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Added grey radiation scheme 

Implemented 3D grey radiation and variable optical depth with latitude.
This commit is contained in:
Simon Clark 2020-08-12 20:53:41 +01:00
parent 243d1785c7
commit 3fd7ce1892
2 changed files with 52 additions and 21 deletions
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toy_model.py
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@ -13,7 +13,7 @@ day = 60*60*24 # define length of day (used for calculating Coriolis as well
dt = 60*9 # <----- TIMESTEP (s)
resolution = 5 # how many degrees between latitude and longitude gridpoints
nlevels = 5 # how many vertical layers in the atmosphere
top = 10E3 # top of atmosphere (m)
top = 50E3 # top of atmosphere (m)
planet_radius = 6.4E6 # define the planet's radius (m)
insolation = 1370 # TOA radiation from star (W m^-2)
gravity = 9.81 # define surface gravity for planet (m s^-2)
@ -22,7 +22,7 @@ advection = True # if you want to include advection set this to be True
advection_boundary = 3 # how many gridpoints away from poles to apply advection
save = False
load = False
load = True
###########################
@ -44,6 +44,13 @@ v = np.zeros_like(temperature_atmosp)
w = np.zeros_like(temperature_atmosp)
air_density = np.zeros_like(temperature_atmosp)
#######################
upward_radiation = np.zeros(nlevels)
downward_radiation = np.zeros(nlevels)
optical_depth = np.zeros(nlevels)
Q = np.zeros(nlevels)
#######################
# read temperature and density in from standard atmosphere
f = open("standard_atmosphere.txt", "r")
standard_height = []
@ -82,6 +89,8 @@ thermal_diffusivity_air = 20E-6
thermal_diffusivity_roc = 1.5E-6
sigma = 5.67E-8
air_pressure = air_density*specific_gas*temperature_atmosp
# define planet size and various geometric constants
circumference = 2*np.pi*planet_radius
circle = np.pi*planet_radius**2
@ -127,12 +136,21 @@ def scalar_gradient_y(a,i,j,k=999):
return (a[i+1,j,k]-a[i-1,j,k])/dy
def scalar_gradient_z(a,i,j,k):
if k == 0:
return (a[i,j,k+1]-a[i,j,k])/dz[k]
elif k == nlevels-1:
return (a[i,j,k]-a[i,j,k-1])/dz[k]
output = np.zeros_like(a)
if output.ndim == 1:
if k == 0:
return (a[k+1]-a[k])/dz[k]
elif k == nlevels-1:
return (a[k]-a[k-1])/dz[k]
else:
return (a[k+1]-a[k-1])/(2*dz[k])
else:
return (a[i,j,k+1]-a[i,j,k-1])/(2*dz[k])
if k == 0:
return (a[i,j,k+1]-a[i,j,k])/dz[k]
elif k == nlevels-1:
return (a[i,j,k]-a[i,j,k-1])/dz[k]
else:
return (a[i,j,k+1]-a[i,j,k-1])/(2*dz[k])
# laplacian of scalar field a
def laplacian(a):
@ -140,13 +158,13 @@ def laplacian(a):
if output.ndim == 2:
for i in np.arange(1,nlat-1):
for j in range(nlon):
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
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
return output
if output.ndim == 3:
for i in np.arange(1,nlat-1):
for j in range(nlon):
for k in range(nlevels-1):
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]
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]
return output
# divergence of (a*u) where a is a scalar field and u is the atmospheric velocity field
@ -166,6 +184,9 @@ def solar(insolation, lat, lon, t):
if value < 0: return 0
else: return value
def surface_optical_depth(lat):
return 3.75 + np.cos(lat*np.pi/90)*4.5/2
#################### SHOW TIME ####################
# set up plot
@ -215,18 +236,26 @@ while True:
# 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*((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]
for k in range(nlevels):
if k == 0:
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*dz[k])
elif k == nlevels-1:
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*dz[k])
else:
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*dz[k])
temperature_planet[i,j] += dt*((1-albedo[i,j])*solar(insolation,lat[i],lon[j],t))/heat_capacity_earth[i,j]
pressure_profile = air_pressure[i,j,:]
fl = 0.1
optical_depth = surface_optical_depth(lat[i])*(fl*(pressure_profile/pressure_profile[0]) + (1-fl)*(pressure_profile/pressure_profile[0])**4)
upward_radiation[0] = sigma*temperature_planet[i,j]**4
for k in np.arange(1,nlevels):
upward_radiation[k] = upward_radiation[k-1] + (optical_depth[k]-optical_depth[k-1])*(upward_radiation[k-1] - sigma*np.mean(temperature_atmosp[:,:,k])**4)
downward_radiation[-1] = 0
for k in np.arange(0,nlevels-1)[::-1]:
downward_radiation[k] = downward_radiation[k+1] + (optical_depth[k]-optical_depth[k-1])*(sigma*np.mean(temperature_atmosp[:,:,k])**4 - downward_radiation[k+1])
for k in np.arange(nlevels):
Q[k] = -scalar_gradient_z(upward_radiation-downward_radiation,0,0,k)/(1E3*density_profile[k])
temperature_atmosp[i,j,:] += Q
# update air pressure
air_pressure = air_density*specific_gas*temperature_atmosp
print(heights/1E3,np.mean(np.mean(air_pressure,axis=0),axis=0))
if velocity:
@ -238,7 +267,7 @@ while True:
# calculate acceleration of atmosphere using primitive equations on beta-plane
for i in np.arange(1,nlat-1):
for j in range(nlon):
for k in range(nlevels-2):
for k in range(nlevels):
if k == 0:
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] )
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] )
@ -248,7 +277,7 @@ while True:
else:
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] )
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] )
w_temp[i,j,k] += -1E-3*dt*( scalar_gradient_z(air_pressure,i,j,k)/air_density[i,j,k] + gravity )
w_temp[i,j,k] += 1E-3*dt*( scalar_gradient_z(air_pressure,i,j,k)/air_density[i,j,k] + gravity )
u += u_temp
v += v_temp
@ -325,3 +354,5 @@ while True:
if save:
pickle.dump((temperature_atmosp,temperature_planet,u,v,t,air_density,albedo), open("save_file.p","wb"))
# sys.exit()