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OCN_fct.py
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OCN_fct.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Jul 5 12:11:54 2023
@author: ricij
"""
import matplotlib.pyplot as plt
import numpy as np
import scipy
from scipy import sparse
from scipy import special
import Functions
def calc_albedo(phi, phi_i_n, phi_i_s, mesh): #Berechung des Coalbedo, wobei phi der Breitengrad und phi_i der Breitengrad der südlichsten Eisschicht ist
a0 = 0.72
ai = 0.36
a2 = (a0 - ai)/((np.pi/2)**2)
equator = int((mesh.n_latitude - 1) / 2)
north_h = 0.5 * ((a0-a2*phi[equator:(len(phi))]**2 + ai) - (a0-a2*phi[equator:len(phi)]**2 - ai) * special.erf((phi[equator:len(phi)]-phi_i_n)/0.04))
south_h = 0.5 * ((a0-a2*phi[0:equator]**2 + ai) - (a0-a2*phi[0:equator]**2 - ai) * special.erf((phi_i_s-phi[0:equator])/0.04))
return np.concatenate(( south_h, north_h))
def calc_albedo_n(phi, phi_i_n): #Berechung des Coalbedo, wobei phi der Breitengrad und phi_i der Breitengrad der südlichsten Eisschicht ist
a0 = 0.72
ai = 0.36
a2 = (a0 - ai)/((np.pi/2)**2)
return 0.5 * ((a0-a2*phi**2 + ai) - (a0-a2*phi**2 - ai) * special.erf((phi-phi_i_n)/0.04))
def BasalFlux(phi):
def f(phi):
return -(1.3E16/(2*np.pi*6.37E6**2)) * np.cos(phi)**8 * (1-11*np.sin(phi)**2)
def f_schlange(phi):
return (1-3*np.cos(2*phi))/4
F_bp = 2
return f(phi) + F_bp * f_schlange(phi)
def calc_jacobian_ocn(mesh, diffusion_coeff, heat_capacity, phi):
jacobian = np.zeros((mesh.n_latitude, mesh.n_latitude))
test_temperature = np.zeros(diffusion_coeff.size)
index = 0
for j in range(mesh.n_latitude):
test_temperature[j] = 1.0
diffusion_op = Functions.calc_diffusion_operator(mesh, diffusion_coeff, test_temperature, phi)
op = diffusion_op/heat_capacity
jacobian[:, index] = op
# Reset test_temperature
test_temperature[j] = 0.0
index += 1
return jacobian
def timestep_euler_forward_ocn(T_OCN, t, delta_t, mesh, heat_capacity, solar_forcing, Fb, T_S, T_ATM, H_I):
# Note that this function modifies the first argument instead of returning the result
#diffusion_op = Functions.calc_diffusion_operator(mesh, diffusion_coeff, T_OCN, phi)
T_OCN_New = T_OCN + delta_t * ((solar_forcing - mesh.A_up - mesh.B_up * T_S + mesh.A_dn + mesh.B_dn * T_ATM + Fb)/ heat_capacity) * (H_I<= 0)
return T_OCN_New
def timestep_euler_backward_ocn(jacobian, delta_t, T_OCN, T_S, T_ATM, t, mesh, heat_capacity, solar_forcing, F_b, H_I):
m, n = jacobian.shape
eye = sparse.eye(m, n, format="csc")
jacobian = sparse.csc_matrix(jacobian)
solve = sparse.linalg.factorized(eye - delta_t * jacobian)
source_terms = ((solar_forcing - mesh.A_up - mesh.B_up *T_S + mesh.A_dn + mesh.B_dn * T_ATM + F_b) / heat_capacity) * (H_I <=0)
T_OCN_New = solve(T_OCN + delta_t * source_terms)
return T_OCN_New