2.7. Passive scalar transport and dispersion over an idealized hill

2.7.1. Background

This is an example of transport and dispersion of a scalar in the presence of idealized topography. The idealized terrain is based on the Witch of Agnesi, and a passive tracer is released on the lee side of the hill.

2.7.2. Input parameters

  • Number of grid points: \([N_x,N_y,N_z]=[504,498,90]\)

  • Isotropic grid spacings in the horizontal directions: \([\Delta x,\Delta y]=[4,4]\) m, the minimum vertical grid at the surface is \(\Delta z=3.6\) m and stretched with verticalDeformFactor \(=0.26\)

  • Domain size: \([2.16 \times 1.99 \times 1.44]\) km

  • Model time step: \(0.01\) s

  • Advection scheme: 5th-order upwind

  • Time scheme: 3rd-order Runge Kutta

  • Geostrophic wind: \([U_g,V_g]=[8,0]\) m/s

  • Latitude: \(54.0^{\circ}\) N

  • Surface potential temperature: \(300\) K

  • Potential temperature profile:

\[\begin{split}\partial{\theta}/\partial z = \begin{cases} 0 & \text{if $z$ $\le$ 500 m}\\ 0.003 & \text{if $z$ > 500 m} \end{cases}\end{split}\]

  • Rayleigh damping layer: uppermost \(600\) m of the domain

  • Initial perturbations: \(\pm 0.25\) K

  • Depth of perturbations: \(375\) m

  • Top boundary condition: free slip

  • Lateral boundary conditions: periodic

  • Time period: \(1\) h

2.7.3. Execute FastEddy

See Build and Run for general instructions on how to build and run FastEddy on NSF NCAR’s High Performance Computing machines.

Note that this example requires creation of a terrain and source specification files. Follow the sequence of steps below.

  1. Execute the Jupyter notebook provided in tutorials/notebooks/Dispersion_PrepTerrain.ipynb to create the topography file Topography_504x498.dat that corresponds to a Witch of Agnesi hill of 15 m height.

  2. Execute the Jupyter notebook provided in /tutorial/notebooks/Dispersion_PrepAuxSrc.ipynb to create the source specification input file. This example will add two sources at the first vertical grid levels upstream (x = 930 m) and downstream (x = 1082 m) of the hill. The emissions begin \(45\) min into the simulation.

Two FastEddy simulation setups are provided for this tutorial, corresponding to weakly stable (Example07_DISPERSION_SBL.in) and convective conditions (Example07_DISPERSION_CBL.in). The terrain preparation and source input file steps only need to be carried out once. Additionally, the CBL case is set up to demonstrate the use of a rank-wise binary output mode in FastEddy for efficient dumping of the model state to file. Personalize and use the batch submission script /scripts/batch_jobs/fasteddy_convert_pbs_script_casper.sh which will invoke a python script (/scripts/python_utilities/post-processing/FEbinaryToNetCDF.py) to convert the rank-wise binary files from each output timestep into a single aggregate NetCDF output file per timestep analogous to those resulting from the SBL case. Users can run the following conda activate command if running on Casper:

conda activate /glade/u/fehelp/casper/conda-envs/mpi4py-casper-oneapi-2024.2.1-openmpi-5.0.6

2.7.4. Visualize the output

  1. Open the Jupyter notebook entitled MAKE_FE_TUTORIAL_PLOTS.ipynb.

  2. Under the “Define parameters” section, modify path_base, specifying the full path to the Example07_DISPERSION_SBL subdirectory, but don’t include Example07_DISPERSION_SBL subdirectory. Be sure to include a trailing slash /).

  3. Under the “Define parameters” section, modify case to set its value to dispersion.

  4. Run the Jupyter notebook.

  5. The resulting XY cross section png plots will be placed in a FIGS subdirectory of the Example07_DISPERSION_SBL directory.

XY-plane views of instantaneous velocity components and potential temperature for the SBL case at \(t=1\) h (FE_DISPERSION.360000). The contour lines in the \(u\) panel display terrain elevation:

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XY-plane views of instantaneous velocity components and potential temperature for the CBL case at \(t=1\) h (FE_DISPERSION.360000). The contour lines in the \(u\) panel display terrain elevation:

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XY-plane views of instantaneous plume dispersion for the SBL case at \(z=30\) m AGL and different times (\(t=50,55,60\) min), corresponding to the windward release:

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XY-plane views of instantaneous plume dispersion for the CBL case at \(z=30\) m AGL and different times (\(t=50,55,60\) min), corresponding to the windward release:

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YZ-plane views of instantaneous plume dispersion for the SBL case at several downstream distances (\(t=1\) h, FE_DISPERSION.360000), corresponding to the windward release:

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YZ-plane views of instantaneous plume dispersion for the CBL case at several downstream distances (\(t=1\) h, FE_DISPERSION.360000), corresponding to the windward release:

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2.7.5. Analyze the output

  • How does the terrain impact gets altered by the different stability conditions?

  • What are the differences in plume dispersion between stable and convective condtions?

  • How does downstream distance affect structure of the plume?