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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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Bowen Zhou, Jason S. Simon, and Fotini K. Chow

Abstract

Numerical simulations of a convective boundary layer (CBL) are performed to investigate model behavior in the terra incognita, also known as the gray zone. The terra incognita of the CBL refers to a range of model grid spacing that is comparable to the size of the most energetic convective eddies, which are on the order of the boundary layer depth. Using the Rayleigh–Bénard thermal instability as reference, a set of idealized simulations is used to show that gray zone modeling is not only a numerical challenge, but also poses dynamical difficulties. When the grid spacing falls within the CBL gray zone, grid-dependent convection can occur. The size of the initial instability structures is set by the grid spacing rather than the natural state of the flow. This changes higher-order flow statistics and poses fundamental difficulties for gray zone modeling applications.

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Susanne Drechsel, Georg J. Mayr, Michel Chong, and Fotini K. Chow

Abstract

Dual-Doppler lidar volume scans for 3D wind retrieval must accommodate the conflicting goals of dense spatial coverage and short scan duration. In this work, various scanning strategies are evaluated with semisynthetic wind fields from analytical solutions and numerical simulations over flat and complex terrain using the Multiple-Doppler Synthesis and Continuity Adjustment Technique (MUSCAT) retrieval algorithm. The focus of this study is to determine how volume scan strategies affect performance of the wind retrieval algorithm. Interlaced scanning methods that take into account actual maximum measurement ranges are found to be optimal because they provide the best trade-off between retrieval accuracy, volume coverage, and scan time. A recommendation for scanning strategies is given, depending on actual measurement ranges, the variability of the wind situation, and the trade-off between spatial coverage and temporal smoothing.

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Juerg Schmidli, Gregory S. Poulos, Megan H. Daniels, and Fotini K. Chow

Abstract

The dynamics that govern the evolution of nighttime flows in a deep valley, California’s Owens Valley, are analyzed. Measurements from the Terrain-Induced Rotor Experiment (T-REX) reveal a pronounced valley-wind system with often nonclassical flow evolution. Two cases with a weak high pressure ridge over the study area but very different valley flow evolution are presented. The first event is characterized by the appearance of a layer of southerly flow after midnight local time, sandwiched between a thermally driven low-level downvalley (northerly) flow and a synoptic northwesterly flow aloft. The second event is characterized by an unusually strong and deep downvalley jet, exceeding 15 m s−1. The analysis is based on the T-REX measurement data and the output of high-resolution large-eddy simulations using the Advanced Regional Prediction System (ARPS). Using horizontal grid spacings of 1 km and 350 m, ARPS reproduces the observed flow features for these two cases very well. It is found that the low-level along-valley forcing of the valley wind is the result of a superposition of the local thermal forcing and a midlevel (2–2.5 km MSL) along-valley pressure forcing. The analysis shows that the large difference in valley flow evolution derives primarily from differences in the midlevel pressure forcing, and that the Owens Valley is particularly susceptible to these midlevel external influences because of its specific geometry. The results demonstrate the delicate interplay of forces that can combine to determine the valley flow structure on any given night.

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Andreas P. Weigel, Fotini K. Chow, Mathias W. Rotach, Robert L. Street, and Ming Xue

Abstract

This paper analyzes the three-dimensional flow structure and the heat budget in a typical medium-sized and steep Alpine valley—the Riviera Valley in southern Switzerland. Aircraft measurements from the Mesoscale Alpine Programme (MAP)-Riviera field campaign reveal a very pronounced valley-wind system, including a strong curvature-induced secondary circulation in the southern valley entrance region. Accompanying radio soundings show that the growth of a well-mixed layer is suppressed, even under convective conditions. Our analyses are based on the MAP-Riviera measurement data and the output of high-resolution large-eddy simulations using the Advanced Regional Prediction System (ARPS). Three sunny days of the measurement campaign are simulated. Using horizontal grid spacings of 350 and 150 m (with a vertical spacing as fine as 20 m), the model reproduces the observed flow features very well. The ARPS output data are then used to calculate the components of the heat budget of the valley atmosphere, first in profiles over the valley base and then as averages over almost the entire valley volume. The analysis shows that the suppressed growth of the well-mixed layer is due to the combined effect of cold-air advection in the along-valley direction and subsidence of warm air from the free atmosphere aloft. It is further influenced by the local cross-valley circulation. This had already been hypothesized on the basis of measurement data and is now confirmed through a numerical model. Averaged over the entire valley, subsidence turns out to be one of the main heating sources of the valley atmosphere and is of comparable magnitude to turbulent heat flux divergence. On the mornings of two out of the three simulation days, this subsidence is even identified as the only major heating source and thus appears to be an important driving mechanism for the onset of thermally driven upvalley winds.

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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.

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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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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
Luca Delle Monache, Julie K. Lundquist, Branko Kosović, Gardar Johannesson, Kathleen M. Dyer, Roger D. Aines, Fotini K. Chow, Rich D. Belles, William G. Hanley, Shawn C. Larsen, Gwen A. Loosmore, John J. Nitao, Gayle A. Sugiyama, and Philip J. Vogt

Abstract

A methodology combining Bayesian inference with Markov chain Monte Carlo (MCMC) sampling is applied to a real accidental radioactive release that occurred on a continental scale at the end of May 1998 near Algeciras, Spain. The source parameters (i.e., source location and strength) are reconstructed from a limited set of measurements of the release. Annealing and adaptive procedures are implemented to ensure a robust and effective parameter-space exploration. The simulation setup is similar to an emergency response scenario, with the simplifying assumptions that the source geometry and release time are known. The Bayesian stochastic algorithm provides likely source locations within 100 km from the true source, after exploring a domain covering an area of approximately 1800 km × 3600 km. The source strength is reconstructed with a distribution of values of the same order of magnitude as the upper end of the range reported by the Spanish Nuclear Security Agency. By running the Bayesian MCMC algorithm on a large parallel cluster the inversion results could be obtained in few hours as required for emergency response to continental-scale releases. With additional testing and refinement of the methodology (e.g., tests that also include the source geometry and release time among the unknown source parameters), as well as with the continuous and rapid growth of computational power, the approach can potentially be used for real-world emergency response in the near future.

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