The PiSpec instrument design is described in detail in Wilkes et al. (2017). It is based on a Czerny-Turner optical bench layout, with off-the-shelf optical components mounted in a 3D-printed housing. Light enters through a slit aperture and is collimated using a mirror, before falling incident onto a diffraction grating; the dispersed light is then focused onto a detector, to provide a system spectral resolution and range of ≈1 nm and ≈280–340 nm, respectively. The detector is an Omnivision OV5647 sensor, primarily designed for the smartphone market, but here packaged as part of the Raspberry Pi v1.3 camera module (Raspberry Pi Foundation). This camera board has the advantage of greater user control, such as raw 10-bit data access and better gain control, relative to sensors incorporated into smartphone units themselves. Furthermore, this board-based configuration makes the sensor more readily accessible, such that we are able to chemically remove the Bayer filter, as described by Wilkes et al. (2016); this produces a uniformly responding sensor with enhanced UV sensitivity, both of which are crucial features for this application area. The detector acquisition is controlled by a Raspberry Pi computer, which in turn is controlled by a custom Python 3 graphical user interface run on a Windows laptop. As in Wilkes et al. (2017), all spectra captured herein have been generated by co-adding 11 rows across the PiSpec sensor, to increase the signal-to-noise ratio (SNR).

We have previously demonstrated that the instrument has ≈1 nm spectral resolution and a spectral range of ≈280–340 nm, with a 30 μm slit in place. This implementation makes it well tailored for DOAS retrievals of SO₂, following approaches which are extensively documented elsewhere (Galle et al., 2003; Platt and Stutz, 2008). In brief, the method involves collection of a clear-sky Fraunhofer spectrum, I₀(λ), with which subsequent in-plume spectra, I(λ), can be used to calculate the plume optical density, D(λ):

The differential optical density, D′(λ), can then be isolated through applying a high-pass filter to D(λ); here, we use a Butterworth high-pass filter implemented in MATLAB^®. A reference spectrum of the SO₂ absorption cross-section, such as that provided by Vandaele et al. (2009), is then convolved with the instrument’s line shape and high-pass filtered also. This spectrum is then fitted to D′(λ), using a least-squares method, such that the scaling factor of the fit provides the column density of SO₂ for that spectral acquisition. An O₃ absorption spectrum (taken from the HITRAN database; Gordon et al., 2017) is similarly fitted, to remove effects from this species, which also has distinct absorption features within the spectral fitting window; SO₂ column densities retrieved with and without this O₃ correction differed by <2%. In this work, the fitting window was manually determined for each spectrum, by assessing the degree of saturation present at shorter wavelengths when large column densities of SO₂ were present; we then ensured that a sufficiently long start wavelength for the fitting window was chosen in order to avoid this saturation. Typically, for larger column densities a fit window of ≈314–324 nm was used, which we later show is linear up to ≈4000 ppm ⋅ m. Whilst fitting window determination could be automated for the PiSpec, as with any other DOAS instrument (Vogel et al., 2013), this was not the purpose of this study.

In practice, spectra I₀(λ) and I(λ) first must be corrected for dark current and stray light. Firstly, for the former a dark spectrum was acquired with the entrance optics blocked, in this case with a lens cap covering the lens. On Masaya, the dark acquisitions were made immediately prior to or after a full scan/traverse sequence. The dark spectrum is then subtracted from all spectra. Stray light was subsequently corrected for by subtracting the average digital number (DN) between ≈285–295 nm from the entire spectrum. At these wavelengths, the irradiance at the Earth’s surface is negligible, due to strong absorption by Ozone, therefore, the signal at the detector should be ≈0. In reality this is not the case, due to stray light within the spectrometer, which is assumed to be uniform across the detector.

For the PiSpec’s entrance slit we predominantly used the 30 μm slit aperture; however, for some field traverses we tested a 50 μm slit to explore the outcomes of increased light throughput, with associated reduction in required exposure times. This modification does, however, result in decreased spectral resolution, which can be detrimental to the DOAS retrievals.

Volcanoes can be located in a range of extreme environments, often found at low temperatures due to their altitude, or in hot conditions from direct sun exposure at lower latitudes. Since spectrometers can be sensitive to changes in thermal conditions, shifting and warping the line function (e.g., Platt and Stutz, 2008), it is important to address this issue as part of evaluating the PiSpec’s utility in volcanic surveillance operations.

These tests were performed by acquiring spectra from a Hg-Ar lamp (Ocean Optics, Inc.) coupled to the PiSpec by an optical fiber. This setup was placed in an incubator (Panasonic MIR-254-PE), set on Low Humidity Mode, to expose it to temperatures between ≈0 and 50°C. The PiSpec was further placed inside a plastic pouch containing silica gel, to reduce humidity and prevent condensation; within this pouch the lowest temperature actually achieved was 2.5°C. Temperature was logged every minute using a LogTag^® HAXO-8 recorder. At each temperature setting a repose period of ≈1 h was applied before acquisition, to allow the pouch to equilibrate with the incubator temperature. The tests spanned 2 days, 19–20 June 2018.

The PiSpec was tested on Masaya volcano, Nicaragua, on the 14th (19:20 to 21:30 UTC) and 16th of June 2017 (16:40 to 18:20 UTC). At this time, a vigorously overturning lava lake was emplaced in Masaya’s Santiago crater. The lake, which has been visible since late 2015 (Venzke, 2017), has been the subject of only a few published articles to date (Aiuppa et al., 2018; Stephens and Wauthier, 2018; Wilkes et al., 2018; Pering et al., 2019). SO₂ emission rates from the crater, measured with a NOVAC scanning-DOAS system, have been highly variable since the lake appeared, with measured fluxes ranging between 0 and 50 kg s⁻¹ (Aiuppa et al., 2018). Between 2005 and 2015, Carn et al. (2017) listed Masaya as the 18th largest passive volcanic emitter of SO₂ on earth. Furthermore, due to the low elevation of Masaya’s crater, and hence its plume, emissions can have a considerable impact on surrounding vegetation and communities (Delmelle et al., 2002).

We deployed the PiSpec to acquire under two distinct observation modes: scanning-DOAS (14th June) and road traverses (16th June). For the former set up, tests were performed close to the vent, manually scanning horizontally through the plume whilst it was still rising buoyantly from the crater. Contemporaneous visible video was acquired with a DSLR camera, allowing plume transport speed determinations by tracking the condensed plume. This was based on integrating the pixel brightness over two cross sections through the rising plume, then generating time series for each of these feeds, which were cross correlated in order to determine the temporal lag between them. This follows the commonly applied approach in both spectral and image based determinations of plume speed in volcanic SO₂ emission rate estimations (McGonigle et al., 2005; Mori and Burton, 2006). Indeed, in settings where a volcanic plume is persistently condensed, this also demonstrates that visible imagery can provide an effective low-cost method of retrieving plume speeds for a DOAS instrument.

Uncertainties associated with the cross-correlation technique are dominated by knowledge of the distance from observer to camera, and the angle of plume motion relative to the normal of the camera viewing direction, i.e., plume speed has a 1/cosα dependency on relative angle of plume motion, where α is the angular offset from a plume motion that is perpendicular to the camera viewing direction (Klein et al., 2017). For the scans in particular, since they were located close to the source, the relative uncertainty associated with distance to the plume dominates the total uncertainty; it was estimated to be ≈± 0.2 (20%). Conversely, even with a relatively large absolute uncertainty for the angle of plume motion (estimated to be ≈± 10°), the associated relative uncertainty is small (≈± 0.02).

Road traverses were performed by supporting the PiSpec out of a car window and continuously acquiring GPS receiver (Adafruit Ultimate GPS breakout) geo-referenced spectra whilst driving under the plume on La Carretera a Masaya, located to the north east of the Santiago crater (see Figure 1). These measurements were made under rather rare conditions, with the plume blowing approximately north-north-east, making La Carretera a Masaya the optimal route for traverses; the prevailing wind direction is approximately from the east, as evidenced by the SO₂ impacts on plant growth on the western side of the volcano. At times, overhanging trees may have interfered with the traverse spectra; however, we were careful to pause acquisitions when large regions of obstruction were encountered. In general, the quality of fitted SO₂ spectra suggests that significant issues from trees were avoided. Plume speed, again, was estimated using visible video acquired shortly before we began the traverses, and using cross correlation. Traverse emission rates were then computed from the wind, GPS and spectral concentration data following the methodology outlined by McGonigle (2007).

A number of commercial spectrometers are currently used for DOAS applications in volcanology. Although it has now been discontinued, the USB2000 (Ocean Optics) was once perhaps the most commonly used spectrometer (e.g., Galle et al., 2003; Mori et al., 2006; Kantzas et al., 2009; Bobrowski et al., 2010), and therefore provides a good benchmark to compare the PiSpec against. This instrument is also very similar to the USB2000+ and Flame-S spectrometers, the next generation versions of the USB2000, which are currently market available and frequently used today. Table 1 provides some useful features of these PiSpec, USB2000 and USB2000+ spectrometers, for comparison; the Flame-S specifications are very similar to that of the USB2000+, but the former instrument is manufactured with new techniques to improve thermal stability and reduce unit-to-unit variability. As may be expected, the Ocean Optics instruments have some advantages, such as a higher bit-depth (12-/16-bit for the USB2000/2000+ vs. 10-bit for the PiSpec) and, in this configuration, a greater spectral resolution (0.65 nm for the USB2000/2000+ vs. 1 nm for the PiSpec).

Contemporaneously acquired clear-sky spectra from both the PiSpec and USB2000 are displayed in Figure 2. Both spectra have been corrected for dark current by subtracting a dark spectrum, and the signals have been normalized to the peak at ≈330 nm to facilitate comparison. Prior to normalization, the 330 nm signals were 2147 and 487 for the USB2000 and PiSpec, respectively; for the 12- and 10-bit A/D converters, this corresponds to saturation of 52 and 48%, respectively. Shutter speeds of approximately 1.5 and 6 s were used in this case, for the USB2000 and PiSpec respectively, highlighting the greater sensitivity of the USB2000 device, as would be expected.

In general, the spectra show similar features, although the peaks and troughs of the USB2000 spectrum are more pronounced than the PiSpec’s. This is in accordance with the smaller instrument line shape (ILS) of the USB2000, which will more precisely preserve the high frequency oscillations in sky intensity. Below 330 nm, the signal in the PiSpec drops off somewhat faster than the USB2000. It is likely that this is due to the detector in the USB2000 being coated with a UV fluorescent coating, to enhance its UV sensitivity by absorbing UV radiation and emitting visible light which is sensed at the detector.

From these spectra, the stray light was quantified following the method of Kantzas et al. (2009), by taking the ratio of stray light signal at approximately 290 nm to signal at 320 nm. Here, the stray light was quantified as 0.033 and 0.034 for the USB2000 and the PiSpec, respectively. These remarkably similar values are also toward the lower end of the range of values found by Kantzas et al. (2009), who investigated three USB2000s, two USB2000+s, one USB4000 and one Avantes B.V. Avaspec-2048-USB2. Values ranged between 0.012 (Avaspec) and 0.12 (one USB2000). On a separate occasion, the PiSpec stray light was quantified as 0.13 (Wilkes et al., 2017), which remains comparable to the upper end of the aforementioned commercial spectrometers.

Of particular pertinence to this work, some comparison of the PiSpec and USB2000 was made by Wilkes et al. (2017), where DOAS retrievals of quartz-filled SO₂ cells were performed with both instruments. The analysis of sets of 10 spectra acquired by each instrument showed that both resulted in similar column density retrievals when measuring ≈300 and ≈1200 ppm ⋅ m gas cells: 304 ± 31 (±1 SD) and 1257 ± 58 ppm ⋅ m for the PiSpec; 296 ± 12 and 1184 ± 30 ppm ⋅ m for the USB2000. Shutter speeds of 6 and 1.5 s were used for the PiSpec and USB2000, respectively. Whilst the performance of the USB2000 was somewhat more consistent for each cell (smaller standard deviation), the PiSpec’s performance was still quite reasonable considering its lower price. From these tests, the maximum cell uncertainty for the PiSpec was ≈10%, for the cell with the lower of the two SO₂ column densities. This value will be combined with the plume speed uncertainty to give a rough estimate of overall uncertainty in emission rate measurements presented in Section “Traverse and Scanning DOAS.”

Here, we discuss thermally induced changes in ILS and spectral calibration using the 313.150 nm emission line from the Hg-Ar lamp, in order to investigate the system robustness to variations in ambient conditions during field operations. This peak is located within typical fit windows for SO₂ DOAS retrievals, which are generally somewhere in the 300–325 nm range. Our results suggest that the spectrometer calibration has a generally linear dependence on temperature across the considered range (Figure 3); however, a few notable deviations from this trend are also apparent. Firstly, there appears to be no change in peak location between 20 and 25°C. This may partly be a result of the pixel discretization of a continuous spectrum. There is, however, some change in line shape, in keeping with the general trend (see Figure 4). The second effect is apparent at the highest temperature measurements, ≈50°C. Here, there is a large shift in the peak, which jumps ≈1 nm from the 45°C spectrum. This notable displacement may be caused by a significant mechanical movement in one of the PiSpec’s components, for example, the detector, via some release mechanism activated above a particular threshold. The similarity in line shape between the 45 and 50°C would corroborate this argument (Figure 4). The detector and associated Pi Camera board is currently mounted to the spectrometer with nuts and bolts which may allow movement, especially under changing thermal conditions. Securing this part more stringently, with glue for instance, may prevent such issues, and it ought to be emphasized that the current hardware is very much a first version of this instrument. As we believe this issue to be independent of the general thermal stability characteristics of the spectrometer, we omit these data points from the regression analysis; we then also propose that above 45°C the PiSpec alignment may become unstable.

The linear dependence, omitting the high temperature data as discussed above, indicates that the PiSpec displays wavelength shifts of ≈0.046 nm/°C (≈0.5 pixel/°C) between ≈2.5–45°C; the coefficient of determination, r² = 0.97, indicates that this linear model fits the wavelength shifts well across this temperature range. This thermal stability is in extremely good agreement with shifts quoted by Platt and Stutz (2008) of 0.05 nm/°C for commercial spectrometers, indicating that in this sense there is no trade off in using this lower cost unit for these spectral measurements. In terms of pixel shifts, Platt and Stutz (2008) quote a typical value of 0.1 pixel/°C, which is lower than the 0.5 pixel/°C for the PiSpec. This should not impact the PiSpec’s performance, since the shift can be corrected for using software.

Thermal instabilities of spectrometers can also lead to a stretch or squeeze of spectra which goes beyond a simple linear shift of all wavelengths across the sensor (McGonigle, 2007; Platt and Stutz, 2008). To investigate this effect, widely separated emission lines (296.728 and 334.148 nm) were tracked through the spectra captured across the studied temperature range, and their separation in numbers of pixels were recorded. For all temperatures below 40°C these two peaks were separated by exactly 393 pixels, indicating that the peaks shifted simultaneously in the same direction. For the three spectra above 40°C the pixel separation moved to 392 pixels. Since each pixel in the PiSpec represents a 0.095 nm band, this squeeze in spectra remains relatively insignificant even at the quite extreme temperatures.

There is, however, a change in the ILS of the unit across this temperature range (see Figure 4). In particular, at cooler temperatures the PiSpec’s ILS is notably wider, with the spectral resolution, defined as the full-width-at-half-maximum of an emission line, increasing markedly. At 2.5°C this increases to 2.9 nm, which would likely be too broad to enable conventional SO₂ DOAS measurements. At 25°C the spectral resolution measured here is ≈1.1 nm. An instrument with a broader ILS (lower spectral resolution) can have a lower sensitivity to SO₂, especially when the ILS approaches the line width of the SO₂ absorption structures, where response can also become non-linear (Frankenberg et al., 2005; Platt and Stutz, 2008). This is likely to be the case beyond a spectral resolution of ≈1 nm, therefore, a changing line shape induced by thermal instability could affect the PiSpec’s retrievals of SO₂. Linearity/non-linearity is discussed in more detail in Section “Detection Limit and Linearity.”

Kantzas et al. (2009) show that the spectral resolution of commercial units (USB2000, Ocean Optics) is also impacted by changing ambient temperatures; however, the temperature range considered therein was not as extreme as that presented here. Another point made by Kantzas et al. (2009), is that the line widths and thermal responses vary between spectrometers, even for the same model, and we note that the same should be expected of the PiSpec; to date, only one PiSpec instrument has been built and tested.

As discussed by Platt and Stutz (2008), thermostating a spectrometer is the best means of preventing thermal instabilities from affecting DOAS retrievals. As with commercial spectrometers, here we highlight that the PiSpec would similarly benefit from such measures. Nevertheless, DOAS measurements with commercial instruments are frequently made without such controls in place, and our tests described later (see Traverse and Scanning DOAS) show that the PiSpec does appear to work adequately, at least within the range of conditions encountered in this study, without thermal stabilization. To some extent post processing of spectra, by wavelength shifting and squeezing/stretching the differential optical density array such that it better fits the SO₂ reference spectrum, can account for calibration error caused by thermal instability, as can measurements of gas cells containing known column amounts of SO₂, and/or regular calibration with mercury lamps under the conditions encountered in the field. However, the change in ILS is more difficult to correct for, unless the change is well characterized. Inspecting the changes in ILS in Figure 4, we may, therefore, suggest that the PiSpec could function acceptably within ≈± 5°C of its calibration temperature; although this will still result in some error in retrieved column densities, as discussed earlier. Meroni et al. (2010) present a method for calibrating spectrometers using Fraunhofer lines and atmospheric absorption features, therefore providing a possible means of recalibration without the need for a calibration lamp in the field. In general, whilst short term deployments, such as the scans and traverses presented herein, are unlikely to be significantly affected by changing temperatures, permanent DOAS installations for automated monitoring can be subject to considerable changes in temperatures both on daily and seasonal timescales. As such, permanent installations with the PiSpec, as with commercial spectrometers, should consider measures to prevent or compensate for thermal instabilities in the instrumentation.

Seven spectrometer scans (Table 2) were performed on the Santiago crater rim. A typical scan and example DOAS retrieval are displayed in Figure 5. The estimated plume rise speed of 3.9 ± 0.8 m s⁻¹, obtained through cross-correlation, resulted in emission rates of between 3.2 ± 0.7 and 7.3 ± 1.7 kg s⁻¹, with a mean of 5.1 kg s⁻¹. Within these scans, column densities of up to ≈2000 ppm ⋅ m SO₂ were measured. SO₂ emission rates from six road traverses ranged between 11.3 ± 1.9 and 45.6 ± 7.6 kg s⁻¹ (Figure 1 shows two typical traverses); the mean traverse rate was 23.1 kg s⁻¹. In this case, a plume speed of 5.3 ± 0.7 m s⁻¹ was estimated, again from video imagery. Considering both the scan and traverse data, our mean recorded emission rate was 13.4 ± 12.3 kg s⁻¹ (±1 standard deviation).

Other available data to compare our emission rates against come from Aiuppa et al. (2018) and Stix et al. (2018). The former data are derived from the NOVAC network scanning spectrometers in the period 19/07/2016–01/03/2017, and range widely from ≈0–50 kg s⁻¹; however, most emission rates are below 25 kg s⁻¹. The mean emission rate is 7.9 ± 3.5 kg s⁻¹ (±1 standard deviation), with significant day to day variability in this period and no clear overall trend over this timescale. The work of Stix et al. (2018) implemented a drone-mounted DOAS system (DROAS) for traversing the Masaya plume between 04/05/2017 and 06/04/2017. Their measured fluxes ranged between 15 and 22 kg s⁻¹, with a mean of 18 kg s⁻¹. These measurements, which were made closer to the time of the work presented herein, are significantly higher than those of Aiuppa et al. (2018) on average, although they are comfortably within the extremes presented by the latter.

In general, our data are commensurate with the above fluxes from other authors, which were captured in the same activity period, in which Masaya’s crater contained the lava lake. Notwithstanding the potential for changes in degassing between the three observation periods, the datasets do compare rather favorably, with all bar two of our fluxes falling within the range 0–25 kg s⁻¹, which encompassed the majority of the Aiuppa et al. (2018) fluxes; all emission rates herein fall below their quoted maximum flux of 50 kg s⁻¹ in this interval. Our traverse values are also in quite good agreement with the traverses of Stix et al. (2018), with mean values of 23 and 18 kg s⁻¹, respectively.

Our scan data correspond to the quoted Aiuppa et al. (2018) fluxes rather better than the traverse data, with 4 of 7 scans falling within one standard deviation of their quoted mean; the further 3 are comfortably within 2 standard deviations. This might be expected given the comparison of scan to scan data, however, pushing this comparison further is perhaps tenuous in the sense that the scan orientations are rather different, e.g., the NOVAC scans are from a rather different vantage point; there is also the difference in the acquisition period. Our scan emission rates are rather lower than those from the traverse observations, which might be simply a manifestation of considerable and rapid (timescales of hours to days) variation in emission rate from the volcano, which is also apparent in the NOVAC fluxes reported in Aiuppa et al. (2018). The traverse data are more commensurate with the traverses of Stix et al. (2018), with both datasets containing notably larger average fluxes than the average of scans presented in Aiuppa et al. (2018). Recently, de Moor et al. (2017) also found that a scanning-DOAS system systematically retrieved lower SO₂ fluxes than traverses when studying emissions from Turrialba in Costa Rica. It is not clear whether this is simply coincidental or whether it is caused by fundamental differences in how the scan/traverse retrieval modes are performed and processed. In their Supplementary Information, de Moor et al. (2017) provide a good discussion of possible causes for discrepancies, such as ash on the optics or sub-optimal scanning position; for a permanent station the latter is of course impossible to always prevent since wind direction is changeable. Some systematic over-/under-estimation in our data may also come from the plume speed scalar, since all scan emission rates are derived from a single plume speed and, likewise, all traverse emission rates are derived from a separate single plume speed. Any error in this calculated speed will therefore be propagated through all emission rates of that retrieval mode.

In concordance with our earlier vindication of the capacity of the PiSpec to accurately constrain cell SO₂ column amounts, via comparison with a USB2000 spectrometer (Wilkes et al., 2017), we suggest that the comparisons with NOVAC and DROAS data demonstrate the capability of the PiSpec to accurately retrieve volcanic SO₂ emission rates. Following the substantial contribution to volcano monitoring and research made by the NOVAC project in recent years (e.g., Galle et al., 2010; Lübcke et al., 2014; Granieri et al., 2015; Hidalgo et al., 2015; Dingwell et al., 2016; Aiuppa et al., 2018), we suggest that the low-cost self-built PiSpec could augment efforts to assess and mitigate volcanic hazards globally, by enabling further dissemination of DOAS measurement systems on active volcanoes.

Due to the relatively modest UV sensitivity of the low-cost PiSpec sensor, as we highlighted in Wilkes et al. (2017), relatively long shutter speeds are required to provide the high SNR required for sensitive DOAS measurements. In the case of these scans and traverses, shutter speeds of up to 6 s were used when the unit was fitted with the 30 μm slit. This, coupled with apparently large overheads in the camera module’s image capture, means that acquisition and transfer of each spectrum took ≈30–40 s. Whilst there is likely to be a software fix for this issue, at present this means that a scan takes some ≈10 min to complete. This current performance would preclude the PiSpec from being used for high time resolution (≈1 Hz) applications, such as that presented by McGonigle et al. (2009) for integration of SO₂ fluxes with other high time resolution geophysical data. Traverse temporal durations are unaffected by this issue, but it will act to reduce the spatial resolution in comparison with what could be achieved with a commercial spectrometer, for a given traverse speed.

One hardware solution to capturing spectra faster is to implement a larger 50 μm slit aperture, which allowed shutter speeds to be reduced from 4.5–6.0 s to 2.5–4.0 s, with a considerable reduction in acquisition rate (capturing every 15–20 s). This configuration was implemented in the final three traverses of the day. Both instrument setups measured similar emission rates, with no trend of over- or under-estimation for the larger aperture; this suggests that, at least in this context, the larger aperture configuration is a suitable solution to this issue. A further approach could be to co-add more rows of the sensor, e.g., essentially co-adding spectra, which could also result in significant increases in SNR, and hence the prospect to obtain higher acquisition rates by reducing shutter speeds (Wilkes et al., 2017). Such improvements to this system should be investigated further in the future.

Many volcanoes emit much smaller quantities of SO₂ than those measured here on Masaya volcano, whilst others can emit far more. It is therefore important that DOAS instruments are able to detect low column densities of SO₂ accurately, with a high SNR, and that the DOAS retrieval remains linear for higher column densities. Here we provide a quantitative assessment of the PiSpec’s performance for detection of both low and high column densities of SO₂.

As with other spectrometers, the PiSpec’s ability to resolve SO₂ will depend on the measurement conditions and acquisition settings. This is highlighted by Figure 6, which displays retrievals of relatively low column densities (86 and 112 ppm ⋅ m) from a PiSpec traverse (Figure 6A) and scan (Figure 6B) captured during the Masaya campaign. The scan retrieval shows much noisier absorbances, which is a result of lower signal during these measurements. The clear sky spectrum associated with this scan had a DN of just 50 at 311 nm, whilst the DN of the traverse clear spectrum was 326 at 311 nm. The latter will have a considerably larger SNR, which is preserved in the absorbance spectrum. Both spectra were acquired at the upper limit of the PiSpec’s shutter speed range, i.e., with 6 s exposures; therefore, the lower signal in the scan could be caused by the time of day (≈3 pm local for the scan vs. ≈11 am for the traverse), different sky conditions between these acquisition periods, and/or different viewing orientations.

More exact determination of the instrument’s detection limit was performed by analyzing the noise in an absorbance spectrum generated from two clear-sky images. Following Stutz and Platt (1996), an estimation of the detection limit can be made with:

where σ is the standard deviation of an absorbance spectrum generated from two spectra containing no absorbing species and n is the number of pixels in the spectrum. D¯limit is the detection limit of the average optical density, which itself is defined by Stutz and Platt as three times the standard deviation of the reference spectrum; it provides a measure of the absorption strength of a given spectrum. It should be noted that the detection limit presented here is somewhat simplified; a much more complex procedure is discussed by Stutz and Platt (1996) and Platt and Stutz (2008), however, this simplified algorithm has been shown to provide a relatively accurate estimation (within 10–20% of the more complex method).

From clear sky spectra acquired in Masaya on the end of a traverse sequence, the absorbance noise σ was 3.10 × 10⁻³. In a fitting window of 85 pixels, such as that used in the DOAS fits in Figure 6, this noise corresponds to a detection limit D¯limit of 2.03 × 10⁻³. In the presence of residual structures, from unknown gas species or the instrument itself, the detection limit must be scaled by a correction factor of 3–4 (Platt and Stutz, 2008). Here, we conservatively use 4, therefore, the average optical density detection limit is 8.11 × 10⁻³. The resulting column density detection limit is 26 ppm ⋅ m SO₂. Following the same methodology for the scan associated with Figure 6B, a detection limit of 50 ppm ⋅ m was estimated. As can be seen, these values are case-specific and it is not possible to generate a single detection limit for the PiSpec instrument for all scenarios. Indeed, D¯limit will depend on field conditions, PiSpec acquisition settings and the DOAS fitting procedure. Nevertheless, the conservative detection limits presented here are quite reasonable.

The detection limits are an order of magnitude larger than the 2.5 ppm ⋅ m quoted by Galle et al. (2003) for a mini-DOAS instrument; however, it is not clear how they have defined the limit in their work. The limits discussed for the PiSpec are quite conservative, since they include a factor of four increase in D¯limit associated with the potential presence of residual structures in the spectra, following Platt and Stutz (2008). Omitting this factor, the detection limit for the traverse discussed above would be 6.5 ppm ⋅ m, which is quite similar to the mini-DOAS. We suggest, however, that the more conservative estimate, 26 ppm ⋅ m in this case, is likely to be more realistic. This general picture of the PiSpec providing a somewhat reduced performance in terms of resolving gas column densities is also borne out in the prior work of Wilkes et al. (2017), which is discussed in Section 3.1. Therein a series of 10 measurements of gas cells were made, with both a USB2000 and PiSpec unit, and the standard deviations of the retrieved column densities were assessed. In this case, the variability in gas column densities from the USB2000 was typically a factor of two below that of the PiSpec. This was for instrument integration times of 1.5 and 6 s for the USB2000 and PiSpec, respectively, which provided very similar levels of detector saturation at 330 nm (52 and 48%, respectively).

Conversely, at large column densities DOAS retrievals can become non-linear due to the spectral resolution of the spectrometer not perfectly resolving high frequency variations in the SO₂ absorption cross-section, and due to the fact that the natural logarithm and convolution with the ILS are not commutative operations (Frankenberg et al., 2005; Wenig et al., 2005; Bobrowski et al., 2010). Linearity of PiSpec DOAS retrievals was assessed by modeling the instrument response following Wagner et al. (2003) and Kern et al. (2017). First a column density of SO₂ was assumed. This was used to generate an absorption spectrum through the Beer-Lambert law and use of a high resolution absorption cross-section from Vandaele et al. (2009). This absorption spectrum was convolved with the PiSpec ILS and the natural logarithm taken; the resultant spectrum was then down-sampled to the pixel resolution of the PiSpec. Finally, a typical DOAS fit procedure was applied to this spectrum, using the ILS-convolved high resolution absorption cross-section spectrum.

The results of this model are displayed in Figure 7, run for column densities of 0–10000 ppm ⋅ m, in 1000 ppm ⋅ m increments, and for a fit window of 314–324 nm. Up to 4000 ppm ⋅ m the fit is extremely linear, producing a retrieval of 3957 ppm ⋅ m for a true SO₂ column density of 4000 ppm ⋅ m. This indicates that for the majority of volcanic applications the PiSpec will perform linearly. In particular, all PiSpec measurements made on Masaya were comfortably within this extremely linear response interval. Since non-linearity becomes more pronounced at higher optical densities, shifting to longer wavelengths, where SO₂ is less strongly absorbing, is one method which could account for this saturation effect where necessary (Bobrowski et al., 2010); alternatively, the modeled response can be used to correct retrievals (Wagner et al., 2003; Kern et al., 2017).