Implemented ERA5 radiation properties
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import cdsapi
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c = cdsapi.Client()
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r = c.retrieve(
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'reanalysis-era5-pressure-levels',
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{
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'product_type': 'reanalysis',
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'variable': [
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'fraction_of_cloud_cover', 'geopotential', 'relative_humidity',
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'specific_humidity', 'temperature', 'u_component_of_wind',
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'v_component_of_wind', 'vertical_velocity',
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],
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'pressure_level': [
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'1', '2', '3',
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'5', '7', '10',
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'20', '30', '50',
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'70', '100', '125',
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'150', '175', '200',
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'225', '250', '300',
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'350', '400', '450',
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'500', '550', '600',
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'650', '700', '750',
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'775', '800', '825',
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'850', '875', '900',
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'925', '950', '975',
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'1000',
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],
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'year': '2016',
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'month': '07',
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'day': [
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'11', '12', '13',
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'14', '15', '16',
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'17', '18',
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],
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'time': [
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'00:00', '01:00', '02:00',
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'03:00', '04:00', '05:00',
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'06:00', '07:00', '08:00',
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'09:00', '10:00', '11:00',
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'12:00', '13:00', '14:00',
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'15:00', '16:00', '17:00',
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'18:00', '19:00', '20:00',
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'21:00', '22:00', '23:00',
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],
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'area': [
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72, -111, 67,
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22,
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],
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'format': 'netcdf',
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})
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r.download('test2021.nc')
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720
main.py
720
main.py
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@ -4,324 +4,423 @@ import xarray as xr
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import matplotlib.pyplot as plt
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import matplotlib.pyplot as plt
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from scipy.spatial import cKDTree
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from scipy.spatial import cKDTree
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from scipy import interpolate
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from scipy import interpolate
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from scipy.integrate import odeint, solve_ivp
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import cartopy.crs as ccrs
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import cartopy.crs as ccrs
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from datetime import datetime
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from datetime import datetime
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start = datetime.now()
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start = datetime.now()
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print(start)
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print(start)
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begin_time = datetime.now()
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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_analytical, tau
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from models.sun import sun_angles_astropy
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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 models.drag import drag, Cd_model
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from models.transformation import visible_cells, transform, radii
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from input.user_input import *
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from input.user_input import *
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from input.natural_constants import *
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from input.natural_constants import *
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from astropy.time import Time
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from astropy.time import Time
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import astropy.units as unit
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import astropy.units as unit
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from models.thermal import AirMass
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# from models.thermal import
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from netCDF4 import Dataset
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from netCDF4 import Dataset
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import pandas as pd
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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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data = pd.read_excel(r'C:\Users\marcel\PycharmProjects\MasterThesis\Mappe1.xls', sheet_name='Tabelle3') # Tabelle3
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comp_time = pd.DataFrame(data, columns= ['Time'])
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comp_time = pd.DataFrame(data, columns=['Time']).to_numpy().squeeze()
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comp_height = pd.DataFrame(data, columns= ['Height'])
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comp_height = pd.DataFrame(data, columns=['Height']).to_numpy().squeeze()
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comp_lat = pd.DataFrame(data, columns= ['Latitude'])
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comp_lat = pd.DataFrame(data, columns=['Latitude']).to_numpy().squeeze()
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comp_lon = pd.DataFrame(data, columns= ['Longitude'])
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comp_lon = pd.DataFrame(data, columns=['Longitude']).to_numpy().squeeze()
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Reynolds = [0.0, 0.002, 0.004, 0.007, 0.01] #, 0.04, 0.07, 0.1, 0.2, 0.3, 0.5, 0.7, 1, 2, 3, 5, 7, 10, 20, 30, 50, 70, 100, 200,
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print("Initialisiere Simulation...")
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# 300, 500, 700, 1000, 2000, 3000, 5000, 7000, 10000, 20000, 30000, 50000]
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print("STARTORT: Längengrad %.4f, Breitengrad: %.4f" % (start_lon, start_lat))
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drag_coeff = [20000, 12000, 6000, 3429, 2400] #, 600, 343, 240, 120, 80, 49, 36.5, 26.5, 14.4, 10.4, 6.9, 5.4, 4.1, 2.55, 2, 1.5,
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print("STARTZEIT: " + str(start_utc) + " (UTC)")
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# 1.27, 1.07, 0.77, 0.65, 0.55, 0.5, 0.46, 0.42, 0.4, 0.385, 0.39, 0.405, 0.45, 0.47, 0.49]
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#print("SIMULATION INITIALISIERT. Simulierte Flugdauer %.2f Stunden (oder %.2f Tage)" % (
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#t_end / 3600, t_end / (3600 * 24)))
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#print("GESCHÄTZE SIMULATIONSDAUER: %.2f Minuten" % (t_end / (3600 * 10)))
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cd_interp1d = interpolate.interp1d(Reynolds, drag_coeff)
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Re_list = []
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level_data = Dataset("level.nc", "r", format="NETCDF4")
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single_data = Dataset("single.nc", "r", format="NETCDF4")
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def cd_func(Re):
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ERAtime = level_data.variables['time'][:] # time
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w = np.log10(Re)
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if Re <= 0.01:
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ERAlat = level_data.variables['latitude'][:] # latitude (multi-level)
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c_d = 9/2 + 24/Re
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ERAlon = level_data.variables['longitude'][:] # longitude (multi-level)
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elif Re <= 20:
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ERAlats = single_data.variables['latitude'][:] # latitude (single level)
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c_d = 24/Re * (1 + 0.1315 * Re ** (0.82 - 0.05 * w))
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ERAlons = single_data.variables['longitude'][:] # longitude (single level)
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elif Re <= 260:
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c_d = 24/Re * (1 + 0.1935 * Re ** 0.6305)
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elif Re <= 1.5 * 10e3:
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c_d = 10 ** (1.6435 - 1.1242 * w + 0.1558 * w ** 2)
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elif Re <= 1.2 * 10e4:
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c_d = 10 ** (-2.4571 + 2.5558 * w - 0.9295 * w ** 2 + 0.1049 * w ** 3)
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elif Re <= 4.4 * 10e4:
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c_d = 10 ** (-1.9181 + 0.6370 * w - 0.0636 * w ** 3)
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elif Re <= 3.38 * 10e5:
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c_d = 10 ** (-4.3390 + 1.5809 * w - 0.1546 * w ** 2)
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elif Re <= 4 * 10e5:
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c_d = 29.78 - 5.3 * w
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elif Re <= 10 ** 6:
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c_d = 0.1 * w - 0.49
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elif Re > 10e6:
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c_d = 0.19 - 8 * 10e4/Re
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else:
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c_d = 0.47
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return c_d
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def cd_func_garg(Re):
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ERAz = level_data.variables['z'][:] / g # geopotential to geopotential height
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if Re == 0:
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ERApress = level_data.variables['level'][:] # pressure level
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c_d = 2.0
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ERAtemp = level_data.variables['t'][:] # air temperature in K
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elif Re < 2 * 10e5:
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c_d = 5.4856 * 10e9 * np.tanh(4.3774 * 10e-9 / Re) + 0.0709 * np.tanh(700.6575 / Re) + 0.3894 * np.tanh(74.1539 / Re) - 0.1198 * np.tanh(7429.0843 / Re) + 1.7174 * np.tanh(9.9851 / Re + 2.3384) + 0.4744
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elif 2 * 10e5 < Re <= 10e6:
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c_d = 8 * 10e-6 * ((Re/6530) ** 2 + np.tanh(Re) - 8 * np.log(Re) / np.log(10)) - 0.4119 * np.exp(-2.08 * 10 ** 43 / (Re + Re ** 2) ** 4) - 2.1344 * np.exp(-((np.log(Re ** 2 + 10.7563) / np.log(10)) ** 2 + 9.9867) / Re) + 0.1357 * np.exp(-((Re / 1620) ** 2 + 10370) / Re) - 8.5 * 10e-3 * (2 * np.log(np.tanh(np.tanh(Re))) / np.log(10) - 2825.7162) / Re + 2.4795
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elif Re > 10e6:
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c_d = 0.212546
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else:
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c_d = 2.0
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return 0.80 # c_d
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#cd_interp1d = interpolate.interp1d(Reynolds, drag_coeff)
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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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ERAtcc = single_data.variables['tcc'][:] # total cloud cover [0 to 1]
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lat = start_lat # deg
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ERAal = single_data.variables['fal'][:] # forecast albedo [0 to 1]
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lon = start_lon # deg
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# ERAst = single_data.variables['skt'][:] # skin (ground) temperature in K
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ERAcbh = single_data.variables['cbh'][:] # cloud base height in m
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t = 0 # simulation time in seconds
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ERAlcc = single_data.variables['lcc'][:] # low cloud cover
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h = start_height
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ERAmcc = single_data.variables['mcc'][:] # medium cloud cover
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utc = Time(start_utc)
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ERAhcc = single_data.variables['hcc'][:] # high cloud cover
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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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ERAssr = single_data.variables['ssr'][:] # surface net solar radiation
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t_epoch = epoch_diff
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ERAstrn = single_data.variables['str'][:] # surface net thermal radiation
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ERAstrd = single_data.variables['strd'][:] # surface thermal radiation downwards
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ERAssrd = single_data.variables['ssrd'][:] # surface solar radiation downwards
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ERAtsr = single_data.variables['tsr'][:] # top net solar radiation
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ERAttr = single_data.variables['ttr'][:] # top net thermal radiation
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ERAsst = single_data.variables['sst'][:] # sea surface temperature
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ERAtisr = single_data.variables['tisr'][:] # TOA incident solar radiation
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ERAstrdc = single_data.variables['strdc'][:] # surface thermal radiation downward clear-sky
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vw_x = level_data.variables['u'][:] # v_x
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vw_y = level_data.variables['v'][:] # v_y
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vw_z = level_data.variables['w'][:] # v_z
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xt, yt, zt, tt = transform(lon, lat, t) # test coordinates
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lon_era2d, lat_era2d = np.meshgrid(ERAlon, ERAlat)
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lon_era2ds, lat_era2ds = np.meshgrid(ERAlons, ERAlats)
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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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xs, ys, zs = transform(lon_era2d.flatten(), lat_era2d.flatten())
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w = 1.0 / d[0] ** 2
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xs2, ys2, zs2 = transform(lon_era2ds.flatten(), lat_era2ds.flatten())
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lat_sel = np.unravel_index(inds[0], lon_era2d.shape)[0]
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tree = cKDTree(np.column_stack((xs, ys, zs)))
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lon_sel = np.unravel_index(inds[0], lon_era2d.shape)[1]
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tree2 = cKDTree(np.column_stack((xs2, ys2, zs2)))
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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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# INITIALISATION TIME-COUNTERS
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# MAYBE LATER
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# t_pre = int(t_epoch)
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# t_post = t_pre + 1
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# t1 = np.searchsorted(ERAtime, t_pre, side='left')
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# t2 = t1 + 1
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def ERA5Data(lon, lat, h, t, deltaT_ERA):
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t_epoch = deltaT_ERA + t/3600
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t_pre = int(t_epoch)
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# t_post = t_pre + 1
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t_pre_ind = t_pre - ERAtime[0]
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t_post_ind = t_pre_ind + 1
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xt, yt, zt = transform(lon, lat) # current coordinates
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d1, inds1 = tree.query(np.column_stack((xt, yt, zt)), k=4) # longitude, latitude
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d2, inds2 = tree2.query(np.column_stack((xt, yt, zt)), k=visible_cells(h)) # longitude, latitude
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w1 = 1.0 / d1[0] # ** 2
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w2 = 1.0 / d2[0] ** 2
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lat_ind1 = np.unravel_index(inds1[0], lon_era2d.shape)[0]
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lon_ind1 = np.unravel_index(inds1[0], lon_era2d.shape)[1]
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lat_ind2 = np.unravel_index(inds2[0], lon_era2ds.shape)[0]
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lon_ind2 = np.unravel_index(inds2[0], lon_era2ds.shape)[1]
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interp4d_temp_pre = np.ma.dot(w1, ERAtemp[t_pre_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
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interp4d_temp_post = np.ma.dot(w1, ERAtemp[t_post_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
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interp4d_temp = (interp4d_temp_post - interp4d_temp_pre) * (t_epoch - t_pre) + interp4d_temp_pre
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interp4d_height_pre = np.ma.dot(w1, ERAz[t_pre_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
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interp4d_height_post = np.ma.dot(w1, ERAz[t_post_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
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interp4d_height = (interp4d_height_post - interp4d_height_pre) * (t_epoch - t_pre) + interp4d_height_pre
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interp4d_vw_x_pre = np.ma.dot(w1, vw_x[t_pre_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
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interp4d_vw_x_post = np.ma.dot(w1, vw_x[t_post_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
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interp4d_vw_x = (interp4d_vw_x_post - interp4d_vw_x_pre) * (t_epoch - t_pre) + interp4d_vw_x_pre
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interp4d_vw_y_pre = np.ma.dot(w1, vw_y[t_pre_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
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||||||
|
interp4d_vw_y_post = np.ma.dot(w1, vw_y[t_post_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
|
||||||
|
interp4d_vw_y = (interp4d_vw_y_post - interp4d_vw_y_pre) * (t_epoch - t_pre) + interp4d_vw_y_pre
|
||||||
|
|
||||||
|
interp4d_vw_z_pre = np.ma.dot(w1, vw_z[t_pre_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
|
||||||
|
interp4d_vw_z_post = np.ma.dot(w1, vw_z[t_post_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
|
||||||
|
interp4d_vw_z = (interp4d_vw_z_post - interp4d_vw_z_pre) * (t_epoch - t_pre) + interp4d_vw_z_pre
|
||||||
|
|
||||||
|
albedo_pre = np.ma.dot(w2, ERAal[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
albedo_post = np.ma.dot(w2, ERAal[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
al = (albedo_post - albedo_pre) * (t_epoch - t_pre) + albedo_pre
|
||||||
|
|
||||||
|
tcc_pre = np.ma.dot(w2, ERAtcc[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
tcc_post = np.ma.dot(w2, ERAtcc[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
tcc = (tcc_post - tcc_pre) * (t_epoch - t_pre) + tcc_pre
|
||||||
|
|
||||||
|
cbh_pre = np.ma.dot(w2, ERAcbh[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
cbh_post = np.ma.dot(w2, ERAcbh[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
cbh = (cbh_post - cbh_pre) * (t_epoch - t_pre) + cbh_pre
|
||||||
|
|
||||||
|
lcc_pre = np.ma.dot(w2, ERAlcc[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
lcc_post = np.ma.dot(w2, ERAlcc[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
lcc = (lcc_post - lcc_pre) * (t_epoch - t_pre) + lcc_pre
|
||||||
|
|
||||||
|
mcc_pre = np.ma.dot(w2, ERAmcc[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
mcc_post = np.ma.dot(w2, ERAmcc[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
mcc = (mcc_post - mcc_pre) * (t_epoch - t_pre) + mcc_pre
|
||||||
|
|
||||||
|
hcc_pre = np.ma.dot(w2, ERAhcc[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
hcc_post = np.ma.dot(w2, ERAhcc[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
hcc = (hcc_post - hcc_pre) * (t_epoch - t_pre) + hcc_pre
|
||||||
|
|
||||||
|
ssr_pre = np.ma.dot(w2, ERAssr[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
ssr_post = np.ma.dot(w2, ERAssr[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
ssr = ((ssr_post - ssr_pre) * (t_epoch - t_pre) + ssr_pre)/3600
|
||||||
|
|
||||||
|
strn_pre = np.ma.dot(w2, ERAstrn[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
strn_post = np.ma.dot(w2, ERAstrn[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
strn = ((strn_post - strn_pre) * (t_epoch - t_pre) + strn_pre)/3600
|
||||||
|
|
||||||
|
strd_pre = np.ma.dot(w2, ERAstrd[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
strd_post = np.ma.dot(w2, ERAstrd[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
strd = ((strd_post - strd_pre) * (t_epoch - t_pre) + strd_pre)/3600
|
||||||
|
|
||||||
|
strdc_pre = np.ma.dot(w2, ERAstrdc[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
strdc_post = np.ma.dot(w2, ERAstrdc[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
strdc = ((strdc_post - strdc_pre) * (t_epoch - t_pre) + strdc_pre) / 3600
|
||||||
|
|
||||||
|
ssrd_pre = np.ma.dot(w2, ERAssrd[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
ssrd_post = np.ma.dot(w2, ERAssrd[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
ssrd = ((ssrd_post - ssrd_pre) * (t_epoch - t_pre) + ssrd_pre)/3600
|
||||||
|
|
||||||
|
tsr_pre = np.ma.dot(w2, ERAtsr[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
tsr_post = np.ma.dot(w2, ERAtsr[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
tsr = ((tsr_post - tsr_pre) * (t_epoch - t_pre) + tsr_pre)/3600
|
||||||
|
|
||||||
|
tisr_pre = np.ma.dot(w2, ERAtisr[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
tisr_post = np.ma.dot(w2, ERAtisr[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
tisr = ((tisr_post - tisr_pre) * (t_epoch - t_pre) + tisr_pre)/3600
|
||||||
|
|
||||||
|
ttr_pre = np.ma.dot(w2, ERAttr[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
ttr_post = np.ma.dot(w2, ERAttr[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
|
||||||
|
ttr = ((ttr_post - ttr_pre) * (t_epoch - t_pre) + ttr_pre)/3600
|
||||||
|
|
||||||
|
pressure_hPa = np.array([1, 2, 3, 5, 7, 10, 20, 30, 50, 70, 100, 125, 150, 175, 200, 225, 250, 300, 350, 400,
|
||||||
450, 500, 550, 600, 650, 700, 750, 775, 800, 825, 850, 875, 900, 925, 950, 975, 1000])
|
450, 500, 550, 600, 650, 700, 750, 775, 800, 825, 850, 875, 900, 925, 950, 975, 1000])
|
||||||
|
|
||||||
pressure = 100 * pressure_hPa
|
pressure = 100 * pressure_hPa
|
||||||
# print(pressure)
|
|
||||||
|
|
||||||
|
|
||||||
# height_interp1d = interpolate.interp1d(interp4d_height, pressure)
|
|
||||||
temp_interp1d = interpolate.interp1d(interp4d_height, interp4d_temp)
|
|
||||||
press_interp1d = interpolate.interp1d(interp4d_height, pressure)
|
|
||||||
vw_x_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_x)
|
|
||||||
vw_y_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_y)
|
|
||||||
vw_z_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_z)
|
|
||||||
|
|
||||||
|
|
||||||
#u = 0
|
|
||||||
#v = 0
|
|
||||||
#w = 0
|
|
||||||
T_air = temp_interp1d(h)
|
|
||||||
p_air = press_interp1d(h)
|
|
||||||
rho_air = p_air/(R_air * T_air)
|
|
||||||
|
|
||||||
u = vw_x_interp1d(h)
|
|
||||||
v = vw_y_interp1d(h)
|
|
||||||
w = -1 / g * vw_z_interp1d(h) * R_air * T_air / p_air
|
|
||||||
|
|
||||||
|
|
||||||
v_x = 0
|
|
||||||
v_y = 0
|
|
||||||
v_z = 0
|
|
||||||
|
|
||||||
v_rel = 0
|
|
||||||
|
|
||||||
T_gas = T_air
|
|
||||||
T_film = T_gas
|
|
||||||
|
|
||||||
t_list = []
|
|
||||||
h_list = []
|
|
||||||
v_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)
|
|
||||||
v_list.append(v_rel)
|
|
||||||
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
|
|
||||||
|
|
||||||
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]
|
|
||||||
|
|
||||||
d, inds = tree.query(np.column_stack((xt, yt, zt, tt)), k=8) # longitude, latitude, time in h # !
|
|
||||||
w = 1.0 / d[0] ** 2
|
|
||||||
|
|
||||||
lat_sel = np.unravel_index(inds[0], lon_era2d.shape)[0]
|
|
||||||
lon_sel = np.unravel_index(inds[0], lon_era2d.shape)[1]
|
|
||||||
time_sel = np.unravel_index(inds[0], lon_era2d.shape)[2]
|
|
||||||
|
|
||||||
interp4d_height = np.ma.dot(w, ERAz[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
|
|
||||||
interp4d_temp = np.ma.dot(w, ERAtemp[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
|
|
||||||
interp4d_vw_x = np.ma.dot(w, vw_x[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
|
|
||||||
interp4d_vw_y = np.ma.dot(w, vw_y[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
|
|
||||||
interp4d_vw_z = np.ma.dot(w, vw_z[time_sel, :, lat_sel, lon_sel]) / np.sum(w)
|
|
||||||
|
|
||||||
press_interp1d = interpolate.interp1d(interp4d_height, pressure)
|
|
||||||
temp_interp1d = interpolate.interp1d(interp4d_height, interp4d_temp)
|
temp_interp1d = interpolate.interp1d(interp4d_height, interp4d_temp)
|
||||||
|
press_interp1d = interpolate.interp1d(interp4d_height, pressure)
|
||||||
vw_x_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_x)
|
vw_x_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_x)
|
||||||
vw_y_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_y)
|
vw_y_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_y)
|
||||||
vw_z_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_z)
|
vw_z_interp1d = interpolate.interp1d(interp4d_height, interp4d_vw_z)
|
||||||
|
|
||||||
|
if h > interp4d_height[0]:
|
||||||
try:
|
p_air = press_interp1d(interp4d_height[0])
|
||||||
p_air = press_interp1d(h)
|
T_air = temp_interp1d(interp4d_height[0])
|
||||||
T_air = temp_interp1d(h)
|
u = vw_x_interp1d(interp4d_height[0])
|
||||||
except:
|
v = vw_y_interp1d(interp4d_height[0])
|
||||||
if (h > interp4d_height[0]):
|
w = -1 / g * vw_z_interp1d(interp4d_height[0]) * R_air * T_air / p_air
|
||||||
h = interp4d_height[0]
|
elif h < interp4d_height[-1]:
|
||||||
|
p_air = press_interp1d(interp4d_height[-1])
|
||||||
|
T_air = temp_interp1d(interp4d_height[-1])
|
||||||
|
u = vw_x_interp1d(interp4d_height[-1])
|
||||||
|
v = vw_y_interp1d(interp4d_height[-1])
|
||||||
|
w = -1 / g * vw_z_interp1d(interp4d_height[-1]) * R_air * T_air / p_air
|
||||||
else:
|
else:
|
||||||
h = interp4d_height[-1]
|
|
||||||
|
|
||||||
p_air = press_interp1d(h)
|
p_air = press_interp1d(h)
|
||||||
T_air = temp_interp1d(h)
|
T_air = temp_interp1d(h)
|
||||||
|
|
||||||
#print("height")
|
|
||||||
#print(h)
|
|
||||||
#print("temperature")
|
|
||||||
#print(temp_interp1d(h))
|
|
||||||
#print("pressure")
|
|
||||||
#print(press_interp1d(h))
|
|
||||||
#print("vw_x")
|
|
||||||
#print(vw_x_interp1d(h))
|
|
||||||
|
|
||||||
p_gas = p_air
|
|
||||||
rho_air = p_air / (R_air * T_air)
|
|
||||||
u = vw_x_interp1d(h)
|
u = vw_x_interp1d(h)
|
||||||
v = vw_y_interp1d(h)
|
v = vw_y_interp1d(h)
|
||||||
w = -1/g * vw_z_interp1d(h) * R_air * T_air / p_air
|
w = -1 / g * vw_z_interp1d(h) * R_air * T_air / p_air
|
||||||
|
|
||||||
v_relx = u - v_x
|
rho_air = p_air / (R_air * T_air)
|
||||||
v_rely = v - v_y
|
|
||||||
v_relz = w - v_z
|
|
||||||
|
|
||||||
v_rel = (v_relx ** 2 + v_rely ** 2 + v_relz ** 2) ** (1/2)
|
return p_air, T_air, rho_air, u, v, w, cbh, tcc, lcc, mcc, hcc, ssr, strn, strd, ssrd, tsr, ttr, al, tisr, strdc
|
||||||
|
# p_air, T_air, rho_air, u, v, w, cbh, tcc, lcc, mcc, hcc, ssr, strn, strd, ssrd, tsr, ttr, al, tisr
|
||||||
|
|
||||||
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
|
deltaT_ERA = (Time(start_utc).jd - Time('1900-01-01 00:00:00.0').jd) * 24.000000
|
||||||
|
p_air0, T_air0, rho_air0, u0, v0, w0, cbh0, tcc0, lcc0, mcc0, hcc0, ssr0, strn0, strd0, ssrd0, tsr0, ttr0, al0, tisr0, strdc0 = ERA5Data(start_lon, start_lat, start_height, 0, deltaT_ERA)
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
y0 = [start_lon, start_lat, start_height, 0, 0, 0, T_air0, T_air0, m_gas_init, 0]
|
||||||
|
## y = [longitude [deg], latitude [deg], height [m], v_x (lon) [m/s], v_y [m/s], v_z [m/s], T_gas [K], T_film [K], m_gas_init [kg], c2_init [-]]
|
||||||
|
|
||||||
|
valving = False
|
||||||
|
|
||||||
|
def model(t, y, m_pl, m_film, m_bal, c_virt):
|
||||||
|
utc = Time(start_utc) + t * unit.second
|
||||||
|
lon = y[0] # 1
|
||||||
|
lat = y[1] # 2
|
||||||
|
h = y[2] # 3
|
||||||
|
v_x = y[3] # 4
|
||||||
|
v_y = y[4] # 5
|
||||||
|
v_z = y[5] # 6
|
||||||
|
T_gas = y[6] # 7
|
||||||
|
T_film = y[7] # 8
|
||||||
|
m_gas = y[8] # 9
|
||||||
|
c2 = y[9] # 10
|
||||||
|
|
||||||
|
r_lon, r_lat = radii(lat, h)
|
||||||
|
|
||||||
|
deltaT_ERA = (Time(start_utc).jd - Time('1900-01-01 00:00:00.0').jd) * 24.000000 # conversion to ERA5 time format
|
||||||
|
|
||||||
|
p_air, T_air, rho_air, u, v, w, cbh, tcc, lcc, mcc, hcc, ssr, strn, strd, ssrd, tsr, ttr, al, tisr, strdc = ERA5Data(lon, lat, h, t, deltaT_ERA)
|
||||||
|
p_gas = p_air
|
||||||
|
|
||||||
|
h_valve = 1.034 * V_design ** (1 / 3)
|
||||||
|
h_duct = 0.47 * h_valve
|
||||||
|
|
||||||
|
v_relx = u - v_x # relative wind velocity x-dir (balloon frame)
|
||||||
|
v_rely = v - v_y # relative wind velocity y-dir (balloon frame)
|
||||||
|
v_relz = w - v_z # relative wind velocity z-dir (balloon frame)
|
||||||
|
|
||||||
|
v_rel = np.sqrt(v_relx ** 2 + v_rely ** 2 + v_relz ** 2) # total relative wind velocity (balloon frame)
|
||||||
|
|
||||||
|
alpha = np.arcsin(v_relz / v_rel) # "angle of attack": angle between longitudinal axis and rel. wind (in [rad])
|
||||||
|
|
||||||
|
rho_gas = p_gas / (R_gas * T_gas) # calculate gas density through *ideal* gas equation
|
||||||
|
|
||||||
|
dP_valve = g * (rho_air - rho_gas) * h_valve
|
||||||
|
dP_duct = g * (rho_air - rho_gas) * h_duct
|
||||||
|
|
||||||
|
V_b = m_gas / rho_gas # calculate balloon volume from current gas mass and gas density
|
||||||
|
|
||||||
if V_b > V_design:
|
if V_b > V_design:
|
||||||
V_b = V_design
|
c_duct = c_ducts
|
||||||
m_gas = V_design * rho_gas
|
|
||||||
else:
|
else:
|
||||||
pass
|
c_duct = 0
|
||||||
|
|
||||||
m_gross = m_pl + m_film
|
#if valving == True: # opening valve process
|
||||||
|
# if c2 == 0:
|
||||||
|
# c2 = 1.0
|
||||||
|
# c2dot = 0
|
||||||
|
# elif c_valve < c2 <= 1.0:
|
||||||
|
# c2dot = (c_valve - 1.0) / t_open
|
||||||
|
# else:
|
||||||
|
# c2dot = 0
|
||||||
|
# c2 = c_valve
|
||||||
|
|
||||||
|
#if valving == False: # closing valve process
|
||||||
|
# if c2 == 0:
|
||||||
|
# c2dot = 0
|
||||||
|
# elif c_valve <= c2 < 1.0:
|
||||||
|
# c2dot = (1.0 - c_valve) / t_close
|
||||||
|
# else:
|
||||||
|
# c2dot = 0
|
||||||
|
# c2 = 0
|
||||||
|
|
||||||
|
## m_gas/dt = -(A_valv * c2 * np.sqrt(2 * dP_valve * rho_gas)) # mass loss due to valving
|
||||||
|
m_gross = m_pl + m_film + m_bal
|
||||||
m_tot = m_pl + m_film + m_gas
|
m_tot = m_pl + m_film + m_gas
|
||||||
m_virt = m_tot + c_virt * rho_air * V_b
|
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
|
d_b = 1.383 * V_b ** (1 / 3) # calculate diameter of balloon from its volume
|
||||||
L_goreB = 1.914 * V_b ** (1/3)
|
L_goreB = 1.914 * V_b ** (1 / 3)
|
||||||
h_b = 0.748 * d_b
|
A_surf = 4.94 * V_b ** (2 / 3)
|
||||||
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_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_eff = 0.65 * A_surf + 0.35 * A_surf1
|
||||||
A_top = np.pi/4 * d_b ** 2
|
A_top = np.pi / 4 * d_b ** 2
|
||||||
|
|
||||||
AZ, ELV = sun_angles_analytical(lat, lon, utc)
|
AZ, ELV = sun_angles_analytical(lat, lon, utc)
|
||||||
|
|
||||||
A_proj = A_top * (0.9125 + 0.0875 * np.cos(np.pi - 2 * np.deg2rad(ELV)))
|
A_proj = A_top * (0.9125 + 0.0875 * np.cos(np.pi - 2 * np.deg2rad(ELV))) # projected area for sun radiation
|
||||||
|
A_drag = A_top * (0.9125 + 0.0875 * np.cos(np.pi - 2 * alpha)) # projected area for drag
|
||||||
|
|
||||||
# CALCULATIONS FOR THERMAL MODEL
|
# CALCULATIONS FOR THERMAL MODEL
|
||||||
|
|
||||||
if ELV >= -(180 / np.pi * np.arccos(R_E / (R_E + h))):
|
tau_atm, tau_atmIR = tau(ELV, h, p_air)
|
||||||
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_atm0, tau_atmIR0 = tau(ELV, 0, p_0)
|
||||||
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"
|
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))
|
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_Sun = 1367.5 * ((1 + e * np.cos(np.deg2rad(TA))) / (1 - e ** 2)) ** 2
|
||||||
I_SunZ = I_Sun * tau_atm
|
I_SunZ = I_Sun * tau_atm
|
||||||
q_sun = I_SunZ
|
I_Sun0 = I_Sun * tau_atm0
|
||||||
q_IRground = epsilon_ground * sigma * T_ground ** 4
|
## q_sun = I_SunZ
|
||||||
|
## q_IRground = np.abs(str) #epsilon_ground * sigma * T_ground ** 4
|
||||||
|
## q_IREarth = q_IRground * tau_atmIR
|
||||||
|
|
||||||
|
tcc = 0
|
||||||
|
|
||||||
|
if tcc <= 0.01:
|
||||||
|
q_IRground = strd - strn
|
||||||
q_IREarth = q_IRground * tau_atmIR
|
q_IREarth = q_IRground * tau_atmIR
|
||||||
|
q_sun = I_SunZ
|
||||||
|
if ELV <= 0:
|
||||||
|
q_Albedo = 0
|
||||||
|
else:
|
||||||
|
q_Albedo = (1 - ssr/ssrd) * I_Sun0 * np.sin(np.deg2rad(ELV)) # ssrd - ssr
|
||||||
|
else:
|
||||||
|
q_IRground_bc = (strd - strn) + (strd - strdc)
|
||||||
|
q_IREarth_bc = q_IRground_bc * tau_atmIR
|
||||||
|
q_sun_bc = I_SunZ * (1 - tcc)
|
||||||
|
q_Albedo_bc = (1 - ssr/ssrd) * (1 - tcc) * I_Sun * np.sin(np.deg2rad(ELV))
|
||||||
|
|
||||||
|
q_IREarth_ac = np.abs(ttr) #q_IRground_bc * tau_atmIR * (1 - tcc)
|
||||||
|
q_sun_ac = I_SunZ
|
||||||
|
q_Albedo_ac = (tisr - tsr)/tisr * I_Sun * np.sin(np.deg2rad(ELV))
|
||||||
|
|
||||||
|
if h <= cbh: # "below clouds"
|
||||||
|
q_IREarth = q_IREarth_bc
|
||||||
|
q_sun = q_sun_bc
|
||||||
|
if ELV <= 0:
|
||||||
|
q_Albedo = 0
|
||||||
|
else:
|
||||||
|
q_Albedo = q_Albedo_bc
|
||||||
|
elif h >= 12000: # "above clouds"
|
||||||
|
q_IREarth = q_IREarth_ac
|
||||||
|
q_sun = q_sun_ac
|
||||||
|
if ELV <= 0:
|
||||||
|
q_Albedo = 0
|
||||||
|
else:
|
||||||
|
q_Albedo = q_Albedo_ac
|
||||||
|
elif h >= 6000:
|
||||||
|
if hcc >= 0.01:
|
||||||
|
q_IREarth = ((h - 6000) / 6000 * hcc + mcc + lcc) / (hcc + mcc + lcc) * (q_IREarth_ac - q_IREarth_bc) + q_IREarth_bc
|
||||||
|
q_sun = ((h - 6000) / 6000 * hcc + mcc + lcc) / (hcc + mcc + lcc) * (q_sun_ac - q_sun_bc) + q_sun_bc
|
||||||
|
if ELV <= 0:
|
||||||
|
q_Albedo = 0
|
||||||
|
else:
|
||||||
|
q_Albedo = ((h - 6000) / 6000 * hcc + mcc + lcc) / (hcc + mcc + lcc) * (q_Albedo_ac - q_Albedo_bc) + q_Albedo_bc
|
||||||
|
else:
|
||||||
|
q_IREarth = q_IREarth_ac
|
||||||
|
q_sun = q_sun_ac
|
||||||
|
if ELV <= 0:
|
||||||
|
q_Albedo = 0
|
||||||
|
else:
|
||||||
|
q_Albedo = q_Albedo_ac
|
||||||
|
|
||||||
|
elif h >= 2000:
|
||||||
|
if mcc > 0.01 or hcc > 0.01:
|
||||||
|
q_IREarth = ((h - 2000)/4000 * mcc + lcc)/(hcc + mcc + lcc) * (q_IREarth_ac - q_IREarth_bc) + q_IREarth_bc
|
||||||
|
q_sun = ((h - 2000)/4000 * mcc + lcc)/(hcc + mcc + lcc) * (q_sun_ac - q_sun_bc) + q_sun_bc
|
||||||
|
if ELV <= 0:
|
||||||
|
q_Albedo = 0
|
||||||
|
else:
|
||||||
|
q_Albedo = ((h - 2000)/4000 * mcc + lcc)/(hcc + mcc + lcc) * (q_Albedo_ac - q_Albedo_bc) + q_Albedo_bc
|
||||||
|
else:
|
||||||
|
q_IREarth = q_IREarth_ac
|
||||||
|
q_sun = q_sun_ac
|
||||||
|
if ELV <= 0:
|
||||||
|
q_Albedo = 0
|
||||||
|
else:
|
||||||
|
q_Albedo = q_Albedo_ac
|
||||||
|
else:
|
||||||
|
q_IREarth = (h/2000 * lcc)/(hcc + mcc + lcc) * (q_IREarth_ac - q_IREarth_bc) + q_IREarth_bc
|
||||||
|
q_sun = (h/2000 * lcc)/(hcc + mcc + lcc) * (q_sun_ac - q_sun_bc) + q_sun_bc
|
||||||
|
|
||||||
if ELV <= 0:
|
if ELV <= 0:
|
||||||
q_Albedo = 0
|
q_Albedo = 0
|
||||||
else:
|
else:
|
||||||
q_Albedo = Albedo * I_Sun * np.sin(np.deg2rad(ELV))
|
q_Albedo = (h/2000 * lcc)/(hcc + mcc + lcc) * (q_Albedo_ac - q_Albedo_bc) + q_Albedo_bc
|
||||||
|
|
||||||
|
|
||||||
my_air = (1.458 * 10 ** -6 * T_air ** 1.5) / (T_air + 110.4)
|
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_air = 0.0241 * (T_air / 273.15) ** 0.9
|
||||||
k_gas = 0.144 * (T_gas / 273.15) ** 0.7
|
k_gas = 0.144 * (T_gas / 273.15) ** 0.7
|
||||||
Pr_air = 0.804 - 3.25 * 10 ** (-4) * T_air
|
Pr_air = 0.804 - 3.25 * 10 ** (-4) * T_air
|
||||||
Pr_gas = 0.729 - 1.6 * 10 ** (-4) * T_gas
|
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)
|
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
|
Nu_air = 2 + 0.45 * (Gr_air * Pr_air) ** 0.25
|
||||||
HC_free = Nu_air * k_air / d_b
|
HC_free = Nu_air * k_air / d_b
|
||||||
Re = np.abs(v_relz) * d_b * rho_air / my_air
|
Re = np.abs(v_rel) * d_b * rho_air / my_air
|
||||||
|
Fr = np.abs(v_rel) / np.sqrt(g * d_b)
|
||||||
Re_list.append(Re)
|
|
||||||
|
|
||||||
HC_forced = k_air / d_b * (2 + 0.41 * Re ** 0.55)
|
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)) ** (
|
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)
|
1 / 3)
|
||||||
HC_external = np.maximum(HC_free, HC_forced)
|
HC_external = np.maximum(HC_free, HC_forced)
|
||||||
|
|
||||||
|
|
@ -331,123 +430,78 @@ while t <= t_end and h >= 0:
|
||||||
Q_Sun = alpha_VIS * A_proj * q_sun * (1 + tau_VIS / (1 - r_VIS))
|
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_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_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_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_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_ConvExt = HC_external * A_eff * (T_air - T_film)
|
||||||
Q_ConvInt = HC_internal * A_eff * (T_film - T_gas)
|
Q_ConvInt = HC_internal * A_eff * (T_film - T_gas)
|
||||||
|
|
||||||
try:
|
c_d = Cd_model(Fr, Re, A_top)
|
||||||
c_d = cd_func(Re)
|
|
||||||
except:
|
|
||||||
print(Re)
|
|
||||||
|
|
||||||
D = drag(c_d, rho_air, d_b, v_rel) # calculate drag force
|
D = drag(c_d, rho_air, A_drag, v_rel) # calculate drag force
|
||||||
|
|
||||||
if v_rel == 0:
|
if v_rel == 0:
|
||||||
Drag_x = 0
|
Drag_x, Dray_y, Drag_z = 0, 0, 0
|
||||||
Drag_y = 0
|
|
||||||
Drag_z = 0
|
|
||||||
else:
|
else:
|
||||||
Drag_x = D * v_relx / v_rel
|
Drag_x, Drag_y, Drag_z = D * v_relx / v_rel, D * v_rely / v_rel, D * v_relz / 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
|
F = g * V_b * (rho_air - rho_gas) - g * m_gross + Drag_z # gross inflation - weight + drag
|
||||||
W = g * m_gross # calculate weight (force)
|
|
||||||
F = I - W + Drag_z
|
|
||||||
|
|
||||||
# RoC = -v_z
|
a_x, a_y, a_z = Drag_x / m_virt, Drag_y / m_virt, F / m_virt
|
||||||
# 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
|
eqn1 = np.rad2deg(y[3] / r_lon)
|
||||||
|
eqn2 = np.rad2deg(y[4] / r_lat)
|
||||||
|
eqn3 = y[5]
|
||||||
|
eqn4 = a_x
|
||||||
|
eqn5 = a_y
|
||||||
|
eqn6 = a_z
|
||||||
|
eqn7 = Q_ConvInt/(gamma * c_v * m_gas) - (gamma - 1)/gamma * (rho_air * g)/(rho_gas * R_gas) * y[5]
|
||||||
|
eqn8 = (Q_Sun + Q_Albedo + Q_IREarth + Q_IRFilm + Q_ConvExt - Q_ConvInt - Q_IRout) / (c_f * m_film)
|
||||||
|
eqn9 = -(A_ducts * c_duct * np.sqrt(2 * dP_duct * rho_gas)) # - (A_valve * c2 * np.sqrt(2 * dP_valve * rho_gas))
|
||||||
|
eqn10 = 0 #c2dot
|
||||||
|
|
||||||
a_x = Drag_x/m_virt
|
return [eqn1, eqn2, eqn3, eqn4, eqn5, eqn6, eqn7, eqn8, eqn9, eqn10]
|
||||||
a_y = Drag_y/m_virt
|
|
||||||
a_z = F/m_virt
|
|
||||||
|
|
||||||
# DIFFERENTIAL EQUATIONS
|
m_pl = 1728 + 172 + 500 # + 500 # mass of payload and flight chain in [kg]
|
||||||
|
m_bal = 0 # initial ballast mass in [kg]
|
||||||
|
m_film = 1897 # mass of balloon film in [kg]
|
||||||
|
FreeLift = 4 # [%]
|
||||||
|
|
||||||
dx = dt * v_x + 0.5 * a_x * dt ** 2 # lon
|
t_max = 100000 #0
|
||||||
dy = dt * v_y + 0.5 * a_y * dt ** 2 # lat
|
dt = 1.0
|
||||||
|
t = np.arange(2.0, t_max, dt)
|
||||||
|
|
||||||
lon = lon + np.rad2deg(np.arctan(dx/((6371229.0 + h) * np.cos(np.deg2rad(lat)))))
|
m_gas = ((m_pl + m_bal + m_film) * (FreeLift/100 + 1))/(R_gas/R_air - 1)
|
||||||
lat = lat + np.rad2deg(np.arctan(dy/(6371229.0 + h)))
|
|
||||||
|
|
||||||
v_xn = v_x + dt * a_x
|
def ending(t, y): return y[2]
|
||||||
v_yn = v_y + dt * a_y
|
|
||||||
|
|
||||||
s_n = s + dt * v_z + 0.5 * a_z * dt ** 2
|
sol = solve_ivp(fun=model, t_span=[2.0, t_max], y0=y0, t_eval=t, args=(m_pl, m_film, m_bal, c_virt), max_step=35.0) #, events=ending.terminal) # events=
|
||||||
dh = s_n - s
|
print("hier:")
|
||||||
v_n = v_z + dt * a_z
|
print(sol.message)
|
||||||
|
|
||||||
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))
|
res = sol.y[2, :]
|
||||||
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
|
end = datetime.now()
|
||||||
T_e = T_en
|
print(end-start)
|
||||||
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
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
#print(len(lon_list), len(lat_list))
|
|
||||||
#"""
|
|
||||||
ax = plt.axes(projection=ccrs.Mollweide())
|
|
||||||
#ax.coastlines()
|
|
||||||
ax.stock_img()
|
|
||||||
plt.plot(start_lon, start_lat, 'rx', transform=ccrs.Geodetic())
|
|
||||||
plt.plot(lon_list, lat_list, 'k--', transform=ccrs.Geodetic())
|
|
||||||
plt.plot(comp_lon, comp_lat, 'r-', transform=ccrs.Geodetic())
|
|
||||||
#plt.xticks()
|
|
||||||
plt.show()
|
|
||||||
#"""
|
|
||||||
|
|
||||||
|
|
||||||
### WORKS!
|
|
||||||
###
|
|
||||||
###dset = xr.open_dataset("test2021.nc")
|
|
||||||
###
|
|
||||||
###print(dset['t'][1][0]) # [time] [level]
|
|
||||||
###
|
|
||||||
#fig = plt.figure() #figsize=[120,50])
|
|
||||||
###
|
|
||||||
#ax = fig.add_subplot(111, projection=ccrs.PlateCarree())
|
|
||||||
###
|
|
||||||
###dset['t'][1][0].plot(ax=ax, cmap='jet', transform=ccrs.PlateCarree())
|
|
||||||
###ax.coastlines()
|
|
||||||
###plt.show()
|
|
||||||
|
|
||||||
#print(len(ERAlat))
|
|
||||||
#print(len(ERAlon))
|
|
||||||
#print(len(ERAz))
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
#"""
|
|
||||||
plt.plot(comp_time, comp_height, 'r--', label='PoGo Flight Test')
|
plt.plot(comp_time, comp_height, 'r--', label='PoGo Flight Test')
|
||||||
#plt.plot(t_list, Re_list, 'k-', label="Reynolds-Number")
|
plt.plot(t, res)
|
||||||
#plt.plot(t_list, v_list, 'k--', label='Ballon v_rel')
|
|
||||||
plt.plot(t_list, h_list, 'k-', label='Balloon Altitude')
|
|
||||||
#plt.plot(t_list, p_list, 'r-', label='Air Pressure [Pa]')
|
|
||||||
#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.xlabel('time in s')
|
||||||
plt.ylabel('Balloon Altitude in m')
|
plt.ylabel('Balloon Altitude in m')
|
||||||
plt.legend()
|
|
||||||
|
plt.xlim(0, t_max)
|
||||||
|
plt.show()
|
||||||
|
|
||||||
|
plt.clf()
|
||||||
|
ax = plt.axes(projection=ccrs.Mollweide())
|
||||||
|
ax.coastlines()
|
||||||
|
ax.gridlines()
|
||||||
|
ax.stock_img()
|
||||||
|
ax.set_extent([-120, 30, 60, 80], crs=ccrs.PlateCarree())
|
||||||
|
|
||||||
|
|
||||||
|
plt.plot(start_lon, start_lat, 'rx', transform=ccrs.Geodetic())
|
||||||
|
plt.plot(sol.y[0, :], sol.y[1, :], 'k--', transform=ccrs.Geodetic())
|
||||||
|
plt.plot(comp_lon, comp_lat, 'r-', transform=ccrs.Geodetic())
|
||||||
|
# plt.xticks()
|
||||||
|
# figname = "LatLon_%.2f_%.2f.png" % (Albedo, epsilon_ground)
|
||||||
|
# plt.savefig(os.path.join(rootdir, figname))
|
||||||
plt.show()
|
plt.show()
|
||||||
#"""
|
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue
Block a user