BASTET/main_netCDF.py

import numpy as np
import matplotlib.pyplot as plt
from datetime import datetime
start = datetime.now()
print(start)
begin_time = datetime.now()
from models.sun import sun_angles_analytical
from models.sun import sun_angles_astropy
from models.drag import drag, c_d
from input.user_input import *
from input.natural_constants import *
from astropy.time import Time
import astropy.units as unit
from models.thermal import AirMass
from netCDF4 import Dataset

data = Dataset("test2021.nc", "r", format="NETCDF4")

ERAtime = data.variables['time'][:]      # time
ERAlat = data.variables['latitude'][:]   # latitude
ERAlon = data.variables['longitude'][:]  # longitude
ERAz = data.variables['z'][:]/g          # geopotential to geopotential height
ERApress = data.variables['level'][:]    # pressure level
ERAtemp = data.variables['t'][:]
vw_x = data.variables['u'][:]  # v_x
vw_y = data.variables['v'][:]  # v_y
vw_z = data.variables['w'][:]  # v_z

# t: simulation time (0 .. t_max) in [s]
# utc = Time(start_utc) + t * u.second  # current time (UTC)

lat = start_lat   # deg
lon = start_lon   # deg

# date = Time('2020-12-13 12:00:00.000')


# INITIALISATION

t = 0  # simulation time in seconds
h = start_height
utc = Time(start_utc)
epoch_diff = (Time(start_utc).jd - Time('1900-01-01 00:00:00.0').jd) * 24.000000
t_epoch = epoch_diff

sq_diff_lat = (ERAlat - lat) ** 2
sq_diff_lon = (ERAlon - lon) ** 2
sq_diff_time = (ERAtime - t_epoch) ** 2

min_index_lat = sq_diff_lat.argmin()
min_index_lon = sq_diff_lat.argmin()
min_index_time = sq_diff_time.argmin()

sq_diff_h = (ERAz[min_index_time, :, min_index_lat, min_index_lon] - h) ** 2

min_index_h = sq_diff_h.argmin()

h_grid = ERAz[min_index_time, min_index_h, min_index_lat, min_index_lon]
p_grid = ERApress[min_index_h] * 100
T_grid = ERAtemp[min_index_time, min_index_h, min_index_lat, min_index_lon]
u_grid = vw_x[min_index_time, min_index_h, min_index_lat, min_index_lon]
v_grid = vw_y[min_index_time, min_index_h, min_index_lat, min_index_lon]
w_grid = -1/g * vw_z[min_index_time, min_index_h, min_index_lat, min_index_lon] * R_air * T_grid / p_grid

v = v_grid
u = u_grid
w = w_grid
T_air = T_grid
p_air = p_grid
rho_air = p_air/(R_air * T_air)

v_x = 0
v_y = 0
v_z = 0

T_gas = T_air
T_film = T_gas

t_list = []
h_list = []
lat_list = []
lon_list = []
p_list = []
Temp_list = []
rho_list = []

while t <= t_end and h >= 0:
    t_list.append(t)
    h_list.append(h)
    lat_list.append(lat)
    lon_list.append(lon)

    p_list.append(p_air)
    Temp_list.append(T_air)
    rho_list.append(rho_air)

    t_epoch = epoch_diff + t/3600

    sq_diff_lat = (ERAlat - lat) ** 2
    sq_diff_lon = (ERAlon - lon) ** 2
    sq_diff_time = (ERAtime - t_epoch) ** 2

    min_index_lat = sq_diff_lat.argmin()
    min_index_lon = sq_diff_lat.argmin()
    min_index_time = sq_diff_time.argmin()

    sq_diff_h = (ERAz[min_index_time, :, min_index_lat, min_index_lon] - h) ** 2

    min_index_h = sq_diff_h.argmin()

    h_grid = ERAz[min_index_time, min_index_h, min_index_lat, min_index_lon]
    p_grid = ERApress[min_index_h] * 100
    T_grid = ERAtemp[min_index_time, min_index_h, min_index_lat, min_index_lon]
    u_grid = vw_x[min_index_time, min_index_h, min_index_lat, min_index_lon]
    v_grid = vw_y[min_index_time, min_index_h, min_index_lat, min_index_lon]
    w_grid = -1/g * vw_z[min_index_time, min_index_h, min_index_lat, min_index_lon] * R_air * T_grid / p_grid

    p_air = p_grid
    p_gas = p_air
    T_air = T_grid
    rho_air = p_air / (R_air * T_air)
    u = u_grid
    v = v_grid
    w = w_grid

    v_relx = u - v_x
    v_rely = v - v_y
    v_relz = w - v_z

    v_rel = (v_relx ** 2 + v_rely ** 2 + v_relz ** 2) ** (1/2)

    p_gas = p_air
    rho_gas = p_gas/(R_gas * T_gas)  # calculate gas density through ideal(!) gas equation

    V_b = m_gas/rho_gas  # calculate balloon volume from current gas mass and gas density

    if V_b > V_design:
        V_b = V_design
        m_gas = V_design * rho_gas
    else:
        pass

    m_gross = m_pl + m_film
    m_tot = m_pl + m_film + m_gas
    m_virt = m_tot + c_virt * rho_air * V_b

    d_b = 1.383 * V_b ** (1/3)  # calculate diameter of balloon from its volume
    L_goreB = 1.914 * V_b ** (1/3)
    h_b = 0.748 * d_b
    A_surf = 4.94 * V_b ** (2/3)
    A_surf1 = 4.94 * V_design ** (2/3) * (1 - np.cos(np.pi * L_goreB/L_goreDesign))
    A_eff = 0.65 * A_surf + 0.35 * A_surf1
    A_top = np.pi/4 * d_b ** 2

    D = drag(c_d, rho_air, d_b, v_rel)  # calculate drag force

    if v_rel == 0:
        Drag_x = 0
        Drag_y = 0
        Drag_z = 0
    else:
        Drag_x = D * v_relx/v_rel
        Drag_y = D * v_rely/v_rel
        Drag_z = D * v_relz/v_rel

    I = g * V_b * (rho_air - rho_gas)  # calculate gross inflation
    W = g * m_gross  # calculate weight (force)
    F = I - W + Drag_z

    AZ, ELV = sun_angles_analytical(lat, lon, utc)

    A_proj = A_top * (0.9125 + 0.0875 * np.cos(np.pi - 2 * np.deg2rad(ELV)))

    # CALCULATIONS FOR THERMAL MODEL

    if ELV >= -(180 / np.pi * np.arccos(R_E / (R_E + h))):
        tau_atm = 0.5 * (np.exp(-0.65 * AirMass(p_air, p_0, ELV, h)) + np.exp(-0.095 * AirMass(p_air, p_0, ELV, h)))
        tau_atmIR = 1.716 - 0.5 * (np.exp(-0.65 * p_air / p_0) + np.exp(-0.095 * p_air / p_0))
    else:
        tau_atm = 0
        tau_atmIR = 0

    doy = int(utc.doy)

    MA = (357.52911 + 0.98560028 * (utc.jd - 2451545)) % 360  # in degree, reference: see folder "literature"
    TA = MA + 2 * e * np.sin(np.deg2rad(MA)) + 5 / 4 * e ** 2 * np.sin(np.deg2rad(2 * MA))
    I_Sun = 1367.5 * ((1 + e * np.cos(np.deg2rad(TA))) / (1 - e ** 2)) ** 2
    I_SunZ = I_Sun * tau_atm
    q_sun = I_SunZ
    q_IRground = epsilon_ground * sigma * T_ground ** 4
    q_IREarth = q_IRground * tau_atmIR

    if ELV <= 0:
        q_Albedo = 0
    else:
        q_Albedo = Albedo * I_Sun * np.sin(np.deg2rad(ELV))

    my_air = (1.458 * 10 ** -6 * T_air ** 1.5) / (T_air + 110.4)
    my_gas = 1.895 * 10 ** -5 * (T_gas / 273.15) ** 0.647
    k_air = 0.0241 * (T_air / 273.15) ** 0.9
    k_gas = 0.144 * (T_gas / 273.15) ** 0.7
    Pr_air = 0.804 - 3.25 * 10 ** (-4) * T_air
    Pr_gas = 0.729 - 1.6 * 10 ** (-4) * T_gas

    Gr_air = (rho_air ** 2 * g * np.abs(T_film - T_air) * d_b ** 3) / (T_air * my_air ** 2)
    Nu_air = 2 + 0.45 * (Gr_air * Pr_air) ** 0.25
    HC_free = Nu_air * k_air / d_b
    Re = np.abs(v_relz) * d_b * rho_air / my_air

    HC_forced = k_air / d_b * (2 + 0.41 * Re ** 0.55)
    HC_internal = 0.13 * k_gas * ((rho_gas ** 2 * g * np.abs(T_film - T_gas) * Pr_gas) / (T_gas * my_air ** 2)) ** (
                1 / 3)
    HC_external = np.maximum(HC_free, HC_forced)

    HalfConeAngle = np.arcsin(R_E / (R_E + h))
    ViewFactor = (1 - np.cos(HalfConeAngle)) / 2

    Q_Sun = alpha_VIS * A_proj * q_sun * (1 + tau_VIS / (1 - r_VIS))
    Q_Albedo = alpha_VIS * A_surf * q_Albedo * ViewFactor * (1 + tau_VIS / (1 - r_VIS))
    Q_IREarth = alpha_IR * A_surf * q_IREarth * ViewFactor * (1 + tau_IR / (1 - r_IR))
    Q_IRfilm = sigma * epsilon * alpha_IR * A_surf * T_film ** 4 * 1 / (1 - r_IR)
    Q_IRout = sigma * epsilon * A_surf * T_film ** 4 * (1 * tau_IR / (1 - r_IR))
    Q_ConvExt = HC_external * A_eff * (T_air - T_film)
    Q_ConvInt = HC_internal * A_eff * (T_film - T_gas)

    # RoC = -v_z
    # dT_gas = (Q_ConvInt / (gamma * m_gas * c_v) - (gamma - 1) / gamma * rho_air(h) * g / (rho_gas * R_gas) * RoC) * dt
    # dT_film = ((Q_Sun + Q_Albedo + Q_IREarth + Q_IRfilm + Q_ConvExt - Q_ConvInt - Q_IRout) / (c_f * m_film)) * dt
    #  v_w = w
    #  v = v_z

    s = h

    a_x = Drag_x/m_virt
    a_y = Drag_y/m_virt
    a_z = F/m_virt

    # DIFFERENTIAL EQUATIONS

    dx = dt * v_x + 0.5 * a_x * dt ** 2   # lon
    dy = dt * v_y + 0.5 * a_y * dt ** 2   # lat

    lon = lon + np.rad2deg(np.arctan(dx/((6371229.0 + h) * np.cos(np.deg2rad(lat)))))
    lat = lat + np.rad2deg(np.arctan(dy/(6371229.0 + h)))

    v_xn = v_x + dt * a_x
    v_yn = v_y + dt * a_y

    s_n = s + dt * v_z + 0.5 * a_z * dt ** 2
    dh = s_n - s
    v_n = v_z + dt * a_z

    T_gn = T_gas + dt * (Q_ConvInt / (gamma * c_v * m_gas) - g * R_gas * T_gas * dh / (c_v * gamma * T_air * R_air))
    T_en = T_film + (Q_Sun + Q_Albedo + Q_IREarth + Q_IRfilm + Q_ConvExt - Q_ConvInt - Q_IRout) / (c_f * m_film) * dt

    T_g = T_gn
    T_e = T_en
    s = s_n
    v_x = v_xn
    v_y = v_yn
    v_z = v_n

    h = s
    T_gas = T_g
    T_film = T_e
#   v_z = v

    t += dt  # time increment
    utc = Time(start_utc) + t * unit.second

end = datetime.now()
print(end)
plt.plot(t_list, h_list, 'k-')
plt.plot(t_list, p_list, 'r-')
plt.plot(t_list, Temp_list, 'b-')
plt.plot(t_list, rho_list, 'g-')
plt.show()