We thank all the referees for their constructive comments and valuable feedback. We appreciate the positive appraisals and the recommendation to revise our submitted manuscript. Below are our short responses to the major comments of each reviewer, outlining how we intend to address them in our revised manuscript. The revised manuscript, along with a detailed response to both major and minor comments of each reviewer, will be uploaded at a later date.

Referee #1

1. We will present a clearer motivation for associating extreme rainfall with the three tropical weather system categories rather than with the equatorial waves or the MJO. Our main goal is to define a set of synoptic weather systems in the tropics in a similar manner to those in the extratropics, that is, on a scale between the planetary-scale "background waves" and the smaller mesoscale thunderstorms. We believe our method provides a useful decomposition of extreme rainfall, complementary to those based on the wave spectrum.
2. We will make the sentence clearer in stating the fact that certain moisture modes like the MJO do not appear in any dry atmosphere models, while others like moist ER waves are just a modification of the dry version.
3. While the reviewer is correct that we only use zonal propagation in our filtering, meridionally propagating signals will nevertheless be included at a phase speed close to zero. However, this is also true of traditional equatorial wave analysis. Including meridional propagation in our framework would involve the development of a fundamentally new methodology, which we postpone to future work. However, we will further discuss the limitations of using only zonal propagation in our revised manuscript.
4. We will show that the displacement of the convective region towards the poleward flow of the cyclonic vortex is one of the "general" characteristics of the off-equatorial moisture modes, although it may not be universally true for ER waves, because our moisture modes are not only driven by the ER waves, but also other slowly-propagating waves and the interaction among them. We will also show a decomposition of our Eq. (4) to determine which term contributes the most to the deviation from nonlinear balance evident in the faster-propagating systems.
5. We will show that this wave-like appearance is related to how we filter the OLR anomaly signals into moisture modes, mixed systems, and IG waves.