Integrated full ERA5 netCDF-Interpolation, model-framework now considered to be complete
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import numpy as np
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import math
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import xarray as xr
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import matplotlib.pyplot as plt
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from scipy.spatial import cKDTree
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from scipy import interpolate
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import cartopy.crs as ccrs
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from datetime import datetime
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start = datetime.now()
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print(start)
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begin_time = datetime.now()
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from models.sun import sun_angles_analytical
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from models.sun import sun_angles_astropy
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from models.drag import drag, c_d
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from input.user_input import *
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from input.natural_constants import *
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from astropy.time import Time
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import astropy.units as unit
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from models.thermal import AirMass
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from netCDF4 import Dataset
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import pandas as pd
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data = pd.read_excel(r'C:\Users\marcel\PycharmProjects\MasterThesis\Mappe1.xls', sheet_name='Tabelle3')
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comp_time = pd.DataFrame(data, columns= ['Time'])
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comp_height = pd.DataFrame(data, columns= ['Height'])
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def transform(lon, lat, t):
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# WGS 84 reference coordinate system parameters
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A = 6378137.0 # major axis [m]
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E2 = 6.69437999014e-3 # eccentricity squared
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t_s = 1000 * t
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lon_rad = np.radians(lon)
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lat_rad = np.radians(lat)
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# convert to cartesian coordinates
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r_n = A / (np.sqrt(1 - E2 * (np.sin(lat_rad) ** 2)))
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x = r_n * np.cos(lat_rad) * np.cos(lon_rad)
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y = r_n * np.cos(lat_rad) * np.sin(lon_rad)
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z = r_n * (1 - E2) * np.sin(lat_rad)
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return x, y, z, t_s
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data = Dataset("test2021.nc", "r", format="NETCDF4")
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ERAtime = data.variables['time'][:] # time
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ERAlat = data.variables['latitude'][:] # latitude
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ERAlon = data.variables['longitude'][:] # longitude
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ERAz = data.variables['z'][:]/g # geopotential to geopotential height
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ERApress = data.variables['level'][:] # pressure level
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ERAtemp = data.variables['t'][:] # temperature in K
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vw_x = data.variables['u'][:] # v_x
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vw_y = data.variables['v'][:] # v_y
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vw_z = data.variables['w'][:] # v_z
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lon_era2d, lat_era2d, time_era = np.meshgrid(ERAlon, ERAlat, ERAtime)
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xs, ys, zs, ts = transform(lon_era2d.flatten(), lat_era2d.flatten(), time_era.flatten())
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tree = cKDTree(np.column_stack((xs, ys, zs, ts))) # !
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lat = start_lat # deg
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lon = start_lon # deg
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t = 0 # simulation time in seconds
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h = start_height
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utc = Time(start_utc)
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epoch_diff = (Time(start_utc).jd - Time('1900-01-01 00:00:00.0').jd) * 24.000000
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t_epoch = epoch_diff
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xt, yt, zt, tt = transform(lon, lat, t) # test coordinates
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d, inds = tree.query(np.column_stack((xt, yt, zt, tt)), k=8) # longitude, latitude, time in h # !
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w = 1.0 / d[0] ** 2
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lat_sel = np.unravel_index(inds[0], lon_era2d.shape)[0]
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lon_sel = np.unravel_index(inds[0], lon_era2d.shape)[1]
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time_sel = np.unravel_index(inds[0], lon_era2d.shape)[2]
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interp4d_height = np.ma.dot(w, ERAz[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
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interp4d_temp = np.ma.dot(w, ERAtemp[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
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interp4d_vw_x = np.ma.dot(w, vw_x[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
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interp4d_vw_y = np.ma.dot(w, vw_y[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
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interp4d_vw_z = np.ma.dot(w, vw_z[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
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pressure_hPa = np.array([1, 2, 3, 5, 7, 10, 20, 30, 50, 70, 100, 125, 150, 175, 200,225, 250, 300, 350, 400,
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450, 500, 550, 600, 650, 700, 750, 775, 800, 825, 850, 875, 900, 925, 950, 975, 1000])
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pressure = 100 * pressure_hPa
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print(pressure)
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# height_interp1d = interpolate.interp1d(interp4d_height, pressure)
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temp_interp1d = interpolate.interp1d(interp4d_height, interp4d_temp)
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press_interp1d = interpolate.interp1d(interp4d_height, pressure)
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vw_x_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_x)
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vw_y_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_y)
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vw_z_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_z)
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#u = 0
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#v = 0
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#w = 0
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T_air = temp_interp1d(h)
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p_air = press_interp1d(h)
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rho_air = p_air/(R_air * T_air)
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u = vw_x_interp1d(h)
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v = vw_y_interp1d(h)
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w = -1 / g * vw_z_interp1d(h) * R_air * T_air / p_air
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v_x = 0
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v_y = 0
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v_z = 0
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v_rel = 0
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T_gas = T_air
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T_film = T_gas
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t_list = []
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h_list = []
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v_list = []
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lat_list = []
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lon_list = []
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p_list = []
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Temp_list = []
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rho_list = []
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while t <= t_end and h >= 0:
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t_list.append(t)
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h_list.append(h)
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v_list.append(v_rel)
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lat_list.append(lat)
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lon_list.append(lon)
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p_list.append(p_air)
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Temp_list.append(T_air)
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rho_list.append(rho_air)
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t_epoch = epoch_diff + t/3600
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xt, yt, zt, tt = transform(lon, lat, t_epoch) # current balloon coordinates in cartesian coordinates: x [m], y [m], z [m], time [h since 1900-01-01 00:00:00.0]
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d, inds = tree.query(np.column_stack((xt, yt, zt, tt)), k=8) # longitude, latitude, time in h # !
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w = 1.0 / d[0] ** 2
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lat_sel = np.unravel_index(inds[0], lon_era2d.shape)[0]
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lon_sel = np.unravel_index(inds[0], lon_era2d.shape)[1]
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time_sel = np.unravel_index(inds[0], lon_era2d.shape)[2]
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interp4d_height = np.ma.dot(w, ERAz[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
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interp4d_temp = np.ma.dot(w, ERAtemp[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
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interp4d_vw_x = np.ma.dot(w, vw_x[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
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interp4d_vw_y = np.ma.dot(w, vw_y[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
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interp4d_vw_z = np.ma.dot(w, vw_z[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
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press_interp1d = interpolate.interp1d(interp4d_height, pressure)
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temp_interp1d = interpolate.interp1d(interp4d_height, interp4d_temp)
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vw_x_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_x)
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vw_y_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_y)
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vw_z_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_z)
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try:
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p_air = press_interp1d(h)
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T_air = temp_interp1d(h)
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except:
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if (h > interp4d_height[0]):
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h = interp4d_height[0]
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else:
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h = interp4d_height[-1]
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p_air = press_interp1d(h)
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T_air = temp_interp1d(h)
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#print("height")
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#print(h)
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#print("temperature")
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#print(temp_interp1d(h))
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#print("pressure")
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#print(press_interp1d(h))
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#print("vw_x")
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#print(vw_x_interp1d(h))
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p_gas = p_air
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rho_air = p_air / (R_air * T_air)
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u = vw_x_interp1d(h)
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v = vw_y_interp1d(h)
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w = -1/g * vw_z_interp1d(h) * R_air * T_air / p_air
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v_relx = u - v_x
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v_rely = v - v_y
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v_relz = w - v_z
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v_rel = (v_relx ** 2 + v_rely ** 2 + v_relz ** 2) ** (1/2)
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rho_gas = p_gas/(R_gas * T_gas) # calculate gas density through ideal(!) gas equation
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V_b = m_gas/rho_gas # calculate balloon volume from current gas mass and gas density
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if V_b > V_design:
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V_b = V_design
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#m_gas = V_design * rho_gas
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else:
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pass
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m_gross = m_pl + m_film
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m_tot = m_pl + m_film + m_gas
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m_virt = m_tot + c_virt * rho_air * V_b
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d_b = 1.383 * V_b ** (1/3) # calculate diameter of balloon from its volume
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L_goreB = 1.914 * V_b ** (1/3)
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h_b = 0.748 * d_b
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A_surf = 4.94 * V_b ** (2/3)
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A_surf1 = 4.94 * V_design ** (2/3) * (1 - np.cos(np.pi * L_goreB/L_goreDesign))
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A_eff = 0.65 * A_surf + 0.35 * A_surf1
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A_top = np.pi/4 * d_b ** 2
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D = drag(c_d, rho_air, d_b, v_rel) # calculate drag force
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if v_rel == 0:
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Drag_x = 0
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Drag_y = 0
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Drag_z = 0
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else:
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Drag_x = D * v_relx/v_rel
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Drag_y = D * v_rely/v_rel
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Drag_z = D * v_relz/v_rel
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I = g * V_b * (rho_air - rho_gas) # calculate gross inflation
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W = g * m_gross # calculate weight (force)
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F = I - W + Drag_z
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AZ, ELV = sun_angles_analytical(lat, lon, utc)
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A_proj = A_top * (0.9125 + 0.0875 * np.cos(np.pi - 2 * np.deg2rad(ELV)))
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# CALCULATIONS FOR THERMAL MODEL
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if ELV >= -(180 / np.pi * np.arccos(R_E / (R_E + h))):
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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)))
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tau_atmIR = 1.716 - 0.5 * (np.exp(-0.65 * p_air / p_0) + np.exp(-0.095 * p_air / p_0))
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else:
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tau_atm = 0
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tau_atmIR = 0
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doy = int(utc.doy)
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MA = (357.52911 + 0.98560028 * (utc.jd - 2451545)) % 360 # in degree, reference: see folder "literature"
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TA = MA + 2 * e * np.sin(np.deg2rad(MA)) + 5 / 4 * e ** 2 * np.sin(np.deg2rad(2 * MA))
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I_Sun = 1367.5 * ((1 + e * np.cos(np.deg2rad(TA))) / (1 - e ** 2)) ** 2
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I_SunZ = I_Sun * tau_atm
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q_sun = I_SunZ
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q_IRground = epsilon_ground * sigma * T_ground ** 4
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q_IREarth = q_IRground * tau_atmIR
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if ELV <= 0:
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q_Albedo = 0
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else:
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q_Albedo = Albedo * I_Sun * np.sin(np.deg2rad(ELV))
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my_air = (1.458 * 10 ** -6 * T_air ** 1.5) / (T_air + 110.4)
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my_gas = 1.895 * 10 ** -5 * (T_gas / 273.15) ** 0.647
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k_air = 0.0241 * (T_air / 273.15) ** 0.9
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k_gas = 0.144 * (T_gas / 273.15) ** 0.7
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Pr_air = 0.804 - 3.25 * 10 ** (-4) * T_air
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Pr_gas = 0.729 - 1.6 * 10 ** (-4) * T_gas
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Gr_air = (rho_air ** 2 * g * np.abs(T_film - T_air) * d_b ** 3) / (T_air * my_air ** 2)
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Nu_air = 2 + 0.45 * (Gr_air * Pr_air) ** 0.25
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HC_free = Nu_air * k_air / d_b
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Re = np.abs(v_relz) * d_b * rho_air / my_air
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HC_forced = k_air / d_b * (2 + 0.41 * Re ** 0.55)
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HC_internal = 0.13 * k_gas * ((rho_gas ** 2 * g * np.abs(T_film - T_gas) * Pr_gas) / (T_gas * my_air ** 2)) ** (
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1 / 3)
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HC_external = np.maximum(HC_free, HC_forced)
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HalfConeAngle = np.arcsin(R_E / (R_E + h))
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ViewFactor = (1 - np.cos(HalfConeAngle)) / 2
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Q_Sun = alpha_VIS * A_proj * q_sun * (1 + tau_VIS / (1 - r_VIS))
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Q_Albedo = alpha_VIS * A_surf * q_Albedo * ViewFactor * (1 + tau_VIS / (1 - r_VIS))
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Q_IREarth = alpha_IR * A_surf * q_IREarth * ViewFactor * (1 + tau_IR / (1 - r_IR))
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Q_IRfilm = sigma * epsilon * alpha_IR * A_surf * T_film ** 4 * 1 / (1 - r_IR)
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Q_IRout = sigma * epsilon * A_surf * T_film ** 4 * (1 * tau_IR / (1 - r_IR))
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Q_ConvExt = HC_external * A_eff * (T_air - T_film)
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Q_ConvInt = HC_internal * A_eff * (T_film - T_gas)
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# RoC = -v_z
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# dT_gas = (Q_ConvInt / (gamma * m_gas * c_v) - (gamma - 1) / gamma * rho_air(h) * g / (rho_gas * R_gas) * RoC) * dt
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# dT_film = ((Q_Sun + Q_Albedo + Q_IREarth + Q_IRfilm + Q_ConvExt - Q_ConvInt - Q_IRout) / (c_f * m_film)) * dt
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# v_w = w
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# v = v_z
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s = h
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a_x = Drag_x/m_virt
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a_y = Drag_y/m_virt
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a_z = F/m_virt
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# DIFFERENTIAL EQUATIONS
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dx = dt * v_x + 0.5 * a_x * dt ** 2 # lon
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dy = dt * v_y + 0.5 * a_y * dt ** 2 # lat
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lon = lon + np.rad2deg(np.arctan(dx/((6371229.0 + h) * np.cos(np.deg2rad(lat)))))
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lat = lat + np.rad2deg(np.arctan(dy/(6371229.0 + h)))
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v_xn = v_x + dt * a_x
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v_yn = v_y + dt * a_y
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s_n = s + dt * v_z + 0.5 * a_z * dt ** 2
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dh = s_n - s
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v_n = v_z + dt * a_z
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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))
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T_en = T_film + (Q_Sun + Q_Albedo + Q_IREarth + Q_IRfilm + Q_ConvExt - Q_ConvInt - Q_IRout) / (c_f * m_film) * dt
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T_g = T_gn
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T_e = T_en
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s = s_n
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v_x = v_xn
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v_y = v_yn
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v_z = v_n
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h = s
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T_gas = T_g
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T_film = T_e
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# v_z = v
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t += dt # time increment
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utc = Time(start_utc) + t * unit.second
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#print(len(lon_list), len(lat_list))
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#"""
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#plt.plot(start_lon, start_lat, 'rx')
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#plt.plot(ax=ax, lon_list, lat_list, transform=ccrs.PlateCarree())
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#plt.show()
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#"""
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### WORKS!
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###
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###dset = xr.open_dataset("test2021.nc")
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###
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###print(dset['t'][1][0]) # [time] [level]
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###
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#fig = plt.figure() #figsize=[120,50])
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###
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#ax = fig.add_subplot(111, projection=ccrs.PlateCarree())
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###
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###dset['t'][1][0].plot(ax=ax, cmap='jet', transform=ccrs.PlateCarree())
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###ax.coastlines()
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###plt.show()
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#print(len(ERAlat))
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#print(len(ERAlon))
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#print(len(ERAz))
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#"""
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plt.plot(comp_time, comp_height, 'r--', label='PoGo Flight Test')
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#plt.plot(t_list, v_list, 'k--', label='Ballon v_rel')
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plt.plot(t_list, h_list, 'k-', label='Balloon Altitude')
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#plt.plot(t_list, p_list, 'r-', label='Air Pressure [Pa]')
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#plt.plot(t_list, Temp_list, 'b-', label='Air Temperature [K]')
|
||||
#plt.plot(t_list, rho_list, 'g-', label='Air Density in [kg/m$^3$]')
|
||||
plt.xlabel('time in s')
|
||||
plt.ylabel('Balloon Altitude in m')
|
||||
plt.legend()
|
||||
plt.show()
|
||||
#"""
|
||||
Loading…
Reference in New Issue