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233 | def temporal_evolution(paths, dpt1, zlon, zlat, date_vec=[2020, [], [], []], extent=[-180, 180, -90, 90],parameters= [1/12, 1/2], c_file = '../../data/C.nc', prefix = 'WW3-GLOB-30M', **kwargs):
"""Compute the temporal evolution of the seismic sources in a given region.
Args:
paths (list): A list containing the paths to the file with bathymetry data and the local path for WW3 data.
dpt1 (xarray.DataArray): The bathymetry data.
zlon (xarray.DataArray): The longitude values of the bathymetry data.
zlat (xarray.DataArray): The latitude values of the bathymetry data.
date_vec (list, optional): A list containing the year, month, day, and hour of the dates to compute the temporal evolution.
extent (list, optional): A list containing the longitude and latitude extent of the region.
parameters (list, optional): A list containing the minimum and maximum frequencies for integration (f1 and f2).
c_file (str, optional): The path to the file with the amplification coefficient data.
prefix (str, optional): The prefix for the WW3 data file name.
Returns:
time (list): A list of datetime objects representing the time of each computation.
temporal_variation (ndarray): An array containing the temporal variation of force of the seismic sources.
"""
file_bathy = paths[0]
ww3_local_path = paths[1]
# Constants
radius = 6.371*1e6 # radius of the earth in meters
lg10 = log(10) # log of 10
res_mod = radians(0.5) # angular resolution of the model
#
f1 = parameters[0]
f2 = parameters[1]
## Initialize variables
if 'temporal_resolution' in kwargs:
temporal_resolution = kwargs['temporal_resolution']
if temporal_resolution == 'hourly':
temporal_resol_hourly = True
else:
temporal_resol_hourly = False
F_f1_concat = []
if temporal_resolution == 'daily':
temporal_resol_daily = True
else:
temporal_resol_daily = False
if temporal_resolution == 'monthly':
temporal_resol_monthly = True
else:
temporal_resol_monthly = False
else:
# Default temporal resolution
temporal_resol_hourly = True
## Adapt latitude and longitude to values in parameters file
lon_min = extent[0]
lon_max = extent[1]
lat_min = extent[2]
lat_max = extent[3]
## Open bathymetry
dpt1 = dpt1.sel(latitude = slice(lat_min, lat_max), longitude = slice(lon_min, lon_max))
zlat = zlat.sel(latitude = slice(lat_min, lat_max))
zlon = zlon.sel(longitude = slice(lon_min, lon_max))
## Open Amplification Coefficient
# check for refined bathymetry
res_bathy = abs(zlon[1] - zlon[0])
amplification_coeff = xr.open_dataarray(c_file)
if res_bathy == 0.5:
refined = False
else:
print("Refined bathymetry grid \n PLEASE RUN amplification_coefficients.ipynb before running this script")
refined = True
## Surface Element
msin = np.array([np.sin(np.pi/2 - np.radians(zlat))]).T
ones = np.ones((1, len(zlon)))
res_mod = radians(abs(zlat[1] - zlat[0]))
dA = radius**2*res_mod**2*np.dot(msin,ones)
## Loop over dates
YEAR = date_vec[0]
MONTH = date_vec[1]
DAY = date_vec[2]
HOUR = date_vec[3]
temporal_variation = []
time = []
for iyear in np.array([YEAR]):
if isinstance(MONTH, int):
MONTH = np.array([MONTH])
elif not len(MONTH):
MONTH = np.arange(1, 13)
else:
MONTH = np.array(MONTH)
for imonth in MONTH:
TOTAL_month = np.zeros(dpt1.shape) # Initiate monthly source of Rayleigh wave matrix
daymax = monthrange(iyear,imonth)[1]
filename_p2l = '%s/%s_%d%02d_p2l.nc'%(ww3_local_path, prefix, iyear, imonth)
print("File WW3 ", filename_p2l)
try:
day = np.array(DAY)
if day[0] > day[-1]:
index = np.squeeze(np.argwhere(day==daymax))
if imonth == MONTH[0]:
day = day[:index+1]
elif imonth == MONTH[-1]:
index = np.squeeze(np.argwhere(day==monthrange(iyear, imonth-1)[1]))
day = day[index+1:]
else:
day = np.arange(1,daymax+1)
except:
try:
day = int(np.squeeze(day))
except:
day= np.arange(1,(monthrange(iyear,imonth)[1])+1)
for iday in day:
if isinstance(HOUR, int):
HOUR = np.array([HOUR])
elif not len(HOUR):
HOUR = np.arange(0,24,3)
else:
HOUR = np.array(HOUR)
for ih in HOUR:
## Open F_p3D
(lati, longi, freq_ocean, p2l, unit1) = read_p2l(filename_p2l, [iyear, imonth, iday, ih], [lon_min, lon_max], [lat_min, lat_max])
nf = len(freq_ocean) # number of frequencies
xfr = np.exp(np.log(freq_ocean[-1]/freq_ocean[0])/(nf-1)) # determines the xfr geometric progression factor
df = freq_ocean*0.5*(xfr-1/xfr) # frequency interval in wave model times 2
freq_seismic = 2*freq_ocean # ocean to seismic waves freq
## Check units of the model, depends on version
if unit1 == 'log10(Pa2 m2 s+1E-12':
p2l = np.exp(lg10*p2l) - (1e-12-1e-16)
elif unit1 == 'log10(m4s+0.01':
p2l = np.exp(lg10*p2l) - 0.009999
elif unit1 == 'log10(Pa2 m2 s+1E-12)':
p2l = np.exp(lg10*p2l) - (1e-12-1e-16)
## Integral over a frequency band
if f1 < f2:
index_freq = np.logical_and(f1 <= freq_seismic, freq_seismic <= f2)
## Single frequency
elif f1 == f2:
index_freq = np.squeeze(np.argmin(abs(freq-f1)))
print('unique frequency ', f1)
## Exception in parametrization of frequencies
else:
print('two frequencies with f2 < f1 were given')
df = df[index_freq]
freq_seismic = freq_seismic[index_freq]
n_freq = len(df)
Fp = p2l.sel(frequency = freq_ocean[index_freq], latitude = slice(lat_min, lat_max), longitude = slice(lon_min, lon_max))
Fp = Fp.where(np.isfinite(Fp))
Fp = Fp.assign_coords({"freq": freq_seismic})
Fp = Fp.swap_dims({"frequency": "freq"})
Fp = Fp.drop_vars('frequency')
Fp = Fp.rename({"freq": "frequency"})
res_p2l = abs(Fp.latitude[1] - Fp.latitude[0])
if res_bathy != res_p2l:
# interpolate Fp
Fp = Fp.interp(longitude=zlon, latitude=zlat, method='linear')
## Amplification coefficient
amplification_coeff = amplification_coeff.sel(frequency = freq_seismic, method='nearest')
amplification_coeff = amplification_coeff.sel(latitude = slice(lat_min, lat_max), longitude = slice(lon_min, lon_max))
amplification_coeff = amplification_coeff.reindex_like(Fp, method='nearest', tolerance=0.01)
F_f = Fp*amplification_coeff**2
## Compute Equivalent Vertical Force
F = F_f
# Integrate over the frequency band
for ifq, fq in enumerate(freq_seismic.values):
df_fq = df[ifq]
F_fi = F_f[ifq, :, :]
F_fi *= dA
F[ifq, :, :] = F_fi*df_fq
# Force
F = 2*np.pi*np.sqrt(F.sum(axis = 0))
if temporal_resol_hourly:
time.append(datetime(iyear, imonth, iday, ih))
## Concatenate temporal variation of sources + spatial averaging
temporal_variation.append(np.nanmean(F))
else:
F_f1_concat.append(F)
if temporal_resol_daily:
time.append(datetime(iyear, imonth, iday))
## Concatenate temporal variation of daily sources averaging + spatial averaging
temporal_variation.append(np.nanmean(F_f1_concat))
F_f1_concat = []
if temporal_resol_monthly:
# need to define the day! or chage datetime
time.append(datetime(iyear, imonth, 15))
## Concatenate temporal variation of monthly sources averaging + spatial averaging
temporal_variation.append(np.nanmean(F_f1_concat))
F_f1_concat = []
return time, np.asarray(temporal_variation)
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