Defining GUNW cubes

[bbuzz31]

Need to spec out the delay cube generation that will cover the GUNW product.
Height levels? lat/lon spacing? Needs to be able to be stitched

Comments from PR:
#439 (comment)
#439 (comment)
#439 (comment)

[dbekaert]

This is the recommendation that the NISAR tropo working group made to NISAR project.

The tropospheric layer as planned in the product description/spec is proposed to be a 3D cube.
The tropo working group recommends:
- For the vertical posting to have the height levels to be approximately at the native vertical levels of the weather model, with levels replicated/mirrored below sea-level.
- The height range to be slightly larger than the dynamic range of heights on earth. (see below for a detailed description)
- For the lateral posting to keep this at the native weather model posting. (see below for a detailed description)
- Given the 3D implementation of tropo layer (as well as the meta-data cubes layers) we request the project to implement and distribute tools that allows for easy extraction and application in the 2D domain.

More details:

The general idea is not to fabricate any data at locations other than the source grid.
For the horizontal posting we use the native model grid.
For HRES, this is equivalent to WGS84 at 0.1 degree posting.
For the vertical posting its slightly more complex and we have two scenario’s.
We would suggest the vertical levels to be the closest to the average global level of the model.
However, we would only need all the height level and one more than the maximum topography on earth to be able to intersect with a DEM and recover the delay (see color below).
This approach does not account for elevations below mean sea-level; which is maximum at -430m near the dead sea.
To account for that we propose to add negative layers up to the -500m elevation (roughly reverse scheme)
Off course the below height might be rounded, but give the general idea of what we propose.
 
The decision to choose between model/pressure levels would depend on what the project can arrange to get access too
However it does not make sense to apply the model level height to that of the pressure level as the information was lost before ingestion into RAIDER.
 
Pressure levels.
                                                               i.      HRES has 25 pressure levels, where each pressure maps to an average fixed heigh-level
The pressure files are generated from the model outputs and have lower vertical resolution and are interpolated leading to some errors.
                                                             ii.      The average global height levels are:
[ 4.841394e+04  4.373855e+04  3.985056e+04  3.656972e+04  3.376305e+04
  3.133096e+04  2.663556e+04  2.441350e+04  2.069490e+04  1.839425e+04
  1.632283e+04  1.372718e+04  1.189024e+04  1.042264e+04  9.255700e+03
  7.214090e+03  5.469300e+03  4.074410e+03  3.089250e+03  1.910760e+03
  1.459910e+03  9.871500e+02  7.987200e+02  5.665400e+02  1.065400e+02
0.000000e+00  -1.000000e+02 -3.000000e+02 -5.000000e+02]
 
Model levels:
                                                               i.      HRES has 137 model levels, which maps to different heights based on location: https://www.ecmwf.int/en/forecasts/documentation-and-support/137-model-levels
                                                             ii.      Here average global height levels are:
[ 8.030165e+04  7.458491e+04  7.191879e+04  6.936577e+04  6.690653e+04
  6.453743e+04  6.225439e+04  6.005346e+04  5.793078e+04  5.588268e+04
  5.390562e+04  5.199621e+04  5.015936e+04  4.841394e+04  4.675698e+04
  4.519969e+04  4.373855e+04  4.236493e+04  4.107120e+04  3.985056e+04
  3.869694e+04  3.760495e+04  3.656972e+04  3.558689e+04  3.465252e+04
  3.376305e+04  3.291527e+04  3.210657e+04  3.133096e+04  3.058471e+04
  2.986609e+04  2.917350e+04  2.850547e+04  2.786064e+04  2.723773e+04
  2.663556e+04  2.605304e+04  2.548915e+04  2.494293e+04  2.441350e+04
  2.390002e+04  2.340171e+04  2.291785e+04  2.244775e+04  2.199082e+04
  2.154662e+04  2.111477e+04  2.069490e+04  2.028666e+04  1.988988e+04
  1.950309e+04  1.912561e+04  1.875634e+04  1.839425e+04  1.803835e+04
  1.768777e+04  1.734162e+04  1.699908e+04  1.665955e+04  1.632283e+04
  1.598888e+04  1.565770e+04  1.532924e+04  1.500350e+04  1.468044e+04
  1.436005e+04  1.404230e+04  1.372718e+04  1.341465e+04  1.310470e+04
  1.279730e+04  1.249244e+04  1.219010e+04  1.189024e+04  1.159286e+04
  1.129793e+04  1.100569e+04  1.071422e+04  1.042264e+04  1.013098e+04
  9.839260e+03  9.547490e+03  9.255700e+03  8.963900e+03  8.672110e+03
  8.380360e+03  8.088670e+03  7.797040e+03  7.505510e+03  7.214090e+03
  6.922800e+03  6.631660e+03  6.340680e+03  6.049890e+03  5.759300e+03
  5.469300e+03  5.180980e+03  4.896020e+03  4.615920e+03  4.341730e+03
  4.074410e+03  3.814820e+03  3.563690e+03  3.321670e+03  3.089250e+03
  2.866830e+03  2.654690e+03  2.452990e+03  2.261800e+03  2.081090e+03
  1.910760e+03  1.750630e+03  1.600440e+03  1.459910e+03  1.328700e+03
  1.206440e+03  1.092730e+03  9.871500e+02  8.892900e+02  7.987200e+02
  7.150200e+02  6.377600e+02  5.665400e+02  5.009500e+02  4.406100e+02
  3.851600e+02  3.342400e+02  2.875200e+02  2.446900e+02  2.054400e+02
  1.695100e+02  1.366200e+02  1.065400e+02  7.904000e+01  5.392000e+01
  3.096000e+01  1.000000e+01]
0.000000e+00 -1.000000e+01 -2.000000e+01  -5.000000e+01 -1.000000e+02
-2.000000e+02 -3.000000e+02 -5.000000e+02

[dbekaert]

We should clean this up a little bit for ourselves and then hard-code it for the aria gunw. I do not believe we need every level either. @piyushrpt thoughts?

[piyushrpt]

While the levels are closely spaced at the lower heights - the ray lengths are also super short between levels here. So, their total contribution to the integral may not be that different. It would be good to do a numerical test of 500m vertical spacing vs say 50 or 100m vertical spacing - to see if these actually make much of a difference. You don't need to do this at all heights but say just the lower 1 km where the theory is that this improved sampling is important.

1. Having vertical height levels on a standard grid would allow for concatenation of products over large area (if desired).
2. Minimum number of height levels might be needed for interpolator support when intersecting with DEM. So, you can choose not to go [-500, 9500] all over but just based on min/max height of scene being processed to speed up computation.