Eddy Diffusivity Profiles Research Articles

One-dimensional Microphysics Model of Venusian Clouds from 40 to 100 km: Impact of the Middle-atmosphere Eddy Transport and SOIR Temperature Profile on the Cloud Structure

We conducted a simulation of H2SO4 vapor, H2O vapor, and H2SO4–H2O liquid aerosols from 40 to 100 km, using a 1D Venus cloud microphysics model based on the one detailed in Imamura & Hashimoto. The cloud distribution obtained is in good agreement with in situ observations by Pioneer Venus and remote-sensing observations from Venus Express (VEx). Case studies were conducted to investigate sensitivities to atmospheric parameters, including eddy diffusion and temperature profiles. We find that efficient eddy transport is important for determining upper haze population and its microphysical properties. Using the recently updated eddy diffusion coefficient profile by Mahieux et al., our model replicates the observed upper haze distribution. The H2O vapor distribution is highly sensitive to the eddy diffusion coefficient in the 60–70 km region. This indicates that updating the eddy diffusion coefficient is crucial for understanding the H2O vapor transport through the cloud layer. The H2SO4 vapor abundance varies by several orders of magnitude above 85 km, depending on the temperature profile. However, its maximum value aligns well with observational upper limits found by Sandor et al., pointing to potential sources other than H2SO4 aerosols in the upper haze layer that contribute to the SO2 inversion layer. The best-fit eddy diffusion profile is determined to be ∼2 m2 s−1 between 60 and 70 km and ∼360 m2 s−1 above 85 km. Furthermore, the observed increase of H2O vapor concentration above 85 km is reproduced by using the temperature profile from the VEx/SOIR instrument.

Solving the one dimensional vertical suspended sediment mixing equation with arbitrary eddy diffusivity profiles using temporal normalized physics-informed neural networks

Analytical solutions are practical tools in ocean engineering, but their derivation is often constrained by the complexities of the real world. This underscores the necessity for alternative approaches. In this study, the potential of Physics-Informed Neural Networks (PINN) for solving the one-dimensional vertical suspended sediment mixing (settling-diffusion) equation which involves simplified and arbitrary vertical Ds profiles is explored. A new approach of temporal Normalized Physics-Informed Neural Networks (T-NPINN), which normalizes the time component is proposed, and it achieves a remarkable accuracy (Mean Square Error of 10−5 and Relative Error Loss of 10−4). T-NPINN also proves its ability to handle the challenges posed by long-duration spatiotemporal models, which is a formidable task for conventional PINN methods. In addition, the T-NPINN is free of the limitations of numerical methods, e.g., the susceptibility to inaccuracies stemming from the discretization and approximations intrinsic to their algorithms, particularly evident within intricate and dynamic oceanic environments. The demonstrated accuracy and versatility of T-NPINN make it a compelling complement to numerical techniques, effectively bridging the gap between analytical and numerical approaches and enriching the toolkit available for oceanic research and engineering.

Parameterizing Vertical Mixing Coefficients in the Ocean Surface Boundary Layer Using Neural Networks

AbstractVertical mixing parameterizations in ocean models are formulated on the basis of the physical principles that govern turbulent mixing. However, many parameterizations include ad hoc components that are not well constrained by theory or data. One such component is the eddy diffusivity model, where vertical turbulent fluxes of a quantity are parameterized from a variable eddy diffusion coefficient and the mean vertical gradient of the quantity. In this work, we improve a parameterization of vertical mixing in the ocean surface boundary layer by enhancing its eddy diffusivity model using data‐driven methods, specifically neural networks. The neural networks are designed to take extrinsic and intrinsic forcing parameters as input to predict the eddy diffusivity profile and are trained using output data from a second moment closure turbulent mixing scheme. The modified vertical mixing scheme predicts the eddy diffusivity profile through online inference of neural networks and maintains the conservation principles of the standard ocean model equations, which is particularly important for its targeted use in climate simulations. We describe the development and stable implementation of neural networks in an ocean general circulation model and demonstrate that the enhanced scheme outperforms its predecessor by reducing biases in the mixed‐layer depth and upper ocean stratification. Our results demonstrate the potential for data‐driven physics‐aware parameterizations to improve global climate models.

A physically derived eddy parametrization for giant planet atmospheres with application on hot-Jupiters

ABSTRACT We present a parametrization for the eddy diffusion profile of gas giant exoplanets based on physical phenomena and we explore how the parametrized eddy profile impacts the chemical composition, the thermal structure, the haze microphysics, and the transit spectra of eight hot-Jupiters. Our eddy parametrization depends on the planetary intrinsic temperature (Tint), we thus evaluate how the increase of this parameter to values higher than those typically used (∼100 K) impacts the atmospheric structure and composition. Our investigation demonstrates that despite the strong impact of Tint on the chemical composition of the deep atmosphere, the upper atmosphere is not affected for Teq > 1300 K owing to high altitude quench levels at these conditions. Below this threshold, however, the larger atmospheric temperatures produced by increasing Tint affect the quenched chemical composition. Our eddy parametrization depends on two parameters, the eddy magnitude at the radiative–convective boundary (K0) and the corresponding magnitude at the homopause (Ktop). We demonstrate that, when using common K0 and Ktop values among most of the different planet cases studied, we derive transit spectra consistent with Hubble Space Telescope (HST) observations. Moreover, our simulations show that increasing the eddy profile enhances the photochemical production of haze particles and reduces their average radius, thus providing a steeper UV-Visible slope. Finally, we demonstrate for WASP-39b that the James Webb Space Telescope(JWST) observations provide improved constraints for the hazes and clouds and we show that both components seem necessary to interpret the combined transit spectrum from HST and JWST observations.

Analysis and modelling of non-local eddy diffusivity for turbulent scalar flux

The local eddy diffusivity model for the turbulent scalar flux is widely used to understand and predict scalar transport in turbulence. However, local approximation in space and time is not always valid for actual turbulent flow. An exact non-local expression for the scalar flux was previously derived by the author using Green's function. Even though the profile of the non-local eddy diffusivity in a turbulent channel flow was evaluated, its model expression was only discussed phenomenologically. In this study, the non-local eddy diffusivity approach was validated with help of direct numerical simulation (DNS) data of homogeneous isotropic turbulence with an inhomogeneous mean scalar to propose a systematic model expression. Initially, it was verified that the non-local expression for the scalar flux agrees with the value directly obtained from the DNS. In addition, the non-local effect accounts for the overestimation of the scalar flux by the local model and the counter-gradient diffusion phenomenon. The temporal behaviour of the non-local eddy diffusivity was further evaluated using the DNS data. Its model expression being proportional to the two-point velocity correlation was proposed in a manner customary in the statistical theory of turbulence. The profile of the non-local eddy diffusivity obtained from the model expression agrees well with the DNS value, and the non-local model reproduced the scalar flux. These results substantiate the potential of the non-local eddy diffusivity model.

Role of submesoscale processes in the isopycnal mixing associated with subthermocline eddies in the Philippine Sea

Submesoscale processes are very typical in the ocean interior with a front formed by mesoscale eddies, and contribute to ocean mixing. However, the role of submesoscale processes in the isopycnal mixing associated with ocean eddies has never been explored from observations. Based on hourly velocity and temperature data from the mooring at 8.5°N, 130°E between 26 September 2015 and 22 December 2016, this study provides the horizontal eddy diffusivity using a mixing-length framework and a parameterization related to the Rhines scale, and estimates the contribution of submesoscale processes to isopycnal mixing for the first time. The subthermocline eddies in the Philippine Sea exist between 200 m and 800 m depth, have characteristic speeds of 0.1–0.5 m/s with a typical period of 40–100 days, and can cause the temperature fluctuation of ∼0.5 °C. The horizontal diffusivity due to subthermocline eddies is about 4000–11,000 m2/s, and has a significant maximum near ∼400 m depth but the horizontal diffusivity associated with mixing length gradually increases below ∼700 m. The submesoscale processes can change the current velocity and temperature by ∼5 cm/s and ∼0.1 °C, respectively. The submesoscale processes in the ocean interior can increase the isopycnal mixing associated with subthermocline eddies by about 6–7%. The profile of horizontal eddy diffusivity derived in this study is useful for parameterization of ocean eddies and submesoscale processes in the Philippine Sea in coarse-resolution ocean models.

Improving stratocumulus cloud turbulence and entrainment parametrizations in OpenIFS

AbstractA series of modifications to the stratocumulus cloud turbulence and entrainment parametrizations in the Open Integrated Forecasting System (OpenIFS) model are performed in a Lagrangian single‐column model framework to determine whether they are able to improve the representation of the stratocumulus‐topped boundary layer and its transition to cloud break‐up. Two very different regimes are studied and compared with large‐eddy simulations: a subtropical marine stratocumulus‐to‐cumulus transition case driven by a warming sea‐surface temperature, and an Arctic air‐mass transformation case where warm and moist air is advected over sea ice during wintertime. The addition of nonlocal mixing driven by stratocumulus cloud‐top cooling for stable and dry convective boundary‐layer types is found to sustain the cloud deck for longer in the Arctic case, while it dissipates around one day earlier in the original OpenIFS. The assumption that cloud‐top‐driven mixing reaches the surface, forming a coupled boundary layer, is relaxed. The resulting eddy diffusivity profile is altered such that mixing at cloud top may be enhanced relative to cloud base, promoting decoupling. Decoupling in the subtropical boundary layer is further promoted when the cloud‐top turbulent velocity scale is based on the integral of the in‐cloud buoyancy flux, accounting for the turbulence generated by latent heat release within the cloud, which increases cloud‐top entrainment further relative to cloud base. Some long‐standing model issues persist, such as underestimation of the subtropical boundary‐layer deepening rate, which leads to a cold and moist bias in the boundary layer. In the Arctic, the boundary layer is generally too well mixed and warm at the surface. The degree of decoupling is also underestimated in both cases. However, the modifications discussed here lead to some improvement in OpenIFS.

Observation of vertical eddy diffusivity and mixing length during landfalling Super Typhoons

Understanding the vertical turbulent mixing processes in the planetary boundary layer (PBL) of tropical cyclones (TCs, or typhoons, hurricanes) and improving the PBL parameterization in numerical models of TCs is of paramount importance for TC modeling and forecasting. Based on the multi-level, high-resolution observations from Asia's tallest meteorological tower, the 356-m-high Shenzhen Meteorological Gradient Tower, this paper investigates the characteristics and vertical profiles of vertical eddy diffusivity and mixing length during two landfalling typhoons, namely Super Typhoons Mangkhut and Hato. The observed vertical eddy diffusivity and mixing length are compared with several widely-used parametrization schemes to assess the performance of the schemes. The results demonstrate that the K-profile parameterization scheme with the coefficient α = 1.5 satisfactorily portrays the magnitude and vertical distribution of the vertical eddy diffusivity. Moreover, a novel parametrization for mixing length is proposed, which is shown effective in reproducing the vertical mixing when used in conjunction with the Mellor–Yamada scheme. This study aims to enhance the understanding of vertical turbulent mixing in TC boundary layer and facilitate the numerical simulation of TCs over land.

The Diurnal Cycle of Entrainment and Detrainment in LES of the Southern Ocean Driven by Observed Surface Fluxes and Waves

AbstractEmpirical rules for both entrainment and detrainment are developed from LES of the Southern Ocean boundary layer when the turbulence, stratification, and shear cannot be assumed to be in equilibrium with diurnal variability in surface flux and wave (Stokes drift) forcing. A major consequence is the failure of downgradient eddy viscosity, which becomes more serious with Stokes drift and is overcome by relating the angle between the stress and shear vectors to the orientations of Lagrangian shear to the surface and of local Eulerian shear over 5 m. Thus, the momentum flux can be parameterized as a stress magnitude and this empirical direction. In addition, the response of a deep boundary layer to sufficiently strong diurnal heating includes boundary layer collapse and the subsequent growth of a morning boundary layer, whose depth is empirically related to the time history of the forcing, as are both morning detrainment and afternoon entrainment into weak diurnal stratification. Below the boundary layer, detrainment rules give the maximum buoyancy flux and its depth, as well a specific stress direction. Another rule relates both afternoon and nighttime entrainment depth and buoyancy flux to surface layer turbulent kinetic energy production integrals. These empirical relationships are combined with rules for boundary layer transport to formulate two parameterizations; one based on eddy diffusivity and viscosity profiles and another on flux profiles of buoyancy and of stress magnitude. Evaluations against LES fluxes show the flux profiles to be more representative of the diurnal cycle, especially with Stokes drift.

A Na density lidar method and measurements of turbulence to 105 km at the Andes Lidar Observatory

This study presents a method of measuring atmospheric turbulence from resonance-fluorescence lidar observations of atmospheric Na layer density fluctuations, which is used to characterize turbulent eddy diffusion (kzzTurb) from 85 km to 105 km altitude over the Andes Lidar Observatory (ALO) in Cerro Pachón, Chile, (30.3°S, 70.7°W) at timescales between 12 seconds and 78 seconds. Na lidar measurements of heat, momentum, and constituent fluxes at turbulence scales have traditionally been limited to the 85–100 km region due to signal limitations; however, the ”Na density” method described herein offers a 3x signal-to-noise ratio improvement over Doppler heat flux measurements, enabling determination of eddy diffusion to higher altitudes and at shorter timescales. The presented mean turbulent eddy diffusion profile is determined from 115 h of zenith data acquired over 25 nights via the Na density method. Results are supplemented by off-zenith data for all 25 nights, which is used to examine atmospheric stability. Mean kzzTurb over the timescales analyzed ranged between 1.2×105 cm2s−1 and 5.7×105 cm2s−1 in the 85–100 km region and increased from a minimum at 98 km to a maximum of 4.5×106 cm2s−1 near 105 km altitude. The mean profile is compared with the Doppler method for (i) the same ALO dataset discussed herein and (ii) vertical-only ALO data between 85 km and 100 km altitude. The critical region (95–110 km) of diffusive coupling in the mesosphere and lower thermosphere (MLT) differs in forcing uniquely with a dominance of wind shear and associated instabilities. Source investigations pertaining to the induced transport difference from the critical to the lower MLT region (80–95 km), where the effects of damped atmospheric gravity waves and convective instabilities are well-established, require an ability to gather data on the variability of turbulence with altitude, latitude, and season, as well as atmospheric wave activity.

Vertical Structure of the Beaufort Gyre Halocline and the Crucial Role of the Depth-Dependent Eddy Diffusivity

AbstractTheories of the Beaufort Gyre (BG) dynamics commonly represent the halocline as a single layer with a thickness depending on the Eulerian-mean and eddy-induced overturning. However, observations suggest that the isopycnal slope increases with depth, and a theory to explain this profile remains outstanding. Here we develop a multilayer model of the BG, including the Eulerian-mean velocity, mesoscale eddy activity, diapycnal mixing, and lateral boundary fluxes, and use it to investigate the dynamics within the Pacific Winter Water (PWW) layer. Using theoretical considerations, observational data, and idealized simulations, we demonstrate that the eddy overturning is critical in explaining the observed vertical structure. In the absence of the eddy overturning, the Ekman pumping and the relatively weak vertical mixing would displace isopycnals in a nearly parallel fashion, contrary to observations. This study finds that the observed increase of the isopycnal slope with depth in the climatological state of the gyre is consistent with a Gent–McWilliams eddy diffusivity coefficient that decreases by at least 10%–40% over the PWW layer. We further show that the depth-dependent eddy diffusivity profile can explain the relative magnitude of the correlated isopycnal depth and layer thickness fluctuations on interannual time scales. Our inference that the eddy overturning generates the isopycnal layer thickness gradients is consistent with the parameterization of eddies via a Gent–McWilliams scheme but not potential vorticity diffusion. This study implies that using a depth-independent eddy diffusivity, as is commonly done in low-resolution ocean models, may contribute to misrepresentation of the interior BG dynamics.

Determination of the Venus eddy diffusion profile from CO and CO2 profiles using SOIR/Venus Express observations

We present a study of the SOIR/Venus Express CO2 and CO profiles in order to constrain the eddy diffusion profile in the Venus mesosphere (80 to 130 km of altitude). We compute the mean number density profile of both species, and the hydrostatic temperature based on the CO2 mean density profile. We use a 1D-photochemical/diffusion model to adjust the eddy diffusion profile such that the 1D-model and SOIR CO profiles best agree. We compare our results with eddy diffusion profiles found in the literature. We use our approach to revisit the He and CO2 profiles from Pioneer Venus probe mass spectrometer in order to derive an eddy diffusion profile extending from 80 to 200 km of altitude. Our eddy diffusion profile is different in shape and in magnitude compared to the Pioneer Venus profile: it is equal to 3.6 × 106 cm2/s at 110 km, 7.5 × 106 cm2/s at 120 km, 0.4 × 106 cm2/s at 130 km, and 201 × 106 cm2/s at 140 km, and constant below 110 km and above 140 km. This new eddy diffusion profile can be used in Venus Global Circulation Models as well as 1D-photochemical models.

Impact of physical process on propagating oil spills in the Caspian Sea

This study aims to inspect the oil spill propagation in the Caspian Sea using Sentinel-1 data as well as wind and observation data. Detection processes clearly show that although the north and middle basin are the main sources of oil pollution, the southern basin would be the final destination of these oil slicks. Comparison of oil spill clusters in the southern and on the Apsheron indicates that the size of these clusters decreases under the physical process of the southern basin like eddies. Further, the mixed layer is estimated at 25–35 m in the southern basin. After applying the analytical formulas, the eddy diffusivity profile is plotted, leading to an estimate of nearly 5 × 10−4 m2/s on the surface water. The droplet oil diameters are calculated which vary from 150 μm to 250 μm based on an analytical model in a steady-state mode.

Numerical model for primary and secondary air pollutants emitted from an area and point source in an urban area with chemical reaction and removal mechanisms

A complete numerical mathematical model is presented to study the consequence of chemical reaction and removal mechanisms on the pollutant radiated from the point source on the boundary of the city region. Life span of secondary pollutant is more than the primary pollutant and it is dangerous to human being and its surroundings so in this model, we are considering secondary and primary pollutants. The realistic wind velocity and eddy diffusivity profiles are considered in this model. The intricate problem is simplified numerically with Crank-Nicolson finite difference technique. In stable and neutral atmospheric conditions primary and secondary pollutant concentration is maximum on the boundary of point source and as well as at bottom surface.

Diffusive–Nondiffusive Flux Decompositions in Atmospheric Boundary Layers

AbstractEddy diffusivity models are a common method to parameterize turbulent fluxes in the atmospheric sciences community. However, their inability to handle convective boundary layers leads to the addition of a nondiffusive flux component (usually called nonlocal) alongside the original diffusive term (usually called local). Both components are often modeled for convective conditions based on the shape of the eddy diffusivity profile for neutral conditions. This assumption of shape is traditionally employed due to the difficulty of estimating both components based on numerically simulated turbulent fluxes without any a priori assumptions. In this manuscript we propose a novel method to avoid this issue and estimate both components from numerical simulations without having to assume any a priori shape or scaling for either. Our approach is based on optimizing results from a modeling perspective and taking as much advantage as possible from the diffusive term, thus maximizing the eddy diffusivity. We use our method to diagnostically investigate four different large-eddy simulations spanning different stability regimes, which reveal that nondiffusive fluxes are important even when trying to minimize them. Furthermore, the calculated profiles for both diffusive and nondiffusive fluxes suggest that their shapes change with stability, which is an effect that is not included in most models currently in use. Finally, we use our results to discuss modeling approaches and identify opportunities for improving current models.

Mathematical Model in Air Pollution with Area Source

A steady state two-dimensional atmospheric advection- diffusion numerical model of area source air pollution is presented. This model takes into account the actual form of variable settling velocity and eddy-diffusivity profile. Here the influence of settling velocity must be taken into account for the study of atmosphere dispersion. Therefore in the present analysis the two dimensional steady state dispersion of air pollutants over an area source under the settling effect has been investigated. The results obtained are compared with the known results and are found in close agreement.

Chemical Cycling in the Venusian Atmosphere: A Full Photochemical Model From the Surface to 110 km

AbstractVenus is an exceptional natural experiment to test our understanding of atmospheric sulfur chemistry. Previous modeling efforts have focused on understanding either the middle or lower atmosphere. In this work, we performed the first full atmosphere analysis of the chemical transport processes on Venus from the surface to 110 km using a 1‐D diffusion model with photochemistry. We focused on the cycling of chemical species between the upper and lower atmospheres and interactions between distinct species groups including SO , CO + OCS, chlorides, NO , O , and S . We tested different eddy diffusivity profiles and investigated their influences on the vertical profiles of important species. We find that the assumed boundary conditions in previous models strongly impacted their simulation results. This has a particularly large effect for SO . We find the high SO abundance in the lower atmosphere is readily transported into the middle atmosphere, far exceeding observed values. This implies some yet unknown chemistry or process limiting SO mixing. We summarize outstanding questions raised by this work and note chemical reactions that should be the highest priority for future laboratory studies and ab initio calculations.

Analytical Solutions of the Advection–Diffusion Equation with Variable Vertical Eddy Diffusivity and Wind Speed Using Hankel Transform

Hankel transform was employed to solve the two-dimensional steady state advection–diffusion equation considering a continuous point source with vertical eddy diffusivity as a power law of vertical height and downwind distance, also, taking wind speed as power law. The analytical model was evaluated and compared with Hanford diffusion experiment in stable conditions and Copenhagen diffusion experiment in unstable and neutral conditions which was done by reducing the general analytical model to a one with linear vertical eddy diffusivity and constant downwind speed profile. Comparison with other analytical models was held. The presented model predictions show a good agreement with observations and lay inside a factor of two with observed data of both Hanford and Copenhagen diffusion experiments.

Estimating vertical mixing in the deep north Aegean Sea using argo data corrected for conductivity sensor drift

Successive CTD profiles of an Argo float trapped within a deep (~1250 m) sub-basin of the North Aegean Sea during 2014–2015 enabled identification of deep-water ventilation episodes and inference of a bulk (budget-based) vertical eddy diffusivity during the period that followed these events. Independent effective eddy diffusivity profiles were computed under the assumption that the turbulent exchange of heat, salt and buoyancy through each isobath below 400 m will balance the rate of change of the corresponding variable's content of the water volume within the basin below that depth. The initially estimated thermal, saline and density diffusivity profiles were significantly different from each other. Assuming turbulence was the dominant mixing process between the intermediate and deep water masses led to identification of conductivity sensor drift rate of 4.6 × 10−6 S m−1 day−1. After correcting the sensor's drift, bulk eddy diffusivities Kρ,KS and KT were found to span (2–30) × 10−3 m2 s−1, in close agreement below 400 m depth. These estimates are at least one order of magnitude higher than eddy diffusivities based on a finescale internal-wave strain parameterization. Enhanced boundary mixing and double diffusion are examined as candidates to explain the high effective diffusivity values. A hypsometric correction appears to provide sufficient diapycnal transport along the boundaries to reproduce bulk buoyancy transports.

(Invited) Thoughts on the Viscous Sublayer

Years ago people postulated that there is a laminar sublayer near a solid wall in turbulent flow. Murphree (1932) and Levich (1942, 1944) postulated that the turbulence eddies decay only gradually as the solid wall is approached. There are two schools of thought: one says that the eddy diffusivity is proportional to y 3 near the wall; the other says y 4. Which is right? Perhaps there is some truth in both views. It may be that y 4 prevails near the outer limit of the viscous sublayer, adjacent to the outer turbulent flow, but that y3 prevails very close to the wall. It has been thought that this was important only for mass transfer in turbulent flow at high Schmidt numbers, that is, for diffusion coefficients much smaller than the kinematic viscosity. However, it is shown that Nikuradse’s data (1932) for pressure drops (or friction factors) in turbulent pipe flow do not agree with his very careful measurements of profiles of the eddy viscosity. In other words, the viscous sublayer cannot be ignored even in fluid flow. The profile of predicted eddy diffusivity of Wasan, Tien, and Wilke (1963) show regions of y 3 dependence very close to the wall and y dependence in the outer turbulent flow with perhaps a y 4 dependence in the intermediate region. On this diagram, one can identify the thickness of the diffusion layer as a function of the Schmidt number. As is well known, the diffusion layer gets very thin at high Schmidt numbers. Using this profile, one can show that the y 4 dependence will not show up clearly in mass-transfer data at any Schmidt number. Any region of y 4 dependence of the eddy diffusivity is outside the diffusion layer where the concentration does not change (at high Schmidt numbers). These thoughts inspire a method of calculating the profiles of eddy diffusivity and eddy viscosity from consideration of fluctuations themselves. Hopefully this can be a subject of future work.