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Update toy_model.py 

Fixed geometry of radiative forcing, testing problems with derivatives
This commit is contained in:
Simon Clark 2020-06-15 18:24:09 +01:00
parent 59393eecbb
commit bb6c00a2e5
1 changed files with 17 additions and 10 deletions
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toy_model.py
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@ -9,7 +9,7 @@ import time, sys
# 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)
day = 60*60*24
dt = 60*5 ###### <----- TIMESTEP
dt = 60*1 ###### <----- TIMESTEP
# power incident on (lat,lon) at time t
def solar(insolation, lat, lon, t):
@ -76,7 +76,7 @@ for i in range(nlat):
# define various useful differential functions:
# gradient of scalar field a in the local x direction at point i,j
def scalar_gradient_x(a,i,j):
return (a[i,(j+1)%nlon]-a[i,(j-1)%nlon])/dx[i]
return 0#(a[i,(j+1)%nlon]-a[i,(j-1)%nlon])/dx[i]
# gradient of scalar field a in the local y direction at point i,j
def scalar_gradient_y(a,i,j):
if i == 0 or i == nlat-1:
@ -113,36 +113,43 @@ plt.ion()
plt.show()
# if you want to include advection set this to be True (currently this breaks the model!)
advection = False
advection = True
while True:
# print current time in simulation to command line
print("t = " + str(round(24*t/day,2)) + " days", end='\r')
print(u.max())
# calculate change in temperature of ground and atmosphere due to radiative imbalance
for i in range(nlat):
for j in range(nlon):
temperature_planet[i,j] += dt*(albedo[i,j]*circle*solar(insolation,lat[i],lon[j],t) + sphere*epsilon*sigma*temperature_atmosp[i,j]**4 - sphere*sigma*temperature_planet[i,j]**4)/(heat_capacity_earth[i,j]*sphere)
temperature_atmosp[i,j] += dt*(sphere*epsilon*sigma*temperature_planet[i,j]**4 - 2*sphere*epsilon*sigma*temperature_atmosp[i,j]**4)/(heat_capacity_atmos*sphere)
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]
temperature_atmosp[i,j] += dt*(epsilon*sigma*temperature_planet[i,j]**4 - 2*epsilon*sigma*temperature_atmosp[i,j]**4)/heat_capacity_atmos
# update air pressure
air_pressure = air_density*specific_gas*temperature_atmosp
u_temp = np.zeros_like(u)
v_temp = np.zeros_like(v)
# calculate acceleration of atmosphere using primitive equations on beta-plane
for i in np.arange(1,nlat-1):
for j in range(nlon):
u[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] )
v[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] )
u_temp[i,j] += 0.001*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] )
v_temp[i,j] += 0.001*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] )
u += u_temp
v += v_temp
if advection:
# allow for thermal advection in the atmosphere, and heat diffusion in the atmosphere and the ground
atmosp_addition = dt*(thermal_diffusivity_air*laplacian(temperature_atmosp) + divergence_with_scalar(temperature_atmosp))
temperature_atmosp[5:-5,:] += atmosp_addition[5:-5,:]
# temperature_atmosp[5:-5,:] += atmosp_addition[5:-5,:]
# as density is now variable, allow for mass advection
density_addition = dt*divergence_with_scalar(air_density)
air_density[5:-5,:5] += density_addition[5:-5,:5]
# air_density[5:-5,:5] += density_addition[5:-5,:5]
temperature_planet += dt*(thermal_diffusivity_roc*laplacian(temperature_planet))