Please see the attached report.

The manuscript presents an approach of increasing ensemble size during the analysis step of data assimilation by generating pseudo-members orthogonal to the original ensemble, and explores how this affects the data assimilation system on a Lorenz 40-variable toy problem.

Major comments and questions:

1. It would be beneficial to conduct more experiments and include their results and analysis of the results in the manuscript to demonstrate how the use of this method affects data assimilation. In particular, I would recommend exploring how varying localization, observation density and observation errors affect the results, since all of those parameters influence the “effective observation dimension” (the degrees of freedom that are required for assimilating observations (Kirchgessner et al, 2014)).
2. The results presented in Figure 6 suggest a bigger benefit from using N+1=7 ensemble members in DA vs using N ensemble members + 1 pseudomember. While I agree that using pseudomember vs ensemble member saves on running an ensemble forecast, the savings are only N/(N+1) for the ensemble forecast runs. It would be interesting to see if there are benefits of using more than one or two ensemble pseudomembers so the savings on not running extra ensemble forecasts may be more justifiable.
3. Experiments in section 3.2 include analysis (in Figure 5) of results when IESV1 and EMV are used with and without orthogonalization. Please include description of what the difference between those are.
4. Please describe what “average RSV” means for the experiments in section 3.2 (Figure 5). From Figure 5 it appears that results with “average RSV” are similar to results with orthogonal IESV1. It may be good to include the statistical significance of the differences between the experiments and also discuss this particular result.

Minor comments:

1. Figure 5: the gray line is very hard to see, I suggest changing the color.
2. Figure 3c: it is very hard to see the distinction between different experiments, it may be good to include statistics of the error differences.