One aspect of ENSO that I haven't analyzed too deeply is the spatial part of the standing wave dipole. In solving Laplace's Tidal Equations, the separation of the partial diffEq leads to a family of terms

where f(t) is the tidal forcing and a & b are the two strongest terms in any model fit, corresponding to the main dipole and a higher wavenumber solution.

Each spatial term is simply a sine wave with a wavenumber proportional to the a,b,.. value, with a phase aligned to the oceanic boundary conditions.

![soi](https://imagizer.imageshack.com/img924/4284/T6Vj8Y.png)

So the a term is locked to a dipole that spans the equatorial Pacific, with the node crossing at a location in between Darwin and Tahiti denoted by the arrow. All the other factors scale from the temporal to spatial domain accordingly (via the fixed k term).

Thus, when I do the time-domain fit of ENSO while keeping track of all terms a,b,... , the spatial result is automatically set in place, apart from aligning the phase and selecting the spatial scaling factor k.

This is an initial stab at a spatially aligned fit of the generated standing wave as a [Hovmoller diagram](https://en.wikipedia.org/wiki/Hovm%C3%B6ller_diagram), with the left side measurements from [1] and the right side the model:

![sw](https://imagizer.imageshack.com/img924/2853/qRlhIH.png)

The node is right around 160E. The faster cycles in the model are what I think are related to the formation of Tropical Instability Waves, which has some character of a traveling wave. Will see if any of that fine structure is revealed in the other sources of data.

[1] Pinker, R. T., S. A. Grodsky, B. Zhang, A. Busalacchi, and W. Chen. “ENSO Impact on Surface Radiative Fluxes as Observed from Space: ENSO IMPACT ON SURFACE RADIATIVE FLUXES.” Journal of Geophysical Research: Oceans 122, no. 10 (October 2017): 7880–96. https://doi.org/10.1002/2017JC012900.

EDITED 5/22:

A possible source of the fine structure via ocean currents, from https://earth.nullschool.net/#current/ocean/surface/currents/orthographic=-158.02,2.78,819

![nullschool](https://imagizer.imageshack.com/img924/8424/TjDW0v.png)

If the data is available, a Hovmoller diagram could be created from a time-series sequence

sin(a f(t)) sin(k a x) + sin(b f(t)) sin(k b x) + ...

where f(t) is the tidal forcing and a & b are the two strongest terms in any model fit, corresponding to the main dipole and a higher wavenumber solution.

Each spatial term is simply a sine wave with a wavenumber proportional to the a,b,.. value, with a phase aligned to the oceanic boundary conditions.

![soi](https://imagizer.imageshack.com/img924/4284/T6Vj8Y.png)

So the a term is locked to a dipole that spans the equatorial Pacific, with the node crossing at a location in between Darwin and Tahiti denoted by the arrow. All the other factors scale from the temporal to spatial domain accordingly (via the fixed k term).

Thus, when I do the time-domain fit of ENSO while keeping track of all terms a,b,... , the spatial result is automatically set in place, apart from aligning the phase and selecting the spatial scaling factor k.

This is an initial stab at a spatially aligned fit of the generated standing wave as a [Hovmoller diagram](https://en.wikipedia.org/wiki/Hovm%C3%B6ller_diagram), with the left side measurements from [1] and the right side the model:

![sw](https://imagizer.imageshack.com/img924/2853/qRlhIH.png)

The node is right around 160E. The faster cycles in the model are what I think are related to the formation of Tropical Instability Waves, which has some character of a traveling wave. Will see if any of that fine structure is revealed in the other sources of data.

[1] Pinker, R. T., S. A. Grodsky, B. Zhang, A. Busalacchi, and W. Chen. “ENSO Impact on Surface Radiative Fluxes as Observed from Space: ENSO IMPACT ON SURFACE RADIATIVE FLUXES.” Journal of Geophysical Research: Oceans 122, no. 10 (October 2017): 7880–96. https://doi.org/10.1002/2017JC012900.

EDITED 5/22:

A possible source of the fine structure via ocean currents, from https://earth.nullschool.net/#current/ocean/surface/currents/orthographic=-158.02,2.78,819

![nullschool](https://imagizer.imageshack.com/img924/8424/TjDW0v.png)

If the data is available, a Hovmoller diagram could be created from a time-series sequence