PB-MS-AnDA is a Python library for Patch-Based Multi-scale Analog Data Assimilation, applications to ocean remote sensing. We presented a novel data-driven model for the spatio-temporal interpolation of satellite-derived geophysical fields fields, an extension of analog data assimilation framework (https://github.com/ptandeo/AnDA) to high-dimensional satellite-derived geophysical fields.
This Python library is an additional material of the publication "Data-driven Models for the Spatio-Temporal Interpolation of satellite-derived SST Fields", from R. Fablet, P. Huynh Viet, R. Lguensat, accepted to IEEE Transactions on Computational Imaging
The toolbox includes 3 main modules:
- Module Parameters (AnDA_variables.py):
- Class PR: to specify general parameters
- Use multi-scale or single-scale (global-scale) assimilation ?
- Dimension of state vector (or reduced dimensionality in PCA space)
- Size of patch (eg. 20 × 20)
- Size of training dataset, testing dataset (number of images)
- Directories of datasets: sst (sla), observation, OI product (ostia)...
# Example of setting parameter for SST PR_ = PR() PR_.flag_scale = True # True: multi scale AnDA, False: global scale AnDA PR_.n = 50 # dimension state vector PR_.patch_r = 20 # r_size of patch PR_.patch_c = 20 # c_size of patch PR_.training_days = 2558 # num of training images: 2008-2014 PR_.test_days = 364 # num of test images: 2015 PR_.lag = 1 # lag of time series: t -> t+lag PR_.G_PCA = 20 # N_eof for global PCA # Input dataset (format should be NETCDF (.nc)) PR_.path_X = './data/AMSRE/sst.nc' # directory of sst data PR_.path_OI = './data/AMSRE/OI.nc' # directory of OI product (ostia sst, in this case) PR_.path_mask = './AMSRE/metop_mask.nc' # directory of observation mask # Dataset automatically created during execution PR_.path_X_lr = './data/AMSRE/sst_lr.nc' # directory of LR product PR_.path_dX_PCA = './data/AMSRE/dX_pca.nc' # directory of PCA transformation of detail fields PR_.path_index_patches = './data/AMSRE/list_pos.pickle' # directory to store all position of each patch over image PR_.path_neighbor_patches = './data/AMSRE/pair_pos.pickle' # directory to store position of each path's neighbors
- Class VAR: to store all necessary datasets
- Training and testing catalog for detail fields in both original and EOF space
- Observation
- LR product
- Condition dataset used in AF (if exists)
- Indexing set that points out the position of a patch over original image
# Program will automatically load all data into this variable according the parameters described in class **PR** class VAR: X_lr = [] dX_orig = [] Optimal_itrp = [] dX_train = [] # training catalogs for dX in EOF space dX_eof_coeff = [] # EOF base vector dX_eof_mu = [] # EOF mean vector dX_GT_test = [] # dX GT in test year Obs_test = [] # Observation in test year, by applying mask to dX GT dX_cond = [] # condition used for AF gr_vl_train = [] # gradient, velocity used as physical condition gr_vl_test = {} gr_vl_coeff = {} index_patch = [] # store order of every image patch: 0, 1,..total_patchs neighbor_patchs = [] # store order of neighbors of every image patch
- Class General_AF: to specify parameters for Analog Forecasting
- Use condition for analog forecasting ?. If using condition, specify where is the condition
- Use clusterized version ?. If using, specify number of k clusters
- Use global or local analog by specifying form of neighborhood
- Select three forecasting strategies: locally constant, increment, local linear
- Variance of initial error, observation error
- Pre-trained nearest neighbor searchers ( FLANN )
# Example of Analog Forecasting for SST AF_ = General_AF() AF_.flag_reduced = True # True: Clusterized version of Local Linear AF AF_.flag_cond = False # True: use Obs at t+lag as condition to select successors # False: no condition in analog forecasting AF_.flag_model = False # True: Use gradient, velocity as additional regressors in AF AF_.flag_catalog = True # True: Use each catalog for each patch position # False: Use only one big catalog for all positions AF_.cluster = 1 # number of cluster for clusterized ver. AF_.k = 200 # number of analogs AF_.k_initial = 200 # retrieving k_initial nearest neighbors, then using condition to retrieve k analogs, k_initial must >= k AF_.neighborhood = np.ones([PR_.n,PR_.n]) # global analogs AF_.neighborhood = np.eye(PR_.n)+np.diag(np.ones(PR_.n-1),1)+ np.diag(np.ones(PR_.n-1),-1)+ \ np.diag(np.ones(PR_.n-2),2)+np.diag(np.ones(PR_.n-2),-2) AF_.neighborhood[0:2,:5] = 1 AF_.neighborhood[PR_.n-2:,PR_.n-5:] = 1 # local analogs AF_.neighborhood[PR_.n-2:,PR_.n-5:] = 1 # local analogs AF_.regression = 'local_linear' # forecasting strategies. select among: locally_constant, increment, local_linear AF_.sampling = 'gaussian' AF_.B = 0.05 # variance of initial state error AF_.R = 0.1 # variance of observation error
- Class AnDA_result: store AnDA’s results, such as GT, Observation, Optimal Interpolation, AnDA Interpolations and statistical errors (rmse, correlation)
# All results will be computed and stored in this class. class AnDA_result: itrp_AnDA = [] # AnDA interpolation itrp_OI = [] # OI product, for comparison itrp_postAnDA = [] # Post_processing AnDA interpolation (removing block artifacts) GT = [] # groundtruth Obs = [] # Observation LR = [] # Low resolution product # stats: rmse & correlation of interpolation to the groundtruth rmse_AnDA = [] corr_AnDA = [] rmse_OI = [] corr_OI = [] rmse_postAnDA = [] corr_postAnDA = []
- Class PR: to specify general parameters
- Module Transform functions (AnDa_transform_functions.py):
- Perform Global PCA (to find LR), patch-based PCA for multi-scale assimilation
- Post-processing to remove block artifact due to overlapping patches
- Perform VE-DINEOF
- Find gradient, Fourier power spectrum
- Loading and preprocessing data according to the parameters described in PR
- Module Multi-scale Assimilation (Multiscale_Assimilation.py): based on informations from PR, VAR, AF, defining a specific kind of assimilation
- Class Single_patch_assimilation:
- Processing on one single patch.
- Input: position of patch (rows, columns) over initial image.
- Class Multi_patch_assimilation:
- Processing on a zone of image (defined by its size and coordinates of top-left point), by dividing into multiples patches, then plugging them into Single_patch_assimilation
- Input: number of parallel jobs, or number of patches are executed simultaneously.
- Class Single_patch_assimilation:
Specify all necessary parameters described in class PR, and General_AF.
Load data into class VAR:
VAR_ = VAR()
VAR_ = Load_data(PR_) Visualize an example of reference Groundtruth (GT), Observation (Obs) and Low resolution Optimal Interpolation (OI) product
day = 50
colormap='nipy_spectral'
plt.clf()
gt = VAR_.dX_GT_test[day,:,:]
obs = VAR_.Obs_test[day,:,:]
itrp = VAR_.Optimal_itrp[day,:,:]
vmin = np.nanmin(gt)
vmax = np.nanmax(gt)
plt.subplot(1,3,1)
plt.imshow(gt,aspect='auto',cmap=colormap,vmin=vmin,vmax=vmax)
plt.colorbar()
plt.title('GT')
plt.subplot(1,3,2)
plt.imshow(obs,aspect='auto',cmap=colormap,vmin=vmin,vmax=vmax)
plt.colorbar()
plt.title('Obs')
plt.subplot(1,3,3)
plt.imshow(itrp,aspect='auto',cmap=colormap,vmin=vmin,vmax=vmax)
plt.colorbar()
plt.title('OI')
plt.draw()
Define test zone (top-left point and size of zone) (note: must 4 values must be divisible by 5):
r_start = 0
c_start = 0
r_length = 150
c_length = 300 Define multiprocessing level:
level = 22 # 22 patches executed simultaneouslyRun Assimilation:
saved_path = 'path_to_save.pickle'
MS_AnDA_itrp = AnDA_result()
MS_AnDA_ = MS_AnDA(VAR_sst, PR_sst, AF_sst)
MS_AnDA_itrp = MS_AnDA_sst.multi_patches_assimilation(level, r_start, r_length, c_start, c_length)Save result:
with open(saved_path, 'wb') as handle:
pickle.dump(MS_AnDA_itrp, handle)Reload result: Save result:
with open(saved_path, 'rb') as handle:
MS_AnDA_itrp = pickle.load(handle) To compare with AnDA interpolation:
- Run VE-DINEOF algorithms to compare with AnDA interpolation.
itrp_dineof = VE_Dineof(PR_, VAR_.dX_orig+VAR_.X_lr, VAR_.Optimal_itrp+VAR_.X_lr[PR_.training_days:], VAR_.Obs_test, 100, 50)
- Run G-AnDA: applying AnDA on region scale. We need to reset parameters in PR and General_AF:
Then reload data (because we now assimilate high resolution (original) fields, not detail fields):
PR_.flag_scale = False # True: multi scale AnDA, False: global scale AnDA PR_.n = 200 # choose higher than the one from local scale, because we want to keep 99% variance after applying global PCA. PR_.patch_r = 200 # r_size of image PR_.patch_c = 120 # c_size of image AF_.flag_reduced = False or True AF_.flag_cond = False AF_.flag_model = False AF_.flag_catalog = False AF_.cluster = 1 # number of cluster for clusterized ver. AF_.k = 500 # number of analogs, should be higher than state vector's dimension AF_.k_initial = 500 # retrieving k_initial nearest neighbors, then using condition to retrieve k analogs, k_initial must >= k AF_.neighborhood = np.ones([PR_.n,PR_.n]) # global analogs
Then run single patch assimilation (this case isn't patch-based):VAR_ = VAR() VAR_ = Load_data(PR_)saved_path = 'path_to_save.pickle' itrp_G_AnDA = AnDA_result() MS_AnDA_ = MS_AnDA(VAR_, PR_, AF_) itrp_G_AnDA = MS_AnDA_.single_patch_assimilation([np.arange(r_start,r_start+r_length),np.arange(c_start,c_start+c_length)])
Display interpolation performance & Fourier power spectrum (note that the input of raPsd2dv1 should be without land pixel (avoid NaN values).
day =11 # 82
res_ = 0.25
f0, Pf_ = raPsd2dv1(itrp_G_AnDA[day,:,:],resSLA,True)
wf1 = 1/f1
plt.figure()
plt.loglog(wf1,Pf_AnDA,label='G-AnDA')
plt.gca().invert_xaxis()
plt.legend()
plt.xlabel('Wavelength (km)')
plt.ylabel('Fourier power spectrum')