Intraseasonal atmospheric variability under climate trends

The paper convincingly documents—numerically and with clear definitions—that at the same instantaneous forcing F=1.99 the autonomous forward attractor can be the disconnected union of a fixed point and a limit cycle, whereas the July snapshot under seasonal forcing plus a negative trend shows only a thickened loop (no fixed point) . It also sets out the pullback/snapshot framework and notes forward–pullback equivalence under periodic forcing via uniform attractors , and it provides a standard dissipativity calculation for the L84 system (Appendix B) . However, the paper stops short of a rigorous theorem establishing why the fixed point is excluded from the snapshot in the combined seasonal+trend case; the authors explicitly characterize their result as an “extreme effect” illustrated numerically and acknowledge the need for more rigorous examination . The model’s solution advances a plausible connectedness-based proof idea (selecting an interval [s1,t0) with a unique limit cycle so that A(t0)=ϕ(t0,s1)A(s1) remains connected), but it does not fully justify critical hypotheses (existence of such an interval for the frozen system, continuity/connectedness of PBA sections under the assumed forcing, and the precise transfer from frozen-system uniqueness to the nonautonomous PBA). Hence both the paper and the model are incomplete in rigor, even though they agree on the qualitative phenomenon and its mechanisms.