In the present study we explore the capability of the
intercalibrated HIRS brightness temperature data at channel 12 (the
HIRS water vapour channel;

Ice supersaturation is a frequent phenomenon in cold regions of the
troposphere (below 0

An ideal data set with which to study long-term changes
of upper-tropospheric humidity (UTH) is provided by the series of
polar-orbiting satellites of the National Oceanic and Atmospheric
Administration (NOAA), which started in the late 1970s and is
still ongoing, meanwhile in co-operation with the European
Organisation for the Exploitation of Meteorological Satellites
(EUMETSAT). The satellites all carry the High-Resolution Infrared
Radiation Sounder (HIRS). Channel 12 of this instrument can be used to
retrieve UTH. It is a radiance-based quantity that represents a
weighted mean over a vertical profile of relative humidity with a peak
of weighting function in the upper troposphere. The retrieval method
has been developed by

All the NOAA satellites from N06 (launched 1979) to N14 (launched 1994) carried
version 2 of the HIRS instrument, while from N15 on (launched 1998)
version 3 and later version 4 of HIRS were installed. The transition
from HIRS 2 to HIRS 3 involved a shift of the central wavelength in
channel 12, from 6.7 to 6.5

Such a strong discontinuity would break the desired long-term time
series, but

The intercalibrated HIRS brightness temperature (BT) data for the
past 35 years (1979–2014) have been used to study long-term changes
in the upper-tropospheric water vapour

In the present paper this radiance-based quantity is used for the
first time to study ice supersaturation cases in the upper troposphere
with such a long time series. As ice-supersaturated layers are
typically much shallower than the layer where channel 12 of HIRS is
sensitive to, only a very small fraction of UTHi values exceed 100 %

In the following we first show how high values of UTHi and
ice supersaturation behave when the transition between the two HIRS
instruments occurs. Then we discuss several refinements to the
intercalibration

When we used these intercalibrated data to set up a time series of the number of occurrences of cases with ice supersaturation, we found a strong increase, seemingly coincident with the transition from HIRS 2 to HIRS 3, and this unwanted surprise led us to check the intercalibration especially for the transition again. The check disclosed problems especially at the low end of channel 12 brightness temperatures, i.e. at those data that are characteristic for the supersaturation cases.

We believe that the intercalibration of

Scatter plot of data of upper-tropospheric
humidity with respect to ice (UTHi, in percent), retrieved from
channel 12 brightness temperatures from the HIRS 2 instrument on
NOAA 14 and from the corresponding HIRS 3 instrument on NOAA 15. The
data pairs represent daily average values taken in

In order to make progress and avoid excessive averaging we consider
daily averages of

Figure

The
abscissa shows values measured by N14, while the ordinate shows
corresponding values measured by N15. Ideally the data pairs should
lie on the diagonal (the dashed red

Two-dimensional histogram of

Let us make a step back and consider the brightness temperatures

The diagonal does not,
therefore, represent the best (least squares) fit, that is, the
intercalibration can be improved.
Ordinary least squares (OLS)
linear regression (black solid line) yields the following fit:

The stars in Fig.

For the moment this demonstrates that the intercalibration of the channel 12 brightness temperatures can be improved using common daily data for single grid cells instead of zonal/monthly averages. Whether this improvement is also useful for the retrieval of upper-tropospheric humidity values has yet to be shown.

We have performed the retrieval of UTHi

As Fig.

It is obvious that the N15-retrieved values are lower than before and that the excess of data points above the diagonal line is no longer present.

Unfortunately, however, we must note that the range of UTHi (N15) is
dramatically decreased at the high end and that all cases of
supersaturation are eliminated when this kind of intercalibration is
indeed applied. Therefore, ironically, instead of reducing the number of
supersaturation cases in N15 data to a level given by the
corresponding number of such events in N14 data, the new
regression-based intercalibration eliminates all supersaturation.
The comparison of this feature between N14 and N15 has in no way been
improved – it has merely been turned upside-down. We note that similar
procedures like bin-wise intercalibration with and without outlying
data pairs (more than

Cumulative distribution functions (cdf) of
channel 12 brightness temperatures, measured with HIRS 2 on N14
(red) and with HIRS 3 on N15 (blue). Note the quite large
discrepancy (in relative terms) between both cdf's at low values of

The goal of the new intercalibration exercise is to have a similar
number of supersaturation cases for the data overlap period of N14 and
N15 because the strong jump detected in the original data seems
implausible even when one acknowledges that the two satellites see the
same grid cell at different times during a day. The
cumulative distribution functions (cdf's) of the corresponding
channel 12 brightness temperatures (Fig.

We devised an alternative intercalibration procedure that yields
similar distribution functions (with the N14 cdf as reference) as
follows: the data sets are grouped in

We start with the lowest bin and compare

What is the best bin width

Corrections determined for
1

The corrections for 1

The result of this kind of intercalibration for the intercomparison of
the two brightness temperature data sets is shown in Fig.

As Fig.

The result of the cdf-based intercalibration is shown for UTHi in
Fig.

It is not necessary to show the

As Fig.

Simple statistical measures, computed with the set of the common daily
and grid-based data, may show that an improvement indeed results from
the cdf-based intercalibration. The indicators are the following:

The mean difference of channel 12 brightness temperature (N15
minus N14) is

The mean difference of the corresponding UTHi is

Collection of 256 data pairs where both satellites report ice supersaturation (black points) and their modification after application of the cdf-based intercalibration (red points). Top: effect of the modification on the N15-measured brightness temperature. Bottom: effect of the modification on UTHi. More than two-thirds of all N15 supersaturation cases are shifted to a UTHi value between 90 and 100 %.

For testing the procedure further we consider the 256 data records indicating ice
supersaturation in both measurements (N14 and N15). These pairs of
brightness temperature and UTHi are shown in Fig.

Raw time series of fraction of exceedances for
UTHi thresholds from 70 to 100 % before (top) and after (bottom)
application of the cdf-based

Figure

A similar analysis with the modified data shows no obvious signs of a trend and it will need sophisticated time-series analytical methods to find out whether there are any trends in the data at all. A deeper analysis of the four time series will be reported in a forthcoming paper.

There are, in fact, two questions to be discussed:

Is it justified at all to combine all HIRS

Is it justified to use a cdf-based intercalibration procedure?

The first of these questions is a difficult one, and it is just the
basic question of a number of subsequent problems such as
“Under which circumstances is it justified or not?” and “Which assumptions
have to be made about the structure of temperature and moisture
profiles?” This technical note is not the place to answer these
questions, but it certainly deserves much more research in order to be
sure that results obtained so far

In order to discuss the second question, an analysis and comparison of
what is effectively done in the cdf-based and the regression-like
methods are needed. It should be noted that the only subjective element in the
intercalibration problem is the choice of the method. Once the method
has been chosen, everything else is based on fixed rules and is
therefore objective. The difference in the methods is the different
set of rules and the reasoning from which these rules are derived. In
the end, the procedures are similar again: all methods are used to
determine a

The OLS regression method is based on the postulate that the mean squared difference between all data pairs is a minimum (regression of the second kind).

The method of

The cdf-based method is based on the postulate that

One essential difference between regression-based and cdf-based methods is that the first considers the data as pairs while this connection is given up in the latter method. The latter instead considers the statistical properties of the data as two independent populations. Both views have pros and cons. Considering the data as pairs is justified to a certain degree since they are taken on the same day in the same grid cell. However, they are also taken at different times of the day, which loosens the connection. In addition, statistical errors arising from the use of OLS regression (i.e. regression dilution) may cause difficulties in determining a correct connection between data pairs.

Average fraction of exceedances and corresponding
standard deviations (both in percent) for UTHi thresholds from 70 to 100 %
during 1980–1998 (period before the transition from HIRS 2 to HIRS 3/4),
1999–2005 (transition period) and 2006–2014 (post-transition
period), before

Since the truth is unknown, no decision can be made regarding which method gives results closer to reality. However, it would be very implausible that supersaturation would suddenly occur much more frequently than before (original data), or not anymore (OLS regression-based method). If the NOAA HIRS channel 12 time series can be combined at all (a question not to be solved here) we need an intercalibration that keeps a certain level of supersaturation frequency, and the most conservative choice is then that a change of the UTH distribution functions during the 1004-day transition period from one to the next satellite should be small. Thus, for us it was simply a practical decision guided by this conservative assumption to choose the cdf-based method.

Further evidence for choosing the cdf-based method, as a plausible
intercalibration method to account for values found at the low tail of

For the case of the 70 % UTHi threshold, the original data suggest that
the mean fraction of exceedances increased from about 1.6 % in the
period 1980–1999 to about 3.8 % in 2006–2014, corresponding to an
overall increase of about 138 % within about two decades or so. The
respective changes for the cases of 80, 90 and 100 % UTHi
thresholds by the original data were even larger. Although the mean
fraction of exceedances is generally small for the examined UTHi
thresholds, such large changes from one period to another do not sound
reasonable and are indicative that something may be wrong in the data.
Application of the cdf-based correction to the UTHi threshold data of
70 % reduces the change from 138 to 9 %. Significant
improvements are also found at the other UTHi thresholds. The
differences between the cdf-corrected data and the original data in
the periods examined are obvious (Table

Our proposed intercalibration method is based on the
assumption that the probability of supersaturation did not change
during the transition period from the HIRS 2 to the HIRS 3
instrument. This is indeed a working hypothesis that is necessary to
do the correction. Of course, the frequency of supersaturation might
have changed over time, which is not known and which is a reason for
studying high UTHi values. It is, however, very implausible that it
has changed so dramatically just at the transition to HIRS 3. The
increase in the frequency of threshold exceedances is not small; it
is more than a

Finally, we want to stress that it is of great importance to have
homogeneous time series over the whole range of brightness
temperature and UTHi values. For applications where the mean of

We developed a new method for intercalibration of satellite data that
is based on a comparison of distribution functions of brightness
temperatures instead of regression methods. We applied this
intercalibration to channel 12 brightness temperatures measured with
the HIRS 2 instrument on NOAA 14 and the HIRS 3 instrument on NOAA 15.
These data had already been intercalibrated by

We tried regression-based intercalibration procedures first but without success. Instead of less ice supersaturation in HIRS 3 data, all supersaturation cases were eliminated because the corrections were too large. This again seemed to us unphysical and implausible.

The new intercalibration method is constructed in such a way that the probability of supersaturation does not change in the transition from HIRS 2 to HIRS 3. Of course, we do not know whether this assumption is correct; it is simply the most conservative assumption. Other data sets for the transition period (1999–2005) are needed to check the validity of this assumption. This is beyond the scope of the present paper.

The overall discrepancies between the

A fundamental question is whether and under which conditions HIRS 2 and HIRS 3 data can be combined into a single time series at all, since the instruments sense different layers in the upper troposphere. For the present investigation we have assumed, as a working hypothesis, that such a combination is admissible. It is not within the scope of this paper to begin an investigation of this difficult problem, but it is certainly a topic for the near future.

IDL code for the cdf nudging can be obtained from the first author on request.

HIRS data in general are available from NOAA. The data used for the present paper can be obtained from the authors on request.

Following the suggestion of one reviewer, we added bivariate regression
lines to Figs.

Specifically, for the original data we have

For the cdf-corrected data we have

Although the bivariate regression line provides in some sense the best
fit through a bivariate distribution of data with uncertainties in
both dimensions, it seems simply inappropriate to derive corrections to the quantity on the

Consistent (red points) and inconsistent (blue points) use of the
bivariate regression coefficients for correction of channel 12
brightness temperatures from NOAA 15. The black line is the diagonal

The result of both corrections is plotted in
Fig.

Bivariate regression is a method to avoid regression dilution

Kostas Eleftheratos provided the raw UTHi and BT data; Klaus Gierens wrote and ran the IDL codes. Both analysed the results and wrote the text.

The authors declare that they have no conflict of interest.

We thank Lei Shi (NOAA) for providing 35 years worth of HIRS brightness temperature data and for her help and advice when problems occurred. Christoph Kiemle and Robert Sausen read a manuscript version of the paper and helped to improve it. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: B. Kahn Reviewed by: three anonymous referees