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da_utils.py
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da_utils.py
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#==============================================================================
# Different function for use in the Holocene DA project.
# author: Michael P. Erb
# date : 3/16/2022
#==============================================================================
import numpy as np
from scipy.linalg import sqrtm
import da_utils_lmr
import xarray as xr
import xesmf as xe
# A function to do the data assimilation. It is based on '2_darecon.jl',
# originally written by Nathan Steiger.
#Xb,HXb,R,y = Xb,np.transpose(model_estimates_selected),R_diagonal,proxy_values_selected
def damup(Xb,HXb,R,y):
#
# Data assimilation matrix update step, assimilating all observations
# for a given time step at once. Variables with their dimensions are
# indicated by [dim1 dim2] given below. This set of update equations
# follow those from Whitaker and Hamill 2002: Eq. 2, 4, 10, & Sec 3.
# ARGUMENTS:
# Xb = background (prior) [n_state, n_ens]
# HXb = model estimate of observations H(Xb) [n_proxies_valid, n_ens]
# y = observation (with implied noise) [n_proxies_valid]
# R = diagonal observation error variance matrix [n_proxies_valid, n_proxies_valid]
# infl = inflation factor [scalar] **Note: modify code to include**
# RETURNS:
# Xa = analysis (posterior) [n_state, n_ens]
# Xam = analysis mean [n_state]
#
# Number of ensemble members
nens = Xb.shape[1]
#
# Decompose Xb and HXb into mean and perturbations (for Eqs. 4 & Sec 3)
Xbm = np.mean(Xb,axis=1)
Xbp = Xb - Xbm[:,None]
#
HXbm = np.mean(HXb,axis=1)
HXbp = HXb - HXbm[:,None]
#
# Kalman gain for mean and matrix covariances (Eq. 2)
PbHT = np.dot(Xbp, np.transpose(HXbp))/(nens-1)
HPbHTR = np.dot(HXbp,np.transpose(HXbp))/(nens-1)+R
K = np.dot(PbHT,np.linalg.inv(HPbHTR))
#
# Kalman gain for the perturbations (Eq. 10)
sHPbHTR = sqrtm(HPbHTR)
sR = sqrtm(R)
Ktn = np.dot(PbHT,np.transpose(np.linalg.inv(sHPbHTR)))
Ktd = np.linalg.inv(sHPbHTR+sR)
Kt = np.dot(Ktn,Ktd)
#
# Update mean and perturbations (Eq. 4 & Sec 3)
Xam = Xbm + np.dot(K,(y-HXbm))
Xap = Xbp - np.dot(Kt,HXbp)
#
# Reconstitute the full ensemble state vector
Xa = Xap + Xam[:,None]
#
# Output both the full ensemble and the ensemble mean
return Xa,Xam,K
# Read in a string and a lat and return a set of months
def interpret_seasonality(seasonality_txt,lat,unknown_option):
#
# Terms which are not dependent on latitude
if (str(seasonality_txt).lower() == 'annual'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'ann'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'annua'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'tann; 2'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'year'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == '1 2 3 4 5 6 7 8 9 10 11 12'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'subannual'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'nan'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'not specified'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'n/a'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'n/a (subannually resolved)'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'not indicated'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'aug+ann'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == '2 2 3 4 5 6 7 8 9 10 11 12'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'annual (but 80% of precipitation from nov to may)'): seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == 'jan'): seasonality = '1'
elif (str(seasonality_txt).lower() == 'may'): seasonality = '5'
elif (str(seasonality_txt).lower() == 'july'): seasonality = '7'
elif (str(seasonality_txt).lower() == 'july air'): seasonality = '7'
elif (str(seasonality_txt).lower() == 'jul'): seasonality = '7'
elif (str(seasonality_txt).lower() == 'tjul'): seasonality = '7'
elif (str(seasonality_txt).lower() == 'mean july air temperature estimate'): seasonality = '7'
elif (str(seasonality_txt).lower() == '7'): seasonality = '7'
elif (str(seasonality_txt).lower() == '8'): seasonality = '8'
elif (str(seasonality_txt).lower() == 'jul+jan'): seasonality = '1 7'
elif (str(seasonality_txt).lower() == 'warmest+coldest'): seasonality = '1 7'
elif (str(seasonality_txt).lower() == 'coldest+warmest'): seasonality = '1 7'
elif (str(seasonality_txt).lower() == 'warmest + coldest'): seasonality = '1 7'
elif (str(seasonality_txt).lower() == 'warmest + coldest months'): seasonality = '1 7'
elif (str(seasonality_txt).lower() == 'warmest + coldest month'): seasonality = '1 7'
elif (str(seasonality_txt).lower() == 'coldest + warmest month'): seasonality = '1 7'
elif (str(seasonality_txt).lower() == 'jja'): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'jjas'): seasonality = '6 7 8 9'
elif (str(seasonality_txt).lower() == '6 7 8 9 10'): seasonality = '6 7 8 9 10'
elif (str(seasonality_txt).lower() == '6 7 8 9'): seasonality = '6 7 8 9'
elif (str(seasonality_txt).lower() == '6 7 8'): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == '5'): seasonality = '5'
elif (str(seasonality_txt).lower() == 'aug'): seasonality = '8'
elif (str(seasonality_txt).lower() == 'summer (may-oct)'): seasonality = '5 6 7 8 9 10'
elif (str(seasonality_txt).lower() == 'summer (6,7,8)'): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'winter+summer'): seasonality = '-12 1 2 6 7 8'
elif (str(seasonality_txt).lower() == 'winter + summer'): seasonality = '-12 1 2 6 7 8'
elif (str(seasonality_txt).lower() == 'winter; summer'): seasonality = '-12 1 2 6 7 8'
elif (str(seasonality_txt).lower() == 'summer + winter'): seasonality = '-12 1 2 6 7 8'
elif (str(seasonality_txt).lower() == 'summer and winter'): seasonality = '-12 1 2 6 7 8'
elif (str(seasonality_txt).lower() == 'dec-feb'): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == '6 7 2008'): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == '7 8 2009'): seasonality = '7 8 9'
elif (str(seasonality_txt).lower() == '12 1 2002'): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == '1'): seasonality = '1'
elif (str(seasonality_txt).lower() == '1 (summer)'): seasonality = '1'
elif (str(seasonality_txt).lower() == '1; summer'): seasonality = '1'
elif (str(seasonality_txt).lower() == '2'): seasonality = '2'
elif (str(seasonality_txt).lower() == '1; 7'): seasonality = '1 7'
elif (str(seasonality_txt).lower() == '1 7'): seasonality = '1 7'
elif (str(seasonality_txt).lower() == '1,7'): seasonality = '1 7'
elif (str(seasonality_txt).lower() == '1,8'): seasonality = '1 8'
elif (str(seasonality_txt).lower() == '1,9'): seasonality = '1 9'
elif (str(seasonality_txt).lower() == '1,10'): seasonality = '1 10'
elif (str(seasonality_txt).lower() == '1,11'): seasonality = '1 11'
elif (str(seasonality_txt).lower() == '4 5 6 7 8 9 10 11 12'): seasonality = '4 5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == '4 5 6 7 8 9 10 12'): seasonality = '4 5 6 7 8 9 10 12'
elif (str(seasonality_txt).lower() == '5 6 7 8 9 10 11 12'): seasonality = '5 6 7 8 9 10 11 12'
elif (str(seasonality_txt).lower() == '12 1 2 3 4 5'): seasonality = '-12 1 2 3 4 5'
elif (str(seasonality_txt).lower() == '11 12 1 2 3 4 5'): seasonality = '-11 -12 1 2 3 4 5'
elif (str(seasonality_txt).lower() == '-11 -12 1 2 3 4 5'): seasonality = '-11 -12 1 2 3 4 5'
elif (str(seasonality_txt).lower() == '12 1 2; 6 7 8'): seasonality = '-12 1 2 6 7 8'
elif (str(seasonality_txt).lower() == '1 2 3'): seasonality = '1 2 3'
elif (str(seasonality_txt).lower() == '6 7'): seasonality = '6 7'
elif (str(seasonality_txt).lower() == '7 8 9'): seasonality = '7 8 9'
elif (str(seasonality_txt).lower() == '8 9 10'): seasonality = '8 9 10'
elif (str(seasonality_txt).lower() == '12 1 2; 6 7 8'): seasonality = '-12 1 2 6 7 8'
elif (str(seasonality_txt).lower() == '12 1 2'): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == '6 7 8 9 10 11'): seasonality = '6 7 8 9 10 11'
elif (str(seasonality_txt).lower() == '9 10 11 12 1 2 3 4 5 6 7'): seasonality = '-9 -10 -11 -12 1 2 3 4 5 6 7'
elif (str(seasonality_txt).lower() == '-9 -10 -11 -12 1 2 3 4 5 6 7'): seasonality = '-9 -10 -11 -12 1 2 3 4 5 6 7'
elif (str(seasonality_txt).lower() == '5 6 7 8 9 10'): seasonality = '5 6 7 8 9 10'
elif (str(seasonality_txt).lower() == '5 6 7 8 9 10 11'): seasonality = '5 6 7 8 9 10 11'
elif (str(seasonality_txt).lower() == '6 7 8 9 10 11'): seasonality = '6 7 8 9 10 11'
elif (str(seasonality_txt).lower() == '-12 1 2 6 7 8'): seasonality = '-12 1 2 6 7 8'
elif (str(seasonality_txt).lower() == '-12 1 2'): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == '-12 1 2 3 4 5'): seasonality = '-12 1 2 3 4 5'
elif (str(seasonality_txt).lower() == '1 6 7 8'): seasonality = '1 6 7 8'
elif (str(seasonality_txt).lower() == '-12 1 2 7'): seasonality = '-12 1 2 7'
elif (str(seasonality_txt).lower() == '12,1,2'): seasonality = '12 1 2'
elif (str(seasonality_txt).lower() == '1,2,3'): seasonality = '1 2 3'
elif (str(seasonality_txt).lower() == '6,7'): seasonality = '6 7'
elif (str(seasonality_txt).lower() == '6,7,8'): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == '7,8,9'): seasonality = '7 8 9'
elif (str(seasonality_txt).lower() == '8,9,10'): seasonality = '8 9 10'
elif (str(seasonality_txt).lower() == '((( 6 7 2008 ))) 6 7 8 /// 6 7 8'): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == '((( 7 8 2009 ))) 7 8 9 /// 7 8 9'): seasonality = '7 8 9'
elif (str(seasonality_txt).lower() == '((( 12 1 2002 ))) 12 1 2 /// 12 1 2'): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == '((( 1 2 2003 ))) 1 2 3 /// 1 2 3'): seasonality = '1 2 3'
#
# Terms which are dependent on latitude
elif (str(seasonality_txt).lower() == 'summer') and (lat >= 0): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'summer') and (lat < 0): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == 'mean summer') and (lat >= 0): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'mean summer') and (lat < 0): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == 'warmest quarter yr') and (lat >= 0): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'warmest quarter yr') and (lat < 0): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == 'growing') and (lat >= 0): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'growing') and (lat < 0): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == 'growing season') and (lat >= 0): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'growing season') and (lat < 0): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == 'warm season') and (lat >= 0): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'warm season') and (lat < 0): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == 'winter') and (lat >= 0): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == 'winter') and (lat < 0): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'cold season') and (lat >= 0): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == 'cold season') and (lat < 0): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'autumn') and (lat >= 0): seasonality = '9 10 11'
elif (str(seasonality_txt).lower() == 'autumn') and (lat < 0): seasonality = '3 4 5'
elif (str(seasonality_txt).lower() == 'warmest month + winter') and (lat >= 0): seasonality = '-12 1 2 7'
elif (str(seasonality_txt).lower() == 'warmest month + winter') and (lat < 0): seasonality = '1 6 7 8'
elif (str(seasonality_txt).lower() == 'coldest month + summer') and (lat >= 0): seasonality = '1 6 7 8'
elif (str(seasonality_txt).lower() == 'coldest month + summer') and (lat < 0): seasonality = '-12 1 2 7'
elif (str(seasonality_txt).lower() == 'mtwa') and (lat >= 0): seasonality = '7' # MTWA: Mean Temperature of the Warmest Month
elif (str(seasonality_txt).lower() == 'mtwa') and (lat < 0): seasonality = '1' # MTWA: Mean Temperature of the Warmest Month
elif (str(seasonality_txt).lower() == 'warmest') and (lat >= 0): seasonality = '7'
elif (str(seasonality_txt).lower() == 'warmest') and (lat < 0): seasonality = '1'
elif (str(seasonality_txt).lower() == 'warmest month') and (lat >= 0): seasonality = '7'
elif (str(seasonality_txt).lower() == 'warmest month') and (lat < 0): seasonality = '1'
elif (str(seasonality_txt).lower() == 'coldest') and (lat >= 0): seasonality = '1'
elif (str(seasonality_txt).lower() == 'coldest') and (lat < 0): seasonality = '7'
elif (str(seasonality_txt).lower() == 'coldest month') and (lat >= 0): seasonality = '1'
elif (str(seasonality_txt).lower() == 'coldest month') and (lat < 0): seasonality = '7'
elif (str(seasonality_txt).lower() == 'early summer') and (lat >= 0): seasonality = '6 7'
elif (str(seasonality_txt).lower() == 'early summer') and (lat < 0): seasonality = '-12 1'
elif (str(seasonality_txt).lower() == 'winter/spring') and (lat >= 0): seasonality = '-12 1 2 3 4 5'
elif (str(seasonality_txt).lower() == 'winter/spring') and (lat < 0): seasonality = '6 7 8 9 10 11'
elif (str(seasonality_txt).lower() == 'summer and early autumn') and (lat >= 0): seasonality = '6 7 8 9 10'
elif (str(seasonality_txt).lower() == 'summer and early autumn') and (lat < 0): seasonality = '-12 1 2 3 4'
elif (str(seasonality_txt).lower() == 'summer + early autumn') and (lat >= 0): seasonality = '6 7 8 9 10'
elif (str(seasonality_txt).lower() == 'summer + early autumn') and (lat < 0): seasonality = '-12 1 2 3 4'
elif (str(seasonality_txt).lower() == 'mean temperature of the warmest quarter (twarm)') and (lat >= 0): seasonality = '6 7 8'
elif (str(seasonality_txt).lower() == 'mean temperature of the warmest quarter (twarm)') and (lat < 0): seasonality = '-12 1 2'
elif (str(seasonality_txt).lower() == 'spring-fall') and (lat >= 0): seasonality = '3 4 5 6 7 8 9 10 11'
elif (str(seasonality_txt).lower() == 'spring-fall') and (lat < 0): seasonality = '-9 -10 -11 -12 1 2 3 4 5'
#
# Unsure if this term is dependent on latitude
elif (str(seasonality_txt).lower() == 'spring/fall') and (lat >= 0): seasonality = '3 4 5 9 10 11'
#
# Try to parse the seasonality as numbers. If that doesn't work, use the default value or return as-is.
else:
text_list = str(seasonality_txt).split(' ')
if all(isinstance(i,int) for i in text_list):
print('ATTENTION! Seasonality text unknown, parsing as numbers. Seasonality: |'+str(seasonality_txt)+'|')
seasonality = np.array([int(i) for i in text_list])
elif unknown_option == 'annual':
print('ATTENTION! Seasonality text unknown, using annual. Seasonality: |'+str(seasonality_txt)+'|')
seasonality = '1 2 3 4 5 6 7 8 9 10 11 12'
else:
print('ATTENTION! Seasonality text unknown, returning as-is. Seasonality: |'+str(seasonality_txt)+'|')
seasonality = seasonality_txt
#
return seasonality
# A function to regrid an age-month-lat-lon array to a standardized grid
def regrid_model(var,lat,lon,age,regrid_method='conservative_normed',make_figures=False):
#
# Put the data in an xarray
var_xarray = xr.Dataset(
{
'variable':(['age','month','lat','lon'],var)
},
coords={
'lat': (['lat'],lat,{'units':'degrees_north'}),
'lon': (['lon'],lon,{'units':'degrees_east'}),
'month': (['month'],np.arange(1,13)),
'age': (['age'],age),
},
)
#
# Set up output variable on a 96 x 64 grid
lat_regrid = np.arange(-88.59375,90,2.8125)
lon_regrid = np.arange(0,360,3.75)
data_format = xr.Dataset(
{
'lat': (['lat'],lat_regrid,{'units':'degrees_north'}),
'lon': (['lon'],lon_regrid,{'units':'degrees_east'}),
}
)
#
# Set up the regridder and do the regridding
regridder = xe.Regridder(var_xarray,data_format,regrid_method,periodic=True)
var_regridded = regridder(var_xarray,keep_attrs=True)
#
"""
# Figures to compare the original data to the regridded data
import matplotlib.pyplot as plt
import cartopy.crs as ccrs
#
ax1 = plt.subplot2grid((2,1),(0,0),projection=ccrs.PlateCarree())
ax2 = plt.subplot2grid((2,1),(1,0),projection=ccrs.PlateCarree())
var_xarray.variable.isel(age=0,month=0).plot.pcolormesh(ax=ax1)
var_regridded.variable.isel(age=0,month=0).plot.pcolormesh(ax=ax2)
ax1.coastlines()
ax2.coastlines()
plt.plot()
#
ax1 = plt.subplot2grid((1,1),(0,0))
var_xarray.variable.isel(age=0,month=0,lon=0).plot(ax=ax1)
var_regridded.variable.isel(age=0,month=0,lon=0).plot(ax=ax1)
plt.plot()
"""
#
# Get the regridded values
var_regrid = var_regridded.variable.values
lat_new = var_regridded.lat.values
lon_new = var_regridded.lon.values
#
return var_regrid,lat_new,lon_new
# This function takes an array and computes the global-mean, after being told the axes of lat and lon.
def global_mean(variable,lats,index_lat,index_lon):
variable_zonal = np.nanmean(variable,axis=index_lon)
if index_lon < index_lat: index_lat = index_lat-1
lat_weights = np.cos(np.radians(lats))
variable_global = np.average(variable_zonal,axis=index_lat,weights=lat_weights)
return variable_global
# This function takes a time-lat-lon variable and computes the mean for a given range of lon and lat.
def spatial_mean(variable,lats,lons,lat_min,lat_max,lon_min,lon_max,index_lat,index_lon,verbose=False):
#
j_selected = np.where((lats >= lat_min) & (lats <= lat_max))[0]
i_selected = np.where((lons >= lon_min) & (lons <= lon_max))[0]
if verbose: print('Computing spatial mean. lats='+str(lats[j_selected[0]])+'-'+str(lats[j_selected[-1]])+', lons='+str(lons[i_selected[0]])+'-'+str(lons[i_selected[-1]])+'. Points are inclusive.')
#
if index_lon == 1: variable_zonal = np.nanmean(variable[:,i_selected], axis=1)
elif index_lon == 2: variable_zonal = np.nanmean(variable[:,:,i_selected], axis=2)
elif index_lon == 3: variable_zonal = np.nanmean(variable[:,:,:,i_selected],axis=3)
else: print('Invalid lon dimension chosen'); return None
#
lat_weights = np.cos(np.radians(lats))
if index_lon < index_lat: index_lat = index_lat-1
if index_lat == 0: variable_mean = np.average(variable_zonal[j_selected], axis=0,weights=lat_weights[j_selected])
elif index_lat == 1: variable_mean = np.average(variable_zonal[:,j_selected], axis=1,weights=lat_weights[j_selected])
elif index_lat == 2: variable_mean = np.average(variable_zonal[:,:,j_selected],axis=2,weights=lat_weights[j_selected])
else: print('Invalid lat dimension chosen'); return None
#
return variable_mean
# A function to compute a localization matrix
def loc_matrix(options,model_data,proxy_data):
#
lat_model = model_data['lat']
lon_model = model_data['lon']
#
# Get dimensions
n_proxies = proxy_data['values_binned'].shape[0]
n_vars = len(options['vars_to_reconstruct'])
n_latlon = len(lat_model) * len(lon_model)
n_state = (n_latlon*n_vars) + n_proxies
#
# Compute the localization values for every proxy
proxy_localization_all = np.ones((n_proxies,n_state))
if options['localization_radius'] != 'None':
#
# Get lat and lon values for the prior
lon_model_2d,lat_model_2d = np.meshgrid(lon_model,lat_model)
lat_prior = np.reshape(lat_model_2d,(n_latlon))
lon_prior = np.reshape(lon_model_2d,(n_latlon))
prior_coords = np.concatenate((lat_prior[:,None],lon_prior[:,None]),axis=1)
#
# Repeat the prior coords for all reconstructed variables
if n_vars > 1: prior_coords = np.tile(prior_coords,(n_vars,1))
#
# Include the proxy coordinates with the model coordinates
proxy_coords_all = np.zeros((n_proxies,2)); proxy_coords_all[:] = np.nan
for i in range(n_proxies):
proxy_coords_all[i,0] = proxy_data['lats'][i]
proxy_coords_all[i,1] = proxy_data['lons'][i]
#
prior_coords = np.append(prior_coords,proxy_coords_all,axis=0)
#
for i in range(n_proxies):
#
# Get proxy metdata
proxy_lat = proxy_data['lats'][i]
proxy_lon = proxy_data['lons'][i]
#
# Compute the localization values and save it to a common variable
#locRad, proxy_lat, proxy_lon, X_coords = options['localization_radius'],proxy_lat,proxy_lon,prior_coords
proxy_localization = da_utils_lmr.cov_localization(options['localization_radius'],proxy_lat,proxy_lon,prior_coords)
proxy_localization_all[i,:] = proxy_localization
#
return proxy_localization_all