Parameterization Of Eddy Diffusivity Research Articles

A modified vertical eddy diffusivity parameterization in the HWRF model based on large eddy simulations and its impact on the prediction of two landfalling hurricanes

Vertical eddy diffusivity (VED) in the planetary boundary layer (PBL) has a significant impact on forecasts of tropical cyclone (TC) structure and intensity. VED uncertainties in PBL parameterizations can be partly attributed to the model’s inability to represent roll vortices (RV). In this study, RV effects on turbulent fluxes derived from a large eddy simulation (LES) by Li et al. (Geophys. Res. Lett., 2021, 48, e2020GL090703) are added to the VED parameterization of the PBL scheme within the operational Hurricane Weather Research and Forecasting (HWRF) model. RV contribution to VED is parameterized through a coefficient and varies with the RV intensity and velocity scale. A modification over land has also been implemented. This modified VED parameterization is compared with the original wind-speed-dependent VED scheme in HWRF. Retrospective HWRF forecasts of Hurricanes Florence (2018) and Laura (2020) are analyzed to evaluate the impacts of the modified VED scheme on landfalling hurricane forecasts. Results show that the modified PBL scheme with the RV effect leads to an improvement in 10-m maximum wind speed forecasts of 14%–31%, with a neutral to positive improvement for track forecasts. Improved wind structure and precipitation forecasts against observations are also noted with the modified PBL scheme. Further diagnoses indicate that the revised PBL scheme enhances moist entropy in the boundary layer over land, leading to improved TC intensity prediction compared to the original scheme.

The Stratospheric Diurnal Cycle in COSMIC GPS Radio Occultation Data: Scientific Applications

AbstractThe diurnal cycle throughout the stratosphere is analyzed by applying Bayesian interpolation to Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) Global Positioning System radio occultation (RO) data and three scientific applications of the analysis are introduced. First, the migrating thermal tides are analyzed with unprecedented accuracy and precision, with an uncertainty in the analysis of the vertically propagating tides ranging from 0.1 in the lower stratosphere to 0.6 K in the upper stratosphere for an individual month of RO data and with an uncertainty in a 10‐year climatological diurnal cycle a factor of 10 less. Moreover, the midlatitude trapped tide is found to be smaller than what is produced by an atmospheric model and lags the model in phase, a likely consequence of a faulty parameterization of eddy diffusivity in the upper stratosphere. Second, a clear signal of solar cycle influence on the diurnal cycle is evident in this analysis, but whether the cause is the systematic bias of ionospheric residual associated with RO retrieval or it is an actual atmospheric phenomenon is less clear. Third, RO satellites and missions that obtain inadequate coverage of the diurnal cycle will be biased by under‐sampling it, whether or not subsampling weather forecasts is used to removal sampling error. The analysis of the diurnal cycle in COSMIC RO data can be used to diagnose the systematic sampling error incurred by incomplete coverage of the diurnal cycle, which is of the order of 0.2 K for a Metop‐based RO climatology.

Vertical Eddy Diffusivity Parameterization Based on a Large‐Eddy Simulation and Its Impact on Prediction of Hurricane Landfall

AbstractThe vertical eddy diffusivity (VED) in the planetary boundary layer (PBL) affects tropical cyclones' structure and evolution. Uncertainties of VED in the PBL parametrization scheme of a mesoscale model could be caused by the model's inability to represent large eddies (LEs). Using a large‐eddy simulation (LES) of Hurricane Harvey (2017) as a benchmark, the YSU PBL scheme is improved by adding effects of LEs derived from the LES. It is found that LEs' maximum intensity is linearly significantly related to the square of mean horizontal divergence below 400 m of height at the same air column with a slope coefficient of 1.97. The revised YSU scheme relates the VED of momentum (Km) to the square root of LEs' intensity with a slope coefficient of 0.08 in PBL and 0.20 in a free atmosphere. Compared to the original scheme, the modified YSU scheme leads to improved forecasts of landfalling hurricanes.

ТРАЕКТОРНОЕ МОДЕЛИРОВАНИЕ СРЕДНЕЙ АТМОСФЕРЫ

A short description and some applications of the trajectory and dispersion models developed in Central Aerological Observatory (CAO) for studying the stratospheric and tropospheric transport of pollutants are presented. The TRACAO trajectory model is applied to investigate the processes related to the ozone depletion in the winter polar stratosphere, in order to study the mid-latitude stratosphere-troposphere exchange, as well as to analyze balloon and aircraft (M55 “Geophysics,” Yak-42D “Roshydromer”) observations. Then based on the TRACAO, the GLADIM dispersion model that simulates trajectories of the set of particles with the eddy diffusion parameterization and determines the pollutant concentration at the regular grid points, was developed. The dispersion model was applied to simulate volcanic ash dispersion and carbon dioxide profile reconstruction. The model validation was done by comparisons with the results of the widely used FLEXPART model. Nowadays these models are used at the “Middle Atmosphere” Regional Information and Analytic Center established in CAO.

Modelling of Water Surface Temperature of Three Lakes on the Tibetan Plateau using a Physically Based Lake Model

ABSTRACTThis study was carried out to quantify the physical processes of lakes in the Tibetan Plateau using the Community Land Model, version 4.5 (CLM4.5), coupled with a physically based, 10-layer lake model developed by the National Center for Atmospheric Research. The CLM was forced with 10 km resolution reanalysis data to attempt to understand detailed lake processes and how these processes affect lake surface temperature. In this study, we simulated seasonal and interannual variations of lake surface temperature for Lake Qinghai, Zhaling Co, and Nam Co in the Tibetan Plateau and compared these simulations with observations. The results showed that the CLM4.5 lake model simulations reproduced the observed lake surface temperatures for Lake Qinghai and Zhaling Co well but reproduced those for Nam Co poorly. Through detailed analysis, we found that the simulated biases for Nam Co result largely from the unrealistic parameterization of eddy diffusivity. By expanding this parameter, the lake surface temperature simulations improved remarkably. In addition, erroneous lake ice cover simulations contributed to the simulated lake surface temperature bias in the cold seasons.

Global Observations of Horizontal Mixing from Argo Float and Surface Drifter Trajectories

AbstractMixing by mesoscale eddies in the ocean plays a major role in setting the distribution of oceanic tracers, with important implications for physical and biochemical systems at local to global scales. Roach et al. (2016; https://doi.org/10.1002/2015JC011440) demonstrated that a two‐particle analysis of Argo trajectories produces robust estimates of horizontal mixing in the Southern Ocean. Here we extend this analysis to produce global 1° × 1° maps of eddy diffusivity at the nominal Argo parking depth of 1,000 m. We also applied this methodology to estimate surface eddy diffusivities from Global Drifter Program (GDP) surface drifters. The global mean eddy diffusivity was 543 ± 155 m2/s at 1,000 m and 2637 ± 311 m2/s at the surface, with elevated diffusivities in regions of enhanced eddy kinetic energy, such as western boundary currents and along the Antarctic Circumpolar Current. The eddy kinetic energy at the equator is high at both the surface and depth, but the eddy diffusivity is only enhanced near the surface. At depth the eddy diffusivity is strongly suppressed due to the presence of mean flow. We used our observational estimates to test the validity of an eddy diffusivity parameterization that accounts for mixing suppression in the presence of zonal mean flows. Our results indicated that this parameterization generally agrees with the directly observed eddy diffusivities in the midlatitude and high‐latitude oceans.

Observed and Modeled Global Ocean Turbulence Regimes as Deduced from Surface Trajectory Data

Abstract A large-scale tool for systematic analyses of the dispersal and turbulent properties of ocean currents and the subsequent separation of dynamical regimes according to the prevailing trajectories taxonomy in a certain area was proposed by Rupolo. In the present study, this methodology has been extended to the analysis of model trajectories obtained by analytical computations of the particle advection equation using the Lagrangian open-source software package Tracing the Water Masses of the North Atlantic and the Mediterranean (TRACMASS), and intercomparisons have been made between the surface velocity fields from three different configurations of the global Nucleus for European Modelling of the Ocean (NEMO) ocean/sea ice general circulation model. Lagrangian time scales of the observed and synthetic trajectory datasets have been calculated by means of inverse Lagrangian stochastic modeling, and the influence of the model field spatial and temporal resolution on the analyses has been investigated. In global-scale ocean modeling, compromises are frequently made in terms of grid resolution and time averaging of the output fields because high-resolution data require considerable amounts of storage space. Here, the implications of such approximations on the modeled velocity fields and, consequently, on the particle dispersion, have been assessed through validation against observed drifter tracks. This study aims, moreover, to shed some light on the relatively unknown turbulent properties of near-surface ocean dynamics and their representation in numerical models globally and in a number of key regions. These results could be of interest for other studies within the field of turbulent eddy diffusion parameterization in ocean models or ocean circulation studies involving long-term coarse-grid model experiments.

Lessons in uncertainty quantification for turbulent dynamical systems

The modus operandi of modern applied mathematics in developing very recent mathematical strategies for uncertainty quantification in partially observed high-dimensional turbulent dynamical systems is emphasized here. The approach involves the synergy of rigorous mathematical guidelines with a suite of physically relevant and progressively more complex test models which are mathematically tractable while possessing such important features as the two-way coupling between the resolved dynamics and the turbulent fluxes, intermittency and positive Lyapunov exponents, eddy diffusivity parameterization and turbulent spectra. A large number of new theoretical and computational phenomena which arise in the emerging statistical-stochastic framework for quantifying and mitigating model error in imperfect predictions, such as the existence of information barriers to model improvement, are developed and reviewed here with the intention to introduce mathematicians, applied mathematicians, and scientists to these remarkable emerging topics with increasing practical importance.

Parameterization of the eddy diffusivity in a dispersion model over homogeneous terrain in the atmospheric boundary layer

Parameterizations of the vertical eddy diffusivity over homogeneous terrain in neutral, stable and unstable conditions for the entire atmospheric boundary layer are proposed using the mixing length theory. The formulation utilizes the theoretically derived local mixing length scale that is composed of three component length scales. Proposed profiles of the eddy diffusivity in various stability conditions are compared to those reported in the literature. The proposed profiles of the eddy diffusivity are used in a generalized analytical model for dispersion of pollutants released from a continuous source in the atmospheric boundary layer. The dispersion model describing the crosswind integrated concentrations is briefly presented. By considering the proposed and other commonly applied parameterizations of eddy diffusivity, the dispersion model is evaluated with the tracer observations obtained from Copenhagen diffusion experiment in unstable conditions, Prairie Grass experiment in both unstable and stable conditions and Hanford experiment in stable conditions. The dispersion model with proposed parameterizations of the eddy diffusivity is performing reasonably well with the observations and demonstrates throughout a consistent and good performance in the concentration estimation for elevated and surface releases from a continuous point source in various stability conditions. Though the magnitudes of the various eddy diffusivities are different from the proposed one, the profiles of all parameterizations in terms of the shape have almost similar characteristics. The differences in the magnitudes of diffusion produced by various parameterizations cause minor but noticeable changes in the simulation of ground level concentrations from the dispersion model. In very stable conditions, the agreement of the model evaluations with measurements is less satisfactory and none of the parameterizations used here including proposed one is adequate to describe the atmospheric dispersion process in these conditions.

Improving model fidelity and sensitivity for complex systems through empirical information theory.

In many situations in contemporary science and engineering, the analysis and prediction of crucial phenomena occur often through complex dynamical equations that have significant model errors compared with the true signal in nature. Here, a systematic information theoretic framework is developed to improve model fidelity and sensitivity for complex systems including perturbation formulas and multimodel ensembles that can be utilized to improve both aspects of model error simultaneously. A suite of unambiguous test models is utilized to demonstrate facets of the proposed framework. These results include simple examples of imperfect models with perfect equilibrium statistical fidelity where there are intrinsic natural barriers to improving imperfect model sensitivity. Linear stochastic models with multiple spatiotemporal scales are utilized to demonstrate this information theoretic approach to equilibrium sensitivity, the role of increasing spatial resolution in the information metric for model error, and the ability of imperfect models to capture the true sensitivity. Finally, an instructive statistically nonlinear model with many degrees of freedom, mimicking the observed non-Gaussian statistical behavior of tracers in the atmosphere, with corresponding imperfect eddy-diffusivity parameterization models are utilized here. They demonstrate the important role of additional stochastic forcing of imperfect models in order to systematically improve the information theoretic measures of fidelity and sensitivity developed here.

Parameterizations of the daytime friction velocity, temperature scale, and upslope flow over gently inclined terrain in calm synoptic conditions

A set of new parameterizations for the friction velocity and temperature scale over gently sloped terrain and in calm synoptic conditions are theoretically derived. The friction velocity is found to be proportional to the product of the square root of the total accumulated heating in the boundary layer and the sinusoidal function of the slope angle, while the temperature scale is proportional to the product of the boundary layer depth, the sinusoidal function of the slope angle and the potential temperature gradient in the free atmosphere. Using the new friction velocity parameterization, together with a parameterization of eddy diffusivity and an initial potential temperature profile around sunrise, an improved parameterization for the thermally induced upslope flow profile is derived by solving the Prandtl equations. The upslope flow profile is found to be simply proportional to the friction velocity.

Influence of vertical eddy diffusivity parameterization on daily and monthly mean concentrations of O3 and NOy

Two parameterization schemes for vertical eddy diffusivity were utilized to investigate their impacts on both the daily and monthly mean concentrations of ozone and NOy, which are the major fractions of the sum of all reactive nitrogen species, i.e., NOy=NO+NO2+HNO3+PAN. Simulations indicate that great changes in the vertical diffusivity usually occur within the planetary boundary layer (PBL). Daily and monthly mean concentrations of NOy are much more sensitive to changes in the vertical diffusivity than those of ozone and ozone and NOy levels only at or in (relatively) clean sites and areas, where long-range transport plays a crucial role, display roughly equivalent sensitivity. The results strongly suggest that a widely-accepted parameterization scheme be selected and the refinement of the model’s vertical resolution in the PBL be required, even for regional and long-term studies, and ozone only being examined in an effort to judge the model’s performance be unreliable, and NOy be included for model evaluations.

A Lagrangian-Based Approach for Determining Trajectories Taxonomy and Turbulence Regimes

Abstract The use of the ratio between the acceleration and velocity time scales y = Ta/Tυ to separate Lagrangian trajectories in homogeneous classes is proposed. In fact, when analyzing subsurface floats data in the Atlantic Ocean and surface drifters data in the world’s ocean basins, it is observed that trajectories having different values of y are characterized by different shapes, correlation, and dispersal properties. In particular, trajectories having similar values of the acceleration and velocity time scales clearly show the influence of eddies and are characterized by an oscillating velocity correlation function. It is shown here that this trajectory screening is a useful procedure to rationalize the analysis of real Lagrangian trajectories and to avoid a mixture of different regimes, when averaging quantities. The mean statistical quantities computed averaging on quasi-homogeneous datasets put in evidence the role of the coherent structures in the dispersion properties, both in time and in the main oceanic current systems. These results are discussed in the context of the parameterization of eddy diffusivity in general circulation models.

Optimal estimation of catch by the continuous underway fish egg sampler based on a model of the vertical distribution of American plaice (Hippoglossoides platessoides) eggs

Abstract Pepin, P., Curtis, K.A., Snelgrove, P.V.R., de Young, B., and Helbig, J.A. 2007. Optimal estimation of catch by the continous underway fish egg sampler based on a model of the vertical distribution of American plaice (Hippoglossoides platessoides) eggs – ICES Journal of Marine Science, 64, 18–30. We investigate how the vertical stratification of the water column (specifically density) affects predictions of the catch of American plaice eggs (Hipploglossoides platessoides) from a fixed-depth sampler [the continuous underway fish egg sampler (CUFES)] relative to the integrated abundance in the water column measured in bongo tows. A steady-state model of the vertical distribution of fish eggs coupled with a simple model of the vertical profile of eddy diffusivity (i.e. mixing) is applied. Key model parameters are estimated through optimization of a one-to-one relationship between predicted and observed catches fit, using a generalized linear model with a Poisson, negative binomial, or gamma error structure. The incorporation of data on the vertical structure of the water column significantly improved the ability to forecast CUFES catches when using Poisson or negative binomial error structure, but not using a gamma distribution. Optimal maximum likelihood parameter estimates for eddy diffusivity and egg buoyancy fell within the range of expected values. The degree of uncertainty in the parameterization of eddy diffusivity suggests, however, that greater understanding of the forces that determine the vertical profile of mixing is critical to achieving strong predictive capabilities. The inverse problem of predicting integrated abundance from CUFES catches did not benefit from the environmental-driven model because of the high uncertainty in the catches from the CUFES.

A Simple Mixing Length Formulation for the Eddy-Diffusivity Parameterization of Dry Convection

In this paper a simple mixing length formulation for the eddy-diffusivityparameterization of dry convection is suggested. The new formulation relates the mixinglength to the square root of the turbulent kinetic energy (e) and a time scale (τ ):l = τ √e. To close the parameterization the time scale is calculated as a functionof the boundary-layer height (h) and the convective velocity scale (w*), τ ∝ h/w*. Thesimpler approach of a constant time scale is also studied. The simulation of a case of dry atmosphericconvection with a one-dimensional boundary-layer model shows that the model with the new formulationreproduces quite well the main properties of the convective boundary layer. In particular,the entrainment is realistically represented by the new mixing length, which has the advantage of naturallydecreasing with the turbulent kinetic energy. Sensitivity studies to the surface flux and the lapserate, in the context of a simplified situation, show the robustness of the new formulation.

Large-eddy-simulation closures of passive scalar turbulence: a systematic approach

The issue of the parameterization of small scale (``subgrid'') turbulence is addressed in the context of passive scalar transport. We focus on the Kraichnan advection model which lends itself to the analytical investigation of the closure problem. We derive systematically the dynamical equations which rule the evolution of the coarse-grained scalar field. At the lowest-order approximation in $l/r$, $l$ being the characteristic scale of the filter defining the coarse-grained scalar field and $r$ the inertial range separation, we recover the classical eddy-diffusivity parameterization of small scales. At the next-leading order a dynamical closure is obtained. The latter outperforms the classical model and is therefore a natural candidate for subgrid modelling of scalar transport in generic turbulent flows.

The effects of closure-based eddy diffusion on the climate and spectra of a GCM

A recently developed horizontal eddy diffusion parameterization based on closure theory has been implemented in the CSIRO atmospheric global climate model (GCM). Detailed studies of the effects of the parameterization on the simulated atmospheric circulation, transient kinetic energy and kinetic energy spectra have been carried out for different months throughout the year. These diagnostics have been compared with corresponding results from observations and from control simulations using an ad hoc diffusion parameterization also employed in earlier works with this model. The new diffusion parameterization has improved the simulated atmospheric circulation in the following ways. Zonal and total wavenumber spectra now have approximate -3 power laws for ranges of intermediate wavenumbers, as in the observations, while the control simulation spectra are considerably flatter. Peak values of transient kinetic energy near the tropospheric jet cores are considerably larger than in the control and in better agreement with observations, particularly in boreal winter. The strength and location of the tropospheric jets are also improved with the new diffusion parameterization, with monthly averaged zonal mean winds in the Northern Hemisphere and Southern Hemisphere jet cores stronger than for the control by as much as 5 m s-1 in boreal winter and spring. The GCM simulations are also stable with longer timesteps with the new eddy diffusion parameterization. It is suggested that further improvements in GCM simulations may be achievable through parameterizations of the nondiagonal elements of the covariance matrix of eddy fluxes such as the eddy-topographic force.

The effects of closure-based eddy diffusion on the climate and spectra of a GCM

A recently developed horizontal eddy diffusion parameterization based on closure theory has been implemented in the CSIRO atmospheric global climate model (GCM). Detailed studies of the effects of the parameterization on the simulated atmospheric circulation, transient kinetic energy and kinetic energy spectra have been carried out for different months throughout the year. These diagnostics have been compared with corresponding results from observations and from control simulations using an ad hoc diffusion parameterization also employed in earlier works with this model. The new diffusion parameterization has improved the simulated atmospheric circulation in the following ways. Zonal and total wavenumber spectra now have approximate −3 power laws for ranges of intermediate wavenumbers, as in the observations, while the control simulation spectra are considerably flatter. Peak values of transient kinetic energy near the tropospheric jet cores are considerably larger than in the control and in better agreement with observations, particularly in boreal winter. The strength and location of the tropospheric jets are also improved with the new diffusion parameterization, with monthly averaged zonal mean winds in the Northern Hemisphere and Southern Hemisphere jet cores stronger than for the control by as much as 5 m s−1 in boreal winter and spring. The GCM simulations are also stable with longer timesteps with the new eddy diffusion parameterization. It is suggested that further improvements in GCM simulations may be achievable through parameterizations of the nondiagonal elements of the covariance matrix of eddy fluxes such as the eddy-topographic force. DOI: 10.1034/j.1600-0870.2003.201329.x

Diffusion from a line source deployed in a homogeneous roughness layer: interpretation of wind-tunnel measurements by means of simple mathematical models

In wind-tunnel studies of atmospheric dispersion, the pollutant emission by traffic is usually considered as ground-level line source. The source performance under different flow conditions is therefore important for the adequate description of pollutant dispersion. The dispersion from a line source in the wind-tunnel model of the atmospheric boundary layer has been investigated in the present study. Specially conducted mean flow and turbulence measurements have proved the similarity between the wind-tunnel flow and the flow in the lower portion of the atmospheric boundary layer. Lateral and vertical distributions of mean concentration downwind of the source have been measured with varying source parameters and wind velocities. The concentration pattern has not revealed a significant dependence on the parameter variations. The wind-tunnel results have been further evaluated by means of analytical and numerical dispersion models. The evaluation has shown a good general agreement of measured and calculated concentration fields. Two alternative sets of equations with different parameterizations of eddy diffusivity and different values of the turbulent Schmidt number have been employed in the analytical model calculations. A better agreement with the wind-tunnel results has been achieved with a similarity-theory expression for eddy diffusivity rather than with the eddy diffusivity parameterization based on the conjugate-power-law formula. The numerical model has provided the best match for the wind-tunnel concentration data at large distances from the source. However, certain discrepancies between the wind-tunnel and numerical predictions have been marked out close to the source.

Simulating vertical mixing in a shelf-break region: addition of a shear instability model, accounting for the overall effect of internal tides, on top of a one-dimensional turbulence closure mixed layer model

A simple parameterization of eddy diffusivity is used to simulate the shear mixing from tidally induced internal waves generated in the continental slope region southwest of Brittany. Near the edge of the shelf, the seasonal thermocline oscillates under the forcing of the barotropic tide which propagates over the shelf break. A composite model is constructed to simulate the mixing of the upper ocean from both external (wind stress) and internal (internal waves) sources. A simple one-dimensional eddy kinetic energy model, which predicts the temperature profile from heat flux and wind stress inputs, is validated with respect to regional hydroelimatic conditions, then coupled with a two-layer model of non-linear internal waves, to simulate the mixing encountered in shelf break fronts submitted to tidal forcing. Numerical runs on a transect perpendicular to the shelf break show the formation of a spot of cool water over the edge of the continental margin. The one-dimensional eddy kinetic energy model has been validated over a decade with temperature profiles over the abyssal plain adjacent to the continental slope. An annual validation experiment has also been conducted for the combined models, beginning on 1st January 1985, as well as a short-term validation experiment, using a set of high-frequency temperature measurements at two stations near the shelf edge in September and early October 1985. The simulation has also been spatially validated against three sets of infrared satellite images. The one-dimensional model is calibrated for the minimum turbulent kinetic energy, whereas the best fit to the high-frequency measurements in autumn 1985 above the slope provides the optimum values for the initial thermal content and for the parameterization constant of internal wave diffusivity. The combined model reproduces successfully the seasonal and the high-frequency (neap-spring tidal cycle) variation of the temperature field in the upper ocean along a transect perpendicular to the shelf break. Horizontal advection and mesoscale turbulence somewhat limit the performance of the model at low-amplitude tides and over the shallower part of the shelf, but the satisfactory overall agreement between the results and the measurements is consistent with the formation of a shelf break front in the northern Bay of Biscay and southern Celtic Sea, mainly as a result of mixing enhanced by tidally induced internal waves.