Devices to measure irradiance typically report raw values as voltages (V), and thus VG(λ)=VH(λ)+VD(λ), where λ is wavelength, G is global, H is horizontal direct, and D is diffuse. See Table 1 for a glossary of symbols and definitions. The volts directed onto the horizontal plane, VH(λ), are normalised by the solar zenith angle (θs) using VN(λ)=VH(λ)sec⁡θs. The instrument can be calibrated against known standard instruments in the laboratory or in the field. It is also necessary to carry out a Langley calibration (Adler-Golden and Slusser, 2007) of the instrument during clear and stable atmospheric conditions over the course of a day using Beer's Law to obtain the top-of-atmosphere voltage, VT(λ). This can be represented as VN(λ)=VT(λ)exp⁡-τ(λ)m, where τ(λ) is the optical depth and m is the atmospheric air-mass, in this paper defined as m=1cos⁡θs+a(b-θs)-c. In Eq. (4) the constants a, b and c are set to 0.50572, 96.07995 and 1.6364 respectively (Kasten and Young, 1989). To account for the elliptical nature of Earth's orbit, the following expression is used: V0T(λ)=VT(λ)r2, where r=(1-εcos⁡(aJ-4)), with J being the serial day of the year, ε being the eccentricity of the orbit (0.01673) and a= 2π/365.25. Expanding Eq. (3) into the component parts of the optical depth, Rayleigh (R), aerosol (a) and atmospheric trace gases (g) results in VN(λ)=V0T(λ)r2exp(-τR(λ)+τa(λ)+τg(λ)m). The trace gas component (such as ozone, nitrous oxide, water vapour) can be derived from measurements or distribution climatologies in conjunction with models such as SMARTS2 (Simple Model of the Atmospheric Radiative Transfer of Sunshine 2; Gueymard, 2001); the Rayleigh component can be calculated from (Reynolds et al., 2001) τR(λ)=PP0a1λ4+a2λ2+a3+a4λ-2-1, where P is the atmospheric pressure (mbar), P0= 1013.25 mbar; a1 = 117.2594; a2=-1.3215; a3= 0.00032073; and a4=-0.000076842. Rearranging Eq. (7) allows the aerosol optical depth to be calculated for each individual optical wavelength. The trace gas components are not corrected for in this study as we have chosen to compare against existing instrumentation which operate within atmospheric windows where gas absorption is negligible or very small.

This analysis is presented in terms of voltages with arbitrary scaling. After calibration, the spectrometer system gives outputs in radiometric units, so the top-of-atmosphere values give an extra-terrestrial spectrum which should match the SMARTS2 model. The SMARTS2 spectrum is used as reference in subsequent AOD calculations.

Both spectrometer systems were deployed on the Atlantic Meridional Transect expedition cruise, which sailed between the UK and the Falkland Islands on board the RRS James Clark Ross, from 22 September to 4 November 2014. The spectrometers were mounted on the top of the foremast of the British Antarctic Survey research ship RRS James Clark Ross on a dedicated instrument platform (Fig. 3). Access was only possible via the ship's crane and hoist when in port at the beginning and end of the cruise, so once installed there was no further opportunity for modifications or maintenance. The spectrometers were both mounted in IP67 weatherproof enclosures and fitted with desiccant packs. The heat generated by the electronics increased the internal temperature by around 10–15 ∘C above the ambient, and this helped to keep the internal humidity to less than 30 % during the cruise. An SPN1 radiometer was also mounted alongside the two spectrometers to give a broadband irradiance reference. The instruments were powered by a 12 V power cable, and communications were provided by an ethernet cable, both routed up the mast. The performance of the spectrometers was monitored throughout the cruise, remotely from inside the ship, via the ethernet connection. A Satlantic hyperspectral radiometer, Kipp & Zonen photosynthetically available radiation (PAR) sensors, and Kipp & Zonen pyranometers were also mounted on the instrument platform throughout the cruise.

The AMT encounters a wide variety of aerosol optical properties, from the low τa background marine aerosols of the South Atlantic Ocean (Lin et al., 2016) to the higher turbidities to the west of Africa under the influence of airborne desert dust (Caquineau et al., 2002; Baker et al., 2006). Values of τa(λ) were determined using a manually operated handheld Microtops II instrument at 380, 440, 500, 675, 870 and 1020 nm and the data processed to level 2.0 (cloud screened, visually inspected and post-cruise calibrated) using the protocols adopted by the AERONET Maritime Aerosol Network (Smirnov et al., 2009). The estimated absolute uncertainty in individual level 2 observations does not exceed 0.02 in any of the spectral channels.

Prior to the AMT cruise, Spectrometer 1 (AS161) was deployed on the roof of the Plymouth Marine Laboratory (Plymouth, UK: 50∘21.95′ N, 4∘8.85′ W), in close proximity to the established ESR network (Campanelli et al., 2012) PREDE POM01-L sun photometer, between 14 July and 8 September 2014. The site is generally characterised by aerosols of a marine origin (Estellés et al., 2012). Aerosol optical properties, including τa(λ), were determined from the POM01-L measurements at 400, 500, 670, 870 and 1020 nm using the inversion technique of Nakajima et al. (1996).

Following the AMT cruise, Spectrometer 2 (Zeiss) was deployed at the Burjassot site (Valencia, Spain: 39∘30.58′ N, 0∘25.08′ W), which has both ESR-POM01-L and AERONET-CIMEL CE318 sun photometers, between January 2015 and June 2016. The site is affected by many different aerosol types, including urban, marine (Mediterranean) and Saharan dust (Estellés et al., 2007). Values of τa(λ) were determined using the CIMEL CE318 measurements at 440, 500, 670, 870 and 1020 nm, processed by AERONET algorithm version 2 (level 2 until April 2015 and level 1.5 from April 2015 to June 2016).

The values of τa(λ) calculated using the two spectrometers were compared against the coincidental land-based sun photometers (PML, Burjassot) and marine sun-photometer (AMT) deployments. The spectrometer hyperspectral values were integrated to give similar bandwidths (∼ 10 nm) to the sun photometers for AOD calculations. To give an accurate comparison, all the different instruments were referred to GPS time. The spectrometer datasets were filtered to select stable conditions in which AOD500nm varied by less than 0.05 over a 5 min window, as measured by the spectrometer. The spectrometer filtered 1 min readings were interpolated to the time of the comparison instrument reading.

There are two requirements for calibration of this spectrometer system. Firstly, the seven individual channels should have an identical response to incident light. Secondly the response should be matched to the absolute irradiance scale across the whole spectrum. To achieve this, the spectrometers were first calibrated using a 300 mm diameter integrating sphere illuminated by a halogen lamp to give a uniform diffuse irradiance across all seven sensors. The irradiance at the integrating sphere port was calibrated to an Ocean Optics LS-1 calibration lamp to give an approximately correct calibration for each sensor. In particular, because the halogen lamp has a smoothly varying spectral distribution, the relative values will be correct over moderate wavelength intervals, even if the absolute scaling is incorrect. Following this, the spectral calibration was adjusted using the Langley method on Mt Teide, Tenerife (2300 m, near the base of the teleferico). The calibration was adjusted smoothly across the whole spectrum using the Langley values outside the gas absorption bands to give a final absolute calibration. The instrument outputs were calibrated to radiometric units, so the Langley calculated TOA values should match the SMARTS2 extra-terrestrial spectrum outside the of gas absorption bands.

After the AMT24 cruise, Spectrometer 2 (Zeiss) was co-located with a CIMEL sun photometer in Burjassot for 18 months. Its calibration was further checked using the Langley method during selected clear-sky periods and also by a direct comparison with the CIMEL IN(λ) measurements at the specific CIMEL wavelengths. Figure 4 shows how these different methods compare, by plotting the extra-terrestrial irradiance values they predict. It is evident that the Langley plot performed at Mt Teide closely matches the SMARTS2 spectrum due to the site pristine conditions, except for the gas absorption bands where the Langley method cannot be applied correctly. The effect of the gases in these bands is even clearer for the Langley extra-terrestrial spectrum obtained at Valencia, as the water vapour amount is higher at sea level. In any case the absorption bands will not be used for deriving the aerosol optical depth.

Both spectrometer systems were fitted with a VectorNav VN100 inertial orientation sensor, containing three-axis sensors for each of linear acceleration, angular acceleration and magnetic field. From these measurements, the sensor calculates values of yaw (heading), pitch and roll. These measurements allowed the spectral measurements to be corrected for the tilt of the instruments away from the horizontal. Following analysis of the orientation values after the AMT cruise, the VectorNav yaw values showed significant drift compared to the yaw values calculated from both the GPS track and the ship's heading record. This was due magnetic interference from the ship's ironwork, which had not been compensated for when the spectrometers were installed. However, the pitch and roll values could still be used in combination with yaw values either taken from the ship's data records after the cruise or calculated from the GPS track values.

Long et al. (2010) demonstrated a method for correcting pyranometer measurements on an aircraft using SPN1 measurements. We have used a similar technique to correct both the SPN1 and Spectrometer 2 values in this study. In correcting the Spectrometer 2 values, it is assumed that the diffuse part of the incident light is unaffected by tilt. The diffuse value is calculated from the minimum of the seven channels. This is subtracted from all the other channels to give the direct beam part of the reading on the instrument plane (IHmeas). The direct beam part is then corrected according to the known position of the sun, and the angle of incidence on the tilted instrument plane is calculated from the orientation values. IHcorr=IHmeascos⁡θrscos⁡θs, where cos⁡θrs=cos⁡θscos⁡αsf+sin⁡θssin⁡αsfcos⁡(ϕs-βsf). See Table 1 for definition of the various angles. The seven channels are then recalculated from the Imin+IHcorr and used to calculate the corrected IG, ID and IN using Eqs. (9)–(11). This correction is also applied to the SPN1 values.

There are two contributions to irradiance variation during the reading period – variations in the overall irradiance values (e.g. variable cloud cover, particularly obscuring the solar disc) and variations due to tilt of the ship. This correction strategy will correct for the ship's movement but not variations in light levels during the reading period.

The repeated SPN1 readings give the best indication of the effectiveness of the tilt correction strategy. Detailed results are shown for the afternoon of 30 October 2014 (Fig. 5), as this was a day with relatively high pitch and roll values (peak amplitude around 5∘) and also a relatively sunny day. The time-series plot for the day shows the IN (green), IG (red) and ID (blue) values as measured directly and the corrected IN and IG (darker colours). It is clear that the corrected values show a large improvement for the stable clear-sky periods (e.g. 17:30 to 19:30), with the standard deviation in the readings of IN being reduced by up to a factor of four. Taking an average of the burst of SPN1 readings gives an even smoother trace, but this option is not possible using Spectrometer 2 (Zeiss) because of the time taken to observe the entire spectrum (20 s).

Figure 5 summarises this improvement by showing the standard deviation of the eight measurements within each 1 min burst. During periods of broken cloud, variability is high. This is caused by large light level variations due to cloud edges during the 20s burst. During clear-sky periods (e.g. 17:30 to 19:30) the burst variability is reduced to 20–30 % of the uncorrected value by implementing the correction procedure. During wholly overcast periods (e.g. 20:00 to 21:00) the variability is obviously minimised. This correction procedure is applied to all readings for Spectrometer 2 (Zeiss) during the AMT24 cruise. As a direct consequence of this, the subsequently calculated AOD values show less variability during stable periods.

Prior to the AMT24 cruise, Spectrometer 1 (AS161) was mounted on the roof at PML in Plymouth, adjacent to a PREDE POM-01 sun photometer, between 14 July and 8 September 2014. The AOD intercomparison (Fig. 6) between the two instrument datasets results in a high R2 (ranging between 0.768 at 870 nm and 0.940 at 500 nm) and an RMSE of between 0.040 (675 nm) and 0.075 (400 nm). This is similar to differences found between LICOR LI1800 spectrometers (Estellés et al., 2006). The 400 nm channel performance was somewhat worse than the other wavelengths using the RMSE metric (0.0705). This is due largely to the diminishing sensitivity of the AS161 spectrometer at 400 nm and below. There are also noticeable changes in the regression slope with the wavelength in Fig. 6, this varying between 0.911 (500 nm) and 0.710 (870 nm). The intercept value also varies between -0.012 (400 nm) and 0.037 (870 nm). Some of the outliers shown in Fig. 6 are likely to be caused by imperfect cloud screening of data from either or both sensors.

Following the AMT24 cruise, Spectrometer 2 (Zeiss) was co-located with a CIMEL sun photometer at the Burjassot site, between January 2015 and June 2016. These land-based results (Fig. 7) show that there is a consistent relationship between the spectrometer and sun-photometer-derived AOD measurements. The regression slope varies between 0.786 at 440 nm and 0.687 at 870 nm (decreasing slope with increasing wavelength), with a broad decrease in the intercept from ∼ 0.03 to 0.02 (decreasing intercept with increasing wavelength). There is also a reduction in the residuals from 0.029 at 440 nm to 0.015 at 870 nm. The value of R2 remains largely unchanged at around 0.95. A notable feature of both Figs. 6 and 7 is the significant, but consistent, deviation away from the 1:1 line when comparing the different instrument retrievals of AOD. One possible source of this behaviour is thought to be the wider field of view of the SPN1 optical design. This is typically between 5 and 10∘, whereas the POM and CIMEL instruments' FOV is ∼ 1∘. The difference between shadowband radiometer and sun-photometric retrievals of AOD has previously been observed, and subsequently empirically corrected for by di Sarra et al. (2015), and attributed to the radiant impact of aerosol forward scattering on different instrumental FOVs. Here we investigate this further with a modelling study using the SMARTS2 (Gueymard, 2001) solar model. This has the facility for calculating the spectral IN received for different aerosol conditions and different detector FOVs. The model was run for a range of different solar zenith angles (0–85 with 10∘ increments) and AODs (0.01–0.50 in 0.01 increments), and the IN was calculated for a detector FOV of 7.5∘, at 500 nm. The AOD that would be calculated from the measured IN using the spectrometer AOD Eqs. (1)–(8) was compared with the AOD value inputted into the model (Fig. 8). This shows two distinct features that aid in interpreting the intercomparison with the CIMEL (Fig. 7): (1) a regression slope of approximately 0.8 and (2) a slight dependency on solar zenith angle. Significantly, however, the over prediction of AOD at low atmospheric turbidities (AOD < 0.1) is not reproduced. This behaviour can be replicated by introducing small calibration errors to the model data. At 500 nm the extra-terrestrial irradiance used in the SMARTS2 model is 1.932 Wm-2 nm-1, but in the region between 495 and 505 nm (typical instrument bandwidth of 10 nm) it varies between 2.059 (497 nm) and 1.878 (502 nm). This range of values can account for a variation in the retrieved AOD500 of approximately 0.08. Not only does this highlight the importance of the accuracy of the instrument calibration, but also an understanding of instrument characteristics are required (spectral response function and resolution). At low optical depths, even in the most transparent atmospheric window, gaseous absorption is also likely to play a role in accurately determining AOD.

Using these insights from modelling, we are able to give a much closer correspondence to the Valencia CIMEL CE318 by (1) using the calibration transferred from the CIMEL CE318 for all values, rather than the original (Mt Teide) Langley calibration. The calibration adjustment for wavelength values between the CIMEL CE318 channel values is done using a linear interpolation, (2) applying a correction function for each CIMEL wavelength consisting of an offset related to solar zenith angle (air mass), and then a further linear transformation in AOD to give a true estimate of AOD as measured by the CIMEL CE318. The calculated correction factors (Table 2) are selected to give the best fit to the CIMEL CE318 AOD values and applied using an equation of the form AOD(λ)corr=(AOD(λ)meas-OffsetA(airmass)-OffsetW(λ))×SlopeW(λ). These corrections show an RMSE of 0.02 to 0.03 when compared with the CIMEL CE318 (Fig. 9). While not perfect, this is approaching the uncertainty of AERONET field-deployed CIMEL instruments (0.01–0.02) and the level of agreement between different sun photometers when they are compared together in the field (0.01–0.02) using different AOD methodologies (Estellés et al., 2006). LICOR 1800 spectroradiometers calibrated by lamps also have a nominal AOD uncertainty of about 0.02–0.05 (Estellés et al., 2006). These corrections were then applied to the Spectrometer 2 AOD results from the AMT cruise.

We configured the spectrometer operating software to routinely calculate four distinct datasets. The first is a daily time series of the spectrally integrated values of global and diffuse irradiance (Fig. 10). This can be presented as either an integrated Wm-2 value across the full spectrum or weighted by wavelength to give, for example, PAR over the range 400–700 nm. Other bands or weightings can be calculated from the raw data. The second is a daily time series of τa at specific wavelengths chosen to match the output of other instruments such as the Microtops II or CIMEL CE318 sun photometer. The third is the instantaneous IG(λ) and ID(λ) spectra for each measurement time (Fig. 11), and the fourth is the instantaneous τa(λ) across the whole spectrum, outside of gaseous absorption bands, for each measurement time.

Comparisons of 1 min spectrally integrated data from the two spectrometers with the co-located SPN1 radiometer and Kipp & Zonen PAR sensors (see Table 3 for instrument details) showed good agreement (Fig. 12). PAR measurements were 4 % below and 0.6 % above the Kipp & Zonen PAR sensors respectively for the two spectrometers and 26 % below the SPN1 radiometer. This latter difference is largely accounted for by the different spectral ranges measured, i.e. 380–1050 nm for the spectrometers, 400–2800 nm for the SPN1. Figure 13 shows an intercomparison with the co-located Satlantic HyperSAS hyperspectral radiometer (see Table 3 for instrument details). In the range 400–1050 nm, Spectrometer 1 (AS161) agrees on average within 2.3 % with the HyperSAS with a maximum difference of 0.05 Wm-2 nm-1 at 752.5 nm; Spectrometer 2 (Zeiss) is within 4.7 % of the HyperSAS with a maximum difference of 0.025 Wm-2 nm-1 at 927.1 nm. Spectrometers 1 and 2 are within 2.2 % of each other with a maximum difference of 0.07 Wm-2 nm-1 at 754.0 nm. Visually from Fig. 13, the largest inter-sensor differences occur within absorption bands, therefore different spectral resolutions may play a role in these regions.

During the AMT cruise, Microtops readings were taken when the sky was deemed sufficiently clear (clear view of the solar disc unobscured by clouds), and research schedules permitted time. Figure 14 shows these results plotted against latitude for the entire cruise for both Spectrometer 2 (Zeiss) and the Microtops (observations shown are single retrievals measured daily around solar noon if conditions allowed). The spectrometer results have been corrected for using the values determined using the 18-month intercomparison at the Burjassot site (Figs. 7 and 9 and Table 2). Background marine aerosol (AOD500nm < 0.05) values are apparent in the region around 40∘ N and between 20 and 40∘ S. Elevated values of AOD are clearly visible in locations associated with the Saharan dust plume (20∘ N: AOD500nm ∼ 0.5) and European anthropogenic pollution emitted by a combination of industrial and urban sources (50∘ N: AOD500nm ∼ 0.4). Comparisons between Spectrometer 2 (Zeiss) and Microtops at four different wavelengths (440, 500, 675 and 870 nm – Fig. 15) results in an RMSE between 0.04 and 0.05, which is poorer than the results presented against the CIMEL (RMSE ∼ 0.03: Fig. 9), but the coefficient of determination (R2) remains high at around 0.95 for all wavelengths. Previous (unpublished) comparisons between Microtops and CIMEL CE318 resulted in an RMSE of between 0.01 and 0.02; an agreement to within 10 % between Microtops, CIMEL and POM instruments has been reported in Poland under a variety of conditions (Evgenieva et al., 2008). However, the previous studies alluded to above have been for land-based observations and therefore no uncertainties due to the platform motion are present. Moreover, the Microtops AOD has a somewhat larger uncertainty than the CIMEL.