Fig. 9: Shifted-mean SST flow formulation.

a Hovmoller of SST centered on WPEP, i.e. \([{\phi }_{{\chi }^{{\prime} }(t)}\cdot T](x,t)=T[x+{\chi }^{{\prime} }(t),t]\), as a function of time and position x (deg E). White areas are out of bounds (with \(x+{\chi }^{{\prime} }(t)\) outside of the equatorial Pacific 120° E–80° W). Centered SST within bounds is roughly constant with time. b Same as a but reordered by quantiles of WPEP. With this representation, it is even clearer that centered SST is roughly constant with time, thus approximable by \(S(x)=\overline{[{\phi }_{{\chi }^{{\prime} }(t)}\cdot T](x,t)}\) (omitting out-of-bounds areas in the averaging). c Hovmoller of shifted mean SST flow \(\widetilde{T}(x,t)=[{\phi }_{-{\chi }^{{\prime} }(t)}\cdot S](x,t)=S[x-{\chi }^{{\prime} }(t)]\).