Dear Daan,

Both referees are now generally satisfied with your revised manuscript, although referee #2 asks that you make some additional revisions before the manuscript can be accepted for publication. The referee's comments are detailed below.

Regards
Andrew Moore

Review of: “Multidecadal Polynya Formation in a Conceptual (Box) Model”, first revision, by Boot, van Westen, and Dijkstra.

In this paper the authors explore polynya behavior in a conceptual model. In particular, they focus on the role of heat accumulation at depth in preconditioning the area for deep convection. I think the authors have done a good job in addressing my concerns. That said, there are still a few minor issues left, which, when addressed, would make this paper acceptable for publication.

First, the authors now make the distinction between MRPs and WSPs. I’m a bit surprised that the authors present the box model as model for MRPs, whereas in my mind it is more appropriately applied to WSPs. WSPs are thought to be associated with convection due to large-scale instabilities of the water column, as modeled here. In contrast, MRPs appear to have a significant dynamic driver, namely the Taylor cap dynamics. It would be good to understand why the authors apply this model to MRPs, but not to WSPs. Besides, Martinson et al., Dufour et al. all consider WSPs.

Also, there are still a few issues with the set of equations. For starters, Eq. 5b is missing the exchange term with the layer below. Second, there is still a problem with the freshwater flux. I now realize that my previous comment about F was ignoring a bigger issue with how the term F is treated and described; I realize that Martinson et al. (1981) are treating this term rather loosely, but it would be good to be consistent here. The simplest fix is to simply replace F by F S_0 in Eqs. 2b, 3b, 4b and 5b; as well as in 4c and 5c. Martinson et al. use a conversion factor of 35 g/kg. In that way, F still represent the freshwater flux (positive if into the ocean), with units of m/s (or similar); while –F S_0 represents the associated virtual salt flux. Please verify that the code is correct, and that these issues are addressed in the manuscript.

In the sections on p. 6 please be more consistent in the terminology: l. 12, ocean atmosphere heat flux is given by Q_ia --without the terms in the denominator, which convert the flux to a temperature change. Similarly in ll. 15, 17, 19, 22, 24, and 25.