In this article the authors explore the use of ocean dynamic persistence for seasonal sea level forecasting on the US east coast. They show that ocean dynamic persistence, based on ECCO-based initialized ocean model forecasts forced with climatological atmospheric forcing show substantial improvements in forecasts of monthly-mean sea level anomalies beyond the first lead month over damped persistence or a full-feature coupled seasonal forecast model.

This is an excellent article that presents a novel approach to ocean forecasting that holds potential for addressing poor seasonal forecasting of sea level on the US east coast. The methods and analysis used are robust, and the results will be of wide interest and applicability. I particularly appreciated the concise presentation without unnecessary complicating detail. I have a series of minor comments that should be considered before publication.

General comments:

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- Can the authors please clarify whether the monthly climatological forcing used in the ECCO dynamical persistence forecasts is based on flux-forcing (e.g. specified wind stresses and heat fluxes) or bulk-forcing (fluxes computed from specified atmospheric state; wind speed, air temperature etc.)? Frederikse et al. use flux-forcing. I presume flux-forcing is used, as bulk forcing based on monthly-averaged atmospheric state will contain significant biases due to non-linearities in the bulk formula (e.g. quadratic wind stress dependence on wind speed). This question is also relevant to whether ocean-sourced dynamical anomalies are damped by the atmospheric forcing (e.g. the statement at line 306). If bulk forcing is used then, for example, ocean SST anomalies will be overly damped toward the climatology, which would then also impact sea level anomalies. On the other hand, with flux forcing there is no damping of ocean anomalies whatsoever, which is also somewhat unrealistic.

- The authors emphasize that the dynamical persistence forecasts suffer from weak variability, and that if this could be fixed it would improve their skill. To me, this is not an issue with the forecast itself, but a property of the system. The weak variance of the dynamical persistence forecast suggests that the seasonally-predictable signal is a small fraction of the total signal. Unlike an ensemble prediction from a full-feature seasonal forecast model, which includes an ensemble spread as well as an ensemble mean, the ocean-dynamic persistence forecast is designed to only capture the seasonally-predictable signal. Thus this feature could be considered an advantage, not a drawback. I would suggest some reframing of the text to make this point clear (e.g. lines 276-278, 282, 337). This point is also relevant to how the forecasts can be utilized in high-tide flooding outlooks (e.g. lines 336-338). It seems clear that when including predictions for monthly-mean sea level anomalies in these high-tide flooding outlooks, the stochastic component of the monthly-mean sea level still needs to be retained for the purposes of computing, for example, probabilities of threshold exceedance.

Specific comments:

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- Lines 33-34; check the grammar. "yet to be" -> "been".

- Line 41; "understanding" -> "forecast"?

- Line 45; suggest adding "seasonal" or "monthly" in front of sea level anomalies.

- Line 58; "seems reasonable to expect the possibility of achieving" - this is somewhat convoluted. Suggest a rewrite.

- Line 60: For non-US readers, can you clarify what is meant by "Southeast coast"? I presume this is mainly referring to the east coast of Florida, not in the Gulf?

- Line 61; "likely to continue to" -> again, suggest a rewrite, their influence is not trending.

- Lines 67-74; it may be worth pointing out that Frederikse et al.'s approach is distinct from the approach taken here. They use ECCO adjoint sensitivities, a linear-combinations-of-forcings etc. and thus their approach is not ocean dynamical persistence in the sense examined in this paper. Otherwise, readers may be confused that this paper is just a generalization of that study to the whole East and Gulf coasts.

- Lines 86-90: Please mention whether or not detiding is performed on the tide gauge data prior to the computation of monthly means (it shouldn't make much difference).

- Lines 161-167: It seems to me that this is most likely associated with the low-resolution of the ECCO model (and SEAS5). I would expect that a well-initialized (altimetry assimilating) high-resolution eddy-resolving ocean model making a forecast in dynamical-persistence mode would be able to beat simple damped persistence in the first month in strongly ocean-internal driven dynamics eddying regions. This would be worth mentioning here (i.e. it's specifically *this* ocean dynamical persistence forecast that doesn't perform well here, not all ocean dynamical persistence forecasts).

- Lines 183: This statement is a bit misleading, since it is difficult to see what is happening with RMSE on the coast given the weak variability and colorbar choice. There is no obvious decay in RMSE with lead time in these plots. Perhaps remove the statement? The same thing goes for the reference to Fig. 2 at line 191.

- Lines 220-223: There is a positive ACC difference in Fig. 4c for a few sites around Delaware, although the differences are not significant. So I'm not sure these statements are completely true.

- Line 306-307: As mentioned above, I'm not sure I agree that the dissipation of these anomalies is due to the climatological forcing. Initial ocean perturbations will dissipate over time due to internal ocean dynamics (planetary wave generation and propagation, friction etc.). The reason that the variability is much weaker is just because you have removed a strong source of variability (the weather/non-climatological atmospheric forcing).

- Lines 318-319: Zhu et al. 2024 (cited in the introduction) computed the contribution of remote forcings via wave propagation to sea level anomalies along the east coast, including at seasonal time-scales (e.g. see their Fig. 3). Thus, a more definite statement could likely be made here. Comparison to their results could yield some insights.

- Lines 324-326: I wonder whether the relatively low number of ensemble members in the SEAS5 hindcast considered here means that stochastic, non-predictable processes still have a significant impact on the SEAS5 ensemble mean? See general comment #2 above.

General comments

This study evaluates the seasonal forecast by statistical and model forecast methods. Among the three forecasts, ocean inertia in the ECCO forecast seems to outperform the other two at lead time of four months. It is interesting but not surprised to see the importance of model initial conditions and ocean inertia. One important unanswered question is why the climate model forecast (SEAS5) including both ocean initial conditions, ocean dynamics and full atmospheric forcing has less predictability than the ECCO forecast without atmospheric forcing. It could be better to have seasonal forecasts with ECCO that include both inertial condition and atmospheric forcing to answer the above question.If there is no such ECCO forecast, it is better to think about some method to illustrate how atmospheric forcing act along with or counteract ocean inertia in the ECCO or SEAS5 model.  

Specific comments

One concern is how well ECCO or climate model simulates coastal sea level at the tide gauges along the coast compared to observations, even though the authors shows evaluation at four locations in Fig. 5. For example, both ECCO and SEAS5 have low-resolution so that they may not be able to resolve the coastal sea level variability. It’s not a good idea to use one model that cannot simulate the coastal sea level very well.

Atmospheric forcing cannot be neglected in the sea level forecast. Is there ECCO seasonal forecast that includes atmospheric forcing so that you can compare the roles of atmospheric forcing with ocean inertia? If observed wind forcing make the forecast worse, the bad forecast might be related to some deficiencies of numerical models.

Line 171-172. Comparing Fig. 1a with Fig. 1e seems not supportive for this statement. Pointing out the specific region where the climate model has better performance might be helpful.

Line 256-258. Because sea level in the targeted month is derived from previous months, “damped persistence of ECCO or observation” somehow considered all processes including ocean dynamics but in a statistical way.

Fig. 6 might also suggest that ECCO data with full forcing (damped ECCO) cannot capture coastal sea level very well. Are there other model forecast results with good performances in simulating coastal sea level?

Line 270-271. The weak variability in this model’s predicted monthly sea level anomalies is expected because atmospheric forcing except the climatology is included in the ECCO forecast and ECCO has coarse resolution to resolve coastal sea level. Again, some numerical models have difficulty to simulate coastal sea level variability.

Line 301-304. The differences between climate models might also contribute to the forecast differences.