Can downwelling far-infrared radiances over Antarctica be estimated from mid-infrared information?

. Far-infrared (FIR: 100 cm -1 < wavenumber, ν < 667 cm -1 ) radiation emitted by the Earth and its atmosphere plays a key role in the Earth’s energy budget. However, because of a lack of spectrally resolved measurements, radiation schemes in climate models suffer from a lack of constraint across this spectral range. Exploiting a method developed to estimate upwelling far-infrared radiation from mid-infrared (MIR: 667 cm -1 < ν < 1400 cm -1 ) observations, we explore the possibility of inferring zenith FIR downwelling radiances in zenith-looking observation geometry, focusing on clear-sky conditions in Antarctica. The 5 methodology selects a MIR predictor wavenumber for each FIR wavenumber based on the maximum correlation seen between the different spectral ranges. Observations from the REFIR-PAD instrument (Radiation Explorer in the Far Infrared - Prototype for Application and Development) and high resolution radiance simulations generated from co-located radio soundings are used to develop and assess the method. We highlight the impact of noise on the correlation between MIR and FIR radiances by comparing the observational and theoretical cases. Using the observed values in isolation, between 150 and 360 cm -1 , 10 differences between the ’true’ and ’extended’ radiances are less than 5 %. However, in spectral bands of low signal, between 360 and 667 cm -1 , the impact of instrument noise is strong and increases the differences seen. When the extension of the observed spectra is performed using regression coefﬁcients based on noise-free radiative-transfer simulations the results show strong biases, exceeding 100 % where the signal is low. These biases are reduced to just a few percent if the noise in the observations is accounted for the simulation procedure. Our results imply that while it is feasible to use this type of approach 15 to extend mid infrared spectral measurements to the far-infrared, the quality of the extension will be strongly dependent on the noise characteristics of the observations. A good knowledge of the atmospheric state associated with the measurements is also required in order to build a representative regression model. a methodology radiances by exploiting correlated behaviour in the They applied this to nadir radiance measurements from the Infrared Atmospheric Sounding Interferometer (IASI, and evaluated their approach by comparing spectrally integrated radiances across the infrared with measurements from the Clouds and the Earth’s Radiant Energy System (CERES, Wielicki 1996) broadband radiometers taken during simultaneous nadir overpasses. Overall mean broadband agreement is encouraging but the evaluation technique precludes the identiﬁcation of any compensating biases within the FIR itself and is 25 limited to polar regions. Correlation maps between the observed FIR and MIR radiances show peak correlations at wavenumbers around 700 cm -1 . Noise-free simulated spectra also show strong correlations at wavenumbers between 1340 and 1400 cm -1 . With the addition of 20 realistic noise to the simulations the pattern of the correlation map alters and looks more similar to the one created using the REFIR-PAD observations, with reduced correlations at wavenumbers < 180 cm -1 and between 470-570 cm -1 This indicates that the selected wavenumbers and the associated MIR to FIR correlation are both highly dependent on instrumental noise.

PAD wavenumber range) to infer FIR spectral behaviour using actual observations. This endeavour is particularly timely given the recent selection of the Far infrared Outgoing Radiation Understanding and Monitoring (FORUM) concept (Palchetti et al., 2016) as an ESA Earth Explorer 9 candidate mission.
In section 2, the instrumental data are described along with the radiative transfer model used to produce simulated spectra 5 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 section 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 are for model evaluation. Finally we draw conclusions in section 5.

REFIR-PAD
The REFIR-PAD instrument is currently located at the Italian-French Concordia research station in Antarctica (75°06'S, 123°23'E) at 3,230 m above sea level. It was installed in the Physics Shelter, south of the main station buildings for the PRANA project (Proprietà Radiative dell'Atmosfera e delle Nubi in Antartide), financed by the Italian PNRA (Progetto Nazionale per la Ricerca in Antartide). The project aims to supply the first complete dataset of the spectral downwelling longwave radiances over 15 a polar region, and has been recording data autonomously since 2011 (Palchetti et al., 2015) and within later project CoMPASS (COncordia Multi-Process Atmospheric StudieS), the currently active DoCTOR (DOme C Tropospheric ObserveR) and FIR-CLOUDS (Far Infrared Radiative Closure Experiment For Antarctic Clouds). A protective chimney separates the instrument from the outside temperature and the ingress of wind and snow is prevented by a barrier on the rooftop. The instrument, fully described in Bianchini et al. (2006), is composed of a Fourier transform spectroradiometer  Zehnder type) with an operating spectral bandwidth of 100 -1400 cm -1 (100 -7.1 µm) at a resolution of 0.4 cm -1 and with an acquisition time of 80 s. One calibrated spectra is based on the average of four zenith observations for an overall measurement time of 6.5 min every 14 min. The noise equivalent spectral radiance (NESR) due to detector noise is approximately 1 mW m -2 sr -1 (cm -1 ) -1 at 400 cm -1 . In addition to the radiometric NESR, the calibration error and the standard deviation of the four observations composing the calibrated spectrum are calculated. The standard deviation is a posteriori estimation that includes 25 the NESR and possible scene variations (Palchetti et al., 2015).
In the study, only clear-sky cases from 2013 are used. The selection of the clear-sky spectra uses the classification outlined in Rizzi et al. (2016) to discriminate between clear and cloudy scenes. Twenty-four spectral intervals are selected and seven tests are applied, comparing the mean radiances, the standard deviation and the brightness temperature in the specified spectral intervals. This approach yields 5126 clear sky spectra for 2013. An example of a clear-sky spectrum is displayed in figure 1 and   30 shows unphysically high radiances and standard deviations in two bands within the atmospheric window region, from 1095 -1140 cm -1 and 1230 -1285 cm -1 . These are a manifestation of absorption by the polyethylene terephthalate (Mylar) substrate which composes the wideband beam splitter and hence radiances within these bands are not used in this study. Outside these two regions and where the downwelling signal is typically high (below 400 cm -1 and between 600 and 800 cm -1 ), the standard Figure 1. 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).
deviations are relatively small. However, in the most transparent regions, where the radiance is low (micro-windows between 400 -600 cm -1 and in the atmospheric window from 800 -1000 cm -1 for example), the standard deviations can exceed the measured radiances with values around 2 r.u. (radiance unit), where 1 r.u. is equivalent to 1 mW m -2 sr -1 (cm -1 ) -1 .

5
Since 2005, the radiosonde system routinely operative at Dome C has provided atmospheric pressure, temperature and humidity profiles at 12 UTC. From 2009 onwards these observations have been made using the Vaisala RS-92SPGW. The daily profiles are available at www.climantartide.it.
Data are recorded every 2 seconds, corresponding to around 800 measurements in the troposphere, and between 900 to 1900 measurements in the stratosphere, reaching up to 26-30 km (Tomasi et al., 2011). However, the relative humidity is only 10 measured up to 15 km. Due to the balloon ascent rate (5-6 m s -1 ) and the recording rate, the vertical resolution is about 10-12 m.
Raw water vapour profiles are provided in relative humidity and the conversion to mixing ratio assumes saturation over water as advised by the World Meteorological Organisation (WMO) guide to meteorological instruments and methods of observation (https://www.wmo.int/pages/prog/www/IMOP/CIMO-Guide.html).

15
We use the Line-By-Line Radiative Transfer Model (LBLRTM) developed by Clough et al. (2005) to simulate the downwelling radiance. The version used in this study is LBLRTM v12.7, with an updated line parameter database AER version 3.5 (following HITRAN 2012, Rothman et al. (2013)) and a continuum code MT_CKD_3.0 which includes modifications to the H2O foreign  (Anderson, 1986) and CO 2 has been scaled to 2013 values as reported by NOAA's Global Monitoring Division, Earth System Research Laboratory (https://www.esrl.noaa.gov/gmd/ccgg/trends/). To achieve consistency with the REFIR-PAD instrumental characteristics, each simulated spectrum is Fourier transformed and a maximum optical path difference of 1.25 cm is applied in the interferogram domain. The truncated interferogram is then re-transformed and the resulting spectrum is sampled at the 10 REFIR-PAD sampling frequency.

Extension methodology
Based on the methodology developed by T15, FIR wavenumbers between 100 and 667 cm -1 are correlated with (predictor) wavenumbers from 667 to 1400 cm -1 . The estimated radiance in the FIR I ν,F IR can be written as a function of the predictor radiance I ν,predictor , and two regression coefficients, a 0 and a 1 , using: 15 ln (I ν,F IR ) = a 0 + a 1 ln (I ν,predictor ) (1) given the assumption of a logarithmic relationship between the predictor and estimated radiances and for a linear assumption.
We start by selecting the REFIR-PAD spectra that will be used to calculate the regression coefficients. All clear-sky spectra 20 that are closest in time to the daily radiosonde measurement at 12 UTC are selected. If the closest spectrum on a given day is measured more than two hours before or after 12 UTC, the spectrum is discarded. 125 days during 2013 are retained using this criterion. These spectra are randomly divided into two sets. The first set is used as a creation set, from which the regression coefficients are derived and the second is used as a test set, on which the regression coefficients derived from the creation set are tested.

25
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 emphasize 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 CO 2 line, a H 2 O line or a combination of both.  3 Results

Application to observed spectra
Figure 2(a) displays the correlation between FIR and MIR radiances using the REFIR-PAD creation set, displayed at the nominal instrument spectral resolution of 0.4 cm -1 . As noted previously, the bands corresponding to regions of high noise due to the absorption by the beam-splitter (1095 -1140 cm -1 and 1230 -1285 cm -1 ) have been removed from the analysis. 10 We observe specific spectral regions that maximise the correlation. A large portion of the spectral region between 150 and 500 cm -1 is highly correlated with wavenumbers between 667 and 720 cm -1 . Figure 2 show a narrower range of higher correlations of between 0.96 and 0.98. We note that the predictor wavenumbers are mainly 20 localised in a spectral area dominated by the CO 2 band coexisting with typically weaker vapour lines.
As noted in section 2.4, regression coefficients a 0 and a 1 in equations 1 and 2 are computed between each FIR wavenumber and the corresponding predictor MIR wavenumber. Figure 3 shows an example of the relationship between a predictor wavenumber at 698.4 cm -1 and its corresponding predictand wavenumber at 301.6 cm -1 across all creation set spectra. Logarithmic (Eqn 1) and linear (Eqn 2) fits between the radiances are also displayed.  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 figure 4(a) with the radiance and relative differences in figure   4(b) at 10 cm -1 resolution. In this case, linear regressions have been used to perform all the extensions. Displaying the results at 10 cm -1 allows a clearer picture to emerge in terms of the performance of the extension.
At 10 cm -1 resolution the mean absolute standard error across the FIR over the entire test set is relatively small at less than 10 0.6 r.u. It is worth nothing that below 370 cm -1 the mean error fluctuates around zero but at higher wavenumbers (370 cm -1 < ν < 600 cm -1 ) there does appear to be a small positive bias of ∼ 0.5 r.u. Under clear-sky conditions this region is generally more transmissive than the lower wavenumber regime -as evidenced by the comparatively lower radiances in figure 4(a). These lower radiances, particularly between 400 and 570 cm -1 , contribute to slightly higher relative differences and variability across this range in figure 4(b). Above 570 cm -1 , both absolute and relative differences diminish as the radiance increases.  The same spectra integrated over 10 cm -1 bands are also shown by the diamond lines. (b) Mean difference (black) and relative variation (red) between the original and the extended spectra at 10 cm -1 resolution calculated over the entire test set. Shaded areas are the associated standard errors.

Application to simulated spectra
The previous section suggests that a reasonable reconstruction of observed clear-sky downwelling FIR surface spectral radiances at a moderate (10 cm -1 ) resolution can be obtained using simultaneous observations of MIR radiances. In this section we explore whether similar results are obtained using simulations.
Therefore, we apply the same process of extension using simulated LBLRTM spectra. For each clear-sky case used to build 10 the creation and test sets for REFIR-PAD data, the corresponding radiosonde profile is selected and used as input for LBLRTM as described in section 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: where I ν,LBLRT M is the spectral radiance from LBLRTM with noise, I ν,LBLRT M is the 'noise-free' spectral radiance directly simulated by LBLRTM, r is a normally distributed random number between -1 and 1 and σ ν,REF IR−P AD is the standard deviation from the corresponding REFIR-PAD spectrum.
The correlation maps of LBLRTM with and without noise are displayed in figures 5(a) and 5(b) respectively. Taking the no-noise case first, most wavenumbers show a strong correlation with all others, with values typically above 0.5. The FIR band sees an enhanced correlation with the MIR between 667-950 cm -1 and wavenumbers between 1300 and 1400 cm -1 . When noise is added, the correlations reduce and show a much greater spectral variation which is more consistent with the observational case. The same bands seen in figure 2(a) which maximise the correlation appear.
The predictor wavenumbers are displayed in figure 5 without noise (c) and with noise (d). In the case of a perfect simulation, the number of predictor wavenumbers is relatively small, indicating a high degree of correlation in the spectra. Below 600 15 cm -1 , most of the predictor wavenumbers are located between 1340 and 1400 cm -1 . Below 300 cm -1 , a second band is visible around 700 cm -1 . Between 600 and 667 cm -1 , the predictor wavenumbers are spread over a range of discrete values close to 700 cm -1 . When the LBLRTM simulations are perturbed with noise, consistent with the change in the correlation map, the selected predictor channels show similar behaviour to REFIR-PAD ( figure 2(b)). Below 160 cm -1 , the predictor wavenumbers are located in a wide band between 667 and 1400 cm -1 , but with a correlation of about 0.5. Between 200 and 400 cm -1 , the 20 predictor wavenumbers are distributed in a band centred at 700 cm -1 . Above 400 cm -1 , predictor wavenumbers up to 800 cm -1 also begin to appear while between 500 and 600 cm -1 the spread in predictors again extends across the whole 667 -1400 cm -1 range with typically lower correlations.
At the time of writing there is only very limited spectrally resolved data in the FIR. One goal of this research is thus to see whether the LBLRTM simulations are able to provide coefficients to transfer observed MIR data into the FIR. So we now 25 test the accuracy of going from MIR to the FIR using different approaches. All predictions are then compared against the REFIR-PAD FIR observations. The 3 different sets of regression coefficients we use are: -LBLRTM simulations (LBL), -LBLRTM simulations + realistic noise (LBN), -Coupled LBLRTM (LBC) where predictor wavenumbers are generated from LBLRTM + realistic noise but regression 30 coefficients are generated from LBLRTM without noise.
By coupling the predictor wavenumbers from LBLRTM + noise and the regression coefficients from LBLRTM without noise in the last approach, we obtain the best estimate of regression coefficients at the wavenumbers where the expected relationship is strongest.
In all cases shown a linear regression is used although the findings are essentially unchanged if a logarithmic fit is employed (see table 1). Figure 6 displays the mean differences (a) and mean relative variations (b) between the 'true' and extended FIR radiances for all cases, with their associated standard errors. For ease of comparison, the extension of REFIR-PAD based on REFIR-PAD derived regression coefficients (previously shown in figure 4(b)) is also included. The extension to the FIR  using regression coefficients based on noise-free simulations (LBL) fails to capture the observed FIR behaviour. A strong bias is visible with a mean difference of -45 %. In this case, the selected predictor wavenumbers are close to 1400 cm -1 ( figure   5(b)), however, at these wavenumbers, the observed correlation for REFIR-PAD is very low (figure 2(a)), due to increased noise (figure 1), leading to large differences between the extended spectra and observations. If the predictor wavenumbers are selected from the noise adjusted simulations (LBN and LBC), the mean differences and standard errors show a marked 10 decrease, reducing the mean difference to 1.1 % and -0.4 % for LBN and LBC respectively.  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 cm -1 , 490 cm -1 , with a peak at 540 cm -1 , see figures 6(a) and (b)).
More specific to this study, it is worth noting that the temperature and water vapour profiles very close to the ground (within 2 m) may also be affected by the presence of the chimney connecting the physics shelter to the outside environment. Palchetti et al. (2015) perform a least square minimisation of the radiance differences between the observation and the simulation, with the addition of a first level inside the chimney into the fitted profiles. Rizzi et al. (2016) include a first level inside the chimney based on the average between the internal PAD temperature and the shelter temperature. We find that the vertical resolution and assumptions made in our modelling approach are sufficient to reduce radiance biases to within 2 r.u., consistent with .

15
In this study, the extension of REFIR-PAD has been performed on its native grid (∆ν = 0.4 cm -1 ) and the results have been predominantly presented over averaged bands of ∆ν = 10 cm -1 . At present, climate and Earth-system models do not operate at such a high spectral resolution. It is thus of interest to investigate how the differences presented in figures 4 and 6 are affected by integration over the wider spectral bands more typical of these general circulation models. As an exemplar, we consider the Met Office Unified Model (UM). In the UM, there are three bands with FIR contributions, from 1 -400, 400 -550 and 550 -800 cm -1 .
The extensions of REFIR-PAD using the various prediction models described in section 3.2 were integrated over these bands and the corresponding results are shown in table 1. For each band and each case, the median value of the variations is provided along with the one sigma standard deviation of the relative variation across spectra in the test set. Because of the boundaries of 5 the extension, the bands from 1 -400 cm -1 and 550 -800 cm -1 are reduced to 100.4 -400 cm -1 and 550 -667 cm -1 respectively.
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 -119 %) seen in the 400-550 cm -1 region, the most transparent of the three bands and hence the most susceptible to noise due to the low radiance level. When 10 looking at LBN and LBC cases, the extension shows median biases which are only marginally larger than those seen using the observations themselves. In addition, the difference between using a linear or logarithmic extension is small.

Conclusions
In this study we have used REFIR-PAD downwelling observations for clear-sky cases from 2013 over Dome C in Antarctica to assess whether it is possible to build a model capable of using MIR radiances to predict values in the FIR. We have described 15 a correlation and regression based methodology based on Turner et al. (2015) which we have used to search for predictor wavenumbers and to extract regression coefficients at these specified wavenumbers. In addition to the observations, radiosonde soundings are used to create a corresponding simulated spectral database with the radiative transfer model LBLRTM.   3.2 ± 4.6 1.2 ± 1.8 2.9 ± 13.9 0.5 ± 2.3 -2.1 ± 3.9 -0.8 ± 1.5 LBC 2.3 ± 4.9 0.9 ± 1.9 -6.9 ± 16.3 -1.3 ± 2.2 -4.0 ± 3.4 -1.5 ± 1.2