mirror of https://github.com/Askill/claude.git
3D atmosphere!
Added multiple layers to the atmosphere. These have adjacent radiation exchange but not cross-level exchange, and no vertical momentum calculated. Also tweaked the absorption in different levels of the atmosphere. Differential sections of the code have been generalised for 3D fields
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Simon Clark
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72247c418d
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119
toy_model.py
119
toy_model.py
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@ -7,10 +7,12 @@ import numpy as np
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import matplotlib.pyplot as plt
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import time, sys, pickle
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### CONTROL
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### CONTROL ###
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day = 60*60*24 # define length of day (used for calculating Coriolis as well) (s)
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dt = 60*9 # <----- TIMESTEP (s)
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resolution = 3 # how many degrees between latitude and longitude gridpoints
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nlevels = 4 # how many vertical layers in the atmosphere
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planet_radius = 6.4E6 # define the planet's radius (m)
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insolation = 1370 # TOA radiation from star (W m^-2)
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@ -18,7 +20,7 @@ advection = True # if you want to include advection set this to be True (cur
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advection_boundary = 7 # how many gridpoints away from poles to apply advection
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save = False
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load = True
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load = False
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###########################
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@ -28,14 +30,16 @@ lon = np.arange(0,360,resolution)
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nlat = len(lat)
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nlon = len(lon)
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lon_plot, lat_plot = np.meshgrid(lon, lat)
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heights = np.arange(0,100E3,100E3/nlevels)
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# initialise arrays for various physical fields
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temperature_planet = np.zeros((nlat,nlon)) + 270
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temperature_atmosp = np.zeros_like(temperature_planet) + 270
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air_pressure = np.zeros_like(temperature_planet)
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u = np.zeros_like(temperature_planet)
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v = np.zeros_like(temperature_planet)
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air_density = np.zeros_like(temperature_planet) + 1.3
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temperature_atmosp = np.zeros((nlat,nlon,nlevels)) + 270
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air_pressure = np.zeros_like(temperature_atmosp)
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u = np.zeros_like(temperature_atmosp)
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v = np.zeros_like(temperature_atmosp)
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w = np.zeros_like(temperature_atmosp)
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air_density = np.zeros_like(temperature_atmosp) + 1.3
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albedo = np.zeros_like(temperature_planet) + 0.5
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heat_capacity_earth = np.zeros_like(temperature_planet) + 1E7
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@ -54,7 +58,10 @@ for i in range(nlat):
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# heat_capacity_earth[2:30,85:110] = 1E6
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# define physical constants
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epsilon = 0.75
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epsilon = np.zeros(nlevels)
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epsilon[0] = 0.75
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for i in np.arange(1,nlevels):
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epsilon[i] = epsilon[i-1]*0.5
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heat_capacity_atmos = 1E7
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specific_gas = 287
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@ -75,35 +82,67 @@ angular_speed = 2*np.pi/day
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for i in range(nlat):
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dx[i] = dy*np.cos(lat[i]*np.pi/180)
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coriolis[i] = angular_speed*np.sin(lat[i]*np.pi/180)
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dz = np.zeros(nlevels)
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for k in range(nlevels-1): dz[k] = heights[k+1] - heights[k]
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dz[-1] = dz[-2]
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###################### FUNCTIONS ######################
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# define various useful differential functions:
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# gradient of scalar field a in the local x direction at point i,j
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def scalar_gradient_x(a,i,j):
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return (a[i,(j+1)%nlon]-a[i,(j-1)%nlon])/dx[i]
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def scalar_gradient_x(a,i,j,k=999):
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if k == 999:
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return (a[i,(j+1)%nlon]-a[i,(j-1)%nlon])/dx[i]
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else:
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return (a[i,(j+1)%nlon,k]-a[i,(j-1)%nlon,k])/dx[i]
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# gradient of scalar field a in the local y direction at point i,j
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def scalar_gradient_y(a,i,j):
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if i == 0 or i == nlat-1:
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return 0
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def scalar_gradient_y(a,i,j,k=999):
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if k == 999:
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if i == 0:
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return 2*(a[i+1,j]-a[i,j])/dy
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elif i == nlat-1:
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return 2*(a[i,j]-a[i-1,j])/dy
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else:
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return (a[i+1,j]-a[i-1,j])/dy
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else:
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return (a[i+1,j]-a[i-1,j])/dy
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if i == 0:
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return 2*(a[i+1,j,k]-a[i,j,k])/dy
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elif i == nlat-1:
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return 2*(a[i,j,k]-a[i-1,j,k])/dy
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else:
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return (a[i+1,j,k]-a[i-1,j,k])/dy
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# laplacian of scalar field a in the local x direction
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def scalar_gradient_z(a,i,j,k):
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if k == 0:
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return (a[i,j,k+1]-a[i,j,k])/dz[k]
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elif k == nlevels-1:
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return (a[i,j,k]-a[i,j,k-1])/dz[k]
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else:
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return (a[i,j,k+1]-a[i,j,k-1])/(2*dz[k])
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# laplacian of scalar field a
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def laplacian(a):
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output = np.zeros_like(a)
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for i in np.arange(1,len(a[:,0])-1):
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for j in range(len(a[0,:])):
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output[i,j] = (scalar_gradient_x(a,i,(j+1)%nlon) - scalar_gradient_x(a,i,(j-1)%nlon)/dx[i]) + (scalar_gradient_y(a,i+1,j) - scalar_gradient_y(a,i-1,j))/dy
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return output
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if output.ndim == 2:
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for i in np.arange(1,nlat-1):
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for j in range(nlon):
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output[i,j] = (scalar_gradient_x(a,i,(j+1)%nlon) - scalar_gradient_x(a,i,(j-1)%nlon)/dx[i]) + (scalar_gradient_y(a,i+1,j) - scalar_gradient_y(a,i-1,j))/dy
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return output
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if output.ndim == 3:
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for i in np.arange(1,nlat-1):
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for j in range(nlon):
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for k in range(nlevels-1):
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output[i,j,k] = (scalar_gradient_x(a,i,(j+1)%nlon,k) - scalar_gradient_x(a,i,(j-1)%nlon,k)/dx[i]) + (scalar_gradient_y(a,i+1,j,k) - scalar_gradient_y(a,i-1,j,k))/dy + (scalar_gradient_z(a,i,j,k+1)-scalar_gradient_z(a,i,j,k-1))/2*dz[k]
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return output
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# divergence of (a*u) where a is a scalar field and u is the atmospheric velocity field
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def divergence_with_scalar(a):
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output = np.zeros_like(a)
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for i in range(len(a[:,0])):
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for j in range(len(a[0,:])):
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output[i,j] = scalar_gradient_x(a*u,i,j) + scalar_gradient_y(a*v,i,j)
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for i in range(nlat):
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for j in range(nlon):
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for k in range(nlevels):
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output[i,j] = scalar_gradient_x(a*u,i,j,k) + scalar_gradient_y(a*v,i,j,k) + scalar_gradient_z(a*w,i,j,k)
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return output
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# power incident on (lat,lon) at time t
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@ -120,7 +159,7 @@ def solar(insolation, lat, lon, t):
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f, ax = plt.subplots(2,figsize=(9,9))
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f.canvas.set_window_title('CLAuDE')
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ax[0].contourf(lon_plot, lat_plot, temperature_planet, cmap='seismic')
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ax[1].contourf(lon_plot, lat_plot, temperature_atmosp, cmap='seismic')
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ax[1].contourf(lon_plot, lat_plot, temperature_atmosp[:,:,0], cmap='seismic')
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plt.subplots_adjust(left=0.1, right=0.75)
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ax[0].set_title('Ground temperature')
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ax[1].set_title('Atmosphere temperature')
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@ -153,8 +192,14 @@ while True:
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# calculate change in temperature of ground and atmosphere due to radiative imbalance
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for i in range(nlat):
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for j in range(nlon):
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temperature_planet[i,j] += dt*((1-albedo[i,j])*solar(insolation,lat[i],lon[j],t) + epsilon*sigma*temperature_atmosp[i,j]**4 - sigma*temperature_planet[i,j]**4)/heat_capacity_earth[i,j]
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temperature_atmosp[i,j] += dt*(epsilon*sigma*temperature_planet[i,j]**4 - 2*epsilon*sigma*temperature_atmosp[i,j]**4)/heat_capacity_atmos
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temperature_planet[i,j] += dt*((1-albedo[i,j])*solar(insolation,lat[i],lon[j],t) + epsilon[0]*sigma*temperature_atmosp[i,j,0]**4 - sigma*temperature_planet[i,j]**4)/heat_capacity_earth[i,j]
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for k in range(nlevels):
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if k == 0:
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temperature_atmosp[i,j,k] += dt*epsilon[k]*sigma*(temperature_planet[i,j]**4 + epsilon[k+1]*temperature_atmosp[i,j,k+1]**4 - 2*temperature_atmosp[i,j,k]**4)/(air_density[i,j,k]*heat_capacity_atmos)
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elif k == nlevels-1:
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temperature_atmosp[i,j,k] += dt*epsilon[k]*sigma*(epsilon[k-1]*temperature_atmosp[i,j,k-1]**4 - 2*temperature_atmosp[i,j,k]**4)/(air_density[i,j,k]*heat_capacity_atmos)
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else:
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temperature_atmosp[i,j,k] += dt*epsilon[k]*sigma*(epsilon[k+1]*temperature_atmosp[i,j,k+1]**4 + epsilon[k-1]*temperature_atmosp[i,j,k-1]**4 - 2*temperature_atmosp[i,j,k]**4)/(air_density[i,j,k]*heat_capacity_atmos)
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# update air pressure
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air_pressure = air_density*specific_gas*temperature_atmosp
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@ -164,15 +209,19 @@ while True:
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# introduce temporary arrays to update velocity in the atmosphere
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u_temp = np.zeros_like(u)
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v_temp = np.zeros_like(v)
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w_temp = np.zeros_like(w)
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# calculate acceleration of atmosphere using primitive equations on beta-plane
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for i in np.arange(1,nlat-1):
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for j in range(nlon):
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u_temp[i,j] += dt*( -u[i,j]*scalar_gradient_x(u,i,j) - v[i,j]*scalar_gradient_y(u,i,j) + coriolis[i]*v[i,j] - scalar_gradient_x(air_pressure,i,j)/air_density[i,j] )
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v_temp[i,j] += dt*( -u[i,j]*scalar_gradient_x(v,i,j) - v[i,j]*scalar_gradient_y(v,i,j) - coriolis[i]*u[i,j] - scalar_gradient_y(air_pressure,i,j)/air_density[i,j] )
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for k in range(nlevels):
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u_temp[i,j,k] += dt*( -u[i,j,k]*scalar_gradient_x(u,i,j,k) - v[i,j,k]*scalar_gradient_y(u,i,j,k) + coriolis[i]*v[i,j,k] - scalar_gradient_x(air_pressure,i,j,k)/air_density[i,j,k] )
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v_temp[i,j,k] += dt*( -u[i,j,k]*scalar_gradient_x(v,i,j,k) - v[i,j,k]*scalar_gradient_y(v,i,j,k) - coriolis[i]*u[i,j,k] - scalar_gradient_y(air_pressure,i,j,k)/air_density[i,j,k] )
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w_temp[i,j,k] += 0
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u += u_temp
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v += v_temp
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w += w_temp
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u *= 0.99
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v *= 0.99
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@ -180,15 +229,15 @@ while True:
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if advection:
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# allow for thermal advection in the atmosphere, and heat diffusion in the atmosphere and the ground
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atmosp_addition = dt*(thermal_diffusivity_air*laplacian(temperature_atmosp) + divergence_with_scalar(temperature_atmosp))
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temperature_atmosp[advection_boundary:-advection_boundary,:] -= atmosp_addition[advection_boundary:-advection_boundary,:]
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temperature_atmosp[advection_boundary-1,:] -= 0.5*atmosp_addition[advection_boundary-1,:]
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temperature_atmosp[-advection_boundary,:] -= 0.5*atmosp_addition[-advection_boundary,:]
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temperature_atmosp[advection_boundary:-advection_boundary,:,:] -= atmosp_addition[advection_boundary:-advection_boundary,:,:]
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temperature_atmosp[advection_boundary-1,:,:] -= 0.5*atmosp_addition[advection_boundary-1,:,:]
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temperature_atmosp[-advection_boundary,:,:] -= 0.5*atmosp_addition[-advection_boundary,:,:]
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# as density is now variable, allow for mass advection
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density_addition = dt*divergence_with_scalar(air_density)
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air_density[advection_boundary:-advection_boundary,:] -= density_addition[advection_boundary:-advection_boundary,:]
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air_density[(advection_boundary-1),:] -= 0.5*density_addition[advection_boundary-1,:]
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air_density[-advection_boundary,:] -= 0.5*density_addition[-advection_boundary,:]
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air_density[advection_boundary:-advection_boundary,:,:] -= density_addition[advection_boundary:-advection_boundary,:,:]
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air_density[(advection_boundary-1),:,:] -= 0.5*density_addition[advection_boundary-1,:,:]
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air_density[-advection_boundary,:,:] -= 0.5*density_addition[-advection_boundary,:,:]
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temperature_planet += dt*(thermal_diffusivity_roc*laplacian(temperature_planet))
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@ -196,8 +245,8 @@ while True:
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test = ax[0].contourf(lon_plot, lat_plot, temperature_planet, cmap='seismic')
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ax[0].set_title('$\it{Ground} \quad \it{temperature}$')
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ax[1].contourf(lon_plot, lat_plot, temperature_atmosp, cmap='seismic')
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ax[1].streamplot(lon_plot,lat_plot,u,v,density=0.75,color='black')
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ax[1].contourf(lon_plot, lat_plot, temperature_atmosp[:,:,0], cmap='seismic')
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ax[1].streamplot(lon_plot,lat_plot,u[:,:,0],v[:,:,0],density=0.75,color='black')
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ax[1].set_title('$\it{Atmospheric} \quad \it{temperature}$')
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for i in ax:
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i.set_xlim((lon.min(),lon.max()))
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