Resolve the projected finite-band production residual

Determine the projected finite-band production residual in the analyzed surface-quasigeostrophic simulations sufficiently to establish whether the conditional production closure and the resulting logistic coefficient comparison are valid.

Background

The exact full-field error budget has a vanishing conservative error self-interaction, but projection onto a finite spectral band introduces interband-transfer leakage and other residual terms. The paper defines a normalized production diagnostic and states that the logistic reduction requires its agreement with the remaining covariance fraction after all relevant terms are controlled.

In the reported SQG experiments, the projection residual was not resolved. Consequently, the prespecified coefficient comparison cannot yet be interpreted as a test of the logistic spectral reduction.