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GitHub Pull Request: ​https://github.com/myroms/roms/pull/25

In 4D-Var, the background (prior) error covariance, B, is a large matrix that cannot be computed or stored directly. Still, its effects can be modeled using spatial correlations, C, and spatial convolutions via diffusion operators. To convert correlations into error covariance, we multiply by a diagonal matrix of the background error standard deviations, S. Hence,

B = L S C S^T L^T

where L is a balance operator, if BALANCE_OPERATOR is activated in ROMS. It allows the information on unobserved state variables to be extracted from directly observed quantities by imposing linear balance relationships between temperature and other state variables using T-S empirical formulas, the linear equation of state, hydrostatic balance, and geostrophic balance. Please check Moore et al. (2011) for more information.

This update includes an approach to computing the standard deviation, S, directly from the background state field as an alternative to climatological values read from the input NetCDF files. It follows the work of Mogensen et al. (2012) by assuming the background errors are proportional to the vertical derivatives of the background field. The field error has a similar profile shape, but the difference with the actual error values is due to a vertical displacement.

In the past, the standard deviation was read from input NetCDF files and computed from a long simulation of the ROMS application. The climatological S can be categorized as monthly, seasonal, or annual values.

The modeling of the standard deviation from the background (prior) is activated with the STD_MODEL option and done in the new module background_std.F. For further information about this capability in ROMS, check Moore et al. (2020).

New parameters are added to 4D-Var input script s4dvar.in to constraint the standard deviation profile at the mixed-layer depth and deep ocean:

! Modeled standard deviation (STD) of Background Error Covariance parameters.
!
! The Mogensen et al. (2012) formulation assumes that the background errors
! are proportional to vertical derivatives of the state vector field. Its
! error has a similar field profile shape, but the difference with its
! ture error value is due to a vertical displacement.
!
! If COMPUTE_MLD is activated, the mixed-layer depth is computed using the
! criterion from Kara et al. (2000). Otherwise, it will be set to a uniform
! value provided below.

Sigma_max(isFsur) == 0.025d0           ! free surface  maximum STD value

Sigma_max(isUvel) == 0.06d0            ! U-velocity maximum STD value
 Sigma_ml(isUvel) == 0.05d0            ! U-velocity minimum STD at mixed layer
 Sigma_do(isUvel) == 0.02d0            ! U-velocity minimum STD in deep ocean
 Sigma_dz(isUvel) == 500.0d0           ! U-velocity vertical displacement

Sigma_max(isVvel) == 0.06d0            ! V-velocity maximum STD
 Sigma_ml(isVvel) == 0.05d0            ! V-velocity minimum STD at mixed layer
 Sigma_do(isVvel) == 0.02d0            ! V-velocity minimum STD in deep ocean
 Sigma_dz(isVvel) == 500.0d0           ! V-velocity vertical displacement

Sigma_max(isTvar) == 0.33d0   0.056d0  ! 1:NT tracers maximum STD
 Sigma_ml(isTvar) == 0.05d0   0.05d0   ! 1:NT tracers minimum STD at the mixed layer
 Sigma_do(isTvar) == 0.02d0   0.0028d0 ! 1:NT tracers minimum STD in the deep ocean
 Sigma_dz(isTvar) == 40.0d0   40.0d0   ! 1:NT tracer vertical displacement

      mld_uniform == -75.0d0           ! Uniform mixed layer depth value

Notice we have the option COMPUTE_MLD to compute the mixed-layer depth using the approach of Kara et al. (2000) or set a constant value of mld_uniform.

Two new routines are added, def_std.F and wrt_std.F, to write the standard deviation modeled from the background into an output NetCDF file. It will be needed in the split 4D-Var algorithms and for postprocessing. The new filename is also specified in s4dvar.in:

! If computing the standard deviation from the background (prior) state
! vector as an alternative to climatological values read from the
! input NetCDF file, enter the output standard deviation file name,
! [1:Ngrids].

       STDnameC == roms_std_c.nc

We foresee enhancing this capability in the future. We only model the standard deviation for adjusting the initial state vector (zeta, u, v, T, and S). We don't have options for background error on the model (weak constraint), lateral model boundary conditions, surface tracer fluxes, and surface momentum stress. Thus, those standard deviation values are still read from input files.

Notice that the standard deviation structure for I/O management increased its inner dimension from 4 to 5 in mod_iounits.F:

       IF (.not.allocated(STD)) THEN
         allocate ( STD(5,Ngrids) )
       END IF

WARNING:

• The s4dvar.in has the additional parameters mentioned above. Please update your 4D-Var input script to use his new capability.

References:

• Kara A., P. Rochford, and E. Hulburt, 2000: An optimal definition for ocean mixed layer depth, J. Geophys. Res., 105, NoC7, pp 16, 803-16, 821.

• Mogensen, K., M.A. Balmaseda, and A.T. Weaver, 2012: The NEMOVAR ocean data assimilation system implemented in the ECMWF ocean analysis for system 4, ECMWF Tech. Memorandum 668, 59.

• Moore, A.M., H.G. Arango, G. Broquet, B.S. Powell, A.T. Weaver, and J. Zavala-Garay, 2011: The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilations systems, Part I - System overview and formulation, Prog. Oceanogr., 91, 34-49, ​https://doi:10.1016/j.pocean.2011.05.004.

• Moore, A., J. Zavala-Garay, H.G. Arango, C.A. Edwards, J. Anderson, and T. Hoar, 2020: Regional and basin scale applications of ensemble adjustment Kalman filter and 4D-Var ocean data assimilation systems, Progress in Oceanography, 189, 102450, ​https://doi.org/10.1016/j.pocean.2020.102450.

The ROMS Native Sea Model was updated and tested with the LAKE_ICE test case. It is an idealized application 200x100x30 at 1km resolution:

The location of the output stations is denoted as S1, S2, S3, S4, S5, S6, S7, and S8 and used to store the time series of the solution at hourly intervals. The vertical grid is well resolved in the upper 20m with a bathymetry range between 20-200m.

ROMS is initialized on Jan-1-2010 and runs for 800 days until Apr-13-2012. Please check the following link for more information, instructions, and solution plots:

​https://github.com/myroms/roms_test/blob/main/lake_ice/Forward/Readme.md

• Many thanks to Scott Durski for updating and improving the existing sea ice model, which was initially written by Paul Budgell and maintained and documented by Kate Hedstrom.

• Many thanks to Mike Dinniman for his help in debugging and testing this new version of the sea ice model.

The ROMS and WRF NUOPC cap modules were updated to exchange surface current (Usur, Vsur) between ocean and atmosphere couple components.

We are currently using the WRF code from ​https://github.com/myroms, which we applied a couple of corrections to the code submitted to its developers and will appear in future releases. As before, there will be no need to patch WRF for each release version.

Test Case

The Hurricane IRENE application has a new test case in the IRENE/Coupling/data_wrf_roms_wmc subdirectory. For more details, please check the link to the roms_test repository inGitHub for detailed information and instructions:

​https://github.com/myroms/roms_test/blob/main/IRENE/Coupling/data_wrf_roms_wmc/Readme.md

The ROMS and WRF grids are incongruent in this test case. Since ROMS doesn't cover all the ocean points in the WRF grid (red domain below), a DATA component is used to supply such values from the 3-hour HyCOM dataset. ROMS and DATA components export surface ocean current at the cell center (RHO-points). Then, the ocean currents from DATA and ROMS are melded smoothly using the appropriate weights.

Surface Ocean U-velocity	Surface Ocean V-velocity

The meldes surface currents are imported by WRF into variables grid%uoce and grid%voce. We will continue exploring WRF internal parameters to study the effects of the surface currents on the winds and wind stress. As shown by Renault et al. (2016), the feedback from surface ocean currents to the atmosphere is an eddy-killing effect stabilizing the Gulf Stream separation at Cape Hatteras in WRF-ROMS fully coupled applications. The result is around 0.3 N/m² weaker surface wind stress in the core of the Gulf Stream.