Far-infrared (FIR:

Defined here as wavelengths above 15

Despite its role in the energy budget, due to the inherent difficulties
involved, only a few instruments have measured hyperspectral radiances
across the FIR. Aircraft and ground-based measurements available from the
Tropospheric Airborne Fourier Transform Spectrometer (TAFTS)

Almost all of the available FIR radiance measurements originate from limited
field campaigns. Recognising the key role that the FIR plays in determining
the Earth's energy budget, the information that may be contained in the
spectrum and the lack of available measurements,

REFIR-PAD has been measuring spectral downwelling longwave radiances at
Dome-C Antarctica since 2011, providing a long-term database covering the
spectral range from 100 to 1400

Given the constrained nature of the REFIR-PAD dataset, if the results show that the approach fails to capture the observed spectral behaviour, it would cast serious doubt on whether our ability to model the full infrared spectrum is sufficient for us to expect a similar approach to give a robust spectral prediction over a wider range of conditions and/or viewing geometries. Conversely, while a successful implementation does not directly imply that a similar level of agreement will be seen in other locations and for other viewing geometries, it does give confidence that the general principle is robust.

In Sect. 2, the instrumental data are described along with the radiative transfer model used to produce simulated spectra for comparisons. We also describe the distinct steps of the spectral extension method. Section 3 displays the results, with comparison between instrumental and theoretical extensions, which are discussed in Sect. 4. We also investigate the impact of spectral averaging, consistent with the type of resolution currently employed in global climate models as a key potential use of such data for model evaluation. Finally we draw conclusions in Sect. 5.

The REFIR-PAD instrument is currently located at the Italian–French Concordia
research station in Antarctica (75

The instrument, fully described in

The selection of the clear-sky spectra uses the classification outlined in

We choose to focus only on clear-sky conditions because this gives us a
reasonably well-constrained dataset to use in testing the extension approach.
Including cloudy conditions would require a successful detection of
cloud type, height and microphysics to incorporate into the radiative
transfer modelling described in Sect. 2.3, adding significant complexity to
the study. From previous theoretical studies and ongoing work analysing the
REFIR-PAD spectra, we also expect unique information related to ice crystal
habit to be contained within the FIR micro-windows

An example of a clear-sky spectrum is displayed in Fig.

Example of a clear-sky spectrum as seen from REFIR-PAD (in black) and its associated standard deviation (in red), the noise equivalent spectral radiance (in green) and the calibration error (in blue).

Since 2005, the radiosonde system routinely operative at Dome C has provided
atmospheric pressure, temperature and humidity profiles at 12:00 UTC. From 2009
onwards these observations have been made using the Vaisala RS-92SPGW. The
daily profiles are available at

During a radiosonde launch, data are recorded every 2

We use the Line-By-Line Radiative Transfer Model

The radiosonde profiles described in Sect. 2.2 provide the temperature and
water vapour inputs for the radiative transfer simulations. The radiosonde
profiles are interpolated onto 100 levels, with the highest vertical
resolution being 26

Based on the methodology developed by T15, FIR wavenumbers between 100 and
667

We start by selecting the REFIR-PAD spectra that will be used to calculate
the regression coefficients. All clear-sky spectra that are closest in time
to the daily radiosonde measurement at 12:00 UTC are selected. If the closest
spectrum on a given day is measured more than 2 h before or after 12:00 UTC,
the spectrum is discarded. 125

To choose the predictor wavenumbers, we select a FIR wavenumber and create a
vector composed of all radiances in the creation set at this wavenumber. We
compute the correlation of this vector with a similar vector at a MIR
wavenumber. We repeat this analysis for all MIR wavenumbers and select the
MIR wavenumber that shows the highest correlation as the predictor for the
given FIR wavenumber. Finally, the linear (or logarithmic) regression
coefficients are calculated. The whole process is repeated for each FIR
wavenumber. We emphasise that the methodology described here is only based on
analytical considerations with the computation of the correlation. No
spectral assumptions are made, and as a consequence the MIR predictor
wavenumbers can be associated either with, for example, a

Figure

We observe specific spectral regions that maximise the correlation. A large
portion of the spectral region between 150 and 500

As noted in Sect. 2.4, regression coefficients

FIR radiances at 301.6

Using the test set of spectra we examined the robustness of the extension
method. An example of a single REFIR-PAD observation (in black) and its
extension (in blue) is displayed in Fig.

At 10

Far-infrared extension based on REFIR-PAD data (linear case).

The previous section suggests that a reasonable reconstruction of observed
clear-sky downwelling FIR surface spectral radiances at a moderate (10

Therefore, we apply the same process of extension using simulated LBLRTM spectra. For each clear-sky case used to build the creation and test sets for REFIR-PAD data, the corresponding radiosonde profile is selected and used as input for LBLRTM as described in Sect. 2.2. The output spectra are used to generate the equivalent simulated creation and test sets.

We consider two cases. The first uses the LBLRTM spectra as directly
simulated, while the second adds noise in order to be more representative of
the REFIR-PAD observations. Noise is introduced using the following equation:

The correlation maps of LBLRTM with and without noise are displayed in
Fig.

The predictor wavenumbers are displayed in Fig.

Correlation map using noiseless LBLRTM spectra

At the time of writing there are only very limited spectrally resolved data
in the FIR. The goal of this research is thus to see whether the LBLRTM
simulations are able to provide coefficients to correctly map the observed
MIR data into the FIR. So we now test the accuracy of going from observed MIR
to FIR radiances using three different approaches. All predictions are then
compared against the REFIR-PAD FIR observations. The three different sets of
regression coefficients we use are

LBLRTM simulations (LBL);

LBLRTM simulations with added realistic noise (LBN);

coupled LBLRTM (LBC), whereby predictor wavenumbers are generated from LBLRTM with added realistic noise, but regression coefficients are generated from LBLRTM without noise.

In all cases shown, a linear regression is used, although the findings are
essentially unchanged if a logarithmic fit is employed (see Table

As Fig. 4b for all cases of linear extension, with

Noise-free simulations of downwelling spectrally resolved clear-sky radiances
over Antarctica imply a high level of correlation between the MIR and FIR.
However, the prediction model based on these simulations fails to adequately
capture observed behaviour under clear skies as exhibited by REFIR-PAD.
Instrumental noise characteristics strongly affect the choice of predictor
wavenumbers. Including the effects of this noise in the simulations markedly
improves the prediction model, which is capable of capturing the observed
mean radiance in the FIR to within 2 %, except in selected bands where the
downwelling radiance is low (for example 410 and 490

More specific to this study, it is worth noting that the temperature and
water vapour profiles very close to the ground (within 2

In this study, the extension of REFIR-PAD has been performed on its native
grid (

The extensions of REFIR-PAD using the various prediction models described in
Sect. 3.2 were integrated over these bands, and the corresponding results
are shown in Table

Distribution of the differences and relative variations between the
extension and the original spectra within the three bands (100.4–400, 400–550 and 550–667

Using the REFIR-PAD prediction model, integrating over wide spectral bands
results in relatively small differences between the observed and extended
spectra, below 3 %. However, as described earlier, the extension using
simulated noise-free regression coefficients leads to strong biases, with
maximum percentage differences (up to

In this study we have used REFIR-PAD downwelling radiance observations
covering the spectral range 100–1400

Correlation maps between the observed FIR and MIR radiances show peak values
at wavenumbers around 700

Using a prediction model built solely with REFIR-PAD observations, the
extension from the MIR to the FIR works satisfactorily, with mean relative
variations below 5 % over most of the spectral range. Between 400 and 570

Our results show that while it is feasible to use the type of approach we have outlined here to extend mid-infrared spectral measurements to the far infrared, the quality of the extension is strongly dependent on the noise characteristics of the observations. This in turn implies that if a similar approach is developed to extend existing mid-infrared ground- or satellite-based observations, the instrument noise must be explicitly accounted for in building the model due to its potential role in altering the choice of predictor wavenumbers from the noise-free case. In addition, the quality of any extension using this type of method will also be critically dependent on whether the creation set of atmospheric profiles correctly represents the conditions which are actually sampled by the MIR instruments.

An obvious next step for this work would be to include cloudy conditions in
the approach. However, this is challenging, as, given the results here, one
would anticipate that a good knowledge of cloud microphysics and optical
properties as well as vertical location, including any impact on the
associated temperature and water vapour profiles, would be required to
perform the forward modelling with the requisite accuracy. The frequency of
radiosonde ascents at Concordia precludes knowledge of the last effect. Cloud
microphysics are not measured directly, and cirrus bulk optical properties are
poorly constrained in the FIR

More generally, one would want to test whether such a synthetic approach
could be applied at the global scale and for potentially more interesting
satellite viewing geometries. If selected, the candidate ESA Earth Explorer 9
mission, the Far infrared Outgoing Radiation Understanding and Monitoring
concept

The REFIR-PAD data are available at

CB, HEB and SFBT designed and carried out the study. RR provided clear-sky data. GDN, LP and GB provided REFIR-PAD data. All co-authors contributed to the preparation of the article.

The authors declare that they have no conflict of interest.

The analysis was supported by the NERC-funded International Consortium for the Exploitation of Infrared Measurements of PolAr ClimaTe (ICE-IMPACT) project (grant NE/N01376X/1) and by the National Centre for Earth Observation, UK. The deployment of REFIR-PAD in Antarctica was supported by the Italian National Program for Research in Antarctica PNRA (Programma Nazionale di Ricerche in Antartide) under the following projects: 2009/A04.03, 2013/AC3.01 and 2013/AC3.06.

This research was supported by the NERC (grant no. NE/N01376X/1).

This paper was edited by Qiang Fu and reviewed by three anonymous referees.