WIP: azimuth component calculation of solid earth tide

[seongsujeong]

This PR is to add azimuth component of the solid earth tide conversion, as well as integrating and finalizing the other LUT corrections that are implemented so far.

The conversion algorithm is based on ETAD ATBD available here.

Note that the 3D tidal displacement computation is performed in units of meters in the global ITRF. Therefore, the outcome needs conversion into slant-range and azimuth timing geometry of the correction grid. This conversion is performed by computing the zero Doppler radar times of the grid position 𝑋𝑔 including the tidal displacement Δ𝑋𝑆𝐸𝑇 and forming the difference to the grid nominal grid radar times.

This PR needs to be merged after the PRs below are merged. Until then, this PR will be labeled as work in progress.
#103 #102

Also note that the algorithm here calculates range component as well as azimuth component by its nature.

[LiangJYu]

Suggested change

	rg_set_temp, az_set_temp = solid_earth_tides(burst,
	lat[dec_slice, dec_slice],
	lon[dec_slice, dec_slice],
	height[dec_slice, dec_slice],
	dec_slice = np.s_[::dec_factor, ::dec_factor]
	rg_set_temp, az_set_temp = solid_earth_tides(burst,
	lat[dec_slice],
	lon[dec_slice],
	height[dec_slice],

I think the slice only needs to be altered once.

[seongsujeong]

I've tested the original code, and it seems the slicing is happening on the first axis of the array only. In my test case (Rosamond, 10/16/2022, t064_135523_iw1), the radargrid rasters' shapes were (109,418), and dec_factor was 42.
dec_slice was as below:

dec_slice
slice(None, None, 42)

Below are the shapes of the decimated arrays:

lat.shape
(109, 418)
lat[dec_slice].shape
(3, 418)
lat[dec_slice, dec_slice].shape
(3, 10)

So it seems we need to provide the slice instance twice for the 2d arrays. @vbrancat Can you take a look at the information above and confirm that the shape of the decimated array makes sense?

Below is a toy code to show how the slicing works in 2D numpy array:

import numpy as np

arr_original = np.arange(150).reshape((10,15))
dec_slice = np.s_[::5]
print(arr_original.shape)
arr_slice_1 = arr_original[dec_slice]
print(arr_slice_1.shape)

arr_slice_2 = arr_original[dec_slice, dec_slice]
print(arr_slice_2.shape)

[vbrancat]

You are right. I have fixed this in the next commit.

[vbrancat]

Thank you @seongsujeong, I do not have major comments at this stage. We discussed the algorithm in our CSLC tag-up meeting and the implementation looks fine to me.

I have noticed that your branch contains commits from PRs which have been already merged. You might want to rebase this branch to avoid this https://www.google.com/search?q=git+merge+war&tbm=isch&ved=2ahUKEwjs9rjl8Iv-AhWiPkQIHfpEDSEQ2-cCegQIABAA&oq=git+merge+war&gs_lcp=CgNpbWcQAzoHCAAQigUQQzoFCAAQgAQ6BggAEAgQHjoHCAAQgAQQGFDlBVjCDWDvEGgAcAB4AIABOogBkwKSAQE1mAEAoAEBqgELZ3dzLXdpei1pbWfAAQE&sclient=img&ei=sdApZKzaNaL9kPIP-om1iAI&bih=800&biw=1454&rlz=1C5GCEM_en#imgrc=PImq13_QtYFdDM while merging. An alternative is to hand-pick your commits and submit a PR using the main branch.

[vbrancat]

Would it make sense to separate this function in a enu2los and en2az? Just in case, we want to use them separately in the code

[seongsujeong]

The conversion in this PR is based on geo2rdr, meaning that it will calculate range and azimuth displacements simultaneously. I'm not sure how much useful separating them would be.
In case we want to use only one of the components, I think we can suppress the unnecessary return values. For example,

rg_arr, _ = enu2rgaz(radargrid_ref, orbit, ellipsoid, ...)
_, az_arr = enu2rgaz(radargrid_ref, orbit, ellipsoid, ...)

[vbrancat]

Uhm, what do you think of separating the functionalities? 1) Have a conversion from en2az where the azimuth component is in meters 2) convert azimuth component from meters to seconds.

I can see both these functionalities be reused in several parts of the code

[seongsujeong]

Same response as above.

[vbrancat]

Can we add a comment on how we got the numbers for the threshold and delta_range?

[vbrancat]

Let's document what are the other plausible units that the code support

[vbrancat]

Formatting

[seongsujeong]

Thanks for catching this. I've adjusted the indentation spaces.