TIW-smoothing

# Smoothing the TIW Curl and the Sverdrup balance

This page documents a week of messing around with smoothing the Curl pattern due to TIW, in a possibly-misguided attempt to make it look like some XBT data. But those data may be wrong. In any case, this page saves those plots in case I need them again.

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).

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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
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A better (simpler, property-conserving) way to smooth the winds is to set the value of Curl(Tau) to its average over a region. That is, imagine the TIW completely homogenize the vorticity input felt by the ocean.
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

See work with the Johnson CTD/ADCP data set
See work with the Sverdrup balance
See work with the Pacific Subtropical Countercurrent
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