With the correct intermediate manifold, those of AMO and PDO are nearly indistinguishable. The ocean response is subtle — AMO has the basin-wide slow response, whereas PDO doesn’t, and both have a similar LTE modulation as shown in the middle-right panel below.

This is not a teleconnection but a common-mode forcing manifold each with a distinct response.

https://github.com/pukpr/gem-lte-core – experiments/Feb2026

All the quads in the global SST grid follow from these two as seeded values and with NINO4, which seems to have more of a split winding character than PDO – see experiments/Oct2026_layer_ir

The essential fitting equation is the following, where $F_\theta$ is the integrated annual impulse response to the calibrated LOD tidal forcing¹. The term $\beta$ is a spherical fitted sinusoidal phase correction. The winding $k_f$ is small and represents the basin friction layer. For AMO, the sum is essentially a single $j=1$ winding and with ENSO, a second winding emerges so $j = 1…2$.

Model = $\sum_{j}a_j \sin(2\pi k_j \cdot A \sin (2\pi k_f (F_\theta + \beta(F_\theta)) + \phi_f) +\phi_j)$

where

$\beta(F_\theta) = B sin(2\pi k_\beta F_\theta +\phi_\beta)$

This cascaded sinusoidal modulation is not complex nor computational-intensive in comparison to a GCM

Probably doesn't but a full CFD climate simulation (GCM) using the fastest supercomputer takes the power of keeping a 737 flying at altitude. That's an exaflop of computing.

— Puͣkiͧte̍ (@pukite.com) 2026-10-04T21:32:14.188Z

And an empirical neural network representation, which features an analogous set of convolutional layers, would be impossible to reverse engineer.

Global SST

The variations observed in global SST are largely accounted for by the ENSO, AMO, and PDO indices. A linear trend, corresponding to AGW, is needed to model global SST below, of which the model is a composite of all the modeled quads in the Kaplan extend SST V2.

References

1. P. Pukite, D. Challou, and D.Coyne, Mathematical Geoenergy, (Wiley, 2018), https://agupubs.onlinelibrary.wiley.com/doi/book/10.1002/9781119434351 ↩︎ ↩︎