def test_decimal_dates(YEAR, MONTH): #-- days per month in a leap and a standard year #-- only difference is February (29 vs. 28) dpm_leap = np.array([31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]) dpm_stnd = np.array([31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]) DPM = dpm_stnd if np.mod(YEAR, 4) else dpm_leap #-- calculate Modified Julian Day (MJD) from calendar date DAY = np.random.randint(1, DPM[MONTH - 1] + 1) HOUR = np.random.randint(0, 23 + 1) MINUTE = np.random.randint(0, 59 + 1) SECOND = 60.0 * np.random.random_sample(1) #-- calculate year-decimal time tdec = convert_calendar_decimal(YEAR, MONTH, DAY=DAY, HOUR=HOUR, MINUTE=MINUTE, SECOND=SECOND) #-- day of the year 1 = Jan 1, 365 = Dec 31 (std) day_temp = np.mod(tdec, 1) * np.sum(DPM) DofY = np.floor(day_temp) + 1 #-- cumulative sum of the calendar dates day_cumulative = np.cumsum(np.concatenate(([0], DPM))) + 1 #-- finding which month date is in i = np.nonzero((DofY >= day_cumulative[0:-1]) & (DofY < day_cumulative[1:])) month_range = np.arange(1, 13) month = month_range[i] #-- finding day of the month day = (DofY - day_cumulative[i]) + 1 #-- convert residuals into time (hour, minute and second) hour_temp = np.mod(day_temp, 1) * 24.0 minute_temp = np.mod(hour_temp, 1) * 60.0 second = np.mod(minute_temp, 1) * 60.0 #-- assert dates eps = np.finfo(np.float16).eps assert (np.floor(tdec) == YEAR) assert (month == MONTH) assert (day == DAY) assert (np.floor(hour_temp) == HOUR) assert (np.floor(minute_temp) == MINUTE) assert (np.abs(second - SECOND) < eps)
def compute_OPT_icebridge_data(tide_dir, arg, METHOD=None, VERBOSE=False, MODE=0o775): #-- extract file name and subsetter indices lists match_object = re.match(r'(.*?)(\[(.*?)\])?$', arg) input_file = os.path.expanduser(match_object.group(1)) #-- subset input file to indices if match_object.group(2): #-- decompress ranges and add to list input_subsetter = [] for i in re.findall(r'((\d+)-(\d+)|(\d+))', match_object.group(3)): input_subsetter.append(int(i[3])) if i[3] else \ input_subsetter.extend(range(int(i[1]),int(i[2])+1)) else: input_subsetter = None #-- output directory for input_file DIRECTORY = os.path.dirname(input_file) #-- calculate if input files are from ATM or LVIS (+GH) regex = {} regex[ 'ATM'] = r'(BLATM2|ILATM2)_(\d+)_(\d+)_smooth_nadir(.*?)(csv|seg|pt)$' regex['ATM1b'] = r'(BLATM1b|ILATM1b)_(\d+)_(\d+)(.*?).(qi|TXT|h5)$' regex['LVIS'] = r'(BLVIS2|BVLIS2|ILVIS2)_(.*?)(\d+)_(\d+)_(R\d+)_(\d+).H5$' regex['LVGH'] = r'(ILVGH2)_(.*?)(\d+)_(\d+)_(R\d+)_(\d+).H5$' for key, val in regex.items(): if re.match(val, os.path.basename(input_file)): OIB = key #-- invalid value fill_value = -9999.0 #-- output netCDF4 and HDF5 file attributes #-- will be added to YAML header in csv files attrib = {} #-- latitude attrib['lat'] = {} attrib['lat']['long_name'] = 'Latitude_of_measurement' attrib['lat']['description'] = ('Corresponding_to_the_measurement_' 'position_at_the_acquisition_time') attrib['lat']['units'] = 'Degrees_North' #-- longitude attrib['lon'] = {} attrib['lon']['long_name'] = 'Longitude_of_measurement' attrib['lon']['description'] = ('Corresponding_to_the_measurement_' 'position_at_the_acquisition_time') attrib['lon']['units'] = 'Degrees_East' #-- ocean pole tides attrib['tide_oc_pole'] = {} attrib['tide_oc_pole']['long_name'] = 'Ocean_Pole_Tide' attrib['tide_oc_pole']['description'] = ( 'Ocean_pole_tide_radial_' 'displacements_at_the_measurement_position_at_the_acquisition_time_due_' 'to_polar_motion') attrib['tide_oc_pole']['reference'] = ( 'ftp://tai.bipm.org/iers/conv2010/' 'chapter7/opoleloadcoefcmcor.txt.gz') attrib['tide_oc_pole']['units'] = 'meters' #-- Modified Julian Days attrib['time'] = {} attrib['time']['long_name'] = 'Time' attrib['time']['units'] = 'days since 1858-11-17T00:00:00' attrib['time']['description'] = 'Modified Julian Days' attrib['time']['calendar'] = 'standard' #-- extract information from first input file #-- acquisition year, month and day #-- number of points #-- instrument (PRE-OIB ATM or LVIS, OIB ATM or LVIS) if OIB in ('ATM', 'ATM1b'): M1, YYMMDD1, HHMMSS1, AX1, SF1 = re.findall(regex[OIB], input_file).pop() #-- early date strings omitted century and millenia (e.g. 93 for 1993) if (len(YYMMDD1) == 6): ypre, MM1, DD1 = YYMMDD1[:2], YYMMDD1[2:4], YYMMDD1[4:] if (np.float(ypre) >= 90): YY1 = '{0:4.0f}'.format(np.float(ypre) + 1900.0) else: YY1 = '{0:4.0f}'.format(np.float(ypre) + 2000.0) elif (len(YYMMDD1) == 8): YY1, MM1, DD1 = YYMMDD1[:4], YYMMDD1[4:6], YYMMDD1[6:] elif OIB in ('LVIS', 'LVGH'): M1, RG1, YY1, MMDD1, RLD1, SS1 = re.findall(regex[OIB], input_file).pop() MM1, DD1 = MMDD1[:2], MMDD1[2:] #-- read data from input_file print('{0} -->'.format(input_file)) if VERBOSE else None if (OIB == 'ATM'): #-- load IceBridge ATM data from input_file dinput, file_lines, HEM = read_ATM_icessn_file(input_file, input_subsetter) elif (OIB == 'ATM1b'): #-- load IceBridge Level-1b ATM data from input_file dinput, file_lines, HEM = read_ATM_qfit_file(input_file, input_subsetter) elif OIB in ('LVIS', 'LVGH'): #-- load IceBridge LVIS data from input_file dinput, file_lines, HEM = read_LVIS_HDF5_file(input_file, input_subsetter) #-- extract lat/lon lon = dinput['lon'][:] lat = dinput['lat'][:] #-- convert time from UTC time of day to modified julian days (MJD) #-- J2000: seconds since 2000-01-01 12:00:00 UTC t = dinput['time'][:] / 86400.0 + 51544.5 #-- convert from MJD to calendar dates YY, MM, DD, HH, MN, SS = convert_julian(t + 2400000.5, FORMAT='tuple') #-- convert calendar dates into year decimal tdec = convert_calendar_decimal(YY, MM, DAY=DD, HOUR=HH, MINUTE=MN, SECOND=SS) #-- elevation h1 = dinput['data'][:] #-- degrees to radians and arcseconds to radians dtr = np.pi / 180.0 atr = np.pi / 648000.0 #-- earth and physical parameters (IERS) G = 6.67428e-11 #-- universal constant of gravitation [m^3/(kg*s^2)] GM = 3.986004418e14 #-- geocentric gravitational constant [m^3/s^2] ge = 9.7803278 #-- mean equatorial gravity [m/s^2] a_axis = 6378136.6 #-- equatorial radius of the Earth [m] flat = 1.0 / 298.257223563 #-- flattening of the ellipsoid omega = 7.292115e-5 #-- mean rotation rate of the Earth [radians/s] rho_w = 1025.0 #-- density of sea water [kg/m^3] ge = 9.7803278 #-- mean equatorial gravitational acceleration [m/s^2] #-- Linear eccentricity and first numerical eccentricity lin_ecc = np.sqrt((2.0 * flat - flat**2) * a_axis**2) ecc1 = lin_ecc / a_axis #-- tidal love number differential (1 + kl - hl) for pole tide frequencies gamma = 0.6870 + 0.0036j #-- convert from geodetic latitude to geocentric latitude #-- geodetic latitude in radians latitude_geodetic_rad = lat * dtr #-- prime vertical radius of curvature N = a_axis / np.sqrt(1.0 - ecc1**2.0 * np.sin(latitude_geodetic_rad)**2.0) #-- calculate X, Y and Z from geodetic latitude and longitude X = (N + h1) * np.cos(latitude_geodetic_rad) * np.cos(lon * dtr) Y = (N + h1) * np.cos(latitude_geodetic_rad) * np.sin(lon * dtr) Z = (N * (1.0 - ecc1**2.0) + h1) * np.sin(latitude_geodetic_rad) rr = np.sqrt(X**2.0 + Y**2.0 + Z**2.0) #-- calculate geocentric latitude and convert to degrees latitude_geocentric = np.arctan(Z / np.sqrt(X**2.0 + Y**2.0)) / dtr #-- pole tide displacement scale factor Hp = np.sqrt(8.0 * np.pi / 15.0) * (omega**2 * a_axis**4) / GM K = 4.0 * np.pi * G * rho_w * Hp * a_axis / (3.0 * ge) K1 = 4.0 * np.pi * G * rho_w * Hp * a_axis**3 / (3.0 * GM) #-- read ocean pole tide map from Desai (2002) ocean_pole_tide_file = get_data_path(['data', 'opoleloadcoefcmcor.txt.gz']) iur, iun, iue, ilon, ilat = read_ocean_pole_tide(ocean_pole_tide_file) #-- pole tide files (mean and daily) # mean_pole_file = os.path.join(tide_dir,'mean-pole.tab') mean_pole_file = os.path.join(tide_dir, 'mean_pole_2017-10-23.tab') pole_tide_file = os.path.join(tide_dir, 'finals_all_2017-09-01.tab') #-- read IERS daily polar motion values EOP = read_iers_EOP(pole_tide_file) #-- create cubic spline interpolations of daily polar motion values xSPL = scipy.interpolate.UnivariateSpline(EOP['MJD'], EOP['x'], k=3, s=0) ySPL = scipy.interpolate.UnivariateSpline(EOP['MJD'], EOP['y'], k=3, s=0) #-- bad value fill_value = -9999.0 #-- output ocean pole tide HDF5 file #-- form: rg_NASA_OCEAN_POLE_TIDE_WGS84_fl1yyyymmddjjjjj.H5 #-- where rg is the hemisphere flag (GR or AN) for the region #-- fl1 and fl2 are the data flags (ATM, LVIS, GLAS) #-- yymmddjjjjj is the year, month, day and second of the input file #-- output region flags: GR for Greenland and AN for Antarctica hem_flag = {'N': 'GR', 'S': 'AN'} #-- use starting second to distinguish between files for the day JJ1 = np.min(dinput['time']) % 86400 #-- output file format args = (hem_flag[HEM], 'OCEAN_POLE_TIDE', OIB, YY1, MM1, DD1, JJ1) FILENAME = '{0}_NASA_{1}_WGS84_{2}{3}{4}{5}{6:05.0f}.H5'.format(*args) #-- print file information print('\t{0}'.format(FILENAME)) if VERBOSE else None #-- open output HDF5 file fid = h5py.File(os.path.join(DIRECTORY, FILENAME), 'w') #-- interpolate ocean pole tide map from Desai (2002) if (METHOD == 'spline'): #-- use scipy bivariate splines to interpolate to output points f1 = scipy.interpolate.RectBivariateSpline(ilon, ilat[::-1], iur[:, ::-1].real, kx=1, ky=1) f2 = scipy.interpolate.RectBivariateSpline(ilon, ilat[::-1], iur[:, ::-1].imag, kx=1, ky=1) UR = np.zeros((file_lines), dtype=np.complex128) UR.real = f1.ev(lon, latitude_geocentric) UR.imag = f2.ev(lon, latitude_geocentric) else: #-- use scipy regular grid to interpolate values for a given method r1 = scipy.interpolate.RegularGridInterpolator((ilon, ilat[::-1]), iur[:, ::-1], method=METHOD) UR = r1.__call__(np.c_[lon, latitude_geocentric]) #-- calculate angular coordinates of mean pole at time tdec mpx, mpy, fl = iers_mean_pole(mean_pole_file, tdec, '2015') #-- interpolate daily polar motion values to t using cubic splines px = xSPL(t) py = ySPL(t) #-- calculate differentials from mean pole positions mx = px - mpx my = -(py - mpy) #-- calculate radial displacement at time Urad = np.ma.zeros((file_lines), fill_value=fill_value) Urad.data[:] = K * atr * np.real( (mx * gamma.real + my * gamma.imag) * UR.real + (my * gamma.real - mx * gamma.imag) * UR.imag) #-- replace fill values Urad.mask = np.isnan(Urad.data) Urad.data[Urad.mask] = Urad.fill_value #-- add latitude and longitude to output file for key in ['lat', 'lon']: #-- Defining the HDF5 dataset variables for lat/lon h5 = fid.create_dataset(key, (file_lines, ), data=dinput[key][:], dtype=dinput[key].dtype, compression='gzip') #-- add HDF5 variable attributes for att_name, att_val in attrib[key].items(): h5.attrs[att_name] = att_val #-- attach dimensions h5.dims[0].label = 'RECORD_SIZE' #-- output tides to HDF5 dataset h5 = fid.create_dataset('tide_oc_pole', (file_lines, ), data=Urad, dtype=Urad.dtype, fillvalue=fill_value, compression='gzip') #-- add HDF5 variable attributes h5.attrs['_FillValue'] = fill_value for att_name, att_val in attrib['tide_oc_pole'].items(): h5.attrs[att_name] = att_val #-- attach dimensions h5.dims[0].label = 'RECORD_SIZE' #-- output days to HDF5 dataset h5 = fid.create_dataset('time', (file_lines, ), data=t, dtype=t.dtype, compression='gzip') #-- add HDF5 variable attributes for att_name, att_val in attrib['time'].items(): h5.attrs[att_name] = att_val #-- attach dimensions h5.dims[0].label = 'RECORD_SIZE' #-- HDF5 file attributes fid.attrs['featureType'] = 'trajectory' fid.attrs['title'] = 'Tidal_correction_for_elevation_measurements' fid.attrs['summary'] = ('Ocean_pole_tide_radial_displacements_' 'computed_at_elevation_measurements.') fid.attrs['project'] = 'NASA_Operation_IceBridge' fid.attrs['processing_level'] = '4' fid.attrs['date_created'] = time.strftime('%Y-%m-%d', time.localtime()) #-- add attributes for input files fid.attrs['elevation_file'] = os.path.basename(input_file) #-- add geospatial and temporal attributes fid.attrs['geospatial_lat_min'] = dinput['lat'].min() fid.attrs['geospatial_lat_max'] = dinput['lat'].max() fid.attrs['geospatial_lon_min'] = dinput['lon'].min() fid.attrs['geospatial_lon_max'] = dinput['lon'].max() fid.attrs['geospatial_lat_units'] = "degrees_north" fid.attrs['geospatial_lon_units'] = "degrees_east" fid.attrs['geospatial_ellipsoid'] = "WGS84" fid.attrs['time_type'] = 'UTC' #-- convert start/end time from MJD into Julian days JD_start = np.min(t) + 2400000.5 JD_end = np.max(t) + 2400000.5 #-- convert to calendar date with convert_julian.py cal = convert_julian(np.array([JD_start, JD_end]), ASTYPE=np.int) #-- add attributes with measurement date start, end and duration args = (cal['hour'][0], cal['minute'][0], cal['second'][0]) fid.attrs['RangeBeginningTime'] = '{0:02d}:{1:02d}:{2:02d}'.format(*args) args = (cal['hour'][-1], cal['minute'][-1], cal['second'][-1]) fid.attrs['RangeEndingTime'] = '{0:02d}:{1:02d}:{2:02d}'.format(*args) args = (cal['year'][0], cal['month'][0], cal['day'][0]) fid.attrs['RangeBeginningDate'] = '{0:4d}-{1:02d}-{2:02d}'.format(*args) args = (cal['year'][-1], cal['month'][-1], cal['day'][-1]) fid.attrs['RangeEndingDate'] = '{0:4d}-{1:02d}-{2:02d}'.format(*args) duration = np.round(JD_end * 86400.0 - JD_start * 86400.0) fid.attrs['DurationTimeSeconds'] = '{0:0.0f}'.format(duration) #-- close the output HDF5 dataset fid.close() #-- change the permissions level to MODE os.chmod(os.path.join(DIRECTORY, FILENAME), MODE)
def compute_OPT_displacements(tide_dir, input_file, output_file, METHOD=None, VERBOSE=False, MODE=0775): #-- read input *.csv file to extract MJD, latitude, longitude and elevation dtype = dict(names=('MJD', 'lat', 'lon', 'h'), formats=('f', 'f', 'f', 'f')) dinput = np.loadtxt(input_file, delimiter=',', dtype=dtype) file_lines, = np.shape(dinput['h']) #-- convert from MJD to calendar dates, then to year-decimal YY, MM, DD, HH, MN, SS = convert_julian(dinput['MJD'] + 2400000.5, FORMAT='tuple') tdec = convert_calendar_decimal(YY, MM, DAY=DD, HOUR=HH, MINUTE=MN, SECOND=SS) #-- degrees to radians and arcseconds to radians dtr = np.pi / 180.0 atr = np.pi / 648000.0 #-- earth and physical parameters (IERS and WGS84) G = 6.67428e-11 #-- universal constant of gravitation [m^3/(kg*s^2)] GM = 3.98004418e14 #-- geocentric gravitational constant [m^3/s^2] a_axis = 6378136.6 #-- WGS84 equatorial radius of the Earth [m] flat = 1.0 / 298.257223563 #-- flattening of the WGS84 ellipsoid omega = 7.292115e-5 #-- mean rotation rate of the Earth [radians/s] rho_w = 1025.0 #-- density of sea water [kg/m^3] #-- Linear eccentricity and first numerical eccentricity lin_ecc = np.sqrt((2.0 * flat - flat**2) * a_axis**2) ecc1 = lin_ecc / a_axis #-- tidal love number differential (1 + kl - hl) for pole tide frequencies gamma = 0.6870 + 0.0036j #-- convert from geodetic latitude to geocentric latitude #-- geodetic latitude in radians latitude_geodetic_rad = dinput['lat'] * dtr #-- prime vertical radius of curvature N = a_axis / np.sqrt(1.0 - ecc1**2.0 * np.sin(latitude_geodetic_rad)**2.0) #-- calculate X, Y and Z from geodetic latitude and longitude X = (N + dinput['h']) * np.cos(latitude_geodetic_rad) * np.cos( dinput['lon'] * dtr) Y = (N + dinput['h']) * np.cos(latitude_geodetic_rad) * np.sin( dinput['lon'] * dtr) Z = (N * (1.0 - ecc1**2.0) + dinput['h']) * np.sin(latitude_geodetic_rad) #-- calculate geocentric latitude and convert to degrees latitude_geocentric = np.arctan(Z / np.sqrt(X**2.0 + Y**2.0)) / dtr #-- pole tide displacement scale factor Hp = np.sqrt(8.0 * np.pi / 15.0) * (omega**2 * a_axis**4) / GM K = 4.0 * np.pi * G * rho_w * Hp * a_axis**3 / (3.0 * GM) #-- pole tide files (mean and daily) mean_pole_file = os.path.join(tide_dir, 'mean_pole_2017-10-23.tab') pole_tide_file = os.path.join(tide_dir, 'finals_all_2017-09-01.tab') #-- calculate angular coordinates of mean pole at time tdec mpx, mpy, fl = iers_mean_pole(mean_pole_file, tdec, '2015') #-- read IERS daily polar motion values EOP = read_iers_EOP(pole_tide_file) #-- interpolate daily polar motion values to t1 using cubic splines xSPL = scipy.interpolate.UnivariateSpline(EOP['MJD'], EOP['x'], k=3, s=0) ySPL = scipy.interpolate.UnivariateSpline(EOP['MJD'], EOP['y'], k=3, s=0) px = xSPL(dinput['MJD']) py = ySPL(dinput['MJD']) #-- calculate differentials from mean pole positions mx = px - mpx my = -(py - mpy) #-- read ocean pole tide map from Desai (2002) ocean_pole_tide_file = os.path.join(tide_dir, 'opoleloadcoefcmcor.txt.gz') iur, ilon, ilat = read_ocean_pole_tide(ocean_pole_tide_file) #-- interpolate ocean pole tide map from Desai (2002) if (METHOD == 'spline'): #-- use scipy bivariate splines to interpolate to output points f1 = scipy.interpolate.RectBivariateSpline(ilon, ilat[::-1], iur[:, ::-1].real, kx=1, ky=1) f2 = scipy.interpolate.RectBivariateSpline(ilon, ilat[::-1], iur[:, ::-1].imag, kx=1, ky=1) UR = np.zeros((file_lines), dtype=np.complex128) UR.real = f1.ev(dinput['lon'], latitude_geocentric) UR.imag = f2.ev(dinput['lon'], latitude_geocentric) else: #-- create mesh grids of latitude and longitude gridlon, gridlat = np.meshgrid(ilon, ilat, indexing='ij') interp_points = zip(gridlon.flatten(), gridlat.flatten()) #-- use scipy griddata to interpolate to output points UR = scipy.interpolate.griddata(interp_points, iur.flatten(), zip(dinput['lon'], latitude_geocentric), method=METHOD) #-- calculate radial displacement at time Urad = K * atr * np.real((mx * gamma.real + my * gamma.imag) * UR.real + (my * gamma.real - mx * gamma.imag) * UR.imag) #-- output to file with open(output_file) as f: for d, lt, ln, u in zip(dinput['MJD'], dinput['lat'], dinput['lon'], Urad): print('{0:g},{1:g},{2:g},{3:f}'.format(d, lt, ln, u), file=f) #-- change the permissions level to MODE os.chmod(output_file, MODE)
def compute_OPT_displacements(tide_dir, input_file, output_file, FORMAT='csv', VARIABLES=['time', 'lat', 'lon', 'data'], TIME_UNITS='days since 1858-11-17T00:00:00', PROJECTION='4326', METHOD='spline', VERBOSE=False, MODE=0o775): #-- invalid value fill_value = -9999.0 #-- output netCDF4 and HDF5 file attributes #-- will be added to YAML header in csv files attrib = {} #-- latitude attrib['lat'] = {} attrib['lat']['long_name'] = 'Latitude' attrib['lat']['units'] = 'Degrees_North' #-- longitude attrib['lon'] = {} attrib['lon']['long_name'] = 'Longitude' attrib['lon']['units'] = 'Degrees_East' #-- ocean pole tides attrib['tide_oc_pole'] = {} attrib['tide_oc_pole']['long_name'] = 'Ocean_Pole_Tide' attrib['tide_oc_pole']['description'] = ( 'Ocean_pole_tide_radial_' 'displacements_time_due_to_polar_motion') attrib['tide_oc_pole']['reference'] = ( 'ftp://tai.bipm.org/iers/conv2010/' 'chapter7/opoleloadcoefcmcor.txt.gz') attrib['tide_oc_pole']['units'] = 'meters' attrib['tide_oc_pole']['_FillValue'] = fill_value #-- Modified Julian Days attrib['time'] = {} attrib['time']['long_name'] = 'Time' attrib['time']['units'] = 'days since 1858-11-17T00:00:00' attrib['time']['description'] = 'Modified Julian Days' attrib['time']['calendar'] = 'standard' #-- read input file to extract time, spatial coordinates and data if (FORMAT == 'csv'): dinput = pyTMD.spatial.from_ascii(input_file, columns=VARIABLES, header=0, verbose=VERBOSE) elif (FORMAT == 'netCDF4'): dinput = pyTMD.spatial.from_netCDF4(input_file, timename=VARIABLES[0], xname=VARIABLES[2], yname=VARIABLES[1], varname=VARIABLES[3], verbose=VERBOSE) elif (FORMAT == 'HDF5'): dinput = pyTMD.spatial.from_HDF5(input_file, timename=VARIABLES[0], xname=VARIABLES[2], yname=VARIABLES[1], varname=VARIABLES[3], verbose=VERBOSE) #-- converting x,y from projection to latitude/longitude #-- could try to extract projection attributes from netCDF4 and HDF5 files try: crs1 = pyproj.CRS.from_string("epsg:{0:d}".format(int(PROJECTION))) except (ValueError, pyproj.exceptions.CRSError): crs1 = pyproj.CRS.from_string(PROJECTION) crs2 = pyproj.CRS.from_string("epsg:{0:d}".format(4326)) transformer = pyproj.Transformer.from_crs(crs1, crs2, always_xy=True) lon, lat = transformer.transform(dinput['x'].flatten(), dinput['y'].flatten()) #-- extract time units from netCDF4 and HDF5 attributes or from TIME_UNITS try: time_string = dinput['attributes']['time']['units'] except (TypeError, KeyError): epoch1, to_secs = pyTMD.time.parse_date_string(TIME_UNITS) else: epoch1, to_secs = pyTMD.time.parse_date_string(time_string) #-- convert dates to Modified Julian days (days since 1858-11-17T00:00:00) MJD = pyTMD.time.convert_delta_time(to_secs * dinput['time'].flatten(), epoch1=epoch1, epoch2=(1858, 11, 17, 0, 0, 0), scale=1.0 / 86400.0) #-- add offset to convert to Julian days and then convert to calendar dates Y, M, D, h, m, s = convert_julian(2400000.5 + MJD, FORMAT='tuple') #-- calculate time in year-decimal format time_decimal = convert_calendar_decimal(Y, M, DAY=D, HOUR=h, MINUTE=m, SECOND=s) #-- number of data points n_time = len(time_decimal) #-- degrees to radians and arcseconds to radians dtr = np.pi / 180.0 atr = np.pi / 648000.0 #-- earth and physical parameters (IERS and WGS84) G = 6.67428e-11 #-- universal constant of gravitation [m^3/(kg*s^2)] GM = 3.986004418e14 #-- geocentric gravitational constant [m^3/s^2] a_axis = 6378136.6 #-- WGS84 equatorial radius of the Earth [m] flat = 1.0 / 298.257223563 #-- flattening of the WGS84 ellipsoid omega = 7.292115e-5 #-- mean rotation rate of the Earth [radians/s] rho_w = 1025.0 #-- density of sea water [kg/m^3] ge = 9.7803278 #-- mean equatorial gravitational acceleration [m/s^2] #-- Linear eccentricity and first numerical eccentricity lin_ecc = np.sqrt((2.0 * flat - flat**2) * a_axis**2) ecc1 = lin_ecc / a_axis #-- tidal love number differential (1 + kl - hl) for pole tide frequencies gamma = 0.6870 + 0.0036j #-- convert from geodetic latitude to geocentric latitude #-- geodetic latitude in radians latitude_geodetic_rad = lat * dtr #-- prime vertical radius of curvature N = a_axis / np.sqrt(1.0 - ecc1**2.0 * np.sin(latitude_geodetic_rad)**2.0) #-- calculate X, Y and Z from geodetic latitude and longitude X = (N + dinput['data']) * np.cos(latitude_geodetic_rad) * np.cos( lon * dtr) Y = (N + dinput['data']) * np.cos(latitude_geodetic_rad) * np.sin( lon * dtr) Z = (N * (1.0 - ecc1**2.0) + dinput['data']) * np.sin(latitude_geodetic_rad) #-- calculate geocentric latitude and convert to degrees latitude_geocentric = np.arctan(Z / np.sqrt(X**2.0 + Y**2.0)) / dtr #-- pole tide displacement scale factor Hp = np.sqrt(8.0 * np.pi / 15.0) * (omega**2 * a_axis**4) / GM K = 4.0 * np.pi * G * rho_w * Hp * a_axis / (3.0 * ge) K1 = 4.0 * np.pi * G * rho_w * Hp * a_axis**3 / (3.0 * GM) #-- pole tide files (mean and daily) mean_pole_file = os.path.join(tide_dir, 'mean_pole_2017-10-23.tab') pole_tide_file = os.path.join(tide_dir, 'finals_all_2017-09-01.tab') #-- calculate angular coordinates of mean pole at time mpx, mpy, fl = iers_mean_pole(mean_pole_file, time_decimal, '2015') #-- read IERS daily polar motion values EOP = read_iers_EOP(pole_tide_file) #-- interpolate daily polar motion values to t1 using cubic splines xSPL = scipy.interpolate.UnivariateSpline(EOP['MJD'], EOP['x'], k=3, s=0) ySPL = scipy.interpolate.UnivariateSpline(EOP['MJD'], EOP['y'], k=3, s=0) px = xSPL(MJD) py = ySPL(MJD) #-- calculate differentials from mean pole positions mx = px - mpx my = -(py - mpy) #-- read ocean pole tide map from Desai (2002) ocean_pole_tide_file = get_data_path(['data', 'opoleloadcoefcmcor.txt.gz']) iur, iun, iue, ilon, ilat = read_ocean_pole_tide(ocean_pole_tide_file) #-- interpolate ocean pole tide map from Desai (2002) if (METHOD == 'spline'): #-- use scipy bivariate splines to interpolate to output points f1 = scipy.interpolate.RectBivariateSpline(ilon, ilat[::-1], iur[:, ::-1].real, kx=1, ky=1) f2 = scipy.interpolate.RectBivariateSpline(ilon, ilat[::-1], iur[:, ::-1].imag, kx=1, ky=1) UR = np.zeros((n_time), dtype=np.complex128) UR.real = f1.ev(lon, latitude_geocentric) UR.imag = f2.ev(lon, latitude_geocentric) else: #-- use scipy regular grid to interpolate values for a given method r1 = scipy.interpolate.RegularGridInterpolator((ilon, ilat[::-1]), iur[:, ::-1], method=METHOD) UR = r1.__call__(np.c_[lon, latitude_geocentric]) #-- calculate radial displacement at time Urad = np.ma.zeros((n_time), fill_value=fill_value) Urad.data[:] = K * atr * np.real( (mx * gamma.real + my * gamma.imag) * UR.real + (my * gamma.real - mx * gamma.imag) * UR.imag) #-- replace fill values Urad.mask = np.isnan(Urad.data) Urad.data[Urad.mask] = Urad.fill_value #-- output to file output = dict(time=MJD, lon=lon, lat=lat, tide_oc_pole=Urad) if (FORMAT == 'csv'): pyTMD.spatial.to_ascii(output, attrib, output_file, delimiter=',', columns=['time', 'lat', 'lon', 'tide_oc_pole'], verbose=VERBOSE) elif (FORMAT == 'netCDF4'): pyTMD.spatial.to_netCDF4(output, attrib, output_file, verbose=VERBOSE) elif (FORMAT == 'HDF5'): pyTMD.spatial.to_HDF5(output, attrib, output_file, verbose=VERBOSE) #-- change the permissions level to MODE os.chmod(output_file, MODE)
def compute_LPT_icebridge_data(tide_dir, arg, VERBOSE=False, MODE=0o775): #-- extract file name and subsetter indices lists match_object = re.match('(.*?)(\[(.*?)\])?$', arg) input_file = os.path.expanduser(match_object.group(1)) #-- subset input file to indices if match_object.group(2): #-- decompress ranges and add to list input_subsetter = [] for i in re.findall('((\d+)-(\d+)|(\d+))', match_object.group(3)): input_subsetter.append(int(i[3])) if i[3] else \ input_subsetter.extend(range(int(i[1]),int(i[2])+1)) else: input_subsetter = None #-- output directory for input_file DIRECTORY = os.path.dirname(input_file) #-- calculate if input files are from ATM or LVIS (+GH) regex = {} regex['ATM'] = '(BLATM2|ILATM2)_(\d+)_(\d+)_smooth_nadir(.*?)(csv|seg|pt)$' regex['ATM1b'] = '(BLATM1b|ILATM1b)_(\d+)_(\d+)(.*?).(qi|TXT|h5)$' regex['LVIS'] = '(BLVIS2|BVLIS2|ILVIS2)_(.*?)(\d+)_(\d+)_(R\d+)_(\d+).H5$' regex['LVGH'] = '(ILVGH2)_(.*?)(\d+)_(\d+)_(R\d+)_(\d+).H5$' for key, val in regex.items(): if re.match(val, os.path.basename(input_file)): OIB = key #-- HDF5 file attributes attrib = {} #-- latitude attrib['lat'] = {} attrib['lat']['long_name'] = 'Latitude_of_measurement' attrib['lat']['description'] = ('Corresponding_to_the_measurement_' 'position_at_the_acquisition_time') attrib['lat']['units'] = 'Degrees_North' #-- longitude attrib['lon'] = {} attrib['lon']['long_name'] = 'Longitude_of_measurement' attrib['lon']['description'] = ('Corresponding_to_the_measurement_' 'position_at_the_acquisition_time') attrib['lon']['units'] = 'Degrees_East' #-- load pole tides attrib['tide_pole'] = {} attrib['tide_pole']['long_name'] = 'Solid_Earth_Pole_Tide' attrib['tide_pole']['description'] = ( 'Solid_Earth_pole_tide_radial_' 'displacements_at_the_measurement_position_at_the_acquisition_' 'time_due_to_polar_motion') attrib['tide_pole']['reference'] = ('ftp://tai.bipm.org/iers/conv2010/' 'chapter7/opoleloadcoefcmcor.txt.gz') attrib['tide_pole']['units'] = 'meters' #-- Modified Julian Days attrib['MJD'] = {} attrib['MJD']['long_name'] = 'Time' attrib['MJD']['description'] = 'Modified Julian Days' attrib['MJD']['units'] = 'Days' #-- extract information from first input file #-- acquisition year, month and day #-- number of points #-- instrument (PRE-OIB ATM or LVIS, OIB ATM or LVIS) if OIB in ('ATM', 'ATM1b'): M1, YYMMDD1, HHMMSS1, AX1, SF1 = re.findall(regex[OIB], input_file).pop() #-- early date strings omitted century and millenia (e.g. 93 for 1993) if (len(YYMMDD1) == 6): ypre, MM1, DD1 = YYMMDD1[:2], YYMMDD1[2:4], YYMMDD1[4:] if (np.float(ypre) >= 90): YY1 = '{0:4.0f}'.format(np.float(ypre) + 1900.0) else: YY1 = '{0:4.0f}'.format(np.float(ypre) + 2000.0) elif (len(YYMMDD1) == 8): YY1, MM1, DD1 = YYMMDD1[:4], YYMMDD1[4:6], YYMMDD1[6:] elif OIB in ('LVIS', 'LVGH'): M1, RG1, YY1, MMDD1, RLD1, SS1 = re.findall(regex[OIB], input_file).pop() MM1, DD1 = MMDD1[:2], MMDD1[2:] #-- read data from input_file print('{0} -->'.format(input_file)) if VERBOSE else None if (OIB == 'ATM'): #-- load IceBridge ATM data from input_file dinput, file_lines, HEM = read_ATM_icessn_file(input_file, input_subsetter) elif (OIB == 'ATM1b'): #-- load IceBridge Level-1b ATM data from input_file dinput, file_lines, HEM = read_ATM_qfit_file(input_file, input_subsetter) elif OIB in ('LVIS', 'LVGH'): #-- load IceBridge LVIS data from input_file dinput, file_lines, HEM = read_LVIS_HDF5_file(input_file, input_subsetter) #-- extract lat/lon lon = dinput['lon'][:] lat = dinput['lat'][:] #-- convert time from UTC time of day to modified julian days (MJD) #-- J2000: seconds since 2000-01-01 12:00:00 UTC t = dinput['time'][:] / 86400.0 + 51544.5 #-- convert from MJD to calendar dates YY, MM, DD, HH, MN, SS = convert_julian(t + 2400000.5, FORMAT='tuple') #-- convert calendar dates into year decimal tdec = convert_calendar_decimal(YY, MM, DAY=DD, HOUR=HH, MINUTE=MN, SECOND=SS) #-- elevation h1 = dinput['data'][:] #-- degrees to radians dtr = np.pi / 180.0 atr = np.pi / 648000.0 #-- earth and physical parameters (IERS and WGS84) G = 6.67428e-11 #-- universal constant of gravitation [m^3/(kg*s^2)] GM = 3.98004418e14 #-- geocentric gravitational constant [m^3/s^2] ge = 9.7803278 #-- mean equatorial gravity [m/s^2] a_axis = 6378136.6 #-- semimajor axis of the WGS84 ellipsoid [m] flat = 1.0 / 298.257223563 #-- flattening of the WGS84 ellipsoid b_axis = (1.0 - flat) * a_axis #-- semiminor axis of the WGS84 ellipsoid [m] omega = 7.292115e-5 #-- mean rotation rate of the Earth [radians/s] #-- tidal love number appropriate for the load tide hb2 = 0.6207 #-- Linear eccentricity, first and second numerical eccentricity lin_ecc = np.sqrt((2.0 * flat - flat**2) * a_axis**2) ecc1 = lin_ecc / a_axis ecc2 = lin_ecc / b_axis #-- m parameter [omega^2*a^2*b/(GM)]. p. 70, Eqn.(2-137) m = omega**2 * ((1 - flat) * a_axis**3) / GM #-- flattening components f_2 = -flat + (5.0/2.0)*m + (1.0/2.0)*flat**2.0 - (26.0/7.0)*flat*m + \ (15.0/4.0)*m**2.0 f_4 = -(1.0 / 2.0) * flat**2.0 + (5.0 / 2.0) * flat * m #-- convert from geodetic latitude to geocentric latitude #-- geodetic latitude in radians latitude_geodetic_rad = lat * dtr #-- prime vertical radius of curvature N = a_axis / np.sqrt(1.0 - ecc1**2.0 * np.sin(latitude_geodetic_rad)**2.0) #-- calculate X, Y and Z from geodetic latitude and longitude X = (N + h1) * np.cos(latitude_geodetic_rad) * np.cos(lon * dtr) Y = (N + h1) * np.cos(latitude_geodetic_rad) * np.sin(lon * dtr) Z = (N * (1.0 - ecc1**2.0) + h1) * np.sin(latitude_geodetic_rad) rr = np.sqrt(X**2.0 + Y**2.0 + Z**2.0) #-- calculate geocentric latitude and convert to degrees latitude_geocentric = np.arctan(Z / np.sqrt(X**2.0 + Y**2.0)) / dtr #-- colatitude and longitude in radians theta = dtr * (90.0 - latitude_geocentric) phi = lon * dtr #-- compute normal gravity at spatial location and elevation of points. #-- normal gravity at the equator. p. 79, Eqn.(2-186) gamma_a = (GM / (a_axis * b_axis)) * (1.0 - (3.0 / 2.0) * m - (3.0 / 14.0) * ecc2**2.0 * m) #-- Normal gravity. p. 80, Eqn.(2-199) gamma_0 = gamma_a * (1.0 + f_2 * np.cos(theta)**2.0 + f_4 * np.sin(np.pi * latitude_geocentric / 180.0)**4.0) #-- Normal gravity at height h. p. 82, Eqn.(2-215) gamma_h = gamma_0 * ( 1.0 - (2.0 / a_axis) * (1.0 + flat + m - 2.0 * flat * np.cos(theta)**2.0) * h1 + (3.0 / a_axis**2.0) * h1**2.0) #-- pole tide files (mean and daily) # mean_pole_file = os.path.join(tide_dir,'mean-pole.tab') mean_pole_file = os.path.join(tide_dir, 'mean_pole_2017-10-23.tab') pole_tide_file = os.path.join(tide_dir, 'finals_all_2017-09-01.tab') #-- read IERS daily polar motion values EOP = read_iers_EOP(pole_tide_file) #-- create cubic spline interpolations of daily polar motion values xSPL = scipy.interpolate.UnivariateSpline(EOP['MJD'], EOP['x'], k=3, s=0) ySPL = scipy.interpolate.UnivariateSpline(EOP['MJD'], EOP['y'], k=3, s=0) #-- bad value fill_value = -9999.0 #-- output load pole tide HDF5 file #-- form: rg_NASA_LOAD_POLE_TIDE_WGS84_fl1yyyymmddjjjjj.H5 #-- where rg is the hemisphere flag (GR or AN) for the region #-- fl1 and fl2 are the data flags (ATM, LVIS, GLAS) #-- yymmddjjjjj is the year, month, day and second of the input file #-- output region flags: GR for Greenland and AN for Antarctica hem_flag = {'N': 'GR', 'S': 'AN'} #-- use starting second to distinguish between files for the day JJ1 = np.min(dinput['time']) % 86400 #-- output file format args = (hem_flag[HEM], 'LOAD_POLE_TIDE', OIB, YY1, MM1, DD1, JJ1) FILENAME = '{0}_NASA_{1}_WGS84_{2}{3}{4}{5}{6:05.0f}.H5'.format(*args) #-- print file information print('\t{0}'.format(FILENAME)) if VERBOSE else None #-- open output HDF5 file fid = h5py.File(os.path.join(DIRECTORY, FILENAME), 'w') #-- calculate angular coordinates of mean pole at time tdec mpx, mpy, fl = iers_mean_pole(mean_pole_file, tdec, '2015') #-- interpolate daily polar motion values to time using cubic splines px = xSPL(t) py = ySPL(t) #-- calculate differentials from mean pole positions mx = px - mpx my = -(py - mpy) #-- calculate radial displacement at time dfactor = -hb2 * atr * (omega**2 * rr**2) / (2.0 * gamma_h) Sr = dfactor * np.sin(2.0 * theta) * (mx * np.cos(phi) + my * np.sin(phi)) #-- add latitude and longitude to output file for key in ['lat', 'lon']: #-- Defining the HDF5 dataset variables for lat/lon h5 = fid.create_dataset(key, (file_lines, ), data=dinput[key][:], dtype=dinput[key].dtype, compression='gzip') #-- add HDF5 variable attributes for att_name, att_val in attrib[key].items(): h5.attrs[att_name] = att_val #-- attach dimensions h5.dims[0].label = 'RECORD_SIZE' #-- output tides to HDF5 dataset h5 = fid.create_dataset('tide_pole', (file_lines, ), data=Sr, dtype=Sr.dtype, compression='gzip') #-- add HDF5 variable attributes h5.attrs['_FillValue'] = fill_value for att_name, att_val in attrib['tide_pole'].items(): h5.attrs[att_name] = att_val #-- attach dimensions h5.dims[0].label = 'RECORD_SIZE' #-- output days to HDF5 dataset h5 = fid.create_dataset('MJD', (file_lines, ), data=t, dtype=t.dtype, compression='gzip') #-- add HDF5 variable attributes for att_name, att_val in attrib['MJD'].items(): h5.attrs[att_name] = att_val #-- attach dimensions h5.dims[0].label = 'RECORD_SIZE' #-- HDF5 file attributes fid.attrs['featureType'] = 'trajectory' fid.attrs['title'] = 'Load_Pole_Tide_correction_for_elevation_measurements' fid.attrs['summary'] = ('Solid_Earth_pole_tide_radial_displacements_' 'computed_at_elevation_measurements.') fid.attrs['project'] = 'NASA_Operation_IceBridge' fid.attrs['processing_level'] = '4' fid.attrs['date_created'] = time.strftime('%Y-%m-%d', time.localtime()) #-- add attributes for input files fid.attrs['elevation_file'] = os.path.basename(input_file) #-- add geospatial and temporal attributes fid.attrs['geospatial_lat_min'] = dinput['lat'].min() fid.attrs['geospatial_lat_max'] = dinput['lat'].max() fid.attrs['geospatial_lon_min'] = dinput['lon'].min() fid.attrs['geospatial_lon_max'] = dinput['lon'].max() fid.attrs['geospatial_lat_units'] = "degrees_north" fid.attrs['geospatial_lon_units'] = "degrees_east" fid.attrs['geospatial_ellipsoid'] = "WGS84" fid.attrs['time_type'] = 'UTC' #-- convert start/end time from MJD into Julian days JD_start = np.min(t) + 2400000.5 JD_end = np.max(t) + 2400000.5 #-- convert to calendar date with convert_julian.py cal = convert_julian(np.array([JD_start, JD_end]), ASTYPE=np.int) #-- add attributes with measurement date start, end and duration args = (cal['hour'][0], cal['minute'][0], cal['second'][0]) fid.attrs['RangeBeginningTime'] = '{0:02d}:{1:02d}:{2:02d}'.format(*args) args = (cal['hour'][-1], cal['minute'][-1], cal['second'][-1]) fid.attrs['RangeEndingTime'] = '{0:02d}:{1:02d}:{2:02d}'.format(*args) args = (cal['year'][0], cal['month'][0], cal['day'][0]) fid.attrs['RangeBeginningDate'] = '{0:4d}-{1:02d}-{2:02d}'.format(*args) args = (cal['year'][-1], cal['month'][-1], cal['day'][-1]) fid.attrs['RangeEndingDate'] = '{0:4d}-{1:02d}-{2:02d}'.format(*args) duration = np.round(JD_end * 86400.0 - JD_start * 86400.0) fid.attrs['DurationTimeSeconds'] = '{0:0.0f}'.format(duration) #-- close the output HDF5 dataset fid.close() #-- change the permissions level to MODE os.chmod(os.path.join(DIRECTORY, FILENAME), MODE)
def compute_LPT_displacements(tide_dir, input_file, output_file, FORMAT='csv', VARIABLES=['time', 'lat', 'lon', 'data'], TIME_UNITS='days since 1858-11-17T00:00:00', PROJECTION='4326', VERBOSE=False, MODE=0o775): #-- invalid value fill_value = -9999.0 #-- output netCDF4 and HDF5 file attributes #-- will be added to YAML header in csv files attrib = {} #-- latitude attrib['lat'] = {} attrib['lat']['long_name'] = 'Latitude' attrib['lat']['units'] = 'Degrees_North' #-- longitude attrib['lon'] = {} attrib['lon']['long_name'] = 'Longitude' attrib['lon']['units'] = 'Degrees_East' #-- load pole tides attrib['tide_pole'] = {} attrib['tide_pole']['long_name'] = 'Solid_Earth_Pole_Tide' attrib['tide_pole']['description'] = ('Solid_Earth_pole_tide_radial_' 'displacements_due_to_polar_motion') attrib['tide_pole']['reference'] = ('ftp://tai.bipm.org/iers/conv2010/' 'chapter7/opoleloadcoefcmcor.txt.gz') attrib['tide_pole']['units'] = 'meters' attrib['tide_pole']['_FillValue'] = fill_value #-- time attrib['time'] = {} attrib['time']['long_name'] = 'Time' attrib['time']['units'] = 'days since 1858-11-17T00:00:00' attrib['time']['description'] = 'Modified Julian Days' attrib['time']['calendar'] = 'standard' #-- read input file to extract time, spatial coordinates and data if (FORMAT == 'csv'): dinput = pyTMD.spatial.from_ascii(input_file, columns=VARIABLES, header=0, verbose=VERBOSE) elif (FORMAT == 'netCDF4'): dinput = pyTMD.spatial.from_netCDF4(input_file, timename=VARIABLES[0], xname=VARIABLES[2], yname=VARIABLES[1], varname=VARIABLES[3], verbose=VERBOSE) elif (FORMAT == 'HDF5'): dinput = pyTMD.spatial.from_HDF5(input_file, timename=VARIABLES[0], xname=VARIABLES[2], yname=VARIABLES[1], varname=VARIABLES[3], verbose=VERBOSE) #-- converting x,y from projection to latitude/longitude #-- could try to extract projection attributes from netCDF4 and HDF5 files try: crs1 = pyproj.CRS.from_string("epsg:{0:d}".format(int(PROJECTION))) except (ValueError, pyproj.exceptions.CRSError): crs1 = pyproj.CRS.from_string(PROJECTION) crs2 = pyproj.CRS.from_string("epsg:{0:d}".format(4326)) transformer = pyproj.Transformer.from_crs(crs1, crs2, always_xy=True) lon, lat = transformer.transform(dinput['x'].flatten(), dinput['y'].flatten()) #-- extract time units from netCDF4 and HDF5 attributes or from TIME_UNITS try: time_string = dinput['attributes']['time']['units'] except (TypeError, KeyError): epoch1, to_secs = pyTMD.time.parse_date_string(TIME_UNITS) else: epoch1, to_secs = pyTMD.time.parse_date_string(time_string) #-- convert dates to Modified Julian days (days since 1858-11-17T00:00:00) MJD = pyTMD.time.convert_delta_time(to_secs * dinput['time'].flatten(), epoch1=epoch1, epoch2=(1858, 11, 17, 0, 0, 0), scale=1.0 / 86400.0) #-- add offset to convert to Julian days and then convert to calendar dates Y, M, D, h, m, s = convert_julian(2400000.5 + MJD, FORMAT='tuple') #-- calculate time in year-decimal format time_decimal = convert_calendar_decimal(Y, M, DAY=D, HOUR=h, MINUTE=m, SECOND=s) #-- number of data points n_time = len(time_decimal) #-- degrees to radians dtr = np.pi / 180.0 atr = np.pi / 648000.0 #-- earth and physical parameters (IERS and WGS84) GM = 3.986004418e14 #-- geocentric gravitational constant [m^3/s^2] a_axis = 6378136.6 #-- semimajor axis of the WGS84 ellipsoid [m] flat = 1.0 / 298.257223563 #-- flattening of the WGS84 ellipsoid b_axis = (1.0 - flat) * a_axis #-- semiminor axis of the WGS84 ellipsoid [m] omega = 7.292115e-5 #-- mean rotation rate of the Earth [radians/s] #-- tidal love number appropriate for the load tide hb2 = 0.6207 #-- Linear eccentricity, first and second numerical eccentricity lin_ecc = np.sqrt((2.0 * flat - flat**2) * a_axis**2) ecc1 = lin_ecc / a_axis ecc2 = lin_ecc / b_axis #-- m parameter [omega^2*a^2*b/(GM)]. p. 70, Eqn.(2-137) m = omega**2 * ((1 - flat) * a_axis**3) / GM #-- flattening components f_2 = -flat + (5.0/2.0)*m + (1.0/2.0)*flat**2.0 - (26.0/7.0)*flat*m + \ (15.0/4.0)*m**2.0 f_4 = -(1.0 / 2.0) * flat**2.0 + (5.0 / 2.0) * flat * m #-- convert from geodetic latitude to geocentric latitude #-- geodetic latitude in radians latitude_geodetic_rad = lat * dtr #-- prime vertical radius of curvature N = a_axis / np.sqrt(1.0 - ecc1**2.0 * np.sin(latitude_geodetic_rad)**2.0) #-- calculate X, Y and Z from geodetic latitude and longitude X = (N + dinput['data']) * np.cos(latitude_geodetic_rad) * np.cos( lon * dtr) Y = (N + dinput['data']) * np.cos(latitude_geodetic_rad) * np.sin( lon * dtr) Z = (N * (1.0 - ecc1**2.0) + dinput['data']) * np.sin(latitude_geodetic_rad) rr = np.sqrt(X**2.0 + Y**2.0 + Z**2.0) #-- calculate geocentric latitude and convert to degrees latitude_geocentric = np.arctan(Z / np.sqrt(X**2.0 + Y**2.0)) / dtr #-- geocentric colatitude and longitude in radians theta = dtr * (90.0 - latitude_geocentric) phi = lon * dtr #-- compute normal gravity at spatial location and elevation of points. #-- normal gravity at the equator. p. 79, Eqn.(2-186) gamma_a = (GM / (a_axis * b_axis)) * (1.0 - (3.0 / 2.0) * m - (3.0 / 14.0) * ecc2**2.0 * m) #-- Normal gravity. p. 80, Eqn.(2-199) gamma_0 = gamma_a * (1.0 + f_2 * np.cos(theta)**2.0 + f_4 * np.sin(np.pi * latitude_geocentric / 180.0)**4.0) #-- Normal gravity at height h. p. 82, Eqn.(2-215) gamma_h = gamma_0 * ( 1.0 - (2.0 / a_axis) * (1.0 + flat + m - 2.0 * flat * np.cos(theta)**2.0) * dinput['data'] + (3.0 / a_axis**2.0) * dinput['data']**2.0) #-- pole tide files (mean and daily) mean_pole_file = os.path.join(tide_dir, 'mean_pole_2017-10-23.tab') pole_tide_file = os.path.join(tide_dir, 'finals_all_2017-09-01.tab') #-- calculate angular coordinates of mean pole at time mpx, mpy, fl = iers_mean_pole(mean_pole_file, time_decimal, '2015') #-- read IERS daily polar motion values EOP = read_iers_EOP(pole_tide_file) #-- interpolate daily polar motion values to t1 using cubic splines xSPL = scipy.interpolate.UnivariateSpline(EOP['MJD'], EOP['x'], k=3, s=0) ySPL = scipy.interpolate.UnivariateSpline(EOP['MJD'], EOP['y'], k=3, s=0) px = xSPL(MJD) py = ySPL(MJD) #-- calculate differentials from mean pole positions mx = px - mpx my = -(py - mpy) #-- calculate radial displacement at time dfactor = -hb2 * atr * (omega**2 * rr**2) / (2.0 * gamma_h) Srad = np.ma.zeros((n_time), fill_value=fill_value) Srad.data[:] = dfactor * np.sin( 2.0 * theta) * (mx * np.cos(phi) + my * np.sin(phi)) #-- replace fill values Srad.mask = np.isnan(Srad.data) Srad.data[Srad.mask] = Srad.fill_value #-- output to file output = dict(time=MJD, lon=lon, lat=lat, tide_pole=Srad) if (FORMAT == 'csv'): pyTMD.spatial.to_ascii(output, attrib, output_file, delimiter=',', columns=['time', 'lat', 'lon', 'tide_pole'], verbose=VERBOSE) elif (FORMAT == 'netCDF4'): pyTMD.spatial.to_netCDF4(output, attrib, output_file, verbose=VERBOSE) elif (FORMAT == 'HDF5'): pyTMD.spatial.to_HDF5(output, attrib, output_file, verbose=VERBOSE) #-- change the permissions level to MODE os.chmod(output_file, MODE)