scholarly journals Nonlinear Balance in Terrain-Following Coordinates

2010 ◽  
Vol 138 (2) ◽  
pp. 605-624 ◽  
Author(s):  
Steven G. Decker
Keyword(s):  
Fluid Dynamics ◽  
Potential Vorticity ◽  
Wrf Model ◽  
Real Data ◽  
The Other ◽  
Weather Research And Forecasting ◽  
Geophysical Fluid Dynamics ◽  
Vertical Coordinate ◽  
Flat Terrain ◽  
Terrain Following

Abstract Potential vorticity (PV) is a powerful concept in geophysical fluid dynamics. One property of PV that makes it so powerful is that it may be inverted under certain conditions, one of which is the imposition of a balance constraint. Previous studies have made use of a particular nonlinear balance constraint suited to isobaric coordinates as part of their inversion procedures. The present study constructs and tests a new nonlinear balance constraint that may be applied directly to the output of the Weather Research and Forecasting (WRF) model on its native terrain-following vertical coordinate. Output from the nonlinear balance operator is examined in the context of idealized and real-data WRF forecasts, and the results indicate that the simplifications necessary to derive the nonlinear balance operator are justified on the synoptic and meso-α scales. On the other hand, once the scales resolved by the model are small enough, neglected terms reach magnitudes on the order of the retained terms, even over flat terrain. This suggests that the use of this operator within a PV inversion scheme that also uses the WRF vertical coordinate would not capture a divergent portion of the flow that may be significant.

An Evaluation of a Hybrid, Terrain-Following Vertical Coordinate in the WRF-Based RAP and HRRR Models

2020 ◽  
Vol 35 (3) ◽  
pp. 1081-1096 ◽  
Author(s):  
Jeffrey Beck ◽  
John Brown ◽  
Jimy Dudhia ◽  
David Gill ◽  
Tracy Hertneky ◽  
...  
Keyword(s):  
Complex Terrain ◽  
Wrf Model ◽  
Vertical Motion ◽  
Weather Research And Forecasting ◽  
Mountainous Terrain ◽  
Vertical Coordinate ◽  
Numerical Noise ◽  
Terrain Following ◽  
Model Equations ◽  
Real Time Simulations

Abstract A new hybrid, sigma-pressure vertical coordinate was recently added to the Weather Research and Forecasting (WRF) Model in an effort to reduce numerical noise in the model equations near complex terrain. Testing of this hybrid, terrain-following coordinate was undertaken in the WRF-based Rapid Refresh (RAP) and High-Resolution Rapid Refresh (HRRR) models to assess impacts on retrospective and real-time simulations. Initial cold-start simulations indicated that the majority of differences between the hybrid and traditional sigma coordinate were confined to regions downstream of mountainous terrain and focused in the upper levels. Week-long retrospective simulations generally resulted in small improvements for the RAP, and a neutral impact in the HRRR when the hybrid coordinate was used. However, one possibility is that the inclusion of data assimilation in the experiments may have minimized differences between the vertical coordinates. Finally, analysis of turbulence forecasts with the new hybrid coordinate indicate a significant reduction in spurious vertical motion over the full length of the Rocky Mountains. Overall, the results indicate a potential to improve forecast metrics through implementation of the hybrid coordinate, particularly at upper levels, and downstream of complex terrain.

scholarly journals Estimating Daytime Planetary Boundary Layer Heights over a Valley from Rawinsonde Observations at a Nearby Airport: An Application to the Page Valley in Virginia, United States

2016 ◽  
Vol 55 (3) ◽  
pp. 791-809 ◽  
Author(s):  
Temple R. Lee ◽  
Stephan F. J. De Wekker
Keyword(s):  
Boundary Layer ◽  
Planetary Boundary Layer ◽  
Weather Forecasting ◽  
Wrf Model ◽  
Heat Fluxes ◽  
Weather Research And Forecasting ◽  
Dispersion Modeling ◽  
Blue Ridge Mountains ◽  
Terrain Following ◽  
Regional Reanalysis

AbstractThe planetary boundary layer (PBL) height is an essential parameter required for many applications, including weather forecasting and dispersion modeling for air quality. Estimates of PBL height are not easily available and often come from twice-daily rawinsonde observations at airports, typically at 0000 and 1200 UTC. Questions often arise regarding the applicability of PBL heights retrieved from these twice-daily observations to surrounding locations. Obtaining this information requires knowledge of the spatial variability of PBL heights. This knowledge is particularly limited in regions with mountainous terrain. The goal of this study is to develop a method for estimating daytime PBL heights in the Page Valley, located in the Blue Ridge Mountains of Virginia. The approach includes using 1) rawinsonde observations from the nearest sounding station [Dulles Airport (IAD)], which is located 90 km northeast of the Page Valley, 2) North American Regional Reanalysis (NARR) output, and 3) simulations with the Weather Research and Forecasting (WRF) Model. When selecting days on which PBL heights from NARR compare well to PBL heights determined from the IAD soundings, it is found that PBL heights are higher (on the order of 200–400 m) over the Page Valley than at IAD and that these differences are typically larger in summer than in winter. WRF simulations indicate that larger sensible heat fluxes and terrain-following characteristics of PBL height both contribute to PBL heights being higher over the Page Valley than at IAD.

scholarly journals Hybrid Mass Coordinate in WRF-ARW and Its Impact on Upper-Level Turbulence Forecasting

2019 ◽  
Vol 147 (3) ◽  
pp. 971-985 ◽  
Author(s):  
Sang-Hun Park ◽  
Joseph B. Klemp ◽  
Jung-Hoon Kim
Keyword(s):  
Wrf Model ◽  
Real Data ◽  
Artificial Noise ◽  
Test Case ◽  
Surface Boundary ◽  
Vertical Coordinate ◽  
Numerical Errors ◽  
Mountainous Regions ◽  
Upper Level ◽  
Upper Level Jet

Abstract Although a terrain-following vertical coordinate is well suited for the application of surface boundary conditions, it is well known that the influences of the terrain on the coordinate surfaces can contribute to increase numerical errors, particularly over steep topography. To reduce these errors, a hybrid sigma–pressure coordinate is formulated in the Weather Research and Forecasting (WRF) Model, and its effects are illustrated for both an idealized test case and a real-data forecast for upper-level turbulence. The idealized test case confirms that with the basic sigma coordinate, significant upper-level disturbances can be produced due to numerical errors that arise as the advection of strong horizontal flow is computed along coordinate surfaces that are perturbed by smaller-scale terrain influences. With the hybrid coordinate, this artificial noise is largely eliminated as the mid- and upper-level coordinate surfaces correspond much more closely to constant pressure surfaces. In real-data simulations for upper-level turbulence forecasting, the WRF Model using the basic sigma coordinate tends to overpredict the strength of upper-air turbulence over mountainous regions because of numerical errors arising as a strong upper-level jet is advected along irregular coordinate surfaces. With the hybrid coordinate, these errors are reduced, resulting in an improved forecast of upper-level turbulence. Analysis of kinetic energy spectra for these simulations confirms that artificial amplitudes in the smaller scales at upper levels that arise with the basic sigma coordinate are effectively removed when the hybrid coordinate is used.

Introduction to Geophysical Fluid Dynamics

1998 ◽  
Author(s):  
Rick Salmon
Keyword(s):  
Fluid Dynamics ◽  
Shallow Water ◽  
Potential Vorticity ◽  
Shallow Water Equations ◽  
Coordinate Frame ◽  
Geophysical Fluid Dynamics ◽  
Homogeneous Fluid ◽  
The One ◽  
Quasigeostrophic Equations ◽  
Inertia Gravity Waves

This second chapter offers a brief introduction to geophysical fluid dynamics—the dynamics of rotating, stratified flows. We start with the shallow water equations, which govern columnar motion in a thin layer of homogeneous fluid. Roughly speaking, the solutions of the shallow-water equations comprise two types of motion: ageostrophic motions, including inertia-gravity waves, on the one hand, and nearly geostrophic motions on the other. In rapidly rotating flow, these two types of motion may, in some sense, decouple. We seek simpler equations that describe only the nearly geostrophic motion. The simplest such equations are the quasigeostrophic equations. In the quasigcostrophic equations, potential vorticity plays the key role: The potential vorticity completely determines the velocity field that transports it, thereby controlling the whole dynamics. We begin by generalizing our previously derived fluid equations to a rotating coordinate frame.

scholarly journals Prediction of Clouds and Rain Using a z-Coordinate Nonhydrostatic Model

2006 ◽  
Vol 134 (12) ◽  
pp. 3625-3643 ◽  
Author(s):  
J. Steppeler ◽  
H. W. Bitzer ◽  
Z. Janjic ◽  
U. Schättler ◽  
P. Prohl ◽  
...  
Keyword(s):  
Numerical Models ◽  
Real Data ◽  
High Mountains ◽  
Grid Spacing ◽  
Physical Processes ◽  
Atmospheric Flow ◽  
Vertical Coordinate ◽  
The Earth ◽  
Systematic Improvement ◽  
Terrain Following

Abstract The most common option for numerical models of the atmosphere is to use model layers following the surface of the earth, using a terrain-following vertical coordinate. The present paper investigates the forecast of clouds and precipitation using the z-coordinate nonhydrostatic version of the Lokalmodell (LM-z). This model uses model layers that are parallel to the surface of the sphere and consequently intersect the orography. Physical processes are computed on a special grid, allowing adequate grid spacing even over high mountains. In other respects the model is identical to the nonhydrostatic terrain-following version of the LM, which in a number of European countries is used for operational mesoscale forecasting. The terrain-following version of the LM (LM-tf) is used for comparison with the forecasts of the LM-z. Terrain-following coordinates are accurate when the orography is shallow and smooth, while z-coordinate models need not satisfy this condition. Because the condition of smooth orography is rarely satisfied in reality, z-coordinate models should lead to a better representation of the atmospheric flow near mountains and consequently to a better representation of fog, low stratus, and precipitation. A number of real-data cases, computed with a grid spacing of 7 and 14 km, are investigated. A total of 39 real-data cases have been used to evaluate forecast scores. A rather systematic improvement of precipitation forecasts resulted in a substantial increase of threat scores. Furthermore, RMS verification against radiosondes showed an improvement of the 24-h forecast, both for wind and temperature. To investigate the possibility of flow separation at mountain tops, the flow in the lee of southern Italy was investigated.

An Immersed Boundary Method for the Weather Research and Forecasting Model

2010 ◽  
Vol 138 (3) ◽  
pp. 796-817 ◽  
Author(s):  
Katherine A. Lundquist ◽  
Fotini Katopodes Chow ◽  
Julie K. Lundquist
Keyword(s):  
Immersed Boundary Method ◽  
Complex Terrain ◽  
Wrf Model ◽  
Neumann Boundary ◽  
Weather Research And Forecasting ◽  
Immersed Boundary ◽  
Mesoscale Models ◽  
Boundary Method ◽  
Terrain Following ◽  
Weather Research

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.

Large-Eddy Simulation over Complex Terrain Using an Improved Immersed Boundary Method in the Weather Research and Forecasting Model

2018 ◽  
Vol 146 (9) ◽  
pp. 2781-2797 ◽  
Author(s):  
Jingyi Bao ◽  
Fotini Katopodes Chow ◽  
Katherine A. Lundquist
Keyword(s):  
Boundary Condition ◽  
Immersed Boundary Method ◽  
Complex Terrain ◽  
Weather Research And Forecasting ◽  
Immersed Boundary ◽  
Flat Terrain ◽  
Boundary Method ◽  
Terrain Following ◽  
Bolund Hill ◽  
Askervein Hill

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.

scholarly journals Mesoscale to Microscale Simulations over Complex Terrain with the Immersed Boundary Method in the Weather Research and Forecasting Model

2020 ◽  
Vol 148 (2) ◽  
pp. 577-595 ◽  
Author(s):  
David J. Wiersema ◽  
Katherine A. Lundquist ◽  
Fotini Katopodes Chow
Keyword(s):  
Boundary Conditions ◽  
Immersed Boundary Method ◽  
Complex Terrain ◽  
Wrf Model ◽  
Weather Research And Forecasting ◽  
Immersed Boundary ◽  
Eddy Simulation ◽  
Boundary Method ◽  
Large Eddy ◽  
Terrain Following

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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