Geostrophic Balance Breakdown? 4D-Var near the equator...

[lmp4]

Over the past few months I have been running into an issue I think I’ve finally got a grasp on!
For context I am looking to perform some observational simulation studies in the Angola /Congo oceanic region (Lat: -1 to -21 S and Lon: 4.3 to 13.8 E).

Now I have come across several setbacks in performing assimilation within ROMS using the strong-constraint I4D-Var. Time and time again the model has been blowing up (for states u and v) at various points along areas to the north of my domain. Locations usually include areas of increased steepness, around a sea mound for example or the shelf region.

When running the model without assimilation I have a completely stable setup. However the data assimilation quickly changes this and the model blowups numerous times.

At first I thought the elliptic solver (involved in the SSH balance equations) was doing strange things around my sea mound creating unreasonable currents that are propagating along north part of my domain. However I have since run the assimilation choosing different states of balance that contradicts this.

When I keep the balance original settings;

Code: Select all

!  balance        Balance operator logical switches for state variables to
!                 consider in the error covariance off-diagonal multivariate
!                 constraints:
!
!                   balance(isSalt) = T,         salinity
!                   balance(isFsur) = T,         free-sruface
!                   balance(isVbar) = F,         2D momentum (ubar, vbar)
!                   balance(isVvel) = T,         3D momentum (u, v)

I get the following when assimilating SSTs, SSHs and Argo floats in the Figure 1 below. Here I am showing a vertical slice (black line) of northward velocity V (m/s) prior to the assimilation (top left) and after becoming the posterior (top right). The velocity increment (bottom left) i.e. the posterior minus the prior and scaled for +- 1.
This figure clearly shows that something is going wrong around this sea mound. Looking at the horizontal structure of this error along the bottom of my domain in Figure 2 it can be seen that these superiors’ currents dominate in the north of my domain.

FIGURE 1

Figure 2

Still focused that this error was an issue of balance I starting reading about the balance within the ROMS 4D-Var system, specifically the Weaver et al paper entitled ‘A multivariate balance operator for variational ocean data assimilation’. To my understanding the ROMS 4D-Var balance operator is based on Weaver et al’s (2005) approach.

Interestingly this paper suggests

‘Special treatment of the geostrophic velocity balance is required near the equator’

The paper goes on to explain a methodology for this involving correction terms and weighting function to account for this.

So my question is whether the ROMS 4D-Var takes this into account equatorial geostrophic velocity?
And if not could this be the reason why my model blows up for u and v in the north of my domain (near -1 N).

The following extract is taken from the ROMS 4D-Var part one paper

‘Balance relations KxT, KxS and Kxf for x = u and x = v are computed based on the assumption of geostrophic balance’

(Moore et al. The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems Part I – System overview and formulation 2011). This is all what is mentioned for the 3D momentum balance. Looking into the code I can also see no mention of weighting functions or corrections terms to account for the equator.

A quick test for this was to simply switch off the balance for 3D-momentum (u,v ). i.e.

Code: Select all

 !                   balance(isVvel) = F,         3D momentum (u, v)

The results shown in Figure 3 that the balance for 3D-monetum is having a significant effect for hindering the DA process in my domain as these spurious currents seen in the previous figures completely vanish!

FIGURE 3

Anyways I was wondering if anyone had any thoughts on this. Would running the 4D-Var assimilation without imposing geostrophic balance be completely incorrect? Since I am looking at the impact of observations for ocean currents I feel this could be a real problem.

[Ahumada]

Hi,

Your question is also of interest to me... Our model domain is from -4 to 18°N and 76 to 114°W... as a first step, ROMS was implemented with any data assimilation... However, recently, we estimate geostrophic currents from SSH altimetry data (AVISO) without the equatorial beta-plane constraint and very strong currents appear near the equatorial zone. I suggest reducing your domain, for example, from -4 to -21 S, and see what happens!

Happy modeling!

M.-A.

[dhd_1979]

The reason may be the Coriolis parameter (f(i,j-1)+f(i,j)) in tl_balance.F90 and ad_balance.F90 becomes to or near to zero in the equator, which may cause unstable results.

code in tl_balance.F90, which using (f(i,j-1)+f(i,j)):

Code: Select all

Compute balanced, surface U-momentum from baroclinic and barotropic
!  surface pressure gradient.
!
      IF (balance(isFsur).or.balance(isUvel)) THEN
        DO j=Jstr,Jend+1
          DO i=Istr-1,Iend
            cff1=z_w(i,j  ,N(ng))-z_r(i,j  ,N(ng))+                     &
     &           z_w(i,j-1,N(ng))-z_r(i,j-1,N(ng))
            tl_phie(i)=fac1*(tl_rho(i,j  ,N(ng))-                       &
     &                       tl_rho(i,j-1,N(ng)))*cff1+                 &
     &                 fac2*(tl_zeta(i,j  ,Linp)-                       &
     &                       tl_zeta(i,j-1,Linp))
            tl_gradP(i,j,N(ng))=0.5_r8*tl_phie(i)*                      &
     &                          (pn(i,j-1)+pn(i,j))/(f(i,j-1)+f(i,j))

[lmp4]

Yeah that seems logical. Since I am running at such a high resolution shifting my domain away from the equator will take a while to set up so for now I think I'll create a 10km test model and see if it improves.