Moisture Decomposition With Normal Modes in Global Data: Balanced and Unbalanced Components

Abstract

Decompositions with normal modes have been useful for numerous purposes, such as theoretical understanding of balanced and unbalanced circulations, and applications to data assimilation. However, normal mode decompositions have typically been formulated for dry dynamics without moisture. Here, a normal mode decomposition is investigated, including an eigenmode decomposition of moisture, on the sphere. One main aim is to investigate how much moisture is associated with each of the different eigenmodes, for different latitudes and different spatial scales. Another main aim is to investigate the additional moist eigenmode that is not present in a dry system. The moist decomposition was applied to ERA5 reanalysis data for August 2018. The results of this decomposition suggest that, on sub‐synoptic scales, the balanced component of moisture has the largest contribution to the variance, in contrast to velocity and temperature which are known to be dominated by unbalanced inertio‐gravity wave mode contributions on sub‐synoptic scales. Furthermore, on sub‐synoptic scales, among the two balanced eigenmodes of moisture (Rossby/vortical mode and slow moist eigenmode), it is the slow moist eigenmode that has the dominant contribution. Lastly, a case study is examined of an extreme rainfall event in the extratropics over North America, and the moisture anomalies on synoptic scales have appreciable contributions from both the Rossby/vortical mode and slow moist eigenmode. As other topics, a possible extension is discussed on including cloud latent heating into the eigenmode definitions in future work, and the vertical basis functions for moisture are connected with a Sturm–Liouville problem and orthogonality condition.