Manuscript 2007JD009041 by Feldmanet al.
Short Title: On the Information Content of the Thermal Infrared Cooling Rate Profile
Dr. John Austin
Editor
JGR-Atmospheres
Dear Dr. Austin,
We thank the referees for their detailed comments and suggestions regarding our submission. All the points are well taken, and we have made revisions accordingly. With respect to the grammatical errors in the original manuscript, we would like to express a sincere apology and note that care has been taken in the revised version to make the paper read easily. We address the points individually by first reproducing the referee’s questions/commentsin italics, followed by our response.
Thanks for your consideration of this submission,
Daniel Feldman ( ; 626-395-6447)
Responses to Reviewer 1 Comments:
4.a.
The objective of the paper is not established as it might be. What is the message that the reader should take from the paper? This should be made much clearer. Is this interesting approach being proposed as a general method for evaluating the contribution of satellite instruments to the cooling rate profile problem? Is this the best way to achieve this objective? Why was TES included here? This is a chemistry instrument. IASI, an NWP instrument, would have been a much more appropriate choice. Is it too late?
Response:
There are several messages that we hope the reader can take away from this paper. The end of the introduction and the conclusion have been rewritten to convey the messages of the paper more clearly
Given the work of Liou and Xue [1988] and Feldman et al [2006], we do not feel that standard retrieval techniques are necessarily the most optimal for cooling rate analysis. That is, the importance of certain standard retrieval quantities (e g. surface skin temperature) is considered only insofar as the a priori constraint dictates their level of uncertainty. The importance of that quantity towards constraining the cooling rate (for the case of the skin temperature, constraining boundary layer cooling and O3 10 µm band IR heating in the upper troposphere and lower stratosphere) is not cons/idered whatsoever in standard retrievals.
TES was included here becauseit is useful to compare with AIRS because the 2 instruments have similar spectral coverage and TES has much superior spectral resolution though inferior channel noise. The trade-off of these spectrometer characteristics is interesting to explore in the context of cooling rate profile information. In response to the reviewer’s recommendation, the IASI instrument has also been included in the instrument comparison and has an entry in Table 1.
4.b.
The method is totally dependent on the linearity of the problem. Cooling rates are obtained from the flux divergence and with the maximum contribution coming from the transition region from full opacity to transparency. This is the region that includes the highest nonlinearity. This is evidently seen in comparing Figures 6A and 6B. The magnitude of the diagonal regime at 400 mb is a factor of two greater using the system that depends on the propagation analysis. Why isn’t this commented upon in the text? This whole issue of linearity and Gaussian statistics needs to be addressed properly- presumably in the context of the objective of the paper.
Response:
The reviewer’s comments are well-taken and we have addressed the issues of nonlinearity in the text (Section 3, lines 341-356). In addition, we have included an extra figure (Fig. 6) in order to illustrate the linearity in the Jacobians which shows that in clear-sky scenes, even fairly large uncertainties in the cooling rate calculation inputs can be tolerated.
The discrepancies between the sample covariance matrix from the ERA-40 data and the covariance matrix calculated from error propagation (formerly Fig. (6a) and (6b)) have been addressed in more detail (lines 385-397). The new figures (now Figure 8a, 8b) show much better agreement with each other which implies that the pdfs of the input variables need to be considered carefully.
Several paragraphs were added to Section 3 regarding the assumptions of linearity and Gaussian statistics and we expect that the paper should bring more clarity to these issues now.
4.c.
The entire paper requires more explication. In addition to providing graphs, e.g. cooling rate ‘errors’, and a rigorous interpretation of each element is required. I don’t believe that Figures 4B and 4C are commented upon in the text. Doesn’t Figure 4B, interpreted as ‘cooling rate error’, strike the authors as unrealistic. We know in actual implementations, e.g. ecmwf, that we are doing much better than this- granted that sondes may play a role in this regard.
Response:
Many sections have been updated in the revised manuscript regarding the significance of cooling rate analysis and why it is important to consider how remote sensing data imparts information to the cooling rate profile. To this end, several sentences have been added to clarify the messages that Figs. (4a-d) are meant to convey (lines 269-295).
4.d.
Not enough care has been exercised in putting the paper together: some plot titles are not appropriate; tick marks are either too light or non-existent (e.g. Fig. 6), etc. There are a number of grammatical and typographical errors that need to be fixed.
Response:
The revised manuscript has been modified significantly. Plot titles have been changed so that each figure’s purpose can be more easily understood. In response to the comment that the tick marks are too light or non-existent, we have changed the figures so that there are more major tick marks to orient the reader and the minor tick marks were made larger. The revised manuscript has been proofread several times and we hope that corrections are acceptable to the reviewer.
5.
Acceptable. It is of some interest that ERA-40 used RRTM to generate the cooling rates. Is this of significance in the current context?
Response:
While there are some differences between fast radiative transfer codes, we chose to work with RRTM because it is standard, well-documented and reasonably accurate with respect to line-by-line calculations from LBLRTM. Of course, it is also implemented in the ERA-40 reanalysis so that our calculations faithfully reflect the internally-calculated (though not explicitly posted) cooling rates from that dataset.
7.
The authors should justify the inclusion of the Appendix. It is well written but isn’t this material generally known and available?
Response:
Following the suggestion, the appendix has been stricken from the revised version of the paper. However, given the comments of several reviewers, a reference to the descriptions of heating/cooling rate calculations in the textbooks of Goody and Yung (1989) and Liou (2002) has been included in place of the appendix.
11.
94 its should be the
Response:
The correction has been made.
119 nu3 covers 985-1085; nu1 covers 1070- 1180
Response:
Respectfully, we refer to Goody and Yung (1989) in Chapter 5, Section 6.2 which describes the significant O3 bands:“An unusual feature of the ozone molecule is that the ν 1 and ν2 fundamentals, at 1103.14 and 700.93 cm-1, respectively, are very weak compared to ν3 at 1042.06 cm-1, weaker in fact than the combination band ν1 + ν3 at 2110.79 cm-1. In addition, ν1 is very close to ν3and strong resonances make it difficult to assign line positions and to calculate good line intensities.” Therefore, while ν1 transitions contribute to the observed features, the ν3 are much more prominent.
126 Is a priori and uncertainty really the appropriate perspective here. Why not simply variability?
Response:
The sentence has been changed (lines 141-144, revised manuscript).
130 Figure 2 would be better in color
Response:
The 3 panels of Figure (2) have been rendered in color per the reviewer’s recommendation.
138-140 This whole issue of Gaussian behavior needs expansion and figures to support the authors’ claims.
Response:
A more detailed look at the issue of Gaussian statistics has been included in the revised manuscript (see Section 3,lines 358-370). For the ERA-40 data, Fig. (7) has been included to show an example of a distribution of T, H2O, O3, and cooling rate profile.
170 Var(x_i,x_j) should be Var(x_i)
Response:
The correction has been made.
177 del_f needs parens.
Response:
The correction has been made.
186 profile calculations at each level
Response:
The correction has been made.
198 right bracket
Response:
The correction has been made.
211 confound?
Response:
The sentence has been changed (lines 341-344, revised manuscript).
218 The preferred reference for the AFGL atmospheres is
Anderson, G.P., S.A. Clough, F.X. Kneizys, J.H. Chetwynd, and E.P. Shettle (1986): AFGL atmospheric constituent profiles (0-120 km). AFGL-TR-86-0110.
Response:
The correction has been made and other references to the McClatchey work have been replaced by the Anderson et al. reference.
229 229 produces > produce
Response:
The correction has been made.
234 – 249 This paragraph is important and needs a fair bit of work: It is very hard to imagine that Figure 4A represents a subset of 4B. If it truly is, a full explanation is required. Furthermore, if Figure 4B represents the uncertainty in the cooling rates, e.g. calculated at ecmwf, the ‘error’ would seem much too large. Figure 4A would seem to be more consistent with detailed evaluations of cooling rate uncertainties. This section, the discussion of the figures, etc. requires much more clarity of exposition so that one can better appreciate the results. A related point the authors need to address is the issue of increased uncertainty in the profiles in the lower altitude regime. Even if the percentage error in vmr(???) is constant, the absolute error in the cooling rate should be much larger in the lower atmosphere due to the increased number density. Figure 4C would seem to be consistent with this perspective. Is this the reason 4C appears as it does? Why don’t we see this behavior in 4B?
Response:
The descriptions for Figs. (4a-d) have been modified significantly. In the original manuscript, the description of what was Fig. (4a) and is now Fig. (4b) was incorrect but has been replaced (see lines 269-282).
In order to clarify the point that Figs. (4a-d) are notional and not representative of uncertainties in ERA-40 cooling rates, a sentence was included to Section 3 (lines 293-295, revised manuscript),
The implementation of cooling rate error estimation using Monte Carlo methods in the original manuscript had several mistakes and they have been corrected. The new Figs. (4c-d) do not have the behavior seen in the lower altitudes of the original manuscript. However, all of the figures show a decrease in the cooling rate profile at the lowest level of the atmosphere which is not very realistic, as pointed out by the reviewer. This results from the fact that we generally fix the surface temperature to the temperature at the lowest level of the atmosphere. Surface cooling various quite dramatically as the surface temperature changes.
Another issue in this paragraph is the distinction between error, variability and uncertainty. 3K and 20% is certainly not appropriate as profile error for all profile levels. The distinction between covariance and error covariance has becomequite blurred- at least to this reader.
Response:
The 3K/km T uncertainty and 20% vmr/km H2O and O3 uncertainties are meant to establish reasonable a priori constraints for cooling rate analysis, not to characterize uncertainties in ERA-40 and AIRS-derived cooling rates.
The paper uses covariance and error covariance frequently. For Fig. (2a-c), the purpose is to conveywhat a reasonable a priori understanding of the cooling rate profile would be before the introduction of a measurement. Figs. (4a-d) are an extension of Fig. (2a-b) in that cooling rate profile prior uncertainty is calculated through propagation of error analysis. Then, the a priori and a posteriori cooling rate covariance matrices are shown in Figs. (5a-b). Figs. (8a) and (8b) get back to the issue of prior cooling rate uncertainty by using ERA-40 T, H2O, and O3 data to see how sample covariance matrices compare to those derived from propagation of error analysis.
The last sentence in the paragraph is confusing and in need of justification. In the troposphere, temperature and watervapor are highly correlated, but for retrieved profiles this correlation is much reduced. Selection of spectral elements CO2, H2O, etc., are utilized to achieve this reduction. It is the case that all passive IR sounders by their nature have adirect dependence on the temperature field. Has this all been handled correctly in the development? Again, more and clearer exposition is needed and a stronger connection with our current understanding of cooling rate uncertainties in GCMs is required.
Response:
We agree that the correlation between different constituents is reduced by the retrieval, but note that the error correlation between vertical levels for a single constituent are not necessarily uncorrelated, even after a retrieval. Most retrievals from remote sounders operate at a higher vertical resolution than is warranted by the averaging kernels. Because more discussion of the effects of error correlation were included elsewhere in the paper, this last sentence was stricken.
To provide more context to this work with respect to GCMs, a sentence was added to the conclusion (564-568, revised manuscript).
235 the troposphere
Response:
The correction has been made.
240 uncertainty, and water vapor … > uncertainty; water vapor …
Response:
The correction has been made.
243 atmospheric > atmosphere
Response:
The correction has been made.
257 Run on sentence that needs rewriting. It is still not clear how AIRS profiles can reduce the cooling rate uncertainty to the extent shown here at 900 mb given the lack of contrast as discussed. If the argument is that this happens through the correlations I am quite skeptical- supporting evidence is required.
Response:
The sentence has been modified (lines 304-309, revised manuscript).
The cooling rate in the lowest 1 km of the atmosphere is determined substantially by surface temperature, the lapse rate in the boundary layer, and the amount of water vapor present. Since the vertical details of the temperature and water vapor profiles in the boundary layer are not retrievable given the AIRS averaging kernels to better than 1 km, the vertical details of boundary layer cooling are not well-constrained by the AIRS instrument. Consequently, discussion was added regarding cooling rate profile vertical resolution in the boundary layer on lines (329-331, revised manuscript).
276 ff Back to the issue of uncertainty/variability. Isn’t this variability that we are looking at here? The hot spot at 300 mb is quite significant and presented without comment? I have the impression that if these plots were differenced, the result would be only modestly less than 6A itself. Are these differences attributed to the Gaussian/linearity assumption in which case the last sentence should state this clearly. The reality of such a result does not detract from the paper. The qualitative aspect stands and the difference represents important information
Response:
The comparison of sample ERA-40 cooling rate covariance and that derived from error propagation analysis looks at cooling rate variability in the tropics. We have added a sentence to Section 3 to reinforce this point (line 392-394).
The discrepancies between sample and derived covariance matrices were explored further in the revisions of this paper. It was found that different treatments of water vapor covariance led to significantly different cooling rate covariance matrices in the upper troposphere. Consequently, several sentences were added regarding Gaussian pdfs (lines 387-397, revised manuscript).
336 absence compelling > absence of compelling
Response:
The correction has been made.
413 The mention of the limb seems quite gratuitous. In the linear regime the information comes from the tangent point and represents ~300km in horizontal extent; much to great for current GCMs. Further, in the tropics one can never see below ~500 mb. I suggest the sentence be dropped.
Response:
The sentence regarding limb measurements has been dropped.
422 Similarly, the contribution of active sensors for clear sky cases is not obvious and needs explication.
Response:
To address this issue, sentences were added to the conclusions (lines 571-588, revised manuscript).
Responses to Reviewer 2 Comments:
1)
What is being done here is closely related to basic retrieval theory, except for the choice to target Q instead of X. Those are equivalent if one assumes perfect knowledge of the radiative transfer Q=Q(X), which seems to be the case in this paper. I therefore think the authors need to make a stronger connection to the existing literature on retrieval and inverse methods, to highlight what they have done that is different, and how it might be useful to the retrieval community or vice-versa.
Also, Li et al 1997 (Clim. Dyn. 13:429) might be a useful paper, as it did something similar except that by inverting the Jacobian the authors calculated climate equilibria and their linear sensitivity to forcing.
Response:
This paper quotes the stated radiometric accuracy of RRTM with respect to line-by-line models at less than 0.1 K/day in the troposphere and 0.3 K/day in the stratosphere. While this is a non-insignificant source of error, the analysis in this paper does not take this into account explicitly. Rather, the paper explores how remote sensing uncertainty is relevant to cooling rate analysis.
The introduction has been modified to include a much more-detailed description of the existing literature related to the material in this paper. What is unique about this paper is that it formally introduces the covariance matrix to cooling rate analysis which, as far as we know, has not been described in the literature so far. Also, the paper ties standard retrieval methods using remote-sensing data to cooling rate profile knowledge, and it forms a basis for the comparison of GCM and reanalysis cooling rates with those derived from the remote-sensing data.
We thank the reviewer for bringing the Li at al 1997 reference to our attention. The results of that paper will be relevant for subsequent cooling rate analysis, especially when comparing cooling rates of GCMs with results from remote sensing.
2)
A better discussion is needed of the impact of correlations between different elements of X on the results, and on how Q is weighted. Any quantification of the impact of "off-diagonal" influences will depend totally on this correlation structure. For example, if T variations are highly coherent in the vertical, then the impact of a given amount of T variance on local heating rates will be relatively small, but the impact on the column-average heating (thus divergence of net fluxes into space and the surface) will be large. Conversely, if the same amount of T variance is vertically incoherent, the point impact on Q will be larger but the impact on the column mean of Q will be smaller than for the coherent variability. It is not obvious that we should be more concerned about the point values of Q as opposed to, say, the tropospheric and stratospheric means of Q. Finally, the authors don't pay enough attention to correlations between different constituents in X, as opposed to different levels.