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Jeffrey D. Mirocha and Katherine A. Lundquist

Abstract

To facilitate multiscale simulation using the Weather Research and Forecasting Model, vertical mesh refinement for one-way concurrent nested simulation was recently introduced. Grid refinement in the vertical dimension removes the requirement of different grid aspect ratios on the bounding versus the nested domain, such that results from refinement are in the horizontal directions only, and thereby can also reduce numerical errors on the bounding domain arising from large aspect ratios in the presence of complex terrain. Herein, the impacts of vertical grid refinement on the evolving downstream flow in nested large-eddy simulations are evaluated in relation to other model configuration choices, including turbulence subfilter-scale (SFS) stress models, mesh configuration, and alternative methods for calculating several near-surface flow parameters. Although vertical nesting requires coarsening of the vertical grid on the bounding domain, leading to a smaller range of resolved turbulence scales in the nest’s lateral boundary conditions, parameter values within the nested domains are generally only minimally impacted, relative to nesting using the same vertical grid on each domain. Two dynamic SFS models examined herein generally improved the simulated mean wind speed, turbulence kinetic energy, stresses and spectra, on both domains, and accelerated equilibration rates within nested domains, relative to two constant coefficient models. A new method of extrapolating horizontal velocity components to near-surface locations at nested domain lateral boundaries, and a correction to the calculation of deformation elements near the surface, are each shown to slightly alter the mean parameter values, yet only minimally impact equilibration rates within the nested domain.

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Katherine A. Lundquist, Fotini Katopodes Chow, and Julie K. Lundquist

Abstract

This paper describes a three-dimensional immersed boundary method (IBM) that facilitates the explicit resolution of complex terrain within the Weather Research and Forecasting (WRF) model. Two interpolation methods—trilinear and inverse distance weighting (IDW)—are used at the core of the IBM algorithm. This work expands on the previous two-dimensional IBM algorithm of Lundquist et al., which uses bilinear interpolation. Simulations of flow over a three-dimensional hill are performed with WRF’s native terrain-following coordinate and with both IB methods. Comparisons of flow fields from the three simulations show excellent agreement, indicating that both IB methods produce accurate results. IDW proves more adept at handling highly complex urban terrain, where the trilinear interpolation algorithm fails. This capability is demonstrated by using the IDW core to model flow in Oklahoma City, Oklahoma, from intensive observation period 3 (IOP3) of the Joint Urban 2003 field campaign. Flow in Oklahoma City is simulated concurrently with an outer domain with flat terrain using one-way nesting to generate a turbulent flow field. Results from the IBM-WRF simulation of IOP3 compare well with observations from the field campaign, as well as with results from an urban computational fluid dynamics code, Finite Element Model in 3-Dimensions and Massively Parallelized (FEM3MP), which used body-fitted coordinates. Using the FAC2 performance metric from Chang and Hanna, which is the fraction of predictions within a factor of 2 of observations, IBM-WRF achieves 100% and 71% for velocity predictions using cup and sonic anemometer observations, respectively. For the passive scalar, 53% of the model predictions meet the FAC5 (factor of 5) criteria.

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Katherine A. Lundquist, Fotini Katopodes Chow, and Julie K. Lundquist

Abstract

This paper describes an immersed boundary method that facilitates the explicit resolution of complex terrain within the Weather Research and Forecasting (WRF) model. Mesoscale models, such as WRF, are increasingly used for high-resolution simulations, particularly in complex terrain, but errors associated with terrain-following coordinates degrade the accuracy of the solution. The use of an alternative-gridding technique, known as an immersed boundary method, alleviates coordinate transformation errors and eliminates restrictions on terrain slope that currently limit mesoscale models to slowly varying terrain. Simulations are presented for canonical cases with shallow terrain slopes, and comparisons between simulations with the native terrain-following coordinates and those using the immersed boundary method show excellent agreement. Validation cases demonstrate the ability of the immersed boundary method to handle both Dirichlet and Neumann boundary conditions. Additionally, realistic surface forcing can be provided at the immersed boundary by atmospheric physics parameterizations, which are modified to include the effects of the immersed terrain. Using the immersed boundary method, the WRF model is capable of simulating highly complex terrain, as demonstrated by a simulation of flow over an urban skyline.

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Jingyi Bao, Fotini Katopodes Chow, and Katherine A. Lundquist

Abstract

The Weather Research and Forecasting (WRF) Model is increasingly being used for higher-resolution atmospheric simulations over complex terrain. With increased resolution, resolved terrain slopes become steeper, and the native terrain-following coordinates used in WRF result in numerical errors and instability. The immersed boundary method (IBM) uses a nonconformal grid with the terrain surface represented through interpolated forcing terms. Lundquist et al.’s WRF-IBM implementation eliminates the limitations of WRF’s terrain-following coordinate and was previously validated with a no-slip boundary condition for urban simulations and idealized terrain. This paper describes the implementation of a log-law boundary condition into WRF-IBM to extend its applicability to general atmospheric complex terrain simulations. The implementation of the improved WRF-IBM boundary condition is validated for neutral flow over flat terrain and the complex terrain cases of Askervein Hill, Scotland, and Bolund Hill, Denmark. First, comparisons are made to similarity theory and standard WRF results for the flat terrain case. Then, simulations of flow over the moderately sloped Askervein Hill are used to demonstrate agreement between the IBM and terrain-following WRF results, as well as agreement with observations. Finally, Bolund Hill simulations show that WRF-IBM can handle steep topography (standard WRF fails) and compares well to observations. Overall, the new WRF-IBM boundary condition shows improved performance, though the leeside representation of the flow can be potentially further improved.

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David J. Wiersema, Katherine A. Lundquist, and Fotini Katopodes Chow

Abstract

Improvements to the Weather Research and Forecasting (WRF) Model are made to enable multiscale simulations over highly complex terrain with dynamically downscaled boundary conditions from the mesoscale to the microscale. Over steep terrain, the WRF Model develops numerical errors that are due to grid deformation of the terrain-following coordinates. An alternative coordinate system, the immersed boundary method (IBM), has been implemented into WRF, allowing for simulations over highly complex terrain; however, the new coordinate system precluded nesting within mesoscale simulations using WRF’s native terrain-following coordinates. Here, the immersed boundary method and WRF’s grid-nesting framework are modified to seamlessly work together. This improved framework for the first time allows for large-eddy simulation over complex (urban) terrain with IBM to be nested within a typical mesoscale WRF simulation. Simulations of the Joint Urban 2003 field campaign in Oklahoma City, Oklahoma, are performed using a multiscale five-domain nested configuration, spanning horizontal grid resolutions from 6 km to 2 m. These are compared with microscale-only simulations with idealized lateral boundary conditions and with observations of wind speed/direction and SF6 concentrations from a controlled release from intensive observation period 3. The multiscale simulation, which is configured independent of local observations, shows similar model skill predicting wind speed/direction and improved skill predicting SF6 concentrations when compared with the idealized simulations, which require use of observations to set mean flow conditions. Use of this improved multiscale framework shows promise for enabling large-eddy simulation over highly complex terrain with dynamically downscaled boundary conditions from mesoscale models.

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Robert S. Arthur, Katherine A. Lundquist, and Joseph B. Olson

Abstract

The terrain-following vertical coordinate system used by many atmospheric models, including the Weather Research and Forecasting (WRF) Model, is prone to errors in regions of complex terrain. These errors stem, in part, from the calculation of horizontal gradients within the diffusion term of the momentum or scalar evolution equations. In WRF, such gradients can be calculated along coordinate surfaces, or using metric terms that help account for grid skewness. However, neither of these options ensures a truly horizontal gradient calculation, especially if a grid cell is skewed enough that the heights of the neighboring grid points used in the calculation fall outside the vertical range of the cell. In this work, an improved scheme that uses Taylor series approximations to vertically interpolate variables to the level necessary for a truly horizontal gradient calculation is implemented in WRF for the diffusion of potential temperature. The scheme is validated using an atmosphere-at-rest configuration, in which spurious flows develop only as a result of numerical errors and can thus be used as a proxy for model performance. Following validation, the method is applied to the simulation of cold-air pools (CAPs), which occur in regions of complex terrain and are characterized by strong near-surface temperature gradients. Using the truly horizontal scheme, idealized simulations demonstrate reduced numerical mixing in a quiescent CAP, and a realistic case study in the Columbia River basin shows a reduction in positive wind speed bias by up to roughly 20% compared to observations from the Second Wind Forecast Improvement Project.

Open access
Robert S. Arthur, Katherine A. Lundquist, Jeffrey D. Mirocha, and Fotini K. Chow

Abstract

Topographic effects on radiation, including both topographic shading and slope effects, are included in the Weather Research and Forecasting (WRF) Model, and here they are made compatible with the immersed boundary method (IBM). IBM is an alternative method for representing complex terrain that reduces numerical errors over sloped terrain, thus extending the range of slopes that can be represented in WRF simulations. The implementation of topographic effects on radiation is validated by comparing land surface fluxes, as well as temperature and velocity fields, between idealized WRF simulations both with and without IBM. Following validation, the topographic shading implementation is tested in a semirealistic simulation of flow over Granite Mountain, Utah, where topographic shading is known to affect downslope flow development in the evening. The horizontal grid spacing is 50 m and the vertical grid spacing is approximately 8–27 m near the surface. Such a case would fail to run in WRF with its native terrain-following coordinates because of large local slope values reaching up to 55°. Good agreement is found between modeled surface energy budget components and observations from the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) program at a location on the east slope of Granite Mountain. In addition, the model captures large spatiotemporal inhomogeneities in the surface sensible heat flux that are important for the development of thermally driven flows over complex terrain.

Open access
Robert S. Arthur, Katherine A. Lundquist, David J. Wiersema, Jingyi Bao, and Fotini K. Chow

Abstract

The terrain-following coordinate system used by many atmospheric models can cause numerical instabilities due to discretization errors as resolved terrain slopes increase and the grid becomes highly skewed. The immersed boundary (IB) method, which does not require the grid to conform to the terrain, has been shown to alleviate these errors, and has been used successfully for high-resolution atmospheric simulations over steep terrain, including vertical building surfaces. Since many previous applications of IB methods to atmospheric models have used very fine grid resolution (5 m or less), the present study seeks to evaluate IB method performance over a range of grid resolutions and aspect ratios. Two classes of IB algorithms, velocity reconstruction and shear stress reconstruction, are tested within the common framework of the Weather Research and Forecasting (WRF) Model. Performance is evaluated in two test cases, one with flat terrain and the other with the topography of Askervein Hill, both under neutrally stratified conditions. WRF-IB results are compared to similarity theory, observations, and native WRF results. Despite sensitivity to the location at which the IB intersects the model grid, the velocity reconstruction IB method shows consistent performance when used with a hybrid RANS/LES surface scheme. The shear stress reconstruction IB method is not sensitive to the grid intersection, but is less consistent and near-surface velocity errors can occur at coarse resolutions. This study represents an initial investigation of IB method variability across grid resolutions in WRF. Future work will focus on improving IB method performance at intermediate to coarse resolutions.

Open access
Robert S. Arthur, Jeffrey D. Mirocha, Katherine A. Lundquist, and Robert L. Street

Abstract

A canopy model framework is implemented in the Weather Research and Forecasting Model to improve the accuracy of large-eddy simulations (LES) of the atmospheric boundary layer (ABL). The model includes two options that depend on the scale of surface roughness elements. A resolved canopy model, typically used to model flow through vegetation canopies, is employed when roughness elements are resolved by the vertical LES grid. In the case of unresolved roughness, a modified “pseudocanopy model” is developed to distribute drag over a shallow layer above the surface. Both canopy model options are validated against idealized test cases in neutral stability conditions and are shown to improve surface layer velocity profiles relative to simulations employing Monin–Obukhov similarity theory (MOST), which is commonly used as a surface boundary condition in ABL models. Use of the canopy model framework also leads to increased levels of resolved turbulence kinetic energy and turbulent stresses. Because LES of the ABL has a well-known difficulty recovering the expected logarithmic velocity profile (log law) in the surface layer, particular focus is placed on using the pseudocanopy model to alleviate this issue over a range of model configurations. Tests with varying surface roughness values, LES closures, and grid aspect ratios confirm that the pseudocanopy model generally improves log-law agreement relative to simulations that employ a standard MOST boundary condition. The canopy model framework thus represents a low-cost, easy-to-implement method for improving LES of the ABL.

Open access
Megan H. Daniels, Katherine A. Lundquist, Jeffrey D. Mirocha, David J. Wiersema, and Fotini K. Chow

Abstract

Mesoscale atmospheric models are increasingly used for high-resolution (<3 km) simulations to better resolve smaller-scale flow details. Increased resolution is achieved using mesh refinement via grid nesting, a procedure where multiple computational domains are integrated either concurrently or in series. A constraint in the concurrent nesting framework offered by the Weather Research and Forecasting (WRF) Model is that mesh refinement is restricted to the horizontal dimensions. This limitation prevents control of the grid aspect ratio, leading to numerical errors due to poor grid quality and preventing grid optimization. Herein, a procedure permitting vertical nesting for one-way concurrent simulation is developed and validated through idealized cases. The benefits of vertical nesting are demonstrated using both mesoscale and large-eddy simulations (LES). Mesoscale simulations of the Terrain-Induced Rotor Experiment (T-REX) show that vertical grid nesting can alleviate numerical errors due to large aspect ratios on coarse grids, while allowing for higher vertical resolution on fine grids. Furthermore, the coarsening of the parent domain does not result in a significant loss of accuracy on the nested domain. LES of neutral boundary layer flow shows that, by permitting optimal grid aspect ratios on both parent and nested domains, use of vertical nesting yields improved agreement with the theoretical logarithmic velocity profile on both domains. Vertical grid nesting in WRF opens the path forward for multiscale simulations, allowing more accurate simulations spanning a wider range of scales than previously possible.

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