mirror of https://github.com/Askill/claude.git
Update toy_model.py
Stream update from 24/6/2020 - Fixed advection - Fixed coriolis - Added spinup - Add time functionality
This commit is contained in:
Simon Clark
parent
dd1cd70ee6
commit
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162
toy_model.py
162
toy_model.py
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@ -5,24 +5,22 @@
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import numpy as np
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import matplotlib.pyplot as plt
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import time, sys
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import time, sys, pickle
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# define temporal parameters, including the length of time between calculation of fields and the length of a day on the planet (used for calculating Coriolis as well)
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day = 60*60*24
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dt = 60*17 ###### <----- TIMESTEP
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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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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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# 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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advection = True # if you want to include advection set this to be True (currently this breaks the model!)
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advection_boundary = 7 # how many gridpoints away from poles to apply advection
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t = 0
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save = False
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load = True
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# how many degrees between latitude and longitude gridpoints
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resolution = 5
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###########################
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# define coordinate arrays
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lat = np.arange(-90,91,resolution)
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@ -33,36 +31,38 @@ lon_plot, lat_plot = np.meshgrid(lon, lat)
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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((nlat,nlon)) + 270
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albedo = np.zeros((nlat,nlon)) + 0.5
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heat_capacity_earth = np.zeros((nlat,nlon)) + 1E6
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air_pressure = np.zeros((nlat,nlon))
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u = np.zeros((nlat,nlon))
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v = np.zeros((nlat,nlon))
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air_density = np.zeros_like(air_pressure) + 1.3
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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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# custom oceans with lower albedo and higher heat capacity
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ocean = True
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if ocean:
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albedo[5:55,9:20] = 0.7
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albedo[23:50,45:70] = 0.7
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albedo[2:30,85:110] = 0.7
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heat_capacity_earth[5:55,9:20] *= 2
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heat_capacity_earth[23:50,45:70] *= 2
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heat_capacity_earth[2:30,85:110] *= 2
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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_variance = 0.001
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for i in range(nlat):
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for j in range(nlon):
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albedo[i,j] += np.random.uniform(-albedo_variance,albedo_variance)
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# if including an ocean, uncomment the below
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# albedo[5:55,9:20] = 0.2
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# albedo[23:50,45:70] = 0.2
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# albedo[2:30,85:110] = 0.2
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# heat_capacity_earth[5:55,9:20] = 1E6
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# heat_capacity_earth[23:50,45:70] = 1E6
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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 = 0.75
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heat_capacity_atmos = 1E7
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specific_gas = 287
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thermal_diffusivity_air = 20E-6
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thermal_diffusivity_roc = 1.5E-6
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insolation = 1370
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sigma = 5.67E-8
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# define planet size and various geometric constants
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planet_radius = 6.4E6
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circumference = 2*np.pi*planet_radius
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circle = np.pi*planet_radius**2
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sphere = 4*np.pi*planet_radius**2
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@ -76,16 +76,20 @@ 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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###################### 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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# 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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else:
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return (a[i+1,j]-a[i-1,j])/dy
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# laplacian of scalar field a in the local x direction
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def laplacian(a):
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output = np.zeros_like(a)
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@ -93,6 +97,7 @@ def laplacian(a):
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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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# 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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@ -101,7 +106,15 @@ def divergence_with_scalar(a):
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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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return output
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#####
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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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#################### SHOW TIME ####################
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# set up plot
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f, ax = plt.subplots(2,figsize=(9,9))
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@ -115,64 +128,80 @@ ax[1].set_title('Atmosphere temperature')
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plt.ion()
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plt.show()
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advection = True # can turn thermal and mass advection on or off
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boundary = 5 # advection will occur starting from this many gridpoints away from the poles
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# INITIATE TIME
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t = 0
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if load:
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# load in previous save file
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temperature_atmosp,temperature_planet,u,v,t,air_density,albedo = pickle.load(open("save_file.p","rb"))
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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.max(),u.min(),v.max(),v.min(),air_density.max(),air_density.min())
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initial_time = time.time()
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if t < day*7:
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dt = 60*71
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if t < 7*day:
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dt = 60*47
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velocity = False
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else:
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dt = 60*7
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dt = 60*9
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velocity = 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())
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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*(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*air_density[i,j])
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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*divergence_with_scalar(temperature_atmosp)
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temperature_atmosp[boundary:-boundary,:] -= atmosp_addition[boundary:-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[boundary:-boundary,:boundary] -= density_addition[boundary:-boundary,:boundary]
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temperature_atmosp += dt*(thermal_diffusivity_air*laplacian(temperature_atmosp))
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temperature_planet += dt*(thermal_diffusivity_roc*laplacian(temperature_planet))
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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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# update air pressure
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air_pressure = air_density*specific_gas*temperature_atmosp
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if velocity:
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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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# calculate acceleration of atmosphere using primitive equations on beta-plane
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for i in np.arange(boundary,nlat-boundary):
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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*( - scalar_gradient_x(air_pressure,i,j)/air_density[i,j] + coriolis[i]*v[i,j] - u[i,j]*scalar_gradient_x(u,i,j) - v[i,j]*scalar_gradient_y(u,i,j))
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v_temp[i,j] = dt*( - scalar_gradient_y(air_pressure,i,j)/air_density[i,j] - coriolis[i]*u[i,j] - u[i,j]*scalar_gradient_x(v,i,j) - v[i,j]*scalar_gradient_y(v,i,j))
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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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u += u_temp
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v += v_temp
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u *= 0.99
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v *= 0.99
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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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# 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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temperature_planet += dt*(thermal_diffusivity_roc*laplacian(temperature_planet))
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# update plot
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ax[0].contourf(lon_plot, lat_plot, temperature_planet, cmap='seismic')
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test = ax[1].contourf(lon_plot, lat_plot, temperature_atmosp, cmap='seismic')
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# ax[1].quiver(lon_plot[::3, ::3],lat_plot[::3, ::3],u[::3, ::3],v[::3, ::3])
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ax[1].streamplot(lon_plot,lat_plot,u,v,density=0.75,color='black')
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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].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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i.set_ylim((lat.min(),lat.max()))
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i.set_ylabel('Latitude')
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i.axhline(y=0,color='black',alpha=0.3)
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ax[-1].set_xlabel('Longitude')
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@ -186,3 +215,10 @@ while True:
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# advance time by one timestep
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t += dt
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time_taken = float(round(time.time() - initial_time,3))
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print('Time: ',str(time_taken),'s')
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if save:
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pickle.dump((temperature_atmosp,temperature_planet,u,v,t,air_density,albedo), open("save_file.p","wb"))
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