Surface Layer Similarity Theory Research Articles

A global thermal node model for no-load indirect solar dryer

ABSTRACT This paper presents a global thermal node model for predicting heat transfer in no-load indirect solar dryer. The overall influence of the interaction of the indirect solar dryer with the uppermost soil layer is considered. The mathematical model describing the solar drying system with a double-pass air-circulation collector is derived. Based on the Moore and Fisch approach, the soil surface fluxes are calculated using the surface layer similarity theory. The drying air temperature distribution based on dynamic descriptions of the drying environment is studied. The unsteady convection heat transfer results low thermal efficiency of the dryer at low air speed. The linear increase of the inner air speed from to makes the maximum efficiency increases of . When the offsetting air speed undergoes a convex quadratic increase, the average value of the energy efficiency in this case increases of compared to the scenario of constant air speed.

A novel model to estimate sensible heat fluxes in urban areas using satellite-derived data

A novel model for estimating sensible heat flux in urban areas using satellite data is presented here. Sensible heat flux (QH) is a primary component of the urban surface energy budget and is critical to regulating air temperature in cities. The model employs data from the NASA & NOAA GOES-16 geostationary satellite, ground-based observations from NOAA Automated Surface Observation Stations (ASOS), and land cover data from the National Land Cover Database (NLCD) as inputs for an iterative algorithm that is based on surface-layer similarity theory for turbulence parameterization. The application of this model specifically to urban areas is enabled by the spatial extent of the GOES-16 satellite and an element roughness height estimation method based on NLCD land cover data. Model results were independently validated using three flux towers located in different areas of New York City. Statistics generated over a year-long validation period from June 2019 to May 2020 show a root-mean-square error (RMSE) of 47.32 W-m−2, a mean bias error (MBE) of 16.58 W-m−2, and an R2 correlation value of 0.70. Model results were also compared to results from the urbanized Weather Research and Forecasting (uWRF) model relative to flux tower observational data to allow for a comparison between numerical models. The dedicated QH model outperformed the uWRF model relative to observational data, with an RMSE reduction of 63.5 W-m−2, an MBE reduction of 17.5 W-m−2, and an R2 increase of 0.08. Validation results show good agreement between model and observed values and performance comparison results show an improvement over a current numerical method for estimation of QH, suggesting the use of satellite data as a cost-effective and accessible option for estimating QH in urban areas.

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.

A Stochastic Unified Convection Scheme (UNICON). Part I: Formulation and Single-Column Simulation for Shallow Convection

AbstractBy extending the previously developed unified convection scheme (UNICON), we develop a stochastic UNICON with convective updraft plumes at the surface randomly sampled from the correlated multivariate Gaussian distribution for updraft vertical velocity w^ and thermodynamic scalars ϕ^, of which standard deviations and intervariable correlations are derived from the surface-layer similarity theory. The updraft plume radius R^ at the surface follows a power-law distribution with a specified scale break radius. To enhance computational efficiency, we also develop a hybrid stochastic UNICON consisting of n bin plumes and a single stochastic plume, each of which mainly controls the ensemble mean and variance of grid-mean convective tendency, respectively. We evaluated the stochastic UNICON using the large-eddy simulation (LES) of the Barbados Oceanographic and Meteorological Experiment (BOMEX) shallow convection case in a single-column mode. Consistent with the assumptions in the stochastic UNICON, the LES w^ and ϕ^ at the surface follow approximately the half- and full-Gaussian distributions, respectively. LES showed that a substantial portion of the variability in ϕ^ at the cloud base stems from the surface, which also supports the concept of stochastic UNICON that simulates various types of moist convection based on the dry stochastic convection launched from the surface. Overall, stochastic UNICON adequately reproduces the LES grid-mean thermodynamic states as well as the mean and variance of ϕ^, including their dependency on the domain size and R^. A sensitivity test showed that the perturbations of ϕ^ as well as R^ at the surface are important for the correct simulation of the grid-mean thermodynamic states.

GRADIENT-DIFFUSION CLOSURE AND THE EJECTION-SWEEP CYCLE IN CONVECTIVE BOUNDARY LAYERS

The inadequacy of conventional gradient-diffusion closure in modeling turbulent heat flux within the convective atmospheric boundary-layer is often alleviated by accounting for nonlocal transport. Such nonlocal effects are a manifestation of the inherent asymmetry in vertical transport in the convective boundary layer, which is in turn associated with third-order moments (skewness and fluxes of fluxes). In this work, the role of these third-order moments in second-order turbulence closure of the sensible heat flux is examined with the goal of reconciling the models to various closure assumptions. Surface layer similarity theory and mixed-layer parametrizations are used here, complemented by LES results when needed. The turbulent heat flux with various closure assumptions of the flux transport term is solved, including both local and nonlocal approaches. We connect to ejection-sweep cycles in the flow field using the GramCharlier cumulant expansion of the joint probability distribution of vertical velocity and potential temperature. In this nonlocal closure, the transport asymmetry models that include the vertical velocity skewness as a correction term to H originate from ejection-sweep events. Vertical inhomogeneity results in a modified-skewness correction to the nonlocal contribution to the heat flux associated with the relative intensity of ejections and sweeps.

Formulation of stability-dependent empirical relations for turbulent intensities from surface layer turbulence measurements for dispersion parameterization in a lagrangian particle dispersion model

Season- and stability-dependent turbulence intensity (σu/u*, σv/u*, σw/u*) relationships are derived from experimental turbulence measurements following surface layer scaling and local stability at the tropical coastal site Kalpakkam, India for atmospheric dispersion parameterization. Turbulence wind components (u′, v′, w′) measured with fast response UltraSonic Anemometers during an intense observation campaign for wind field modeling called Round Robin Exercise are used to formulate the flux–profile relationships using surface layer similarity theory and Fast Fourier Transform technique. The new relationships (modified Hanna scheme) are incorporated in a Lagrangian Particle Dispersion model FLEXPART-WRF and tested by conducting simulations for a field tracer dispersion experiment at Kalpakkam. Plume dispersion analysis of a ground level hypothetical release indicated that the new turbulent intensity formulations provide slightly higher diffusivity across the plume relative to the original Hanna scheme. The new formulations for σu, σv, σw are found to give better agreement with observed turbulent intensities during both stable and unstable conditions under various seasonal meteorological conditions. The simulated concentrations using the two methods are compared with those obtained from a classical Gaussian model and the observed SF6 concentration. It has been found that the new relationships provide comparatively higher diffusion across the plume relative to the model default Hanna scheme and provide downwind concentration results in better agreement with observations.

Validation of surface layer similarity theory to describe far offshore marine conditions in the Dutch North Sea in scope of wind energy research

With the ongoing development of offshore wind farms it becomes increasingly important to have an accurate description of offshore atmospheric conditions. A new meteorological mast constructed in 2011 sited 85km offshore in the Dutch North-sea area has been used to validate the relations expected from Monin–Obukhov similarity theory. It is shown that wind shear and turbulence (second order moments and turbulence spectra) are a function of the non-dimensional stability parameter ζ, which is in agreement with literature.Wind shear is well described by the stability corrected logarithmic wind shear profile, though scatter is significant for stable conditions. This is explained by considering the relative height within the boundary layer where observations are taken. The non-dimensional second order moments of the three wind components are found to be either constant (neutral), proportional to (-ζ)−1/3 (unstable) or proportional to ζ−1/2 (stable). The Kaimal spectrum has been validated for specified stability classes. The non-dimensional scaling frequency f0 for the three wind components increases for stable conditions, and decreases for unstable conditions. Besides, we find that f0 is smallest for the longitudinal wind component, and largest for the vertical wind component. These results support the validity and applicability of Monin–Obukhov similarity theory to describe atmospheric conditions far offshore.

Interaction between coherent structures and surface temperature and its effect on ground heat flux in an unstably stratified boundary layer

Surface layer plumes, thermals, downdrafts and roll vortices are the most prominent coherent structures in an unstably stratified boundary layer. They contribute most of the temperature and vertical velocity variance, and their time scales increase with height. The effects of these multi-scale structures (surface layer plumes scale with surface layer depth, thermals scale with boundary layer height and the resulting roll vortices scale with convective time scale) on the surface temperature and ground heat flux were studied using turbulence measurements throughout the atmospheric boundary layer and the surface temperature measurements from an infrared camera. Plumes and thermals imprint on the surface temperature as warm structures and downdrafts imprint as cold structures. The air temperature trace shows a ramp-like pattern, with small ramps overlaid on a large ramp very close to the surface; on the other hand, surface temperature gradually increases and decreases. Turbulent heat flux and ground heat flux show similar patterns, with the former lagging the latter. The maximum values of turbulent heat flux and ground heat flux are 4 and 1.2 times the respective mean values during the ejection event. Surface temperature fluctuations follow a similar power-law exponent relationship with stability as suggested by surface layer similarity theory.

Note on turbulence statistics in z-less stratification

In boundary layer meteorology, surface layer similarity theory plays a critical role in measuring and modeling biospheric fluxes. In stable boundary layer, surface layer similarity called z-less stratification has been one of main research topics for over than two decades and the issue has yet to be settled in micrometeorology. In this scientific discussion on z-less turbulence, different turbulence statistics were used inconsistently and it was argued that z-less turbulence was valid if only any turbulence statistics were constant with different atmospheric stabilities. Consequently, such inconsistently tested turbulence statistics and misconception on z-less turbulence hinder us from correctly understanding turbulence structure in the stable boundary layer. This note revisits z-less turbulence and emphasizes that different dimensionless turbulence statistics generally do not exhibit a common behavior in the limit of z-less stratification.

Bulk Transfer Relations for the Roughness Sublayer

In the roughness sublayer (RSL), Monin-Obukhov surface layer similarity theory fails. This is problematic for atmospheric modelling applications over domains that include rough terrain such as forests or cities, since in these situations numerical models often have the lowest model level located within the RSL. Based on empirical RSL profile functions for momentum and scalar quantities, and scaling the height with the RSL height z∗, we derive a simple bulk transfer relation that accounts for RSL effects. To verify the validity of our approach, these relations are employed together with wind speed and temperature profiles measured over boreal forest during the BOREAS experimental campaign to esti- mate momentum and heat fluxes. It is demonstrated that, when compared with observed flux values, the inclusion of RSL effects in the transfer relations yields a considerable improve- ment in the estimated fluxes.

Reference crop evapotranspiration estimate using high-resolution meteorological network's data

Abstract. Water management authorities need detailed information about each component of the hydrological balance. This document presents a method to estimate the evapotranspiration rate, initialized in order to obtain the reference crop evapotranspiration rate (ET0). By using an Optimal Interpolation (OI) scheme, the hourly observations of several meteorological variables, measured by a high-resolution local meteorological network, are interpolated over a regular grid. The analysed meteorological fields, containing detailed meteorological information, enter a model for turbulent heat fluxes estimation based on Monin-Obukhov surface layer similarity theory. The obtained ET0 fields are then post-processed and disseminated to the users.

Characterization of the Martian Convective Boundary Layer

Abstract The authors have carried out an extensive characterization of the Martian mixed layer formed under convective conditions. The values of the mixed layer height, convective velocity scale, convective temperature scale, mean temperature standard deviation, mean horizontal and vertical velocity standard deviations, and mean turbulent viscous dissipation rate have been obtained during the strongest convective hours for the mixed layer. In addition, the existing database of the surface layer has been improved by recalculating some parameters (e.g., Monin–Obukhov length, friction velocity, or scale temperature) that had already been obtained in previous papers by other means and also by calculating new ones, such as the standard deviation of the vertical wind speed velocity, the turbulent viscous dissipation rate, and eddy transfer coefficients for momentum and heat. The Earth counterparts of all these magnitudes are also shown. In this paper, a comprehensive database concerning the whole convective planetary boundary layer on Mars is displayed, and a detailed terrestrial comparison is established. The inputs of this work are hourly in situ temperature, hourly in situ horizontal wind speed, and hourly simulated ground temperature for specific selected Sols of the Viking and Pathfinder landers. These data correspond to typical low and midlatitude northern summertime conditions, with weak prevailing winds. To handle this set of data, surface layer and mixed layer similarity theory have been used at the strongest convective hours. In addition, the inclusion of a parameterization of a molecular sublayer and prescribed values of the surface roughness has been considered.

다중 수증기/이산화탄소 프로파일 관측 시스템의 원리와 활용

The multi-level profile system is designed to measure the vertical profile of and concentrations in the surface layer to estimate the storage effects within the plant canopy. It is suitable for long-term experiments and can be used also in advection studies for estimating the spatial variability and vertical gradients in concentration. It enables the user to calculate vertical fluxes of water vapor, and other trace gases using the surface layer similarity theory and to infer their sources or sinks. The profile system described in this report includes the following components: sampling system, calibration and flow control system, closed path infrared gas analyzer(IRGA), vacuum pump and a datalogger. The sampling system draws air from 8 inlets into the IRGA in a sequence, so that for 80 seconds air from all levels is measured. The calibration system, controlled by the datalogger, compensates for any deviations in the calibration of the IRGA by using gas sources with known concentrations. The datalogger switches the corresponding valves, measures the linearized voltages from the IRGA, calculates the concentrations for each monitoring level, performs statistical analysis and stores the final data. All critical components are mounted in an environmental enclosure and can operate with little maintenance over long periods of time. This report, as a practical manual, is designed to provide helpful information for those who are interested in using profile system to measure evapotranspiration and net ecosystem exchanges in complex terrain.

A One-Layer Satellite Surface Energy Balance for Estimating Evapotranspiration Rates and Crop Water Stress Indexes

Daily evapotranspiration fluxes over the semi-arid Catania Plain area (Eastern Sicily, Italy) were evaluated using remotely sensed data from Landsat Thematic Mapper TM5 images. A one-source parameterization of the surface sensible heat flux exchange using satellite surface temperature has been used. The transfer of sensible and latent heat is described by aerodynamic resistance and surface resistance. Required model inputs are brightness, temperature, fractional vegetation cover or leaf area index, albedo, crop height, roughness lengths, net radiation, air temperature, air humidity and wind speed. The aerodynamic resistance (rah) is formulated on the basis of the Monin-Obukhov surface layer similarity theory and the surface resistance (rs) is evaluated from the energy balance equation. The instantaneous surface flux values were converted into evaporative fraction (EF) over the heterogeneous land surface to derive daily evapotranspiration values. Remote sensing-based assessments of crop water stress (CWSI) were also made in order to identify local irrigation requirements. Evapotranspiration data and crop coefficient values obtained from the approach were compared with: (i) data from the semi-empirical approach “Kc reflectance-based”, which integrates satellite data in the visible and NIR regions of the electromagnetic spectrum with ground-based measurements and (ii) surface energy flux measurements collected from a micrometeorological tower located in the experiment area. The expected variability associated with ET flux measurements suggests that the approach-derived surface fluxes were in acceptable agreement with the observations.

Comparison of dynamic subgrid-scale models for simulations of neutrally buoyant shear-driven atmospheric boundary layer flows

Several non-dynamic, scale-invariant, and scale-dependent dynamic subgrid-scale (SGS) models are utilized in large-eddy simulations of shear-driven neutral atmospheric boundary layer (ABL) flows. The popular Smagorinsky closure and an alternative closure based on Kolmogorov’s scaling hypothesis are used as SGS base models. Our results show that, in the context of neutral ABL regime, the dynamic modeling approach is extremely useful, and reproduces several establised results (e.g., the surface layer similarity theory) with fidelity. The scale-dependence framework, in general, improves the near-surface statistics from the Smagorinsky model-based simulations. We also note that the local averaging-based dynamic SGS models perform significantly better than their planar averaging-based counterparts. Lastly, we find more or less consistent superiority of the Smagorinsky-based SGS models (over the corresponding Kolmogorov’s scaling hypothesis-based SGS models) for predicting the inertial range scaling of spectra.

Micrometeorology and Atmospheric Boundary Layer

Starting with simple definitions and the scope of micrometeorology and the atmospheric planetary boundary layer (PBL), the importance of small-scale turbulent exchange and energy dissipation processes in the PBL to the evolution of local weather and climate is pointed out. The energy budgets of an “ideal” surface and a near-surface canopy layer are briefly described and typical diurnal variations of measured energy fluxes at two (a rural and a suburban) sites are illustrated. Using the conservation equations of thermodynamic energy and moisture, temporal and spatial variations of mean air temperature and specific humidity are described. Diurnal evolutions of potential temperature profiles and the corresponding PBL height are illustrated with some observed data. Typical mean wind profiles in the daytime convective boundary layer (CBL) and the nighttime stable boundary layer (SBL) are also shown and discussed. The strong influence of stability on the PBL height and structure and their diurnal variations are discussed. The widely used flux-profile relations based on the Monin-Obukhov surface-layer similarity theory are presented with a brief discussion of parameterization of surface roughness and fluxes. The statistical description of the PBL turbulence and its commonly used quantitative measures are presented with an illustration of observed time series of turbulence. Some of the better-known similarity theories and scaling of turbulence in the PBL are described. Finally, different types of turbulence closure theories and numerical simulations/models of the PBL are briefly reviewed.

The Use of Large-Eddy Simulations in Lagrangian Particle Dispersion Models

AbstractA Lagrangian dispersion model driven by velocity fields from large-eddy simulations (LESs) is presented for passive particle dispersion in the planetary boundary layer (PBL). In this combined LES–Lagrangian stochastic model (LSM), the total velocity is divided into resolved or filtered and unresolved or subfilter-scale (SFS) velocities. The random SFS velocity is modeled using an adaptation of Thomson's LSM in which the ensemble-mean velocity and velocity variances are replaced by the resolved velocity and SFS variances, respectively. The random SFS velocity forcing has an amplitude determined by the SFS fraction of the total turbulent kinetic energy (TKE); the fraction is about 0.15 in the bulk of the simulated convective boundary layer (CBL) used here and reaches values as large as 0.31 and 0.37 in the surface layer and entrainment layer, respectively.For the proposed LES–LSM, the modeled crosswind-integrated concentration (CWIC) fields are in good agreement with the 1) surface-layer similarity (SLS) theory for a surface source in the CBL and 2) convection tank measurements of the CWIC for an elevated release in the CBL surface layer. The second comparison includes the modeled evolution of the vertical profile shape with downstream distance, which shows the attainment of an elevated CWIC maximum and a vertically well-mixed CWIC far downstream, in agreement with the tank data. For the proposed model, the agreement with the tank data and SLS theory is better than that obtained with an earlier model in which the SFS fraction of the TKE is assumed to be 1, and significantly better than a model that neglects the SFS velocities altogether.

A numerical study of plume dispersion motivated by a mesoscale atmospheric flow over a complex terrain

A three-dimensional time-dependent mesoscale meteorological model, called HOTMAC, is applied to study the complex terrain airshed of El Paso/Ciudad Juarez staring from November 29 and ending at December 2, 1998. The model numerically solves the equations for mass, momentum, heat and moisture in terrain following coordinates using the alternating direction implicit (ADI) finite difference scheme. The model accounts for solar and terrestrial radiation effects, whereby the lower boundary conditions are defined by a surface energy balance and surface layer similarity theory, and the soil heat flux is obtained by solving a 5-level heat condition equation in the soil. Surface properties are defined for 14 landuse classes and the model includes urban and forest canopy parameterizations. For the Paso del Norte region, four nested meshes (1, 2, 4 and 8 km resolution) horizontally and 22 vertical grid levels were used, with the top of the modeling domain being 6000 m. To account for synoptic-scale weather variations, a nudging scheme was employed. The numerical wind results are compared with observations made in the Paso del Norte area. Finally, using the wind and turbulence output from HOTMAC, the particle plume trajectory information was obtained using the `puff dispersion' model, RAPTAD, to capture details of the pollutant motions.

Surface Turbulent Heat and Momentum Fluxes over Global Oceans Based on the Goddard Satellite Retrievals, Version 2 (GSSTF2)

Information on the turbulent fluxes of momentum, latent heat, and sensible heat at the air–sea interface is essential in improving model simulations of climate variations and in climate studies. A 13.5-yr (July 1987–December 2000) dataset of daily surface turbulent fluxes over global oceans has been derived from the Special Sensor Microwave Imager (SSM/I) radiance measurements. This dataset, Goddard Satellite-based Surface Turbulent Fluxes, version 2 (GSSTF2), has a spatial resolution of 1° × 1° latitude–longitude and a temporal resolution of 1 day. Turbulent fluxes are derived from the SSM/I surface winds and surface air humidity, as well as the 2-m air and sea surface temperatures (SST) of the NCEP–NCAR reanalysis, using a bulk aerodynamic algorithm based on the surface layer similarity theory. The GSSTF2 bulk flux model is validated by comparing hourly turbulent fluxes computed from ship data using the model with those observed fluxes of 10 field experiments over the tropical and midlatitude oceans during 1991–99. In addition, the GSSTF2 daily wind stress, latent heat flux, wind speed, surface air humidity, and SST compare reasonably well with those of the collocated measurements of the field experiments. The global distributions of 1988–2000 annual- and seasonal-mean turbulent fluxes show reasonable patterns related to the atmospheric general circulation and seasonal variations. Zonal averages of latent heat fluxes and input parameters over global oceans during 1992–93 have been compared among several flux datasets: GSSTF1 (version 1), GSSTF2, the Hamburg Ocean–Atmosphere Parameters and Fluxes from Satellite Data (HOAPS), NCEP–NCAR reanalysis, and one based on the Comprehensive Ocean–Atmosphere Data Set (COADS). Significant differences are found among the five. These analyses suggest that the GSSTF2 latent heat flux, surface air humidity, and winds are likely to be more realistic than the other four flux datasets examined, although those of GSSTF2 are still subject to regional biases. The GSSTF2 is useful for climate studies and has been submitted to the sea surface turbulent flux project (SEAFLUX) for intercomparison studies.

Formulation of Turbulent Fluxes in the Stable Boundary Layer

Abstract The mixing lengths for heat and momentum are computed from seven levels of eddy correlation data during the Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99). A number of formulations of the mixing length are evaluated, including surface layer similarity theory, several hybrid similarity theories, a formulation based on the Richardson number, and a formulation based on the local shear. A formulation of the mixing length is examined, which approaches z-less similarity for large z and surface layer similarity close to the ground surface. A generalized version includes a dependence on boundary layer depth, which approaches the usual boundary layer height dependence for neutral conditions. However, for many of the observational cases, a boundary layer did not exist in the usual sense, in that turbulence was generated primarily above the surface inversion layer and occasionally extended downward toward the surface. For these cases, inclusion of z-less turbulence is crucial.