QG-DL-Ekman: Dynamics of a diabatic layer in the quasi-geostrophic framework

2021 ◽  
Keyword(s):  
Potential Temperature ◽  
Internal Gravity Waves ◽  
Ekman Layer ◽  
Heat Fluxes ◽  
Cloud Formation ◽  
Turbulent Heat ◽  
Ekman Pumping ◽  
Turbulent Friction ◽  
Geostrophic Balance ◽  
Middle Latitudes

Abstract Quasi-geostrophic (QG) theory describes the dynamics of synoptic scale flows in the troposphere that are balanced with respect to both acoustic and internal gravity waves. Within this framework, effects of (turbulent) friction near the ground are usually represented by Ekman Layer theory. The troposphere covers roughly the lowest ten kilometers of the atmosphere while Ekman layer heights are typically just a few hundred meters. However, this two-layer asymptotic theory does not explicitly account for substantial changes of the potential temperature stratification due to diabatic heating associated with cloud formation or with radiative and turbulent heat fluxes which can be significant in about the lowest three kilometers and in the middle latitudes. To address this deficiency, this paper extends the classical QG–Ekman layer model by introducing an intermediate dynamically and thermodynamically active layer, called the “diabatic layer” (DL) from here on. The flow in this layer is also in acoustic, hydrostatic, and geostrophic balance but, in contrast to QG flow, variations of potential temperature are not restricted to small deviations from a stable and time independent background stratification. Instead, within the DL diabatic processes are allowed to affect the leading-order stratification. As a consequence, this layer modifies the pressure field at the top of the Ekman layer, and with it the intensity of Ekman pumping seen by the quasi-geostrophic bulk flow. The result is the proposed extended quasi-geostrophic three-layer QG-DL-Ekman model for mid-latitude dynamics.

Dynamics of a Diabatic Layer in the quasi-geostrophic framework

2021 ◽  
Author(s):  
Rupert Klein ◽  
Lisa Schielicke ◽  
Stephan Pfahl ◽  
Boualem Khouider
Keyword(s):  
Potential Temperature ◽  
Internal Gravity Waves ◽  
Ekman Layer ◽  
Heat Fluxes ◽  
Cloud Formation ◽  
Turbulent Heat ◽  
Ekman Pumping ◽  
Turbulent Friction ◽  
Geostrophic Balance ◽  
Diabatic Processes

<p>Quasi-geostrophic (QG) theory describes the dynamics of synoptic scale flows in the trophosphere that are balanced with respect to both acoustic and internal gravity waves. Within this framework, effects of (turbulent) friction near the ground are usually represented by invoking Ekman Layer theory. The troposphere covers roughly the lowest ten kilometers of the atmosphere while Ekman layer heights are typically just a few hundred meters. However, this two-layer asymptotic theory does not explicitly account for substantial changes of the potential temperature stratification due to diabatic heating associated with cloud formation or with radiative or turbulent heat fluxes, which, in the middle latitudes, can be particularly important in roughly the lowest three kilometers. To alleviate this constraint, this work extends the classical QG plus Ekman layer model by introducing an intermediate, dynamically and thermodynamically active layer, called the "Diabatic Layer" here. The flow in this layer is also in acoustic, hydrostatic, and geostrophic balance but, in contrast to QG flow, variations of potential temperature are not restricted to small deviations from a stable and time independent background stratification. Instead, within this layer, diabatic processes are allowed to affect the leading-order stratification. As a consequence, the Diabatic Layer modifies the pressure field at the top of the Ekman layer, and with it the intensity of Ekman pumping seen by the quasi-geostrophic bulk flow. This leads to a new model for the coupled dynamics of the bulk troposphere, the diabatic layer, and the Ekman layer when strong diabatic processes substantially change the stratification in the lower part of the atmosphere. </p>

Numerical Simulation of Baroclinic Waves with a Parameterized Boundary Layer

2007 ◽  
Vol 64 (12) ◽  
pp. 4383-4399 ◽  
Author(s):  
R. S. Plant ◽  
S. E. Belcher
Keyword(s):  
Boundary Layer ◽  
Lower Troposphere ◽  
Conveyor Belt ◽  
Static Stability ◽  
Turbulent Fluxes ◽  
Life Cycles ◽  
Heat Fluxes ◽  
Turbulent Heat ◽  
Ekman Pumping ◽  
Basic States

Abstract A dry three-dimensional baroclinic life cycle model is used to investigate the role of turbulent fluxes of heat and momentum within the boundary layer on midlatitude cyclones. Simulations are performed of life cycles for two basic states: with and without turbulent fluxes. The different basic states produce cyclones with contrasting frontal and mesoscale flow structures. The analysis focuses on the generation of potential vorticity (PV) in the boundary layer and its subsequent transport into the free troposphere. The dynamic mechanism through which friction mitigates a barotropic vortex is that of Ekman pumping. This has often been assumed to also be the dominant mechanism for baroclinic developments. The PV framework highlights an additional, baroclinic mechanism. Positive PV is generated baroclinically due to friction to the northeast of a surface low and is transported out of the boundary layer by a cyclonic conveyor belt flow. The result is an anomaly of increased static stability in the lower troposphere, which restricts the growth of the baroclinic wave. The reduced coupling between lower and upper levels can be sufficient to change the character of the upper-level evolution of the mature wave. The basic features of the baroclinic damping mechanism are robust for different frontal structures, with and without turbulent heat fluxes, and for the range of surface roughness found over the oceans.

scholarly journals Inclusion of a Drag Approach in the Town Energy Balance (TEB) Scheme: Offline 1D Evaluation in a Street Canyon

2008 ◽  
Vol 47 (10) ◽  
pp. 2627-2644 ◽  
Author(s):  
R. Hamdi ◽  
V. Masson
Keyword(s):  
Boundary Layer ◽  
Energy Balance ◽  
Street Canyon ◽  
Potential Temperature ◽  
Single Layer ◽  
Heat Fluxes ◽  
Turbulent Heat ◽  
Surface Boundary ◽  
The Town ◽  
Meteorological Models

Abstract The Town Energy Balance module bridges the micro- and mesoscale and simulates local-scale urban surface energy balance for use in mesoscale meteorological models. Previous offline evaluations show that this urban module is able to simulate in good behavior road, wall, and roof temperatures and to correctly partition radiation forcing into turbulent and storage heat fluxes. However, to improve prediction of the meteorological fields inside the street canyon, a new version has been developed, following the methodology described in a companion paper by Masson and Seity. It resolves the surface boundary layer inside and above urban canopy by introducing a drag force approach to account for the vertical effects of buildings. This new version is tested offline, with one-dimensional simulation, in a street canyon using atmospheric and radiation data recorded at the top of a 30-m-high tower as the upper boundary conditions. Results are compared with simulations using the original single-layer version of the Town Energy Balance module on one hand and with measurements within and above a street canyon on the other hand. Measurements were obtained during the intensive observation period of the Basel Urban Boundary Layer Experiment. Results show that this new version produces profiles of wind speed, friction velocity, turbulent kinetic energy, turbulent heat flux, and potential temperature that are more consistent with observations than with the single-layer version. Furthermore, this new version can still be easily coupled to mesoscale meteorological models.

scholarly journals Estimation of Turbulent Heat Fluxes via Assimilation of Air Temperature and Specific Humidity into an Atmospheric Boundary Layer Model

2020 ◽  
Vol 21 (2) ◽  
pp. 205-225 ◽  
Author(s):  
E. Tajfar ◽  
S. M. Bateni ◽  
S. A. Margulis ◽  
P. Gentine ◽  
T. Auligne
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Air Temperature ◽  
Potential Temperature ◽  
Heat Fluxes ◽  
Specific Humidity ◽  
Turbulent Heat ◽  
Layer Model ◽  
Ground Heat Flux ◽  
Turbulent Heat Fluxes

AbstractA number of studies have used time series of air temperature and specific humidity observations to estimate turbulent heat fluxes. These studies require the specification of surface roughness lengths for heat and momentum (that are directly related to the neutral bulk heat transfer coefficient CHN) and/or ground heat flux, which are often unavailable. In this study, sequences of air temperature and specific humidity are assimilated into an atmospheric boundary layer model within a variational data assimilation (VDA) framework to estimate CHN, evaporative fraction (EF), turbulent heat fluxes, and atmospheric boundary layer (ABL) height, potential temperature, and humidity. The developed VDA approach needs neither the surface roughness parameterization (as it is optimized by the VDA approach) nor ground heat flux measurements. The VDA approach is tested over the First International Satellite Land Surface Climatology Project Field Experiment (FIFE) site in the summers of 1987 and 1988. The results indicate that the estimated sensible and latent heat fluxes agree fairly well with the corresponding measurements. For FIFE 1987 (1988), the daily sensible and latent heat fluxes estimates have a root-mean-square error of 25.72 W m−2 (27.77 W m−2) and 53.63 W m−2 (48.22 W m−2), respectively. In addition, the ABL height, specific humidity, and potential temperature estimates from the VDA system are in good agreement with those inferred from the radiosondes both in terms of magnitude and diurnal trend.

scholarly journals Observations of the Effects of Atmospheric Stability on Turbulence Statistics Deep within an Urban Street Canyon

2007 ◽  
Vol 46 (12) ◽  
pp. 2074-2085 ◽  
Author(s):  
P. Ramamurthy ◽  
E. R. Pardyjak ◽  
J. C. Klewicki
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Street Canyon ◽  
Potential Temperature ◽  
Atmospheric Stability ◽  
Heat Fluxes ◽  
Turbulent Heat ◽  
Turbulence Statistics ◽  
Momentum Fluxes ◽  
Turbulent Momentum

Abstract Data obtained in downtown Oklahoma City, Oklahoma, during the Joint Urban 2003 atmospheric dispersion study have been analyzed to investigate the effects of upstream atmospheric stability on turbulence statistics in an urban core. The data presented include turbulent heat and momentum fluxes at various vertical and horizontal locations in the lower 30% of the street canyon. These data have been segregated into three broad stability classification regimes: stable (z/L > 0.2), neutral (−0.2 < z/L < 0.2), and unstable (z/L < −0.2) based on upstream measurements of the Monin–Obukhov length scale L. Most of the momentum-related turbulence statistics were insensitive to upstream atmospheric stability, while the energy-related statistics (potential temperatures and kinematic heat fluxes) were more sensitive. In particular, the local turbulence intensity inside the street canyon varied little with atmospheric stability but always had large magnitudes. Measurements of turbulent momentum fluxes indicate the existence of regions of upward transport of high horizontal momentum fluid near the ground that is associated with low-level jet structures for all stabilities. The turbulent kinetic energy normalized by a local shear stress velocity collapses the data well and shows a clear repeatable pattern that appears to be stability invariant. The magnitude of the normalized turbulent kinetic energy increases rapidly as the ground is approached. This behavior is a result of a much more rapid drop in the correlation between the horizontal and vertical velocities than in the velocity variances. This lack of correlation in the turbulent momentum fluxes is consistent with previous work in the literature. It was also observed that the mean potential temperatures almost always decrease with increasing height in the street canyon and that the vertical heat fluxes are always positive regardless of upstream atmospheric stability. In addition, mean potential temperature profiles are slightly more unstable during the unstable periods than during the neutral or stable periods. The magnitudes of all three components of the heat flux and the variability of the heat fluxes decrease with increasing atmospheric stability. In addition, the cross-canyon and along-canyon heat fluxes are as large as the vertical component of the heat fluxes in the lower portion of the canyon.

scholarly journals The West Coast Thermal Trough: Mesoscale Evolution and Sensitivity to Terrain and Surface Fluxes

2013 ◽  
Vol 141 (8) ◽  
pp. 2869-2896 ◽  
Author(s):  
Matthew C. Brewer ◽  
Clifford F. Mass ◽  
Brian E. Potter
Keyword(s):  
High Pressure ◽  
West Coast ◽  
Energy Equation ◽  
Potential Temperature ◽  
Wrf Model ◽  
Surface Fluxes ◽  
Heat Fluxes ◽  
The West ◽  
Surface Heat Fluxes ◽  
Thermodynamic Energy

Abstract Despite the significant impacts of the West Coast thermal trough (WCTT) on West Coast weather and climate, questions remain regarding its mesoscale structure, origin, and dynamics. Of particular interest is the relative importance of terrain forcing, advection, and surface heating on WCTT formation and evolution. To explore such questions, the 13–16 May 2007 WCTT event was examined using observations and simulations from the Weather Research and Forecasting (WRF) Model. An analysis of the thermodynamic energy equation for these simulations was completed, as well as sensitivity experiments in which terrain or surface fluxes were removed or modified. For the May 2007 event, vertical advection of potential temperature is the primary driver of local warming and WCTT formation west of the Cascades. The downslope flow that drives this warming is forced by easterly flow associated with high pressure over British Columbia, Canada. When the terrain is removed from the model, the WCTT does not form and high pressure builds over the northwest United States. When the WCTT forms on the east side of the Cascades, diabatic heating dominates over the other terms in the thermodynamic energy equation, with warm advection playing a small role. If surface heat fluxes are neglected, an area of low pressure remains east of the Cascades, though it is substantially attenuated.

scholarly journals Heat transfer in rotating Rayleigh–Bénard convection with rough plates

2017 ◽  
Vol 830 ◽  
Author(s):  
Pranav Joshi ◽  
Hadi Rajaei ◽  
Rudie P. J. Kunnen ◽  
Herman J. H. Clercx
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Ekman Layer ◽  
Ekman Pumping ◽  
Ekman Boundary Layer ◽  
Bénard Convection ◽  
Roughness Elements ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This experimental study focuses on the effect of horizontal boundaries with pyramid-shaped roughness elements on the heat transfer in rotating Rayleigh–Bénard convection. It is shown that the Ekman pumping mechanism, which is responsible for the heat transfer enhancement under rotation in the case of smooth top and bottom surfaces, is unaffected by the roughness as long as the Ekman layer thickness $\unicode[STIX]{x1D6FF}_{E}$ is significantly larger than the roughness height $k$. As the rotation rate increases, and thus $\unicode[STIX]{x1D6FF}_{E}$ decreases, the roughness elements penetrate the radially inward flow in the interior of the Ekman boundary layer that feeds the columnar Ekman vortices. This perturbation generates additional thermal disturbances which are found to increase the heat transfer efficiency even further. However, when $\unicode[STIX]{x1D6FF}_{E}\approx k$, the Ekman boundary layer is strongly perturbed by the roughness elements and the Ekman pumping mechanism is suppressed. The results suggest that the Ekman pumping is re-established for $\unicode[STIX]{x1D6FF}_{E}\ll k$ as the faces of the pyramidal roughness elements then act locally as a sloping boundary on which an Ekman layer can be formed.

scholarly journals Large-Eddy Simulation and Single-Column Modeling of Thermally Stratified Wind Turbine Arrays for Fully Developed, Stationary Atmospheric Conditions

2015 ◽  
Vol 32 (6) ◽  
pp. 1144-1162 ◽  
Author(s):  
Adrian Sescu ◽  
Charles Meneveau
Keyword(s):  
Thermal Stratification ◽  
Layer Structure ◽  
Potential Temperature ◽  
Surface Fluxes ◽  
Heat Fluxes ◽  
Shear Stresses ◽  
Column Model ◽  
Large Eddy ◽  
Single Column ◽  
Single Column Model

AbstractEffects of atmospheric thermal stratification on the asymptotic behavior of very large wind farms are studied using large-eddy simulations (LES) and a single-column model for vertical distributions of horizontally averaged field variables. To facilitate comparisons between LES and column modeling based on Monin–Obukhov similarity theory, the LES are performed under idealized conditions of statistical stationarity in time and fully developed conditions in space. A suite of simulations are performed for different thermal stratification levels and the results are used to evaluate horizontally averaged vertical profiles of velocity, potential temperature, vertical turbulent momentum, and heat flux. Both LES and the model show that the stratification significantly affects the atmospheric boundary layer structure, its height, and the surface fluxes. However, the effects of the wind farm on surface heat fluxes are found to be relatively small in both LES and the single-column model. The surface fluxes are the result of two opposing trends: an increase of mixing in wakes and a decrease in mixing in the region below the turbines due to reduced momentum fluxes there for neutral and unstable cases, or relatively unchanged shear stresses below the turbines in the stable cases. For the considered cases, the balance of these trends yields a slight increase in surface flux magnitude for the stable and near-neutral unstable cases, and a very small decrease in flux magnitude for the strongly unstable cases. Moreover, thermal stratification is found to have a negligible effect on the roughness scale as deduced from the single-column model, consistent with the expectations of separation of scale.

Estimation of turbulent heat fluxes and exchange coefficients for heat at Dumont d'Urville, East Antarctica

1999 ◽  
Vol 11 (1) ◽  
pp. 93-99 ◽  
Author(s):  
S. Argentini ◽  
G. Mastrantonio ◽  
A. Viola
Keyword(s):  
Boundary Layer ◽  
Heat Fluxes ◽  
East Antarctica ◽  
Turbulent Heat ◽  
Convective Boundary ◽  
Doppler Sodar ◽  
Turbulent Heat Fluxes ◽  
Unstable Boundary Layer ◽  
Sodar Measurements ◽  
The Antarctic

Simultaneous acoustic Doppler sodar and tethersonde measurements were used to study some of the characteristics of the unstable boundary layer at Dumont d'Urville, Adélie Land, East Antarctica during the summer 1993–94. A description of the convective boundary layer and its behaviour in connection with the wind regime is given along with the frequency distribution of free convection episodes. The surface heat flux has been evaluated using the vertical velocity variance derived from sodar measurements. The turbulent exchange coefficients, estimated by coupling sodar and tethered balloon measurements, are in strong agreement with those present in literature for the Antarctic regions.

Searching for new physics: Using explainable AI to understand deep learned parameterizations of turbulent heat fluxes

2021 ◽  
Author(s):  
Andrew Bennett ◽  
Bart Nijssen
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Coupled System ◽  
Hydrologic Model ◽  
Heat Fluxes ◽  
Turbulent Heat ◽  
Phase Lag ◽  
Geophysical Research ◽  
Turbulent Heat Fluxes

<p>Machine learning (ML), and particularly deep learning (DL), for geophysical research has shown dramatic successes in recent years. However, these models are primarily geared towards better predictive capabilities, and are generally treated as black box models, limiting researchers’ ability to interpret and understand how these predictions are made. As these models are incorporated into larger models and pushed to be used in more areas it will be important to build methods that allow us to reason about how these models operate. This will have implications for scientific discovery that will ensure that these models are robust and reliable for their respective applications. Recent work in explainable artificial intelligence (XAI) has been used to interpret and explain the behavior of machine learned models.</p><p>Here, we apply new tools from the field of XAI to provide physical interpretations of a system that couples a deep-learning based parameterization for turbulent heat fluxes to a process based hydrologic model. To develop this coupling we have trained a neural network to predict turbulent heat fluxes using FluxNet data from a large number of hydroclimatically diverse sites. This neural network is coupled to the SUMMA hydrologic model, taking imodel derived states as additional inputs to improve predictions. We have shown that this coupled system provides highly accurate simulations of turbulent heat fluxes at 30 minute timesteps, accurately predicts the long-term observed water balance, and reproduces other signatures such as the phase lag with shortwave radiation. Because of these features, it seems this coupled system is learning physically accurate relationships between inputs and outputs. </p><p>We probe the relative importance of which input features are used to make predictions during wet and dry conditions to better understand what the neural network has learned. Further, we conduct controlled experiments to understand how the neural networks are able to learn to regionalize between different hydroclimates. By understanding how these neural networks make their predictions as well as how they learn to make predictions we can gain scientific insights and use them to further improve our models of the Earth system.</p>

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