add python scripts for computing stats of ObsFcstAna output (via intermediate monthly files)

[gmao-qliu]

Add python scripts for computing ObsFcstAna statistics.

Processing is broken down into three steps:

1. Create intermediate monthly stats data (nc4).
2. Compute final stats from intermediate monthly data.
3. Aggregate stats across different species and/or remap stats data.

Steps 1) and 2) are generic for all ObsFcstAna output. Stats are computed in the tile space of the DA experiment and for all obs species (separately) in the associated obs_param file.

Step 3) depends on the assimilation experiment and use case scenario. E.g., SMAP L4_SM stats are defined in the EASEv2 M09 tile space but are usually aggregated across H/V-pol and AM/PM ops and visualized on the EASEv2 M36 grid.

The main script serves as a template to show how to use the pre-processed data to compute and plot the usual O-F and O-A statistical metrics.

The intermediate monthly stats nc4 files contain:

dimensions:

tile    = [NUMBER_OF_TILES] ;
species = [NUMBER_OF_SPECIES] ;

variables:

char obs_param_assim(species) ;      

int N_data(tile, species) ;                ! number of obs

float obsxfcst_sum(tile, species) ;        ! sums of products of variables
float obsxana_sum(tile, species) ;
float fcstxana_sum(tile, species) ;

float obs_obs_sum(tile, species) ;         ! sums of variables
float obs_obsvar_sum(tile, species) ;
float obs_fcst_sum(tile, species) ;
float obs_fcstvar_sum(tile, species) ;
float obs_ana_sum(tile, species) ;
float obs_anavar_sum(tile, species) ;

float obs_obs2_sum(tile, species) ;        ! sums of squared variables
float obs_obsvar2_sum(tile, species) ;
float obs_fcst2_sum(tile, species) ;
float obs_fcstvar2_sum(tile, species) ;
float obs_ana2_sum(tile, species) ;
float obs_anavar2_sum(tile, species) ;

To facilitate the aggregation of the intermediate stats in Step 2), zeros are not replaced with NaNs in the "sum" variables even when the corresponding N_data value is zero.

Related issue: GEOS-ESM/GEOSldas#798 (closed)

[gmao-rreichle]

@gmao-qliu, I added a few thoughts. Please take a look and let me know if you have any questions or concerns. Thanks!

[gmao-rreichle]

@gmao-qliu : I removed the binary files in the pycache/ directories from the repository. I don't think these should be under version control.

[gmao-qliu]

Multi-experiments cross-masking is enabled now. @amfox37 @gmao-rreichle

[amfox37]

I have gone ahead and added the capability to calculate monthly OmF mean etc statistics from the precomputed sums/sum of squares. I'm not entirely sure it belongs in the Main_example.py as I've inserted it, let's discuss.
Also, have only run a very limited test case locally, so will now do some more substantial testing on Discover.

[gmao-rreichle]

@gmao-qliu : I added a few more commits:

1. Here's a link that shows the cumulative changes (white-space differences are hidden): https://github.com/GEOS-ESM/GEOSldas_GridComp/compare/f02efb4..fe2b15a?w=1
   The most likely source of errors in my changes is in my addition of a check for obsparam across the exp_list: d1852a8
   Please take a look and let me know if anything needs fixing.
2. What did we decide to do about the stats of the normalized O-F? If I recall correctly, as implemented the stats differ from what we did with the old Matlab scripts. Are we still thinking of trying to change this so it becomes identical to what we did in Matlab? If not, we need to add documentation in Plot_stats_maps.py.

[gmao-qliu]

2. What did we decide to do about the stats of the normalized O-F? If I recall correctly, as implemented the stats differ from what we did with the old Matlab scripts. Are we still thinking of trying to change this so it becomes identical to what we did in Matlab? If not, we need to add documentation in Plot_stats_maps.py.

I added some comments regarding the current approach. We can change the approach later if needed.

[gmao-rreichle]

@gmao-qliu : I made a few more changes to clean up and clarify things. Here's a link to the cumulative differences of my commits of today: https://github.com/GEOS-ESM/GEOSldas_GridComp/compare/84c3b58..5d42392

This leaves the following comment as the only one that may still need resolution: #87 (comment) (re. the potentially excessive length of the names of the files that hold the monthly sums)

[gmao-qliu]

@gmao-qliu : I made a few more changes to clean up and clarify things. Here's a link to the cumulative differences of my commits of today: https://github.com/GEOS-ESM/GEOSldas_GridComp/compare/84c3b58..5d42392

This leaves the following comment as the only one that may still need resolution: #87 (comment) (re. the potentially excessive length of the names of the files that hold the monthly sums)

@gmao-rreichle, Please review my latest commit to address this issue.

[gmao-qliu]

@gmao-qliu, I added one more commit with clean-up: 990bce2. Besides adding new and clarifying existing comments, I simplified the variables related to exptag, exptag_list, and outid. I think we only need one string for all of this, which I called "exptag". The others seem to be superfluous. Please double check and let me know, thanks!

@gmao-rreichle Looks and tests all good to me.