Monin-Obukhov Similarity Theory Research Articles

Simple method to estimate the optical turbulence over snow and ice.

A simple physics-based method for estimating optical turbulence (Cn2) within the surface layer over snow and ice is proposed, using the Tatarski equation with an improved outer scale model. This improved outer scale model mainly requires the calculation of the wind shear and temperature gradients. Based on the measurements from a mobile polar atmospheric parameter measurement system at the Antarctic Taishan Station in 2014, Cn2 was estimated using two methods: the Tatarski equation and the Monin-Obukhov similarity (MOS) theory. Compared with 16 days of measurements from a micro-thermometer, the correlation coefficient of log10(Cn2) estimated by the Tatarski equation is 0.72, which is a slightly more accurate Cn2 variation in trend and magnitude than the MOS theory. The results suggest that this simple method has potential value for the forecasting applications of optical turbulence.

Mean flow and turbulence characteristics of a nocturnal downburst recorded on a 213 m tall meteorological tower

AbstractThis study presents rare measurements and analysis of a nocturnal thunderstorm downburst on the 213 m tall Cabauw tower in The Netherlands. The event occurred on 12 March 2008 between 02:00 and 03:00 UTC and was measured using four ultrasonic 10-Hz anemometers positioned at 3, 60, 100, and 180 m above ground level. 1-second gusts in the outflow exceeded 30 m s−1 at 60 m and above. This wind event was accompanied by an abrupt change of wind direction from southwest to west. While the shift in wind direction corresponded with the change of upwind surface roughness, the time series of turbulence intensity and other turbulence characteristics were not affected. The statistical properties of this event were compared against the largest European database of thunderstorm winds measured in the Mediterranean. The study also demonstrated that primary and secondary vortex structures—secondary vortex being rarely observed in actual downbursts—developed at the forward edge of the cold outflow. The estimated diameter of the downdraft was 1200 m at 70 m above ground. The measured velocity profiles and friction velocity were compared against theoretical predictions of the Monin-Obukhov Similarity Theory (MOST). MOST without stratification adjustment overestimated measured friction velocity twofold. Alternative values for surface roughness during the outflow were derived based on the measured friction velocity and MOST-based fit of measured velocity profiles. Ceilometer and radar measurements were supplementary data in this analysis.

Impacts of terrain on convective surface layer turbulence over central Himalaya based on Monin–Obukhov similarity theory

In the context of non-uniform Monin–Obukhov similarity scaling of unstable surface layer turbulence over complex terrain, this study attempts to identify the range of slope angles (as a proxy for terrain complexity) over which convective turbulence behaviour is similar to that over flat terrain. Attempts are also made to optimize constants of numerical relationships between integral turbulence parameters (ϕu,v,w) and the stability parameter (z/L) for observations having a significantly strong signature of terrain undulation. High frequency wind observations during the Indian winter season obtained from two field stations (on-slope and ridge-top) in the central Himalaya near Kosi-Katarmal, Uttarakhand, India, are analysed. Convective day-time period observations from rain-free days at these two sites are used with measures of terrain heterogeneity, represented by the vertical wind-derived slope angle (θw), vertical wind-derived slope angle normalized with respect to maximum θw (θwˆ), and the terrain-derived slope angle (θt). When the relationship of wind-derived slope angle and terrain derived slope angle was assessed, we found that wind-derived slope angle(θw) sufficiently represents the terrain undulation with a correlation coefficient of 0.86 at a p-value < 0.001. Optimization was undertaken of the numerical relationships between the integral turbulence parameters (ϕu,v,w) and z/L for observations having a significantly strong signature of terrain undulation characterized by |θˆw|> 0.2. Results indicated that for selected runs with increasing terrain complexity, c1 decreases and d1 increases in ϕu,v,w=c1(1−d1zL)1/3 having ranges of c1 and d1 between 0.85–2.39, and 0.98–13.85, respectively.

Sensitivity to changes in the surface‐layer turbulence parameterization for stable conditions in winter: A case study with a regional climate model over the Arctic

AbstractThe modeling of the atmospheric boundary layer over sea ice is still challenging because of the complex interaction between clouds, radiation and turbulence over the often inhomogeneous sea ice cover. There is still much uncertainty concerning sea ice roughness, near‐surface thermal stability and related processes, and their accurate parameterization. Here, a regional Arctic climate model forced by ERA‐Interim data was used to test the sensitivity of climate simulations to a modified surface flux parameterization for wintertime conditions over the Arctic. The reference parameterization as well as the modified one is based on Monin–Obukhov similarity theory, but different roughness lengths were prescribed and the stability dependence of the transfer coefficients for momentum, heat and moisture differed from each other. The modified parameterization accounts for the most comprehensive observations that are presently available over sea ice in the inner Arctic. Independent of the parameterization used, the model was able to reproduce the two observed dominant winter states with respect to cloud cover and longwave radiation. A stepwise use of the different parameterization assumptions showed that modifications of both surface roughness and stability dependence had a considerable impact on quantities such as air pressure, wind and near‐surface turbulent fluxes. However, the reduction of surface roughness to values agreeing with those observed during the Surface Heat Budget of the Arctic Ocean campaign led to an improvement in the western Arctic, while the modified stability parameterization had only a minor impact. The latter could be traced back to the model's underestimation of the strength of stability over sea ice. Future work should concentrate on possible reasons for this underestimation and on the question of generality of the results for other climate models.

A Universal Approach for the Non‐Iterative Parametrization of Near‐Surface Turbulent Fluxes in Climate and Weather Prediction Models

AbstractWeather prediction and climate simulations need reliable parameterizations of turbulent fluxes in the stable surface layer. Especially in these conditions, the uncertainties of such parametrizations are still large. Most of them rely on the Monin‐Obukhov similarity theory (MOST), for which universal stability functions (SFs) represent important ingredients. The SFs are nonlinear, if so, a numerical iteration of the MOST equations is required. Moreover, presently available SFs are significantly different at large stability. To simplify the calculations, a non‐iterative parametrization of fluxes is derived and corresponding bulk transfer coefficients for momentum and heat for a package of five pairs of state‐of‐the‐art SFs are proposed. For the first time, a parametrization of the related transfer coefficients is derived in a universal framework for all package members. The new parametrizations provide a basis for a cheap systematic study of the impact of surface layer turbulent fluxes in weather prediction and climate models.

Evaluation of Profiles of Standard Deviation of Vertical Wind in the Urban Area of Rome: Performances of Monin–Obukhov Similarity Theory Using Different Scaling Variables

The parametrizations of meteorological variables provided by the Monin–Obukhov similarity theory (MOST) is of major importance for pollutant dispersion assessment. However, the complex flow pattern that characterizes the urban areas limits the applicability of the MOST. In this work, the performance of different existing parametrizations of the standard deviation of vertical wind velocity were tested in the city of Rome. Results were compared with experimental data acquired by a sonic detection and ranging (SODAR) and a sonic anemometer. Different scaling variables estimated from the anemometer data by considering two coordinate systems—one aligned with the geodetic reference frame and the other following the flow streamlines—were used to evaluate the effects of flow distortion due to the presence of buildings. Results suggest that the MOST parametrizations perform better if the scaling variables obtained using the coordinate system following the flow streamlines are used. This estimation of the scaling variables would make it possible to overcome the difficulties in conducting measurements of turbulent fluxes, either at different altitudes or even in the constant flux layer.

Predicting Urban Surface Roughness Aerodynamic Parameters Using Random Forest

AbstractThe surface roughness aerodynamic parameters z0 (roughness length) and d (zero-plane displacement height) are vital to the accuracy of the Monin–Obukhov similarity theory. Deriving improved urban canopy parameterization (UCP) schemes within the conventional framework remains mathematically challenging. The current study explores the potential of a machine-learning (ML) algorithm, a random forest (RF), as a complement to the traditional UCP schemes. Using large-eddy simulation and ensemble sampling, in combination with nonlinear least squares regression of the logarithmic-layer wind profiles, a dataset of approximately 4.5 × 103 samples is established for the aerodynamic parameters and the morphometric statistics, enabling the training of the ML model. While the prediction for d is not as good as the UCP after Kanda et al., the performance for z0 is notable. The RF algorithm also categorizes z0 and d with an exceptional performance score: the overall bell-shaped distributions are well predicted, and the ±0.5σ category (i.e., the 38% percentile) is competently captured (37.8% for z0 and 36.5% for d). Among the morphometric features, the mean and maximum building heights (Have and Hmax, respectively) are found to be of predominant influence on the prediction of z0 and d. A perhaps counterintuitive result is the considerably less striking importance of the building-height variability. Possible reasons are discussed. The feature importance scores could be useful for identifying the contributing factors to the surface aerodynamic characteristics. The results may shed some light on the development of ML-based UCP for mesoscale modeling.

The application of machine learning to predictions of optical turbulence in the surface layer at Baikal Astrophysical Observatory

ABSTRACT In this study, we apply machine learning to predict optical turbulence in the surface layer at the Baikal Astrophysical Observatory. Advance knowledge of optical turbulence is important for maximizing the efficiency of adaptive optics systems, telescope operations, and the scheduling of the planned observations. Typically, optical turbulence is characterized by the structure constant of the refractive index of air $C_n^2$. The Monin–Obukhov similarity theory (MOST) provides a scientific basis for estimating the structure constant of the refractive index from meteorological variables in the surface layer. However, the MOST becomes unreliable for stable atmospheric conditions, which occurred for more periods regardless of the time of day at the Baikal Astrophysical Observatory. We propose the application of a neural network based on the group method of data handling (GMDH), one of the earliest deep-learning techniques, to predict the surface-layer refractive-index structure constant. The magnitudes of the predicted values of the structure constant of the refractive index and measurements are in agreement. Correlation coefficients ranging from 0.79–0.91 for a stably stratified atmosphere have been obtained. The explicit analytical expression is an advantage of the proposed approach, in contrast to many other machine-learning techniques that have a black-box model.

Potential low bias in high-wind drag coefficient inferred from dropsonde data in hurricanes

AbstractUnderstanding momentum exchange at the air-sea interface is important for accurate hurricane predictions and understanding fundamental storm dynamics. One method for estimating air-sea momentum transfer in high winds is the flux-profile method, which infers surface momentum fluxes and the corresponding drag coefficient from mean velocity profiles obtained from either dropsondes or meteorological towers, under the assumption that the boundary-layer wind profile at low altitudes exhibits a logarithmic profile with height. In this study, we use dropsonde data from reconnaissance aircraft, as well as “virtual sondes” from a turbulence-resolving simulation of an intense tropical cyclone, to critically analyze the diagnosis of drag coefficient CD at hurricane-force wind speeds. In particular, the “roll-off” of the drag coefficient, where CD decreases at 10-m wind speeds ¿ 35 m s−1, is called into question based on uncertainty due to relatively low sample size and a lack of robustness of the flux-profile at high winds. In addition, multiple factors appear to favor an underestimate of CD at hurricane-force winds relative to their true values, including uncertainty in the height of recorded dropsonde data, violation of Monin-Obukhov similarity theory near the eyewall, and the short vertical extent of the logarithmic layer. Due to these and other related sources of uncertainty, it is likely that a quantitative limit has been reached in inferring the specific values of u* and CD using the flux-profile method, while at the same time the potential for underestimation may cast doubt on the CD–U10 relationship inferred from this method at high winds.

Uncertainty in the Parameterization of Surface Fluxes under Unstable Conditions

AbstractIn this study, an attempt has been made to analyze the possible uncertainties in the parameterization of surface fluxes associated with the form of non-dimensional wind and temperature profile functions used in weather and climate models under convective conditions within the framework of Monin-Obukhov similarity theory (MOST). For this purpose, these functions, which are commonly known as similarity functions, are classified into four categories based on the resemblance in their functional behaviour. The bulk flux algorithm is used for the estimation of transfer coefficients of momentum and heat using four different classes of similarity functions. Uncertainty in the estimated values of fluxes is presented in the form of deviation in the predicted values of momentum and heat transfer coefficients and their variation with the Monin-Obukhov stability parameter. The analysis suggests that a large deviation in the values of estimated fluxes might occur if different forms of similarity functions are utilized for the estimation of surface fluxes. Recommendations are made for the form of similarity function for momentum based on the analysis of one year-long turbulence observations over an Indian region. The study suggests that there is a distinct need to carry out a careful analysis of turbulence data in free convective conditions for determining a consistent functional form of the similarity functions to be utilized in the atmospheric models universally.

Estimation of behavior of optical turbulence during summer in the surface layer above the Antarctic Plateau using the Polar WRF model.

An optical turbulence ($C_n^2$) was found to be concentrated predominantly in the thin surface layer (SL) above the Antarctic Plateau. We present an estimation of the behavior of the SL $C_n^2$ during the summer time over the entire Antarctic Plateau, using the polar-optimized version of the Weather Research and Forecast model (Polar WRF) coupled with the Monin-Obukhov similarity theory. The results show that the $C_n^2$ is affected by the sunlight direction and terrain height. The $C_n^2$ minimum occurs sometime around the morning and evening transitions, when the condition of neutral stability is achieved inside the SL. These $C_n^2$ minima may be attributed to the relatively weaker thermal convection resulting from a small temperature difference. The simulated $C_n^2$ data coincide well with the measurements taken at the Antarctic Taishan Station using a micro-thermometer and sonic anemometer; the data are also in agreement with the seeing values obtained from a differential image motion monitor. In addition, the Polar WRF captured the $C_n^2$ minimum more precisely compared to the standard WRF.

On the u☆-U Relationship in the Stable Atmospheric Boundary Layer over Arctic Sea Ice

A relationship between the friction velocity u☆ and mean wind speed U in a stable atmospheric boundary layer (ABL) over Arctic sea ice was considered. To that aim, the observations collected during the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment were used. The observations showed the so-called “hockey-stick” shape of the u☆−U relationship, which consists of a slow increase of u☆ with increasing wind speed for U&lt;Utr and a more rapid almost linear increase of u☆ for U&gt;Utr, where Utr is the wind speed of transition between the two regimes. Such a relationship is most pronounced at the highest observational levels, namely at 9 and 14 m, and is also sharper when the air-surface temperature difference exceeds its average values for stable conditions. It is shown that the Monin–Obukhov similarity theory (MOST) reproduces the observed u☆−U relationship rather well. This suggests that at least for the SHEBA dataset, there is no contradiction between MOST and the “hockey-stick” shape of the u☆−U relationship. However, the SHEBA data, as well as the single-column simulations show that for cases with strong stability, u☆ significantly decreases with height due to the shallowness of the ABL. It was shown that when u☆ was assumed independent of height, the value of the normalized drag coefficient, i.e., of the so-called stability correction function for momentum, calculated using observations at a certain level, can be significantly underestimated. To overcome this, the decrease of u☆ with height was taken into account in the framework of MOST using local scaling instead of the scaling with surface fluxes. Using such an extended MOST brought the estimates of the normalized drag coefficient closer to the Businger–Dyer relation.

An Evaluation of the Constant Flux Layer in the Atmospheric Flow Above the Wavy Air‐Sea Interface

AbstractThe constant flux layer assumption simplifies the problem of atmospheric surface layer (ASL) dynamics and is an underlying assumption of Monin‐Obukhov similarity theory (MOST), which is ubiquitously applied to model interfacial exchange and atmospheric turbulence. Within the marine environment, the measurements necessary to confirm the local ASL as a constant flux layer are rarely available, namely: direct observations of the near‐surface flux gradients. Recently, the Research PlatformFLIPwas deployed with a meteorological mast that resolved the momentum and heat flux gradients from 3 to 16 m above the ocean surface. Here, we present an assessment of the prevalence of the constant flux layer within the ASL, using an approach that accounted for the role of wave‐coherent motion in air and evaluated each observed flux gradien. Our analysis revealed that only 30%–40% of momentum flux gradients were approximately constant; for the heat fluxes, this increased to 50%–60%. For low winds, the stationarity of local turbulence was critical to the constant flux layer's validity, but resulted in excising a large proportion of the observed profiles. Under moderate wind speeds, swell‐wind alignment was associated with momentum flux divergence. Our findings suggest that the constant flux layer, as it is conventionally defined, is not generally valid over the ocean. This holds significant implications for measuring air‐sea fluxes from single point sources and marine applications of MOST.

An improved remote sensing based approach for predicting actual Evapotranspiration by integrating LiDAR

Spatially distributed information of actual Evapotranspiration (ET) is essentially required for various applications in agriculture, as well as studies related to water balance. An Energy Balance model that uses optical and thermal remote sensing datasets is appropriate for the spatially distributed estimation of ET, which is primarily controlled by local environmental conditions. In this study, we use the Surface Energy Balance System (SEBS), which is an Energy Balance model, to estimate an improved actual ET, by integrating canopy height information obtained from ICESat/GLAS, the first space-borne LiDAR satellite. Our model estimates latent heat flux (LE) as a residual of energy balance, while sensible heat flux (H) is estimated based on Monin–Obukhov similarity theory. The spatial variability of H and LE estimated from Landsat TM/ETM+ images were compared with eddy covariance (EC) based in situ flux tower observations, in order to document the SEBS model uncertainties in three forest sites in the East and Southeast Asian ecosystem. We identified that canopy height (hc) is one of the critical parameters that can induce uncertainties in SEBS model estimations. Therefore, hc obtained from LiDAR was introduced in parameterization of the roughness length for momentum transfer (z0m). In situ based hc obtained from flux tower stations, and the normalized difference vegetation index based formulation of hc proposed by Su (2001), were also introduced in the SEBS z0m parameterization. Root mean square error of LiDAR integrated SEBS (SEBSLiDar) for estimated H values reduced by (20, 45, and 23)% compared to Landsat integrated SEBS (SEBSLandsat), and (18, 7, and 9)% compared to In situ integrated SEBS (SEBSInsitu) at the three selected forest sites (SMC, QYZ, and SMF), respectively, while the mean coefficient of determination values for the estimated LE improved by (9.09 and 5.88)% compared to SEBSLandsat and SEBSInsitu, respectively, with reference to ground-based flux tower observations. Our analysis reveals that LiDAR-based parameterization of z0m can significantly increase the accuracy of estimated roughness lengths within an ET model, which can therefore improve the accuracy of the estimated turbulent heat fluxes. SEBSLiDAR was further evaluated for the spatially distributed mapping of actual ET. We have observed that ET estimated by SEBSLandsat overestimated in forest sites compared to EC observations; however, LiDAR-integrated SEBS marginally improved the accuracy of ET, thereby leading to an improvement in the mean correlation value of 0.87 and mean normalized standard deviation value of 0.93 approaching unity based on Taylor diagram, which more closely approximates the actual ground-based measurements. The proposed methodology overcomes the current limitation in the energy balance models in estimating roughness lengths, by providing accurate formulation of hc by specifically incorporating LiDAR measurements in areas of tall vegetation canopies. The operational improvement in roughness lengths by next-generation SEBSLiDAR model provides an opportunity to improve the estimation accuracy of water and energy fluxes, specifically ET. Overall, our proposed SEBSLiDAR model provides a benchmark that is useful to policy makers and water resource managers in devising a plan for sustainable use of water resources in the East Asian region, as well as other similar ecosystems.

Study on the characteristics of the pressure fluctuations and their contribution to turbulence kinetic energy

In this study, the integral and microscopic turbulent statistical characteristics of pressure fluctuations, applicability of the pressure gradient and pressure flux divergence to the Monin-Obukhov similarity theory (MOST), and contribution of the pressure transport term to turbulence kinetic energy (TKE) were analyzed using the turbulence observational data obtained from a field observational station over the Horqin Sandy Land in Inner Mongolia, China. The normalized standard deviations of the pressure fluctuations have no obvious relationship with the dimensionless stability parameter (z/L). The turbulent variance spectra of pressure fluctuations Sp(n) follow the n−2 scaling law with a peak frequency of approximately one to two orders of magnitude lower than that of the wind speed and temperature. The spectral gap also shifts to lower frequencies, and the transition from turbulent scale to the larger scale is sharper. The normalized vertical pressure gradient (κzp∗∂p¯∂z) has no significant relationship with z/L. The non-dimensional pressure transport term (φp=κzρ¯u∗3∂w'p'¯∂z) represents the pressure flux divergence and is well related to the z/L with expressions of φp = ± (1 − 14.5z/L) for unstable stratifications and φp = ± (1 + 15.0z/L) for stable stratifications. The relative importance of pressure transport term in the TKE budget equation with respect to the shear production and buoyancy terms is larger at larger scales. The pressure transport term is averagely one order of magnitude larger than the sum of these two terms at scales above 5 min. The contribution of the pressure transport term to the TKE is non-negligible.

A Statistical Evaluation of WRF-LES Trace Gas Dispersion Using Project Prairie Grass Measurements

AbstractIn recent years, new measurement systems have been deployed to monitor and quantify methane emissions from the natural gas sector. Large-eddy simulation (LES) has complemented measurement campaigns by serving as a controlled environment in which to study plume dynamics and sampling strategies. However, with few comparisons to controlled-release experiments, the accuracy of LES for modeling natural gas emissions is poorly characterized. In this paper, we evaluate LES from the Weather Research and Forecasting (WRF) model against Project Prairie Grass campaign measurements and surface layer similarity theory. Using WRF-LES, we simulate continuous emissions from 30 near-surface trace gas sources in two stability regimes: strong and weak convection. We examine the impact of grid resolutions ranging from 6.25 m to 52 m in the horizontal dimension on model results. We evaluate performance in a statistical framework, calculating fractional bias and conducting Welch’s t-tests. WRF-LES accurately simulates observed surface concentrations at 100 m and beyond under strong convection; simulated concentrations pass t-tests in this region irrespective of grid resolution. However, in weakly convective conditions with strong winds, WRF-LES substantially overpredicts concentrations – the magnitude of fractional bias often exceeds 30%, and all but one C-test fails. The good performance of WRF-LES under strong convection correlates with agreement with local free convection theory and a minimal amount of parameterized turbulent kinetic energy. The poor performance under weak convection corresponds to misalignment with Monin-Obukhov similarity theory and a significant amount of parameterized turbulent kinetic energy.

Logarithmic profile of temperature in sheared and unstably stratified atmospheric boundary layers

Wall-bounded turbulent flows are widely observed in natural and engineering systems, such as air flows near the Earth's surface, water flows in rivers, and flows around a car or a plane. The universal logarithmic velocity profile in wall-bounded turbulent flows proposed by von K\'arm\'an in 1930 is one of the few exact physical descriptions of turbulence. However, the mean velocity and temperature profiles cannot be adequately described by this universal log law when buoyancy effects are present. Monin-Obukhov similarity theory (MOST), proposed in 1954, has been the cornerstone theory to account for these buoyancy effects and to describe the atmospheric boundary layer. MOST has been used in almost all global weather, climate and hydrological models to describe the dependence of the mean velocity, temperature and scalar profiles on buoyancy. According to MOST, the logarithmic temperature profile breaks down as buoyancy effects become important. In contrast, here we show that this long-standing MOST theory does not apply for temperature. We propose a new theory for the logarithmic profile of near-wall temperature, which corrects MOST pitfalls and is supported by both high-resolution direct numerical simulations and field observations of the convective atmospheric boundary layer. Buoyancy effects do not modify the logarithmic nature but instead modulate the slope of the temperature profile compared to the universal von K\'arm\'an slope. The new formulation has widespread applications such as in climate models, where the proposed new temperature log law should lead to more realistic continental surface temperature, which are strongly impacted by buoyancy.

Numerical Study of Near‐Surface Jet in the Atmospheric Surface Layer Over an Oceanic Temperature Front

AbstractThe interaction between atmospheres and oceans plays an important role in the global climate. In a field experiment of atmospheric flows over the Gulf Stream, when the wind blew from the cold water to the warm water, we observed a near‐surface jet over the warm water. We then conducted direct numerical simulations and large‐eddy simulations of atmospheric turbulence in the vicinity of the front and captured the near‐surface jet in simulations for the first time. Analyses of the data obtained from the high‐resolution three‐dimensional simulations revealed the dominant generation mechanisms of the near‐surface jet, which are the strong vertical mixing by the enhanced streamwise rolls and the mean downward motion. Around the near‐surface jet, the magnitude of the negatively valued Richardson number significantly increases, indicating the dominance of buoyancy effects in the flow dynamics there. The development of the near‐surface jet suggests that the Monin‐Obukhov similarity theory (MOST) needs to be modified in representing marine atmospheric boundary layers over sea surface temperature fronts.

Universal Wind Profile for Conventionally Neutral Atmospheric Boundary Layers.

Conventionally neutral atmospheric boundary layers (CNBLs), which are characterized with zero surface potential temperature flux and capped by an inversion of potential temperature, are frequently encountered in nature. Therefore, predicting the wind speed profiles of CNBLs is relevant for weather forecasting, climate modeling, and wind energy applications. However, previous attempts to predict the velocity profiles in CNBLs have had limited success due to the complicated interplay between buoyancy, shear, and Coriolis effects. Here, we utilize ideas from the classical Monin-Obukhov similarity theory in combination with a local scaling hypothesis to derive an analytic expression for the stability correction function ψ=-c_{ψ}(z/L)^{1/2}, where c_{ψ}=4.2 is an empirical constant, z is the height above ground, and L is the local Obukhov length based on potential temperature flux at that height, for CNBLs. An analytic expression for this flux is also derived using dimensional analysis and a perturbation method approach. We find that the derived profile agrees excellently with the velocity profile in the entire boundary layer obtained from high-fidelity large eddy simulations of typical CNBLs.

Two‐sided turbulent surface‐layer parameterizations for computing air–sea fluxes

AbstractStandard methods for determining air–sea fluxes typically rely on bulk algorithms set in the frame of Monin–Obukhov similarity theory (MOST), using ocean surface fields and atmosphere near‐surface fields. In the context of coupled ocean–atmosphere simulations, the shallowest ocean vertical level is usually used as bulk input and, by default, the turbulent closure is one‐sided: it extrapolates atmosphere near‐surface solution profiles (for wind speed, temperature, and humidity) to the prescribed ocean surface values. Using near‐surface ocean fields as surface ones is equivalent to considering that, in the ocean surface layer, solution profiles are constant instead of also being determined by turbulent closure. Here we introduce a method for extending existing turbulent parameterizations to a two‐sided framework by explicitly including the ocean surface layer within the aforementioned parameterizations. The formalism we use for this method is derived from that of classical turbulent closures, so that our novelties can easily be implemented within existing formulations. Special care is taken to ensure the smoothness of the resulting solution profiles. Other physical phenomena, such as the penetration of radiative fluxes in the ocean and the formation of waves, are then included within our formalism, and their effects are assessed. We also investigate the impact of such two‐sided bulk formulations on air–sea fluxes evaluated from a setting similar to those of coupled ocean–atmosphere simulations.