Dear authors,

Reviewer 1 has now commented on the revised manuscript (see below), recommending acceptance for publication pending final minor corrections. Pending your response to the comments listed below, I can make a final decision, which should be a straightforward acceptance.

Best Regards,
Bob Marsh


Reviewer 1 report on revised manuscript:

The authors have done a good job addressing my initial comments and concerns. I recommend publication subject to the following minor revisions:

(1) p3, line: "sensitivity of the ocean circulation" - sensitivity to what?

(2) p4, line 3 and 4: This sentence is still awkward. How about something like "We use ROMS to simulate the ocean circulation off the south eastern coast of Australia."

(3) p7, line 18: Reword as "...variational calculus to solve for increments in model..."

(4) p7, line 21: "normalized deviations" - of what?

(5) Equations 1 and 2: In equation (1), t_{i-1} and t_i are used to denote a general time interval, while in equation (2) and beyond the notation is changed to t_0 and t_i. The use of t_i for two different times is confusing - this should be fixed. I assume that t_0 is the initial time for each data assimilation cycle? This should be stated in the text.

(6) p9, lines 7-9: You imply in the text, and in your reply to the other reviewer, that because 4D-Var employs the model equations to constrain the circulation increments they are "consistent with the dynamics of the circulation." This will not generally be true for the circulation estimate at initial time, t_0. Unless dynamical balance (eg quasi-geostrophic balance) is explicitly imposed as a constraint at t_0, the initial condition increments can be quite unbalanced, leading to subsequent initialisation shocks and gravity wave generation. You should clarify this statement, or remove it.

(7) p10, line 1: Reword as "THOSE 4 days after".

(8) p17, line 21: It is stated here that gamma>1 represents an under-estimate of the error covariances, while gamma<1 represents an over-estimate of the error covariances. This is not true in general. It would appear to be so for a system with one observations and a single grid point, but it is not possible to make such a unique claim about the background and observation error covariances based on the ratio of the cost function to its theoretical value for large dimensional systems. This statement should be removed. I suggest that you consult excellent discussions in the published literature of J vs Nobs/2 by Talagrand, Bennett and others to clarify this point.

(9) p22, lines 26 and 27: To say that the system has been "rigorously tuned" through a "careful specification of the prior observation and model background uncertainties" is a big stretch and an overstatement. The covariances R and P are not even likely to be even remotely correct (i.e. you have assumed isotropic, homogeneous, univariate statistics for P, and uncorrelated errors for R). It is very likely that the background error statistics will be highly isotropic and non-homogeneous, and multivariate for the complicated flows that exist in this region. Furthermore, satellite observation errors will be correlated so R will not be a diagonal matrix. You need to tone down this sentence - you are doing well, but probably not because you have nailed down the error statistics correctly as you imply here.

(10) p22, line 28: Change "match with" to "fit to"

(11) p22, line 32: Reword as "WIDE variety"

Dear authors,

I am satisfied that you have fully addressed all comments of Reviewer 1 on the revised manuscript, and I appreciate the effort that you have made to update your results in light of erroneous wind forcing. Your paper is now accepted for publication in GMD - congratulations!

Best Regards,
Bob Marsh