A stochastic model with a low-frequency amplification feedback for the stratospheric northern annular mode

Abstract

We consider three indices to measure the polar stratospheric mass and stratospheric meridional mass circulation variability: anomalies of (1) total mass in the polar stratospheric cap (60–90°N, above the isentropic surface 400 K, PSM), (2) total adiabatic mass transport across 60°N into the polar stratosphere cap (AMT), (3) and total diabetic mass transport across 400 K from the polar stratosphere into the troposphere below (DMT). It is confirmed that the negative stratospheric Northern Annular Mode (NAM) and PSM indices have a nearly indistinguishable temporal evolution and a similar red-noise-like spectrum with a de-correlation timescale of 4 weeks. This enables us to examine the low-frequency nature of the NAM in the framework of mass circulation, namely, $$\frac{d}{{dt}}{\text{PSM}}={\text{AMT}} - {\text{DMT}}$$ . The DMT index tends to be positively correlated with the PSM with a red-noise-like spectrum, representing slow radiative cooling processes giving rise to a de-correlation timescale of 3–4 weeks. The AMT is nearly perfectly correlated with the day-to-day tendency of PSM, reflecting a robust quasi 90° out-of-phase relation between the AMT and PSM at all frequency bands. Variations of vertically westward tilting of planetary waves contribute mainly to the high-frequency portion of AMT. It is the wave amplitude’s slow vacillation that plays the leading role in the quasi 90° out-of-phase relation between the AMT and PSM. Based on this, we put forward a linear stochastic model with a low-frequency amplification feedback from low-frequency amplitude vacillations of planetary waves to explain the amplified low-frequency response of PSM/NAM to a stochastic forcing from the westward tilting variability.