mirror of https://github.com/Askill/claude.git
188 lines
6.9 KiB
Python
188 lines
6.9 KiB
Python
# toy model for use on stream
|
|
# Please give me your Twitch prime sub!
|
|
|
|
# CLimate Analysis using Digital Estimations (CLAuDE)
|
|
|
|
import numpy as np
|
|
import matplotlib.pyplot as plt
|
|
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*17 ###### <----- TIMESTEP
|
|
|
|
# power incident on (lat,lon) at time t
|
|
def solar(insolation, lat, lon, t):
|
|
sun_longitude = -t % day
|
|
sun_longitude *= 360/day
|
|
value = insolation*np.cos(lat*np.pi/180)*np.cos((lon-sun_longitude)*np.pi/180)
|
|
if value < 0: return 0
|
|
else: return value
|
|
|
|
t = 0
|
|
|
|
# how many degrees between latitude and longitude gridpoints
|
|
resolution = 3
|
|
|
|
# define coordinate arrays
|
|
lat = np.arange(-90,91,resolution)
|
|
lon = np.arange(0,360,resolution)
|
|
nlat = len(lat)
|
|
nlon = len(lon)
|
|
lon_plot, lat_plot = np.meshgrid(lon, lat)
|
|
|
|
# initialise arrays for various physical fields
|
|
temperature_planet = np.zeros((nlat,nlon)) + 270
|
|
temperature_atmosp = np.zeros((nlat,nlon)) + 270
|
|
albedo = np.zeros((nlat,nlon)) + 0.5
|
|
heat_capacity_earth = np.zeros((nlat,nlon)) + 1E6
|
|
air_pressure = np.zeros((nlat,nlon))
|
|
u = np.zeros((nlat,nlon))
|
|
v = np.zeros((nlat,nlon))
|
|
air_density = np.zeros_like(air_pressure) + 1.3
|
|
|
|
# custom oceans with lower albedo and higher heat capacity
|
|
ocean = True
|
|
if ocean:
|
|
albedo[5:55,9:20] = 0.7
|
|
albedo[23:50,45:70] = 0.7
|
|
albedo[2:30,85:110] = 0.7
|
|
heat_capacity_earth[5:55,9:20] *= 2
|
|
heat_capacity_earth[23:50,45:70] *= 2
|
|
heat_capacity_earth[2:30,85:110] *= 2
|
|
|
|
# define physical constants
|
|
epsilon = 0.75
|
|
epsilon = 0.75
|
|
heat_capacity_atmos = 1E7
|
|
specific_gas = 287
|
|
thermal_diffusivity_air = 20E-6
|
|
thermal_diffusivity_roc = 1.5E-6
|
|
insolation = 1370
|
|
sigma = 5.67E-8
|
|
|
|
# define planet size and various geometric constants
|
|
planet_radius = 6.4E6
|
|
circumference = 2*np.pi*planet_radius
|
|
circle = np.pi*planet_radius**2
|
|
sphere = 4*np.pi*planet_radius**2
|
|
|
|
# define how far apart the gridpoints are: note that we use central difference derivatives, and so these distances are actually twice the distance between gridboxes
|
|
dy = circumference/nlat
|
|
dx = np.zeros(nlat)
|
|
coriolis = np.zeros(nlat) # also define the coriolis parameter here
|
|
angular_speed = 2*np.pi/day
|
|
for i in range(nlat):
|
|
dx[i] = dy*np.cos(lat[i]*np.pi/180)
|
|
coriolis[i] = angular_speed*np.sin(lat[i]*np.pi/180)
|
|
|
|
# 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]
|
|
# 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:
|
|
return 0
|
|
else:
|
|
return (a[i+1,j]-a[i-1,j])/dy
|
|
# laplacian of scalar field a in the local x direction
|
|
def laplacian(a):
|
|
output = np.zeros_like(a)
|
|
for i in np.arange(1,len(a[:,0])-1):
|
|
for j in range(len(a[0,:])):
|
|
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
|
|
# divergence of (a*u) where a is a scalar field and u is the atmospheric velocity field
|
|
def divergence_with_scalar(a):
|
|
output = np.zeros_like(a)
|
|
for i in range(len(a[:,0])):
|
|
for j in range(len(a[0,:])):
|
|
output[i,j] = scalar_gradient_x(a*u,i,j) + scalar_gradient_y(a*v,i,j)
|
|
return output
|
|
|
|
#####
|
|
|
|
# set up plot
|
|
f, ax = plt.subplots(2,figsize=(9,9))
|
|
f.canvas.set_window_title('CLAuDE')
|
|
ax[0].contourf(lon_plot, lat_plot, temperature_planet, cmap='seismic')
|
|
ax[1].contourf(lon_plot, lat_plot, temperature_atmosp, cmap='seismic')
|
|
plt.subplots_adjust(left=0.1, right=0.75)
|
|
ax[0].set_title('Ground temperature')
|
|
ax[1].set_title('Atmosphere temperature')
|
|
# allow for live updating as calculations take place
|
|
plt.ion()
|
|
plt.show()
|
|
|
|
advection = True # can turn thermal and mass advection on or off
|
|
boundary = 5 # advection will occur starting from this many gridpoints away from the poles
|
|
|
|
while True:
|
|
|
|
# print current time in simulation to command line
|
|
print("t = " + str(round(t/day,2)) + " days", end='\r')
|
|
print(u.max(),u.min(),v.max(),v.min(),air_density.max(),air_density.min())
|
|
|
|
if t < day*2:
|
|
dt = 60*71
|
|
velocity = False
|
|
else:
|
|
dt = 60*7
|
|
velocity = 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*(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*air_density[i,j])
|
|
|
|
if advection:
|
|
# allow for thermal advection in the atmosphere, and heat diffusion in the atmosphere and the ground
|
|
atmosp_addition = dt*divergence_with_scalar(temperature_atmosp)
|
|
temperature_atmosp[boundary:-boundary,:] -= atmosp_addition[boundary:-boundary,:]
|
|
|
|
# as density is now variable, allow for mass advection
|
|
density_addition = dt*divergence_with_scalar(air_density)
|
|
air_density[boundary:-boundary,:boundary] -= density_addition[boundary:-boundary,:boundary]
|
|
|
|
temperature_atmosp += dt*(thermal_diffusivity_air*laplacian(temperature_atmosp))
|
|
temperature_planet += dt*(thermal_diffusivity_roc*laplacian(temperature_planet))
|
|
|
|
# update air pressure
|
|
air_pressure = air_density*specific_gas*temperature_atmosp
|
|
|
|
if velocity:
|
|
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(boundary,nlat-boundary):
|
|
for j in range(nlon):
|
|
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))
|
|
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))
|
|
|
|
u += u_temp
|
|
v += v_temp
|
|
|
|
# update plot
|
|
ax[0].contourf(lon_plot, lat_plot, temperature_planet, cmap='seismic')
|
|
test = ax[1].contourf(lon_plot, lat_plot, temperature_atmosp, cmap='seismic')
|
|
# ax[1].quiver(lon_plot[::3, ::3],lat_plot[::3, ::3],u[::3, ::3],v[::3, ::3])
|
|
ax[1].streamplot(lon_plot,lat_plot,u,v,density=0.75,color='black')
|
|
ax[0].set_title('$\it{Ground} \quad \it{temperature}$')
|
|
ax[1].set_title('$\it{Atmospheric} \quad \it{temperature}$')
|
|
for i in ax:
|
|
i.set_ylabel('Latitude')
|
|
i.axhline(y=0,color='black',alpha=0.3)
|
|
ax[-1].set_xlabel('Longitude')
|
|
cbar_ax = f.add_axes([0.85, 0.15, 0.05, 0.7])
|
|
f.colorbar(test, cax=cbar_ax)
|
|
cbar_ax.set_title('Temperature (K)')
|
|
f.suptitle( 'Time ' + str(round(24*t/day,2)) + ' hours' )
|
|
plt.pause(0.01)
|
|
ax[0].cla()
|
|
ax[1].cla()
|
|
|
|
# advance time by one timestep
|
|
t += dt |