Temperature Structure and Scaling Relations for Heat Transfer in the Stable Boundary Layer

We analyzed 14 days of observations from sonic anemometry and high-resolution fiber-optic distributed sensing collected in the stable boundary layer (SBL). The study sought to evaluate if and under which conditions the sensible heat flux is related to the temperature gradient. Machine learning methods were employed to identify drivers of and model heat fluxes. We found the recently proposed coupling metric Ω defined as the ratio of the buoyancy length scale and measurement height to delineate physically meaningful transport regimes. The regime transition marks the point where static stability, in addition to the vertical turbulence strength, controls the heat transport, which is rather gradual than abrupt. The maximum downward heat flux is reached when one-third of turbulent eddies exceed the opposing buoyancy forces in the SBL. We found evidence that even for large Ω a substantial fraction of the turbulent transport is nonequilibrium. The nondimensional temperature gradient is better explained by variations in Ω than ζ = zL−1 from Monin–Obukhov similarity theory. Its continuous organization with Ω across stabilities suggests that the vertical heat transport always remains coupled to the surface, but its efficiency and the resulting flux vary. Forty-three percent of the total enthalpy is exchanged during conditions of limited transport efficiency in the very SBL despite the small flux magnitude of ≤7 W m−2, which underlines the importance of quantifying the weak surface exchange for polar regions. When predicting sensible heat fluxes using mean quantities from weather stations, the net longwave radiative forcing and the horizontal wind speed are the most important predictors representing stratification and bulk shear. Significance Statement Climate warming is amplified in polar regions, but quantifying heat transfer is complicated since mixing is weak and sporadic. We aim to understand when and why measurements taken in the lowest meters above snow can be used to quantify the surface heat transfer and if common modeling concepts are valid. We found that the measured heat transfer for weak winds and clear skies is connected to the snow surface only to a small degree in 66% of all cases at a much (−65%) reduced magnitude compared to strong wind or cloudy cases. However, 43% of the total heat is exchanged during these conditions and thus must be included in surface heat budgets. Classic modeling concepts systematically underpredicted the exchanged heat budget by 12% across all conditions which limits their utility in polar regions.

A shallow, stable boundary layer is ubiquitous over the cool waters of the Gulf of Maine in summer. This layer affects pollutant transport throughout the region by isolating overlying flow from the surface. In this paper, we explore how the stable boundary layer is formed and describe its characteristics. The temperature profile of the lowest 1–2 km of the atmosphere over the Gulf of Maine is remarkably similar regardless of transport time over water or the time of day when the flow left the land, provided only that the flow is offshore. This similarity is forced by the (roughly) constant water temperature and the (roughly) constant temperature of the free troposphere over the continent. However, the processes leading to the similar profiles are quite different depending on the time of day when the flow crosses the coast. Air leaving the coast at night already has a stable profile, whereas air leaving the coast at midday or afternoon has a deep mixed layer. In the latter case, the stable layer formation over the water is of interest. Using observations of surface fluxes, profiles, and winds on the NOAA Research Vessel Ronald H. Brown from the 2004 International Consortium for Atmospheric Research in Transport and Transformation (ICARTT)/New England Air Quality Study, we show that the formation of the stable layer, which involves cooling a roughly 50‐ to 100‐m‐deep layer by 5–15 K, occurs within 10 km and a half hour after leaving the coast. The internal boundary layer near shore is deeper than predicted by standard relationships. Historical data are explored and also show deeper internal boundary layers than predicted. We also describe one exceptional case where a 200‐m‐deep neutral layer was observed and discuss the degree of isolation of the stable boundary layer and its duration.

A wind tunnel study of dense gas dispersion in a stable boundary layer over a rough surface

Until recently the concern of the traditional theory of the atmospheric stable boundary layer (SBL) was, almost without exception, the nocturnal SBL developing after sunset on the background of a neutral or slightly stable residual layer. In the nocturnal SBLs the nature of turbulence is basically local. Its lower portion is well described by the classical Monin–Obukhov surface‐layer similarity theory. Things are different in long‐lived SBLs situated immediately below the stably stratified free flow. Here, the surface‐layer turbulence is affected by the free‐flow Brunt–Väisälä frequency, N. The surface layer represents approximately one‐tenth of the SBL, so that it is separated from the free atmosphere by the upper nine‐tenths of the SBL comprising hundreds of metres. Traditional concepts fail to explain such distant links. Zilitinkevich and Calanca extended the traditional Monin–Obukhov similarity theory by including N in the surface‐layer scaling, and provided experimental evidence in support of this extension. In the present paper, physical mechanisms responsible for non‐local features of the long‐lived SBL turbulence are identified as: radiation of internal waves from the SBL upper boundary to the free atmosphere, and the internal‐wave transport of the squared fluctuations of velocity and potential temperature. The third‐order wave‐induced fluxes are included in an advanced turbulence‐closure model to correct the wind and temperature profiles in the surface layer. The model explains why developed turbulence in the surface layer can exist at much larger Richardson numbers than the classical theory predicts. Results from the new model are in good agreement with the extended similarity theory and experimental data. Copyright © 2002 Royal Meteorological Society.

Interest in the present problem arose after the publication of the results of the experiments of Kramer [1–3]. In addition to the studies indicated in [4], the articles [5–8] are devoted to the question of the interaction of a flexible elastic surface with the boundary layer. In the present paper the problem of the interaction of an elastic surface with disturbances arising in the boundary layer is posed as in [4]. The approximate nature of the methods of solving the problem of the hydrodynamic stability of the laminar boundary layer leads to a difference in the final computational formulas even in the case when authors use the same Heisenberg-Tollmien-Schlichting-Lin scheme. Therefore, in what follows we present a comparison of the data on the stability of the boundary layer on a solid wall obtained by several authors with the calculations using the formulas, which are then generalized to the case of the elastic surface.

2 Bloom, M., Further Comments on Effect of Surface Cooling on Laminar Boundary-Layer Stability, Readers' Forum, Journal of the Aeronautical Sciences, Vol. 19, No. 5, p. 359, May, 1952. 3 Lees, L., The Stability of the Laminar Boundary Layer in a Compressible Fluid, NACA Report No. 876,1947. 4 Van Driest, E. R., Calculation of the Stability of the Laminar Boundary Layer in a Compressible Fluid on a Flat Plate with Heat Transfer, Journal of the Aeronautical Sciences, Vol. 19, No. 12, pp. 801-812, 829, December, 1952. 5 Bloom, M., Calculation of Stability of Constant-Pressure Boundary Layers on Isothermal Surfaces with an Integral-Method Mean-Flow Solution, Polytechnic Institute of Brooklyn, PIBAL No. 179 (revised September 25, 1953). (To appear as a NACA TN, Contract No. NAw-5809.) 6 Chapman, D. R., and Rubesin, M. W., Temperature and Velocity Profiles in the Compressible Laminar Boundary Layer with Arbitrary Distribution of Surface Temperature, Journal of the Aeronautical Sciences, Vol. 16, No. 9, p. 547, September, 1949. 7 Lin, C. C , On the Stability of the Boundary Layer with Respect to Disturbances of Large Wave Velocity, Readers' Forum, Journal of the Aeronautical Sciences, Vol. 19, No. 2, p. 138, February, 1952. 8 Cheng, S.-I., On the Stability of Laminar Boundary Layer Flow, Quarterly of Applied Mathematics, Vol. XI , No. 3, p. 346, October, 1953.

Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin-Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on the spectral analysis of wind velocity and air temperature fluctuations, it is shown that, when both of the gradient Richardson number, Ri, and the flux Richardson number, Rf, exceed a 'critical value' of about 0.20 - 0.25, the inertial subrange associated with the Richardson-Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in this supercritical regime, but this is non-Kolmogorov turbulence, and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Richardson-Kolmogorov energy cascade weakens; therefore, the applicability of local Monin-Obukhov similarity theory in stable conditions is limited by the inequalities Ri < Ri_cr and Rf < Rf_cr. However, it is found that Rf_cr = 0.20 - 0.25 is a primary threshold for applicability. Applying this prerequisite shows that the data follow classical Monin-Obukhov local z-less predictions after the irrelevant cases (turbulence without the Richardson-Kolmogorov cascade) have been filtered out.

: Under previous support from the Army Research Office (ARO), we developed Lagrangian particle dispersion models (LPDMs) for dispersion in convective and stable planetary boundary layers (PBLs) including some with a forest canopy and showed that predicted concentration fields agreed well with laboratory data and field observations. For the ARO program just completed, this work was extended to dispersion in more stable PBLs and stable boundary layers (SBLs) over horizontally heterogeneous surfaces. This was pursued in part using our new coupled multi-layer canopy - soil model. The program consisted of three main investigations. The first had two parts: a) further development of the coupled-canopy large-eddy simulation (LES) model and comparison with observations from the CHATS (Canopy Horizontal Array Turbulence Study) field program, and b) modeling of canopy dispersion using the LPDM-LES approach and assessment of this with the CHATS dispersion data. The second was an investigation of the effects of a surface-temperature heterogeneity on dispersion in the SBL. The third study a) used the coupled model to produce a more stable boundary layer and applied the LES fields generated from this to drive our LPDM, and b) developed an LPDM based on parameterized turbulence profiles for modeling dispersion in more stable PBLs.

Since turbulent mixing often becomes discontinuous and intermittent in the stable stratified boundary layer, so do nighttime CO2 fluxes observed over an ecosystem. The friction velocity correction (u*-correction) is applied to nighttime CO2 fluxes measured with the eddy covariance technique for evaluating the ecosystem respiration rate. However, the applicability of this procedure is uncertain in intermittently turbulent conditions as the friction velocity oscillates between extremely large and small values.We used a simple numerical model to simulate intermittent mixing in the stable boundary layer and analysed the characteristics of intermittent nighttime CO2 fluxes. We then examined the applicability of the u*-correction in intermittently turbulent conditions. The simulation results showed alternations between highly turbulent periods with large positive CO2 fluxes and quiescent periods with small positive and zero CO2 fluxes. With increasing the geostrophic wind in the range of 5.0 m s-1 to 8.0 m s-1, the magnitude of upward intermittent CO2 fluxes as well as the time intervals between intermittent turbulent periods became smaller. A non-linear dependency of the upward CO2 fluxes on the surface temperature was not clear during intermittently turbulent periods. The fluxes observed in conjunction with high u* values showed a better relationship with the surface temperature although use of such fluxes in the u*-correction procedure overestimated the ecosystem respiration rate: the u*-corrected estimates of the respiration rate were twice as high as the ecosystem respiration rate. During flux events, CO2 storage fluxes became large and negative. In such cases, the CO2 storage flux must be added to the CO2 flux for evaluating the ecosystem respiration rate using the u*-correction procedure.

The paper presents the results of probing the stable atmospheric boundary layer in the coastal zone of Lake Baikal with a coherent Doppler wind lidar and a microwave temperature profiler. Two-dimensional height–temporal distributions of the wind velocity vector components, temperature, and parameters characterizing atmospheric stability and wind turbulence were obtained. The parameters of the low-level jets and the atmospheric waves arising in the stable boundary layer were determined. It was shown that the stable atmospheric boundary layer has an inhomogeneous fine scale layered structure characterized by strong variations of the Richardson number Ri. Layers with large Richardson numbers alternate with layers where Ri is less than the critical value of the Richardson number Ricr = 0.25. The channels of decreased stability, where the conditions are close to neutral stratification 0 &lt; Ri &lt; 0.25, arise in the zone of the low-level jets. The wind turbulence in the central part of the observed jets, where Ri &gt; Ricr, is weak, increases considerably to the periphery of jets, at heights where Ri &lt; Ricr. The turbulence may intensify at the appearance of internal atmospheric waves.

Abstract. Large-eddy simulation (LES) and Lagrangian stochastic modeling of passive particle dispersion were applied to the scalar flux footprint determination in the stable atmospheric boundary layer. The sensitivity of the LES results to the spatial resolution and to the parameterizations of small-scale turbulence was investigated. It was shown that the resolved and partially resolved (“subfilter-scale”) eddies are mainly responsible for particle dispersion in LES, implying that substantial improvement may be achieved by using recovering of small-scale velocity fluctuations. In LES with the explicit filtering, this recovering consists of the application of the known inverse filter operator. The footprint functions obtained in LES were compared with the functions calculated with the use of first-order single-particle Lagrangian stochastic models (LSMs) and zeroth-order Lagrangian stochastic models – the random displacement models (RDMs). According to the presented LES, the source area and footprints in the stable boundary layer can be substantially more extended than those predicted by the modern LSMs.

Understanding and prediction of the stable atmospheric boundary layer is challenging. Many physical processes come into play in the stable boundary layer, i.e. turbulence, radiation, land surface coupling and heterogeneity, orographic turbulent and gravity wave drag. The development of robust stable boundary-layer parameterizations for weather and climate models is difficult because of the multiplicity of processes and their complex interactions. As a result, these models suffer from biases in key variables, such as the 2-m temperature, boundary-layer depth and wind speed. This short paper briefly summarizes the state-of-the-art of stable boundary layer research, and highlights physical processes that received only limited attention so far, in particular orographically-induced gravity wave drag, longwave radiation divergence, and the land-atmosphere coupling over a snow-covered surface. Finally, a conceptual framework with relevant processes and particularly their interactions is proposed.

The stalde atmospl~eric boundary layer has been investigated on the basis of two extencled bo~~ndary-layer xperiments, perforn~ed at the German Antarctic research station Neumayer. Almost all parameterizations of the turbulent exchange in atmospheric models (from boundary-layer models up to global circulation models) are based 011 hydrodynamic theories and empirical laws (universal functions), which are valicl above horizont,al homogeneous surfaces. The conditions a t the Neumayerstation allow the test of such theories as well as their further development. In this thesis empirical and theoretical invest,igations of parameterizations of the surface fluxes, t~he turbulent, fluxes in t,he whole boundary layer and of the height of the st,able boundary layer are performed. Until now only a few experimental investigations exist for moderately to strong stable stratification. The data measured at the Neumayer-station allow the determination of the universal functions for this stability range. The normally used linear dependence of the universal functions from the stability parameter z / L is confirmed even for this range, but only up to an upper limit of z / L = 1. z is the lleight above ground, L tlle Olmchov-length. With increasing stability the universal functions reach constant values. In addition, the turbulent surface fluxes have been calculated from profile ineasurements with methods of optimization theory. The results are in good agreement with directly measured turbulent fluxes. It is shown, that the height of the stable boundary layer a t the Neumayerstation is very low. The main reason for this phenomena is the stability of the free atmosphere above the boundary layer. Based on the equations of motion an ext.ended relation for the pa,rameterization of the height of the stable boundary layer is detern~ined, which takes into account the stability of the free atmosphere. This relation is verified with our mea,surements. Taking into account this paranieterization in a turbulente-closure-scheme of a one-dimensional boundary layer model, the best. agreement bet.ween simulated and measured boundary-layer development is achieved. The improved parameterizations, derived from the performed theoretical and experinient,al investigations, are used in a one-dimensional boundary layer model for the simulation of the stable atmospheric boundary layer. The stationary state as well as the influence of different external fact,ors on the development in time are investigated. The simulated development of the boundary layer is compared with observed results for selected case studies with the use of variable lower and upper bounclary ~ondit~ions and different turbulente-closure-schemes.

The turning of wind with height and the related cross-isobaric (ageostrophic) flow in the thermally stable stratified boundary layer is analysed from a variety of model results acquired in the first Global Energy and Water Cycle Experiment (GEWEX) Atmospheric Boundary Layer Study (GABLS1). From the governing equations in this particular simple case it becomes clear that the cross-isobaric flow is solely determined by the surface turbulent stress in the direction of the geostrophic wind for the quasi-steady state conditions under consideration. Most models indeed seem to approach this relationship but for very different absolute values. Because turbulence closures used in operational models typically tend to give too deep a boundary layer, the integrated total cross-isobaric mass flux is up to three times that given by research numerical models and large-eddy simulation. In addition, the angle between the surface and the geostrophic wind is typically too low, which has important implications for the representation of the larger-scale flow. It appears that some models provide inconsistent results for the surface angle and the momentum flux profile, and when the results from these models are removed from the analysis, the remaining ten models do show a unique relationship between the boundary-layer depth and the surface angle, consistent with the theory given. The present results also imply that it is beneficial to locate the first model level rather close to the surface for a proper representation of the turning of wind with height in the stable boundary layer.

Mass exchange in the stable boundary layer by coherent structures