Meelis J. Zidikheri

Stochastic Subgrid Parameterizations for Simulations of Atmospheric Baroclinic Flows

Abstract A stochastic subgrid modeling method is used to parameterize horizontal and vertical subgrid-scale transfers in large-eddy simulations (LESs) of baroclinic flows with large-scale jets and energy spectra typical of the atmosphere. The approach represents the subgrid-scale eddies for LES (at resolutions of T63 and T31) by a stochastic model that takes into account the memory effects of turbulent eddies. The statistics of the model are determined from a higher-resolution (T126) direct numerical simulation (DNS). The simulations use a quasigeostrophic two-level model and the subgrid terms are inhomogeneous in the vertical and anisotropic in the horizontal and are represented by 2 × 2 matrices at each wavenumber. The parameterizations have the largest magnitudes at a cusp near the largest total wavenumbers of the truncations. At T63 the off-diagonal elements of the matrices are negligible (corresponding to effectively decoupled levels) and the diagonal elements are almost isotropic. At the lower resol...

Subgrid Model with Scaling Laws for Atmospheric Simulations

AbstractSubgrid-scale parameterizations with self-similar scaling laws are developed for large-eddy simulations (LESs) of atmospheric flows. The key new contribution is the development of scaling laws that govern how these parameterizations depend on the LES resolution and flow strength. Both stochastic and deterministic representations of the effects of subgrid-scale eddies on the retained scales are considered. The stochastic subgrid model consists of a backscatter noise term and a drain eddy viscosity, while in the deterministic subgrid model the net effect of these two terms is represented by a net eddy viscosity. In both cases the subgrid transfers are calculated self-consistently from the statistics of higher-resolution-reference direct numerical simulations (DNSs). The dependence of the subgrid parameterizations on the resolution of the LESs is determined for DNSs having resolutions up to triangular 504 wavenumber truncations. The subgrid parameterizations are developed for typical large-scale atmo...

Stochastic subgrid-scale modelling for non-equilibrium geophysical flows

Methods motivated by non-equilibrium statistical mechanics of turbulence are applied to solve an important practical problem in geophysical fluid dynamics, namely the parametrization of subgrid-scale eddies needed in large-eddy simulations (LESs). A direct stochastic modelling scheme that is closely related to techniques based on statistical closure theories, but which is more generally applicable to complex models, is employed. Here, we parametrize the effects of baroclinically unstable subgrid-scale eddies in idealized flows with broad similarities to the Antarctic Circumpolar Current of the Southern Ocean. The subgrid model represents the effects of the unresolved eddies through a generalized Langevin equation. The subgrid dissipation and stochastic forcing covariance matrices as well as the mean subgrid forcing required by the LES model are obtained from the statistics of a high resolution direct numerical simulation (DNS). We show that employing these parametrizations leads to LES in close agreement with DNS.

Stochastic modelling of unresolved eddy fluxes

A subgrid-scale parameterization scheme motivated by statistical closure theory, but employing statistics obtained from high-resolution direct numerical simulations, is applied to large eddy simulations of two-level quasigeostrophic turbulence on the sphere. It is shown that these parameterizations are consistent with the phenomenology of quasigeostrophic turbulence. The parameterizations consist of 2 × 2 dissipation and stochastic forcing covariance matrices at each wavenumber, with the off-diagonal elements of the matrices representing vertical mixing. Two flow regimes, characterized by their deformation scales, are considered, namely atmospheric and oceanic. In the former, the deformation scale is fully resolved, and the truncation scale is within the enstrophy cascading interial range. In the latter, the deformation scale is not fully resolved, and the truncation scale is within the energy cascading inertial range. It is demonstrated through numerical experiments that both stochastic and deterministic variants of the scheme give comparable results for the energy spectra in the atmospheric regime. In the oceanic regime, the stochastic variant again gives excellent results, but the deterministic variant is found to be numerically unstable.

Stochastic subgrid parameterizations for atmospheric and oceanic flows

In this paper, we review recently developed closure-based and stochastic model approaches to subgrid scale modelling of eddy interactions motivated by advances in non-equilibrium statistical dynamical closure theory. We demonstrate how statistical dynamical closure models can be used to self-consistently calculate eddy damping and stochastic backscatter parameters, required in large eddy simulations (LESs), from higher-resolution simulations. A direct stochastic modelling scheme that is more generally applicable to complex models is then described and applied to LESs of quasigeostrophic turbulence of the atmosphere and oceans. We discuss the fundamental difference between atmospheric and oceanic LESs which is related to the difference in the deformation scales in the two classes of flows. We point out why the stochastic approach may be crucial when baroclinic instability is inadequately resolved. Finally, we discuss the application of inhomogeneous closure theory to the complex problem of flow over topography, and show that it can be used to understand the successes and limitations of currently used heuristic schemes and to provide a basis for further developments in the future.

Subgrid modelling for geophysical flows

Recently developed closure-based and stochastic model approaches to subgrid-scale modelling of eddy interactions are reviewed. It is shown how statistical dynamical closure models can be used to self-consistently calculate the eddy damping and stochastic backscatter parameters, required in large eddy simulations (LESs), from higher resolution simulations. A closely related direct stochastic modelling scheme that is more generally applicable to complex models is then described and applied to LESs of quasi-geostrophic turbulence of the atmosphere and oceans. The fundamental differences between atmospheric and oceanic LESs, which are related to the difference in the deformation scales in the two classes of flows, are discussed. It is noted that a stochastic approach may be crucial when baroclinic instability is inadequately resolved. Finally, inhomogeneous closure theory is applied to the complex problem of flow over topography; it is shown that it can be used to understand the successes and limitations of currently used heuristic schemes and to provide a basis for further developments in the future.

A simple inversion method for determining optimal dispersion model parameters from satellite detections of volcanic sulfur dioxide

A simple inversion scheme for optimizing volcanic emission dispersion model parameters with respect to satellite detections is presented in this paper. In this scheme, multiple dispersion model simulations, obtained by varying relevant model parameters, are created and compared against satellite detections using pattern correlation as a measure of model agreement with observations. It is shown that the scheme is successful in inferring emission source parameters such as those describing the vertical extent of the nascent sulfur dioxide emissions in the November 2010 Mount Merapi eruption in Java, Indonesia. These optimal parameter values then become a basis for improved forecasts of the transport of volcanic emissions.

Scaling laws for parametrizations of subgrid interactions in simulations of oceanic circulations

Parametrizations of the subgrid eddy–eddy and eddy–meanfield interactions are developed for the simulation of baroclinic ocean circulations representative of an idealized Antarctic Circumpolar Current. Benchmark simulations are generated using a spectral spherical harmonic quasi-geostrophic model with maximum truncation wavenumber of T=504, which is equivalent to a resolution of 0.24° globally. A stochastic parametrization is used for the eddy–eddy interactions, and a linear deterministic parametrization for the eddy–meanfield interactions. The parametrization coefficients are determined from the statistics of benchmark simulations truncated back to the large eddy simulation (LES) truncation wavenumber, TR<T. A stochastic technique is used to determine the eddy–eddy coefficients, and a new least-squares regression method for the eddy–meanfield terms. Truncations are repeated for various TR, and the resolution dependence of the subgrid coefficients is identified. The mean jet structure and the kinetic and potential energy spectra resulting from the LESs closely agree with those from the benchmark simulations.

Estimation of optimal dispersion model source parameters using satellite detections of volcanic ash

In this paper we demonstrate how parameters describing the geometry of the volcanic ash source for a particular volcanic ash dispersion model (HYSPLIT) may be inferred by the use of satellite data and multiple trial simulations. The areas of space likely to be contaminated by ash are identified with the aid of various remote sensing techniques and polygons are drawn around these areas as they would be in an operational setting. Dispersion model simulations are initialized either by a cylindrical source or a specified ash distribution depending on the context. Parameters of interest such as the base and top height, diameter, and optimal release time of the cylindrical source or the height of the specified ash distribution are inferred by forming a parameter grid and running multiple simulations for each parameter grid-point value. Optimal values of the parameter values are identified by calculating spatial correlations between the model simulations and observations. We demonstrate that the methodology can be used to correctly infer various model parameters and improves volcanic ash forecasts in various eruption case studies.

Toward quantitative forecasts of volcanic ash dispersal: Using satellite retrievals for optimal estimation of source terms

The provision of reliable quantitative forecasts for volcanic ash, such as ash mass load fields, is challenging because ash emission characteristics at the volcanic source are poorly understood. In this paper we show how satellite retrievals of volcanic ash mass load may be used to estimate source terms for dispersion models. The source terms comprise the spatial, temporal, and particle size distribution of mass flux at the ash source. We approach the problem by specifying general functional forms for these quantities that are dependent on a limited number of parameters. Numerous trial dispersion model simulations are then run, each corresponding to a particular configuration of possible source term parameters, with the resulting simulated mass load matched against the satellite retrieved mass load. The parameter values leading to best matches between simulations and satellite retrievals are then used to provide optimal forecasts of volcanic ash mass load distribution. We use several case studies to demonstrate the efficacy of this approach in improving forecasts of ash mass load with the HYSPLIT dispersion model.