High-resolution Infrared Radiation Sounder (HIRS) brightness temperatures at
channel 12 (T12) can be used to assess the water vapour content of the
upper troposphere. The transition from HIRS/2 to HIRS/3 in 1999 involved a
shift in the central wavelength of channel 12 from 6.7 to 6.5µm, causing a discontinuity in the time series of T12. To understand the
impact of this change in the measured brightness temperatures, we have
performed radiative transfer calculations for channel 12 of HIRS/2 and HIRS/3
instruments, using a large set of radiosonde profiles of temperature and
relative humidity from three different sites. Other possible changes within
the instrument, apart from the changed spectral response function, have been
assumed to be of minor importance, and in fact, it was necessary to assume as
a working hypothesis that the spectral and radiometric calibration of the two
instruments did not change during the relatively short period of their common
operation. For each radiosonde profile we performed two radiative transfer
calculations, one using the HIRS/2 channel response function of NOAA 14 and
one using the HIRS/3 channel response function of NOAA 15, resulting in
negative differences of T12 (denoted as ΔT12:=T12/15-T12/14) ranging between -12 and -2 K.
Inspection of individual profiles for large, medium and small values of
ΔT12 pointed to the role of the mid-tropospheric humidity. This
guided us to investigate the relation between ΔT12 and the channel
11 brightness temperatures which are typically used to detect signals from
the mid-troposphere. This allowed us to construct a correction for the HIRS/3
T12, which leads to a pseudo-channel 12 brightness temperature as if a
HIRS/2 instrument had measured it. By applying this correction we find an
excellent agreement between the original HIRS/2 T12 and the HIRS/3 data
inferred from the correction method with R=0.986. Upper-tropospheric
humidity (UTH) derived from the pseudo HIRS/2 T12 data compared well with that
calculated from intersatellite-calibrated data, providing independent
justification for using the two intercalibrated time series (HIRS/2 and
HIRS/3) as a continuous HIRS time series for long-term UTH analyses.
Introduction
Climate variability studies require the analysis of long homogeneous time
series of climate data. For example, a long time series which can be used to study the variability of
upper-tropospheric water vapour can be derived from the brightness
temperature measurements of the High-resolution Infrared Radiation Sounder
(HIRS) instrument aboard the National Oceanic and Atmospheric Administration
(NOAA) polar orbiting satellites. The HIRS measurements started in mid-1979
and are still ongoing. They provide a unique long-term data set (covering
nearly 4 decades) that can be exploited in climate research. When NOAA
launched the weather satellite NOAA 15 in 1998, it was equipped similarly to
all its precursors with a HIRS instrument. This 20-channel instrument
provides information on temperature and humidity in the troposphere, where
channels 10 to 12 are sensitive to water vapour at different altitude bands
lower to upper troposphere,. Unfortunately, with the
launch of NOAA 15 the central frequency in channel 12 has moved from 6.7 to
6.5 µm. This is quite a large change, because it means that the
channel has its maximum sensitivity about 1 km higher (and
accordingly several degrees colder) than channel 12 of all previous
satellites.
With that change, i.e. the transition from HIRS/2 on the older NOAA
satellites to HIRS/3 on NOAA 15, the channel 12 time series became
inhomogeneous. performed an intercalibration based on
statistics of differences between the brightness temperatures measured by
subsequent HIRS instruments (technically a regression of first kind). The
intercalibration solved the problem of a broken time series for some of the
statistics of the data, e.g. for the mean values. The intercalibrated time
series was used for several studies e.g.. Yet
problems remained in the lower tail of the distribution of brightness
temperatures, that is, at the lowest values of brightness temperatures, as
has been detected by in the following cited as GE17.
However, the question arises as to whether it is sufficient to solve a physical
problem (i.e. the different altitudes of peak sensitivity of the channel 12
on HIRS/2 and HIRS/3) with a purely statistical method. Hence, GE17 posed the
following question.
“Is it justified at all to combine all HIRS T12 (the brightness
temperature measured by channel 12) data into a
single time series when it is a matter of fact that HIRS 2 and
HIRS 3/4 sense different layers of the upper troposphere, layers
that overlap heavily but whose centres are more than one kilometre
apart vertically?”
In fact, this question can be broken down into sub-questions. (1) Under
which circumstances is the intercalibration justified or not?
(2) Which assumptions have to be made about the structure of temperature and
moisture profiles? The present paper deals with these questions. Fortunately
it turns out that it is possible and justified to combine the channel 12 time
series on physical reasoning providing a homogeneous time series of 35+ years
that can be used for climatological studies. In this paper we demonstrate
that independent tests based on results from radiative transfer
calculations lead to a comparison between NOAA 14 and NOAA 15 channel 12
brightness temperatures that is very similar to the same comparison performed
with the intercalibrated data from . For these tests we assume
that other potential sources of brightness temperature differences (spectral
and radiometric calibration) are of minor importance compared to the effect
of radiation physics. With this in mind we may say that our new procedure
based on physics of radiative transfer corroborates the statistically based
procedure of and this is good news.
The present paper is organised as follows. First, the radiative transfer
model and its set-up is introduced in Sect. 2. Section 3 presents radiative
transfer calculations for channel 12 on NOAA 14 and NOAA 15, using radiosonde
profiles with high vertical resolution. From these calculations we find that
certain profile characteristics in the mid-troposphere yield either
relatively small or relatively large differences between the computed channel
12 brightness temperatures. In Sect. 4, HIRS channel 11 radiative transfer
calculations are applied to get one more piece of information on these
profile characteristics. It turns out that the channel 12 brightness
temperature differences are linearly correlated with the channel 11
brightness temperatures. A bilinear regression is performed, resulting in a
superposition of HIRS/3 channel 11 and 12 brightness temperatures from
NOAA 15 that produces a pseudo-channel 12 brightness temperature as
if it was measured by the HIRS/2 instrument on NOAA 14. A discussion of the
method and an application to real HIRS data from NOAA 14 and NOAA 15 are
presented in Sect. 5, where we show that the comparison of the original
NOAA 14 channel 12 brightness temperature with the pseudo-channel 12
brightness temperature from NOAA 15 is quite similar in its statistical
properties to a corresponding comparison using the intercalibrated data. The
concluding Sect. 6 summarises the logic of the procedure and gives an
outlook.
Radiative transfer simulations of channel 12 radiation for
HIRS/2 and HIRS/3
In order to analyse the differences between channels 12 of HIRS/2 on NOAA 14
and of HIRS/3 on NOAA 15, respectively, we perform radiative transfer
calculations using the channel 12 spectral response functions of the two
instruments applied to a large set of atmospheric profiles of temperature and
relative humidity. These functions are shown in Fig. . In
particular, for each profile we perform two runs of the libRadtran radiative
transfer code , one for channel 12 on NOAA 14 and one for
channel 12 on NOAA 15; i.e. we calculate the channel 12 brightness
temperatures T12/15 and T12/14, which would have been measured by
NOAA 15 and NOAA 14, respectively. We then calculate the brightness
temperature differences ΔT12:=T12/15-T12/14 and analyse how
a given difference depends on the given profile characteristics. The channel
spectral response functions have been obtained from EUMETSAT's NWP SAF
Satellite Application Facility (SAF) for numerical weather
prediction (NWP)
https://nwpsaf.eu/site/software/rttov/download/coefficients/spectral-response-functions,
last access in March 2017
.
Channel 12 spectral response functions of the
HIRS 2 instrument on NOAA 14 and the HIRS 3 instrument on NOAA 15.
LibRadtran is used with the following set-up: we use the DISORT radiative
transfer solver with 16 discrete angles and the
representative wavelengths band parameterisation
reptran, with fine resolution
(1 cm-1). We assume a ground albedo of zero and cloud-free
scenes as brightness temperatures from the Shi and Bates data set are
cloud cleared, see. The background profiles of the absorbing gases
are taken from implemented standard atmosphere profiles ,
whereby the appropriate profile is automatically selected from the
geographical position and the time to which the radiosonde profile refers. We
calculate the channel-integrated brightness temperatures at the top of the
atmosphere for nadir and 30∘ off-nadir directions for these
profiles.
The atmospheric profiles of temperature and relative humidity (with respect
to liquid water) are taken from large sets of radiosonde data with high
vertical resolution. (1) We use the set of profiles from the German weather
observatory Lindenberg 52.21∘ N,
14.12∘ E,, similarly to earlier satellite studies
. We use this set of more than 1500 profiles to
derive a regression-based solution (our training data set). (2) To see
whether there are also systematic differences between latitude zones
radiosonde profiles from Sodankylä, Finland (67.37∘ N,
26.60∘ E) and Manus, Papua New Guinea (2.06∘ S,
146.93∘ E) are used. These weather observatories belong to the
Global Climate Observing System (GCOS) Reference Upper-Air Network (GRUAN).
The data and products of the GRUAN network are quality-controlled as
described by . We use 1 year of profiles from both stations: 2013 for
Manus and 2014 for Sodankylä. These profiles were used for testing the
regression that we derived from the Lindenberg profiles. The GRUAN profiles
have a very high vertical resolution – too high for the radiative transfer
calculation. Thus, only every 10th record has been used from the surface to
90 hPa. At higher altitudes (mainly in the dry stratosphere) we have
replaced the radiosonde data by data from the standard atmospheres
implemented in libRadtran.
Discussion of radiative transfer results
Figure displays the pseudo-channel 12 brightness temperatures for
T12/15 against the corresponding brightness temperature differences
(NOAA 15 minus NOAA 14), ΔT12, computed with libRadtran for the
Sodankylä and the Manus profiles. T12/15 and ΔT12 are
presented for nadir and 30∘ off-nadir directions. As expected, the
brightness temperatures for the two considered viewing directions differ, and
their difference is rather constantly about 1 to 2 K. More precisely,
the summary statistics for the two
locations are as follows.
At Sodankylä the mean difference at nadir is -6.7 ± 1.2 K, and the
mean difference at 30∘ is -6.7 ± 1.3 K. At Manus the mean
difference at both nadir and at 30∘ are -7.1 ± 0.9 K. It is
thus sufficient to only use the nadir radiances for further analyses. It can
be noted that T12/15 varies between 225 and 242 K for the
Sodankylä profiles, while the corresponding ΔT12 ranges between
-12 and -3 K. There is no obvious correlation between ΔT12 and T12/15. For Manus, the data pairs show values of T12/15
from roughly 229 to 241 K and brightness temperature differences
ranging from -10 to -5 K. Again there is no obvious correlation
between the brightness temperatures themselves and the corresponding
differences.
Scatter plot of brightness temperatures calculated with a radiative
transfer model using radiosonde profiles from Sodankylä,
Finland (a) and Manus, Papua New Guinea (b). The abscissa
represents the brightness temperature obtained with a channel 12 spectral
response function for HIRS/3 on NOAA 15. The ordinate represents the
difference between this brightness temperature and a corresponding one
computed using the channel 12 spectral response function for HIRS/2 on
NOAA 14. The calculations have been performed for both nadir and 30∘
off-nadir viewing directions.
Figure a displays the corresponding results for the radiosonde
profiles from Lindenberg. The data pairs form two groups: a large patch at
low T12/15 and a “tail” at small ΔT12 but higher
T12/15. This tail has been discarded from further analysis since
inspection of the corresponding profiles showed that the relative humidity
sensor was obviously malfunctioning in the middle and upper troposphere (and
in the stratosphere), indicating zero relative humidity. 1558 profiles out of
the total 1660 profiles remain for the analysis. Figure b shows the
same data without the mentioned tail represented as a 2-D histogram. The data
at the maximum frequency (dark blue) have a brightness temperature difference of about -7 K.
Only a small set of the data pairs has ΔT12>-5K and an
even smaller set has ΔT12<-11K.
(a) Scatter plot as in Fig. and
(b) corresponding 2-D histogram for channel 12 brightness
temperatures computed using radiosonde profiles from Lindenberg,
Germany. Note the tail of high values in the scatter plot results
from profiles with a malfunctioning RH instrument. These 102 profiles
have been discarded from further analysis. The 2-D frequency
histogram does not contain them anymore. Calculations have been
performed for nadir and 30∘ off-nadir directions, but the
off-nadir results are only shown in the scatter plot.
At this point it is useful to recall that the weighting functions of the two
considered channels peak at altitudes about 1 km apart because the
water vapour optical thickness is larger at the central frequency of channel
12 on HIRS/3 than that on HIRS/2. The vertical distance of 1 km
implies an air temperature difference of about 6.5K on average in
the upper troposphere, and this explains that an average ΔT12 of
about the same value is found in the radiative transfer calculations. A
similar (average) correction of 8 K has been derived by
and used by .
Now the question arises of how characteristics of humidity profiles are
reflected in the brightness temperature differences. Figure shows
three sets of relative humidity profiles: 5 profiles with ΔT12<-11K (panel a), 6 profiles with
-7.21 K<ΔT12<-7.19K (panel b) and 20
profiles with a small difference, ΔT12>-5K (panel c).
Note that relative humidity values are reported as integers in our data set,
which explains the somewhat angular structure of some of the profiles.
Lindenberg radiosonde profiles of relative humidity vs. pressure
altitude that lead to brightness temperature differences in extreme ranges
(a, c, values indicated in the figures) and to values near to the
mean (b). The profiles are obtained from the following launches
(format yymmddhh): 00042806, 00122312, 01011506, 01021717,
01030712 (a); 00070112, 00111618, 00112318, 00123012, 01021612,
01040218 (b); 00021306, 00021312, 00021406, 00022100, 00022106,
00052912, 00053018, 00060706, 00071506, 00080112, 00080200, 00111606,
00121606, 01020118, 01020218, 01022206, 01022218, 01022306, 01022312,
01022400 (c).
The first set of profiles with ΔT12<-11K is characterised
by high values of RH in the upper troposphere (200 to 400 hPa) and a
very dry mid-troposphere (450 to 650 hPa). Accordingly, channel 12 on
NOAA 15 (ch. 12/15) gets more radiance from the upper levels than channel 12
on NOAA 14 (ch. 12/14) because it is more sensitive there. In turn, ch. 12/14 cannot balance this deficit in the mid-tropospheric levels since it is
too dry at this altitude. The result is a large negative difference in
brightness temperatures. The profiles with ΔT12>-5K are
in turn characterised by a mid-troposphere that has much higher relative
humidity than the upper troposphere. Under this circumstance the peak of the
ch. 12/15 weighting function approaches the peak of the ch. 12/14 weighting
function; that is, the brightness temperatures become more similar. Finally,
an average brightness temperature difference is found for profiles without a
strong humidity contrast between the upper and the mid-tropospheric levels,
as shown in Fig. b.
This analysis shows that one can understand from consideration of the
underlying radiation physics why the brightness temperature differences
sometimes obtain large or relatively small values and why the
average difference is of the order of -7 K. It is, however, clear that
this additional knowledge is not available when satellite data analysis is
confined to channel 12 only. To exploit this knowledge one needs further
pieces of information, in particular on the humidity in the mid-tropospheric levels. Fortunately, this knowledge is available from the same
HIRS instruments, from channel 11 see, e.g..
Construction of a pseudo HIRS/2 channel 12Regression using HIRS/3 channels 11 and 12
HIRS/3 channel 11 is centred at a wavelength of 7.3 µm. While the
strong water vapour ν2 vibration–rotation band has its peak line
strengths at about the channel 12 wavelength (≈6.5µm),
channel 11 is centred on the long-wave side of this band, off the peak with
lower line strengths, and thus channel 11 is characteristic of the water
vapour in lower levels than channel 12. In a standard midlatitude summer
atmosphere channel 11 peaks at about 5 km altitude see Fig. 2
of.
Using the channel spectral response function for channel 11 on NOAA 15,
radiative transfer calculations have been performed for the radiosonde
profiles used above. Figure shows the resulting brightness temperatures, T11/15, plotted against
the previously computed ΔT12 for the set of Lindenberg
profiles. As expected, T11/15 is
generally higher than the channel 12 brightness temperatures because it
characterises the temperature in the mid-troposphere where the channel 11
weighting function peaks. T11/15 ranges from 248 to 268 K for
the Lindenberg profiles. Figure also shows a linear correlation
between ΔT12 and T11/15, although with a large scatter. The
linear Pearson correlation coefficient is -0.68. Its square is 0.46, that
is, variations of T11/15 represent almost half of the variations in
ΔT12. The remaining scatter is not surprising given the tremendous
variability of relative humidity profiles. One additional piece of
information is clearly insufficient to capture all this variability.
Nevertheless, the correlation is clearly visible. We have made use of it to
construct a correction to the HIRS/3 measured channel 12 brightness
temperatures, a correction that leads to a pseudo-channel 12 brightness
temperature as if a HIRS/2 instrument had measured it.
Scatter plot showing a linear correlation for
the difference between channel 12 brightness temperatures (NOAA 15 minus
NOAA 14) and the NOAA 15 channel 11 brightness temperature computed using
the Lindenberg profiles. The linear Pearson correlation coefficient
is -0.68.
(a) Scatter plot showing a linear correlation between a
linear superposition of channel 11 and 12 brightness temperatures from
NOAA 15 (abscissa, T^12/15) with the corresponding channel 12
brightness temperature for the same profile but computed with the NOAA 14
channel response function. Note that the fit line has slope 1.000 and the
intercept is close to zero (2×10-4). The linear correlation is
R=0.986. All data are computed using the Lindenberg profiles. (b) The
same data, plotted with the difference in T12/14-T^12/15 on
the y axis.
For this purpose we try a bilinear regression
The regression
has been performed using IDL (Interactive Data Language) routine
REGRESS.
of the following kind:
T^12/15=a+bT12/15+cT11/15.
Here, T^12/15 is the desired pseudo-channel 12 brightness
temperature that is equivalent to a HIRS/2 measurement. In other words it is the
T12/15 that would have been measured by a HIRS/2 instrument. For the calculation of
T^12/15 only the nadir brightness temperatures have been retained
as it seems that the off-nadir directions do not yield differing information.
The two data vectors containing the brightness temperatures of channels 11
and 12 are linearly correlated with R=0.71, but they point in different
directions; that is, they are not co-linear. Regression thus yields a unique
result, namely
(a) Test of the superposition method using radiosonde
profiles from the two GRUAN stations Sodankylä, Finland, and Manus,
Papua New Guinea. The diagonal line (y=x) is included to check the result:
it is not a fit. (b) The same data, plotted with the difference in
T12/14-T^12/15 on the y axis.
a=-35.4029K,b=0.775623,c=0.370927.
The 1 σ uncertainty estimates of the parameters b,c are both
±0.01. The corresponding data pairs are shown in Fig. . The
slope and intercept of the regression (black line in panel a) are 1.000 and
2×10-4, respectively, and the linear correlation between the linear
superposition of channel 11 and 12 brightness temperatures and that of the
pseudo-channel 12 brightness temperature is 0.986. Panel (b) shows the same
data but with the difference between regressand and regressor on the
y axis. Maximum deviations from the zero line are about +3 and -2 K.
Mean and standard deviation of the residuals are 0.0±0.6 K.
Test with independent radiosonde profiles
Using the linear superposition of channel 11 and 12 brightness temperatures
for the considered atmospheric profiles from the two GRUAN stations,
Sodankylä and Manus, leads to the data pairs shown in Fig. . The
black diagonal line in this figure is not the result of a best fit or a
regression, but is y=x, plotted to guide the eye in checking the result. The
residual means (T12/14-T^12/15) and their standard deviations
are 0.3±1.3 K for Sodankylä and -0.4±1.3 K for Manus. Again, we
see that the regression using just one additional piece of information is not
able to provide a complete correction with an average residual of zero.
At least these residuals are much smaller than the original differences
between T12/14 and T12/15 shown in Fig. . Obviously, the
superposition methods works well for these data, representing a polar and an
equatorial atmosphere.
DiscussionSuperposition of weighting functions
The superposition of channels 11 and 12 is equivalent to a superposition of
their weighting functions. Fig. gives an example. The weighting
functions are generic functions, as in , assuming a water
vapour scale height of 2 km and peak altitudes of 8.5km
for ch. 12/15 (red curve), 7.5km for ch. 12/14 (black) and
5 km for ch. 11/15 (blue). The black curve with circles represents
the superposition of channels 11 and 12 on NOAA 15 with the weights b and
c derived above. The superposition curve (its upper tail, its peak and
about half of its lower tail) is between the corresponding channel 12
weighting functions. We note here that the superposition weighting function
has some weight at lower altitudes where both channel 12 weighting functions
are already very low. Overall, we see that the superposition method
eventually brings the pseudo-channel 12 brightness temperature of NOAA 15
closer to the level of the corresponding channel 12 brightness temperature of
NOAA 14.
Figure (and actual weighting functions shown in the Supplement,
Fig. S1) shows that there is some possibility that channel 11 sees the ground
when the atmosphere is quite dry. In such cases, which might occur at high
latitudes, the superposition will not work. High brightness temperatures in
both channels 10 and 11 could indicate such an event. Indeed, the
(high-latitude) Sodankylä data show larger scatter in Fig. than
the (equatorial) data from Manus, which might result from unwanted ground
influence at the high-latitude station.
An interesting alternative interpretation of the coefficients resulting from
the bilinear regression may derive from the following consideration: it is
possible to rewrite Eq. () as a weighted mean of three temperatures:
T^12/15=a′T0+bT12/15+cT11/15,with3a′+b+c=1.
From this interpretation and Eq. () follows a′=-0.14655 and it
turns out that T0=241.6K, which is remarkably close to
240 K, the T0 used as a reference in the retrieval schemes
developed by , and . At
the altitude where the channel 12 weighting function peaks the temperature
is, on average, close to T0. The remarkable fact is that the regression
results just in this T0 for the constant part and not anything else
– a finding that could not be expected a priori.
Examples of weighting functions for channels 11 and 12 on NOAA 15
(blue and red), their superposition (black with circles) and channel 12 on
NOAA 14 (black).
Application to real data
For the same set of 1004 days of common operation of NOAA 14 and NOAA 15 as
used in GE17, we have compared the channel 12 brightness temperatures and
daily averages on a 2.5∘× 2.5∘ grid in the northern
midlatitudes, 30 to 70∘ N. Differing from the previous paper, we use
the original non-intercalibrated brightness temperatures. For NOAA 15 we
compute the linear superposition derived above, that is, T^12,15,
while for NOAA 14 we use T12,14. The 2-D histogram of these data pairs
is shown in Fig. . It is remarkable how similar this histogram is to
a corresponding one shown as Fig. 2 in GE17, which displays the
intercalibrated data. The ordinary least squares linear fit through the new
data pairs (solid line) has the equation:
(y/K)=47.72+0.8025(x/K),
with a slightly smaller slope and a slightly larger intercept than in GE17
using the intercalibrated data pairs (0.8290 and 41.63, respectively).
These coefficients have been determined using a non-linear least-squares
Marquardt–Levenberg algorithm chap. 14.4. The slope has a
1σ uncertainty of 0.001. Because the linear least squares fit
suffers from regression dilution when errors of the regressor
(T^12,15) are not taken into account, we also compute the bivariate
regression (dash-dotted), which has the equation:
(y/K)=18.24+0.9256(x/K),
and this has a slightly smaller slope and larger intercept than the
corresponding fit through the intercalibrated data (which has 0.994 and
2.007, respectively). As such the quoted uncertainty of the slope
coefficient (0.001) refers only to the ordinary least squares fit. The
difference between the slope coefficients of the ordinary and bivariate
regression is considerably larger than the error estimate given above (i.e.
0.8025 vs. 0.9256). If we take this difference as a measure of
uncertainty of the slope parameter, then the differences between the present
parameters and those in GE17 (i.e. 0.8025 vs. 0.8290 for the ordinary
least squares and 0.9256 vs. 0.994 for the bivariate regression) are
relatively small. In this sense we may state that this comparison remarkably shows
that two essentially different methods used to treat the HIRS 2 to
HIRS 3 transition lead to very similar results.
2-D histogram of brightness temperatures, displaying
T^12/15 on the abscissa and T12/14 on the ordinate axes.
The data are from 1004 common days of operation of NOAA 14 and
NOAA 15. The dashed diagonal line represents x=y, the solid line is the
best fit according to an ordinary least squares regression and the
dashed–dotted line is the bivariate regression line.
In pursuit of the goal to study changes in upper-tropospheric humidity with
respect to ice (UTHi) we applied the retrieval formula of
to T^12,15 and to T12,14 of the common 1004 days. A density
plot of the corresponding data pairs of UTHi is displayed in Fig. .
Obviously the result is not satisfying; the plot closely resembles the
corresponding scatter of data pairs produced from the intercalibrated data
that are shown in Fig. 1 of GE17. Unfortunately the
superposition method does not solve the problem of a considerable
overestimation of the number of supersaturation events recorded with HIRS 3
and 4 instruments and it seems that the pseudo-channel 12 data have to be
treated with the cdf-matching technique developed by GE17 in the same way as
the intercalibrated data. This is beyond the scope of the present paper.
Heat map displaying UTHi computed using
T^12/15 on the ordinate against values computed from the original
T12/14 on the abscissa. Obviously the problem concerning the excess of
supersaturation cases in the NOAA 15 data remains even with this new kind of
data treatment. The colour scale shows the number of events in each
1 % × 1 % pixel.
The new method is an independent approach for an intercalibrated HIRS channel
12 data set, based on results of radiative transfer calculations,
classification of profile characteristics and a superposition with
information delivered by channel 11. The intercalibration of is
instead based on pixelwise direct corrections, where the brightness
temperature-dependent corrections are determined from regressions of the
first kind between subsequent satellite pairs. As Figs. and
show, both methods seem to produce very similar results. The statistically
based method of is thus supported by an independent method, and
results obtained from data intercalibrated with either method should be more
trustworthy. We thus consider our question from the beginning to be answered positively: whether
combining HIRS 2 and HIRS 3 data into a single time series is justified. Although both methods produce similar results, as we see
in Fig. , neither method of intercalibration solves the problems with
the discrepancy in the range of high UTHi values which results from a
corresponding discrepancy at the low tail of channel 12 brightness
temperatures (see GE17). It is probable that this problem does not originate
from the intercalibration procedure, since for the radiative transfer
calculation it makes no difference whether the humidity profile contains a
very humid upper troposphere with supersaturated layers or not. In each case
it provides the corresponding brightness temperature. It is more probable
that the problem with the lower tail of the T12 distribution comes from
the retrieval method, which is based on linearisations around certain
“tangential points”, thermodynamic properties typical of the upper
troposphere (e.g. the T0=240K mentioned above) and that this
linear approach is not completely sufficient in cases in which actual properties
are too far away from the tangential points.
Conclusions
The procedure we have developed in the present paper follows these
steps:
The difference, T12/15-T12/14=:ΔT12, calculated
with libRadtran for a set of radiosonde profiles, ranges from -12 to
-4 K, with most cases around -7 K, which fits to the
approximately 1 km altitude difference between the peaks of the
channel 12 weighting functions of HIRS/2 and HIRS/3.
It turns out that the shape of the RH profile determines whether
ΔT12 is close to one of the extremes or close to the average. It
is particularly the shape of the humidity profile in the lower to mid-troposphere that plays a role here.
Take channel 11 brightness temperatures as
a proxy of that part of the profile, as that channel measures the humidity in
the lower to mid-troposphere.
Indeed, and fortunately, T11/15 is
correlated to ΔT12; thus it can be used to identify in which cases
ΔT12 is large, average or small.
Thus it is possible to find a correction to T12/15 such
that the result is close to (with a mean residual difference of about 1 K)
the brightness temperature that N14 would have measured if it had seen the
same scene. This correction is a linear superposition of T12/15 and
T11/15, measured by the same HIRS instrument.
Application of this superposition method to real data of
1004 common days of operation of NOAA 14 and NOAA 15, comparing T12/14
with the pseudo-channel 12 brightness temperature of NOAA 15,
T^12/15, yields a 2-D distribution that is very similar to the
corresponding distribution obtained with the intercalibrated brightness
temperatures from . Comparing the corresponding values of UTHi again yields a 2-D
distribution very similar to that obtained from the intercalibrated data.
From these findings we conclude that our method, which is based on radiative
transfer calculations, i.e. physics, produces very similar results with the
Shi and Bates statistical intercalibration method. The justification to use
the intercalibrated channel 12 time series including its early HIRS 2 and
later HIRS 3 and 4 phases is thus corroborated.
Note that this paper only shows the principle of method, how a pseudo HIRS/2
channel 12 brightness temperature can be computed from later HIRS versions,
involving channels 11 and 12. As all HIRS instruments have slightly different
channel spectral response functions, the regression parameters (a, b,
c) will differ from one instrument pair to the other. They will also depend
on which HIRS/2 instrument serves as reference. In this paper we used HIRS/2
on NOAA 14, but it certainly makes sense to additionally use HIRS/2 on
NOAA 12 as based their intercalibration on that satellite. This
work is beyond the scope of the current paper and left for future exercise.
We also note that this analysis represents a relatively short period in the
lifetime of two HIRS instruments and that their spectral and radiometric
calibration was assumed to be constant over this period.
Code availability
The libRadtran radiative transfer software package is
freely available under the GNU General Public License from
http://www.libradtran.org/doku.php.
Data availability
The GRUAN radiosonde data are available from the GRUAN
websites. The special Lindenberg radiosonde data set is available from the
first author on request. The NOAA satellite data are available from NOAA
public websites.
The supplement related to this article is available online at: https://doi.org/10.5194/amt-11-939-2018-supplement.
Author contributions
KG made the radiative transfer calculations and
the analyses. KG and RS discussed the procedures and the statistical
methods. KE prepared the satellite data in a useful form. All
authors contributed to the text.
Competing interests
The authors declare no competing interests.
Acknowledgements
The authors thank the LibRadtran developer team for providing the
radiative transfer code and Luca Bugliaro for checking the first
author's set-up of the radiative transfer job. We are grateful to all
the people who provided the data used in this paper, who are
colleagues from NOAA, the GRUAN network and DWD. Christoph Kiemle
read the pre-final version of the manuscript and made good
suggestions for improvement and further discussion. Thanks for this!
The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: Isaac Moradi Reviewed by: two
anonymous referees
References
Anderson, G., Clough, Kneizys, F., Chetwynd, J., and Shettle, E.: AFGL
atmospheric constituent profiles (0–120 km), Tech. Rep. Tech. Rep.
AFGL-TR-86-0110, Air Force Geophys. Lab., Hanscom Air Force Base, Bedford,
Mass., 1986.Chung, E.-S., Soden, B., Huang, X., Shi, L., and John, V.: An assessment of
the
consistency between satellite measurements of upper tropospheric water vapor,
J. Geophys. Res., 121, 2874–2887, 10.1002/2015JD024496, 2016.Dirksen, R. J., Sommer, M., Immler, F. J., Hurst, D. F., Kivi, R., and
Vömel, H.: Reference quality upper-air measurements: GRUAN data
processing for the Vaisala RS92 radiosonde, Atmos. Meas. Tech., 7,
4463–4490, 10.5194/amt-7-4463-2014, 2014.Emde, C., Buras-Schnell, R., Kylling, A., Mayer, B., Gasteiger, J., Hamann,
U., Kylling, J., Richter, B., Pause, C., Dowling, T., and Bugliaro, L.: The
libRadtran software package for radiative transfer calculations (version
2.0.1), Geosci. Model Dev., 9, 1647–1672,
10.5194/gmd-9-1647-2016, 2016.
Gasteiger, J., Emde, C., Mayer, B., Buehler, S., and Lemke, O.:
Representative
wavelengths absorption parameterization applied to satellite channels and
spectral bands, J. Quant. Spectrosc. Ra., 148, 99–115, 2014.Gierens, K. and Eleftheratos, K.: Upper tropospheric humidity changes under
constant relative humidity, Atmos. Chem. Phys., 16, 4159–4169,
10.5194/acp-16-4159-2016, 2016.Gierens, K. and Eleftheratos, K.: Technical note: On the intercalibration of
HIRS channel 12 brightness temperatures following the transition from HIRS 2
to HIRS 3/4 for ice saturation studies, Atmos. Meas. Tech., 10, 681–693,
10.5194/amt-10-681-2017, 2017.Gierens, K., Kohlhepp, R., Spichtinger, P., and Schroedter-Homscheidt, M.:
Ice supersaturation as seen from TOVS, Atmos. Chem. Phys., 4, 539–547,
10.5194/acp-4-539-2004, 2004.Gierens, K., Eleftheratos, K., and Shi, L.: Technical Note: 30 years of HIRS
data of upper tropospheric humidity, Atmos. Chem. Phys., 14, 7533–7541,
10.5194/acp-14-7533-2014, 2014.Immler, F. J., Dykema, J., Gardiner, T., Whiteman, D. N., Thorne, P. W., and
Vömel, H.: Reference Quality Upper-Air Measurements: guidance for
developing GRUAN data products, Atmos. Meas. Tech., 3, 1217–1231,
10.5194/amt-3-1217-2010, 2010.Jackson, D. and Bates, J.: Upper tropospheric humidity algorithm assessment,
J. Geophys. Res., 106, 32259–32270, 2001.
Press, W., Flannery, B., Teukolsky, S., and Vetterling, W.: Numerical
recipes,
Cambridge University Press, Cambridge, UK, 1989.Shi, L. and Bates, J.: Three decades of intersatellite–calibrated
High–Resolution Infrared Radiation Sounder upper tropospheric water vapor,
J. Geophys. Res., 116, D04108, 10.1029/2010JD014847, 2011.Soden, B. and Bretherton, F.: Upper tropospheric relative humidity from the
GOES 6.7 µm channel: Method and climatology for July 1987, J. Geophys.
Res., 98, 16669–16688, 1993.
Soden, B. and Bretherton, F.: Interpretation of TOVS water vapor radiances in
terms of layer–averaged relative humidities: Method and climatology for the
upper, middle, and lower troposphere, J. Geophys. Res., 101, 9333–9343,
1996.
Spichtinger, P., Gierens, K., Leiterer, U., and Dier, H.: Ice supersaturation
in the tropopause region over Lindenberg, Germany, Meteorol. Z., 12,
143–156, 2003.
Stamnes, K., Tsay, S.-C., Wiscombe, W., and Jayaweera, K.: Numerically stable
algorithm for discrete ordinate method radiative transfer in multiple
scattering and emitting layered media, Appl. Optics, 27, 2502–2509, 1988.
Stephens, G., Jackson, D., and Wittmeyer, I.: Global observations of
upper–tropospheric water vapor derived from TOVS radiance data, J. Climate,
9, 305–326, 1996.