Add the new capability for MRI-4DVar

[liujake]

This large PR adds the new capability for multi-resolution incremental 4DVar.

TYPE: new feature

KEYWORDS: MRI-4DVar, Inverse transform, square root of B, 3-stage

SOURCE: Zhiquan (Jake) Liu, Junmei Ban, Jamie Bresch, Yali Wu, Xin Zhang, Jianyu Liu (NCAR/MMM)

DESCRIPTION OF CHANGES:
Existing 4DVar algorithm is run at the same model resolution for inner loop minimization of different outer loops (default namelist setting with multi_inc=0). This adds MRI-4DVar capability that can run 4DVar at lower resolution for inner loop minimization with a 3-stage procedure (observer, minimizer, regridder) as described by Liu et al. (2020) and can substantially speed up 4DVar. Three major changes include:

1. 3-stage procedure controlled by a script and offline programs under ~var/mri4dvar;
   Set multi_inc=1 for the "observer" step and multi_inc=2 for the "minimizer" step. The "regridder' step is done using the offline programs.

2. Inverse transform of square root B introduced under ~var/da/da_vtox_transforms;
   New namelist parameter use_inverse_squarerootb needs to be set .true. when multi_inc=2 and works together with cv_options=5, 6, or 7 and cloud_cv_options=2 or 3.

New namelist parameter use_interpolate_cvt=.false. (default), which is supposed to work together with the obsolete cv_options=3, which is not recommended to use for non-expert users.

3. Additional file I/O for control variable and radar/radiance OMB files from the observer step. This I/O part will need some further code clean-up and improvement in the future.

LIST OF MODIFIED FILES: 48 files
M Registry/registry.var
M var/build/depend.txt
M var/da/da_main/da_solve.inc
M var/da/da_main/da_wrfvar_top.f90
M var/da/da_minimisation/da_get_innov_vector.inc
M var/da/da_minimisation/da_minimisation.f90
M var/da/da_obs_io/da_obs_io.f90
M var/da/da_obs_io/da_read_iv_for_multi_inc.inc
M var/da/da_obs_io/da_read_obs_radar.inc
M var/da/da_obs_io/da_scan_obs_radar.inc
M var/da/da_obs_io/da_search_obs.inc
M var/da/da_obs_io/da_write_iv_for_multi_inc.inc
M var/da/da_radiance/da_radiance1.f90
A var/da/da_radiance/da_read_iv_rad_for_multi_inc.inc
A var/da/da_radiance/da_write_iv_rad_for_multi_inc.inc
M var/da/da_recursive_filter/da_recursive_filter.f90
A var/da/da_recursive_filter/da_recursive_filter_1d_inv.inc
M var/da/da_recursive_filter/da_transform_through_rf.inc
A var/da/da_recursive_filter/da_transform_through_rf_inv.inc
M var/da/da_setup_structures/da_setup_structures.f90
A var/da/da_setup_structures/da_write_vp.inc
M var/da/da_tools/da_llxy.inc
M var/da/da_vtox_transforms/da_transform_vptox.inc
A var/da/da_vtox_transforms/da_transform_vptox_inv.inc
A var/da/da_vtox_transforms/da_transform_vtovv_inv.inc
A var/da/da_vtox_transforms/da_transform_vtox_inv.inc
M var/da/da_vtox_transforms/da_transform_vvtovp.inc
M var/da/da_vtox_transforms/da_transform_vvtovp_adj.inc
A var/da/da_vtox_transforms/da_transform_vvtovp_inv.inc
M var/da/da_vtox_transforms/da_vertical_transform.inc
M var/da/da_vtox_transforms/da_vtox_transforms.f90
A var/mri4dvar/Makefile
A var/mri4dvar/README.MRI-4DVar
A var/mri4dvar/da_bdy.f90
A var/mri4dvar/da_bilin.f90
A var/mri4dvar/da_thin.f90
A var/mri4dvar/da_vp_bilin.f90
A var/mri4dvar/da_vp_split.f90
A var/mri4dvar/nc_increment.ncl
A var/mri4dvar/nc_vpglobal.ncl
A var/mri4dvar/nc_vphires.ncl
A var/mri4dvar/nc_vpinput.ncl
A var/mri4dvar/nc_vplocal.ncl
A var/mri4dvar/rsl_lite.h
A var/mri4dvar/run_mri3d4dvar.csh_lsf
A var/mri4dvar/run_mri3d4dvar.csh_pbs
A var/mri4dvar/task_for_point.c
A var/mri4dvar/wraper_mri3d4dvar.csh

TESTS CONDUCTED: WRFDA regression test passed. Cycling MRI-4DVar tests were performed over an Arctic domain.

RELEASE NOTE: New capability for Multi-Resolution Incremental 4DVar (MRI-4DVar).
Liu, Z., J. Ban, J.-S, Hong, and Y.-H. Kuo, 2020: Multi-resolution incremental 4D-Var for WRF: Implementation and application at convective scale, Q. J. R. Meteorol. Soc., 146, 3661-3674.

[liujake]

@davegill Listed you as a reviewer just in case you'd like to have a quick scan in PR message (and/or code) for this relatively large PR. No impact to the model side. WRFDA regtest passed. Junmei should review it.

[junmeiban]

I tested this PR on OSC HPC owens machine.
Two cycling experiments(135km45km and 45km45km) are conducted, and both of them run successfully.