Parameterization Of Subgrid-scale Processes Research Articles

Frame invariant neural network closures for Kraichnan turbulence

Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models for subgrid scale (SGS) processes using physical insights and mathematical approximations, they remain imperfect and can lead to inaccurate predictions. In recent years, machine learning has been successful in extracting complex patterns from high-resolution spatio-temporal data, leading to improved parameterization models, and ultimately better coarse grid prediction. However, the inability to satisfy known physics and poor generalization hinders the application of these models for real-world problems. In this work, we put forth a frame invariant closure approach to improve the accuracy and generalizability of deep learning-based subgrid scale closure models by embedding physical symmetries directly into the structure of the neural network. Specifically, we utilized specialized layers within the convolutional neural network in such a way that desired constraints are theoretically guaranteed without the need for any regularization terms. We demonstrate our framework for a two-dimensional decaying turbulence test case mostly characterized by the forward enstrophy cascade. We show that our frame invariant SGS model (i) accurately predicts the subgrid scale source term, (ii) respects the physical symmetries such as translation, Galilean, and rotation invariance, and (iii) is numerically stable when implemented in coarse-grid simulation with generalization to different initial conditions and Reynolds number. This work opens up a possibility of connecting physics-based theories and data-driven modeling paradigms, and thus represents a promising step towards the development of physically consistent data-driven turbulence closure models.

Развитие системы долгосрочного прогноза Гидрометцентра России в 2020 году

A brief description is given for the works carried out in 2020 to implement the longrange forecast technology based on the SLAV072L96 multiscale hydrodynamic atmosphere model. The purpose of these works was an improvement in simulating the deep convection and stratosphere dynamics. The works comprised the improvement and verification of the parameterizations for subgrid-scale processes and the whole model using long-range forecasts computed from historical initial data. As a result, the model correctly reproduces the main features of the annual mean precipitation field and zonal mean wind in the stratosphere. Keywords: long-range forecasts, global atmosphere model, parameterizations of subgrid-scale processes

ANALYSIS OF PROBLEMS OF DESCRIPTION AND MODELING THE CLIMATIC SCENARIOS OF THE EARTH

The global climate is a complex system where the gradual accumulation of quantitative changes can lead to an unexpected qualitative leap with unpredictable consequences of processes throughout the climate and ecological system. To date, the best studied and described aero- and hydrodynamic processes generated by solar radiation of the Earth. In fact, we are talking about the work of a giant heat engine, which gives motion to huge masses of air and water due to uneven heating of the Earth's surface. On the one hand, the Earth sciences have already developed a fairly complete picture of the main factors that dictate changes in the Earth's climate. These representations are based on both observable data and theoretical models. On the other hand, the characteristics of individual connections in nature are quantitative, and even the very existence of some connections is not yet sufficiently defined to reliably predict climate change. The reason for the uncertainty is both the lack of observational data and the high degree of self-regulation in the natural system of the Earth. Further development of climate models and methods of weather forecasting is associated with increased spatial resolution and improved physical parameterizations of subgrid scale processes. Level of spatial resolution and largely limited by the complexity of the physical parameterizations performance the most powerful computing systems (supercomputers). Problems of reproduction and prediction of climate change, in contrast to the classical problems of physics, have their own feature: they do not allow direct physical experiment. Moreover, due to the specific characteristics of the climate system (for example, the atmosphere and the ocean are thin films), laboratory experiments are also quite problematic. For a detailed study of the real climate system, there is only a limited set of parameters of the trajectory of the system in the length of several decades, during which fairly complete field measurements were performed. Global climate change is very complex, so modern science can not give an unambiguous answer as to what awaits us in the near future. There are many scenarios for the situation, but here are some of the most important ones. Processing the results of numerical experiments to create a model of modern climate in international programs showed that the main characteristics obtained using different models and then averaged over the whole set of models are closer to the observer actually than the characteristics obtained using individual, even better models. Key words : modeling, climatic system, physical parameters, forecasting.

Energy budget-based backscatter in a shallow water model of a double gyre basin

The parameterization of sub-grid scale processes is one of the key challenges towards improved numerical simulations of the atmospheric and oceanic circulation. Numerical weather prediction models as well as climate models would benefit from more sophisticated turbulence closures that allow for less spurious dissipation at the grid-scale and consequently higher and more realistic levels of eddy kinetic energy (EKE). Recent studies propose to use a hyperviscous closure in combination with an additional deterministic forcing term as a negative viscosity to represent backscatter of energy from unresolved scales. The sub-grid EKE is introduced as an additional prognostic variable that is fed by dissipation at the grid scale, and enables recycling of EKE via the backscatter term at larger scales. This parameterization was previously shown to work well in zonally re-entrant channel configurations. Here, a generalization in the form of a Rossby number-dependent scaling for the strength of the backscatter is introduced to represent the emergence of a forward energy-cascade in unbalanced flows near the boundaries. We apply the parameterization to a shallow water model of a double gyre basin and provide evidence for its general applicability. In terms of mean state and variability, a low resolution model is considerably improved towards a high resolution control run at low additional computational cost.

A coupled model of interior balanced and boundary flow

Ocean circulation modeling requires parameterizations of sub-grid scale processes, which in turn involves two separate issues. First, the parameterization should mirror the effect of important sub-grid dynamics and second, constants and boundary conditions as required by the parameterization must be determined. In modern ocean circulation modeling, many parameterizations take the form of viscous operators with poorly known coefficients, and the boundary conditions options are free-slip, partial-slip or no-slip, suitably adjusted for the order of the operator. The extent to which viscous operators are dynamically apt is unclear and there is virtually no dynamical guidance on how to choose between the boundary conditions. Often the decision about the suitability of the parameterizations and the boundary conditions is made based on qualitative characteristics of the solution, which is somewhat subjective. Here, a dynamical boundary layer model is developed that explicitly determines the boundary potential vorticity fluxes resulting from the sub-grid scale interactions of the resolved flow with the boundaries. When applied to a quasi-geostrophic model, comparisons of model evolution with high resolution primitive equation simulations are favorable. The recipe outlined here, while far from a complete parameterization of boundary dynamics, represents a step toward resolving the issues currently surrounding sub-grid scale parameterization. The results also argue that boundary dynamics naturally dissipate balanced energy and are likely to represent a principal means by which the oceanic mesoscale energy budget is balanced.

Temperature Extremes in the Community Atmosphere Model with Stochastic Parameterizations*

AbstractThis paper evaluates the performance of the NCAR Community Atmosphere Model, version 4 (CAM4), in simulating observed annual extremes of near-surface temperature and provides the first assessment of the impact of stochastic parameterizations of subgrid-scale processes on such performance. Two stochastic parameterizations are examined: the stochastic kinetic energy backscatter scheme and the stochastically perturbed parameterization tendency scheme. Temperature extremes are described in terms of 20-yr return levels and compared to those estimated from ERA-Interim and the Hadley Centre Global Climate Extremes Index 2 (HadEX2) observational dataset. CAM4 overestimates warm and cold extremes over land regions, particularly over the Northern Hemisphere, when compared against reanalysis. Similar spatial patterns, though less spatially coherent, emerge relative to HadEX2. The addition of a stochastic parameterization generally produces a warming of both warm and cold extremes relative to the unperturbed configuration; however, neither of the proposed parameterizations meaningfully reduces the biases in the simulated temperature extremes of CAM4. Adjusting warm and cold extremes by mean conditions in the respective annual extremes leads to good agreement between the models and reanalysis; however, adjusting for the bias in mean temperature does not help to reduce the observed discrepancies. Based on the behavior of the annual extremes, this study concludes that the distribution of temperature in CAM4 exhibits too much variability relative to that of reanalysis, while the stochastic parameterizations introduce a systematic bias in its mean rather than alter its variability.

The Potential for Mesoscale Visibility Predictions with a Multimodel Ensemble

Abstract This work examines the viability of producing short-range (<20 h) probabilistic fog predictions in remote locations, absent an observational history, using an uncalibrated 4-km, 10-member Weather Research and Forecasting Model (WRF) ensemble configured to closely match the Air Force Weather Agency Mesoscale Ensemble Forecast Suite. Three distinct sources of error in the final predictions are considered separately to facilitate a better understanding of the total error and appropriate mitigation strategies. These include initial condition error, parameterization of subgrid-scale processes, and error in the visibility parameterization used to convert NWP model output variables to visibility. The raw WRF predictions are generally not skillful in valley and coastal regions, where they produce a shortage of light fog predictions with visibilities of 1–7 mi (1.6–11.3 km) in favor of excessive forecasts of zero cloud water, corresponding to no fog. Initial condition error and visibility parameterization error are shown to play a relatively minor role compared to error in the parameterization of subgrid-scale processes. This deficiency is caused by a negative relative humidity bias, which results from a warm overnight bias. A second-order source of error arises from an inconsistent delineation of fog and haze in the NWP model compared to the verifying observations. Results show that under most conditions it is necessary to deviate from the perfect-prog assumption, and to introduce some method of statistical postprocessing to obtain skillful visibility predictions from the ensemble.

On closure parameter estimation in chaotic systems

Abstract. Many dynamical models, such as numerical weather prediction and climate models, contain so called closure parameters. These parameters usually appear in physical parameterizations of sub-grid scale processes, and they act as "tuning handles" of the models. Currently, the values of these parameters are specified mostly manually, but the increasing complexity of the models calls for more algorithmic ways to perform the tuning. Traditionally, parameters of dynamical systems are estimated by directly comparing the model simulations to observed data using, for instance, a least squares approach. However, if the models are chaotic, the classical approach can be ineffective, since small errors in the initial conditions can lead to large, unpredictable deviations from the observations. In this paper, we study numerical methods available for estimating closure parameters in chaotic models. We discuss three techniques: off-line likelihood calculations using filtering methods, the state augmentation method, and the approach that utilizes summary statistics from long model simulations. The properties of the methods are studied using a modified version of the Lorenz 95 system, where the effect of fast variables are described using a simple parameterization.

A Theoretical Framework for Energy and Momentum Consistency in Subgrid-Scale Parameterization for Climate Models

Abstract A theoretical framework for the joint conservation of energy and momentum in the parameterization of subgrid-scale processes in climate models is presented. The framework couples a hydrostatic resolved (planetary scale) flow to a nonhydrostatic subgrid-scale (mesoscale) flow. The temporal and horizontal spatial scale separation between the planetary scale and mesoscale is imposed using multiple-scale asymptotics. Energy and momentum are exchanged through subgrid-scale flux convergences of heat, pressure, and momentum. The generation and dissipation of subgrid-scale energy and momentum is understood using wave-activity conservation laws that are derived by exploiting the (mesoscale) temporal and horizontal spatial homogeneities in the planetary-scale flow. The relations between these conservation laws and the planetary-scale dynamics represent generalized nonacceleration theorems. A derived relationship between the wave-activity fluxes—which represents a generalization of the second Eliassen–Palm theorem—is key to ensuring consistency between energy and momentum conservation. The framework includes a consistent formulation of heating and entropy production due to kinetic energy dissipation.

Ocean circulation and sea ice distribution in a finite element global sea ice–ocean model

A newly developed global Finite Element Sea Ice–Ocean Model (FESOM) is presented. The ocean component is based on the Finite Element model of the North Atlantic (FENA) but has been substantially updated and extended. In addition to a faster realization of the numerical code, state-of-the-art parameterizations of subgrid-scale processes have been implemented. A Redi/GM scheme is employed to parameterize the effects of mesoscale eddies on lateral tracer distribution. Vertical mixing and convection are parameterized as a function of the Richardson number and the Monin–Obukhov length. A finite element dynamic-thermodynamic sea ice–model has been developed and coupled to the ocean component. Sea ice thermodynamics have been derived from the standard AWI sea ice model featuring a prognostic snow layer but neglecting internal heat storage. The dynamic part offers the viscous-plastic and elastic-viscous-plastic rheologies. All model components are discretized on a triangular/tetrahedral grid with a continuous, conforming representation of model variables. The coupled model is run in a global configuration and forced with NCEP daily atmospheric reanalysis data for 1948–2007. Results are analysed with a slight focus on the Southern Hemisphere. Many aspects of sea ice distribution and hydrography are found to be in good agreement with observations. As in most coarse-scale models, Gulf Stream transport is underestimated, but transports of the Kuroshio and the Antarctic Circumpolar Current appear realistic. The seasonal cycles of Arctic and Antarctic sea ice extents and Antarctic sea ice thickness are well captured; long- and short-term variability of ice coverage is found to be reproduced realistically in both hemispheres. The coupled model is now ready to be used in a wide range of applications.

Multi-scale modeling: nested-grid and unstructured-mesh approaches

In 1969, the Journal of Computational Physics published a seminal article by K. Bryan presenting the first ocean general circulation model. Since then, many numerical studies of the World Ocean, as well as regional or coastal flows, used models directly or indirectly inspired by the work of Bryan and his colleagues. A number of these models have evolved into highly modular and versatile computational systems, including multiple physical modules and options as well as varied biogeochemical, ecosystem and acoustics modeling capabilities. Several modeling systems are now well-documented tools, which are widely used in research institutions and various organizations around the world. The list of such modeling systems is large and too long to be summarized in this editorial. Over the last three decades, significant progress has been made in the parameterization of subgrid-scale processes, in data assimilation methodologies and in boundary condition schemes, as well as in the efficient implementation of algorithms on fast vector and subsequently parallel computers, allowing higher and higher resolution in space and time. However, many of today’s popular modeling systems can still be regarded as members of the first generation of ocean models: at their core, rather similar geophysical fluid dynamics equations are solved numerically using a conservative finite-difference method on a structured grid. Today, several aspects of structured-grid models could benefit from significant upgrades, learning from major advances in computational fluid dynamics. In particular, the use of a structured grid limits the flexibility in the spatial resolution and does not allow one to take full advantage of numerical algorithms such as finite volumes and finite elements, which can achieve their best performance when implemented on unstructured meshes. Even though many of today’s complex marine modeling and data assimilation systems have evolved significantly since Bryan’s prototype, it would be challenging to modify them step-by-step from a structured-grid approach to an unstructured-grid one. Therefore, novel marine model design research is underway, paving the way for the second generation of ocean modeling systems. It is difficult to predict today if this new generation of ocean models will achieve its chief objective: widening the range of resolved scales of motion with increased efficiencies and accuracies, possibly allowing multi-resolution, multi-scale, and multidynamics numerical simulations of marine flows, all occurring seamlessly within distributed computing environments. In fact, hybrid approaches merging the advantages of structured and unstructured-grid modeling may be the way forward. Whether or not unstructured mesh approaches will prevail is all the more difficult to predict now that structured mesh modelers have developed powerful solutions for increasing the resolution when and where needed. For instance, grid embedding is still a popular and useful method for enhancing model resolution. It can involve multiply nested domains and allows the relatively Ocean Dynamics (2008) 58:335–336 DOI 10.1007/s10236-008-0170-5

Air‐sea interaction: Connecting the ocean and atmosphere

The large‐scale dynamics of the ocean and the atmosphere are closely related. Energy is transferred from the atmosphere to the ocean surface mixed layer driving the circulation of the upper ocean. In turn, energy from the ocean is fed back to the atmosphere affecting the atmospheric circulation, the weather and the climate. The concept is deceptively simple, but as we explore the coupled earth system, we are frequently limited by our lack of understanding of the interchanges between the atmosphere and ocean. As Brown [1990] pointed out, there are two gaps in our knowledge of the air‐sea interface: the theory is inadequate and the data are sparse. More specifically, Kraus and Businger [1994] highlighted several areas that continue to require more attention, the interaction of the wind and surface waves, for example, the parameterization of subgrid scale processes in large‐scale circulation models, and the transfer of gases across the air‐sea interface, among others.

Sub-grid representation of emission source clusters in regional air quality modeling

A key aspect in modeling the fate of pollutants released into the atmosphere is the parameterization of sub-grid scale processes so as to quantify their effect on resolvable scale features. Averaging emissions of species over grid squares characteristic of present-day regional and global models generally results in underpredicting concentrations of these species. This also causes inaccurate predictions for secondary pollutant species derived through complex chemical mechanisms. An algorithm is developed to provide improved sub-grid representation of emissions. A two-dimensional finite element technique is used to discretize the horizontal domain. The three-dimensional transport equation is time-split into this two-dimensional component and a one-dimensional vertical component to represent the transport processes. Compared to the locally one-dimensional finite element method (LOD-FEM), this technique allows use of variable grid sizes in the discretization of the horizontal domain, thus providing for local mesh refinement and consequently improved sub-grid representation in the numerical solution. The advantages of the scheme are inherent: the computational burden in terms of storage requirements is not increased, and the need for developing the troublesome interface boundary condition of a nested-grid procedure is avoided. A simplified first-order chemistry module has been incorporated to test the scheme for both primary and secondary pollutant species. Several test cases are presented to verify the efficacy of the proposed algorithm. Results from test cases for a simplified scenario indicate that the procedure enables one to simulate a more realistic range of concentrations for both the reactant and product species. Furthermore, comparison with the analytical solutions indicates that the numerical scheme is capable of reproducing the analytical solution, both qualitatively as well as quantitatively, in a superior manner compared to a uniform mesh.

A note on subgrid-scale processes in photochemical modelling

The effects of including a parameterization of subgrid-scale dispersion and chemical processes in the Eulerian-Lagrangian transport model of Hess are investigated. A case chosen to maximize the subgrid-scale effects is studied, and it is found that the predicted change in maximum O 3 when subgrid-scale processes are included is small (∼5%) compared with predictions based on direct injection of point emissions. It is also found for this model that the parameterization of subgrid-scale processes is not necessary to provide numerical stability in calculating the chemical kinetics.

The use of general circulation models in the analysis of the ecosystem impacts of climatic change

The use of general circulation models in the estimation of the impact of climatic change on the global ecosystem is seen to depend primarily on their ability to reliably depict the seasonal and geographical distribution of the changes in surface climate variables. While present GCMs generally simulate the observed distribution of surface air temperature reasonably well, they show significantly different changes in the equilibrium temperature as a result of doubled CO2, for example. These disagreements are attributed to differences in the model's resolution and parameterization of subgrid-scale processes. Such model-dependent errors notwithstanding, much more information of possible use in impact analysis can be extracted from general circulation model simulations than has generally been done so far. The completeness, consistency and experimental possibilities offered by simulated data sets permit the systematic extraction of a wide variety of statistics important to the surface ecosystem, such as the length of the growing season, the duration of rainless periods, and the surface moisture stress. Assuming further model improvements, the elements of a model-assisted methodology for climate impact analysis are seen to be: (1) the determination of the seasonal and geographical distribution of that portion of simulated climatic changes which are both statistically and physically significant; (2) the transformation of the (significant) large-scale climatic changes onto the local scale of impact (the climate ‘inversion’ problem); and (3) the design of specific statistical parameters or functions relevant to local ecosystem impacts.

Methode de representation de la turbulence associee aux precipitations dans un modele tri-dimensionnel de convection nuageuse

A method is presented for the parameterization of subgrid-scale processes in the framework of a three-dimensional micro-scale model which simulates the initiation of precipitation in the planetary boundary layer. The method uses truncated second-order moment equations which involve combinations of dynamical, thermodynamical and water variables; the water variables include water vapor, cloud droplets and rain water, with the hypothesis of a Marshall-Palmer raindrop distribution. The method is applied to the case of a trade-wind cumulus layer where water vapor content is artificially increased. As some approximations concerning the water variables are not easy to verify by experimental methods, results should be considered only as indicative; they show the extent to which a more complete parameterization of subgrid-scale processes may compensate for the inevitable lack of spatial resolution in an atmospheric boundary-layer model.