High-resolution Infrared Radiation Sounder (HIRS) brightness temperatures at
channel 12 (

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

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.

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

In fact, this question can be broken down into sub-questions. (1) Under
which circumstances is the

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.

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.

Satellite Application Facility (SAF) for numerical weather
prediction (NWP)

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

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

Figure

Scatter plot of brightness temperatures calculated with a radiative
transfer model using radiosonde profiles from Sodankylä,
Finland

Figure

At this point it is useful to recall that the weighting functions of the two
considered channels peak at altitudes about 1

Now the question arises of how characteristics of humidity profiles are
reflected in the brightness temperature differences. Figure

Lindenberg radiosonde profiles of relative humidity vs. pressure
altitude that lead to brightness temperature differences in extreme ranges
(

The first set of profiles with

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

HIRS/3 channel 11 is centred at a wavelength of 7.3

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

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

For this purpose we try a bilinear regression

The regression
has been performed using IDL (Interactive Data Language) routine

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 superposition of channels 11 and 12 is equivalent to a superposition of
their weighting functions. Fig.

Figure

An interesting alternative interpretation of the coefficients resulting from
the bilinear regression may derive from the following consideration: it is
possible to rewrite Eq. (

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).

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-D histogram of brightness temperatures, displaying

In pursuit of the goal to study changes in upper-tropospheric humidity with
respect to ice (UTHi) we applied the retrieval formula of

Heat map displaying UTHi computed using

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

The procedure we have developed in the present paper follows these
steps:

The difference,

It turns out that the shape of the RH profile determines whether

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,

Thus it is possible to find a correction to

Application of this superposition method to real data of
1004 common days of operation of NOAA 14 and NOAA 15, comparing

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 (

The libRadtran radiative transfer software package is
freely available under the GNU General Public License from

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:

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.

The authors declare no competing interests.

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