Smoothing the TIW Curl and the Sverdrup balance

Can TIW mixing explain the discrepancy from the Sverdrup balance?
Suppose the vorticity input by the wind is mixed meridionally by the TIW. Then the westward integration of the Sverdrup balance would integrate the curl smoothed in y. For the pressure field, the zonal integration is (1), so the quantity smoothed is dP/dx = (f²/B)Curl(Tau/f).

• Reynolds SST RMS (to show TIW region): Total  Low-pass  High-pass 

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
An early attempt to smooth dP/dx is described here. It didn't work, because the triangle filters have unusual non-isotropic properties due to the filter widths being a function of y. That means the filter is hard to describe by the usual measuer like the half-power point (depends on direction). Also it wasn't a very good idea in the first place because the output of the filter is non-conservative of the quantity being filtered. Mixing should conserve the total quantity.

This smoothing was done centered on the (idealized) TIW region, using Gaussian-weight running means or triangle filters. The 2-dimensional Gaussian is described by 5 parameters: Amp*exp{((y-y0)/Y)²}*exp{((x-x0)/X)²}; this expression gives the width (°lat) of the triangle or running mean that was used to smooth dP/dx at each location.

1. Results (P) of integration of smoothed curl (check/compare different smoothing) (all have x0=110°W, X=50°): 
   y0=4°N, Y=4°, RM(5)   y0=4°N, Y=3°, Tr(5)   y0=4°N, Y=4°, Tr(5)   y0=4°N, Y=5°, Tr(5)   y0=3°N, Y=5°, Tr(5)   y0=3°N, Y=4°, RM(6)
2. All 5 smoothings compared (P)
3. All 5 smoothings compared (Ug)  V2  V3  V4  
4. Overlay meridional section at 140°E-170°E: P  Ug
   End of this misguided idea
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

1. Sverdrup, Geostrophic and Ekman zonal currents: 10°S-30°N  5°S-12°N  
2. Meridional sections in the TIW region: Curl  dP/dx  dP/dx to 20°N
       Dots show the smoothing (averaging) applied (try different widths): 1.5°S-6.5°N  V2  1.5°S-5.5°N
3. Result of smoothing: Curl  Streamfunction  Pressure  Ug