This paper presents a method for increasing the ensemble size during the assimilation step of ensemble DA. The method is interesting and the results show that it can improve performance. I have some suggestions for improving the clarity of the discussion though.

Major Comments:

Section 3 could be improved. It attempts to show how PECE-GC could be valuable across a wide range of ensemble DA methods and gives 3 mechanisms whereby PECE-GC could improve performance. I found the whole section to be a bit too vague though. It might help to pick a few specific algorithms and show how PECE-GC could improve each one. For example, the RHF uses a piecewise-linear approximation of the likelihood function; PECE-GC improves this representation. As another example, many EnKFs assume joint Gaussianity of the state and observation vectors, and then approximate the means and cross-covariances of this distribution using an ensemble. If the prior is accurately represented then PECE-GC leads to improved estimates of these means and covariances.

Some things I found confusing about section 3: It starts with two-step ensemble DA, but not all EnKFs operate in a two-step manner. The three mechanisms seem to overlap; e.g. the likelihood function (3.1) is related to the observation operator (3.2), and to observation space ensemble statistics (3.3). Section 4 explains performance in light of these 3 mechanisms, so I also found it confusing.

Minor Comments:

'Gaussian copula' is in the name of the method, but the concept of a Gaussian copula is not explained until section 5.

Line 15/16: I struggle to see how 'small forecast ensembles result in limited representation of observation likelihood functions' is a distinct concept from sampling errors. PECE-GC seems to me to be a way to mitigate certain kinds of sampling errors.

Lines 33/34: It might be more accurate to say that ensemble modulation preserves the first two moments of the ensemble, not that it assumes Gaussian statistics.

Line 218: I think 0.05 model time units is usually interpreted as 6 hours, not 1 hour.

Line 259: The fifth-order GC function is rational, not polynomial.

Line 272: Missing citation for RTPS.

I do not understand why PECE-GC has any impact on the performance of the stochastic EnKF with linear obs. With linear obs the stochastic EnKF update is entirely controlled by the ensemble covariance B, and PECE-GC does not change B (except in the PR configuration).

Line 402: 1,000,00 should probably be 1,000,000?

The GC part of PECE-GC seems to only have been used in the PR configuration, is that right? The EAKF, EnKF, and RHF all use PECE without the GC part?

Please see the attached.