Sensitivities of slantwise convection dynamics to model grid spacing under an idealized framework

2021 ◽  
Author(s):  
Ting‐Chen Chen ◽  
Man‐Kong Yau ◽  
Daniel J. Kirshbaum
Keyword(s):  
Grid Spacing ◽  
Slantwise Convection

scholarly journals Using Fractal Downscaling of Satellite Precipitation Products for Hydrometeorological Applications

2010 ◽  
Vol 27 (3) ◽  
pp. 409-427 ◽  
Author(s):  
Kun Tao ◽  
Ana P. Barros
Keyword(s):  
Spatial Resolution ◽  
Stage Iv ◽  
Tropical Rainfall Measuring Mission ◽  
Skill Score ◽  
Probability Of Detection ◽  
Grid Spacing ◽  
Satellite Precipitation ◽  
Target Field ◽  
Skill Scores ◽  
Central United States

Abstract The objective of spatial downscaling strategies is to increase the information content of coarse datasets at smaller scales. In the case of quantitative precipitation estimation (QPE) for hydrological applications, the goal is to close the scale gap between the spatial resolution of coarse datasets (e.g., gridded satellite precipitation products at resolution L × L) and the high resolution (l × l; L ≫ l) necessary to capture the spatial features that determine spatial variability of water flows and water stores in the landscape. In essence, the downscaling process consists of weaving subgrid-scale heterogeneity over a desired range of wavelengths in the original field. The defining question is, which properties, statistical and otherwise, of the target field (the known observable at the desired spatial resolution) should be matched, with the caveat that downscaling methods be as a general as possible and therefore ideally without case-specific constraints and/or calibration requirements? Here, the attention is focused on two simple fractal downscaling methods using iterated functions systems (IFS) and fractal Brownian surfaces (FBS) that meet this requirement. The two methods were applied to disaggregate spatially 27 summertime convective storms in the central United States during 2007 at three consecutive times (1800, 2100, and 0000 UTC, thus 81 fields overall) from the Tropical Rainfall Measuring Mission (TRMM) version 6 (V6) 3B42 precipitation product (∼25-km grid spacing) to the same resolution as the NCEP stage IV products (∼4-km grid spacing). Results from bilinear interpolation are used as the control. A fundamental distinction between IFS and FBS is that the latter implies a distribution of downscaled fields and thus an ensemble solution, whereas the former provides a single solution. The downscaling effectiveness is assessed using fractal measures (the spectral exponent β, fractal dimension D, Hurst coefficient H, and roughness amplitude R) and traditional operational scores statistics scores [false alarm rate (FR), probability of detection (PD), threat score (TS), and Heidke skill score (HSS)], as well as bias and the root-mean-square error (RMSE). The results show that both IFS and FBS fractal interpolation perform well with regard to operational skill scores, and they meet the additional requirement of generating structurally consistent fields. Furthermore, confidence intervals can be directly generated from the FBS ensemble. The results were used to diagnose errors relevant for hydrometeorological applications, in particular a spatial displacement with characteristic length of at least 50 km (2500 km2) in the location of peak rainfall intensities for the cases studied.

A parameterization of slantwise convection in the WRF model

2021 ◽  
Author(s):  
Ting-Chen Chen ◽  
Man-Kong Yau ◽  
Daniel J. Kirshbaum
Keyword(s):  
General Circulation ◽  
Wrf Model ◽  
Real Data ◽  
General Circulation Models ◽  
Added Value ◽  
Cumulus Parameterization ◽  
Moisture Loss ◽  
Precipitation Event ◽  
Cyclonic Storm ◽  
Slantwise Convection

Abstract In this study, we introduce a parameterization scheme for slantwise convection (SC) to be considered for models that are too coarse to resolve slantwise convection explicitly (with a horizontal grid spacing coarser than 15 km or less). This SC scheme operates in a locally defined 2D cross-section perpendicular to the deep-layer-averaged thermal wind. It applies momentum tendency to adjust the environment toward slantwise neutrality with a prescribed adjustment timescale. Condensational heating and the associated moisture loss are also considered. To evaluate the added value of the SC scheme, we implement it in the Weather Research and Forecasting (WRF) model to supplement the existing cumulus parameterization schemes for upright convection and test for two different numerical setups: a 2D idealized, unforced release of conditional symmetric instability (CSI) in an initially conditionally stable environment, and a 3D real-data precipitation event containing both CSI and conditional instability along the cold front of a cyclonic storm near the UK. Both test cases show significant improvements for the coarse-gridded (40-km) simulations when parameterizing slantwise convection. Compared to the 40-km simulations with only the upright convection scheme, the counterparts with the additional SC scheme exhibit a larger extent of CSI neutralization, generate a stronger grid-resolved slantwise circulation, and produce greater amounts of precipitation, all in better agreement with the corresponding fine-gridded reference simulations. Given the importance of slantwise convection in midlatitude weather systems, our results suggest that there exist potential benefits of parameterizing slantwise convection in general circulation models.

Efficient Two-dimensional Acoustic Wave Finite-Difference Numerical Simulation in Strongly Heterogeneous Media Using the Adaptive Mesh Refinement (AMR) Technique

Geophysics ◽  
2021 ◽  
pp. 1-76
Author(s):  
Chunli Zhang ◽  
Wei Zhang
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Adaptive Mesh Refinement ◽  
Heterogeneous Media ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Grid Spacing ◽  
Time Step ◽  
Velocity Models ◽  
The Stability

The finite-difference method (FDM) is one of the most popular numerical methods to simulate seismic wave propagation in complex velocity models. If a uniform grid is applied in the FDM for heterogeneous models, the grid spacing is determined by the global minimum velocity to suppress dispersion and dissipation errors in the numerical scheme, resulting in spatial oversampling in higher-velocity zones. Then, the small grid spacing dictates a small time step due to the stability condition of explicit numerical schemes. The spatial oversampling and reduced time step will cause unnecessarily inefficient use of memory and computational resources in simulations for strongly heterogeneous media. To overcome this problem, we propose to use the adaptive mesh refinement (AMR) technique in the FDM to flexibly adjust the grid spacing following velocity variations. AMR is rarely utilized in acoustic wave simulations with the FDM due to the increased complexity of implementation, including its data management, grid generation and computational load balancing on high-performance computing platforms. We implement AMR for 2D acoustic wave simulation in strongly heterogeneous media based on the patch approach with the FDM. The AMR grid can be automatically generated for given velocity models. To simplify the implementation, we employ a well-developed AMR framework, AMReX, to carry out the complex grid management. Numerical tests demonstrate the stability, accuracy level and efficiency of the AMR scheme. The computation time is approximately proportional to the number of grid points, and the overhead due to the wavefield exchange and data structure is small.

IZOGRID - A new tool for setting up orthogonal curvilinear grids for oceanic modeling

2021 ◽  
Author(s):  
Alexander Shchepetkin
Keyword(s):  
Iterative Procedure ◽  
Cartesian Grid ◽  
Reference Points ◽  
Curvilinear Coordinates ◽  
Grid Spacing ◽  
Curvilinear Grids ◽  
Curvilinear Grid ◽  
Curvilinear Contour ◽  
Grid Points ◽  
Grid Nodes

<p>Virtually all modern structured-grid ocean modeling codes are written in orthogonal curvilinear coordinates in horizontal directions, yet the overwhelming majority of modeling studies are done using very simple grid setups - mostly rectangular patches of Mercator grids rotated to proper orientation.  Furthermore, in communities like ROMS, we even observe decline in both interest and skill of creating curvilinear grids over long term.  This is caused primarily by the dissatisfaction with the existing tools and procedures for grid generation due to inability to achieve acceptable level of orthogonality errors.  Clearly, this causes underutilization of full potential of the modeling codes.</p><p>To address these issues, a new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a compile-once - use forever software package.  Theoretically one can use Schwartz-Christoffel conformal transform to project a curvilinear contour onto rectangle, then draw a Cartesian grid on it, and, finally, apply the inverse transform (the one which maps the rectangle back to the original contour) to the Cartesian grid in order to obtain the orthogonal curvilinear grid which fits the contour.  However, in the general case, the forward transform is an iterative algorithm of Ives and Zacharias (1989), and it is not easily invertible, nor it is feasible to apply it to a two-dimensional object (grid) as opposite to just one-dimensional (contour) because of very large number of operations.  To circumvent this, the core of the new algorithm is essentially based on the numerical solution of the inverse problem by an iterative procedure - finding such distribution of grid points along the sides of curvilinear contour, that the direct conformal mapping of it onto rectangle turns this distribution into uniform one along each side of the rectangle.  Along its way, this procedure also finds the correct aspect ratio, which makes it possible to automatically chose the numbers of grid points in each direction to yield locally the same grid spacing in both horizontal directions.  The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure.  Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving a Dirichlet elliptic problem.  The latter is fairly standard, except that we use "mehrstellenverfahren" discretization, which yields fourth-order accuracy in the case of equal grid spacing in both directions.  The curvilinear contour is generated using splines (cubic or quintic) passing through the user-specified reference points, and, unlike all previous tools designed for the same purpose, it guarantees by the construction to yield the exact 90-degree angles at the corners of the curvilinear perimeter of grid.</p><p>Overall, with the combination of all the new features, it is shown that it is possible to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes in both directions are equal to each other.</p>

scholarly journals 3D model discretization in assessing urban solar potential: the effect of grid spacing on predicted solar irradiation

Solar Energy ◽  
2018 ◽  
Vol 176 ◽  
pp. 334-349 ◽  
Author(s):  
Giuseppe Peronato ◽  
Emmanuel Rey ◽  
Marilyne Andersen
Keyword(s):  
3D Model ◽  
Solar Irradiation ◽  
Grid Spacing

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

scholarly journals Explicit Prediction of Hail in a Long-Lasting Multicellular Convective System in Eastern China Using Multimoment Microphysics Schemes

2018 ◽  
Vol 75 (9) ◽  
pp. 3115-3137 ◽  
Author(s):  
Liping Luo ◽  
Ming Xue ◽  
Kefeng Zhu ◽  
Bowen Zhou
Keyword(s):  
Eastern China ◽  
Convective System ◽  
Distribution Characteristics ◽  
Grid Spacing ◽  
Particle Size Distributions ◽  
Growth Processes ◽  
Microphysics Scheme ◽  
Advanced Regional Prediction System ◽  
Regional Prediction ◽  
Size Sorting

Abstract During the afternoon of 28 April 2015, a multicellular convective system swept southward through much of Jiangsu Province, China, over about 7 h, producing egg-sized hailstones on the ground. The hailstorm event is simulated using the Advanced Regional Prediction System (ARPS) at 1-km grid spacing. Different configurations of the Milbrandt–Yau microphysics scheme are used, predicting one, two, and three moments of the hydrometeor particle size distributions (PSDs). Simulated reflectivity and maximum estimated size of hail (MESH) derived from the simulations are verified against reflectivity observed by operational S-band Doppler radars and radar-derived MESH, respectively. Comparisons suggest that the general evolution of the hailstorm is better predicted by the three-moment scheme, and neighborhood-based MESH evaluation further confirms the advantage of the three-moment scheme in hail size prediction. Surface accumulated hail mass, number, and hail distribution characteristics within simulated storms are examined across sensitivity experiments. Results suggest that multimoment schemes produce more realistic hail distribution characteristics, with the three-moment scheme performing the best. Size sorting is found to play a significant role in determining hail distribution within the storms. Detailed microphysical budget analyses are conducted for each experiment, and results indicate that the differences in hail growth processes among the experiments can be mainly ascribed to the different treatments of the shape parameter within different microphysics schemes. Both the differences in size sorting and hail growth processes contribute to the simulated hail distribution differences within storms and at the surface.

scholarly journals Calculation of Horseshoe Vortex Flow Without Numerical Mixing

1984 ◽  
Author(s):  
Joan G. Moore ◽  
John Moore
Keyword(s):  
Three Dimensional ◽  
Leading Edge ◽  
Horseshoe Vortex ◽  
Companion Paper ◽  
New Method ◽  
Uniform Grid ◽  
Grid Spacing ◽  
Three Dimensional Flow ◽  
Numerical Mixing ◽  
Well Posed

The usefulness of three-dimensional flow calculations has frequently been obscured by the numerical mixing present in the calculation methods. This paper describes a new method of forming the finite difference momentum equations. The new method results in well posed equations which introduce no numerical mixing. It may be used with orthogonal or non-orthogonal grids and with uniform or highly non-uniform grid spacing. The method is demonstrated by comparing it with upwind differencing on the calculation of a simple example. It is then used in an elliptic pressure-correction calculation procedure to calculate a leading edge horseshoe vortex about a Rankine half body. The results compare well with the experimental data presented in a companion paper.

scholarly journals The climatic mass balance of Svalbard glaciers: a 10-year simulation with a coupled atmosphere–glacier mass balance model

2016 ◽  
Vol 10 (3) ◽  
pp. 1089-1104 ◽  
Author(s):  
Kjetil S. Aas ◽  
Thorben Dunse ◽  
Emily Collier ◽  
Thomas V. Schuler ◽  
Terje K. Berntsen ◽  
...  
Keyword(s):  
Mass Balance ◽  
Detailed Comparison ◽  
Balance Model ◽  
Climate Projections ◽  
Glacier Mass Balance ◽  
Grid Spacing ◽  
Satellite Measurements ◽  
Mean Values ◽  
Ice Cap ◽  
A Site

Abstract. In this study we simulate the climatic mass balance of Svalbard glaciers with a coupled atmosphere–glacier model with 3 km grid spacing, from September 2003 to September 2013. We find a mean specific net mass balance of −257 mm w.e. yr−1, corresponding to a mean annual mass loss of about 8.7 Gt, with large interannual variability. Our results are compared with a comprehensive set of mass balance, meteorological, and satellite measurements. Model temperature biases of 0.19 and −1.9 °C are found at two glacier automatic weather station sites. Simulated climatic mass balance is mostly within about 100 mm w.e. yr−1 of stake measurements, and simulated winter accumulation at the Austfonna ice cap shows mean absolute errors of 47 and 67 mm w.e. yr−1 when compared to radar-derived values for the selected years 2004 and 2006. Comparison of modeled surface height changes from 2003 to 2008, and satellite altimetry reveals good agreement in both mean values and regional differences. The largest deviations from observations are found for winter accumulation at Hansbreen (up to around 1000 mm w.e. yr−1), a site where sub-grid topography and wind redistribution of snow are important factors. Comparison with simulations using 9 km grid spacing reveal considerable differences on regional and local scales. In addition, 3 km grid spacing allows for a much more detailed comparison with observations than what is possible with 9 km grid spacing. Further decreasing the grid spacing to 1 km appears to be less significant, although in general precipitation amounts increase with resolution. Altogether, the model compares well with observations and offers possibilities for studying glacier climatic mass balance on Svalbard both historically as well as based on climate projections.

Warm Cores, Eyewall Slopes, and Intensities of Tropical Cyclones Simulated by a 7-km-Mesh Global Nonhydrostatic Model

2016 ◽  
Vol 73 (11) ◽  
pp. 4289-4309 ◽  
Author(s):  
Tomoki Ohno ◽  
Masaki Satoh ◽  
Yohei Yamada
Keyword(s):  
Tropical Cyclones ◽  
Inner Core ◽  
Grid Spacing ◽  
Satellite Measurements ◽  
Warm Core ◽  
Nonhydrostatic Model ◽  
Proposed Model ◽  
Tangential Wind ◽  
Balanced Model ◽  
Horizontal Grid

Abstract Based on the data of a 1-yr simulation by a global nonhydrostatic model with 7-km horizontal grid spacing, the relationships among warm-core structures, eyewall slopes, and the intensities of tropical cyclones (TCs) were investigated. The results showed that stronger TCs generally have warm-core maxima at higher levels as their intensities increase. It was also found that the height of a warm-core maximum ascends (descends) as the TC intensifies (decays). To clarify how the height and amplitude of warm-core maxima are related to TC intensity, the vortex structures of TCs were investigated. By gradually introducing simplifications of the thermal wind balance, it was established that warm-core structures can be reconstructed using only the tangential wind field within the inner-core region and the ambient temperature profile. A relationship between TC intensity and eyewall slope was investigated by introducing a parameter that characterizes the shape of eyewalls and can be evaluated from satellite measurements. The authors found that the eyewall slope becomes steeper (shallower) as the TC intensity increases (decreases). Based on a balanced model, the authors proposed a relationship between TC intensity and eyewall slope. The result of the proposed model is consistent with that of the analysis using the simulation data. Furthermore, for sufficiently strong TCs, the authors found that the height of the warm-core maximum increases as the slope becomes steeper, which is consistent with previous observational studies. These results suggest that eyewall slopes can be used to diagnose the intensities and structures of TCs.

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