diff --git a/monte_carlo.py b/monte_carlo.py new file mode 100644 index 0000000..8c1af32 --- /dev/null +++ b/monte_carlo.py @@ -0,0 +1,879 @@ +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()