mirror of https://github.com/Askill/claude.git
Big update 26/8/20
Major fixes: - Tweaked radiation scheme to fix representation of equations - Added vertical motion assuming perturbation to hydrostatic equilibriu - Implemented seasons / axial tilt - Added stratospheric heating Minor changes: - Removed old unused code - Added frictional forces throughout atmosphere - Tweaked optical depth parameterisation - Tweaked text output - Removed vertical advection (for now)
This commit is contained in:
Simon Clark
parent
23b65ae1a6
commit
6135e0b849
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save_file.p
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save_file.p
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182
toy_model.py
182
toy_model.py
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@ -10,23 +10,24 @@ import time, sys, pickle
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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 = 5 # how many degrees between latitude and longitude gridpoints
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nlevels = 20 # how many vertical layers in the atmosphere
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top = 20E3 # top of atmosphere (m)
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resolution = 3 # how many degrees between latitude and longitude gridpoints
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nlevels = 10 # how many vertical layers in the atmosphere
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top = 50E3 # top of atmosphere (m)
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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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gravity = 9.81 # define surface gravity for planet (m s^-2)
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axial_tilt = -23.5 # tilt of rotational axis w.r.t. solar plane
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year = 365*day # length of year (s)
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###
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advection = True # if you want to include advection set this to be True
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advection_boundary = 3 # how many gridpoints away from poles to apply advection
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advection_boundary = 4 # how many gridpoints away from poles to apply advection
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save = False
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save = True
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load = False
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plot = True
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plot = False
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level_plots = False
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###########################
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@ -41,7 +42,7 @@ heights = np.arange(0,top,top/nlevels)
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heights_plot, lat_z_plot = np.meshgrid(lat,heights)
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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_planet = np.zeros((nlat,nlon)) + 290
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temperature_atmosp = np.zeros((nlat,nlon,nlevels))
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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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@ -49,11 +50,6 @@ 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)
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# #######################
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upward_radiation = np.zeros(nlevels)
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downward_radiation = np.zeros(nlevels)
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optical_depth = np.zeros(nlevels)
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Q = np.zeros(nlevels)
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# #######################
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def profile(a):
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@ -79,19 +75,17 @@ for k in range(nlevels):
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###########################
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weight_above = np.interp(x=heights/1E3,xp=standard_height,fp=standard_density)
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top_index = np.argmax(np.array(standard_height) >= top/1E3)
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if standard_height[top_index] == top/1E3:
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weight_above = np.trapz(np.interp(x=standard_height[top_index:],xp=standard_height,fp=standard_density),standard_height[top_index:])*gravity*1E3
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else:
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weight_above = np.trapz(np.interp(x=np.insert(standard_height[top_index:], 0, top/1E3),xp=standard_height,fp=standard_density),np.insert(standard_height[top_index:], 0, top/1E3))*gravity*1E3
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weight_above *= 1.1
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# sys.exit()
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# weight_above = np.interp(x=heights/1E3,xp=standard_height,fp=standard_density)
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# top_index = np.argmax(np.array(standard_height) >= top/1E3)
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# if standard_height[top_index] == top/1E3:
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# weight_above = np.trapz(np.interp(x=standard_height[top_index:],xp=standard_height,fp=standard_density),standard_height[top_index:])*gravity*1E3
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# else:
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# weight_above = np.trapz(np.interp(x=np.insert(standard_height[top_index:], 0, top/1E3),xp=standard_height,fp=standard_density),np.insert(standard_height[top_index:], 0, top/1E3))*gravity*1E3
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###########################
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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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albedo = np.zeros_like(temperature_planet) + 0.2
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heat_capacity_earth = np.zeros_like(temperature_planet) + 1E6
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albedo_variance = 0.001
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for i in range(nlat):
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@ -186,48 +180,57 @@ def divergence_with_scalar(a):
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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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output[i,j] = scalar_gradient_x(a*u,i,j,k) + scalar_gradient_y(a*v,i,j,k) #+ 0.1*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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def solar(insolation, lat, lon, t):
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sun_longitude = -t % day
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sun_longitude *= 360/day
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value = insolation*np.cos(lat*np.pi/180)*np.cos((lon-sun_longitude)*np.pi/180)
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if value < 0: return 0
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else: return value
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sun_latitude = axial_tilt*np.cos(t*2*np.pi/year)
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value = insolation*np.cos((lat-sun_latitude)*np.pi/180)
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if value < 0:
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return 0
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else:
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lon_diff = lon-sun_longitude
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value *= np.cos(lon_diff*np.pi/180)
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if value < 0:
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if lat + sun_latitude > 90:
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return insolation*np.cos((lat+sun_latitude)*np.pi/180)*np.cos(lon_diff*np.pi/180)
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elif lat + sun_latitude < -90:
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return insolation*np.cos((lat+sun_latitude)*np.pi/180)*np.cos(lon_diff*np.pi/180)
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else:
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return 0
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else:
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return value
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def surface_optical_depth(lat):
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return 3.75 + np.cos(lat*np.pi/90)*4.5/2
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return 4 + np.cos(lat*np.pi/90)*2.5/2
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def smooth(a,window):
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output = np.zeros_like(a)
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diff = int(np.floor(window/2))
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for i in range(len(output)):
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if i-diff < 0:
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output[i] = np.mean(a[i:i+diff+1])
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elif i+diff+1 > len(output):
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output[i] = np.mean(a[i-diff:i])
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else:
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output[i] = np.mean(a[i-diff:i+diff+1])
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return output
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def thermal_radiation(a):
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return sigma*(a**4)
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#################### SHOW TIME ####################
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# pressure_profile = profile(air_pressure)
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# density_profile = profile(air_density)
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# temperature_profile = profile(temperature_atmosp)
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# print(dz,density_profile,gravity,pressure_profile/1E2,temperature_profile)
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# plt.plot(pressure_profile/1E2,heights/1E3,color='blue',label='Model atmosphere')
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# temp = np.zeros_like(pressure_profile)
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# temp[0] = pressure_profile[0]
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# for k in np.arange(1,nlevels): temp[k] = temp[k-1] - dz[k]*density_profile[k]*gravity
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# plt.plot(temp/1E2,heights/1E3,color='red',label='Implied hydrostatic balance')
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# plt.xlabel('Pressure (hPa)')
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# plt.ylabel('Height (km)')
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# plt.legend()
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# plt.show()
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# plt.plot(temp/pressure_profile)
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# plt.show()
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# sys.exit()
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#################################################
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if plot:
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# set up plot
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f, ax = plt.subplots(2,figsize=(9,7))
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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[:,:,0], cmap='seismic')
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@ -237,10 +240,9 @@ if plot:
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# allow for live updating as calculations take place
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if level_plots:
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plot_subsample = [0,5,10,15]
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g, bx = plt.subplots(len(plot_subsample),figsize=(9,7),sharex=True)
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g, bx = plt.subplots(nlevels,figsize=(9,7),sharex=True)
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g.canvas.set_window_title('CLAuDE atmospheric levels')
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for k in plot_subsample:
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for k in range(nlevels):
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bx[k].contourf(lon_plot, lat_plot, temperature_atmosp[:,:,k], cmap='seismic')
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bx[k].set_title(str(heights[k])+' km')
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bx[k].set_ylabel('Latitude')
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@ -260,8 +262,8 @@ while True:
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initial_time = time.time()
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if t < 14*day:
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dt = 60*47
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if t < 30*day:
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dt = 60*137
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velocity = False
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else:
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dt = 60*9
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@ -269,45 +271,51 @@ while True:
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# print current time in simulation to command line
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print("+++ t = " + str(round(t/day,2)) + " days +++", end='\r')
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print('U:',u.max(),u.min(),'V: ',v.max(),v.min(),'W: ',w.max(),w.min())
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# print(np.mean(np.mean(air_density,axis=0),axis=0))
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print('T: ',round(temperature_planet.max()-273.15,1),' - ',round(temperature_planet.min()-273.15,1),' C')
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print('U: ',round(u.max(),2),' - ',round(u.min(),2),' V: ',round(v.max(),2),' - ',round(v.min(),2),' W: ',round(w.max(),2),' - ',round(w.min(),2))
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# print(profile(air_density))
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# print(profile(air_pressure)/100)
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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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upward_radiation = np.zeros(nlevels)
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downward_radiation = np.zeros(nlevels)
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optical_depth = np.zeros(nlevels)
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Q = np.zeros(nlevels)
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# calculate optical depth
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pressure_profile = air_pressure[i,j,:]
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density_profile = air_density[i,j,:]
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fl = 0.1
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optical_depth = surface_optical_depth(lat[i])*(fl*(pressure_profile/pressure_profile[0]) + (1-fl)*(pressure_profile/pressure_profile[0])**4)
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# calculate upward longwave flux, bc is thermal radiation at surface
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upward_radiation[0] = sigma*temperature_planet[i,j]**4
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upward_radiation[0] = thermal_radiation(temperature_planet[i,j])
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for k in np.arange(1,nlevels):
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upward_radiation[k] = upward_radiation[k-1] + (optical_depth[k]-optical_depth[k-1])*(upward_radiation[k-1] - sigma*temperature_atmosp[i,j,k]**4)
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upward_radiation[k] = (upward_radiation[k-1] - (optical_depth[k]-optical_depth[k-1])*(thermal_radiation(temperature_atmosp[i,j,k])))/(1+optical_depth[k-1]-optical_depth[k])
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# calculate downward longwave flux, bc is zero at TOA (in model)
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downward_radiation[nlevels-1] = 0
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downward_radiation[-1] = 0
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for k in np.arange(0,nlevels-1)[::-1]:
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if k == 0:
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downward_radiation[k] = downward_radiation[k+1] + (optical_depth[k+1]-optical_depth[k])*(sigma*temperature_atmosp[i,j,k]**4 - downward_radiation[k+1])
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else:
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downward_radiation[k] = downward_radiation[k+1] + (optical_depth[k]-optical_depth[k-1])*(sigma*temperature_atmosp[i,j,k]**4 - downward_radiation[k+1])
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downward_radiation[k] = (downward_radiation[k+1] - thermal_radiation(temperature_atmosp[i,j,k])*(optical_depth[k+1]-optical_depth[k]))/(1 + optical_depth[k] - optical_depth[k+1])
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# gradient of difference provides heating at each level
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for k in np.arange(nlevels):
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Q[k] = -scalar_gradient_z(upward_radiation-downward_radiation,0,0,k)/(1E3*density_profile[k])
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temperature_atmosp[i,j,:] += Q
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# make sure model does not have a higher top than 50km!!
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# approximate SW heating of ozone
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if heights[k] > 20E3:
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Q[k] += solar(5,lat[i],lon[j],t)*((((heights[k]-20E3)/1E3)**2)/(30**2))/(24*60*60)
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temperature_atmosp[i,j,:] += Q*dt
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# update surface temperature with shortwave radiation flux
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temperature_planet[i,j] += dt*((1-albedo[i,j])*solar(insolation,lat[i],lon[j],t) + scalar_gradient_z(downward_radiation,0,0,0) - sigma*temperature_planet[i,j]**4)/heat_capacity_earth[i,j]
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# plt.plot(downward_radiation,heights,label='downward',color='blue')
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# plt.plot(upward_radiation,heights,label='upward',color='red')
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# plt.legend()
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# plt.show()
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temperature_planet[i,j] += dt*((1-albedo[i,j])*(solar(insolation,lat[i],lon[j],t) + downward_radiation[0]) - upward_radiation[0])/heat_capacity_earth[i,j]
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# update air pressure
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old_pressure = np.copy(air_pressure)
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air_pressure = air_density*specific_gas*temperature_atmosp
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if velocity:
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@ -323,16 +331,21 @@ while True:
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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] += dt*( (air_pressure[i,j,k] - np.trapz(y=air_density[i,j,k:]*gravity,dx=dz[(k+1):]) - weight_above)/(1E5*dz[k]*air_density[i,j,k]) )
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w_temp[i,j,k] += -(air_pressure[i,j,k]-old_pressure[i,j,k])/(dt*air_density[i,j,k]*gravity)
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# plt.plot(w_temp[i,j,:],heights)
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# plt.title('Vertical acceleration')
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# plt.show()
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# sys.exit()
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u += u_temp
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v += v_temp
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w[:,:,1:-2] += w_temp[:,:,1:-2]
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w += w_temp
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# approximate surface friction
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u[:,:,0] *= 0.99
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v[:,:,0] *= 0.99
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# approximate friction
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u *= 0.95
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v *= 0.95
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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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@ -353,6 +366,7 @@ while True:
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if plot:
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# update plot
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test = ax[0].contourf(lon_plot, lat_plot, temperature_planet, cmap='seismic')
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ax[0].streamplot(lon_plot, lat_plot, u[:,:,0], v[:,:,0], color='white',density=1)
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ax[0].set_title('$\it{Ground} \quad \it{temperature}$')
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ax[0].set_xlim((lon.min(),lon.max()))
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ax[0].set_ylim((lat.min(),lat.max()))
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@ -361,8 +375,8 @@ while True:
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ax[0].set_xlabel('Longitude')
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ax[1].contourf(heights_plot, lat_z_plot, np.transpose(np.mean(temperature_atmosp,axis=1)), cmap='seismic')
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ax[1].contour(heights_plot,lat_z_plot, np.transpose(np.mean(u,axis=1)), colors='white')
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ax[1].streamplot(heights_plot, lat_z_plot, np.transpose(np.mean(v,axis=1)),np.transpose(np.mean(w,axis=1)),color='black',density=0.75)
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ax[1].contour(heights_plot,lat_z_plot, np.transpose(np.mean(u,axis=1)), colors='white',levels=20,linewidths=1,alpha=0.8)
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ax[1].streamplot(heights_plot, lat_z_plot, np.transpose(np.mean(v,axis=1)),np.transpose(np.mean(10*w,axis=1)),color='black',density=0.75)
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ax[1].set_title('$\it{Atmospheric} \quad \it{temperature}$')
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ax[1].set_xlim((-90,90))
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ax[1].set_ylim((0,heights.max()))
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@ -375,10 +389,10 @@ while True:
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f.suptitle( 'Time ' + str(round(24*t/day,2)) + ' hours' )
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if level_plots:
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for k in plot_subsample:
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for k in range(nlevels):
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index = nlevels-1-k
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test = bx[index].contourf(lon_plot, lat_plot, temperature_atmosp[:,:,k], cmap='seismic')
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bx[index].streamplot(lon_plot, lat_plot, u[:,:,k], v[:,:,k],density=0.75,color='black')
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bx[index].streamplot(lon_plot, lat_plot, u[:,:,k], v[:,:,k],density=0.5,color='black')
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# g.colorbar(test,cax=bx[nlevels-1-k])
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bx[index].set_title(str(heights[k]/1E3)+' km')
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bx[index].set_ylabel('Latitude')
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