Merge pull request #16 from firedrakeproject/TBendall/volcanic_ash

Transport of volcanic ash

transport/plot_volcanic_ash.py

@@ -0,0 +1,129 @@
+"""
+Plots the volcanic ash dispersion test case.
+"""
+import cartopy.crs as ccrs
+import matplotlib.pyplot as plt
+from netCDF4 import Dataset
+import numpy as np
+from matplotlib.colors import ListedColormap
+from tomplot import (set_tomplot_style, tomplot_contours, tomplot_cmap,
+                     plot_contoured_field, add_colorbar_fig,
+                     tomplot_field_title, extract_gusto_coords,
+                     extract_gusto_field, plot_field_quivers)
+
+# ---------------------------------------------------------------------------- #
+# Directory for results and plots
+# ---------------------------------------------------------------------------- #
+# When copying this example these should not be relative to this file
+results_dir = f'/home/thomas/firedrake/src/gusto/case_studies/results/volcanic_ash/'
+plot_dir = f'/home/thomas/firedrake/src/gusto/case_studies/figures'
+results_file_name = f'{results_dir}/field_output.nc'
+plot_stem = f'{plot_dir}/volcanic_ash'
+# ---------------------------------------------------------------------------- #
+# Things that should be altered based on the plot
+# ---------------------------------------------------------------------------- #
+field_name = 'ash'
+colour_scheme = 'gist_heat_r'
+field_label = 'Ash / ppm'
+contour_method = 'tricontour'
+plot_wind = False
+wind_name_X, wind_name_Y = 'VelocityX', 'VelocityY'
+pole_longitude = 175.0
+pole_latitude = 35.0
+new_lon_extents = (-30, 30)
+new_lat_extents = (-30, 30)
+new_lon_xlims = (-35, 35)
+new_lat_ylims = (-35, 35)
+Lx = 1000.0
+# ---------------------------------------------------------------------------- #
+# Things that are likely the same for all plots
+# ---------------------------------------------------------------------------- #
+set_tomplot_style()
+data_file = Dataset(results_file_name, 'r')
+# ---------------------------------------------------------------------------- #
+# Work out time idxs and overall min/max
+# ---------------------------------------------------------------------------- #
+time_idxs = range(len(data_file['time'][:]))
+universal_field_data = extract_gusto_field(data_file, field_name)
+contours = tomplot_contours(universal_field_data)
+projection = ccrs.RotatedPole(pole_longitude=pole_longitude, pole_latitude=pole_latitude)
+# ---------------------------------------------------------------------------- #
+# Make a modified cmap with transparent colour instead of white
+# ---------------------------------------------------------------------------- #
+ncolours = len(contours)-1
+cmap = plt.cm.get_cmap(colour_scheme, ncolours)
+colours = cmap(np.linspace(0, 1, ncolours))
+# Set transparency for most colours
+for i in range(ncolours):
+    colours[i,-1] = 0.75
+# Set first colour to transparent
+colours[0,-1] = 0.0
+cmap = ListedColormap(colours)
+# ---------------------------------------------------------------------------- #
+# Loop through points in time
+# ---------------------------------------------------------------------------- #
+for time_idx in time_idxs:
+    # ------------------------------------------------------------------------ #
+    # Data extraction
+    # ------------------------------------------------------------------------ #
+    field_data = extract_gusto_field(data_file, field_name, time_idx=time_idx)
+    coords_X, coords_Y = extract_gusto_coords(data_file, field_name)
+    time = data_file['time'][time_idx] / (24*60*60)
+    # ------------------------------------------------------------------------ #
+    # Extract wind data
+    # ------------------------------------------------------------------------ #
+    if plot_wind:
+        wind_data_X = extract_gusto_field(data_file, wind_name_X, time_idx=time_idx)
+        wind_data_Y = extract_gusto_field(data_file, wind_name_Y, time_idx=time_idx)
+        wind_coords_X, wind_coords_Y = extract_gusto_coords(data_file, wind_name_X)
+    # ------------------------------------------------------------------------ #
+    # Transform coordinates
+    # ------------------------------------------------------------------------ #
+    coords_X = (new_lon_extents[0]
+                + coords_X * (new_lon_extents[1] - new_lon_extents[0]) / Lx)
+    coords_Y = (new_lat_extents[0]
+                + coords_Y * (new_lat_extents[1] - new_lat_extents[0]) / Lx)
+    if plot_wind:
+        wind_coords_X = (wind_coords_X - new_lon_extents[0]) * (new_lon_extents[1] - new_lon_extents[0]) / Lx
+        wind_coords_Y = (wind_coords_Y - new_lat_extents[0]) * (new_lat_extents[1] - new_lat_extents[0]) / Lx
+    # ------------------------------------------------------------------------ #
+    # Plot data
+    # ------------------------------------------------------------------------ #
+    fig = plt.figure(figsize=(5, 5))
+    ax = fig.add_subplot(1, 1, 1, projection=projection)
+    ax.stock_img()
+    ax.coastlines()
+
+    cf, _ = plot_contoured_field(ax, coords_X, coords_Y, field_data, contour_method,
+                                 contours, cmap=cmap, plot_contour_lines=False,
+                                 projection=None, transparency=None)
+
+    if plot_wind:
+        _ = plot_field_quivers(ax, wind_coords_X, wind_coords_Y,
+                               wind_data_X, wind_data_Y,
+                               spatial_filter_step=5, projection=projection)
+
+    tomplot_field_title(ax, f't = {time:.2f} days', minmax=True, field_data=field_data,
+                        minmax_format=".2f")
+    ax.set_xlim(new_lon_xlims)
+    ax.set_ylim(new_lat_ylims)
+
+    # ------------------------------------------------------------------------ #
+    # Manually add colorbar as it is difficult to get it into the correct position
+    # ------------------------------------------------------------------------ #
+    cbar_format = '{x:.0f}'
+    cbar_ticks = [0, 2]
+    cbar_ax = fig.add_axes([0.925, 0.11, 0.025, 0.7725])
+    cb = fig.colorbar(cf, cax=cbar_ax, format=cbar_format, ticks=cbar_ticks,
+                      orientation='vertical', ticklocation='right')
+    cb.set_label(field_label, labelpad=-5)
+
+    # ------------------------------------------------------------------------ #
+    # Save figure
+    # ------------------------------------------------------------------------ #
+    plot_name = f'{plot_stem}_{time_idx:02d}.png'
+    print(f'Saving figure to {plot_name}')
+    fig.savefig(plot_name, bbox_inches='tight')
+    plt.close()
+
+

transport/volcanic_ash.py

@@ -0,0 +1,111 @@
+"""
+An example experiment for volcanic ash dispersion.
+"""
+
+from gusto import *
+from firedrake import (RectangleMesh, exp, SpatialCoordinate,
+                       Constant, sin, cos, sqrt, grad)
+import sys
+
+# ---------------------------------------------------------------------------- #
+# Test case parameters
+# ---------------------------------------------------------------------------- #
+
+dt = 120.                      # 1 mins
+tmax = 5*24*60*60              # End time
+Lx = 1e6                       # Domain length in x direction
+Ly = 1e6                       # Domain length in y direction
+nx = 200                       # Number of cells in x direction
+ny = 200                       # Number of cells in y direction
+dumpfreq = int(tmax / (50*dt)) # Output dump frequency
+tau = 2.0*24*60*60             # Half life of source
+centre_x = 3 * Lx / 8.0        # x coordinate for volcano
+centre_y = 2 * Ly / 3.0        # y coordinate for volcano
+width = Lx / 50.0              # width of volcano
+umax = 12.0                    # Representative wind value
+twind = 5*24*60*60             # Time scale for wind components
+omega22 = 3.0 / twind          # Frequency for sin(2*pi*x/Lx)*sin(2*pi*y/Ly)
+omega21 = 0.9 / twind          # Frequency for sin(2*pi*x/Lx)*sin(pi*y/Ly)
+omega12 = 0.6 / twind          # Frequency for sin(pi*x/Lx)*sin(2*pi*y/Ly)
+omega44 = 0.1 / twind          # Frequency for sin(4*pi*x/Lx)*sin(4*pi*y/Ly)
+
+if '--running-tests' in sys.argv:
+    tmax = dt
+    dumpfreq = 1
+    nx = 20
+    ny = 20
+
+# ---------------------------------------------------------------------------- #
+# Set up model objects
+# ---------------------------------------------------------------------------- #
+
+# Domain
+mesh = RectangleMesh(nx, ny, Lx, Ly, quadrilateral=True)
+domain = Domain(mesh, dt, "RTCF", 1)
+x, y = SpatialCoordinate(mesh)
+
+# Equation
+V = domain.spaces('DG')
+eqn = AdvectionEquation(domain, V, "ash")
+
+# I/O
+dirname = 'volcanic_ash'
+output = OutputParameters(dirname=dirname,
+                          dumpfreq=dumpfreq,
+                          dumplist=['ash'],
+                          dump_nc=True,
+                          dump_vtus=False)
+diagnostic_fields = [CourantNumber(), XComponent('u'), YComponent('u')]
+io = IO(domain, output, diagnostic_fields=diagnostic_fields)
+
+# Transport schemes
+transport_method = [DGUpwind(eqn, "ash")]
+
+# Physics scheme ------------------------------------------------------------- #
+# Source is a Lorentzian centred on a point
+dist_x = x - centre_x
+dist_y = y - centre_y
+dist = sqrt(dist_x**2 + dist_y**2)
+# Lorentzian function
+basic_expression = -width / (dist**2 + width**2)
+
+def time_varying_expression(t):
+    return 2*basic_expression*exp(-t/tau)
+
+physics_parametrisations = [SourceSink(eqn, 'ash', time_varying_expression,
+                                       time_varying=True)]
+
+# Transporting wind ---------------------------------------------------------- #
+def transporting_wind(t):
+    # Divergence-free wind. A series of sines/cosines with different time factors
+    psi_expr = (0.25*Lx/pi)*umax*(
+        sin(pi*x/Lx)*sin(pi*y/Ly)
+        + 0.15*sin(2*pi*x/Lx)*sin(2*pi*y/Ly)*(1.0 + cos(2*pi*omega22*t))
+        + 0.25*sin(2*pi*x/Lx)*sin(pi*y/Ly)*sin(2*pi*omega21*(t-0.7*twind))
+        + 0.17*sin(pi*x/Lx)*sin(2*pi*y/Ly)*cos(2*pi*omega12*(t+0.2*twind))
+        + 0.12*sin(4*pi*x/Lx)*sin(4*pi*y/Ly)*(1.0 + sin(2*pi*omega44*(t-0.83*twind)))
+    )
+
+    return domain.perp(grad(psi_expr))
+
+# Time stepper
+stepper = PrescribedTransport(eqn, SSPRK3(domain, limiter=DG1Limiter(V)),
+                              io, transport_method,
+                              physics_parametrisations=physics_parametrisations,
+                              prescribed_transporting_velocity=transporting_wind)
+
+# ---------------------------------------------------------------------------- #
+# Initial conditions
+# ---------------------------------------------------------------------------- #
+
+ash0 = stepper.fields("ash")
+# Start with some ash over the volcano
+ash0.interpolate(Constant(0.0)*-basic_expression)
+
+# ---------------------------------------------------------------------------- #
+# Run
+# ---------------------------------------------------------------------------- #
+
+num_steps = int(tmax / dt)
+logger.info(f'Beginning run to do {num_steps} steps')
+stepper.run(t=0, tmax=tmax)