claude/claude_top_level_library.pyx

162 lines
7.1 KiB
Cython

# claude_top_level_library
import claude_low_level_library as low_level
import numpy as np
cimport numpy as np
cimport cython
ctypedef np.float64_t DTYPE_f
# laplacian of scalar field a
def laplacian_2D(np.ndarray a,np.ndarray dx,DTYPE_f dy):
cdef np.ndarray output = np.zeros_like(a)
cdef np.int_t nlat,nlon,i,j
cdef DTYPE_f inv_dx, inv_dy
nlat = a.shape[0]
nlon = a.shape[1]
inv_dy = 1/dy
for i in np.arange(1,nlat-1):
inv_dx = dx[i]
for j in range(nlon):
output[i,j] = (low_level.scalar_gradient_x_2D(a,dx,nlon,i,j) - low_level.scalar_gradient_x_2D(a,dx,nlon,i,j))*inv_dx + (low_level.scalar_gradient_y_2D(a,dy,nlat,i+1,j) - low_level.scalar_gradient_y_2D(a,dy,nlat,i-1,j))*inv_dy
return output
def laplacian_3D(np.ndarray a,np.ndarray dx,DTYPE_f dy,np.ndarray dz):
cdef np.ndarray output = np.zeros_like(a)
cdef np.int_t nlat,nlon,nlevels,i,j,k
cdef DTYPE_f inv_dx, inv_dy
nlat = a.shape[0]
nlon = a.shape[1]
nlevels = a.shape[2]
inv_dy = 1/dy
for i in np.arange(1,nlat-1):
inv_dx = 1/dx[i]
for j in range(nlon):
for k in range(nlevels-1):
output[i,j,k] = (low_level.scalar_gradient_x(a,dx,nlon,i,j,k) - low_level.scalar_gradient_x(a,dx,nlon,i,j,k))*inv_dx + (low_level.scalar_gradient_y(a,dy,nlat,i+1,j,k) - low_level.scalar_gradient_y(a,dy,nlat,i-1,j,k))*inv_dy + (low_level.scalar_gradient_z(a,dz,i,j,k+1)-low_level.scalar_gradient_z(a,dz,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
def divergence_with_scalar(np.ndarray a,np.ndarray u,np.ndarray v,np.ndarray w,np.ndarray dx,DTYPE_f dy,np.ndarray pressure_levels):
cdef np.ndarray output = np.zeros_like(a)
cdef np.ndarray au, av, aw
cdef np.int_t nlat, nlon, nlevels, i, j, k
nlat = output.shape[0]
nlon = output.shape[1]
nlevels = output.shape[2]
au = a*u
av = a*v
aw = a*w
for i in range(nlat):
for j in range(nlon):
for k in range(nlevels):
output[i,j,k] = low_level.scalar_gradient_x(au,dx,nlon,i,j,k) + low_level.scalar_gradient_y(av,dy,nlat,i,j,k) + low_level.scalar_gradient_z_1D(aw[i,j,:],pressure_levels,k)
return output
def radiation_calculation(np.ndarray temperature_world, np.ndarray potential_temperature, np.ndarray pressure_levels, np.ndarray heat_capacity_earth, np.ndarray albedo, DTYPE_f insolation, np.ndarray lat, np.ndarray lon, np.int_t t, np.int_t dt, DTYPE_f day, DTYPE_f year, DTYPE_f axial_tilt):
# calculate change in temperature of ground and atmosphere due to radiative imbalance
cdef np.int_t nlat,nlon,nlevels,i,j,k
cdef DTYPE_f fl = 0.1
cdef np.ndarray upward_radiation,downward_radiation,optical_depth,Q,temperature_atmos
cdef DTYPE_f sun_lat, inv_day
inv_day = 1/(24*60*60)
temperature_atmos = low_level.theta_to_t(potential_temperature,pressure_levels)
nlat = temperature_atmos.shape[0]
nlon = temperature_atmos.shape[1]
nlevels = temperature_atmos.shape[2]
upward_radiation = np.zeros(nlevels)
downward_radiation = np.zeros(nlevels)
Q = np.zeros(nlevels)
for i in range(nlat):
sun_lat = low_level.surface_optical_depth(lat[i])
optical_depth = sun_lat*(fl*(pressure_levels/pressure_levels[0]) + (1-fl)*(pressure_levels/pressure_levels[0])**4)
for j in range(nlon):
# calculate upward longwave flux, bc is thermal radiation at surface
upward_radiation[0] = low_level.thermal_radiation(temperature_world[i,j])
for k in np.arange(1,nlevels):
upward_radiation[k] = (upward_radiation[k-1] - (optical_depth[k]-optical_depth[k-1])*(low_level.thermal_radiation(temperature_atmos[i,j,k])))/(1 + optical_depth[k-1] - optical_depth[k])
# calculate downward longwave flux, bc is zero at TOA (in model)
downward_radiation[-1] = 0
for k in np.arange(0,nlevels-1)[::-1]:
downward_radiation[k] = (downward_radiation[k+1] - low_level.thermal_radiation(temperature_atmos[i,j,k])*(optical_depth[k+1]-optical_depth[k]))/(1 + optical_depth[k] - optical_depth[k+1])
# gradient of difference provides heating at each level
for k in np.arange(nlevels):
Q[k] = -287*temperature_atmos[i,j,k]*low_level.scalar_gradient_z_1D(upward_radiation-downward_radiation,pressure_levels,k)/(1000*pressure_levels[k])
# approximate SW heating of ozone
if pressure_levels[k] < 400*100:
Q[k] += low_level.solar(75,lat[i],lon[j],t,day, year, axial_tilt)*inv_day*(100/pressure_levels[k])
temperature_atmos[i,j,:] += Q*dt
# update surface temperature with shortwave radiation flux
temperature_world[i,j] += dt*((1-albedo[i,j])*(low_level.solar(insolation,lat[i],lon[j],t, day, year, axial_tilt) + downward_radiation[0]) - upward_radiation[0])/heat_capacity_earth[i,j]
return temperature_world, low_level.t_to_theta(temperature_atmos,pressure_levels)
def velocity_calculation(np.ndarray u,np.ndarray v,np.ndarray w,np.ndarray pressure_levels,np.ndarray geopotential,np.ndarray potential_temperature,np.ndarray coriolis,DTYPE_f gravity,np.ndarray dx,DTYPE_f dy,DTYPE_f dt):
# introduce temporary arrays to update velocity in the atmosphere
cdef np.ndarray u_temp = np.zeros_like(u)
cdef np.ndarray v_temp = np.zeros_like(v)
cdef np.ndarray w_temp = np.zeros_like(u)
cdef np.ndarray temperature_atmos
cdef np.int_t nlat,nlon,nlevels,i,j,k
nlat = geopotential.shape[0]
nlon = geopotential.shape[1]
nlevels = len(pressure_levels)
# calculate acceleration of atmosphere using primitive equations on beta-plane
for i in np.arange(2,nlat-2).tolist():
for j in range(nlon):
for k in range(nlevels):
u_temp[i,j,k] += dt*( -u[i,j,k]*low_level.scalar_gradient_x(u,dx,nlon,i,j,k) - v[i,j,k]*low_level.scalar_gradient_y(u,dy,nlat,i,j,k) - w[i,j,k]*low_level.scalar_gradient_z_1D(u[i,j,:],pressure_levels,k) + coriolis[i]*v[i,j,k] - low_level.scalar_gradient_x(geopotential,dx,nlon,i,j,k) - 1E-5*u[i,j,k])
v_temp[i,j,k] += dt*( -u[i,j,k]*low_level.scalar_gradient_x(v,dx,nlon,i,j,k) - v[i,j,k]*low_level.scalar_gradient_y(v,dy,nlat,i,j,k) - w[i,j,k]*low_level.scalar_gradient_z_1D(v[i,j,:],pressure_levels,k) - coriolis[i]*u[i,j,k] - low_level.scalar_gradient_y(geopotential,dy,nlat,i,j,k) - 1E-5*v[i,j,k])
temperature_atmos = low_level.theta_to_t(potential_temperature,pressure_levels)
for i in np.arange(2,nlat-2).tolist():
for j in range(nlon):
for k in np.arange(1,nlevels).tolist():
w_temp[i,j,k] = w_temp[i,j,k-1] - (pressure_levels[k]-pressure_levels[k-1])*pressure_levels[k]*gravity*( low_level.scalar_gradient_x(u,dx,nlon,i,j,k) + low_level.scalar_gradient_y(v,dy,nlat,i,j,k) )/(287*temperature_atmos[i,j,k])
u += u_temp
v += v_temp
w += w_temp
# approximate surface friction
u[:,:,0] *= 0.8
v[:,:,0] *= 0.8
# try to eliminate problems at top boundary
u[:,:,-1] *= 0.5
v[:,:,-1] *= 0.5
return u,v,w
def smoothing_3D(np.ndarray a,DTYPE_f smooth_parameter, DTYPE_f vert_smooth_parameter=0.5):
cdef np.int_t nlat = a.shape[0]
cdef np.int_t nlon = a.shape[1]
cdef np.int_t nlevels = a.shape[2]
smooth_parameter *= 0.5
cdef np.ndarray test = np.fft.fftn(a)
test[int(nlat*smooth_parameter):int(nlat*(1-smooth_parameter)),:,:] = 0
test[:,int(nlon*smooth_parameter):int(nlon*(1-smooth_parameter)),:] = 0
test[:,:,int(nlevels*vert_smooth_parameter):int(nlevels*(1-vert_smooth_parameter))] = 0
return np.fft.ifftn(test).real