Journal articles on the topic 'Subgrid'
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NESLITURK, ALI I. "A STABILIZING SUBGRID FOR CONVECTION–DIFFUSION PROBLEM." Mathematical Models and Methods in Applied Sciences 16, no. 02 (February 2006): 211–31. http://dx.doi.org/10.1142/s0218202506001121.
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A stabilizing subgrid which consists of a single additional node in each triangular element is analyzed by solving the convection–diffusion problem, especially in the case of small diffusion. The choice of the location of the subgrid node is based on minimizing the residual of a local problem inside each element. We study convergence properties of the method under consideration and its connection with previously suggested stabilizing subgrids. We prove that the standard Galerkin finite element solution on augmented grid produces a discrete solution that satisfy the same a priori error estimates that are typically obtained with SUPG and RFB methods. Some numerical experiments that confirm the theoretical findings are also presented.
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Yeh, Pat J.-F., and Elfatih A. B. Eltahir. "Representation of Water Table Dynamics in a Land Surface Scheme. Part II: Subgrid Variability." Journal of Climate 18, no. 12 (June 15, 2005): 1881–901. http://dx.doi.org/10.1175/jcli3331.1.
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Abstract A lumped unconfined aquifer model has been developed and interactively coupled to a land surface scheme in a companion paper. Here, the issue of the representation of subgrid variability of water table depths (WTDs) is addressed. A statistical–dynamical (SD) approach is used to account for the effects of the unresolved subgrid variability of WTD in the grid-scale groundwater runoff. The dynamic probability distribution function (PDF) of WTD is specified as a two-parameter gamma distribution based on observations. The grid-scale groundwater rating curve (i.e., aquifer storage–discharge relationship) is derived statistically by integrating a point groundwater runoff model with respect to the PDF of WTD. Next, a mosaic approach is utilized to account for the effects of subgrid variability of WTD in the grid-scale groundwater recharge. A grid cell is categorized into different subgrids based on the PDF of WTD. The grid-scale hydrologic fluxes are computed by averaging all of the subgrid fluxes weighted by their fractions. This new methodology combines the strengths of the SD approach and the mosaic approach. The results of model testing in Illinois from 1984 to 1994 indicate that the simulated hydrologic variables (soil saturation and WTD) and fluxes (evaporation, runoff, and groundwater recharge) agree well with the observations. Because of the paucity of the large-scale observations on WTD, the development of a practical parameter estimation procedure is indispensable before the global implementation of the developed scheme of water table dynamics in climate models.
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Habets, F., and G. M. Saulnier. "Subgrid runoff parameterization." Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere 26, no. 5-6 (January 2001): 455–59. http://dx.doi.org/10.1016/s1464-1909(01)00034-x.
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Valdettaro, L. "Subgrid-Scale modeling." EAS Publications Series 21 (2006): 197–218. http://dx.doi.org/10.1051/eas:2006114.
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Park, Noma, and Krishnan Mahesh. "A velocity-estimation subgrid model constrained by subgrid scale dissipation." Journal of Computational Physics 227, no. 8 (April 2008): 4190–206. http://dx.doi.org/10.1016/j.jcp.2007.12.020.
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Chen, Yaling, Luxi Hao, and Gaowen Yin. "Distributed Energy Management of the Hybrid AC/DC Microgrid with High Penetration of Distributed Energy Resources Based on ADMM." Complexity 2021 (September 14, 2021): 1–9. http://dx.doi.org/10.1155/2021/1863855.
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This paper aims to investigate energy management of the hybrid AC/DC microgrid with the high penetration of distributed energy resources (DERs), such as electrical vehicles, heat pumps, and photovoltaics. In the previous studies, energy management of the hybrid microgrid is usually carried out by the system operator in a centralized manner, which suffers from the compromise of privacy information protection and the risk of single-point failure. Therefore, this paper proposes a distributed energy management scheme of the hybrid microgrid using the projection function-based alternating direction method of multipliers (P-ADMM), which allows each subgrid, i.e., AC subgrid and DC subgrid, to make day-ahead schedules independently with information exchanges while obtaining the optimal energy management solution. The energy management problem of the hybrid microgrid is formulated as a mixed-integer quadratic programming (MIQP) model, considering DER and energy storage system operation constraints, system operation constraints, and converter operation constraints. Then, the MIQP model is decomposed and distributed into smaller-scale QP models between subgrids using the P-ADMM algorithm, which can handle binary variables through projection functions. The numerical results conducted on the hybrid microgrid demonstrate that the proposed distributed scheme can effectively achieve optimal energy management for the hybrid AC/DC microgrid in a distributed manner.
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Zhou, Ye. "Eddy damping, backscatter, and subgrid stresses in subgrid modeling of turbulence." Physical Review A 43, no. 12 (June 1, 1991): 7049–52. http://dx.doi.org/10.1103/physreva.43.7049.
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Brillant, Guillaume, Sabine Husson, and Françoise Bataille. "Subgrid-Scale Diffusivity: Wall Behavior and Dynamic Methods." Journal of Applied Mechanics 73, no. 3 (September 26, 2004): 360–67. http://dx.doi.org/10.1115/1.2173005.
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This study concerns the near-wall behavior of the subgrid-scale diffusivity. This is shown to depend on the thermal boundary conditions. Therefore, the constant subgrid-scale Prandtl number hypothesis is questionable and a direct modeling of the subgrid-scale diffusivity is considered instead. Large-eddy simulations are carried out using the Trio U code in a turbulent channel flow configuration with the three classical thermal boundary conditions (constant temperature, constant heat flux, and adiabatic wall). Different dynamic methods are used to model the subgrid-scale diffusivity and results are compared with constant subgrid-scale Prandtl number large-eddy simulations and with direct numerical simulations.
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Kitsios, Vassili, Jorgen S. Frederiksen, and Meelis J. Zidikheri. "Subgrid Model with Scaling Laws for Atmospheric Simulations." Journal of the Atmospheric Sciences 69, no. 4 (March 30, 2012): 1427–45. http://dx.doi.org/10.1175/jas-d-11-0163.1.
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Abstract Subgrid-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 atmospheric flows and for different strengths and spectra of kinetic energy within a quasigeostrophic spectral model. LESs using the stochastic and deterministic subgrid parameterizations are shown to replicate the kinetic energy spectra of the reference DNS at the scales of the LESs. It is found that the maximum strengths of the drain, net, and backscatter viscosities satisfy scaling laws dependent on the LES truncation wavenumber and that the dependence of these eddy viscosities on total wavenumber can also be written as essentially universal functions that depend on flow strength and resolution. The scaling laws make the subgrid-scale parameterizations more generally applicable in LESs and remove the need to generate them from reference DNSs.
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Verrelle, Antoine, Didier Ricard, and Christine Lac. "Evaluation and Improvement of Turbulence Parameterization inside Deep Convective Clouds at Kilometer-Scale Resolution." Monthly Weather Review 145, no. 10 (October 2017): 3947–67. http://dx.doi.org/10.1175/mwr-d-16-0404.1.
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A challenge for cloud-resolving models is to make subgrid schemes suitable for deep convective clouds. A benchmark large-eddy simulation (LES) was conducted on a deep convective cloud with 50-m grid spacing. The reference turbulence fields for horizontal grid spacings of 500 m, 1 km, and 2 km were deduced by coarse graining the 50-m LES outputs, allowing subgrid fields to be characterized. The highest values of reference subgrid turbulent kinetic energy (TKE) were localized in the updraft core, and the production of subgrid TKE was dominated by thermal effects at coarser resolution (2 and 1 km) and by dynamical effects at finer resolution than 500 m. Countergradient areas due to nonlocal mixing appeared on the subgrid vertical thermodynamical fluxes in the updraft core and near the cloud top. The subgrid dynamical variances were anisotropic but the difference between vertical and horizontal variances diminished with increasing resolution. Then offline and online evaluations were conducted for this deep convective case with two different parameterization approaches at kilometer-scale resolution and gave the same results. A commonly used eddy-diffusivity turbulence scheme underestimated the thermal production of subgrid TKE and did not enable the countergradient structures to be reproduced. In contrast, the approach proposed by Moeng, parameterizing the subgrid vertical thermodynamical fluxes in terms of horizontal gradients of resolved variables, reproduced these characteristics and limited the overestimation of vertical velocity.
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Meneveau, Charles. "Turbulence: Subgrid-Scale Modeling." Scholarpedia 5, no. 1 (2010): 9489. http://dx.doi.org/10.4249/scholarpedia.9489.
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Sagaut, P., P. Comte, and F. Ducros. "Filtered subgrid-scale models." Physics of Fluids 12, no. 1 (January 2000): 233–36. http://dx.doi.org/10.1063/1.870297.
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Vinuesa, Jean-François, and Fernando Porté-Agel. "Dynamic Models for the Subgrid-Scale Mixing of Reactants in Atmospheric Turbulent Reacting Flows." Journal of the Atmospheric Sciences 65, no. 5 (May 1, 2008): 1692–99. http://dx.doi.org/10.1175/2007jas2392.1.
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Abstract The effects of the subgrid scales on chemical transformations in large-eddy simulations of the convective atmospheric boundary layer (CBL) are investigated. Dynamic similarity subgrid-scale models are formulated and used to calculate the subgrid-scale covariance. The dynamic procedure allows for simulations free of parameter tuning since the model coefficients are computed based on the resolved reactant concentrations. A scale-dependent procedure is proposed that allows relaxing the assumption of scale invariance used in the dynamic similarity model. Simulation results show that both models are able to account in part for the effect of the segregation of the scalars at the subgrid scales, considerably reducing the resolution dependence of the results found when no subgrid covariance model is used. The scale-dependent dynamic version yields better results than its scale-invariant counterpart.
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Tesfa, Teklu K., and Lai-Yung Ruby Leung. "Exploring new topography-based subgrid spatial structures for improving land surface modeling." Geoscientific Model Development 10, no. 2 (February 22, 2017): 873–88. http://dx.doi.org/10.5194/gmd-10-873-2017.
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Abstract. Topography plays an important role in land surface processes through its influence on atmospheric forcing, soil and vegetation properties, and river network topology and drainage area. Land surface models with a spatial structure that captures spatial heterogeneity, which is directly affected by topography, may improve the representation of land surface processes. Previous studies found that land surface modeling, using subbasins instead of structured grids as computational units, improves the scalability of simulated runoff and streamflow processes. In this study, new land surface spatial structures are explored by further dividing subbasins into subgrid structures based on topographic properties, including surface elevation, slope and aspect. Two methods (local and global) of watershed discretization are applied to derive two types of subgrid structures (geo-located and non-geo-located) over the topographically diverse Columbia River basin in the northwestern United States. In the global method, a fixed elevation classification scheme is used to discretize subbasins. The local method utilizes concepts of hypsometric analysis to discretize each subbasin, using different elevation ranges that also naturally account for slope variations. The relative merits of the two methods and subgrid structures are investigated for their ability to capture topographic heterogeneity and the implications of this on representations of atmospheric forcing and land cover spatial patterns. Results showed that the local method reduces the standard deviation (SD) of subgrid surface elevation in the study domain by 17 to 19 % compared to the global method, highlighting the relative advantages of the local method for capturing subgrid topographic variations. The comparison between the two types of subgrid structures showed that the non-geo-located subgrid structures are more consistent across different area threshold values than the geo-located subgrid structures. Overall the local method and non-geo-located subgrid structures effectively and robustly capture topographic, climatic and vegetation variability, which is important for land surface modeling.
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Ke, Y., L. R. Leung, M. Huang, and H. Li. "Enhancing the representation of subgrid land surface characteristics in land surface models." Geoscientific Model Development 6, no. 5 (September 27, 2013): 1609–22. http://dx.doi.org/10.5194/gmd-6-1609-2013.
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Abstract. Land surface heterogeneity has long been recognized as important to represent in the land surface models. In most existing land surface models, the spatial variability of surface cover is represented as subgrid composition of multiple surface cover types, although subgrid topography also has major controls on surface processes. In this study, we developed a new subgrid classification method (SGC) that accounts for variability of both topography and vegetation cover. Each model grid cell was represented with a variable number of elevation classes and each elevation class was further described by a variable number of vegetation types optimized for each model grid given a predetermined total number of land response units (LRUs). The subgrid structure of the Community Land Model (CLM) was used to illustrate the newly developed method in this study. Although the new method increases the computational burden in the model simulation compared to the CLM subgrid vegetation representation, it greatly reduced the variations of elevation within each subgrid class and is able to explain at least 80% of the total subgrid plant functional types (PFTs). The new method was also evaluated against two other subgrid methods (SGC1 and SGC2) that assigned fixed numbers of elevation and vegetation classes for each model grid (SGC1: M elevation bands–N PFTs method; SGC2: N PFTs–M elevation bands method). Implemented at five model resolutions (0.1°, 0.25°, 0.5°, 1.0°and 2.0°) with three maximum-allowed total number of LRUs (i.e., NLRU of 24, 18 and 12) over North America (NA), the new method yielded more computationally efficient subgrid representation compared to SGC1 and SGC2, particularly at coarser model resolutions and moderate computational intensity (NLRU = 18). It also explained the most PFTs and elevation variability that is more homogeneously distributed spatially. The SGC method will be implemented in CLM over the NA continent to assess its impacts on simulating land surface processes.
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Erlebacher, G., M. Y. Hussaini, C. G. Speziale, and T. A. Zang. "Toward the large-eddy simulation of compressible turbulent flows." Journal of Fluid Mechanics 238 (May 1992): 155–85. http://dx.doi.org/10.1017/s0022112092001678.
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New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed and tested based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model, in terms of Favre-filtered fields, is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The two dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 963 grid using Fourier collocation methods. Extensive comparisons between the direct and modelled subgrid-scale fields are provided in order to validate the models. A large-eddy simulation of the decay of compressible isotropic turbulence – conducted on a coarse 323 grid – is shown to yield results that are in excellent agreement with the fine-grid direct simulation. Future applications of these compressible subgrid-scale models to the large-eddy simulation of more complex supersonic flows are discussed briefly.
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Zidikheri, Meelis J., and Jorgen S. Frederiksen. "Stochastic subgrid-scale modelling for non-equilibrium geophysical flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1910 (January 13, 2010): 145–60. http://dx.doi.org/10.1098/rsta.2009.0192.
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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.
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Moser, Robert D., Sigfried W. Haering, and Gopal R. Yalla. "Statistical Properties of Subgrid-Scale Turbulence Models." Annual Review of Fluid Mechanics 53, no. 1 (January 5, 2021): 255–86. http://dx.doi.org/10.1146/annurev-fluid-060420-023735.
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This review examines large eddy simulation (LES) models from the perspective of their a priori statistical characteristics. The most well-known statistical characteristic of an LES subgrid-scale model is its dissipation (energy transfer to unresolved scales), and many models are directly or indirectly formulated and tuned for consistency of this characteristic. However, in complex turbulent flows, many other subgrid statistical characteristics are important. These include such quantities as mean subgrid stress, subgrid transport of resolved Reynolds stress, and dissipation anisotropy. Also important are the statistical characteristics of models that account for filters that do not commute with differentiation and of the discrete numerical operators in the LES equations. We review the known statistical characteristics of subgrid models to assess these characteristics and the importance of their a priori consistency. We hope that this analysis will be helpful in continued development of LES models.
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Su, Mingde, Qingyan Chen, and Che-Ming Chiang. "Comparison of Different Subgrid-Scale Models of Large Eddy Simulation for Indoor Airflow Modeling." Journal of Fluids Engineering 123, no. 3 (March 15, 2001): 628–39. http://dx.doi.org/10.1115/1.1378294.
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The Smagorinsky subgrid-scale model, a dynamic subgrid-scale model, and a stimulated subgrid-scale model have been used in a large eddy simulation (LES) program to compute airflow in a room. A fast Fourier transformation (FFT) method and a conventional iteration method were used in solving the Poisson equation. The predicted distributions of indoor air velocity, temperature, and contaminant concentrations show that the three subgrid-scale models can produce acceptable results for indoor environment design. The dynamic and stimulated models performed slightly better than the Smagorinsky model. The use of FFT can significantly reduce the computing time. LES is a tool of the next generation of indoor air distribution design.
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Honnert, Rachel, Valéry Masson, and Fleur Couvreux. "A Diagnostic for Evaluating the Representation of Turbulence in Atmospheric Models at the Kilometric Scale." Journal of the Atmospheric Sciences 68, no. 12 (December 1, 2011): 3112–31. http://dx.doi.org/10.1175/jas-d-11-061.1.
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Abstract Turbulence is well represented by atmospheric models at very fine grid sizes, from 10 to 100 m, for which turbulent movements are mainly resolved, and by atmospheric models with grid sizes greater than 2 km, for which those movements are entirely parameterized. But what happens at intermediate scales, Wyngaard’s so-called terra incognita? Here an original method is presented that provides a new diagnostic by calculating the subgrid and resolved parts of five variables at different scales: turbulent kinetic energy (TKE), heat and moisture fluxes, and potential temperature and mixing ratio variances. They are established at intermediate scales for dry and cumulus-topped convective boundary layers. The similarity theorem allows the determination of the dimensionless variables of the problem. When the subgrid and resolved parts are studied, a new dimensionless variable, the dimensionless mesh size , needs to be added to the Deardorff free convective scaling variables, where h is the boundary layer height and hc is the height of the cloud layer. Similarity functions for the subgrid and resolved parts are assumed to be the product of the similarity function of the total (subgrid plus resolved) variables and a “partial” similarity function that depends only on . In order to determine the partial similarity function form, large-eddy simulations (LES) of five dry and cloudy convective boundary layers are used. The resolved and subgrid parts of the variables at coarser grid sizes are then deduced from the LES fields. The evolution of the subgrid and resolved parts in the boundary layer with is as follows: fine grids mainly resolve variables. As the mesh becomes coarser, more eddies are subgrid. Finally, for very large meshes, turbulence is entirely subgrid. A scale therefore exists for which the subgrid and resolved parts are equal. This is obtained for in the case of TKE, 0.4 for the potential temperature variance, and 0.8 for the mixing ratio variance, indicating that the velocity structures are smaller than those for the potential temperature, which are smaller than those for the mixing ratio. Furthermore, boundary layers capped by convective clouds have structures larger than dry boundary layer ones as displayed by the scaling in the partial similarity functions. This new diagnostic gives a reference for evaluating current and future parameterizations at kilometric scales. As an illustration, the parameterizations of a mesoscale model are eventually evaluated at intermediate scales. In its standard version, the model produces too many resolved movements, as the turbulence scheme does not sufficiently represent the impact of the subgrid thermal. This is not true when a mass-flux scheme is introduced. However in this case, a completely subgrid thermal is modeled leading to an overestimation of the subgrid part.
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Tonttila, J., P. Räisänen, and H. Järvinen. "Monte Carlo-based subgrid parameterization of vertical velocity and stratiform cloud microphysics in ECHAM5.5-HAM2." Atmospheric Chemistry and Physics Discussions 13, no. 2 (February 27, 2013): 5477–507. http://dx.doi.org/10.5194/acpd-13-5477-2013.
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Abstract. A new method for parameterizing the subgrid variations of vertical velocity and cloud droplet number concentration (CDNC) is presented for GCMs. These parameterizations build on top of existing parameterizations that create stochastic subgrid cloud columns inside the GCM grid-cells, which can be employed by the Monte Carlo independent column approximation approach for radiative transfer. The new model version adds a description for vertical velocity in individual subgrid columns, which can be used to compute cloud activation and the subgrid distribution of the number of cloud droplets explicitly. This provides a consistent way for simulating the cloud radiative effects with two-moment cloud microphysical properties defined in subgrid-scale. The primary impact of the new parameterizations is to decrease the CDNC over polluted continents, while over the oceans the impact is smaller. This promotes changes in the global distribution of the cloud radiative effects and might thus have implications on model estimation of the indirect radiative effect of aerosols.
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Zhang, Xu, Jian-Wen Bao, Baode Chen, and Evelyn D. Grell. "A Three-Dimensional Scale-Adaptive Turbulent Kinetic Energy Scheme in the WRF-ARW Model." Monthly Weather Review 146, no. 7 (July 2018): 2023–45. http://dx.doi.org/10.1175/mwr-d-17-0356.1.
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A new three-dimensional (3D) turbulent kinetic energy (TKE) subgrid mixing scheme is developed using the Advanced Research version of the Weather Research and Forecasting (WRF) Model (WRF-ARW) to address the gray-zone problem in the parameterization of subgrid turbulent mixing. The new scheme combines the horizontal and vertical subgrid turbulent mixing into a single energetically consistent framework, in contrast to the conventionally separate treatment of the vertical and horizontal mixing. The new scheme is self-adaptive to the grid-size change between the large-eddy simulation (LES) and mesoscale limits. A series of dry convective boundary layer (CBL) idealized simulations are carried out to compare the performance of the new scheme and the conventional treatment of subgrid mixing to the WRF-ARW LES dataset. The importance of including the nonlocal component in the vertical buoyancy specification in the newly developed general TKE-based scheme is illustrated in the comparison. The improvements of the new scheme with the conventional treatment of subgrid mixing across the gray-zone model resolutions are demonstrated through the partitioning of the total vertical flux profiles. Results from real-case simulations show the feasibility of using the new scheme in the WRF Model in lieu of the conventional treatment of subgrid mixing.
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Im, E.-S., E. Coppola, F. Giorgi, and X. Bi. "Validation of a High-Resolution Regional Climate Model for the Alpine Region and Effects of a Subgrid-Scale Topography and Land Use Representation." Journal of Climate 23, no. 7 (April 1, 2010): 1854–73. http://dx.doi.org/10.1175/2009jcli3262.1.
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Abstract A mosaic-type parameterization of subgrid-scale topography and land use (SubBATS) is applied for a high-resolution regional climate simulation over the Alpine region with a regional climate model (RegCM3). The model coarse-gridcell size in the control simulation is 15 km while the subgridcell size is 3 km. The parameterization requires disaggregation of atmospheric variables from the coarse grid to the subgrid and aggregation of surface fluxes from the subgrid to the coarse grid. Two 10-yr simulations (1983–92) are intercompared, one without (CONT) and one with (SUB) the subgrid scheme. The authors first validate the CONT simulation, showing that it produces good quality temperature and precipitation statistics, showing in particular a good performance compared to previous runs of this region. The subgrid scheme produces much finer detail of temperature and snow distribution following the topographic disaggregation. It also tends to form and melt snow more accurately in response to the heterogeneous characteristics of topography. In particular, validation against station observations shows that the SUB simulation improves the model simulation of the surface hydrologic cycle, in particular snow and runoff, especially at high-elevation sites. Finally, two experiments explore the model sensitivity to different subgrid disaggregation assumptions, namely, the temperature lapse rate and an empirical elevation-based disaggregation of precipitation.
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Tonttila, J., H. Järvinen, and P. Räisänen. "Explicit representation of subgrid variability in cloud microphysics yields weaker aerosol indirect effect in the ECHAM5-HAM2 climate model." Atmospheric Chemistry and Physics Discussions 14, no. 10 (June 12, 2014): 15523–43. http://dx.doi.org/10.5194/acpd-14-15523-2014.
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Abstract. Impacts of representing cloud microphysical processes in a stochastic subcolumn framework are investigated, with emphasis on estimating the aerosol indirect effect. It is shown that subgrid treatment of cloud activation and autoconversion of cloud water to rain reduce the impact of anthropogenic aerosols on cloud properties and thus reduce the global mean aerosol indirect effect by 18%, from 1.59 to 1.30 W m−2. Although the results show the importance of considering subgrid variability in the treatment of autoconversion, representing several processes in a self-consistent subgrid framework is emphasized. This paper provides direct evidence that omitting subgrid variability in cloud microphysics significantly contributes to the apparently chronic overestimation of the aerosol indirect effect by climate models, as compared to satellite-based estimates.
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Huang, Wei, J. W. Bao, Xu Zhang, and Baode Chen. "Comparison of the Vertical Distributions of Cloud Properties from Idealized Extratropical Deep Convection Simulations Using Various Horizontal Resolutions." Monthly Weather Review 146, no. 3 (March 1, 2018): 833–51. http://dx.doi.org/10.1175/mwr-d-17-0162.1.
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ABSTRACT The authors coarse-grained and analyzed the output from a large-eddy simulation (LES) of an idealized extratropical supercell storm using the Weather Research and Forecasting (WRF) Model with various horizontal resolutions (200 m, 400 m, 1 km, and 3 km). The coarse-grained physical properties of the simulated convection were compared with explicit WRF simulations of the same storm at the same resolution of coarse-graining. The differences between the explicit simulations and the coarse-grained LES output increased as the horizontal grid spacing in the explicit simulation coarsened. The vertical transport of the moist static energy and total hydrometeor mixing ratio in the explicit simulations converged to the LES solution at the 200-m grid spacing. Based on the analysis of the coarse-grained subgrid vertical flux of the moist static energy, the authors confirmed that the nondimensional subgrid vertical flux of the moist static energy varied with the subgrid fractional cloudiness according to a function of fractional cloudiness, regardless of the box size. The subgrid mass flux could not account for most of the total subgrid vertical flux of the moist static energy because the eddy-transport component associated with the internal structural inhomogeneity of convective clouds was of a comparable magnitude. This study highlights the ongoing challenge in developing scale-aware parameterizations of subgrid convection.
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LANGFORD, JACOB A., and ROBERT D. MOSER. "Optimal LES formulations for isotropic turbulence." Journal of Fluid Mechanics 398 (November 10, 1999): 321–46. http://dx.doi.org/10.1017/s0022112099006369.
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It is shown that there is an abstract subgrid model that is in all senses ideal. An LES using the ideal subgrid model will exactly reproduce all single-time, multi-point statistics, and at the same time will have minimum possible error in instantaneous dynamics. The ideal model is written as an average over the real turbulent fields whose large scales match the current LES field. But this conditional average cannot be computed directly. Rather, the ideal model is the target for approximation when developing practical models, though no new practical models are presented here. To construct such models, the conditional average can be formally approximated using stochastic estimation. These optimal formulations are presented, and it is shown that a relatively simple but general class of one-point estimates can be computed from two-point correlation data, and that the estimates retain some of the statistical properties of the ideal model.To investigate the nature of these models, optimal formulations were applied to forced isotropic turbulence. A variety of optimal models of increasing complexity were computed. In all cases, it was found that the errors between the real and estimated subgrid force were nearly as large as the subgrid force itself. It is suggested that this may also be characteristic of the ideal model in isotropic turbulence. If this is the case, then it explains why subgrid models produce reasonable results in actual LES while performing poorly in a priori tests. Despite the large errors in the optimal models, one feature of the subgrid interaction that is exactly represented is the energy transfer to the subgrid scales by each wavenumber.
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Yano, J. I. "Mass-flux subgrid-scale parameterization in analogy with multi-component flows: a formulation towards scale independence." Geoscientific Model Development 5, no. 6 (November 21, 2012): 1425–40. http://dx.doi.org/10.5194/gmd-5-1425-2012.
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Abstract. A generalized mass-flux formulation is presented, which no longer takes a limit of vanishing fractional areas for subgrid-scale components. The presented formulation is applicable to a~situation in which the scale separation is still satisfied, but fractional areas occupied by individual subgrid-scale components are no longer small. A self-consistent formulation is presented by generalizing the mass-flux formulation under the segmentally-constant approximation (SCA) to the grid–scale variabilities. The present formulation is expected to alleviate problems arising from increasing resolutions of operational forecast models without invoking more extensive overhaul of parameterizations. The present formulation leads to an analogy of the large-scale atmospheric flow with multi-component flows. This analogy allows a generality of including any subgrid-scale variability into the mass-flux parameterization under SCA. Those include stratiform clouds as well as cold pools in the boundary layer. An important finding under the present formulation is that the subgrid-scale quantities are advected by the large-scale velocities characteristic of given subgrid-scale components (large-scale subcomponent flows), rather than by the total large-scale flows as simply defined by grid-box average. In this manner, each subgrid-scale component behaves as if like a component of multi-component flows. This formulation, as a result, ensures the lateral interaction of subgrid-scale variability crossing the grid boxes, which are missing in the current parameterizations based on vertical one-dimensional models, and leading to a reduction of the grid-size dependencies in its performance. It is shown that the large-scale subcomponent flows are driven by large-scale subcomponent pressure gradients. The formulation, as a result, furthermore includes a self-contained description of subgrid-scale momentum transport. The main purpose of the present paper is to appeal the importance of this new possibility suggested herein to the numerical weather forecast community with implications for the other parameterizations (cloud fraction, mesoscale organization) as well as resolution-dependence of parameterizations.
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Frederiksen, Jorgen, and Terence O’Kane. "Entropy, Closures and Subgrid Modeling." Entropy 10, no. 4 (November 17, 2008): 635–83. http://dx.doi.org/10.3390/e10040635.
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Frederiksen, Jorgen S., Terence J. O'Kane, and Meelis J. Zidikheri. "Subgrid modelling for geophysical flows." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1982 (January 13, 2013): 20120166. http://dx.doi.org/10.1098/rsta.2012.0166.
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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.
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Abbà, A., A. C. Cercignani, and L. Valdettaro. "Analysis of subgrid scale models." Computers & Mathematics with Applications 46, no. 4 (August 2003): 521–35. http://dx.doi.org/10.1016/s0898-1221(03)90014-9.
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Sun, Mingyu. "Volume-tracking of subgrid particles." International Journal for Numerical Methods in Fluids 66, no. 12 (April 8, 2010): 1530–54. http://dx.doi.org/10.1002/fld.2331.
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Casulli, Vincenzo. "Computational grid, subgrid, and pixels." International Journal for Numerical Methods in Fluids 90, no. 3 (January 27, 2019): 140–55. http://dx.doi.org/10.1002/fld.4715.
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Wang, Liqiu. "Modelling of subgrid-scale fluxes." Chaos, Solitons & Fractals 34, no. 2 (October 2007): 368–75. http://dx.doi.org/10.1016/j.chaos.2006.03.049.
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Abraham, G., H. Gerritsen, and G. J. H. Lindijer. "Subgrid tidally induced residual circulations." Continental Shelf Research 7, no. 3 (March 1987): 285–305. http://dx.doi.org/10.1016/0278-4343(87)90070-7.
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Ke, Y., L. R. Leung, M. Huang, and H. Li. "Enhancing the representation of subgrid land surface characteristics in land surface models." Geoscientific Model Development Discussions 6, no. 1 (March 28, 2013): 2177–212. http://dx.doi.org/10.5194/gmdd-6-2177-2013.
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Abstract. Land surface heterogeneity has long been recognized as important to represent in the land surface models. In most existing land surface models, the spatial variability of surface cover is represented as subgrid composition of multiple surface cover types. In this study, we developed a new subgrid classification method (SGC) that accounts for the topographic variability of the vegetation cover. Each model grid cell was represented with a number of elevation classes and each elevation class was further described by a number of vegetation types. The numbers of elevation classes and vegetation types were variable and optimized for each model grid so that the spatial variability of both elevation and vegetation can be reasonably explained given a pre-determined total number of classes. The subgrid structure of the Community Land Model (CLM) was used as an example to illustrate the newly developed method in this study. With similar computational burden as the current subgrid vegetation representation in CLM, the new method is able to explain at least 80% of the total subgrid Plant Functional Types (PFTs) and greatly reduced the variations of elevation within each subgrid class compared to the baseline method where a single elevation class is assigned to each subgrid PFT. The new method was also evaluated against two other subgrid methods (SGC1 and SGC2) that assigned fixed numbers of elevation and vegetation classes for each model grid with different perspectives of surface cover classification. Implemented at five model resolutions (0.1°, 0.25°, 0.5°, 1.0° and 2.0°) with three maximum-allowed total number of classes Nclass of 24, 18 and 12 representing different computational burdens over the North America (NA) continent, the new method showed variable performances compared to the SGC1 and SGC2 methods. However, the advantage of the SGC method over the other two methods clearly emerged at coarser model resolutions and with moderate computational intensity (Nclass = 18) as it explained the most PFTs and elevation variability among the three subgrid methods. Spatially, the SGC method explained more elevation variability in topography-complex areas and more vegetation variability in flat areas. Furthermore, the variability of both elevation and vegetation explained by the new method was more spatially homogeneous regardless of the model resolutions and computational burdens. The SGC method will be implemented in CLM over the NA continent to assess its impacts on simulating land surface processes.
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Zhang, Zhibo, Hua Song, Po-Lun Ma, Vincent E. Larson, Minghuai Wang, Xiquan Dong, and Jianwu Wang. "Subgrid variations of the cloud water and droplet number concentration over the tropical ocean: satellite observations and implications for warm rain simulations in climate models." Atmospheric Chemistry and Physics 19, no. 2 (January 28, 2019): 1077–96. http://dx.doi.org/10.5194/acp-19-1077-2019.
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Abstract. One of the challenges in representing warm rain processes in global climate models (GCMs) is related to the representation of the subgrid variability of cloud properties, such as cloud water and cloud droplet number concentration (CDNC), and the effect thereof on individual precipitation processes such as autoconversion. This effect is conventionally treated by multiplying the resolved-scale warm rain process rates by an enhancement factor (Eq) which is derived from integrating over an assumed subgrid cloud water distribution. The assumed subgrid cloud distribution remains highly uncertain. In this study, we derive the subgrid variations of liquid-phase cloud properties over the tropical ocean using the satellite remote sensing products from Moderate Resolution Imaging Spectroradiometer (MODIS) and investigate the corresponding enhancement factors for the GCM parameterization of autoconversion rate. We find that the conventional approach of using only subgrid variability of cloud water is insufficient and that the subgrid variability of CDNC, as well as the correlation between the two, is also important for correctly simulating the autoconversion process in GCMs. Using the MODIS data which have near-global data coverage, we find that Eq shows a strong dependence on cloud regimes due to the fact that the subgrid variability of cloud water and CDNC is regime dependent. Our analysis shows a significant increase of Eq from the stratocumulus (Sc) to cumulus (Cu) regions. Furthermore, the enhancement factor EN due to the subgrid variation of CDNC is derived from satellite observation for the first time, and results reveal several regions downwind of biomass burning aerosols (e.g., Gulf of Guinea, east coast of South Africa), air pollution (i.e., East China Sea), and active volcanos (e.g., Kilauea, Hawaii, and Ambae, Vanuatu), where the EN is comparable to or even larger than Eq, suggesting an important role of aerosol in influencing the EN. MODIS observations suggest that the subgrid variations of cloud liquid water path (LWP) and CDNC are generally positively correlated. As a result, the combined enhancement factor, including the effect of LWP and CDNC correlation, is significantly smaller than the simple product of Eq⋅EN. Given the importance of warm rain processes in understanding the Earth's system dynamics and water cycle, we conclude that more observational studies are needed to provide a better constraint on the warm rain processes in GCMs.
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Zidikheri, Meelis J., and Jorgen S. Frederiksen. "Stochastic Subgrid Parameterizations for Simulations of Atmospheric Baroclinic Flows." Journal of the Atmospheric Sciences 66, no. 9 (September 1, 2009): 2844–58. http://dx.doi.org/10.1175/2009jas3036.1.
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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 resolution of T31 the off-diagonal elements are more important and even the diagonal elements are more anisotropic. At both resolutions, and for anisotropic or isotropized subgrid terms, LESs are in excellent agreement with higher-resolution DNS.
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Zhang, Yan, and Yinnian He. "A Subgrid Model for the Time-Dependent Navier-Stokes Equations." Advances in Numerical Analysis 2009 (September 6, 2009): 1–20. http://dx.doi.org/10.1155/2009/494829.
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We propose a stabilized subgrid finite-element method for the two-dimensional (2D) nonstationary incompressible Naver-Stokes equation (NSE). This method yields a subgrid eddy viscosity which does not act on the large flow structures. The proposed eddy viscous term is constructed by a fluctuation operator based on an L2-projection. The fluctuation operator can be implemented by the L2-projection from high-order interpolation finite-element spaces to the low-order interpolation finite-element spaces. In this paper, P2/P1 mixed finite-element spaces are adopted to implement the calculation and the analysis. The error analysis is given based on some regular assumptions. Finally, in the part of numerical tests, the numerical computations show that the numerical results agree with theoretical analysis very well. Meanwhile, the numerical investigations demonstrate that the proposed subgrid is very effective for high Reynolds number fluid flows and superior to other referred subgrid models.
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Yano, J. I. "Mass-flux subgrid-scale parameterization in analogy with multi-component flows: a formulation towards scale independence." Geoscientific Model Development Discussions 4, no. 4 (November 24, 2011): 3127–60. http://dx.doi.org/10.5194/gmdd-4-3127-2011.
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Abstract. The mass-flux parameterization formulation is generalized by taking an analogy of the large-scale atmospheric flow with multi-component flows. This generalization permits to include any subgrid-scale variability into the mass-flux parameterization. Those include stratiform clouds as well as cold pools in the boundary layer. An important finding under the present formulation is that the subgrid-scale quantities are advected by the velocities characteristic of given subgrid-scale components (subcomponent flows), rather than by the large-scale flows as simply defined by grid-box average. This formulation, as a result, ensures the lateral interaction of subgrid-scale variability crossing the grid boxes, which are missing in the current parameterizations, and leading to a reduction of the grid-size dependence in its performance. It is shown that the subcomponent flows are driven by subcomponent pressure gradients. The formulation, as a result, furthermore includes a self-contained description of subgrid-scale momentum transport. The formulation is applicable to a situation in which the scale separation is still satisfied, but fractional areas occupied by individual subgrid-scale components are no longer small. A complete formulation is presented and various implementation issues are discussed. The present formulation is also expected to alleviate problems arising from increasing resolutions of operational forecast models without invoking more extensive overhaul of parameterizations. The main purpose of the present paper is to appeal the importance of this new possibility suggested herein to the numerical weather forecast community with implications for the other parameteizations (cloud fraction, mesoscale organization) as well as resolution-dependence of parameterizations.
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Tonttila, J., H. Järvinen, and P. Räisänen. "Explicit representation of subgrid variability in cloud microphysics yields weaker aerosol indirect effect in the ECHAM5-HAM2 climate model." Atmospheric Chemistry and Physics 15, no. 2 (January 19, 2015): 703–14. http://dx.doi.org/10.5194/acp-15-703-2015.
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Abstract. The impacts of representing cloud microphysical processes in a stochastic subcolumn framework are investigated, with emphasis on estimating the aerosol indirect effect. It is shown that subgrid treatment of cloud activation and autoconversion of cloud water to rain reduce the impact of anthropogenic aerosols on cloud properties and thus reduce the global mean aerosol indirect effect by 19%, from −1.59 to −1.28 W m−2. This difference is partly related to differences in the model basic state; in particular, the liquid water path (LWP) is smaller and the shortwave cloud radiative forcing weaker when autoconversion is computed separately for each subcolumn. However, when the model is retuned so that the differences in the basic state LWP and radiation balance are largely eliminated, the global-mean aerosol indirect effect is still 14% smaller (i.e. −1.37 W m−2) than for the model version without subgrid treatment of cloud activation and autoconversion. The results show the importance of considering subgrid variability in the treatment of autoconversion. Representation of several processes in a self-consistent subgrid framework is emphasized. This paper provides evidence that omitting subgrid variability in cloud microphysics contributes to the apparently chronic overestimation of the aerosol indirect effect by climate models, as compared to satellite-based estimates.
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Hoffman, Johan. "Subgrid Modeling for Convection-Diffusion-Reaction in Two Space Dimensions Using a Haar Multiresolution Analysis." Mathematical Models and Methods in Applied Sciences 13, no. 10 (October 2003): 1515–36. http://dx.doi.org/10.1142/s021820250300301x.
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In this paper we study a subgrid model based on extrapolation of a modeling residual, in the case of a linear convection-diffusion-reaction problem Lu=f in two dimensions. The solution u to the exact problem satisfies an equation Lhu=[f]h+Fh(u), where Lh is the operator used in the computation on the finest computational scale h, [f]h is the approximation of f on the scale h, and Fh(u) is a modeling residual, which needs to be modeled. The subgrid modeling problem is to compute approximations of Fh(u) without using finer scales than h. In this study we model Fh(u) by extrapolation from coarser scales than h, where Fh(u) is directly computed with the finest scale h as reference. We show in experiments that a solution with subgrid model on a scale h in most cases corresponds to a solution without subgrid model on a mesh of size less than h/4.
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Shaw, Tiffany A., and Theodore G. Shepherd. "A Theoretical Framework for Energy and Momentum Consistency in Subgrid-Scale Parameterization for Climate Models." Journal of the Atmospheric Sciences 66, no. 10 (October 1, 2009): 3095–114. http://dx.doi.org/10.1175/2009jas3051.1.
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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.
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Park, Sungsu. "A Unified Convection Scheme (UNICON). Part I: Formulation." Journal of the Atmospheric Sciences 71, no. 11 (October 29, 2014): 3902–30. http://dx.doi.org/10.1175/jas-d-13-0233.1.
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Abstract The author develops a unified convection scheme (UNICON) that parameterizes relative (i.e., with respect to the grid-mean vertical flow) subgrid vertical transport by nonlocal asymmetric turbulent eddies. UNICON is a process-based model of subgrid convective plumes and mesoscale organized flow without relying on any quasi-equilibrium assumptions such as convective available potential energy (CAPE) or convective inhibition (CIN) closures. In combination with a relative subgrid vertical transport scheme by local symmetric turbulent eddies and a grid-scale advection scheme, UNICON simulates vertical transport of water species and conservative scalars without double counting at any horizontal resolution. UNICON simulates all dry–moist, forced–free, and shallow–deep convection within a single framework in a seamless, consistent, and unified way. It diagnoses the vertical profiles of the macrophysics (fractional area, plume radius, and number density) as well as the microphysics (production and evaporation rates of convective precipitation) and the dynamics (mass flux and vertical velocity) of multiple convective updraft and downdraft plumes. UNICON also prognoses subgrid cold pool and mesoscale organized flow within the planetary boundary layer (PBL) that is forced by evaporation of convective precipitation and accompanying convective downdrafts but damped by surface flux and entrainment at the PBL top. The combined subgrid parameterization of diagnostic convective updraft and downdraft plumes, prognostic subgrid mesoscale organized flow, and the feedback among them remedies the weakness of conventional quasi-steady diagnostic plume models—the lack of plume memory across the time step—allowing UNICON to successfully simulate various transitional phenomena associated with convection (e.g., the diurnal cycle of precipitation and the Madden–Julian oscillation).
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Tonttila, J., P. Räisänen, and H. Järvinen. "Monte Carlo-based subgrid parameterization of vertical velocity and stratiform cloud microphysics in ECHAM5.5-HAM2." Atmospheric Chemistry and Physics 13, no. 15 (August 6, 2013): 7551–65. http://dx.doi.org/10.5194/acp-13-7551-2013.
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Abstract. A new method for parameterizing the subgrid variations of vertical velocity and cloud droplet number concentration (CDNC) is presented for general circulation models (GCMs). These parameterizations build on top of existing parameterizations that create stochastic subgrid cloud columns inside the GCM grid cells, which can be employed by the Monte Carlo independent column approximation approach for radiative transfer. The new model version adds a description for vertical velocity in individual subgrid columns, which can be used to compute cloud activation and the subgrid distribution of the number of cloud droplets explicitly. Autoconversion is also treated explicitly in the subcolumn space. This provides a consistent way of simulating the cloud radiative effects with two-moment cloud microphysical properties defined at subgrid scale. The primary impact of the new parameterizations is to decrease the CDNC over polluted continents, while over the oceans the impact is smaller. Moreover, the lower CDNC induces a stronger autoconversion of cloud water to rain. The strongest reduction in CDNC and cloud water content over the continental areas promotes weaker shortwave cloud radiative effects (SW CREs) even after retuning the model. However, compared to the reference simulation, a slightly stronger SW CRE is seen e.g. over mid-latitude oceans, where CDNC remains similar to the reference simulation, and the in-cloud liquid water content is slightly increased after retuning the model.
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Malaspinas, Orestis, and Pierre Sagaut. "Consistent subgrid scale modelling for lattice Boltzmann methods." Journal of Fluid Mechanics 700 (April 30, 2012): 514–42. http://dx.doi.org/10.1017/jfm.2012.155.
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AbstractThe lattice Boltzmann method has become a widely used tool for the numerical simulation of fluid flows and in particular of turbulent flows. In this frame the inclusion of subgrid scale closures is of crucial importance and is not completely understood from the theoretical point of view. Here, we propose a consistent way of introducing subgrid closures in the BGK Boltzmann equation for large eddy simulations of turbulent flows. Based on the Hermite expansion of the velocity distribution function, we construct a hierarchy of subgrid scale terms, which are similar to those obtained for the Navier–Stokes equations, and discuss their inclusion in the lattice Boltzmann method scheme. A link between our approach and the standard way on including eddy viscosity models in the lattice Boltzmann method is established. It is shown that the use of a single modified scalar relaxation time to account for subgrid viscosity effects is not consistent in the compressible case. Finally, we validate the approach in the weakly compressible case by simulating the time developing mixing layer and comparing with experimental results and direct numerical simulations.
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Dorrestijn, J., D. T. Crommelin, J. A. Biello, and S. J. Böing. "A data-driven multi-cloud model for stochastic parametrization of deep convection." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1991 (May 28, 2013): 20120374. http://dx.doi.org/10.1098/rsta.2012.0374.
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Stochastic subgrid models have been proposed to capture the missing variability and correct systematic medium-term errors in general circulation models. In particular, the poor representation of subgrid-scale deep convection is a persistent problem that stochastic parametrizations are attempting to correct. In this paper, we construct such a subgrid model using data derived from large-eddy simulations (LESs) of deep convection. We use a data-driven stochastic parametrization methodology to construct a stochastic model describing a finite number of cloud states. Our model emulates, in a computationally inexpensive manner, the deep convection-resolving LES. Transitions between the cloud states are modelled with Markov chains. By conditioning the Markov chains on large-scale variables, we obtain a conditional Markov chain, which reproduces the time evolution of the cloud fractions. Furthermore, we show that the variability and spatial distribution of cloud types produced by the Markov chains become more faithful to the LES data when local spatial coupling is introduced in the subgrid Markov chains. Such spatially coupled Markov chains are equivalent to stochastic cellular automata.
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Zhou, Ye, and George Vahala. "Aspects of subgrid modelling and large-eddy simulation of magnetohydrodynamic turbulence." Journal of Plasma Physics 45, no. 2 (April 1991): 239–49. http://dx.doi.org/10.1017/s0022377800015671.
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Subgrid-scale closures for magnetohydodynamic (MHD) turbulence are examined using the filtering technique. From the similarities between incompressible MHD turbulence and its hydrodynamic counterpart, as well as ideas from dynamo theory, a subgrid model is constructed from the large-eddy simulation (LES) of MHD turbulence. This model should find applicability in treating LES of the reversed-field pinch.
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Isakov, Vlad, John S. Irwin, and Jason Ching. "Using CMAQ for Exposure Modeling and Characterizing the Subgrid Variability for Exposure Estimates." Journal of Applied Meteorology and Climatology 46, no. 9 (September 1, 2007): 1354–71. http://dx.doi.org/10.1175/jam2538.1.
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Abstract Atmospheric processes and the associated transport and dispersion of atmospheric pollutants are known to be highly variable in time and space. Current air-quality models that characterize atmospheric chemistry effects, for example, the Community Multiscale Air Quality model (CMAQ), provide volume-averaged concentration values for each grid cell in the modeling domain given the stated conditions. Given the assumptions made and the limited set of processes included in any model’s implementation, there are many sources of “unresolved” subgrid variability. This raises the question of the importance of the unresolved subgrid variations on exposure assessment results if such models were to be used to assess air toxics exposure. In this study, the Hazardous Air Pollutant Exposure Model (HAPEM) is applied to estimate benzene and formaldehyde inhalation exposure using ambient annually averaged concentrations predicted by CMAQ to investigate how within-grid variability can affect exposure estimates. An urban plume dispersion model was used to estimate the subgrid variability of annually averaged benzene concentration values within CMAQ grid cells for a modeling domain centered on Philadelphia, Pennsylvania. Significant (greater than a factor of 2) increases in maximum exposure impacts were seen in the exposure estimates in comparison with exposure estimates generated using CMAQ grid-averaged concentration values. These results consider only one source of subgrid variability, namely, the discrete location and distribution of emissions, but they do suggest the importance and value of developing improved characterizations of subgrid concentration variability for use in air toxics exposure assessments.
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Bengtsson, Lisa, Heiner Körnich, Erland Källén, and Gunilla Svensson. "Large-Scale Dynamical Response to Subgrid-Scale Organization Provided by Cellular Automata." Journal of the Atmospheric Sciences 68, no. 12 (December 1, 2011): 3132–44. http://dx.doi.org/10.1175/jas-d-10-05028.1.
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Abstract Because of the limited resolution of numerical weather prediction (NWP) models, subgrid-scale physical processes are parameterized and represented by gridbox means. However, some physical processes are better represented by a mean and its variance; a typical example is deep convection, with scales varying from individual updrafts to organized mesoscale systems. This study investigates, in an idealized setting, whether a cellular automaton (CA) can be used to enhance subgrid-scale organization by forming clusters representative of the convective scales and thus yield a stochastic representation of subgrid-scale variability. The authors study the transfer of energy from the convective to the larger atmospheric scales through nonlinear wave interactions. This is done using a shallow water (SW) model initialized with equatorial wave modes. By letting a CA act on a finer resolution than that of the SW model, it can be expected to mimic the effect of, for instance, gravity wave propagation on convective organization. Employing the CA scheme permits the reproduction of the observed behavior of slowing down equatorial Kelvin modes in convectively active regions, while random perturbations fail to feed back on the large-scale flow. The analysis of kinetic energy spectra demonstrates that the CA subgrid scheme introduces energy backscatter from the smallest model scales to medium scales. However, the amount of energy backscattered depends almost solely on the memory time scale introduced to the subgrid scheme, whereas any variation in spatial scales generated does not influence the energy spectra markedly.
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Hirt, Mirjam, Stephan Rasp, Ulrich Blahak, and George C. Craig. "Stochastic Parameterization of Processes Leading to Convective Initiation in Kilometer-Scale Models." Monthly Weather Review 147, no. 11 (October 11, 2019): 3917–34. http://dx.doi.org/10.1175/mwr-d-19-0060.1.
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Abstract Kilometer-scale models allow for an explicit simulation of deep convective overturning but many subgrid processes that are crucial for convective initiation are still poorly represented. This leads to biases such as insufficient convection triggering and late peak of summertime convection. A physically based stochastic perturbation scheme (PSP) for subgrid processes has been proposed (Kober and Craig) that targets the coupling between subgrid turbulence and resolved convection. The first part of this study presents four modifications to this PSP scheme for subgrid turbulence: an autoregressive, continuously evolving random field; a limitation of the perturbations to the boundary layer that removes artificial convection at night; a mask that turns off perturbations in precipitating columns to retain coherent structures; and nondivergent wind perturbations that drastically increase the effectiveness of the vertical velocity perturbations. In a revised version, PSP2, the combined modifications retain the physically based coupling to the boundary layer scheme of the original scheme while removing undesirable side effects. This has the potential to improve predictions of convective initiation in kilometer-scale models while minimizing other biases. The second part of the study focuses on perturbations to account for convective initiation by subgrid orography. Here the mechanical lifting effect is modeled by introducing vertical and horizontal wind perturbations of an orographically induced gravity wave. The resulting perturbations lead to enhanced convective initiation over mountainous terrain. However, the total benefit of this scheme is unclear and we do not adopt the scheme in our revised configuration.