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BASTET/monte_carlo.py

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script for Monte-Carlo simulation of balloon trajectories
2021-05-03 10:44:03 +02:00
import sys
import warnings
import numpy as np
import xarray as xr
import pandas as pd
import cartopy.crs as ccrs
import astropy.units as unit
import matplotlib.pyplot as plt
from dask import delayed
from datetime import datetime
starttime = datetime.now()
from netCDF4 import Dataset
from astropy.time import Time
from scipy import interpolate
from scipy.spatial import cKDTree
from scipy.integrate import solve_ivp
from input.user_input import *
from input.natural_constants import *
from models.gravity import grav
from models.valving import valving
from models.ballasting import ballasting
from models.sun import sun_angles_analytical, tau
from models.drag import drag, cd_PalumboLow, cd_Palumbo, cd_PalumboHigh, cd_sphere
from models.transformation import visible_cells, transform, radii
from multiprocessing import Process
if not sys.warnoptions:
warnings.simplefilter("ignore")
data = pd.read_excel(r'C:\Users\marcel\PycharmProjects\MasterThesis\Mappe1.xls', sheet_name='Tabelle3') # Tabelle3
comp_time = pd.DataFrame(data, columns=['Time']).to_numpy().squeeze()
comp_height = pd.DataFrame(data, columns=['Height']).to_numpy().squeeze()
comp_lat = pd.DataFrame(data, columns=['Latitude']).to_numpy().squeeze()
comp_lon = pd.DataFrame(data, columns=['Longitude']).to_numpy().squeeze()
print("")
print("Initialising simulation...")
print("Launch location : longitude %.4f, latitude: %.4f" % (start_lon, start_lat))
print("Launch time: " + str(start_utc) + " (UTC)")
print("")
print("Reading ERA5-datasets, please wait.")
# ascend_data = xr.open_dataset("ascend_2019_kiruna.nc")
# float_data = xr.open_dataset("float_2019.nc")
first_file = Dataset('float1_2019.nc')
last_file = Dataset('float4_2019.nc')
tstart = int(first_file.variables['time'][0])
tend = int(last_file.variables['time'][-1])
first_file.close()
last_file.close()
df1 = xr.open_mfdataset(['float1_2019.nc', 'float2_2019.nc', 'float3_2019.nc', 'float4_2019.nc'], combine='by_coords', engine='netcdf4', concat_dim="time", parallel=True)
float_data = df1.assign_coords(time=np.linspace(tstart, tend, (tend - tstart) + 1))
df1.close()
# ERA5 MULTI-LEVEL FLOAT (WIND + ATMOSPHERIC DATA DURING FLOAT)
ERAtime = float_data.variables['time'][:] # time
ERAlat1 = float_data.variables['latitude'][:].values # latitude [deg]
ERAlon1 = float_data.variables['longitude'][:].values # longitude [deg]
ERAz_float = float_data.variables['z'][:].values / g # geopotential [m^-2/s^-2] to geopotential height [m]
ERApress_float = float_data.variables['level'][:].values # pressure level [-]
ERAtemp_float = float_data.variables['t'][:].values # air temperature in [K]
vw_x_float = float_data.variables['u'][:].values # v_x in [m/s]
vw_y_float = float_data.variables['v'][:].values # v_y in [m/s]
vw_z_float = float_data.variables['w'][:].values # v_z in [m/s]
float_data.close()
df2 = xr.open_mfdataset(['single1_2019.nc', 'single2_2019.nc', 'single3_2019.nc', 'single4_2019.nc'], combine='by_coords', engine='netcdf4', concat_dim="time", parallel=True)
single_data = df2.assign_coords(time=np.linspace(tstart, tend, (tend - tstart) + 1))
df2.close()
# ERA5 SINGLE-LEVEL (RADIATIVE ENVIRONMENT)
ERAlat2 = single_data.variables['latitude'][:].values # latitude [deg]
ERAlon2 = single_data.variables['longitude'][:].values # longitude [deg]
ERAtcc = single_data.variables['tcc'][:].values # total cloud cover [-]
ERAskt = single_data.variables['skt'][:].values # skin (ground) temperature in [K]
ERAcbh = single_data.variables['cbh'][:].values # cloud base height in [m]
ERAlcc = single_data.variables['lcc'][:].values # low cloud cover [-]
ERAmcc = single_data.variables['mcc'][:].values # medium cloud cover [-]
ERAhcc = single_data.variables['hcc'][:].values # high cloud cover [-]
ERAssr = single_data.variables['ssr'][:].values # hourly accumulated surface net solar radiation [J/m^2]
ERAstrn = single_data.variables['str'][:].values # hourly accumulated surface net thermal radiation [J/m^2]
ERAstrd = single_data.variables['strd'][:].values # hourly accumulated surface thermal radiation downwards [J/m^2]
ERAssrd = single_data.variables['ssrd'][:].values # hourly accumulated surface solar radiation downwards [J/m^2]
ERAtsr = single_data.variables['tsr'][:].values # hourly accumulated top net solar radiation [J/m^2]
ERAttr = single_data.variables['ttr'][:].values # hourly accumulated top net thermal radiation [J/m^2]
ERAtisr = single_data.variables['tisr'][:].values # hourly accumulated TOA incident solar radiation [J/m^2]
ERAstrdc = single_data.variables['strdc'][:].values # hourly accumulated surface thermal radiation downward clear-sky [J/m^2]
ERAsp = single_data.variables['sp'][:].values # surface pressure in [Pa]
single_data.close()
first_file = Dataset('ascend1_2019.nc')
last_file = Dataset('ascend2_2019.nc')
tstart = int(first_file.variables['time'][0])
tend = int(last_file.variables['time'][-1])
first_file.close()
last_file.close()
df3 = xr.open_mfdataset(['ascend1_2019.nc', 'ascend2_2019.nc'], combine='by_coords', engine='netcdf4', concat_dim="time", parallel=True)
ascend_data = df3.assign_coords(time=np.linspace(tstart, tend, (tend - tstart) + 1))
df3.close()
# ERA5 MULTI-LEVEL ASCENT (WIND + ATMOSPHERIC DATA DURING ASCENT)
ERAlat0 = ascend_data.variables['latitude'][:].values # latitude [deg]
ERAlon0 = ascend_data.variables['longitude'][:].values # longitude [deg]
ERAz_ascend = ascend_data.variables['z'][:].values / g # geopotential [m^-2/s^-2] to geopotential height [m]
ERApress_ascend = ascend_data.variables['level'][:].values # pressure level [-]
ERAtemp_ascend = ascend_data.variables['t'][:].values # air temperature in K
vw_x_ascend = ascend_data.variables['u'][:].values # v_x in [m/s]
vw_y_ascend = ascend_data.variables['v'][:].values # v_y in [m/s]
vw_z_ascend = ascend_data.variables['w'][:].values # v_z in [m/s]
ascend_data.close()
print("Finished reading ERA5-datasets.")
lon_era2d0, lat_era2d0 = np.meshgrid(ERAlon0, ERAlat0)
lon_era2d1, lat_era2d1 = np.meshgrid(ERAlon1, ERAlat1)
lon_era2d2, lat_era2d2 = np.meshgrid(ERAlon2, ERAlat2)
xs0, ys0, zs0 = transform(lon_era2d0.flatten(), lat_era2d0.flatten())
xs1, ys1, zs1 = transform(lon_era2d1.flatten(), lat_era2d1.flatten())
xs2, ys2, zs2 = transform(lon_era2d2.flatten(), lat_era2d2.flatten())
print("")
tree0 = cKDTree(np.column_stack((xs0, ys0, zs0)))
tree1 = cKDTree(np.column_stack((xs1, ys1, zs1)))
tree2 = cKDTree(np.column_stack((xs2, ys2, zs2)))
print("Built kd-trees")
def ERA5Data(lon, lat, h, t, deltaT_ERA):
t_epoch = deltaT_ERA + t / 3600
t_pre = int(t_epoch)
t_pre_ind = t_pre - int(ERAtime[0])
t_post_ind = t_pre_ind + 1
xt, yt, zt = transform(lon, lat) # current coordinates
d0, inds0 = tree0.query(np.column_stack((xt, yt, zt)), k=4)
d1, inds1 = tree1.query(np.column_stack((xt, yt, zt)), k=4) # longitude, latitude
d2, inds2 = tree2.query(np.column_stack((xt, yt, zt)), k=visible_cells(h)) # longitude, latitude visible_cells(h)
w0 = 1.0 / d0[0]
w1 = 1.0 / d1[0]
w2 = 1.0 / d2[0] ** 2
lat_ind0 = np.unravel_index(inds0[0], lon_era2d0.shape)[0]
lon_ind0 = np.unravel_index(inds0[0], lon_era2d0.shape)[1]
lat_ind1 = np.unravel_index(inds1[0], lon_era2d1.shape)[0]
lon_ind1 = np.unravel_index(inds1[0], lon_era2d1.shape)[1]
lat_ind2 = np.unravel_index(inds2[0], lon_era2d2.shape)[0]
lon_ind2 = np.unravel_index(inds2[0], lon_era2d2.shape)[1]
if h >= 30000:
try:
interp4d_temp_pre = np.ma.dot(w1, ERAtemp_float[t_pre_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
interp4d_temp_post = np.ma.dot(w1, ERAtemp_float[t_post_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
interp4d_temp = (interp4d_temp_post - interp4d_temp_pre) * (t_epoch - t_pre) + interp4d_temp_pre
interp4d_height_pre = np.ma.dot(w1, ERAz_float[t_pre_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
interp4d_height_post = np.ma.dot(w1, ERAz_float[t_post_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
interp4d_height = (interp4d_height_post - interp4d_height_pre) * (t_epoch - t_pre) + interp4d_height_pre
interp4d_vw_x_pre = np.ma.dot(w1, vw_x_float[t_pre_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
interp4d_vw_x_post = np.ma.dot(w1, vw_x_float[t_post_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
interp4d_vw_x = (interp4d_vw_x_post - interp4d_vw_x_pre) * (t_epoch - t_pre) + interp4d_vw_x_pre
interp4d_vw_y_pre = np.ma.dot(w1, vw_y_float[t_pre_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
interp4d_vw_y_post = np.ma.dot(w1, vw_y_float[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_float[t_pre_ind, :, lat_ind1, lon_ind1]) / np.sum(w1)
interp4d_vw_z_post = np.ma.dot(w1, vw_z_float[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
pressure_hPa = np.array([1, 2, 3, 5, 7, 10, 20])
pressure = 100 * pressure_hPa
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)
except IndexError:
print("Error: Please check time range of ERA5 data!")
elif np.abs(lat - start_lat) <= 10.0 and np.abs(lon - start_lon) <= 10.0:
try:
interp4d_temp_pre = np.ma.dot(w0, ERAtemp_ascend[t_pre_ind, :, lat_ind0, lon_ind0]) / np.sum(w0)
interp4d_temp_post = np.ma.dot(w0, ERAtemp_ascend[t_post_ind, :, lat_ind0, lon_ind0]) / np.sum(w0)
interp4d_temp = (interp4d_temp_post - interp4d_temp_pre) * (t_epoch - t_pre) + interp4d_temp_pre
interp4d_height_pre = np.ma.dot(w0, ERAz_ascend[t_pre_ind, :, lat_ind0, lon_ind0]) / np.sum(w0)
interp4d_height_post = np.ma.dot(w0, ERAz_ascend[t_post_ind, :, lat_ind0, lon_ind0]) / np.sum(w0)
interp4d_height = (interp4d_height_post - interp4d_height_pre) * (t_epoch - t_pre) + interp4d_height_pre
interp4d_vw_x_pre = np.ma.dot(w0, vw_x_ascend[t_pre_ind, :, lat_ind0, lon_ind0]) / np.sum(w0)
interp4d_vw_x_post = np.ma.dot(w0, vw_x_ascend[t_post_ind, :, lat_ind0, lon_ind0]) / np.sum(w0)
interp4d_vw_x = (interp4d_vw_x_post - interp4d_vw_x_pre) * (t_epoch - t_pre) + interp4d_vw_x_pre
interp4d_vw_y_pre = np.ma.dot(w0, vw_y_ascend[t_pre_ind, :, lat_ind0, lon_ind0]) / np.sum(w0)
interp4d_vw_y_post = np.ma.dot(w0, vw_y_ascend[t_post_ind, :, lat_ind0, lon_ind0]) / np.sum(w0)
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(w0, vw_z_ascend[t_pre_ind, :, lat_ind0, lon_ind0]) / np.sum(w0)
interp4d_vw_z_post = np.ma.dot(w0, vw_z_ascend[t_post_ind, :, lat_ind0, lon_ind0]) / np.sum(w0)
interp4d_vw_z = (interp4d_vw_z_post - interp4d_vw_z_pre) * (t_epoch - t_pre) + interp4d_vw_z_pre
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])
pressure = 100 * pressure_hPa
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)
except IndexError:
print("Error: Check time range of ERA5 data!")
else:
pass
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
if isinstance(tcc, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"tcc\"!")
print("Assuming simplified value for parameter \"tcc\".")
tcc = cc
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
if isinstance(tcc, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"cbh\"!")
print("Assuming simplified value for parameter \"cbh\".")
cbh = 2000
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
if isinstance(lcc, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"lcc\"!")
print("Assuming simplified value for parameter \"lcc\".")
lcc = cc/3
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
if isinstance(mcc, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"mcc\"!")
print("Assuming simplified value for parameter \"mcc\".")
mcc = cc/3
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
if isinstance(hcc, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"hcc\"!")
print("Assuming simplified value for parameter \"hcc\".")
hcc = cc/3
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
if isinstance(strn, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"strn\"!")
print("Assuming simplified value for parameter \"strn\".")
strn = 0
skt_pre = np.ma.dot(w2, ERAskt[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
skt_post = np.ma.dot(w2, ERAskt[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
skt = ((skt_post - skt_pre) * (t_epoch - t_pre) + skt_pre)
if isinstance(skt, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"skt\"!")
print("Assuming simplified value for parameter \"skt\".")
skt = T_ground
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
if isinstance(strd, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"strd\"!")
print("Assuming simplified value for parameter \"strd\".")
strd = epsilon_ground * sigma * T_ground ** 4
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
if isinstance(strdc, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"strdc\"!")
print("Assuming simplified value for parameter \"strdc\".")
strdc = epsilon_ground * sigma * T_ground ** 4
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
if isinstance(ssrd, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"ssrd\"!")
print("Assuming simplified value for parameter \"ssrd\".")
ssrd = 1
ssr = 1 - Albedo
if isinstance(ssr, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"ssr\"!")
print("Assuming simplified value for parameter \"ssr\".")
ssrd = 1
ssr = 1 - Albedo
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
if isinstance(tisr, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"tisr\"!")
print("Assuming simplified value for parameter \"tisr\".")
AZ, ELV = sun_angles_analytical(lat, lon, h, utc)
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
tisr = I_Sun * np.sin(np.deg2rad(ELV))
if isinstance(tsr, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"tsr\"!")
print("Assuming simplified value for parameter \"tsr\".")
tsr = (1 - Albedo) * tisr
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
p0_pre = np.ma.dot(w2, ERAsp[t_pre_ind, lat_ind2, lon_ind2]) / np.sum(w2)
p0_post = np.ma.dot(w2, ERAsp[t_post_ind, lat_ind2, lon_ind2]) / np.sum(w2)
p0 = (p0_post - p0_pre) * (t_epoch - t_pre) + p0_pre
if isinstance(p0, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"sp\"!")
print("Assuming simplified value for parameter \"sp\".")
p0 = 101325.0
if isinstance(ttr, float) != True:
print("WARNING: Corrupt ERA5 Data for parameter \"ttr\"!")
print("Assuming simplified value for parameter \"ttr\".")
AZ, ELV = sun_angles_analytical(lat, lon, h, utc)
tau_atm, tau_atmIR = tau(ELV, h, p_air, p0)
HalfConeAngle = np.arcsin(R_E / (R_E + h))
ViewFactor = (1 - np.cos(HalfConeAngle)) / 2
ttr = epsilon_ground * sigma * T_ground ** 4 * tau_atmIR * ViewFactor * 2
if h > interp4d_height[0]:
print("Balloon altitude above interpolation area!")
print(h)
p_air = press_interp1d(interp4d_height[0])
T_air = temp_interp1d(interp4d_height[0])
u = vw_x_interp1d(interp4d_height[0])
v = vw_y_interp1d(interp4d_height[0])
w = -1 / grav(lat, h) * vw_z_interp1d(interp4d_height[0]) * R_air * T_air / p_air
elif h < interp4d_height[-1]:
print("Balloon altitude below interpolation area!")
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 / grav(lat, h) * vw_z_interp1d(interp4d_height[-1]) * R_air * T_air / p_air
else:
p_air = press_interp1d(h)
T_air = temp_interp1d(h)
u = vw_x_interp1d(h)
v = vw_y_interp1d(h)
w = -1 / grav(lat, h) * vw_z_interp1d(h) * R_air * T_air / p_air
rho_air = p_air / (R_air * T_air)
return p_air, p0, T_air, rho_air, u, v, w, cbh, tcc, lcc, mcc, hcc, ssr, strn, strd, strdc, ssrd, tsr, ttr, tisr, skt
begin_time = datetime.now()
# start = Time(start_utc)
def model(t, y, m_pl, m_film, c_virt, t_start):
utc = t_start + 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
m_bal = y[10] # 11
if (lon % 360) > 180: # convert longitude to value in standard interval [-180, 180]
lon = (lon % 360) - 360
else:
lon = (lon % 360)
if lat > 90: # set plausible limits for latitudes
lat = 90
elif lat < -90:
lat = -90
else:
lat = lat
if h > 53700:
h = 53700
elif h < 0:
h = 0
else:
h = h
r_lon, r_lat = radii(lat, h) # calculate radii for velocity conversion between cartesian and Earth reference frame
deltaT_ERA = (t_start.jd - Time('1900-01-01 00:00:00.0').jd) * 24.000000 # conversion to ERA5 time format
try:
p_air, p0, T_air, rho_air, u, v, w, cbh, tcc, lcc, mcc, hcc, ssr, strn, strd, strdc, ssrd, tsr, ttr, tisr, skt = ERA5Data(lon, lat, h, t, deltaT_ERA)
except:
# in case of solver (temporarily) exceeding interpolation area (with subsequent correction)
# or permanent drift out of interpolation area
if h >= 30000 or (np.abs(lat - start_lat) <= 10.0 and np.abs(lon - start_lon) <= 10.0):
print("solver exceeds definition area")
p_air, p0, T_air, rho_air, u, v, w, cbh, tcc, lcc, mcc, hcc, ssr, strn, strd, strdc, ssrd, tsr, ttr, tisr, skt = 0, 101325, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
else:
print("instable trajectory!")
print(h)
print(c_virt)
print(m_gas)
p_air, p0, T_air, rho_air, u, v, w, cbh, tcc, lcc, mcc, hcc, ssr, strn, strd, strdc, ssrd, tsr, ttr, tisr, skt = 0, 101325, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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 = grav(lat, h) * (rho_air - rho_gas) * h_valve
dP_duct = grav(lat, h) * (rho_air - rho_gas) * h_duct
if m_gas < 0: # limit gas mass to plausible value
m_gas = 0 #
V_b = m_gas / rho_gas # calculate balloon volume from current gas mass and gas density
if V_b > V_design:
c_duct = c_ducts
elif V_b < 0:
c_duct = 0
V_b = 0
else:
c_duct = 0
if ballasting(utc) == True:
if m_bal >= 0:
mdot = m_baldot
else:
mdot = 0
else:
mdot = 0
if valving(utc) == 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(utc) == 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_gross = m_pl + m_film + m_bal
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)
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
AZ, ELV = sun_angles_analytical(lat, lon, h, utc)
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
tau_atm, tau_atmIR = tau(ELV, h, p_air, p0)
tau_atm0, tau_atmIR0 = tau(ELV, 0, p0, p0)
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
I_Sun0 = I_Sun * tau_atm0
HalfConeAngle = np.arcsin(R_E / (R_E + h))
ViewFactor = (1 - np.cos(HalfConeAngle)) / 2
if simple == True:
q_IREarth = epsilon_ground * sigma * T_ground ** 4 * tau_atmIR
if ELV <= 0:
q_Albedo = 0
else:
q_Albedo = Albedo * I_Sun * np.sin(np.deg2rad(ELV))
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_sun = I_SunZ
else:
if tcc <= 0.01:
q_IREarth1 = alpha_IR * A_surf * (strd - strn) * tau_atmIR * ViewFactor * (1 + tau_VIS / (1 - r_VIS))
q_IREarth2 = alpha_IR * A_surf * np.abs(ttr) * 0.5 * (1 + tau_IR / (1 - r_IR))
# q_IREarth2 = alpha_IR * A_surf * (0.04321906 * np.abs(ttr) + 84.67820281) * (1 + tau_IR / (1 - r_IR))
if h > 40000:
Q_IREarth = q_IREarth2
else:
Q_IREarth = (q_IREarth2 - q_IREarth1) / 40000 * h + q_IREarth1
if ELV <= 0:
q_Albedo1 = 0
q_Albedo2 = 0
else:
if ssrd == 0:
q_Albedo1 = 0
else:
q_Albedo1 = alpha_VIS * A_surf * (1 - ssr / ssrd) * I_Sun0 * tau_atmIR * np.sin(
np.deg2rad(ELV)) * ViewFactor * (1 + tau_VIS / (1 - r_VIS)) # !
if tisr == 0:
q_Albedo2 = 0
else:
q_Albedo2 = alpha_VIS * A_surf * (1 - tsr / tisr) * I_Sun * np.sin(np.deg2rad(ELV)) * 0.5 * (
1 + tau_VIS / (1 - r_VIS)) # !
if h > 40000:
Q_Albedo = q_Albedo2
else:
Q_Albedo = (q_Albedo2 - q_Albedo1) / 40000 * h + q_Albedo1
q_sun = I_SunZ
else:
q_IRground_bc = (strd - strn) + (strd - strdc)
q_IREarth_bc = alpha_IR * A_surf * q_IRground_bc * tau_atmIR * ViewFactor * (1 + tau_VIS / (1 - r_VIS))
q_sun_bc = I_SunZ * (1 - tcc)
q_Albedo_bc = alpha_VIS * A_surf * (1 - ssr / ssrd) * I_Sun0 * tau_atmIR * np.sin(
np.deg2rad(ELV)) * ViewFactor * (1 + tau_VIS / (1 - r_VIS))
# q_IREarth_ac = alpha_IR * A_surf * (0.04321906 * np.abs(ttr) + 84.67820281) * (1 + tau_IR / (1 - r_IR))
q_IREarth_ac = alpha_IR * A_surf * np.abs(ttr) * 0.5 * (1 + tau_VIS / (1 - r_VIS))
q_sun_ac = I_SunZ
q_Albedo_ac = alpha_VIS * A_surf * (1 - tsr / tisr) * I_Sun * np.sin(np.deg2rad(ELV)) * ViewFactor * (
1 + tau_VIS / (1 - r_VIS))
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:
Q_Albedo = 0
else:
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)
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 * grav(lat, h) * 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_rel) * d_b * rho_air / my_air
Fr = np.abs(v_rel) / np.sqrt(grav(lat, h) * d_b)
HC_forced = k_air / d_b * (2 + 0.41 * Re ** 0.55)
HC_internal = 0.13 * k_gas * (
(rho_gas ** 2 * grav(lat, h) * np.abs(T_film - T_gas) * Pr_gas) / (T_gas * my_air ** 2)) ** (
1 / 3)
HC_external = np.maximum(HC_free, HC_forced)
Q_Sun = alpha_VIS * A_proj * q_sun * (1 + tau_VIS / (1 - r_VIS))
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)
if simple == True:
c_d = 0.47 # sphere
else:
c_d = cd_PalumboHigh(Fr, Re, A_top) # Ref. xx
#c_d = 0.47 # cd_PalumboHigh(Fr, Re, A_top) #cd_sphere(Re) #0.47 # cd_Palumbo(Fr, Re, A_top) # 0.8 #cd_sphere(Re) # cd_palumbo(Fr, Re, A_top) # cd_sphere(Re) / 0.8 / 0.47
D = drag(c_d, rho_air, A_drag, v_rel) # calculate drag force
if v_rel == 0:
Drag_x, Drag_y, Drag_z = 0, 0, 0
else:
Drag_x, Drag_y, Drag_z = D * v_relx / v_rel, D * v_rely / v_rel, D * v_relz / v_rel
F = grav(lat, h) * V_b * (rho_air - rho_gas) - grav(lat, h) * m_gross + Drag_z # gross inflation - weight + drag
a_x, a_y, a_z = Drag_x / m_virt, Drag_y / m_virt, F / m_virt
eqn1 = np.rad2deg(y[3] / r_lon)
eqn2 = np.rad2deg(y[4] / r_lat)
eqn3 = v_z
eqn4 = a_x
eqn5 = a_y
eqn6 = a_z
eqn7 = Q_ConvInt / (gamma * c_v * m_gas) - (gamma - 1) / gamma * (rho_air * grav(lat, h)) / (rho_gas * R_gas) * v_z
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(np.abs(2 * dP_duct * rho_gas))) - (A_valve * c2 * np.sqrt(np.abs(2 * dP_valve * rho_gas)))
if eqn9 > 0:
eqn9 = 0
eqn10 = c2dot
if m_bal > 0:
eqn11 = -mdot
else:
eqn11 = 0
return [eqn1, eqn2, eqn3, eqn4, eqn5, eqn6, eqn7, eqn8, eqn9, eqn10, eqn11]
# DEFINITION OF EVENTS FOR SOLVER
def at_ground(t, y, m_pl, m_film, c_virt):
return y[2]
def above_float(t, y, m_pl, m_film, c_virt):
return 45000 - y[2]
def below_float(t, y, m_pl, m_film, c_virt):
return y[2] - 30050
hit_ground = lambda t, x: at_ground(t, x, m_pl, m_film, c_virt)
hit_ground.terminal = True
hit_ground.direction = -1
excess_ascend = lambda t, x: above_float(t, x, m_pl, m_film, c_virt)
excess_ascend.terminal = True
excess_ascend.direction = -1
instable = lambda t, x: below_float(t, x, m_pl, m_film, c_virt)
instable.terminal = True
instable.direction = -1
print("Beginning Monte-Carlo simulation")
#starttimes = [
# #'2019-05-23 05:00:00.000',
# #'2019-05-23 15:00:00.000',
# #'2019-06-07 05:00:00.000',
# #'2019-06-07 05:00:00.000',
# '2019-06-22 05:00:00.000',
# #'2019-06-22 05:00:00.000'
# ]
def monte_carlo(t_start, m_pl, m_film, m_bal_init, t_end, num_simulations, fig):
t0 = 0.0
tf = t_end
for i in range(num_simulations):
c_virt = c_virt_MC[i]
FreeLift = FL_MC[i]
print("----------------")
print("Starting Monte-Carlo-Run "+str(i))
print(c_virt)
print(FreeLift)
m_gas_init = ((m_pl + m_film + m_bal_init) * (FreeLift / 100 + 1)) / (R_gas / R_air - 1)
deltaT_ERA = (t_start.jd - Time('1900-01-01 00:00:00.0').jd) * 24.000000
p_air0, p00, T_air0, rho_air0, u0, v0, w0, cbh0, tcc0, lcc0, mcc0, hcc0, ssr0, strn0, strd0, strdc0, ssrd0, tsr0, ttr0, tisr0, skt0 = ERA5Data(
start_lon, start_lat, start_height, 0, deltaT_ERA)
y0 = [
start_lon, # start longitude [deg]
start_lat, # start latitude [deg]
start_height, # start altitude [m]
0, # initial v_x [m/s]
0, # initial v_y [m/s]
0, # initial v_z [m/s]
T_air0, # initial gas temperature [K] = initial air temperature [K]
T_air0, # initial film temperature [K] = initial air temperature [K]
m_gas_init, # initial lifting gas mass [kg]
0, # initial factor c2 [-]
m_bal_init # initial ballast mass [kg]
]
sol = solve_ivp(fun=lambda t, x: model(t, x, m_pl, m_film, c_virt, t_start), t_span=[t0, tf], y0=y0,
method='RK45', events=[hit_ground, excess_ascend, instable])
print(sol.t[-1]/(3600 * 24))
print(sol.message)
plt.figure(fig)
ax = plt.axes(projection=ccrs.AzimuthalEquidistant(central_latitude=90))
ax.coastlines()
ax.gridlines(draw_labels=True)
ax.stock_img()
ax.set_extent([-120, 30, 60, 80], crs=ccrs.PlateCarree())
plt.title("Start: " + str(t_start))
plt.plot(start_lon, start_lat, 'rx', transform=ccrs.Geodetic())
plt.plot(sol.y[0, :], sol.y[1, :], 'k--', transform=ccrs.Geodetic())
start1 = Time('2019-05-23 05:00:00.000')
start2 = Time('2019-05-23 15:00:00.000')
start3 = Time('2019-06-07 05:00:00.000')
start4 = Time('2019-06-07 15:00:00.000')
start5 = Time('2019-06-22 05:00:00.000')
start6 = Time('2019-06-22 15:00:00.000')
FL_values = [10.0, 15.0, 20.0]
FL_prob = [1/3, 1/3, 1/3]
num_simulations = 10
FL_MC = np.random.choice(FL_values, 10, p=FL_prob)
c_virt_MC = np.random.normal(0.375, 0.05, 10).round(2)
#m_pl = 917 #2174 # payload mass in [kg] (incl. flight-chain)
#m_bal_init = 540 #500 # initial ballast mass in [kg]
#m_film = 0.74074232733 * 1838 # mass balloon film in [kg]
#FreeLift = 10 # (initial) free lift in [%]
monte_carlo(start5, 917, 1361.48, 540, 2592000, 10, 1) # 3456000
# monte_carlo(start2, 917, 1361.48, 540, 432000, 10, 2)
# monte_carlo(start3, 917, 1361.48, 540, 432000, 10, 3)
"""
if __name__ == '__main__': # t_start m_film t_end fig
p1 = Process(target=monte_carlo(start1, 917, 1361.48, 540, 10000, 10, 1)) # 3456000
p1.start() # m_pl m_bal, num
p2 = Process(target=monte_carlo(start2, 917, 1361.48, 540, 10000, 10, 2)) # 3456000
p2.start() # t_start m_film t_end fig
p3 = Process(target=monte_carlo(start3, 917, 1361.48, 540, 10000, 10, 3)) # 3456000
p3.start() # t_start m_film t_end fig
p1.join()
p2.join()
p3.join()
"""
print(datetime.now() - starttime)
plt.figure(1)
plt.show()
plt.figure(2)
plt.show()
plt.figure(3)
plt.show()
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