skewness and kurtosis of $\hbox {ln}C_\mathrm{T}^{2}$ pdfs were analyzed to show their steady behaviour with height. The standard deviations of the logarithm of $C_\mathrm{T}^{2}$ within the plumes and between them are similar and are 1.5 times less than the total standard deviation. The estimate of the variability index $F_\mathrm{T}$ and its height behaviour were obtained, which can be useful to validate some theoretical and modelling predictions. The vertical profiles of the skewness and kurtosis show the negative asymmetry of pdfs and their flatness, respectively. The spectra of variations in $\hbox {ln}C_\mathrm{T}^{2}$ are shown to be satisfactorily fitted by the power law $f^{-\gamma } $ in the frequency range 0.02 and 0.2 Hz, with the average exponent $\approx $ 1.27  $\pm $  0.22.     

Vertical Distribution of Radiation and Energy Balance Partitioning Within and Above a Lodgepole Pine Stand Recovering from a Recent Insect Attack

The current outbreak of mountain pine beetle (MPB) that started in the late 1990s in British Columbia, Canada, is the largest ever recorded in the north American native habitat of the beetle. The killing of trees is expected to change the vertical distribution of net radiation ( $Q^*$ Q ? ) and the partitioning of latent ( $Q_\mathrm{E}$ Q E ) and sensible ( $Q_\mathrm{H}$ Q H ) heat fluxes in the different layers of an attacked forest canopy. During an intensive observation period in the summer of 2010, eddy-covariance flux and radiation measurements were made at seven heights from ground level up to 1.34 times the canopy height in an MPB-attacked open-canopy forest stand $(\hbox {leaf area index} = 0.55~\mathrm{{m}}^{2}\ \mathrm{{m}}^{-2})$ ( leaf area index = 0.55 m 2 m - 2 ) in the interior of British Columbia, Canada. The lodgepole pine dominated stand with a rich secondary structure (trees and understorey not killed by the beetle) was first attacked by the MPB in 2003 and received no management. In this study, the vertical distribution of the energy balance components and their sources and sinks were analyzed and energy balance closure (EBC) was determined for various levels within the canopy. The low stand density resulted in approximately 60 % of the shortwave irradiance and 50 % of the daily total $Q^*$ Q ? reaching the ground. Flux divergence calculations indicated relatively strong sources of latent heat at the ground and where the secondary structure was located. Only very weak sources of latent heat were found in the upper part of the canopy, which was mainly occupied by dead lodgepole pine trees. $Q_\mathrm{H}$ Q H was the dominant term throughout the canopy, and the Bowen ratio ( $Q_\mathrm{H}/Q_\mathrm{E}$ Q H / Q E ) increased with height in the canopy. Soil heat flux ( $Q_\mathrm{G}$ Q G ) accounted for approximately 4 % of $Q^*$ Q ? . Sensible heat storage in the air ( $\Delta Q_\mathrm{S,H}$ Δ Q S , H ) was the largest of the energy balance storage components in the upper canopy during daytime, while in the lower canopy sensible heat storage in the boles ( $\Delta Q_\mathrm{S,B}$ Δ Q S , B ) and biochemical energy storage ( $\Delta Q_\mathrm{S,C}$ Δ Q S , C ) were the largest terms. $\Delta Q_\mathrm{S,H}$ Δ Q S , H was almost constant from the bottom to above the canopy. $\Delta Q_\mathrm{S,C}$ Δ Q S , C , $\Delta Q_\mathrm{S,B}$ Δ Q S , B and latent heat storage in the air ( $\Delta Q_\mathrm{S,E}$ Δ Q S , E ) varied more than $\Delta Q_\mathrm{S,H}$ Δ Q S , H throughout the canopy. During daytime, energy balance closure was high in and above the upper canopy, and in the lowest canopy level. However, where the secondary structure was most abundant, ${\textit{EBC}} \le 66\,\%$ EBC ≤ 66 % . During nighttime, the storage terms together with $Q_\mathrm{G}$ Q G made up the largest part of the energy balance, while $Q_\mathrm{H}$ Q H and $Q_\mathrm{E}$ Q E were relatively small. These radiation and energy balance measurements in an insect-attacked forest highlight the role of secondary structure in the recovery of attacked stands.     

Turbulence Anisotropy in the Near-Surface Atmosphere and the Evaluation of Multiple Outer Length Scales

Length scales determined by maximum turbulent kinetic energy (TKE), the integral scale, and two length scales based on Reynolds stress-tensor anisotropy are compared to the often stated outer length scales of boundary-layer depth and distance from the earth’s surface, $z$ . The scales are calculated using sonic anemometer data from two elevations, 5 and 50 m above the ground at the main tower site of the CASES-99 field campaign. In general, none of these scales agrees with the other, although the scale of maximum TKE is often similar to the boundary-layer depth during daytime hours, and the length scales derived from anisotropy characteristics are sometimes similar to $\kappa \!z, z$ , and $2z$ depending on scale definition and thermal stability. Except for the scale with the strictest isotropy threshold, the turbulence is anisotropic for each of the various candidates for the outer scale. Length scales for maximum buoyancy flux and temperature variance are evaluated and the turbulence characteristics at these scales are almost always found to be anisotropic.     

A Semi-Analytical Approach for Parametrization of the Obukhov Stability Parameter in the Unstable Atmospheric Surface Layer

A semi-analytical scheme is proposed to parametrize the Obukhov stability parameter \(\zeta \) (= \(z/L\) ; \(z\) is the height above the ground and \(L\) is the Obukhov length) in terms of the bulk Richardson number ( \(R_{iB}\) ) in unstable conditions within the framework of Monin–Obukhov similarity (MOS) theory. The scheme involves, (i) a solution of a cubic equation in \(\zeta \) whose coefficients depend on the gradient Richardson number ( \(R_{i}\) ), and (ii) a relationship between \(R_{i}\) and \(R_{iB}\) . The proposed scheme is applicable for a wide range (i) \(-5\le R_{iB}\le 0\) , (ii) \(0\le \hbox {ln}(z_{0}/z_{h})\le 29.0\) , and (iii) \(10\le z/z_{0}\le 10^{5}\) and performs relatively better than all other schemes in terms of accuracy in computation of surface-layer transfer coefficients. The absolute errors in computing the transfer coefficients do not exceed 7 %. The analysis presented here is found to be valid for different \(\gamma _{m}\) and \(\gamma _{h}\) appearing in the expressions of the similarity functions \(\varphi _{m}\) and \(\varphi _{h}\) (representing non-dimensional wind and temperature profiles), so long as the ratio of \(\gamma _{m}\) to \(\gamma _{h} \ge 1\) . The improved scheme can be easily employed in atmospheric modelling for a comprehensive range of \(R_{iB}\) and a variety of surfaces.     

Turbulent Schmidt Numbers Above a Wheat Crop

Measurements of vertical fluxes and concentration differences above a spring wheat crop (height $h=0.9$ – $0.95$  m, row spacing 0.25 m, displacement height $d=0.5$ – $0.6$  m) were analyzed to determine the Schmidt numbers for water vapour ( $S^\mathrm{v}$ ) and carbon dioxide ( $S^\mathrm{c}$ ) based on concentration differences between intakes 2.55 and 3.54 m above the ground. During nearly-neutral stratification $S^\mathrm{v}(0) = 0.68 \pm 0.1$ while $S^\mathrm{c} = 0.78 \pm 0.2$ , implying that the roughness sublayer extended above $2.5 h$ .