Response to reviewers 3 and 4: (There were no reviewers 1 and 2.) Reviewer #3: (Pierre Lermusaux) 1. Thanks for all the many suggestion for additional references. A through review of existing literature that encompasses alternative methodologies for quantitatively dealing with uncertainties would be highly useful, but it is beyond the scope of this work. However we did add 12 references to the text, which should better place this work within the context of what has previously been done. 2. Additional discussion of the computational costs has been added in the next to last paragraph of the Introduction. 3. Actually, the issue of uncertainty transients is not very deep and needs no further discussion. It is a consequence of the way we prepared our ensemble. Each member started from exactly the same initial conditions, so there was no uncertainty in the model state at t=0. As the uncertainty is introduced at the boundary, after one time step it is confined to grid cells adjacent to the boundary; after two, the nextcells, etc. Until sufficient time has passed for the differences in boundary conditions to pass through the Gulf and from cell to cell and back, there is a memory of the common initial conditions. This is clearly seen in the figures and noted in the text. Title: Thanks for the suggestion. The title has been changed. L10. Rephrased. L13. Cited in footnote 2. L24-30 and pages 2-3. Citations added in footnote 4. L34-36. Yes, the "curse of dimensionality" is universal. It refers to the fact that uncertainties of N parameters requires the exploration of an N-dimensional space. For example, your own work has recognized the need for reducing the dimensionality and has limited the analysis to an error subspace. L40-43. We use the phrase "dynamically evolving uncertainties" to convey your intent of "prediction of uncertainty". L48. "Approximation" leads to "reduced rank". L50-65. Comparison is beyond the scope of this paper. L69-77. We feel that other readers should be able to follow. L83-85. Other treatments were for steady boundary conditions. Ours vary in time. Footnote 7. Because it is a side issue included as supplementary and is not essential to the main line of discussion. L118. Fixed. L147-151. As the expansion is not truncated, no truncation-error term is needed. L147-151. Text is clear. x_0 and x_1 are the center and spread of possible inputs. y_k are coefficients of the polynomial expansion for the output. y_0 is the mean of the output, but the spread involves all the y_k. L163. No. There are no subsections, only sections. This section is on the method and this is a central aspect of the method. L205-212. No. This is a bridge paragraph to the next section. L246-266. Rewritten for clarity. L226-273. That might be done in a review paper, but it isn't needed here. L366-375. Yes, "output" refers to a single number. The paragraph has been revised for clarity. L405-407. Yes. The standard deviation depends on the extent of the uncertainty of the inflow. If the inflow is know fairly well, the uncertainty of the position of the Loop Current will be small, so standard deviations characterizing uncertainty of surface elevation in its vicinity should also be relatively small, even though they might be larger than in other parts of the Gulf. As we chose alpha=1, we considered the case where the uncertainty of the inflow was comparable to its climatic range, and the standard deviations were consequently quite high. Text has been updated. L405-407. Unfortunately, considering smaller values of alpha would require repeating the computational expensive simulations. Exploring uncertainty as a function of alpha would be interesting, but it is not crucial for our purpose of illustrating how the method works. L425-436. Beyond the scope of this paper. L443. Figs 9 and 10 have been improved and the text describing then has been revised. L493-501 Acoustic aand shallow water work has been cited earlier. L515-526. A large ensemble is NOT available. If it were, it most likely would not correspond to quadrature points, so someother approach would be needed for evaluation the coefficients of the polynomial expansions. How to exploiting existing ensembles is an interesting question. Generally allensemble members are regarded as being equally likely, so means are computed as unweighted averages. This is not the case for the quadrature ensemble, and such averages would give different results. L527-539. As explained above, uncertainty transients are really no a big deal. L547-565. Spasis and Lermusiaux is mentioned earlier. L9. We feel that "information about" is a better than "information on". L171. Doesn't fit the text. L243. Fixed. ____________________________________________________________________ Reviewer #4: 1. The smooth pdf's for the outputs result from the combination of the assumed smooth pdf's for the inputs and the polynomial interpolation of the output. The paper tries to make it clear that the nature of the input uncertainty is generally poorly known and that there is no guarantee that polynomial interpolation provides an adequate description of the response. For situations where small changes in the inputs lead to qualitatively different outputs, bifurcations for example, polynomial interpolation is likely not to work. 2. Agreed. Very misleading! And not informative. Unfortunately there is an established community that uses this terminology. To encourage migration from this usage, the word "chaos" no longers appears in the title, and its use in the body of the paper has been minimized. However, to maintain continuity with existing usage, we felt that it should not be completely purged from the paper. 3. The coefficient alpha relates the spread of likely boundary conditions about the favorite to the spread of the boundary climatology about the climatological mean. This has been clarified and the value alpha = 1 is mentioned at the point where alpha is introduced. 4. As the decomposition of the climatology is a singular-value decomposition, the discussion naturally requires mention of singular values. However, as you suggested, there is now a discussion of the fraction of variance climatological explained by the first two modes. Your comment provoked a closer look at figure 2; the axis, which had been incorrectly labeled as eigenvalue, now is properly labeled as singular value. In addition the equations and text were revised to indicate singular values as lambda_k, dropping the awkward square roots. 5. Given the enriching details desired by referee #3, we felt that footnote 16 would be helpful to many readers. Of course, it can easily be dropped. 6. See point 4 above. 7. One year. The climatological seasonal cycle over one year was decomposed and orthogonality of the resulting principal components indicates lack of temporal correlation. 8. A physical interpolation of the EOF's is not obvious. In any case, it would require examination of their other components (T, S, etc.) which are not illustrated. As physical interpretations are often problematic and add nothing to the message of the paper, they were omitted. 9. Bottom topography plots have been omitted. 10. The boundary plots now show depth coordinates. Values are indicated by colors within grid cells bounded above and below by layer interfaces. Because most variability is confined to the upper ocean where the model has more and thinner layers, only the upper 800 meters are shown. 11. The index K indicating the maximum degree of polynomials retained in the expansions has now been indicated as K=6 in the discussion prior to equation (13). In addition a clarifying footnote has been added. 12. It may be possible that Monte Carlo might offer an advantage for propagating the uncertainty of large number of inputs. That is not something we feel we are able to address.