**Final Author Comments for Manuscript Number acpd-2004-si01017**

[Title]{.underline}: Aerosol optical depth measurements by airborne sun
photometer in SOLVE II: Comparisons to SAGE III, POAM III and airborne
spectrometer measurements

[Authors]{.underline}: P. Russell, J. Livingston, B. Schmid, J. Eilers,
R. Kolyer, J. Redemann, S. Ramirez, J.-H. Yee, W. Swartz, R. Shetter, C.
Trepte, A. Risley Jr., B. Wenny, J. Zawodny, W. Chu, M. Pitts, J. Lumpe,
M. Fromm, C. Randall, K. Hoppel, and R. Bevilacqua

[General author comment]{.underline}: We thank the anonymous referees
for their efforts in reading the ms and offering comments that have
helped us improve it. Our specific responses follow each referee comment
below.

**Anonymous Referee #1**

[Referee's General Comments]{.underline}

This paper discusses at length and in great detail, aerosol optical
depth measurements made by the NASA Ames sun photometer mounted aboard a
DC-8 during the SOLVE II campaign. In particular it compares these
multi-wavelength measurements with those of the DIAS instrument and the
SAGE III and POAM III satellites. Most of the paper is devoted to a
detailed consideration of the differences in the sets of results and an
examination of possible causes for the discrepancies - in particular
between the sun photometer (AATS) and SAGE III. Although it seems that
some of the observed differences might be explained by differences in
viewing path, in timing and in solar zenith angle, for the most part
these cannot explain all the differences observed. The authors then
examine other possible causes one by one.

The paper is well-written, clear and very thorough. I have no doubt as
to its accuracy and the scientific methodology employed, and the paper
is fundamentally very sound. It presents new data and new results, which
are scientifically interesting.

[Response]{.underline}: We appreciate the positive comments.

[Referee]{.underline}: Its major weakness stems from the nature of its
conclusion that significant differences exist between the SAGE III and
AATS measurements which are unresolved. This may indeed be the case, but
in order to make a useful contribution to this problem, the authors need
to at least state what they intend to investigate next as the cause, or
what further experiment or data would be needed in order to resolve the
problem. Although there is a valid and significant scientific
contribution made by stating that a problem exists and that they have
examined umpteen different possible causes, which have not led to a
resolution - this is not enough. The authors need to state either where
they intend to look next for an explanation, what further data or
calculations are necessary, or what further experiments must be carried
out.

[Response]{.underline}: We agree that a valid and significant scientific
contribution has been made by stating that a problem exists and that we
have examined many different possible causes, which have not led to a
resolution. To address the statement that this is not enough, we have
added a short discussion of possible future work that would help to
resolve the discrepancies. Specifically, just before Appendix A we have
inserted:

"The analysis presented here clearly reveals that more work must be done
to understand even the satellite comparisons themselves. This will
require quantitative comparisons of both aerosol extinction and
transmission profiles from the SAGE III, SAGE II, and POAM III
instruments, and is the subject of future work. The POAM-SAGE
differences shown in Figures 21 and 22, including their seasonal
evolution, provide important context for the AATS-POAM and AATS-SAGE
comparisons, as well as potentially important clues and a data set that
can be studied in search of a resolution of the AATS-SAGE differences."

[Referee]{.underline}: My other general comment for resolution is the
size of the figures. I cannot read them even with a magnifying lens. All
the figures need to be printed at least twice as big as their current
size in the pdf manuscript.

[Response]{.underline}: We also were concerned by the small size of the
figures in the ACPD version---much smaller than the versions we
submitted. We raised this concern with the EGU Production Office, which
said that figure size can be enlarged when the paper is converted to
two-column style for the final ACP version. The Production Office
thought the small figure size in the ACPD one-column style was big
enough since readers can use the zoom tool of the Acrobat Reader to
enlarge the figures. We feel this is not an adequate solution for ACPD
readers who print pages in ACPD size (two ACPD pages per printed sheet).
The referee's difficulty reading the figures bears out our concern. We
will work with the Production Office to be sure figures are fully
legible in the final ACP version.

[Referee's Specific Comments]{.underline}

There is an enormous amount of detail in the paper, including 4 pages of
Tables and 24 figures. I am not sure that quite as much detail needs to
be presented. The fact that the figures are far too small made it
impossible for me to examine them in much detail. I would suggest making
the paper more readable by eliminating some of the figures - although I
do not have specific recommendations. Many of the discussion points can
be made without reference to a figure, and it would certainly help to
reduce the length of the paper were this done.

[Response]{.underline}: Referee #2 has made some specific
recommendations on which figures to drop, and we have done some of this,
along with some other deletions. See our response to Referee #2 below.

[Referee]{.underline}: I also think that the Appendix is unnecessary.

[Response]{.underline}: Here we disagree---we feel the Appendix is
necessary to demonstrate clearly that the window was frost-free during
the measurements reported here. In fact, Referee #2 has pointed to the
need to assure that the measurements were not affected by deposits on
other parts of the instrument optical path. Providing this assurance is
similar to what we have provided regarding window frost. We now provide
this in a slightly expanded Appendix, with brief mention in the main
text.

[Referee]{.underline}: One other comment - is "airmass" a common term? I
found its use quite confusing because I would not normally consider the
ratio of the slant path optical depth to the vertical optical depth to
be an "airmass" but more of an optical path difference (or ratio).

[Response]{.underline}: "Air mass" or "airmass" is the terminology used
by Thomason et al. (1983), Reagan et al. (1986) and most of the rest of
the atmospheric Sun photometry community to describe the ratio of
line-of-sight (LOS) optical thickness (OT) to vertical OT. The referee
is certainly correct that it is a ratio. That is why Kasten (1966) calls
it "relative optical airmass" and why we have introduced the terminology
as "relative optical airmass (here called airmass for brevity)" on p.
7294, line 4, carefully defining it as "the ratio of LOS optical
thickness (OT) to vertical OT".

Kondratyev (1969, p. 162) calls the same quantity "atmospheric mass" but
hastens to add "It should be emphasized in this connection that the
concept of atmospheric mass has nothing in common with the general idea
of mass. Atmospheric mass in the given case is a dimensionless quantity
indicating by how many times the optical thickness in the direction of
inclination exceeds the optical thickness in the direction of the
vertical."

Hence we certainly empathize with the referee for questioning the use of
the term "airmass" for an optical thickness ratio. It's not very
intuitive terminology. But it is quite standard, and we don't think we
should attempt to change it at this point. We think our introducing it
as we have on p. 7294 is the best way to go.

[Technical Corrections]{.underline}

[Referee]{.underline}: pg 7297, line 21. Figsures should be replaced by
Figures.

[Response]{.underline}: Correction made.

[Referee]{.underline}: pg 7298, line 20. "more-transmission oriented"
should be replaced by "more transmission-oriented"

[Response]{.underline}: Change made.

**Anonymous Referee #2**

[Referee's General Comments]{.underline}

This is an excessively long and detailed intercomparison of AOD
measurements made during SOLVE 2. Four different instruments are
involved: AATS and DIAS on board the DC-8 aircraft, and SAGE3 and POAM3
satellite instruments.

[Response]{.underline}: See below for the deletions of figures and text
we have made to shorten the paper.

[Referee]{.underline}: The challenge is that the instruments on board
the DC-8 typically measure only half the full limb path that the SAGE3
and POAM3 instruments see though. This leaves a high potential for
systematic biases between the air- and space-borne sensors, since the
conversion of the partial-limb-path AODs to full limb path AODs is
critically dependent on the assumed solar zenith angle, refraction,
aircraft altitude, and the aerosol extinction profile.

[Response]{.underline}: Actually, the conversion from half limb to full
limb is a separate issue from the dependence of airmass on solar zenith
angle, refraction, aircraft altitude, and the aerosol extinction
profile. First, note that the conventional AATS analyses involve no
conversion from half limb to full limb. As shown in Figure 10 and noted
in the text, these conventional analyses yield AATS results virtually
identical to those from the transmission-oriented analyses, which make
the half-limb to full-limb conversion for ease of comparisons to SAGE
III transmissions. Second, in this paper the conversion of the
half-limb-path AODs to full limb path AODs is done simply by multiplying
by a factor two, or, equivalently, by squaring the corresponding
transmissions. This is stated clearly on p. 7300, along with the fact
that "This squaring assumes that transmission is equal in the two limb
halves (i.e., from DC-8 to the Sun and from DC-8 away from the Sun)."
Equal transmission in the two limb halves is just a special case of the
homogeneity in spherical shells that is assumed by satellite limb
inversion algorithms. We have now added mention of this in the text. We
do not claim that this equality is exactly true, and, indeed, in Section
6 we are careful to note that:

"Differences in viewing path (including the major difference between
full limb and half limb), in timing, and in SZA each occurred at some
time for the AATS-satellite comparisons.... However, the systematic
nature of the AATS-satellite differences, in which satellite AOD
(especially SAGE) is always less than AATS AOD for λ \>755 nm, suggests
strongly that differences in viewing path, timing, or SZA cannot explain
all the AATS-satellite differences."

The dependence mentioned by the referee "on the assumed solar zenith
angle, refraction, aircraft altitude, and the aerosol extinction
profile" occurs in the calculation of airmass (ratio of LOS OT to
vertical OT), not in the conversion from half limb to full limb. As we
clearly state on p. 7315, "Systematic underestimation of aerosol airmass
factors in the AATS analyses could explain the larger AATS *AOD*s, but
we have to reject such airmass errors on three grounds: the airmass
sensitivity study discussed in conjunction with Figures 4--5, the
success of the Yee LOS integrator (which is used by the Yee airmass
algorithm) in the comparisons reported by Swartz et al. (2004), and,
most of all, the fact that the AATS-satellite differences are apparent
in transmissions and LOS AOTs at refracted *SZA* 90^o^, which do not
depend on airmass values."

[Referee]{.underline}: A major problem is that the paper unearths
significant biases between the DC-8 and the satellite instruments, but
never satisfactorily explains/resolves any of them. The authors try
several different ways of comparing the data (transmission, vertical OD,
slant OD, etc) but they all exhibit the same behavior. To add to the
sense of confusion and futility, the authors tell us that SAGE3 and
POAM3 disagree with each other during the period of the DC-8
measurements, but are in agreement before and after.

[Response]{.underline}: First of all, we think that the phrase
"significant biases between the DC-8 and the satellite instruments"
which lumps the AATS-SAGE and AATS-POAM comparisons together, misses an
important distinction that is made clearly in the paper. The AATS-POAM
differences, shown in Figure 19 and Table 4, and also described in the
text ("RMS percentage differences in *AOD* (\[AATS-POAM\]/AATS) \<31%
for all *λ*, 442--1018nm") are markedly smaller than for AATS-SAGE (RMS
percentage differences in *AOD,* (\[AATS-SAGE\]/AATS), of 59% for 1020nm
and 66% at 1545 nm). The AATS-POAM agreement, to 31% or better, may be
as good as one can expect, given the very small AODs during the
experiment, the half-vs-full limb path difference, and the other sources
of error described in the paper. The 59% AATS-SAGE difference at 1020
nm, shown in Figure 10 and Table 2, is nearly twice as large.

This difference between POAM and SAGE, revealed by the respective
comparisons with AATS, is consistent with the POAM-SAGE differences
shown in Figures 21 and 22. We don't see why this consistency causes a
"sense of confusion and futility" in the referee. On the contrary, we
feel the POAM-SAGE differences shown in Figures 21 and 22, including
their seasonal evolution, provide important context for the AATS-POAM
and AATS-SAGE comparisons, as well as potentially important clues and a
data set that can be studied in search of a resolution of the AATS-SAGE
differences. Text added just before Appendix A now emphasizes this
point.

[Referee]{.underline}: The authors go to great lengths to prove that
there was no ice on the window of the AATS instrument, adding an
appendix, but they don't say anything about non-ice crud on their
optics. The SAGE3 and POAM3 instruments can take a solar spectrum high
above the atmosphere to establish a \"baseline\" exo-atmospheric
spectrum. But for the DC-8 instruments this is much more difficult. How
does AATS distinguish crud on its optics from atmospheric aerosol?

[Response]{.underline}: The optical path of each AATS channel has very
few optical elements: the AATS entrance window, an interference filter,
and a photodiode detector. Of these, the entrance window was the coldest
optical surface during the DC-8 flight segments reported in this paper.
The detectors for wavelengths 354-1241 nm are in tight thermal contact
with a mounting block maintained at an elevated temperature of 45 ±1 C,
and the interference filters are in a mounting block with temperature
that is continuously measured and found to stay within the range 30 to
42 C. Although the detector for wavelength 1558 nm has an internal chip
thermoelectrically maintained at 0 C, its case and detector entrance
window are warm, mounted in tight thermal contact with a block that is
in conductive contact with the 45 C hot-detector block and radiatively
heated by the 30-40 C filter block. Hence, the temperatures of all
detector cases and filters greatly exceeded the AATS entrance window
temperature during the DC-8 flight segments reported in this paper. As a
consequence, any "non-ice crud" available to deposit on optical surfaces
would deposit on the window, not a filter or detector (the only other
optical elements). This is the reason our tests for reduced optical
transmission in the instrument focused on the window. Moreover, if one
were to postulate a deposit on an interference filter or detector, it
would be revealed by the tests described in the Appendix, especially the
plot of AOD difference vs airmass shown in Figure A2. As noted, the
measured dependence on airmass is just the opposite of what would be
caused by a deposit on any surface in the instrument optical path.

We have slightly modified the Appendix to make these points.

[Referee]{.underline}: The paper has a lot of duplication. For example,
lines 4-10 of the abstract are virtually identical to lines 14-21 of the
introduction. I strongly recommend that the authors try to shorten the
text and try to reduce the number of figures. Although there are
\"only\" 24 figures, most of these are multi-panel. I counted a total of
111 figure-panels! The problem with this excessive detail is that
readers \"burn out\" half-way through the paper, before reaching the
important stuff. So I recommend that the number of figure-panels be
reduced by at least a factor 2. This will allow more space for the
remaining figures (improving their legibility) and will allow the text
to be trimmed since the deleted figures don't have to be discussed. A
few suggestions: figures 6-9 are very similar. Is it really necessary to
show this same information for all 4 DC-8 flights? Why not simply choose
one typical flight? And figures 14 and 15 are really very similar --
there is no need for both.

[Response]{.underline}: We have shortened lines 4-10 of the abstract. We
have also deleted Figures 7 and 9. (Figure 8 is needed with Figure 6 to
show the range of SZAs encountered on flights, along with the
corresponding variation in airmasses.) And we have deleted Figures 14
and 17.

[Referee's Specific Comments]{.underline}

The authors say nothing about the spectral resolution of the AATS-14
instrument. Their equations implicitly assume that its spectral
resolution is much higher than any structure in the incident solar
spectrum. They should comment on the validity of this assumption.

[Response]{.underline}: Actually, the spectral resolution is noted on p.
7302, line 20: "Typical channel full widths at half maximum (FWHM) are 5
nm." To make this clearer, we have now inserted in the second paragraph
of Section 1: "The AATS-14 channels used in this paper have full width
at half maximum (FWHM) of 2.0 to 5.6 nm, with most channel FWHMs \~5
nm."

Regarding the effect of solar spectral variations on the validity of our
equations, it is certainly true that the incident solar spectrum (e.g.,
Kurucz, 1995) has a lot of fine structure within the AATS channel
widths. Specifically, solar irradiance can vary by nearly an order of
magnitude over \~0.1 nm within some of these channels, as illustrated in
[Figure
R1](http://geo.arc.nasa.gov/sgg/SOLVE2-website/papers/FACACPD-2004-si01017Russell_fR01.gif)
([http://geo.arc.nasa.gov/sgg/SOLVE2-website/papers/
FACACPD-2004-si01017Russell_fR01.gif](http://geo.arc.nasa.gov/sgg/SOLVE2-website/papers/ FACACPD-2004-si01017Russell_fR01.gif)).
However, the relevant equations, (1)-(6), which are exact for
monochromatic radiation, also apply with sufficient accuracy to the AATS
channels used, and the constituents addressed, in this paper\--despite
this solar fine structure.

To show this, we start by writing the exact equation for *T~j~*(*SZA*),
the transmission of the LOS path from Sun to airborne photometer for
channel *j*:

$T_{j}(\text{SZA}) = \frac{\int_{}^{}{S(\lambda)\text{exp}\lbrack - \sum_{i}^{}{m_{i}(\text{SZA})\text{OD}_{i}(\lambda)\rbrack F_{j}(\lambda)d\lambda}}}{\int_{}^{}{S(\lambda)F_{j}(\lambda)d\lambda}} = \frac{V_{j}}{V_{0,j}}\frac{K_{j}}{K_{j}},$
(6A)

where *S*(*λ*) is the extraterrestrial solar spectral irradiance and
*F~j~*(λ) is the channel filter transmission function. *V~j~* and
*V~0,j~* are the channel *j* output voltages at the photometer's
location and above the atmosphere, respectively, and are given by

$V_{j}(\text{SZA}) = K_{j}\int_{}^{}{S(\lambda)\text{exp}\lbrack - \sum_{i}^{}{m_{i}(\text{SZA})\text{OD}_{i}(\lambda)\rbrack F_{j}(\lambda)}d\lambda}$
(6B)

$V_{0,j}(\text{SZA}) = K_{j}\int_{}^{}{S(\lambda)F_{j}(\lambda)d\lambda},$
(6C)

where *K~j~* is the channel *j* calibration constant.

The key to obtaining Eqs. (1)-(6) for AATS channels is the limited
variation within each channel of the optical depths *OD~i~*(λ) and
transmissions *T~i~*(λ) for the constituents relevant to this paper.
This small variation of constituent *OD* within each channel allows the
exponentials in Eqs. (6A)-(6B) to be extracted from the integrals,
yielding

$T_{j}^{\text{approx}}(\text{SZA}) = \frac{\text{exp}\lbrack - \sum_{i}^{}{m_{i}(\text{SZA})\text{OD}_{i,j}\rbrack}\int_{}^{}{S(\lambda)F_{j}(\lambda)d\lambda}}{\int_{}^{}{S(\lambda)F_{j}(\lambda)d\lambda}} = \prod_{i}^{}{\hat{T}}_{i,j}$**,**
(6D)

where *OD~i,j~* is a representative OD of constituent *i* for channel
*j.* In the AATS data processing routines, this "representative" *OD* is
computed differently for different constituents *i.* For the
calculations reported here we used

$\text{OD}_{i,j} = \int_{}^{}{\text{OD}_{i}(\lambda)F_{j}(\lambda)d\lambda}/\int_{}^{}{F_{j}(\lambda)d\lambda}$,
for *i* = R, NO~2~, O~3~, O~2~-O~2~, .... (6E)

$\text{OD}_{i,j} = \text{OD}_{i}(\lambda_{j})$, for *i* = a (6F)

where *λ~j~* is the center wavelength of channel *j*, *a* stands for
aerosol and *R* for Rayleigh (as also noted under Eq. (1)). For all
constituents *i*,

${\hat{T}}_{i,j} = \text{exp}\lbrack - m_{i}(\text{SZA})\text{OD}_{i,j}\rbrack$.
(6G)

Note that Eqs. (6D) and (6G) are equivalent to Eqs. (1)-(6) (apart from
the factor 2 used in converting from the sunphotometer-viewed path to
the full limb path).

To assess quantitatively the differences between the exact and
approximate channel transmissions *T~j~* and *T~j~* *^approx^* in Eqs.
(6A) and (6D), we have used the Kurucz (1995) solar spectrum, absorbing
gas spectra from MODTRAN (Kneizys et al., 1996), the Rayleigh scattering
results of Bucholtz et al. (1995), and aerosol extinction spectra
typical of those in Figures 8, 10-12, and 15, to calculate the ratios
$T_{j}^{\text{approx}}/T_{j}$ (i.e., Eq. (6D)/Eq. (6A)) for the range of
channel wavelengths, filter functions, *m~i~*(SZA) and constituent
optical depths *OD~i~*(*λ*) covered in this paper (see, e.g., Figs.
6-18).

[Figure
R1](http://geo.arc.nasa.gov/sgg/SOLVE2-website/papers/ FACACPD-2004-si01017Russell_fR01.gif)
illustrates the relevant quantities for two typical AATS channels.

We find the ratios $T_{j}^{\text{approx}}/T_{j}$ differ from 1.00 by at
most 1%. Differences are largest at the shortest wavelengths and are all
\<0.3% for *λ*\> 519 nm.

Since Eq. (2) or (6A) yields d*OD*=-(1/*m*)d*T*/*T*, the typical airmass
values of 20 to 40 in the DC-8 measurements yield *OD* values derived
from (6E) (or equivalently (1)-(6)) that differ from those derived from
an exact transmission formulation by less than \~0.01/20 to \~0.003/40,
or 5 x 10^-4^ to 7 x 10^-5^. These differences are negligible for the
*OD* values of interest in this paper (cf. Figures 8 and 15).

To address potential similar questions from other readers, we have now
inserted at the end of the third paragraph after Eq. (6):

"Although the absorbing gas optical depth and transmission values in
Figure 10 do not account for solar spectral variations within the AATS
channel widths, we have performed other calculations that do account for
these variations and found that transmissions calculated by the two
methods differ by less than 1%. These more detailed calculations use the
Kurucz (1995) solar spectrum, absorbing gas spectra from MODTRAN
(Kneizys et al., 1996), the Rayleigh scattering results of Bucholtz et
al. (1995), and aerosol extinction spectra typical of those in Figures
8, 10-12, and 15. The reason for the small differences is the limited
variation within each AATS channel of the optical depths *OD~i~*(λ) for
the constituents relevant to this paper. These same comparisons also
show that Eqs. (1)-(6), which are exact for monochromatic radiation,
also apply with similar accuracy to the AATS channels used, and the
constituents addressed, in this paper\--despite the solar fine structure
within each channel."

[Referee]{.underline}: P. 7292, line 2: Why is \"Second\" capitalized?
Is this the \"S\" in SOLVE?

[Response]{.underline}: We have now changed "Second" to "second".

[Referee:]{.underline} P. 7292, line 4-5: I prefer \"multi-wavelength\"
to \"mul-tiwavelength\".

[Response:]{.underline} This was the result of an automatic hyphenator.
We've changed it back to \"multiwavelength" (with no hyphen) and hope it
stays that way!

[Referee:]{.underline} P. 7292, line 27: It seems redundant to use the
word \"percentage\" when it says \"%\" after each value.

[Response:]{.underline} We've now changed \"percentage\" to "relative".

[Referee:]{.underline} P. 7292, line 28: Is the 1020nm channel mentioned
here the same as the 1019nm channel cited in Table 2, or are they
different?

[Response]{.underline}: "1020 nm" is used in the text to refer to the
collection of AATS, POAM III, and SAGE III channels near 1020 nm. In
tables and figures, where only one or two sensors are involved, more
exact wavelengths are used.

AATS, POAM III, and SAGE III archive aerosol products at the following
channel-center wavelengths near 1020 nm:

AATS: 1019.3 nm

POAM III: 1018.3 nm

SAGE III: 1021.6 nm

In addition, SAGE provides transmission products for several Pixel
Groups with centers near 1020 nm, including Pixel Group 81 centered at
1019.3 nm. The different sensor wavelengths are shown in tables and
figures as follows:

[Table 2]{.underline}: Wavelengths shown are SAGE III aerosol-archive
wavelengths, except that 1019.3 nm (SAGE III transmission Pixel Group
81) is shown in place of 1021.6 nm to accommodate our SAGE III
transmission-derived results at wavelength 1019.3 nm. (The 1019.3 nm
transmission-derived and 1021 nm conventionally derived SAGE III AODs
are very similar, as shown in Figure 10 and noted in the text.) In
calculating AATS-SAGE differences, AATS results are interpolated to SAGE
wavelengths.

[Table 3]{.underline}: Both AATS and POAM III wavelengths are shown, as
labeled.

[Figure 2]{.underline}: Wavelengths shown are SAGE III aerosol
extinction and AOD archive wavelengths.

[Figure 3]{.underline}: Wavelengths shown are POAM III aerosol
extinction and AOD archive wavelengths.

[Figure 11]{.underline}: Both AATS and SAGE III transmission Pixel Group
wavelengths are shown, as labeled.

[Figure 20]{.underline}: Both AATS and POAM III wavelengths are shown,
as labeled.

To help reduce any confusion, we have now added a footnote to Table 2
stating the material labeled [Table 2]{.underline} above.

[Referee:]{.underline} P. 7294, line 6: The authors state that \"airmass
is defined as the LOS optical thickness (OT) to the vertical OT\". Is
this the vertical OT above the observer or above the lowest point along
the LOS?

[Response]{.underline}: It's vertical OT above the observer. We've now
inserted this on p. 7294, line 4 to answer the question for all readers.

[Referee:]{.underline} P. 7324: Table 2: I don't understand how the rms
values are calculated for this table. Take the right-most column
(1545nm) in Table 2(a). The values are 10.1, 15.3, 16.8, and 19.4. By my
calculation, the mean value is 15.4 and the rms is 3.4. So where does
the tabulated rms value of 15.8 come from? Ditto for all the other rms
values in Table 2 and for Table 4. Obviously, I'm completely missing the
point here.

[Response]{.underline}: The mean and rms values given in the tables are
correct. The value 3.4 obtained by the referee is not the rms of the
given values, but instead their standard deviation. For a set of
numbers, the rms, or root-mean-square, is the square root of the mean of
the squared elements (Weisstein,
<http://mathworld.wolfram.com/Root-Mean-Square.html>). The standard
deviation is the square root of the mean of the squared difference of
each element from the mean (Weisstein,
<http://mathworld.wolfram.com/StandardDeviation.html>). In other words,
the standard deviation is the rms deviation from the mean. In an effort
to avoid similar confusion among other readers, we have added a footnote
defining rms to Tables 2-4.

[Referee:]{.underline} P. 7324: Table 2: Why do the wavelengths in Table
2a have 5 significant figures, but only 4 in Table 2b? Ditto for 2c &
2d.

[Response]{.underline}: This was an inadvertent result of a spreadsheet
column width change coupled with a general format. The values are now
all displayed to resolution 0.1 nm.

[Referee:]{.underline} P. 7335: What is the significance of the
left-pointing arrows in figures 6, 7, 8, and 18?

[Response]{.underline}: They mean "Use the left scale". This is rather
standard graphing practice. We are willing to change each left-pointing
arrow to the words "(left scale)", but we will leave the decision to the
ACP editorial staff.

[Referee:]{.underline} P. 7339: Change \"Aaerosol\" to \"Aerosol\"
(y-axis annotation). Ditto for figure 19.

[Response]{.underline}: Changes made.

[Referee:]{.underline} P. 7341: Panels are not labelled (a), (b), (c).

[Response]{.underline}: We have changed "a", "b", and "c" to "Top
frame", "Middle frame", and "Bottom frame", respectively.

**References**

Bucholtz, A., Rayleigh-scattering calculations for the terrestrial
atmosphere, *Appl. Opt., 34*, 2765-2773, 1995.

Kneizys F.X., Abreu, L.W., Anderson, G. P., Chetwynd, J.H., Shettle,
E.P., Berk, A., Bernstein, L.S., Robertson, D.C., Acharaya, P.,
Rothmann, L.S., Selby, J.E.A., Gallery, W.O., and Clough, S.A., "The
MODTRAN 2/3 Report and LOWTRAN 7 Model", 11 Jan. 1996, Phillips
Laboratory, Geophysics Directorate PL/GPOS, 29 Randolph Road, Hanscom
AFB, MA 01731-3010.

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![](media/image1.png){width="6.125in" height="4.094444444444444in"}

![](media/image2.png){width="6.125in" height="4.129166666666666in"}

**Fig. R1**. Illustration of the variation of solar spectral irradiance
*S*(*λ*), constituent transmissions *T~i~*(λ) and filter transmissions
*F*(*λ*) for typical AATS channels with FWHM \~5 nm. Channel
transmissions *T~j~*, exact and approximate, are as defined by Eqs. (6A)
and (6D).