Parameterization Of Turbulent Fluxes Research Articles

Uncertainties of Drag Coefficient Estimates Above Sea Ice from Field Data

Surface turbulent exchanges play a key role on sea ice dynamics, on ocean and sea ice heat budgets and on the polar atmosphere. Uncertainties in parameterizations of surface turbulent fluxes are mostly held by the transfer coefficients and estimates of those transfer coefficients from field data are required for parameterization development. Measurement errors propagate through the computation of transfer coefficients and contribute to its total error together with the uncertainties in the empirical stability functions used to correct for stability effects. Here we propose a methodology to assess their contributions individually to each coefficient estimate as well as the total drag coefficient uncertainty and we apply this methodology on the example of the SHEBA campaign. We conclude that for most common drag coefficient values (between 1.0×10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.0\ imes 10^{-3}$$\\end{document} and 2.5×10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2.5\ imes 10^{-3}$$\\end{document}), the relative total uncertainty ranges from 25 and 50%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document}. For stable or unstable conditions with a stability parameter |ζ|>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\zeta |>1$$\\end{document} on average, the total uncertainty in the neutral drag coefficient exceeds the neutral drag coefficient value itself, while for |ζ|<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\zeta |<1$$\\end{document} the total uncertainty is around 25%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} of the drag coefficient. For closer-to-neutral conditions, this uncertainty is dominated by measurement uncertainties in surface turbulent momentum fluxes which should therefore be the target of efforts in uncertainty reduction. We also propose an objective data-screening procedure for field data, which consists of retaining data for which the relative error on neutral drag coefficient does not exceed a given threshold. This method, in addition to the commonly used flux quality control procedure, allows for a reduction of the drag coefficient dispersion compared to other data-screening methods, which we take as an indication of better dataset quality.

Modeling snowpack dynamics and surface energy budget in boreal and subarctic peatlands and forests

Abstract. The snowpack has a major influence on the land surface energy budget. Accurate simulation of the snowpack energy and radiation budget is challenging due to, e.g., effects of vegetation and topography, as well as limitations in the theoretical understanding of turbulent transfer in the stable boundary layer. Studies that evaluate snow, hydrology and land surface models against detailed observations of all surface energy balance components at high latitudes are scarce. In this study, we compared different configurations of the SURFEX land surface model against surface energy flux, snow depth and soil temperature observations from four eddy-covariance stations in Finland. The sites cover two different climate and snow conditions, representing the southern and northern subarctic zones, as well as the contrasting forest and peatland ecosystems typical for the boreal landscape. We tested different turbulent flux parameterizations implemented in the Crocus snowpack model. In addition, we examined common alternative approaches to conceptualize soil and vegetation, and we assessed their performance in simulating surface energy fluxes, snow conditions and soil thermal regime. Our results show that a stability correction function that increases the turbulent exchange under stable atmospheric conditions is imperative to simulate sensible heat fluxes over the peatland snowpacks and that realistic peat soil texture (soil organic content) parameterization greatly improves the soil temperature simulations. For accurate simulations of surface energy fluxes, snow and soil conditions in forests, an explicit vegetation representation is necessary. Moreover, we demonstrate the high sensitivity of surface fluxes to a poorly documented parameter involved in snow cover fraction computation. Although we focused on models within the SURFEX platform, the results have broader implications for choosing suitable turbulent flux parameterization and model structures depending on the potential use cases for high-latitude land surface modeling.

A New Hybrid Mass‐Flux/High‐Order Turbulence Closure for Ocean Vertical Mixing

AbstractWhile various parameterizations of vertical turbulent fluxes at different levels of complexity have been proposed, each has its own limitations. For example, simple first‐order closure schemes such as the K‐Profile Parameterization (KPP) lack energetic constraints; two‐equation models like directly solve an equation for the turbulent kinetic energy but do not account for non‐diffusive fluxes, and high‐order closures that include the high‐order transport terms are computationally expensive. To address these, we extend the Assumed‐Distribution Higher‐Order Closure (ADC) framework originally proposed for the atmospheric boundary layer and apply it to the ocean surface boundary layer. By assuming a probability distribution function relationship between the vertical velocity and tracers, all second‐order and higher‐order moments are exactly constructed and turbulence closure is achieved in the ADC scheme. In addition, this ADC parameterization has full energetic constraints and includes non‐diffusive fluxes without the computational cost of a full higher‐order closure scheme. We have tested the ADC scheme against a combination of large eddy simulation (LES), KPP, and for surface buoyancy‐driven convective mixing and found that the ADC scheme is robust with different vertical resolutions and compares well to the LES results.

Scale‐Dependent Estimability of Turbulent Flux in the Unstable Surface Layer for Land Surface Modeling

AbstractSurface flux estimation is essential to land surface modeling in earth system models. In practice, parameterizations of surface turbulent fluxes are almost all based on the similarity theory. That is, the grid or subgrid mean surface‐layer flow is assumed at equilibrium with the underlying earth surface, and therefore some empirical relations can be used to estimate surface fluxes. In this paper, scale‐dependent estimability of turbulent flux in the unstable surface layer is systematically investigated based on high‐resolution large‐eddy simulation data over a flat and homogeneous domain, representing a typical land surface modeling grid. It is found that turbulent flow in the unstable surface layer inherently fluctuates over a wide range of scales. This kind of fluctuation affects the steady‐state relations between mean atmospheric quantities and underlying earth surface, and hence affects the estimability of surface fluxes. Sensitivity tests show that the relative root mean square error of the estimated surface friction velocity for a subdomain generally increases as the subdomain becomes smaller. The error can be as high as 35% as the subdomain size decreases to the order of the surface layer height. To achieve an error of 10% for all cases, the subdomain size should be at least on the order of the boundary layer height. These findings imply that estimability‐based strategies may be needed for representing subgrid heterogeneity for surface flux estimation in land surface modeling.

Observed and Parameterized Roughness Lengths for Momentum and Heat Over Rough Ice Surfaces

AbstractTurbulent heat fluxes, that is, the sensible heat flux and latent heat flux, are important sources/sinks of energy for surface melt over glaciers and ice sheets. Therefore, credible simulations of for example, future Greenland Ice Sheet mass loss need an accurate description of these fluxes. However, the parameterization of surface turbulent heat fluxes in climate models requires knowledge about the surface roughness lengths for momentum, heat and moisture, which are currently either unknown or tuned to indirect observations. In this study we take advantage of a large data set of eddy covariance observations acquired during multiple years and at multiple sites over the Greenland Ice Sheet. These in‐situ observations are used to develop an improved parameterization for the roughness length for momentum, and update the parameterization for the roughness lengths for heat and moisture over rough ice surfaces. The newly derived parameterizations are implemented in a surface energy balance model that is used to compute surface melt. Sensitivity experiments confirm the high sensitivity of surface melt to the chosen roughness length models. The new parameterization models the sensible heat flux to within 10 W m−2, and the cumulative ice ablation within 10% at three out of four sites. Two case studies demonstrate the important contribution of the turbulent heat fluxes to surface ablation. The presented roughness parameterizations can be implemented in climate models to improve the physical representation of surface roughness over rough snow and ice surfaces, which is expected to improve the modeled turbulent heat fluxes and thus surface melt.

To the Origin of a Wintertime Screen-Level Temperature Bias at High Altitude in a Kilometric NWP Model

Abstract High-resolution numerical weather prediction (NWP) systems present a strong potential to provide meteorological information in alpine terrain for diverse applications. However, they still suffer from biases highly detrimental for practical purposes. In this study, we investigate the origin of a significant wintertime screen-level temperature bias in forecasts of the AROME-France NWP system in high-altitude, snow-covered alpine terrain. For this purpose, a thorough set of meteorological and snow observations from two high-altitude instrumental sites is used. Targeted numerical simulations are carried out to disentangle the contributions to this bias coming from atmospheric fields, from the snow scheme, and from the coupling between the snowpack and the atmosphere. At both sites, the wind speed and incoming longwave radiation appear significantly negatively biased in AROME in the winter season. Using targeted offline simulations, we show that the simulation errors in these screen-level fields contribute to an average of 67% of the screen-level temperature bias of AROME, while the contribution of errors in the incoming shortwave radiation is negligible. Additionally, the screen-level temperature of AROME is not majorly impacted by changes in the complexity and especially the vertical layering of the snow model. However, it appears particularly sensitive to the parameterization of turbulent fluxes in stable conditions. Evidence suggest that these findings could at least partially be generalized to the whole AROME-France alpine domain. Hence, reducing the high-altitude, winter screen-level temperature bias in AROME may in great part proceed from improving the simulation of atmospheric fields and eliminating some bias compensations in the model.

Improvements in Diurnal Cycle and Its Impact on Seasonal Mean by Incorporating COARE Flux Algorithm in CFS

The variability of predicted variables at daily to seasonal scales in coupled models is primarily governed by surface boundary conditions between the ocean and atmosphere, namely, sea surface temperature (SST), turbulent heat, and momentum fluxes. Although efforts have been made to achieve good accuracy in surface fluxes and SST in observation and reanalysis products, less attention has been paid toward achieving improved accuracy in coupled model simulations. Improper diurnal phase and amplitude in intra-daily SST and precipitation are well-known problems in most global coupled general circulation models, including the Climate Forecast System v2 (CFSv2) model. The present study attempts to improve the representation of ocean-atmosphere surface boundary conditions in CFSv2, primarily used for India's operational forecasts at different temporal/spatial scales. In this direction, the diurnal warm layer and cool skin temperature correction scheme are implemented along with the surface flux parameterization scheme following Coupled Ocean-Atmosphere Response Experiment (COARE) v 3.0. The coupled model re-forecasts with a revised flux scheme showed better characteristics in various ocean-atmosphere parameters and processes at diurnal and seasonal time scales. At the diurnal scale, the phase and amplitude of intra-daily SST and mixed layer depth variabilities are improved over most tropical oceans. Improved diurnal SSTs helped in enhancing the diurnal range of precipitation by triggering stronger intra-daily convection. The corrected diurnal ocean-atmospheric boundary state translated into a reduction in seasonal mean dry bias over Indian landmass and the wet bias over tropical oceans. Better simulation of non-linearity associated with El Niño–Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), ENSO-Indian Summer Monsoon Rainfall (ISMR), and IOD-ISMR relation is among the most critical improvements achieved by revising the turbulent flux parameterization. The revised flux scheme showed enhanced prediction skills for tropical SST indices and ISMR.

Sensitivity of Northern Hemisphere climate to ice–ocean interface heat flux parameterizations

Abstract. We investigate the impact of three different parameterizations of ice–ocean heat exchange on modeled sea ice thickness, sea ice concentration, and water masses. These three parameterizations are (1) an ice bath assumption with the ocean temperature fixed at the freezing temperature; (2) a two-equation turbulent heat flux parameterization with ice–ocean heat exchange depending linearly on the temperature difference between the underlying ocean and the ice–ocean interface, whose temperature is kept at the freezing point of the seawater; and (3) a three-equation turbulent heat flux approach in which the ice–ocean heat flux depends on the temperature difference between the underlying ocean and the ice–ocean interface, whose temperature is calculated based on the local salinity set by the ice ablation rate. Based on model simulations with the stand-alone sea ice model CICE, the ice–ocean model MPIOM, and the climate model COSMOS, we find that compared to the most complex parameterization (3), the approaches (1) and (2) result in thinner Arctic sea ice, cooler water beneath high-concentration ice and warmer water towards the ice edge, and a lower salinity in the Arctic Ocean mixed layer. In particular, parameterization (1) results in the smallest sea ice thickness among the three parameterizations, as in this parameterization all potential heat in the underlying ocean is used for the melting of the sea ice above. For the same reason, the upper ocean layer of the central Arctic is cooler when using parameterization (1) compared to (2) and (3). Finally, in the fully coupled climate model COSMOS, parameterizations (1) and (2) result in a fairly similar oceanic or atmospheric circulation. In contrast, the most realistic parameterization (3) leads to an enhanced Atlantic meridional overturning circulation (AMOC), a more positive North Atlantic Oscillation (NAO) mode and a weakened Aleutian Low.

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.

New Modified and Extended Stability Functions for the Stable Boundary Layer based on SHEBA and Parametrizations of Bulk Transfer Coefficients for Climate Models

Abstract Climate models still have deficits in reproducing the surface energy and momentum budgets in Arctic regions. One of the reasons is that currently used transfer coefficients occurring in parameterizations of the turbulent fluxes are based on stability functions derived from measurements over land and not over sea ice. An improved parameterization is developed using the Monin–Obukhov similarity theory (MOST) and corresponding stability functions that reproduce measurements over sea ice obtained during the Surface Heat Budget of the Arctic Ocean (SHEBA) campaign. The new stability functions for the stable surface layer represent a modification of earlier ones also based on SHEBA measurements. It is shown that the new functions are superior to the former ones with respect to the representation of the measured relationship between the MOST stability parameter and the bulk Richardson number. Nevertheless, the functions fulfill the same criteria of applicability as the earlier functions and contain, as an extension, a dependence on the neutral-limit turbulent Prandtl number. Applying the new functions we develop an efficient noniterative parameterization of the near-surface turbulent fluxes of momentum and heat with transfer coefficients as a function of the bulk Richardson number (Rib) and roughness parameters. A hierarchy of transfer coefficients is recommended for weather and climate models. They agree better with SHEBA data for strong stability (Rib &amp;gt; 0.1) than previous parameterizations and they agree well with those based on the Businger–Dyer functions in the range Rib ≤ 0.1.

The Improvement of Turbulent Heat Flux Parameterization for Use in the Tropical Regions Using Low Wind Speed Excess Resistance Parameter

AbstractReliable simulation of turbulent heat fluxes needed for modeling land‐atmosphere interactions remains a challenge over the humid tropical region. This may be connected with the inadequate parameterization of the roughness lengths for momentum (z0m) and heat (z0h) transfer usually expressed in terms of excess resistance factor (κB−1). This paper assesses the performance of existing κB−1 schemes developed for high wind speed conditions over the humid tropical region. Thereafter, a more appropriate κB−1 suitable for low wind speed condition is developed for use in the aerodynamic resistance parameterization. Based on observed surface heat fluxes and profile measurements of wind speed and temperature from Nigeria Micrometeorological Experimental site, new κB−1 parameterization was derived through the application of the Monin‐Obukhov similarity theory and Brutsaert theoretical model for heat transfer. The derived , where Re* is the Reynolds number. Turbulent flux parameterization with this new formula provides better estimates of heat fluxes with reference to results from existing κB−1 schemes. The R2 increased by about 85%, while mean bias error and root‐mean‐square error in the parameterized QH based on the derived κB−1 reduced by about 63% and 66.7%, respectively. Similarly, the R2 increased by about 38%, while mean bias error and root‐mean‐square error in the parameterized QE based on the derived κB−1 reduced by about 47.8% and 52.6%, respectively. The derived κB−1 gave better estimates of QH than QE during the daytime. The derived κB−1 scheme corrects a well‐documented, large overestimation of turbulent heat fluxes, and it is therefore recommended for use in regions where low wind speed is prevalent.

Competition Between Atmospheric and Surface Parameterizations for the Control of Air‐Sea Latent Heat Fluxes in Two Single‐Column Models

AbstractA single‐column model approach conducted in the context of the Madden–Julian Oscillation through the CINDY2011/Dynamics of the Madden–Julian Oscillation field campaign is used to disentangle the respective role of the parameterizations of surface turbulent fluxes and of model atmospheric physics in controlling the surface latent heat flux. The major differences between the models used in this study occur during the suppressed phases of deep convection. They are attributed to differences in model atmospheric physics which is shown to control the near‐surface relative humidity and thereby the surface latent heat flux. In contrast, during active phases of deep convection, turbulent air‐sea flux parameterizations impact the latent heat flux through the drag coefficient and can represent two thirds of the divergence caused by the different atmospheric physics. The combined effects need to be accounted for to improve both the representation of latent heat flux and the atmospheric variables used to compute it.

Evaluating the performance of two surface layer schemes for the momentum and heat exchange processes during severe haze pollution in Jing-Jin-Ji in eastern China

Abstract. The turbulent flux parameterization schemes in the surface layer are crucial for air pollution modeling. There have been some deficiencies in the prediction of air pollutants by atmosphere chemical models, which is closely related to the uncertainties of the momentum and sensible heat fluxes calculated in the surface layer. The differences between two surface layer schemes (Li and MM5 schemes) were discussed, and the performances of two schemes were mainly evaluated based on the observed momentum and sensible heat fluxes during a heavy haze episode in Jing-Jin-Ji in eastern China. The results showed that the aerodynamic roughness length z0m and the thermal roughness length z0h played major roles in the flux calculation. Compared with the Li scheme, ignoring the difference between z0m and z0h in the MM5 scheme induced a great error in the calculation of the sensible heat flux (e.g., the error was 54 % at Gucheng station). Besides the roughness length, the algorithm for the surface turbulent flux as well as the roughness sublayer also resulted in certain errors in the MM5 scheme. In addition, magnitudes of z0m and z0h have significant influence on the two schemes. The large z0m and z0m∕z0h in megacities with a rough surface (e.g., Beijing) resulted in much larger differences of momentum and sensible heat fluxes between Li and MM5, compared with the small z0m and z0m∕z0h in suburban areas with a smooth surface (e.g., Gucheng). The Li scheme could better characterize the evolution of atmospheric stratification than the MM5 scheme in general, especially for the transition stage from unstable to stable atmospheric stratification, corresponding to the PM2.5 accumulation. The biases of momentum and sensible heat fluxes from Li were lower, about 38 % and 43 %, respectively, than those from MM5 during this stage. This study indicates the superiority of the Li scheme in describing regional atmospheric stratification and an improved possibility of severe haze prediction in Jing-Jin-Ji in eastern China by coupling it into atmosphere chemical models.

Modelling deep-water formation in the north-west Mediterranean Sea with a new air–sea coupled model: sensitivity to turbulent flux parameterizations

Abstract. In the north-western Mediterranean, the strong, dry, cold winds, the Tramontane and Mistral, produce intense heat and moisture exchange at the interface between the ocean and the atmosphere leading to the formation of deep dense waters, a process that occurs only in certain regions of the world. The purpose of this study is to demonstrate the ability of a new coupled ocean–atmosphere modelling system based on MESONH-SURFEX-SYMPHONIE to simulate a deep-water formation event in real conditions. The study focuses on summer 2012 to spring 2013, a favourable period that is well documented by previous studies and for which many observations are available. Model results are assessed through detailed comparisons with different observation data sets, including measurements from buoys, moorings and floats. The good overall agreement between observations and model results shows that the new coupled system satisfactorily simulates the formation of deep dense water and can be used with confidence to study ocean–atmosphere coupling in the north-western Mediterranean. In addition, to evaluate the uncertainty associated with the representation of turbulent fluxes in strong wind conditions, several simulations were carried out based on different parameterizations of the flux bulk formulas. The results point out that the choice of turbulent flux parameterization strongly influences the simulation of the deep-water convection and can modify the volume of the newly formed deep water by a factor of 2.

Modeling of diurnal pattern of air temperature in a tropical environment: Ile-Ife and Ibadan, Nigeria

Modeling of diurnal pattern of air temperature (Ta) is essential in the parameterization of turbulent heat fluxes in climate models. However, climate models still simulate the nocturnal stable boundary layer surface Ta with biases across the globe. This paper therefore validated five different diurnal Ta models (Ephrath, Hirotaka, de Wit, Parton and Fourier series models) used for estimating hourly Ta from daily maximum, daily minimum, and daily mean air temperature. It also developed an improved fourier series parameterization approach for Ta using surface layer observations from Nigerian micrometeorological experimental (NIMEX) site. The overall performance of the Ephrath, Hirotaka, de Wit and Parton models revealed a large deviation from the measured data during the early hours of the morning and late hours of the nighttime. The original fourier series model showed better performance for unstable air temperature parameterizations while the stable Ta was strongly overestimated. The performance of the model was improved with the inclusion of the atmospheric cooling rate that accounts for the temperature inversion which occurs during the nocturnal boundary layer condition. The mean bias error and root mean square error in estimated Ta by the modified fourier series model reduced by 4.13 and 3.01 °C, respectively during the transition period from dry to wet stable atmospheric conditions. The existing models simulated night time Ta with high biases and could not accurately capture the strong cooling inversion associated with a humid tropical region. The modified Fourier series model that incorporated the night time inversion variables gave the best estimation of the diurnal weather patterns of Ta when compared with other existing models for a tropical environment.

Surface Energy Balance Closure and Turbulent Flux Parameterization on a Mid-Latitude Mountain Glacier, Purcell Mountains, Canada

In the majority of glacier surface energy balance studies, parameterisation rather than direct measurement is used to estimate one or more of the individual heat fluxes, with others, such as the rain and ground heat fluxes, often deemed negligible. Turbulent fluxes of sensible and latent heat are commonly parameterised using the bulk aerodynamic technique. This method was developed for horizontal, uniform surfaces rather than sloped, inhomogeneous glacier terrain, and significant uncertainty remains regarding the selection of appropriate roughness length values, and the validity of the atmospheric stability functions employed. A customised weather station, designed to measure all relevant heat fluxes, was installed on an alpine glacier over the 2014 melt season. Eddy covariance techniques were used to observe the turbulent heat fluxes, and to calculate site-specific roughness values. The obtained dataset was used to drive a point ablation model, and to evaluate the most commonly used bulk methods and roughness length schemes in the literature. Modelled ablation showed good agreement with observed rates at seasonal, daily, and sub-daily timescales, effectively closing the surface energy balance, and giving a high level of confidence in the flux observation method. Net radiation was the dominant contributor to melt energy over the season (65.2%), followed by the sensible heat flux (29.7%), while the rain heat flux was observed to be a significant contributor on daily timescales during periods of persistent heavy rain (up to 20% day-1). Momentum roughness lengths observed for the study surface (snow: 10-3.8 m; ice: 10-2.2 m) showed general agreement with previous findings, while the scalar values (temperature: 10-4.6 m; water vapour: 10-6 m) differed significantly from those for momentum, disagreeing with the assumption of equal roughness lengths. Of the three bulk method stability schemes tested, the functions based on the Monin-Obukhov length returned mean daily flux values closest to those observed, but displayed poor performance on sub-daily timescales, and periods of substantial flux overestimation.

Characteristics of Land–Air Exchange Parameters over Grassland in Southeast Tibet

Abstract Accurate parameters that describe land–air exchange processes are essential for studying and predicting atmospheric processes over the Tibetan Plateau. Radiation, atmospheric thermal and moisture conditions, and turbulent heat and momentum fluxes were measured in the Yarlung Zangbo River, southeast Tibet, in May–July 2013. Based on the data, land–air exchange parameters were derived over the grassland surface, including the aerodynamic roughness length z0m, thermal roughness length z0h, the excess resistance to heat transfer kB−1 (where k represents the von Kármán constant and B−1 represents the Stanton number), and momentum and heat transfer coefficients (CD and CH, respectively). The average z0m was 7.0 cm, with a standard deviation of 1.4 cm; these values are higher than those observed in the central and western plateau regions and may have been affected by the tall grass and bush surface covers that surrounded the observation site. The average kB−1 was 5.7 ± 1.8, which is higher than that in other plateau regions in the same season. The average CD during the observation period, (11.9 ± 1.6) × 10−3, is also higher than that of other plateau regions. The commonly used iterative scheme and three noniterative turbulent flux parameterization schemes were evaluated over southeast Tibet using the above observational data. Parameter CD was underestimated by most schemes, whereas CH was overestimated by all schemes. Additional studies suggested that the iterative scheme performed best in retrieving the land–air exchange parameters and can be applied over southeast Tibet.

The effect of Prandtl number on mixing in low Reynolds number Kelvin-Helmholtz billows

The effect of Prandtl number on mixing in temporally evolving Kelvin-Helmholtz (KH) instabilities at low to moderate Reynolds numbers is studied through direct numerical simulation. We distinguish between the mixing induced by the primary billow and the mixing generated by three-dimensional motions by performing each simulation in two and three dimensions. The results indicate that the time evolution of the rate of two- and three-dimensional mixing through different stages of the life cycle of KH flow is significantly influenced by the Prandtl number. As the Prandtl number increases, the final amount of mixing increases for Reynolds that are too low to support active three-dimensional motions. This trend is the opposite in sufficiently high Reynolds number KH flows that can overcome viscous effects and develop significant three-dimensional instabilities. While the mixing generated in the two-dimensional flows, uniform in the span-wise direction, is not significantly dependent on the Prandtl number, the turbulent mixing induced by three-dimensional motions is a function of the Prandtl number. We observe a steady increase in the total amount of mixing for buoyancy Reynolds numbers above 7, consistent with the results of Shih et al. [“Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations,” J. Fluid Mech. 525, 193-214 (2005)]. Both maximum instantaneous and cumulative mixing efficiencies exhibit a decreasing trend with increasing Prandtl number. We compare the dependence of the mixing efficiency on Prandtl number to previous studies.

The Extrapolation of Near-Surface Wind Speeds under Stable Stratification Using an Equilibrium-Based Single-Column Model Approach

AbstractClassical approaches to modeling the near-surface (i.e., below 200 m) wind profile are equilibrium based (i.e., no time evolution) and either lack a physical basis or are based on surface-layer physics. In this study, the limits of the equilibrium approach in stable stratification are further tested by applying the method within a more physically comprehensive single-column model (SCM) framework. The SCM considered here is a highly idealized momentum and temperature budget model that uses a range of different parameterizations of turbulent fluxes. A 10-yr observational dataset obtained from the 213-m Cabauw tower in the Netherlands is used to drive the SCM and to assess model performance. Results from this study demonstrate several limitations of this SCM-based equilibrium approach. The existence of two physically meaningful equilibrium solutions for a given value of the surface turbulent temperature flux (used as a lower boundary in the SCM) generally results in either a tendency to underestimate stratification or the breakdown of the model because of runaway cooling and collapsed turbulence. Different representations of the geostrophic wind profile accounting for baroclinic effects caused by the strong land–sea temperature gradient at Cabauw are shown to have only a modest influence on the mean wind profile. The local internal boundary layer (IBL) at Cabauw results in a strong tendency for the SCM to overestimate wind speeds in weakly to moderately stable conditions. In very stable conditions (where the IBL influence was low), the equilibrium approach remained limited because of its inability to account for time-evolving phenomena such as the inertial oscillation and the low-level jet.

Evaluation of Surface Fluxes in ERA-Interim Using Flux Tower Data

Abstract Surface air temperature Ta is largely determined by surface net radiation Rn and its partitioning into latent (LE) and sensible heat fluxes (H). Existing model evaluations by comparison of absolute flux values are of limited help because the evaluation results are a blending of inconsistent spatial scales, inaccurate model forcing data, and imperfect parameterizations. This study further evaluates the relationships of LE and H with Rn and environmental parameters, including Ta, relative humidity (RH), and wind speed (WS), using ERA-Interim data at a 0.125° × 0.125° grid with observations at AmeriFlux sites from 1998 to 2012. The results demonstrate ERA-Interim can roughly reproduce the absolute values of environmental parameters, radiation, and turbulent fluxes. The model performs well in simulating the correlation of LE and H with Rn, except for the notable correlation overestimation of H against Rn over high-density vegetation (e.g., deciduous broadleaf forest, grassland, and cropland). The sensitivity of LE to Rn in the model is similar to that observed, but that of H to Rn is overestimated by 24.2%. Over the high-density vegetation, the correlation coefficient between H and Ta is overestimated by over 0.2, whereas that between H and WS is underestimated by over 0.43. The sensitivity of H to Ta is overestimated by 0.72 W m−2 °C−1, whereas that of H to WS in the model is underestimated by 16.15 W m−2 (m s−1)−1 over all of the sites. The model cannot accurately capture the responses of evaporative fraction [EF; EF = LE / (LE + H)] to Rn and environmental parameters. This calls for major research efforts to improve the intrinsic parameterizations of turbulent fluxes, particularly over high-density vegetation.