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metrics.py
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metrics.py
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import datetime
import einops
import numpy as np
import xarray as xr
import matplotlib
matplotlib.use('Agg') # Must be before importing matplotlib.pyplot or pylab!
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import pandas as pd
import shapely
from shapely import wkt
#import geopandas as gpd
from cartopy import crs as ccrs
import cartopy.feature as cfeature
from cartopy.io import shapereader
from cartopy.mpl.gridliner import LONGITUDE_FORMATTER, LATITUDE_FORMATTER
import cv2
import matplotlib.animation as animation
import xrft
from spectral import *
def plot_snr(gt,oi,pred,resfile):
'''
gt: 3d numpy array (Ground Truth)
oi: 3d numpy array (OI)
pred: 3d numpy array (4DVarNet-based predictions)
resfile: string
'''
dt = pred.shape[1]
# Compute Signal-to-Noise ratio
f, pf = avg_err_rapsd2dv1(oi,gt,4.,True)
wf = 1./f
snr_oi = [wf, pf]
f, pf = avg_err_rapsd2dv1(pred,gt,4.,True)
wf = 1./f
snr_pred = [wf, pf]
# plot Signal-to-Noise ratio
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(snr_oi[0],snr_oi[1],color='red',linewidth=2,label='OI')
ax.plot(snr_pred[0],snr_pred[1],color='blue',linewidth=2,label='4DVarNet')
ax.set_xlabel("Wavenumber", fontweight='bold')
ax.set_ylabel("Signal-to-noise ratio", fontweight='bold')
ax.set_xscale('log') ; ax.set_yscale('log')
plt.legend(loc='best',prop=dict(size='small'),frameon=False)
plt.xticks([50, 100, 200, 500, 1000], ["50km", "100km", "200km", "500km", "1000km"])
ax.invert_xaxis()
plt.grid(which='both', linestyle='--')
plt.savefig(resfile) # save the figure
fig = plt.gcf()
plt.close() # close the figure
return fig
def plot_nrmse(gt, oi, pred, resfile, time):
'''
gt: 3d numpy array (Ground Truth)
oi: 3d numpy array (OI)
pred: 3d numpy array (4DVarNet-based predictions)
resfile: string
time: 1d array-like of time corresponding to the experiment
'''
# Compute daily nRMSE scores
nrmse_oi = []
nrmse_pred = []
for i in range(len(oi)):
nrmse_oi.append(nrmse(gt[i], oi[i]))
nrmse_pred.append(nrmse(gt[i], pred[i]))
# plot nRMSE time series
plt.plot(range(len(oi)),nrmse_oi,color='red',
linewidth=2,label='OI')
plt.plot(range(len(pred)),nrmse_pred,color='blue',
linewidth=2,label='4DVarNet')
# graphical options
plt.ylabel('nRMSE')
plt.xlabel('Time (days)')
plt.xticks(range(0,len(gt)),time,rotation=45, ha='right')
plt.margins(x=0)
plt.grid(True,alpha=.3)
plt.legend(loc='upper left',prop=dict(size='small'),frameon=False,bbox_to_anchor=(0,1.02,1,0.2),ncol=2,mode="expand")
plt.savefig(resfile,bbox_inches="tight") # save the figure
fig = plt.gcf()
plt.close() # close the figure
return fig
def plot_mse(gt, oi, pred, resfile, time):
'''
gt: 3d numpy array (Ground Truth)
oi: 3d numpy array (OI)
pred: 3d numpy array (4DVarNet-based predictions)
resfile: string
time: 1d array-like of time corresponding to the experiment
'''
# Compute daily nRMSE scores
mse_oi = []
mse_pred = []
grad_mse_oi = []
grad_mse_pred = []
for i in range(len(oi)):
mse_oi.append(mse(gt[i], oi[i]))
mse_pred.append(mse(gt[i], pred[i]))
grad_mse_oi.append(mse(gradient(gt[i],2), gradient(oi[i],2)))
grad_mse_pred.append(mse(gradient(gt[i],2), gradient(pred[i],2)))
print("mse_oi = ", np.nanmean(mse_oi))
print("mse_pred = ", np.nanmean(mse_pred))
print("grad_mse_oi = ", np.nanmean(grad_mse_oi))
print("grad_mse_pred = ", np.nanmean(grad_mse_pred))
print("percentage_ssh = ", np.abs(np.nanmean(mse_oi)-np.nanmean(mse_pred))/np.nanmean(mse_oi))
print("percentage_ssh_grad = ", np.abs(np.nanmean(grad_mse_oi)-np.nanmean(grad_mse_pred))/np.nanmean(grad_mse_oi))
# plot nRMSE time series
plt.plot(range(len(oi)),mse_oi,color='red',
linewidth=2,label='OI')
plt.plot(range(len(pred)),mse_pred,color='blue',
linewidth=2,label='4DVarNet')
# graphical options
plt.ylabel('MSE')
plt.xlabel('Time (days)')
plt.xticks(range(0,len(gt)),time,rotation=45, ha='right')
plt.margins(x=0)
plt.grid(True,alpha=.3)
plt.legend(loc='upper left',prop=dict(size='small'),frameon=False,bbox_to_anchor=(0,1.02,1,0.2),ncol=2,mode="expand")
plt.savefig(resfile,bbox_inches="tight") # save the figure
fig = plt.gcf()
plt.close() # close the figure
return fig
def plot(ax,lon,lat,data,title,extent=[-65,-55,30,40],cmap="coolwarm",gridded=True,vmin=-2,vmax=2,colorbar=True,orientation="horizontal"):
ax.set_extent(list(extent))
if gridded:
im=ax.pcolormesh(lon, lat, data, cmap=cmap,\
vmin=vmin, vmax=vmax,edgecolors='face', alpha=1, \
transform= ccrs.PlateCarree(central_longitude=0.0))
else:
im=ax.scatter(lon, lat, c=data, cmap=cmap, s=1,\
vmin=vmin, vmax=vmax,edgecolors='face', alpha=1, \
transform= ccrs.PlateCarree(central_longitude=0.0))
im.set_clim(vmin,vmax)
if colorbar==True:
clb = plt.colorbar(im, orientation=orientation, extend='both', pad=0.1, ax=ax)
ax.set_title(title, pad=40, fontsize = 15)
gl = ax.gridlines(alpha=0.5,draw_labels=True)
gl.xformatter = LONGITUDE_FORMATTER
gl.yformatter = LATITUDE_FORMATTER
gl.xlabels_bottom = False
gl.ylabels_right = False
gl.xlabel_style = {'fontsize': 10, 'rotation' : 45}
gl.ylabel_style = {'fontsize': 10}
# ax[i][j].coastlines(resolution='50m')
def gradient(img, order):
""" calcuate x, y gradient and magnitude """
sobelx = cv2.Sobel(img,cv2.CV_64F,1,0,ksize=3)
sobelx = sobelx/8.0
sobely = cv2.Sobel(img,cv2.CV_64F,0,1,ksize=3)
sobely = sobely/8.0
sobel_norm = np.sqrt(sobelx*sobelx+sobely*sobely)
if (order==0):
return sobelx
elif (order==1):
return sobely
else:
return sobel_norm
def plot_maps(gt,obs,oi,pred,lon,lat,resfile,grad=False):
if grad==False:
vmax = np.nanmax(np.abs(oi))
vmin = -1.*vmax
else:
vmax = np.nanmax(np.abs(gradient(oi,2)))
vmin = 0
extent = [np.min(lon),np.max(lon),np.min(lat),np.max(lat)]
id_nan = np.where(np.isnan(gt))
obs[id_nan] = np.nan
fig = plt.figure(figsize=(15,15))
ax1 = fig.add_subplot(221, projection=ccrs.PlateCarree(central_longitude=0.0))
ax2 = fig.add_subplot(222, projection=ccrs.PlateCarree(central_longitude=0.0))
ax3 = fig.add_subplot(223, projection=ccrs.PlateCarree(central_longitude=0.0))
ax4 = fig.add_subplot(224, projection=ccrs.PlateCarree(central_longitude=0.0))
if grad==False:
plot(ax1,lon,lat,gt,'GT',extent=extent,cmap="coolwarm",vmin=vmin,vmax=vmax)
plot(ax2,lon,lat,obs,'OBS',extent=extent,cmap="coolwarm",vmin=vmin,vmax=vmax)
plot(ax3,lon,lat,oi,'OI',extent=extent,cmap="coolwarm",vmin=vmin,vmax=vmax)
plot(ax4,lon,lat,pred,'4DVarNet',extent=extent,cmap="coolwarm",vmin=vmin,vmax=vmax)
else:
plot(ax1,lon,lat,gradient(gt,2),r"$\nabla_{GT}$",extent=extent,cmap="viridis",vmin=vmin,vmax=vmax)
plot(ax2,lon,lat,gradient(obs,2),r"$\nabla_{OBS}$",extent=extent,cmap="viridis",vmin=vmin,vmax=vmax)
plot(ax3,lon,lat,gradient(oi,2),r"$\nabla_{OI}$",extent=extent,cmap="viridis",vmin=vmin,vmax=vmax)
plot(ax4,lon,lat,gradient(pred,2),r"$\nabla_{4DVarNet}$",extent=extent,cmap="viridis",vmin=vmin,vmax=vmax)
plt.savefig(resfile) # save the figure
fig = plt.gcf()
plt.close() # close the figure
return fig
def animate_maps(gt,obs,oi,pred,lon,lat,resfile,orthographic=True,dw=4,grad=False):
if dw>1:
# decrease the resolution
Nlon = len(lon)
Nlat = len(lat)
ilon = np.arange(0,Nlon,4)
ilat = np.arange(0,Nlat,4)
gt = (gt[:,ilat,:])[:,:,ilon]
obs = (obs[:,ilat,:])[:,:,ilon]
oi = (oi[:,ilat,:])[:,:,ilon]
pred = (pred[:,ilat,:])[:,:,ilon]
lon = lon[ilon]
lat = lat[ilat]
def animate(i):
print(i)
id_nan = np.where(np.isnan(gt[i]))
obs[i][id_nan] = np.nan
#oi[i][id_nan] = np.nan
#pred[i][id_nan] = np.nan
if grad==False:
plot(ax1,lon,lat,gt[i],'GT',extent=extent,cmap="coolwarm",vmin=vmin,vmax=vmax)
plot(ax2,lon,lat,obs[i],'OBS',extent=extent,cmap="coolwarm",vmin=vmin,vmax=vmax)
plot(ax3,lon,lat,oi[i],'OI',extent=extent,cmap="coolwarm",vmin=vmin,vmax=vmax)
plot(ax4,lon,lat,pred[i],'4DVarNet',extent=extent,cmap="coolwarm",vmin=vmin,vmax=vmax)
else:
plot(ax1,lon,lat,gradient(gt[i],2),r"$\nabla_{GT}$",extent=extent,cmap="viridis",vmin=vmin,vmax=vmax)
plot(ax2,lon,lat,gradient(obs[i],2),r"$\nabla_{OBS}$",extent=extent,cmap="viridis",vmin=vmin,vmax=vmax)
plot(ax3,lon,lat,gradient(oi[i],2),r"$\nabla_{OI}$",extent=extent,cmap="viridis",vmin=vmin,vmax=vmax)
plot(ax4,lon,lat,gradient(pred[i],2),r"$\nabla_{4DVarNet}$",extent=extent,cmap="viridis",vmin=vmin,vmax=vmax)
if grad==False:
vmax = np.nanmax(np.abs(oi))
vmin = -1.*vmax
else:
vmax = np.nanmax(np.abs(gradient(oi,2)))
vmin = 0
extent = [np.min(lon),np.max(lon),np.min(lat),np.max(lat)]
fig = plt.figure(figsize=(15,15))
if orthographic==False:
ax1 = fig.add_subplot(221, projection=ccrs.PlateCarree(central_longitude=0.0))
ax2 = fig.add_subplot(222, projection=ccrs.PlateCarree(central_longitude=0.0))
ax3 = fig.add_subplot(223, projection=ccrs.PlateCarree(central_longitude=0.0))
ax4 = fig.add_subplot(224, projection=ccrs.PlateCarree(central_longitude=0.0))
else:
ax1 = fig.add_subplot(221, projection=ccrs.Orthographic(-30, 45))
ax2 = fig.add_subplot(222, projection=ccrs.Orthographic(-30, 45))
ax3 = fig.add_subplot(223, projection=ccrs.Orthographic(-30, 45))
ax4 = fig.add_subplot(224, projection=ccrs.Orthographic(-30, 45))
plt.subplots_adjust(hspace=0.5)
ani = animation.FuncAnimation(fig, animate, frames=len(gt), interval=200, repeat=False)
writergif = animation.PillowWriter(fps=3)
writer = animation.FFMpegWriter(fps=3)
ani.save(resfile, writer = writer)
plt.close()
def plot_ensemble(pred,lon,lat,resfile):
vmax = np.nanmax(np.abs(pred))
vmin = -1.*vmax
grad_vmax = np.nanmax(np.abs(gradient(pred,2)))
grad_vmin = 0
extent = [np.min(lon),np.max(lon),np.min(lat),np.max(lat)]
n_members = pred.shape[-1]
fig, ax = plt.subplots(2,n_members,figsize=(5*n_members,15),squeeze=False,
subplot_kw=dict(projection=ccrs.PlateCarree(central_longitude=0.0)))
for i in range(n_members):
plot(ax,0,i,lon,lat,pred[:,:,i],'M'+str(i),extent=extent,cmap="coolwarm",vmin=vmin,vmax=vmax)
plot(ax,1,i,lon,lat,gradient(pred[:,:,i],2),r"$\nabla_{M"+str(i)+"}$",extent=extent,cmap="viridis",vmin=grad_vmin,vmax=grad_vmax)
plt.savefig(resfile) # save the figure
plt.close() # close the figure
def save_netcdf(saved_path1, pred, lon, lat, time,
time_units='days since 2012-10-01 00:00:00'):
'''
saved_path1: string
pred: 3d numpy array (4DVarNet-based predictions)
lon: 1d numpy array
lat: 1d numpy array
time: 1d array-like of time corresponding to the experiment
'''
mesh_lat, mesh_lon = np.meshgrid(lat, lon)
mesh_lat = mesh_lat.T
mesh_lon = mesh_lon.T
dt = pred.shape[1]
xrdata = xr.Dataset( \
data_vars={'longitude': (('lat', 'lon'), mesh_lon), \
'latitude': (('lat', 'lon'), mesh_lat), \
'Time': (('time'), time), \
'ssh': (('time', 'lat', 'lon'), pred[:, int(dt / 2), :, :])}, \
coords={'lon': lon, 'lat': lat, 'time': np.arange(len(pred))})
xrdata.time.attrs['units'] = time_units
xrdata.to_netcdf(path=saved_path1, mode='w')
def nrmse(ref, pred):
'''
ref: Ground Truth fields
pred: interpolated fields
'''
return np.sqrt(np.nanmean(((ref - np.nanmean(ref)) - (pred - np.nanmean(pred))) ** 2)) / np.nanstd(ref)
def nrmse_scores(gt, oi, pred, resfile):
'''
gt: 3d numpy array (Ground Truth)
oi: 3d numpy array (OI)
pred: 3d numpy array (4DVarNet-based predictions)
resfile: string
'''
# Compute daily nRMSE scores
nrmse_oi = []
nrmse_pred = []
for i in range(len(oi)):
nrmse_oi.append(nrmse(gt[i], oi[i]))
nrmse_pred.append(nrmse(gt[i], pred[i]))
tab_scores = np.zeros((2, 3))
tab_scores[0, 0] = np.nanmean(nrmse_oi)
tab_scores[0, 1] = np.percentile(nrmse_oi, 5)
tab_scores[0, 2] = np.percentile(nrmse_oi, 95)
tab_scores[1, 0] = np.nanmean(nrmse_pred)
tab_scores[1, 1] = np.percentile(nrmse_pred, 5)
tab_scores[1, 2] = np.percentile(nrmse_pred, 95)
np.savetxt(fname=resfile, X=tab_scores, fmt='%2.2f')
return tab_scores
def mse(ref, pred):
'''
ref: Ground Truth fields
pred: interpolated fields
'''
return np.nanmean(((ref-np.nanmean(ref))-(pred-np.nanmean(pred)))**2)
def mse_scores(gt, oi, pred, resfile):
'''
gt: 3d numpy array (Ground Truth)
oi: 3d numpy array (OI)
pred: 3d numpy array (4DVarNet-based predictions)
resfile: string
'''
# Compute daily nRMSE scores
mse_oi = []
mse_pred = []
for i in range(len(oi)):
mse_oi.append(mse(gt[i], oi[i]))
mse_pred.append(mse(gt[i], pred[i]))
tab_scores = np.zeros((2, 3))
tab_scores[0, 0] = np.nanmean(mse_oi)
tab_scores[0, 1] = np.percentile(mse_oi, 5)
tab_scores[0, 2] = np.percentile(mse_oi, 95)
tab_scores[1, 0] = np.nanmean(mse_pred)
tab_scores[1, 1] = np.percentile(mse_pred, 5)
tab_scores[1, 2] = np.percentile(mse_pred, 95)
np.savetxt(fname=resfile, X=tab_scores, fmt='%2.2f')
def compute_metrics(x_test, x_rec):
# MSE
mse = np.mean((x_test - x_rec) ** 2)
# MSE for gradient
gx_rec = np.gradient(x_rec, axis=[1, 2])
gx_rec = np.sqrt(gx_rec[0] ** 2 + gx_rec[1] ** 2)
gx_test = np.gradient(x_test, axis=[1, 2])
gx_test = np.sqrt(gx_test[0] ** 2 + gx_test[1] ** 2)
gmse = np.mean((gx_test - gx_rec) ** 2)
ng = np.mean((gx_rec) ** 2)
return {'mse': mse, 'mseGrad': gmse, 'meanGrad': ng}
def get_psd_score(x_t, x, ref, with_fig=False):
def psd_score(da: xr.DataArray) -> xr.DataArray:
err = x_t - da
psd_x_t = (
x_t.copy()
.pipe(
lambda _da: xrft.isotropic_power_spectrum(_da, dim=['lat', 'lon'], window='hann', detrend='linear'))
.mean(['time'])
).compute()
psd_err = (
err.copy()
.pipe(
lambda _da: xrft.isotropic_power_spectrum(_da, dim=['lat', 'lon'], window='hann', detrend='linear'))
.mean(['time'])
).compute()
psd_score = 1 - psd_err / psd_x_t
return psd_score
ref_score = psd_score(ref)
model_score = psd_score(x)
ref_score = ref_score.where(model_score > 0, drop=True).compute()
model_score = model_score.where(model_score > 0, drop=True).compute()
psd_plot_data: xr.DataArray = xr.DataArray(
einops.rearrange([model_score.data, ref_score.data], 'var wl -> var wl'),
name='PSD score',
dims=('var', 'wl'),
coords={
'wl': ('wl', 20 * 5 * 1 / model_score.freq_r, {'long_name': 'Wavelength', 'units': 'km'}),
'var': ('var', ['model', 'OI'], {}),
},
)
spatial_resolution_model = (
xr.DataArray(
psd_plot_data.wl,
dims=['psd'],
coords={'psd': psd_plot_data.sel(var='model').data}
).interp(psd=0.5)
)
spatial_resolution_ref = (
xr.DataArray(
psd_plot_data.wl,
dims=['psd'],
coords={'psd': psd_plot_data.sel(var='OI').data}
).interp(psd=0.5)
)
if not with_fig:
return spatial_resolution_model, spatial_resolution_ref
fig, ax = plt.subplots()
psd_plot_data.plot.line(x='wl', ax=ax)
# Plot vertical line there
for i, (sr, var) in enumerate([(spatial_resolution_ref, 'OI'), (spatial_resolution_model, 'model')]):
plt.axvline(sr, ymin=0, color='0.5', ls=':')
plt.annotate(f"resolution {var}: {float(sr):.2f} km", (sr * 1.1, 0.1 * i))
plt.axhline(0.5, xmin=0, color='k', ls='--')
plt.ylim([0, 1])
plt.close()
return fig, spatial_resolution_model, spatial_resolution_ref