The near-infrared spectrum (defined here in wavenumber space as 2000–10 000 cm-1) is characterised by its spectral band-window structure, where parts of the spectrum are completely opaque to radiation and others are mostly transparent over typical (clear-sky) atmospheric paths. Within this spectral region, in addition to the many discrete spectral lines of various gases, there is additional absorption due to the water vapour continuum absorption (henceforth simply continuum), a smoothly varying (with wavenumber) component of the total absorption which underlies this band-window structure. The cause of this continuum is not known but is postulated to be due to a combination of far-wing broadening, e.g. by collisional effects, and absorption due to water dimers (bound or quasi-bound complexes of two water vapour molecules), as discussed in e.g. Shine et al. (2012). The continuum is normally broken down into two components: a self-continuum component that depends on the square of the vapour pressure and a foreign-continuum component that depends linearly on vapour pressure and the pressure of the ambient air. The foreign continuum is observed to have at most a weak temperature dependence (Ptashnik et al., 2012), while the self-continuum has a negative exponential temperature dependence (Mondelain et al., 2014; Ptashnik et al., 2011a). The temperature dependence of the self-continuum is broadly consistent with a dimer-like theory, but this has not been verified due to the difficulty of performing ab initio calculations of the water dimer spectrum, and the strength of the temperature dependence varies amongst different sets of measurements and may depend on wavenumber (e.g. Ptashnik et al., 2011b).

Since the continuum absorbs radiation (particularly in the atmospheric windows) which would otherwise penetrate further into the atmosphere or reach the surface, it influences the surface–atmosphere partitioning of energy and is therefore important for understanding the global energy budget. In the more transparent window regions, most of the continuum absorption occurs in the troposphere where water vapour is more abundant and has a potential influence on the hydrological cycle. The continuum contribution to climate feedbacks could also be enhanced in a warming climate via the water vapour feedback; the strongly absorbing water vapour bands are already close to saturation, meaning that the window regions, in which the continuum is comparatively more important, could contribute more to the change in absorption in a warming climate. For example, Rädel et al. (2015) found that the near-IR continuum contributes ∼10 %–20 % of the total water vapour shortwave feedback in a scenario with a 33 % increase in water vapour, depending on whether a weaker or a stronger continuum is used. The continuum also impacts upon remote sensing of the Earth's atmosphere and surface. Some remote sensing platforms, e.g. the Orbiting Carbon Observatory 2 (OCO-2) (Oyafuso et al., 2017), have channels observing in the 2.1 and 1.6 µm (∼4000 and 6300 cm-1 respectively) windows, as does the MODIS satellite (Platnick et al., 2017), which is used to retrieve gas concentrations, cloud properties, surface albedo, and aerosol optical depth.

The strength of the near-infrared continuum is uncertain, particularly in the 2.1 and 1.6 µm windows. There have been relatively few attempts to measure the self-continuum in the laboratory, with observed absorption coefficients that differ significantly (e.g. Shine et al., 2016) in the centres of these windows at room temperature. Measuring the continuum in the laboratory is problematic in some ways, due to the need to extrapolate in temperature and pressure to conditions present in the atmosphere (which are frequently below room temperature). The weak absorption strength of the continuum in the windows makes it difficult to measure at typical tropospheric temperatures (∼280 K) without long path lengths (such as that from the top of atmosphere (TOA) to the surface), which are difficult to attain in a laboratory. These issues can be mitigated using certain high-precision techniques, e.g. cavity ring-down spectroscopy (CRDS), at the cost of wide spectral coverage. However, while CRDS measurements exist at room temperature, there are none reported in the literature at the lower temperatures considered here. Additionally, the weak (and featureless) absorption means that the measurements are very sensitive to the experimental conditions, such as the baseline stability of the spectrometer when using Fourier transform spectroscopy (FTS) techniques (e.g. Ptashnik et al., 2015).

The continuum is parameterised in most radiative transfer codes used in models and remote sensing by the MT_CKD (Mlawer-Tobin_Clough-Kneizys-Davies) model (Mlawer et al., 2012), typically using either version 2.5 or version 3.2 (Mlawer et al., 2019). MT_CKD is a semi-empirical model. Examples of codes using this model include the Atmospheric Radiative Transfer Simulator (Buehler et al., 2018), the Reference Forward Model (Dudhia et al., 2017), the Orbiting Carbon Observatory-2 (O'Dell et al., 2018), the Met Office Unified Model (Walters et al., 2019), and the GFDL Global Atmosphere and Land Model (Zhao et al., 2018). In the window regions, the MT_CKD continuum mostly originates from adjustment of the water vapour lineshape using a χ factor derived primarily from measurements at wavenumbers in the mid- and far-infrared (<2000 cm-1), with additional empirical adjustments. It is not an ab initio calculation and uses selected observations to adjust its continuum strength. Any such adjustment should therefore consider the uncertainty and differences in the available measurements. A particularly important aspect is the temperature dependence; atmospheric radiative transfer models generally use the MT_CKD formulation to extrapolate the self-continuum absorption to temperatures at which there are no laboratory measurements.

Measurements of the continuum in the atmosphere are therefore necessary to supplement laboratory measurements. While field measurements present their own issues, explained more in Sects. 3 and 6, they provide data with which to test the experimentally implied temperature dependence, as well as that of MT_CKD. Ideally, a combination of field and laboratory measurements would converge on a set of continua at different temperatures and pressures that could be included in spectroscopic databases such as HITRAN (Gordon et al., 2017) or at least provide a set of robust values (with agreement within the uncertainties) that can be used to adjust MT_CKD.

In this work, we present the first reported derivation of the near-IR atmospheric continuum in the 4, 2.1, and 1.6 µm windows at mean sea level with a well-constrained uncertainty budget, and the first to be derived using a radiometrically calibrated spectrometer. These measurements were made during the CAVIAR (Continuum Absorption at Visible and Infrared wavelengths and its Atmospheric Relevance) field campaign in Camborne, Cornwall, UK, in August–September 2008 (Gardiner et al., 2012). Since these measurements are at mean sea level, it has been estimated that the continuum absorption will be roughly evenly split between the self- and foreign-continua at 1.6 µm and ∼70% self : 30% foreign in the 2.1 µm window based on laboratory measurements (as calculated in Ptashnik et al., 2012). Additionally, observing at sea level allows us to measure the continuum within the windows, as the expected continuum contribution is above the signal-to-noise of our spectrometer (see Sect. 2.2). These conditions set our results apart from those of Reichert and Sussmann (2016), who used an FTS at a high-altitude site to measure the continuum. This allowed observations of the continuum within the bands but restricted the ability to detect it within the windows. Additionally, our measurements are radiometrically calibrated and traceable to SI (Système international d'unités, BIPM, 2006); this allows us to obtain the top-of-atmosphere solar spectral irradiance (SSI) directly (Elsey et al., 2017; Menang et al., 2013), which is itself uncertain to ∼8 % in the 4000–7000 cm-1 region.

This section discusses the current literature in terms of field measurements of the near-IR continuum. Reichert and Sussmann (2016), henceforth “Zugspitze”, presented a continuum absorption obtained in atmospheric conditions at a high-altitude site at the Zugspitze in the German Alps. This used an FTS calibrated using a combination of Langley-derived TOA irradiance, a medium-temperature (∼1970 K) blackbody and an assumed SSI from a radiative transfer model (Reichert et al., 2016). The high altitude allows for measurements of the continuum well into the main water vapour absorption bands and ostensibly allows for an upper limit to be set on the absorption in the windows. These are the most immediately comparable measurements in the literature to the ones presented here. There are several key differences between the two field campaigns, which makes them difficult to compare directly. The Zugspitze measurements were performed in conditions that had a significantly smaller water vapour path, meaning that observations of the continuum in the windows are extremely difficult, while allowing observations in the bands that sea-level observations are not capable of. Additionally, the higher-altitude measurements are dominated by the foreign continuum due to the lower vapour pressures, whereas the sea-level observations are more of a mixture of foreign- and self-continua. The higher-altitude measurements are above the atmospheric boundary layer, mitigating the effect of aerosol extinction, which is a significant problem for sea-level observations. To obtain a long enough path length to mitigate the lack of water vapour, the Zugspitze measurements were taken at large air-mass factors (∼3–9). This may be problematic however since (a) the effects of atmospheric refraction are more pronounced and (b) extrapolating from high air mass to zero air mass using the Langley method increases the effect of the uncertainty in the individual measurements, since these primarily use the closure method and are therefore reliant on their calibration to a prescribed SSI.

These factors mean that Zugspitze observations are available in the 2.1 µm window and within several of the adjacent water vapour bands, but values are not presented in the 1.6 µm window (many of these are in fact negative). Due to the large uncertainties, these are seemingly consistent with both MT_CKD and contemporary laboratory measurements of the foreign continuum (see Sect. 5.2), despite the considerable differences between these datasets. These will be examined in more detail in Sects. 4 and 5. Nevertheless, it should be emphasised that these measurements are a significant advance in our understanding of the in-band continuum. Additionally, as understanding of the near-IR SSI is improved, the calibration used in the Zugspitze measurements could be used to measure the continuum without the need for an expensive and time-consuming blackbody calibration, which would allow for measurements in a wider variety of conditions. This would both help validate radiative transfer models and allow for separation of the foreign-continuum and self-continuum contributions in atmospheric conditions; this task is extremely challenging to do with a single field campaign at one location if only modest changes in water vapour column occur.

This work builds upon the work of Tallis et al. (2011), Menang et al. (2013), and Elsey et al. (2017). These all used observations obtained using an absolutely calibrated ground-based Sun-pointing Fourier transform spectrometer (Gardiner et al., 2012) set up at a field site in Camborne, Cornwall, UK (50.218∘ N, 5.327∘ E). Those papers focused on water vapour spectral lines and SSI respectively. Gardiner et al. (2012) present the calibration procedure and FTS setup in detail. The spectrometer measures the centre of the solar disk (using dedicated solar tracker optics) in the range 2000–10 000 cm-1, with a spectral resolution of 0.03 cm-1. The FTS is radiometrically calibrated, with traceability to SI via calibration to the 3000 K Ultra High Temperature Blackbody (UHTBB) at the UK National Physical Laboratory. The field-of-view of the FTS is 0.26∘.

The total optical depth τtotal can be determined from the irradiance I observed by the FTS at a given air-mass factor m= sec(θ) (with θ the solar zenith angle). This is done using measurements at a range of air masses via the Langley method or given a top-of-atmosphere irradiance I0, the radiative closure method. Taking the logarithm of the Beer–Bouguer–Lambert law, 1ln⁡I=ln⁡I0-mτtotal. The radiative closure method is a simple inversion of this equation to solve for τtotal. In this case, the SSI of Elsey et al. (2017) is used, since this is determined directly by the spectrometer used in this work. This does however introduce significant extra uncertainty, given the large uncertainty in the near-IR SSI, particularly in the lower-wavenumber windows.

The Langley method exploits the fact that Eq. (1) can be solved as a linear equation given observations at various air masses, assuming that the optical depth does not vary significantly between these air masses. This means that the aerosol optical depth (τaerosol) needs to be measured at the same time as a spectrometer measurement and along the same atmospheric path, as does the integrated water vapour (IWV). It also means that measurements must be taken when there are no clouds present. τaerosol was measured using a handheld Microtops II sunphotometer (Solar Light Company, 2001) at 0.38, 0.44, 0.675, 0.936, and 1.02 µm. The Microtops has a field-of-view of 2.5∘ and was operated by hand rather than mounted on a solar tracker, which could lead to some additional uncertainty (see Sect. 2.4). Integrated water vapour was measured using a HATPRO microwave radiometer (Rose and Czekala, 2011). The effects of clouds were minimised by visually checking for clouds at the time of measurement and by using the variation in the observed voltage of the spectrometer detector to determine whether any sub-visible clouds or haze passed into the line-of-sight of the spectrometer during a measurement.

The continuum optical depth, τcont derived from the total optical depth τtotal obtained from the spectrometer measurements, can be characterised as 2τcont=τtotal-τH2Olines-τother_gases-τRayleigh-τother-τaerosol. The retrieval of the continuum mostly relies on accurate determination of the line-by-line absorption from water vapour and other gases, and aerosol extinction. Rayleigh scattering was modelled using the calculations of Bucholtz (1995). It is mostly negligible in the near-IR windows (Elsey et al., 2017) and thus has minimal effect on the derived continuum. The line-by-line optical depth was determined using the Reference Forward Model (version 5.01, Dudhia, 2017), the HITRAN2016 spectroscopic database (Gordon et al., 2017), and the Voigt lineshape cut off at 25 cm-1 (with the line contribution at 25 cm-1 subtracted at wavenumbers less than 25 cm-1, as this is assumed to be part of the continuum following the MT_CKD definition). It follows that the choice of spectroscopic database has an effect on the derived continuum, since a change in line parameters will affect the amount of absorption attributed to the spectral lines rather than the continuum. This may also affect our comparison with earlier studies, since these may use different line databases to HITRAN2016. Since HITRAN2016 is one of the most up-to-date line lists available, we believe it is the most suitable here.

The atmospheric profiles were derived using co-located radiosonde ascents and checked using ECMWF and Met Office analysis data. To minimise the effect of solar lines, all regions within 0.1 cm-1 of a solar line (as observed by Menang et al., 2013, and Elsey et al., 2017) are filtered out. To minimise the effect of line shifting in the measurements or misattributed line positions in HITRAN, the observed continuum is smoothed over 15 cm-1. This smoothing is suitable for observing the continuum, as the continuum varies smoothly with wavenumber. This is necessary in particular due to the high spectral resolution of the measurements, and also filters out any high-frequency noise within these observations that may not be accounted for otherwise. Regions with τtotal above 0.1 are also filtered out to ensure that continuum derivation only takes place within microwindows and in regions where the modelled spectral lines can be reasonably subtracted from the observed ones (where the absorption is not saturated).

Continuum absorption by other molecules (N2, O2, O3, and CO2, defined here as τother) was obtained from MT_CKD_3.2 (Mlawer et al., 2012, 2019). This non-water vapour continuum absorption is mostly important in the 1.25 µm window, where there is significant absorption due to a collision-induced oxygen band; however, this window is not the focus of discussion here. Figure 1 shows a schematic of how this information is put together to retrieve the continuum from the FTS measurements.

The best estimate of the continuum is from measurements made on 18 September 2008, with additional observations from other days. The IWV observed by the HATPRO microwave radiometer on 18 September was 16.25±0.49 kg m-2. The reliance on the observations of 18 September 2008 is due to the need to observe in clear skies and to minimise the effects of atmospheric aerosol; 18 September 2008 had clear skies for most of the day, allowing observations at a wide range of air masses for Langley extrapolation. Additionally, the aerosol optical depth was significantly lower (observed via the sunphotometer) than the other days that fit this criterion. This is a significant issue for a continuum derivation; when deriving SSI a small absolute change in aerosol optical depth across the course of a day has a minimal effect on the y intercept of the Langley plot, but the effect on the gradient (i.e. optical depth) is comparatively much larger. Constraining the aerosol change throughout the day is a significant challenge for such sea-level observations. Since the analysis is reliant mostly on one day of observations, and given the large uncertainties, it is not possible to retrieve the self- or foreign-continua separately. Therefore, to compare with the laboratory measurements, an assumption needs to be made about the relative strength of either the foreign continuum or self-continuum (see Sect. 5). Figure 2 shows four Langley plots from the 18 September 2008 data, at 2500, 4500, 6500 and 9800 cm-1 (in the 4, 2.1, 1.6 and 1 µm windows respectively). These plots demonstrate the quality of fit (and therefore the strong constraint on the observed total optical depth) we were able to obtain from the observations of 18 September 2008.

Figure 3 shows the derivation process in the 1.6 µm window, starting with the Langley-derived τtotal from the FTS observations (panel a), subtracting the line-by-line contributions (panel b), smoothing using a 15 cm-1 boxcar filter and subtracting Rayleigh scattering and other gaseous continua (panel c), and finally obtaining the water vapour continuum by subtracting aerosol extinction (panel d).

Figure 4 shows the minimum detectable optical depth capable of being observed by the FTS. This was calculated using the following method. For a series of repeated observations from the calibration campaign (measurements of the UHTBB; see Gardiner et al., 2012, for more details) the window regions (2500–2800; 4400–4800; 6000–6400; 7900–8400; 9200–10 000 cm-1) were selected. In each window region, the mean signal level was calculated for each measurement. From this, the absolute difference between these levels and the mean level across all the measurements was obtained. The average difference gives a measure of the noise in each region. We then take an observation of the Sun (one used in the Langley analysis) and calculate the mean solar irradiance signal in each spectral window. The ratio of the offset noise to the solar signal gives the fractional offset noise in each window, which in the limit of small absorption is approximately the optical depth noise in that region. The minimum detectable offset is then assumed to be 3 times the optical depth noise. It is found that the minimum detectable optical depth in each of the atmospheric windows is typically 0.001, significantly below the derived continuum optical depth in most cases.

The uncertainty budget on the continuum optical depth is obtained in a similar way to Elsey et al. (2017). The Monte Carlo method used there was extended to obtain the experimental uncertainty in the total optical depth. Uncertainty in the optical depth from the line-by-line model comes from sensitivity tests using the uncertainty limits in temperature, pressure and water vapour from the radiosonde. Due to the increased sensitivity to the atmospheric aerosol (when deriving continuum absorption rather than SSI), τaerosol was determined using the Microtops measurements and a Mie scattering code based on Wiscombe (1980), in addition to the Ångström exponent method described in Elsey et al. (2017). The Mie code was fed with a range of parameters for a comparable atmosphere obtained from Dubovik et al. (2002). This allowed us to test the range of validity of the Ångström exponent method by using a physically based wavelength dependence. The uncertainty budget was more conservative than that of Elsey et al. (2017), since this was estimated using the Mie scattering calculations which were sensitive to various parameters (e.g. size distribution) which had large ranges in Dubovik et al. (2002). Figure 5 shows the optical depth and k=1 (67 % confidence interval) uncertainties of the τaerosol used in this work and the relative contribution this optical depth has to the combined continuum + aerosol optical depth.

An issue with our derivation of τaerosol is our inability to reconcile the observed variation in the sunphotometer τaerosol (+τcont in the 1 µm channel, since this is not corrected for in the Microtops processing algorithm) on 18 September 2008 with the variation in the Langley-derived τaerosol+τcont from the FTS. Figure 6 shows the time variation of the IWV and the continuum plus aerosol optical depth from the FTS and the sunphotometer. The FTS showed a consistent combined continuum and aerosol optical depth throughout the day, while the Microtops showed a significant drop in aerosol optical depth over the course of the day. This is very unlikely due to the continuum, since the IWV observed by the HATPRO varied by only ∼5 % throughout the day, which would not be enough to cause such large changes. The surface temperature as observed by the radiosondes varied by less than 1 K throughout the period of measurement. Additionally, the Microtops does not contain a correction for the water vapour continuum; if there was a significant change in continuum absorption, then this again should be seen in both the Microtops and FTS data.

It is therefore unclear what is causing this discrepancy in the time variation, but it may be due to uncertainties arising from the operation of the sunphotometer or some systematic time-varying effect impacting the FTS measurements. For the continuum derivation it was decided to use the day average of the 18 September 2008 τaerosol measurements, with a corresponding increase in the uncertainty, since we could not determine which aerosol variation was more likely to be the true case.

In addition to the issue with the temporal variation, there is also an irreconcilable difference between the optical depth observed by the FTS at 1 µm (∼0.1) and that observed by the Microtops (0.03–0.08). Due to the small variation in IWV and temperature across the day, the larger signal observed by the FTS is extremely unlikely to be due to water vapour absorption. It is unclear why the FTS and the Microtops do not observe the same signal. If the effect were physical, one would expect the Microtops and FTS to both observe it. While the variability in the Microtops is large, the absolute level of τaerosol is believed to be more reliable than that from the FTS, particularly given the consistency with shorter-wavelength Microtops measurements. This makes it a more reliable instrument for extrapolating optical depth to lower wavenumbers. It was postulated that the discrepancy may be due to a change in forward scattering with wavenumber and the differences between the field-of-view of the Microtops and the FTS (0.26∘ and 2.5∘ respectively), but this correction to τaerosol is less than 10 % at all wavenumbers observed by the FTS (Box and Deepak, 1979).

Another issue is the assumptions made regarding the mirror reflectivity correction. Since the mirrors were exposed to the elements, a correction is made to the observed irradiance based on observations of the mirrors prior to the field campaign and subsequent measurements afterward using the National Reflectance Reflectometer (NRR) at NPL. However, the NRR observations only cover the spectral region 4000–6600 cm-1. The reflectance outside of these regions must be extrapolated based on the observations within this spectral region. It is for this reason that we have more confidence in the observations at these wavenumbers and in the adjacent windows where the extrapolation takes place over fewer wavenumbers. There is significant uncertainty in the behaviour in the 1 µm window, where the mirror correction is extrapolated further, which may be in excess of the uncertainty estimate in Gardiner et al. (2012). The Supplement has more details on the possible effect of this mirror extrapolation.

It was postulated that there could be significant uncertainty at higher wavenumbers (>7500 cm-1) due to some uncertainty or systematic offset in the phase correction used in the OPUS software used to derive spectra from the FTS measurements (see Supplement). This was motivated by the observation of systematic changes in the FTS phase spectrum with respect to time across 18 September 2008 that were particularly large at higher wavenumbers. It was found that uncertainties in this phase correction would have small effects at lower wavenumbers but could significantly impact the observed optical depth at higher wavenumbers. However, we do not have a physical justification for why this may have been the case and cannot ab initio determine the magnitude of this uncertainty.

We believe that the combination of the above factors (mirrors, phase correction issues, larger aerosol effect) warrants significant caution being used when interpreting the results at wavenumbers beyond ∼6700 cm-1. The observed optical depth (see Sect. 3) is seemingly inconsistent with the (admittedly sparse) laboratory estimates or MT_CKD. Therefore, the apparently high continuum optical depth derived from the FTS near 1 µm (∼0.05 optical depths; see Sect. 3) is regarded as an undiagnosed issue (potentially for the reasons postulated above) with the instrument sensitivity at high wavenumbers, and henceforth we focus on the 1.6, 2.1, and 4 µm windows. This is additionally motivated by the lack of laboratory measurements to validate in the larger-wavenumber windows. However, we cannot rule out that the large observed optical depth is some unexplained physical effect (or indeed an unexpectedly large water vapour continuum signal). Further clear-sky observations in this spectral region could affirm whether this is the case.

When deriving the CAVIAR-field self-continuum this way, a representative temperature must be chosen to compare to the laboratory measurements, since the continuum observed by the FTS is the integrated continuum across the entire temperature and pressure range of the atmosphere. Figure 12 shows the fractional contribution to the total continuum optical depth from the surface upwards for selected wavenumbers, as calculated using MT_CKD_3.2 and RFM for the conditions of 18 September 2008 at Camborne. This is calculated as the fractional contribution at each layer as observed by our radiosonde profiles to the total continuum absorption. This shows that more than 95 % of the continuum optical depth is in the bottom 2 km of the atmosphere. This corresponds to a temperature range of ∼275–290 K, which was assumed to be the temperature for which the CAVIAR-field self-continuum is representative.

Shine et al. (2016) present a review of the laboratory data up to 2016 in significant detail. The following paragraphs introduce the main data available across multiple spectral windows used to compare the CAVIAR-field self-continuum. Other datasets will be introduced as required for each specific window.

Ptashnik et al. (2011a) (henceforth the CAVIAR-lab self-continuum) presented laboratory observations of the self-continuum taken by an FTS from 472 to 293 K between 2500 and 10 000 cm-1; because uncertainties become too large for the low-temperature measurements (because of the lower vapour pressures that are necessary at low temperatures), at wavenumbers greater than 5600 cm-1 their measurements are restricted to 374 K and above, with the exception of a few 350 K measurements at the edges of the windows where the continuum is stronger. However, at all wavenumbers, uncertainties are larger at the lower temperatures. Further sets of FTS measurements (Ptashnik et al., 2013, 2015) were taken at the Institute for Atmospheric Optics in Tomsk, Russia. However, recent and ongoing study has indicated that these results may be spurious, due to reflectivity issues arising from adsorption onto the gold mirrors used in their multipass cell (Ptashnik et al., 2019b). For this reason, these results have not been included in our analysis.

Various sets of observations have been made by the Spectroscopy Group at LiPhy (Laboratoire Interdisciplinaire de Physique) at the Université Grenoble-Alpes (henceforth collectively “Grenoble”). Mondelain et al. (2013, 2014) presented observations of the near-IR self-continuum in the 1.6 and 2.1 µm windows at room temperature and above using a cavity ring-down spectrometer (CRDS). Newer measurements (Lechevallier et al., 2018; Richard et al., 2017) by this group in the 2.1 µm window were presented, which generally agree with the Mondelain et al. observations. Vasilchenko et al. (2019) present updated CRDS measurements at a range of wavenumbers at room temperature in the 2.1 and 1.6 µm windows. Ventrillard et al. (2015) present observations in the 2.1 µm window (4302 and 4732 cm-1) using an optical feedback cavity enhanced absorption spectroscopy (OF-CEAS) technique at 293–323 K, while Richard et al. (2017) use the same technique in the 4 µm window (2491 cm-1).

An additional issue of importance is the relative contribution to the total continuum absorption of the self- and foreign-continua, particularly for atmospheric scientists, since the relative contribution of each is strongly dependent on the atmospheric conditions at the time of measurement. Figure 18 shows the percentage of the optical depth originating from the self- and foreign-continua for conditions of 18 September 2008 from MT_CKD_3.2 (the optical depth calculated using MT_CKD_3.2 is shown in Fig. 7). In these conditions (with an integrated water vapour column of about 16 kg m-2; see Sect. 2), the self-continuum dominates in the centres of the windows (∼95 % in the centre of the 4 µm window, 90 % in the centre of the 2.1 µm window, and ∼80 % in the centre of the 1.6 µm window), while the foreign continuum dominates in the bands.

Figure 19 shows the percentage contribution of the CAVIAR-field self-continuum (panel a) and CAVIAR-field foreign continuum (panel b). Each of these panels shows the proportion of the total 18 September 2008 continuum optical depth attributable to the self or foreign optical depth by assuming the contribution from the other component via either CAVIAR-lab or MT_CKD. The relative contribution in this case is as given by Eq. (5). Unlike with MT_CKD, which is well-constrained (and therefore the total contribution of the self- and foreign-continua sums up to the total, as in Fig. 18), the CAVIAR-field estimated continuum is not, in the case where a≠b≠1, as we do not have enough information to derive independent values of the two components of the CAVIAR-field continuum. Therefore, it should not be expected that τforCAV+τselfCAV=τtotCAV. Figure 19 should be interpreted as the values implied by CAVIAR-field when assuming that the self or foreign contribution is well-characterised by either CAVIAR-lab or MT_CKD.

The self-continuum (panel a) contribution is large (>95 %) when using the MT_CKD foreign continuum across all of the windows of interest, similar to the case shown in Fig. 18. However, when using the CAVIAR-lab foreign continuum, this contribution decreases by an amount depending on the window of interest. In the 4 µm window, the contribution varies from ∼50 % to almost 0 % in the centre of the window. Similarly, in the 2.1 µm window, the self-continuum drops from ∼95 % to ∼40 % contribution when using the stronger CAVIAR-lab foreign continuum. At 1.6 µm, almost all of the absorption when assuming the MT_CKD foreign continuum is implied to come from the self-continuum. This is because the MT_CKD_3.2 foreign continuum is extremely weak in this region, and the total CAVIAR-field optical depth is much larger than the MT_CKD_3.2 optical depth (see Fig. 7). Using the CAVIAR-lab foreign continuum decreases the contribution of the self-continuum to ∼80 % in the centre of this window, comparable with the fraction implied when just using MT_CKD (Fig. 18).

Because of the lack of constraint on the CAVIAR-field optical depth, the implied foreign-continuum contribution when assuming the MT_CKD or CAVIAR-lab self-continua (Fig. 17b) is also high (over 60 % across all three windows). Unlike the self-continuum case, there is reasonable consistency between the implied values using either CAVIAR-lab or MT_CKD. At 4 µm, using the CAVIAR-lab self-continuum increases the foreign contribution from ∼60 %–80 % to ∼75 %–90 % in the centre of the window, since the CAVIAR-lab self-continuum is smaller at room temperature than that of MT_CKD in this region (see Fig. 13). At 2.1 µm, the contribution drops from ∼80 % to ∼70 % when using the MT_CKD and CAVIAR-lab self-continua respectively. At 1.6 µm, the CAVIAR-field foreign continuum is almost 100 % in the centre of the window when using the MT_CKD self-continuum, but drops to ∼80 %–90 % when using the CAVIAR-lab self-continuum.

The lack of consistency between the CAVIAR-field estimated self-continuum and foreign continuum is an indication of the lack of constraint on a and b, meaning that there are potentially issues with CAVIAR-field, with the laboratory measurements, and/or MT_CKD.