FAAM flight B895 left Prestwick in the UK on 13 March 2015 and overflew a decaying band of cirrus cloud associated with an occluded front. The main objective of the flight was to characterize both the cirrus cloud microphysics and their associated IR radiative signatures. To achieve this aim, the aircraft performed a series of straight and level runs (SLRs) above the cloud followed by a descent into the cloud deck where a further series of SLRs were performed at varying levels within the cloud. Figure 1a and b show the flight track and altitude of the aircraft as a function of time respectively.

The FAAM aircraft was fitted with a “cloud-radiation” suite of instruments that included radiation sensors, cloud microphysical probes and a lidar. The radiation instruments included two Fourier transform spectrometers: the Tropospheric Airborne Fourier Transform Spectrometer (TAFTS, Canas et al., 1997) with nominal spectral coverage from 80 to 600 cm-1 (two channels: LW from 80 to 300 cm-1 and SW from 320 to 600 cm-1) operating at 0.12 cm-1 resolution, and the Airborne Research Interferometer Evaluation System (ARIES, Wilson et al., 1999) with nominal spectral coverage from 550 to 3000 cm-1 (two channels: LW from 550 to 1800 cm-1 and SW from 1700 to 3000 cm-1) at a 1 cm-1 resolution. The cloud microphysics (PSD and habit) were measured using a series of probes that included a 2-DS, a 3-View Cloud Particle Imager (3V-CPI), a CIP 100 and a holographic cloud probe (HALOHolo; Lawson et al., 2006; O'Shea et al., 2016). The lidar installed on the aircraft was a Leosphere ALS450 355 nm elastic backscatter lidar (Marenco, 2010) which provided cloud vertical extent information and ice volume extinction profiles at 355 nm from the range-corrected backscatter profiles following the two-stage process of Marenco et al. (2011). Vertical profiles of the particle extinction coefficient were estimated (Fox et al., 2019) from which the cloud optical depth at 355 nm, (τ355), was derived. Finally, along with the standard aircraft positioning, temperature and humidity sensors, the aircraft was also equipped with the Airborne Vertical Atmospheric Profiling System (AVAPS) which launched RD94 dropsondes (Vaisala, 2010) at various stages of the flight to enable characterization of the atmospheric column below the aircraft.

The driving factor in selecting periods for analysis was the availability of near-simultaneous TAFTS and ARIES nadir radiance spectra from SLRs above the cloud. Ideally, the simulation of radiance spectra equivalent to those observed at the aircraft level above the cirrus cloud requires knowledge of the cloud microphysical and optical properties, its vertical location and the atmospheric profile from the surface to the aircraft. Hence, the additional selection criteria were that cirrus could be clearly identified and characterized by the lidar observations and that the atmospheric state below the aircraft was well characterized by dropsonde measurements. The final requirement was that the atmosphere above the aircraft was cloud-free in order to ensure that any downwelling radiation from above the aircraft, reflected by the cloud beneath, could be ignored.

Preliminary examination of the available data from the three above-cloud SLRs suggested that there were two periods which satisfied these requirements: one during SLR 1 from 09:48:39 to 09:49:51 UTC and another during SLR 3 from 10:16:22 to 10:17:24 UTC. Unfortunately, ARIES data from the period identified in SLR 3 were found to have deficiencies (Stuart Fox, personal communication, 2019) and were consequently considered to be of insufficient quality for the purpose of this study. Thus, only those data from the period during SLR 1 were considered for further investigation. Three sets of radiance observations were identified from within SLR 1, and the times of these observations along with a summary of the conditions at the aircraft are given in Table 1.

For each of the three cases identified, only a single TAFTS spectrum was available; however, owing to the relatively high temporal sampling frequency of the ARIES instrument, eight ARIES spectra are available within ± 1 s of the TAFTS acquisition time. To provide an indication of the scene variability within the 2 s period around the TAFTS measurement, the mean and the associated standard deviation are calculated for the eight ARIES radiance spectra. The mean ARIES and the associated TAFTS spectra are then converted into equivalent brightness temperature spectra. These are shown for all three cases in Fig. 2. In the MIR, signatures of cirrus are most apparent in the main atmospheric window (∼ 760–1000 and 1080–1250 cm-1) as indicated in Fig. 2c. At FIR frequencies, the atmosphere is less transparent because water vapour absorption fills in many spectral lines, but there are a series of semi-transparent, so-called “micro-windows”, as shown in Fig. 2b, that clearly show the variation in the cirrus properties. For the lowest frequencies in the FIR, the atmosphere is comparatively opaque and generally has a much lower sensitivity (less than 1 K) to the cirrus with the exception of a few wave number regions (e.g. ∼ 110, 218 to 221, 240 cm-1, etc.). It is interesting to note that there is a variation in the order of the three cases between the different spectral regions. For example, the maximum brightness temperature is observed at around 110 cm-1 for case C followed by B and then A; case B shows the highest values in micro-window 3 (around 410 cm-1) followed by A and then C; and the largest values are for case A in the MIR window regions, followed by B and then C. The variation in the relative order of the individual cases indicates a frequency-dependent sensitivity of the cloud's radiative signature to the cirrus properties. This sensitivity to the ice particle size and habit is discussed further in Sect. 4.2.

Figure 3a shows the lidar extinction profiles for the three cases (A–C). Panels (b) and (c) show the respective atmospheric temperature and water vapour mixing ratio profiles obtained from the two dropsondes deployed nearest to the time of the selected radiance observations at 09:47:48 UTC (DS1) and 09:50:52 (DS2). The aircraft altitude is shown by the dashed red line. The extinction profiles derived from the lidar measurements indicate that a band of cirrus was located between an altitude of approximately 6 and 9 km with no evidence of any underlying cloud. Integration of these extinction profiles for the three cases, from 6 to 9 km, indicates that τ355 ranged from approximately 0.53 to 0.59. Therefore these clouds would typically have been classified as optically thin (e.g. Dessler and Yang, 2003). Examination of DS1 and DS2 demonstrates that the atmospheric state remained relatively stable between their deployments, with a noticeably dry layer evident between approximately 3 and 5 km in both water vapour profiles. There is a degree of variability in the temperature profile around 4 km as well as in the water vapour mixing ratio below 3 km. The impact of this variability on the simulated radiance spectra is discussed in Sect. 4.

A single aircraft is not able to simultaneously measure in situ cloud properties and above-cloud radiance spectra. Here, the in situ cloud microphysical measurements were obtained over a period of 1 h and 20 min, starting from approximately 50 min after the radiation observations were obtained (Fig. 1). While the cloud vertical structure remained relatively constant during cases A–C (Fig. 3a), the lidar observations indicated significant variability in the geometrical thickness of the observed cloud during the three SLRs as a whole. Moreover, previous examination of the available in situ cloud microphysical properties indicated a high degree of variability in the PSDs and a wide variety of ice particle habits, which were summarized for seven different temperatures (altitudes) sampled within the cloud (see Figs. 5b and 6b in O'Shea et al., 2016). These issues, combined with the knowledge that the cloud was decaying over time, suggested that it would be impossible to associate a particular observed PSD or habit to the radiation measurements with any confidence. Therefore, we chose to perform an initial simulation for each case for a cloud, split into layers 0.1 km thick, with a vertical extent from 6 to 9 km, taking bulk optical properties from the Baum et al. (2014) ASC ice particle habit model and assuming a fixed reff=30 µm for all layers within the cloud. The relative optical depth for each cloud layer was derived from the lidar observations, ensuring the cloud's total optical depth was equal to the appropriate value from Table 1.

Figure 5 shows the results of such a simulation for case A. For reference, the equivalent clear-sky simulation is also shown. The estimated uncertainty associated with the ARIES spectral calibration is approximately 1 K (Stuart Fox, Met. Office, personal communication, 2019), while the 1σ variability in the eight ARIES spectra matched to the TAFTS acquisition time is approximately ± 0.5 K. Therefore, we estimate the total uncertainty on a mean ARIES spectrum as these values added in quadrature, so ∼ 1.1 K. However, the simulated brightness temperature spectrum overestimates the observed ARIES values in the main atmospheric window by around 4 K, with a smaller (∼ 2 K) overestimate also seen relative to the TAFTS measurements in the FIR micro-windows. Conversely, the level of agreement in the strong CO2 absorption band from 650 to 700 cm-1 (excluding the spike in the centre of the band at 667 cm-1), indicates that the temperature of the uppermost layer in the simulation (i.e. close to the aircraft) is well represented in the temperature profile used in the simulation. These differences point to issues with the cloud properties used in the initial simulation, especially given that interchanging dropsondes 1 and 2 has a comparatively small impact on the simulated spectrum.

It is evident from Fig. 5 that the initial choice of cloud parameters used to simulate the observed radiance was suboptimal. The two key parameters typically required to define the microphysical properties of an ice cloud are reff and the ice particle habit. The sensitivity of the mid-infrared to ice particle size has been known for many years (e.g. Bantges et al., 1999), and more recently sensitivity studies extending into the far-infrared have been performed (e.g. Yang, 2003; Yang et al., 2013). Figure 6a–c show the results of a series of simulations performed to examine the impact of varying reff, ice particle habit and optical depth for case A. As part of this analysis, while we have no direct observational evidence for a variation in reff with height through the cloud, it is reasonable to explore the response to such a variation as it might be expected to be different in the MIR and FIR regimes. Hence, Fig. 6d shows the impact of varying reff in three 1 km thick layers through the cloud.

Figure 6a indicates that there are a wide range of spectral regions that demonstrate sensitivity to size from approximately 300 to 600 cm-1, 750 to 850 cm-1 and 950 to 1250 cm-1. In contrast, there are spectral regions that exhibit sensitivity primarily to ice particle habit (Fig. 6b). Differences between the GHM and SC model are greatest around 500 cm-1, while they are greatest at around 400 cm-1 for GHM and ASC differences. Sensitivity to optical depth (Fig. 6c) is broadly similar across the MIR and FIR from 400 to 1400 cm-1, but it drops off rapidly at wave numbers lower than 400 cm-1 due to the increasing effect of strong water vapour absorption and the overall reduction in radiative energy at these frequencies. Introducing a vertical variation in reff (Fig. 6d) produces a change which has a very similar spectral shape (although much smaller magnitude) to that observed for a bulk change in reff.

Using this information, a scheme was developed to minimize the differences between the simulated and observed spectra in regions showing particular sensitivity to reff and habit. Four wave number channels in the MIR and four in the FIR were used (each of ∼ 2 cm-1 width): 775, 850, 900 and 1200 cm-1 in the MIR and 365, 410, 450 and 497 cm-1 in the FIR. The ultimate goal was to investigate whether there was any combination of parameters that could fit the observations across the MIR and FIR simultaneously given measurement uncertainties. Because of the reduced sensitivity to the vertical profile of reff and the similarity of the associated spectral signature to those generated from vertically uniform perturbations to reff, we do not attempt to account for any vertical variation in our simulations.

To facilitate the minimization, a series of simulations were performed for a range of reff and τ for the three ice particle habits in the Baum et al. (2014) database. Table 2 provides a summary of the ranges covered for each variable. These values were chosen, based on initial simulation attempts to match the observed spectrum, to produce a range of simulations that encompassed the observations and their associated uncertainties.

The simulations were compiled into a database ordered by τ355, reff and ice particle habit. Four different approaches were then adopted to identify the simulation that most closely matched the observations for each case. The first approach comprised two stages. The initial stage identified the simulated radiance spectra that agreed to within the measurement uncertainties for the ARIES spectrum for all four of the selected MIR channels to create a subset of “matched” simulated spectra. This subset was then processed to find the simulation that most closely matched the corresponding TAFTS SW spectrum for the four channels identified in the FIR. The absolute difference between the simulations and observations for each FIR channel was weighted by the observation uncertainty and then summed: 1x=∑i=14Rsimi-RobsiRerrori, where Rsimi and Robsi are the simulated and observed radiances respectively, and Rerrori is the observation uncertainty for FIR channel i. X was then minimized to obtain the “best” solution.

The second approach also comprised two stages, with the first stage mimicking that of the first approach. In the second step, the uncertainty weighting was removed such that the minimum of Eq. (2) was sought, 2x′=∑i=14Rsimi-Robsi.

The third approach focused on determining the best agreement that could be obtained using the individual MIR spectral range. This was achieved by minimizing the integrated absolute difference between the simulation and observation across the MIR from 600 to 1400 cm-1. For completeness, a fourth approach, similar to the third, but in this case minimizing the integrated difference in the FIR from 320 to 540 cm-1, was considered to demonstrate whether agreement solely in the FIR could be achieved.

The combinations of ice particle habit, reff and τ355 that give the simulated spectra which most closely match the observations using each of the three minimization methods are summarized in Table 3. The results for all the methods indicate a need to increase τ355nm above the lidar-derived value by an amount larger than the stated uncertainty in the lidar values of ± 20 % (Stuart Fox, personal communication, 2019). However, the required change to the derived optical depth can be produced by adjusting the lidar backscatter-to-cloud extinction ratio from the flight-averaged value used in this study (Fox et al., 2019) to values that still lie within the typical range observed for ice clouds (e.g. Chen et al., 2002; Heymsfield et al., 2008; Young et al., 2013; Gouveia et al., 2017). We note that changing this value would not significantly impact the lidar-determined relative variation of the extinction or the cloud geometrical thickness used in this study.

Minimization methods 1 and 2 yield very similar results, both indicating that the GHM habit provides the closest agreement, with the only difference that method 1 suggests being a slightly smaller reff compared with method 2 for case A. Method 3 demonstrates that using the MIR in isolation gives markedly different values. In this case, the results would suggest a cloud comprised of relatively small ASC habit ice particles with an optical depth slightly larger than that indicated by methods 1 and 2. Finally, when matching the FIR observations in isolation (method 4), a cloud with lower optical depth composed of relatively large GHM habit ice particles is implied.

The spectral differences between the observations and the best-matching simulations are shown in Fig. 7 for each minimization method, separated into three different spectral regions defined as MIR (600 to 1400 cm-1), SW FIR (320 to 540 cm-1) and LW FIR (110 to 300 cm-1). It is important to note that the large differences consistently found around 667 cm-1 are most likely a measurement artefact due to the extremely strong absorption by CO2 around this frequency. This results in measurements reflecting the temperature of the air inside or very close to the ARIES instrument. Similar effects can be present due to strong water vapour lines and are particularly evident at wave numbers > 1300 cm-1. As evidenced by Fig. 3, cloud signatures are more apparent in the more transparent spectral regions, indicated by the “window” labels in Fig. 7a, and where the atmospheric transmission between the cloud top and aircraft is close to 1 (Fig. 7b, c).

Unsurprisingly, given the values in Table 2, the difference spectra from methods 1 and 2 lie almost on top of each other across the full spectral range analysed. Within the MIR (Fig. 7a), the differences are within the measurement uncertainties with the exception of those spectral regions most strongly influenced by CO2 and water vapour discussed above. Within the TAFTS LW channel (Fig. 7c), the simulations overlie each other, as the models predict a greatly reduced sensitivity to ice particle habit and size for frequencies lower than around 300 cm-1, as shown in Fig. 6. The atmospheric layer above the cloud in this spectral region is also less transparent, further reducing the observed impact of variations in the ice particle properties. However, there are several regions in the SW FIR (e.g. 375, 450 and 475 cm-1) where the differences lie outside of the measurement uncertainty estimates (Fig. 7b). Overall, for case A, a total of 1488 simulations were performed. Of these, 739 matched the observed spectrum to within uncertainties in the MIR and a unique 14 matched (using method 4) the observed spectrum in the FIR. For the bulk optical models tested, this result shows that any combination of τ355 and reff is unable to match the TAFTS and ARIES observations simultaneously within measurement error. Analysis of cases B and C (not shown) yields similar conclusions.

It is worth reiterating that the difference spectra obtained using method 3 demonstrate that it is possible to achieve excellent agreement in the MIR using MIR observations in isolation (Fig. 7a). However, extending the best-fitting parameters to the FIR generates large residuals (Fig. 7b), and using the FIR in isolation yields closer agreement across the FIR (albeit not within measurement uncertainty across all micro-windows) but even larger residuals in the MIR. This highlights that the combined use of MIR and FIR measurements should provide a much tighter constraint on the ability of any given ice cloud optical property model to capture the observed radiative behaviour of cirrus across the infrared spectrum and that FIR observations are needed to refine and test bulk ice cloud optical model development.

To assess the energetic impact of misrepresenting the cirrus spectral signature, a first-order estimate of the upwelling flux difference between the simulations selected by all minimization methods (1–4) and the observations is obtained by multiplying the upwelling nadir radiances by pi (assuming an approximation to the diffusivity-factor approximation; Elsasser, 1942) and integrating over selected spectral ranges (Table 4). For completeness, results from all three cases analysed are shown. Table 4 indicates that there is a compensation effect between the differences seen in the MIR and in the shortwave FIR channel in all cases and for all methods. This compensation means that rather large differences (of the order of 0.6–1.6 W m-2) are seen in the individual bands for methods 1 and 2, but these differences are somewhat masked when looking at the deviation integrated across all three bands. Our results suggest that the use of information solely from the MIR to estimate the cirrus properties (method 3) can result in sizable deviations in both the SW FIR and the total flux, with values exceeding 2.0 W m-2 for one of the cases analysed. Using the FIR only (method 4) can lead to even greater deviations, with values exceeding 3.0 W m-2, dominated by differences in the MIR.