Multi-Scale Sensible Heat Fluxes in the Suburban Environment from Large-Aperture Scintillometry and Eddy Covariance

Sensible heat fluxes ( \(Q_{H}\) ) are determined using scintillometry and eddy covariance over a suburban area. Two large-aperture scintillometers provide spatially integrated fluxes across path lengths of 2.8 and 5.5 km over Swindon, UK. The shorter scintillometer path spans newly built residential areas and has an approximate source area of 2–4 \(\text {km}^{2}\) , whilst the long path extends from the rural outskirts to the town centre and has a source area of around 5–10 \(\text {km}^{2}\) . These large-scale heat fluxes are compared with local-scale eddy-covariance measurements. Clear seasonal trends are revealed by the long duration of this dataset and variability in monthly \(Q_{H}\) is related to the meteorological conditions. At shorter time scales the response of \(Q_{H}\) to solar radiation often gives rise to close agreement between the measurements, but during times of rapidly changing cloud cover spatial differences in the net radiation ( \(Q^{*}\) ) coincide with greater differences between heat fluxes. For clear days \(Q_{H}\) lags \(Q^{*}\) , thus the ratio of \(Q_{H}\) to \(Q^{*}\) increases throughout the day. In summer the observed energy partitioning is related to the vegetation fraction through use of a footprint model. The results demonstrate the value of scintillometry for integrating surface heterogeneity and offer improved understanding of the influence of anthropogenic materials on surface-atmosphere interactions.     

Very-Large-Scale Motions in the Atmospheric Boundary Layer Educed by Snapshot Proper Orthogonal Decomposition

Large-eddy simulations of the atmospheric boundary layer (ABL) under a wide range of stabilities are conducted to educe very-large-scale motions and then to study their dynamics and how they are influenced by buoyancy. Preliminary flow visualizations suggest that smaller-scale motions that resemble hairpins are embedded in much larger scale streamwise meandering rolls. Using simulations that represent more than 150 h of physical time, many snapshots in the \(xy\) -, \(yz\) - and \(xz\) -planes are then collected to perform snapshot proper orthogonal decomposition and further investigate the large structures. These analyses confirm that large streamwise rolls that share several features with the very-large-scale motions observed in laboratory studies arise as the dominant modes under most stabilities, but the effect of the surface kinematic buoyancy flux on the energy content of these dominant modes is very significant. The first two modes in the \(yz\) -plane in the neutral case contain up to 3 % of the total turbulent kinetic energy; they also have a vertical tilt angle in the \(yz\) -plane of about 0 to 30 \(^\circ \) due to the turning effect associated with the Coriolis force. Unstable cases also feature streamwise rolls, but in the convective ABL they are strengthened by rising plumes in between them, with two to four rolls spanning the whole domain in the first few modes; the Coriolis effect is much weaker in the unstable ABL. These rolls are no longer the dominant modes under stable conditions where the first mode is observed to contain sheet-like motions with high turbulent kinetic energy. Using these proper orthogonal decomposition modes, we are also able to extract the vertical velocity fields corresponding to individual modes and then to correlate them with the horizontal velocity or temperature fields to obtain the momentum and heat flux carried by individual modes. Structurally, the fluxes are explained by the topology of their corresponding modes. However, the fraction of the fluxes produced by the modes is invariably smaller than the fraction of energy they contain, particularly under stable conditions where the first modes are found to perform weak counter-gradient fluxes.     

Cross-Validation of Open-Path and Closed-Path Eddy-Covariance Techniques for Observing Methane Fluxes

Methane ( ${\mathrm {CH}}_{4}$ ) fluxes observed with the eddy-covariance technique using an open-path ${\mathrm {CH}}_{4}$ analyzer and a closed-path ${\mathrm {CH}}_{4}$ analyzer in a rice paddy field were evaluated with an emphasis on the flux correction methodology. A comparison of the fluxes obtained by the analyzers revealed that both the open-path and closed-path techniques were reliable, provided that appropriate corrections were applied. For the open-path approach, the influence of fluctuations in air density and the line shape variation in laser absorption spectroscopy (hereafter, spectroscopic effect) was significant, and the relative importance of these corrections would increase when observing small ${\mathrm {CH}}_{4}$ fluxes. A new procedure proposed by Li-Cor Inc. enabled us to accurately adjust for these effects. The high-frequency loss of the open-path ${\mathrm {CH}}_{4}$ analyzer was relatively large (11 % of the uncorrected covariance) at an observation height of 2.5 m above the canopy owing to its longer physical path length, and this correction should be carefully applied before correcting for the influence of fluctuations in air density and the spectroscopic effect. Uncorrected ${\mathrm {CH}}_{4}$ fluxes observed with the closed-path analyzer were substantially underestimated (37 %) due to high-frequency loss because an undersized pump was used in the observation. Both the bandpass and transfer function approaches successfully corrected this flux loss. Careful determination of the bandpass frequency range or the transfer function and the cospectral model is required for the accurate calculation of ${\mathrm {CH}}_{4}$ fluxes with the closed-path technique.     

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.     

Air–Sea \mathrm{CO}_{2} Gas Transfer Velocity in a Shallow Estuary

The air–sea transfer velocity of $\mathrm{CO}_{2}\, (k_{\mathrm{CO}_{2}})$ was investigated in a shallow estuary in March to July 2012, using eddy-covariance measurements of $\mathrm{CO}_{2}$ fluxes and measured air–sea $\mathrm{CO}_{2}$ partial-pressure differences. A data evaluation method that eliminates data by nine rejection criteria in order to heighten parametrization certainty is proposed. We tested the data evaluation method by comparing two datasets: one derived using quality criteria related solely to the eddy-covariance method, and the other derived using quality criteria based on both eddy-covariance and cospectral peak methods. The best parametrization of transfer velocity normalized to a Schmidt number of 600 $(k_{600})$ was determined to be: $k_{600} = 0.3\,{U_{10}}^{2.5}$ where $U_{10}$ is the wind speed in m $\mathrm{s}^{-1}$ at 10 m; $k_{600}$ is based on $\mathrm{CO}_{2}$ fluxes calculated by the eddy-covariance method and including the cospectral peak method criteria. At low wind speeds, the transfer velocity in the shallow water estuary was lower than in other coastal waters, possibly a symptom of low tidal amplitude leading to low intensity water turbulence. High transfer velocities were recorded above wind speeds of 5 m $\mathrm{s}^{-1}$ , believed to be caused by early-breaking waves and the large fetch (6.5 km) of the estuary. These findings indicate that turbulence in both air and water influences the transfer velocity.     

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.     

Estimating a Lagrangian Length Scale Using Measurements of CO2 in a Plant Canopy

Analytical Lagrangian equations capable of predicting concentration profiles from known source distributions offer the opportunity to calculate source/sink distributions through inverted forms of these equations. Inverse analytical Lagrangian equations provide a practical means of estimating source profiles using concentration and turbulence measurements. Uncertainty concerning estimates of the essentially immeasurable Lagrangian length scale ( ${\mathcal{L}}$ ), a key input, impedes the operational practicality of this method. The present study evaluates ${\mathcal{L}}$ within a corn canopy by using field measurements to constrain an analytical Lagrangian equation. Measurements of net CO₂ flux, soil-to-atmosphere CO₂ flux, and in-canopy profiles of CO₂ concentration provided the information required to solve for ${\mathcal{L}}$ in a global optimization algorithm for 30-min time intervals. For days when the canopy was a strong CO₂ sink, the optimization frequently located ${\mathcal{L}}$ profiles that follow a convex shape. A constrained optimization then fit the profile shape to a smooth sigmoidal equation. Inputting the optimized ${\mathcal{L}}$ profiles in the forward and inverse Lagrangian equations leads to strong correlations between measured and calculated concentrations and fluxes. Coefficients of the sigmoidal equation were specific to each 30-min period and did not scale with any measured variable. Plausible looking ${\mathcal{L}}$ profiles were associated with negative bulk Richardson number values. Once the canopy senesced, a simple eddy diffusivity profile sufficed to relate concentrations and sources in the analytical Lagrangian equations.     

Intercomparison of Methods for the Simultaneous Estimation of Zero-Plane Displacement and Aerodynamic Roughness Length from Single-Level Eddy-Covariance Data

We applied three approaches to estimate the zero-plane displacement $d$ through the aerodynamic measurement height $z$ (with $z = z_{m}- d$ and $z_{m}$ being the measurement height above the surface), and the aerodynamic roughness length $z_{0}$ , from single-level eddy covariance data. Two approaches (one iterative and one regression-based) were based on the universal function in the logarithmic wind profile and yielded an inherently simultaneous estimation of both $d$ and $z_{0}$ . The third approach was based on flux–variance similarity, where estimation of $d$ and consecutive estimation of $z_{0}$ are independent steps. Each approach was further divided into two methods differing either with respect to the solution technique (profile approaches) or with respect to the variable (variance of vertical wind and temperature, respectively). All methods were applied to measurements above a large, growing wheat field where a uniform canopy height and its frequent monitoring provided plausibility limits for the resulting estimates of time-variant $d$ and $z_{0}$ . After applying, for each approach, a specific data filtering that accounted for the range of conditions (e.g. stability) for which it is valid, five of the six methods were able to describe the temporal changes of roughness parameters associated with crop growth and harvest, and four of them agreed on $d$ to within 0.3 m most of the time. Application of the same methods to measurements with a more heterogeneous footprint consisting of fully-grown sugarbeet and a varying contribution of adjacent harvested fields exhibited a plausible dependence of the roughness parameters on the sugarbeet fraction. It also revealed that the methods producing the largest outliers can differ between site conditions and stability. We therefore conclude that when determining $d$ for canopies with unknown properties from single-level measurements, as is increasingly done, it is important to compare the results of a number of methods rather than rely on a single one. An ensemble average or median of the results, possibly after elimination of methods that produce outliers, can help to yield more robust estimates. The estimates of $z_{0}$ were almost exclusively physically plausible, although $d$ was considered unknown and estimated simultaneously with the methods and results described above.     

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.     

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.     

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 $2.5 h$ .     

Turbulent Transport of Momentum and Scalars Above an Urban Canopy

Turbulent transport of momentum and scalars over an urban canopy is investigated using the quadrant analysis technique. High-frequency measurements are available at three levels above the urban canopy (47, 140 and 280 m). The characteristics of coherent ejection–sweep motions (flux contributions and time fractions) at the three levels are analyzed, particularly focusing on the difference between ejections and sweeps, the dissimilarity between momentum and scalars, and the dissimilarity between the different scalars (i.e., temperature, water vapour and $\hbox {CO}_{2})$ . It is found that ejections dominate momentum and scalar transfer at all three levels under unstable conditions, while sweeps are the dominant eddy motions for transporting momentum and scalars in the urban roughness sublayer under neutral and stable conditions. The flux contributions and time fractions of ejections and sweeps can be adequately captured by assuming a Gaussian joint probability density function for flow variables. However, the inequality of flux contributions from ejections and sweeps is more accurately reproduced by the third-order cumulant expansion method (CEM). The incomplete cumulant expansion method (ICEM) also works well except for $\hbox {CO}_{2}$ at 47 m where the skewness of $\hbox {CO}_{2}$ fluctuations is significantly larger than that for vertical velocity. The dissimilarity between momentum and scalar transfers is linked to the dissimilarity in the characteristics of ejection–sweep motions and is further quantified by measures of transport efficiencies. Atmospheric stability is the controlling factor for the transport efficiencies of momentum and heat, and fitted functions from the literature describe their behaviour fairly accurately. However, transport efficiencies of water vapour and $\hbox {CO}_{2}$ are less affected by the atmospheric stability. The dissimilarity among the three scalars examined in this study is linked to the active role of temperature and to the surface heterogeneity effect.     

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.     

Asymmetric effects of soil moisture on mean daily maximum and minimum temperatures over eastern China

This study statistically investigates the effects of soil moisture on mean daily maximum ( $T_{\rm{max} }$ ) and minimum temperatures ( $T_{\rm{min} }$ ) over eastern China in spring (from March to May), summer (from June to August) and fall (from September to November), using the Global Land Data Assimilation System (GLDAS) soil moisture and observational temperatures. The results show that soil moisture exerts asymmetric effects on $T_{\rm{max} }$ and $T_{\rm{min} }$ , thereby has substantial effects on the diurnal temperature range (DTR) in the three seasons. The soil moisture feedbacks on $T_{\rm{max} }$ , $T_{\rm{min} }$ , and DTR are found to evidently vary with season. In spring and summer, soil moisture exerts stronger negative forcing on $T_{\rm{max} }$ than $T_{\rm{min} }$ , and thus has negative effects on the DTR over many areas of northern China. In fall, soil moisture has much stronger positive effects on $T_{\rm{min} }$ than $T_{\rm{max} }$ , and thus has significant negative effects on the DTR over Northeast China and some areas of the climatic and ecological transition zone of northern China. The uncertainties in the employed data and method should be noted. Therefore, the results need to be further investigated by other data sets and methods in the future.     

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.     

Surface Heterogeneity Effects on Regional-Scale Fluxes in the Stable Boundary Layer: Aerodynamic Roughness Length Transitions

The effects of abrupt streamwise transitions of the aerodynamic roughness length ( $z_\mathrm{o}$ z o ) on the stable atmospheric boundary layer are evaluated using a series of large-eddy simulations based on the first Global Energy and Water Cycle Experiment Atmospheric Boundary Layer intercomparison study (GABLS1). Four $z_\mathrm{o}$ z o values spanning three orders of magnitude are used to create all possible binary distributions with each arranged into patches of characteristic length scales equal to roughly one-half, one, and two times the equivalent homogeneous boundary-layer height. The impact of the heterogeneity on mean profiles of wind speed and temperature, on surface fluxes of heat and momentum, and on internal boundary-layer dynamics are considered. It is found that $z_\mathrm{o}$ z o transitions do not significantly alter the functional relationship between the average surface fluxes and the mean profiles of wind speed and potential temperature. Although this suggests that bulk similarity theory is applicable for modelling the stable boundary layer over $z_\mathrm{o}$ z o heterogeneity, effective surface parameters must still be specified. Existing models that solve for effective roughness lengths of momentum and heat are evaluated and compared to values derived from the simulation data. The existing models are unable to accurately reproduce both the values of the effective aerodynamic roughness lengths and their trends as functions of patch length scale and stability. A new model for the effective aerodynamic roughness length is developed to exploit the benefits of the other models tested. It accurately accounts for the effects of the heterogeneity and stratification on the blending height and effective aerodynamic roughness length. The new model provides improved average surface fluxes when used with bulk similarity.     

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.