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Main.py
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Main.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Jul 5 08:51:38 2023
@author: ricij
"""
import copy
import matplotlib.pyplot as plt
import numpy as np
import scipy
from scipy import sparse
from scipy import special
import Functions
import ATM_fct
import OCN_fct
class Mesh:
def __init__(self):
self.n_latitude = 361
self.n_longitude = 128
self.ndof = self.n_latitude **2
self.h = np.pi / (self.n_latitude - 1)
self.RE = 6.37E6 #Radius der Erde
self.Tf = -1.8 # Freezing point of sea water [degC]
self.ki = 2.0 #Thermal conductivity of sea ice [W m^-1 degC^-1]
self.Tm = -0.1 # Melting Temperature of sea water
self.Lf = 10.0 # Latent heat of fusion of sea ice [W yr m^-3]
self.A_up = 380 # Fluxes
self.B_up = 7.9
self.A_dn = 335
self.B_dn = 5.9
self.A_olr = 241
self.B_olr = 2.4
#self.csc2 = np.array([1 / np.sin(self.h * j) ** 2 for j in range(1, self.n_latitude - 1)])
#self.cot = np.array([1 / np.tan(self.h * j) for j in range(1, self.n_latitude - 1)])
class P_atm:
def __init__(self):
self.heat_capacity = 0.3 * np.ones(mesh.n_latitude) #Atmosphere column heat capacity [W yr m^-2 degC^-1]
self.diffusion_coeff = 2E14 #Large-scale atmospheric diffusivity [m^2 yr^-1]
class P_ocn:
def __init__(self):
self.K_O = 4.4E11 #Large-scale ocean diffusivity [m^2 yr^-1]
self.c_O = 1.27E-4 #Ocean specific heat capacity [W yr kg^-1 degC^-1]
self.rhoo = 1025 #Density of sea water [kg m^-3]
self.Hml_const = 75 #Mixed-layer depth when set constant [m]
def ice_edge(H_I, phi):
if H_I[len(H_I)-1] == 0:
index = len(H_I)
ice_latitude = phi[len(phi)-1]
else:
index = 0
while (H_I[index] <= 0):
index = index + 1
ice_latitude = phi[index]
return index, ice_latitude
def surface_temp(T_ATM, T_OCN, H_I, solar_forcing_ocn, phi, mesh):
T_S = copy.copy(T_OCN)
if any(H_I) > 0 : #sea ice exists
phi_i_index, phi_i = ice_edge(H_I,phi)
T_d = (mesh.ki * mesh.Tf + H_I * (solar_forcing_ocn - mesh.A_up + mesh.A_dn + mesh.B_dn * T_ATM))/(mesh.ki + mesh.B_up * H_I)
for j in range(phi_i_index,len(phi)):
T_S[j] = mesh.Tm * (T_d[j] > mesh.Tm) + T_d[j] * (T_d[j] <= mesh.Tm)
return T_S
def FreezeAndMelt(T_OCN, H_I, Hml, mesh):
T_OCN_new = copy.copy(T_OCN)
H_I_new = copy.copy(H_I)
z = mesh.Lf/(P_ocn.c_O*P_ocn.rhoo*Hml);
for j in range(len(T_OCN)):
if H_I[j] < 0:
H_I_new[j] = 0
T_OCN_new[j] = T_OCN[j] - z[j]*H_I[j]
if T_OCN_new[j] < mesh.Tf:
H_I_new[j] = (mesh.Tf-T_OCN_new[j])/z[j]
T_OCN_new[j] = mesh.Tf
elif H_I[j] == 0 and T_OCN[j] < mesh.Tf:
H_I_new[j] = (mesh.Tf-T_OCN[j])/z[j]
T_OCN_new[j] = mesh.Tf
elif H_I[j] > 0:
H_I_new[j] = H_I[j] + (mesh.Tf-T_OCN[j])/z[j]
T_OCN_new[j] = mesh.Tf
if H_I_new[j] < 0:
T_OCN_new[j] = mesh.Tf -z[j]*H_I_new[j]
H_I_new[j] = 0
return T_OCN_new, H_I_new
def timestep_euler_forward(mesh,T_S, T_ATM, Fb, solar_forcing, H_I, t, delta_t):
# Note that this function modifies the first argument instead of returning the result
H_I_new = H_I - delta_t * (1/mesh.Lf * (-mesh.A_up - mesh.B_up * T_S + mesh.A_dn + mesh.B_dn * T_ATM + Fb + solar_forcing) * (H_I >0))
return H_I_new
def compute_equilibrium(mesh, diffusion_coeff_atm, heat_capacity_atm, T_ATM_0, T_OCN_0, T_S_0,P_ocn,
diffusion_coeff_ocn, heat_capacity_ocn, solar_forcing_ocn, phi, true_longitude, max_iterations=150, rel_error=2e-5, verbose=True):
# Number of time steps per year
ntimesteps = 48
# Step size
delta_t = 1 / ntimesteps
T_ATM = np.zeros((mesh.n_latitude, ntimesteps))
T_ATM[:,-1] = T_ATM_0
T_OCN = np.zeros((mesh.n_latitude, ntimesteps))
T_OCN[:,-1] = T_OCN_0
T_S = np.zeros((mesh.n_latitude, ntimesteps))
T_S[:,-1] = T_S_0
H_I = np.zeros((mesh.n_latitude, ntimesteps))
H_I[:,-1] = H_I_0
# Area-mean in every time step
temp_atm = np.zeros(ntimesteps)
temp_ocn= np.zeros(ntimesteps)
temp_s = np.zeros(ntimesteps)
# Average temperature over all time steps from the previous iteration to approximate the error
old_avg_atm = 0
old_avg_ocn = 0
old_avg_s = 0
jacobian_atm = ATM_fct.calc_jacobian_atm(mesh, diffusion_coeff_atm, P_atm.heat_capacity, phi)
jacobian_ocn = OCN_fct.calc_jacobian_ocn(mesh, diffusion_coeff_ocn, heat_capacity_ocn, phi)
for i in range(max_iterations):
print(i)
for t in range(ntimesteps):
phi_i = ice_edge(H_I[:,t-1], phi)[1] # neuer Ice_Edge Index
Fb = OCN_fct.BasalFlux(phi)
Hml = P_ocn.Hml_const * np.ones(len(phi))
albedo_ocn = OCN_fct.calc_albedo(phi, phi_i)
solar_forcing_ocn = Functions.calc_solar_forcing(albedo_ocn, true_longitude)[:,t]
# T_ATM[:,t] = ATM_fct.timestep_euler_forward_atm(T_ATM[:,t-1], t, delta_t, mesh, diffusion_coeff_atm, P_atm.heat_capacity, T_S[:,t-1], phi)
T_ATM[:,t] = ATM_fct.timestep_euler_backward_atm(jacobian_atm, 1 / ntimesteps, T_ATM[:,t-1], T_S[:,t-1], t, mesh, P_atm.heat_capacity)
# T_OCN[:,t] = OCN_fct.timestep_euler_forward_ocn(T_OCN[:,t-1], t, delta_t, mesh, diffusion_coeff_ocn, heat_capacity_ocn, solar_forcing_ocn, Fb, T_S[:,t-1], T_ATM[:,t-1], H_I[:,t-1], phi)
T_OCN[:,t] = OCN_fct.timestep_euler_backward_ocn(jacobian_ocn, 1 / ntimesteps, T_OCN[:,t-1], T_S[:,t-1], T_ATM[:,t-1], t, mesh, heat_capacity_ocn, solar_forcing_ocn, Fb, H_I[:,t-1])
H_I[:,t] = timestep_euler_forward(mesh,T_S[:,t-1], T_ATM[:,t-1], Fb, solar_forcing_ocn, H_I[:,t-1], t, delta_t)
T_OCN[:,t], H_I[:,t] = FreezeAndMelt(T_OCN[:,t], H_I[:,t], Hml, mesh)
T_S[:,t] = surface_temp(T_ATM[:,t], T_OCN[:,t], H_I[:,t], solar_forcing_ocn, phi, mesh)
temp_atm[t] = np.mean(T_ATM[:,t])
temp_ocn[t] = np.mean(T_OCN[:,t])
temp_s[t] = np.mean(T_S[:,t])
avg_temperature_atm = np.sum(temp_atm) / ntimesteps
avg_temperature_ocn = np.sum(temp_ocn) / ntimesteps
avg_temperature_s = np.sum(temp_s) / ntimesteps
print(np.abs(avg_temperature_atm - old_avg_atm))
if (np.abs(avg_temperature_atm - old_avg_atm) and np.abs(avg_temperature_ocn - old_avg_ocn) and np.abs(avg_temperature_s - old_avg_s)) < rel_error:
# We can assume that the error is sufficiently small now.
verbose and print("Equilibrium reached!")
break
else:
old_avg_atm = avg_temperature_atm
old_avg_ocn = avg_temperature_ocn
old_avg_s = avg_temperature_s
return T_ATM, T_S, T_OCN, H_I
# Run code
if __name__ == '__main__':
file_path_lambda = '/Users/ricij/Documents/Universität/Master/Masterarbeit/VL_Klimamodellierung/input/True_Longitude.dat.txt'
file_path = '/Users/ricij/Documents/Universität/Master/Masterarbeit/VL_Klimamodellierung/input/The_World128x65.dat.txt'
true_longitude = Functions.read_true_longitude(file_path_lambda)
ntimesteps = len(true_longitude)
mesh = Mesh()
phi = np.linspace(0,np.pi/2,mesh.n_latitude) # nur noch bis zum Äquator
phi_i_deg = 75 #belibiger Startwert für den Breitengrad der Eisschicht
P_atm = P_atm() #Parameter für die Atmosphäre
P_ocn = P_ocn() #Parameter für den Ozean
diffusion_coeff_atm = P_atm.heat_capacity * P_atm.diffusion_coeff /mesh.RE**2
heat_capacity_ocn = P_ocn.c_O * P_ocn.rhoo * P_ocn.Hml_const * np.ones(mesh.n_latitude) # Hml kann man auch variable setzen
diffusion_coeff_ocn = heat_capacity_ocn * P_ocn.K_O / mesh.RE**2 #Diffusionskoeffizient
#Inital Conditions
T_ATM_0 = 0.5 * (-15 + 35 * np.cos(2*phi))
T_OCN_0 = 0.5 * (28.2 + 31.8 * np.cos(180*phi/phi_i_deg))
B = 3/((np.pi/2) - phi_i_deg * np.pi/180)
A = -B *phi_i_deg * np.pi/180
H_I_0 = A + B * phi
H_I_0 = H_I_0 * (H_I_0 > 0) #da Eisdicke nicht negativ sein kann
T_OCN_0 = T_OCN_0 * (H_I_0 <= 0) + mesh.Tf * (H_I_0 > 0)
Functions.plot_annual_temperature(T_OCN_0, mesh.Tf , "Ocean inital temperature") #begrenzen uns hier auf die Nordhalbkugel
Functions.plot_annual_temperature(T_ATM_0, mesh.Tf , "Atmosphere inital temperature")
phi_index, phi_i = ice_edge(H_I_0, phi)
albedo_ocn = OCN_fct.calc_albedo(phi, phi_i)
solar_forcing_ocn = Functions.calc_solar_forcing(albedo_ocn, true_longitude)
T_S_0 = surface_temp(T_ATM_0, T_OCN_0, H_I_0, solar_forcing_ocn[:,-1], phi, mesh)
Functions.plot_annual_temperature(T_S_0, mesh.Tf , "Surface inital temperature")
T_ATM, T_S, T_OCN, H_I = compute_equilibrium( mesh, diffusion_coeff_atm, P_atm.heat_capacity, T_ATM_0, T_OCN_0, T_S_0, P_ocn, diffusion_coeff_ocn, heat_capacity_ocn, solar_forcing_ocn, phi, true_longitude)
Functions.plot_annual_temperature(np.mean(T_S, axis = 1), np.mean(T_S), "Surface Temp ")
Functions.plot_annual_temperature(np.mean(T_ATM, axis=1),np.mean(T_ATM), "Atmosphere Temp")
Functions.plot_annual_temperature(np.mean(T_OCN, axis = 1), np.mean(T_OCN) , "Ocean Temp")
Functions.plot_annual_temperature(np.mean(H_I, axis = 1), np.mean(H_I) , "Mean Ice Thickness")