Retrieval of absolute SO2 column amounts from scattered-light spectra: implications for the evaluation of data from automated DOAS networks

Abstract

Scanning spectrometer networks using scattered solar radiation in the ultraviolet spectral region have become an increasingly important tool for monitoring volcanic sulfur dioxide (SO₂) emissions. Often measured spectra are evaluated using the differential optical absorption spectroscopy (DOAS) technique. In order to obtain absolute column densities (CDs), the DOAS evaluation requires a Fraunhofer reference spectrum (FRS) that is free of absorption structures of the trace gas of interest. For measurements at volcanoes such a FRS can be readily obtained if the scan (i.e. series of measurements at different elevation angles) includes viewing directions where the plume is not seen. In this case, it is possible to use these viewing directions (e.g. zenith) as FRS. Possible contaminations of the FRS by the plume can then be corrected by calculating and subtracting an SO₂ offset (e.g. the lowest SO₂ CD) from all viewing directions of the respective scan. This procedure is followed in the standard evaluations of data from the Network for Observation of Volcanic and Atmospheric Change (NOVAC). While this procedure is very efficient in removing Fraunhofer structures and instrumental effects it has the disadvantage that one can never be sure that there is no SO₂ from the plume in the FRS. Therefore, using a modelled FRS (based on a high-resolution solar atlas) has a great advantage. We followed this approach and investigated an SO₂ retrieval algorithm using a modelled FRS. In this paper, we present results from two volcanoes that are monitored by NOVAC stations and which frequently emit large volcanic plumes: Nevado del Ruiz (Colombia) recorded between January 2010 and June 2012 and from Tungurahua (Ecuador) recorded between January 2009 and December 2011. Instrumental effects were identified with help of a principal component analysis (PCA) of the residual structures of the DOAS evaluation. The SO₂ retrieval performed extraordinarily well with an SO₂ DOAS retrieval error of 1 - 2 × 10¹⁶[moleculescm^-2]. Compared to a standard evaluation, we found systematic differences of the differential slant column density (dSCD) of only up to [approximate] 15% when looking at the variation of the SO₂ within one scan. The major advantage of our new retrieval is that it yields absolute SO₂ CDs and that it does not require complicated instrumental calibration in the field (e.g. by employing calibration cells or broadband light sources), since the method exploits the information available in the measurements.We compared our method to an evaluation that is similar to the NOVAC approach, where a spectrum that is recorded directly before the scan is used as an FRS and an SO₂ CD offset is subtracted from all retrieved dSCD in the scan to correct for possible SO₂ contamination of the FRS. The investigation showed that 21.4% of the scans (containing significant amounts of SO₂) at Nevado del Ruiz and 7% of the scans at Tungurahua showed much larger SO₂ CDs when evaluated using modelled FRS (more than a factor of 2). For standard evaluations the overall distribution of the SO₂ CDs in a scan can in some cases indicate whether the plume affects all viewing directions and thus these scans need to be discarded for NOVAC emission rate evaluation. However, there are other cases where this is not possible and thus the reported SO₂ emission rates would be underestimated. The new method can be used to identify these cases and thus it can considerably improve SO₂ emission budgets.

Atmos. Meas. Tech., 9, 56775698, 2016 www.atmos-meas-tech.net/9/5677/2016/ doi:10.5194/amt-9-5677-2016 Author(s) 2016. CC Attribution 3.0 License.

Peter Lbcke1, Johannes Lampel1,2, Santiago Arellano3, Nicole Bobrowski1,6, Florian Dinger1,2, Bo Galle3, Gustavo Garzn4, Silvana Hidalgo5, Zoraida Chacn Ortiz4, Leif Vogel1,a, Simon Warnach1,2, and Ulrich Platt1

1Institute of Environmental Physics, University of Heidelberg, Heidelberg, Germany

2Max Planck Institute for Chemistry (MPI-C), Mainz, Germany

3Department of Earth and Space Sciences, Chalmers University of Technology, Gothenburg, Sweden

4FISQUIM, Direccin de Laboratorios, Servicio Geolgico Colombiano, Cali & Manizales, Colombia

5Instituto Geofsico, Escuela Politcnica Nacional, Quito, Ecuador

6Institute of Geosciences, Johannes Gutenberg University Mainz, Germany

anow at: Basque Centre for Climate Change (BC3), 48008, Bilbao, Spain

Correspondence to: Peter Lbcke ([email protected])

Received: 26 January 2016 Published in Atmos. Meas. Tech. Discuss.: 11 April 2016 Revised: 29 August 2016 Accepted: 3 October 2016 Published: 29 November 2016

Abstract. Scanning spectrometer networks using scattered solar radiation in the ultraviolet spectral region have become an increasingly important tool for monitoring volcanic sulfur dioxide (SO2) emissions. Often measured spectra are evaluated using the differential optical absorption spectroscopy (DOAS) technique. In order to obtain absolute column densities (CDs), the DOAS evaluation requires a Fraunhofer reference spectrum (FRS) that is free of absorption structures of the trace gas of interest. For measurements at volcanoes such a FRS can be readily obtained if the scan (i.e. series of measurements at different elevation angles) includes viewing directions where the plume is not seen. In this case, it is possible to use these viewing directions (e.g. zenith) as FRS. Possible contaminations of the FRS by the plume can then be corrected by calculating and subtracting an SO2 offset (e.g. the lowest SO2 CD) from all viewing directions of the respective scan. This procedure is followed in the standard evaluations of data from the Network for Observation of Volcanic and Atmospheric Change (NOVAC). While this procedure is very efcient in removing Fraunhofer structures and instrumental effects it has the disadvantage that one can never be sure that there is no SO2 from the plume in the FRS.

Therefore, using a modelled FRS (based on a high-resolution solar atlas) has a great advantage. We followed this approach and investigated an SO2 retrieval algorithm using a modelled

Retrieval of absolute SO2 column amounts from scattered-light spectra: implications for the evaluation of data from automated DOAS networks

FRS. In this paper, we present results from two volcanoes that are monitored by NOVAC stations and which frequently emit large volcanic plumes: Nevado del Ruiz (Colombia) recorded between January 2010 and June 2012 and from Tungurahua (Ecuador) recorded between January 2009 and December 2011. Instrumental effects were identied with help of a principal component analysis (PCA) of the residual structures of the DOAS evaluation. The SO2 retrieval performed extraordinarily well with an SO2 DOAS retrieval error of 121016 [molecules cm2]. Compared to a standard

evaluation, we found systematic differences of the differential slant column density (dSCD) of only up to 15 % when

looking at the variation of the SO2 within one scan. The major advantage of our new retrieval is that it yields absolute SO2 CDs and that it does not require complicated instrumental calibration in the eld (e.g. by employing calibration cells or broadband light sources), since the method exploits the information available in the measurements.

We compared our method to an evaluation that is similar to the NOVAC approach, where a spectrum that is recorded directly before the scan is used as an FRS and an SO2 CD offset is subtracted from all retrieved dSCD in the scan to correct for possible SO2 contamination of the FRS. The investigation showed that 21.4 % of the scans (containing signicant amounts of SO2) at Nevado del Ruiz and 7 % of the

Published by Copernicus Publications on behalf of the European Geosciences Union.

5678 P. Lbcke et al.: DOAS evaluation with a solar atlas

scans at Tungurahua showed much larger SO2 CDs when evaluated using modelled FRS (more than a factor of 2).For standard evaluations the overall distribution of the SO2

CDs in a scan can in some cases indicate whether the plume affects all viewing directions and thus these scans need to be discarded for NOVAC emission rate evaluation. However, there are other cases where this is not possible and thus the reported SO2 emission rates would be underestimated. The new method can be used to identify these cases and thus it can considerably improve SO2 emission budgets.

1 Introduction

Since the introduction of the correlation spectrometer (COSPEC; Moffat and Millan, 1971; Stoiber et al., 1983) measurements of volcanic sulfur dioxide (SO2) emission rates have become an additional tool for volcanologists to study the activity of volcanoes. More recently the availability of miniature spectrometers allowed the widespread application of the well-known differential optical absorption spectroscopy (DOAS) technique (e.g. Perner and Platt, 1979;Platt and Stutz, 2008) in volcanic environments (e.g. Galle et al., 2003; McGonigle et al., 2005; Elias et al., 2006).Automated systems for plume measurements were subsequently developed based on scanning the volcanic plume from different stationary positions: the so-called scanning-DOAS method (Edmonds et al., 2003). Scanning-DOAS instruments are now installed at many volcanoes in order to monitor SO2 emission rates. The rst installations of scanning-DOAS networks were done at Montserrat volcano (Edmonds et al., 2003). The Network for Observation of Volcanic and Atmospheric Change (NOVAC; Galle et al., 2010) is at present composed of more than 80 scanning-DOAS instruments at about 30 volcanoes worldwide. Furthermore, Mt. Etna and Stromboli, Italy, are both monitored by a comparable scanning-DOAS network (FLAME network; Burton et al., 2009; Salerno et al., 2009a). Another approach using similar instruments is the Hawaiian FLYSPEC fence line at Kilauea volcano which consists of 10 xed, upward-looking spectrometers (Businger et al., 2015).

In order to correctly retrieve absolute SO2 CDs from the recorded spectra via the DOAS method, and thus calculate accurate SO2 emission rates, a background Fraunhofer reference spectrum (FRS), which is free of volcanic absorption features, is required. Typically, DOAS SO2 evaluations use a

FRS recorded in the scan (for example with a different viewing direction) to correct for the strong Fraunhofer lines of the solar spectrum. Contamination of this FRS with volcanic SO2 absorption structures can in principle be corrected for by introducing an SO2 CD offset that is subtracted from all SO2 CDs of the respective scan (details about the calculation of this offset is provided in Sect. 2). However, if all viewing directions contain absorption signatures of volcanic SO2, this

approach leads to an incorrect offset and thus erroneous SO2 CDs.

Therefore it is desirable to use a universal FRS, which is free of SO2 (or in general free of the trace gas to be measured). First investigations on using a modelled background spectrum as an FRS for the DOAS evaluation of volcanic SO2 were performed by Salerno et al. (2009b). Different implementations of this approach were used by Lbcke (2014) and Hibert et al. (2015) for evaluating NOVAC data collected at Nevado del Ruiz and at Piton de la Fournaise on Runion island, respectively. Burton and Sawyer (2016) use a similar approach of modelling the background spectrum based on a high-resolution solar atlas for their iFit method, a direct tting approach for the evaluation of volcanic SO2 and BrO.

This work will follow the idea of using a high-resolution solar atlas spectrum (we used the solar atlas by Chance and Kurucz, 2010) in order to calculate a gas-free background spectrum which is used as an FRS for the DOAS evaluation of SO2.

The paper is structured in the following way. We applied the SO2 retrieval with the modelled FRS to data from NO

VAC in order to study how frequently differences between the standard evaluation and the approach using an articial reference spectrum can be observed. In addition, we investigated the remaining residual structure of the DOAS evaluation with help of a principal component analysis (PCA).The results of the PCA were used in order to take instrumental effects into account and improve the retrieval. The evaluation process and possible pitfalls will be described in detail. We focussed on two large volcanic emission sources for our study: spectra were evaluated from two instruments at Nevado del Ruiz (Colombia), covering the time between January 2010 and June 2012, and from three instruments at Tungurahua (Ecuador), covering the time between January 2010 and December 2012.

The results of an evaluation using a modelled FRS were compared to a standard NOVAC evaluation, which uses a spectrum measured with an upward-looking viewing direction as FRS and subtracts an SO2 offset to correct for possible contamination. Data from the NOVAC volcanoes Nevado del Ruiz and Tungurahua allowed us to determine how frequently all spectra from a particular scan of a scanning-DOAS instrument are contaminated with (volcanic) SO2 absorption structures at these volcanoes. Additionally, it allowed us to investigate under which conditions scans occur with SO2 absorptions present in all viewing directions.

2 Background spectra for scanning-DOAS instrument networks at volcanoes

DOAS (e.g. Perner and Platt, 1979; Platt and Stutz, 2008) is a well-established spectroscopic technique, based on BouguerBeerLamberts law, which uses the differential structures of molecules to remotely measure their slant col-

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P. Lbcke et al.: DOAS evaluation with a solar atlas 5679

umn density (SCD) S. For sunlight measurements, an FRS I0( ) is needed to remove the shape of the incident solar radiation, in particular the strongly structured Fraunhofer lines, and possible instrumental structures from the measurement.In this case, the evaluation procedure relies on the ratio of measurement spectrum I ( ) and FRS. For one absorber, the optical depth is directly related to the absorption cross section ( ) of the molecule and the SCD S of the measurement spectrum. However, in the case of a contaminated FRS the result only gives the difference in column density between measurement spectrum and the column density S0 of the FRS:

( ) = ln

[parenleftbigg]

I ( ) I0( )

structures are present at all viewing directions of the instrument.

For the FLAME network, Salerno et al. (2009b) investigated the use of a modelled background spectrum based on a high-resolution solar atlas for the DOAS evaluation of SO2. The authors noted that wide volcanic plumes, which may cover the entire eld of view of the instrument and prevent acquisition of a plume-free reference spectrum, are relatively frequently observed at Mt. Etna, Italy. The authors recorded spectra of calibration cells (with known SO2 content) and tuned the parameters of the DOAS evaluation in order to reproduce the known SO2 CD of the cells. This makes this approach rather labour intensive and it does not appear to be practical for instruments which are already installed at remote locations. In addition, Salerno et al. (2009b) used three different values for the full width at half maximum (FWHM) of the instrument line function (ILF) for the convolution of the different trace gas absorption cross sections and the convolution of the high-resolution solar atlas spectrum (i.e. the FWHM for the O3 convolution was different from the FWHM for the SO2 convolution). However, the ILF is an instrument property. While there are inuences, e.g. variations of the FWHM over the detector or variations with instrument temperature, it does not depend on the trace gas itself, and therefore there is no physical reason to encounter three different FWHM values of the ILF.

In our new evaluation scheme, we followed the approach to model the FRS on the basis of a solar atlas instead of measuring it on site; the required instrumental properties are retrieved from the measurement data itself. We modelled the FRS I0 by convolving the high-resolution solar atlas IK( )

by Chance and Kurucz (2010) using the ILF as a convolution kernel H( ).

We used the same ILF for the convolution of the high-resolution solar atlas spectrum as well as for the convolution of all trace gas cross sections. Unfortunately there are only records of the ILF at room temperature available for most NOVAC instruments. This introduces an additional error source, since the ILF varies with instrument temperature (Pinardi et al., 2007). All reference cross sections were convolved using the 334.15 nm line of a mercury emission lamp which was recorded at room temperature as a convolution kernel.

In reality, the recorded signal due to the incident solar radiation is inuenced not only by the spectral resolution of the spectrometer but also by the wavelength-dependent efciency of the detector, the efciency of the spectrometers grating or the instruments optical system. We combine these wavelength-dependent effects in a factor Q( ) (neglecting detector effects like offset and dark current, which were corrected beforehand) and describe a measured spectrum as

I0,measured( ) = (Iincident( ) H( )) Q( ). (2)

Only the high-frequency variations (in wavelength) of Q( ) need to be corrected for in the retrieval, since slow varia-

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[parenrightbigg] =

ln Isolar( ) eS( )Isolar( ) eS

0( )

[parenrightBigg]

= ( ) (S S0). (1) The great advantage of the ratio method is that the highly structured solar Fraunhofer spectrum Isolar( ) is eliminated in the evaluation; the potential weakness is that it actually always determines the difference of two CDs, the so-called differential SCD (dSCD). This property also helps to eliminate potential stratospheric contributions to the trace gas column (if the solar zenith angle (SZA) is sufciently constant between the measurement of I ( ) and I0( )); in addition, possible instrumental structures are also removed. However, one has to make sure by proper choice of I0( ) that S0 is negligible compared to S.

At volcanoes, during traverse measurements or campaign based scanning measurements a gas-free FRS I0( ) is typically obtained by choosing a spectrum recorded with a viewing direction that is believed not to intersect the plume. However, the choice of FRS is more difcult for automatised scanning-DOAS networks, like NOVAC (Galle et al., 2010) or the FLAME network (Burton et al., 2009; Salerno et al., 2009a), since it is not always clear whether the FRS contains signicant volcanic SO2 absorption structures or not.

Galle et al. (2010) suggested for NOVAC to use a zenith-looking spectrum as FRS for the DOAS evaluation. Possible contamination of the FRS is taken into account during the evaluation by subtracting an offset SO2 CD (that corresponds to S0) from the derived CD S. Based on preliminary tests

on measurements at a few volcanoes, the authors suggested using the average of the lowest 20 % SO2 CDs from the valid retrievals in each scan as the offset CD S0 but other op

tions (e.g. using the lowest SO2 CD obtained in a scan) are possible as well. The offset value is determined individually for each scan (i.e. recordings of spectra from one horizon to the other) and subtracted from all SO2 CDs of the respective scan. However, if all spectra of one scan are inuenced by SO2 absorption (i.e. S0 is not negligible compared to S)

subtracting the offset will lead to an underestimation of the SO2 CDs. Therefore, this approach can lead to a systematic underestimation of the SO2 emission rate if SO2 absorption

5680 P. Lbcke et al.: DOAS evaluation with a solar atlas

tions are eliminated by the high-pass ltering inherent to the DOAS. Burton and Sawyer (2016) additionally mentioned small variations between different pixels. In their paper, these variations are taken into account by characterising them with the help of a deuterium lamp (i.e. recording a so-called at spectrum). Here we use a different approach and include the above mentioned wavelength-dependent effects Q( ) and the pixel-to-pixel variations as a pseudo-absorber in the DOAS retrieval. Assuming that IK( ) is an ideal representation of the incident radiation Iincident( ) (i.e. IK( ) = Iincident( ))

we are left with a wavelength-dependent residual structure when calculating the optical depth using Eqs. (1) and (2):

= ln

I0,measured( )

I0,model( ) = lnQ( ). (3)

Two pseudo-absorbers were included in the DOAS t scenario in order to account for these instrumental effects. Information about these absorbers was obtained from the spectra themselves by using a PCA on the residuals from a DOAS t for each instrument individually. We interpret the rst principal component to be caused by detector effects as given by Q( ) in Eq. (3). Including the second principal component in the DOAS t greatly improved the stability of the retrieval, in particular for the instruments installed at Tungurahua. This second principal component appears to account largely for variations of the instrument calibration and temperature-induced changes of instrument properties. However, the principal components could additionally contain structures from the Chance and Kurucz (2010) solar atlas as suggested by Burton and Sawyer (2016). This solar atlas is based on measured spectra synthesised from two different measurement platforms and corrected for atmospheric absorption lines.

3 Data evaluation

This section discusses the details of the SO2 retrieval. A summary of the evaluation steps can be found in the Appendix.

3.1 Settings of the DOAS retrieval

All spectra were evaluated for SO2 using the DOASIS software package (Kraus, 2006) with two different settings.

Method A: an evaluation similar to the regular NOVAC evaluation. This method used a spectrum that was acquired by the instrument immediately before the scan with a scan angle of 0 as FRS (smallest deviation from the zenith direction; see Galle et al., 2010, for the exact denition of the scan angle). After evaluation of a complete scan through the sky, which means recording spectra from one horizon to the other horizon, an SO2

CD offset was calculated and subtracted from all SO2 CDs of the respective scan.

Method B: an evaluation using a modelled background spectrum, based on a high-resolution solar atlas spec-

trum as an FRS. In this case the same FRS was used for the evaluation of all spectra from one instrument.The FRS was calculated on the basis of the Chance and Kurucz (2010) solar atlas by convolving the high-resolution solar atlas spectrum with the ILF of the respective spectrometer. First a DOAS evaluation using this t scenario was performed to create a set of residual spectra which were analysed with help of a principal component analysis. In a second evaluation round the rst two principal components were included in the t scenario as pseudo-absorbers in order to account for instrumental effects (see Eqs. 2 and 3, above). The results of the second run were used in order to investigate the relative difference between the two methods.

As a rst step before the DOAS t, all spectra were corrected for dark current and offset by subtracting a dark spectrum, which is recorded using the same parameters (number of co-added spectra and exposure time) as the measurement spectra but with the telescope pointing to the ground, where the eld of view of the spectrometer is blocked by a closed window of the scanner. Afterwards spectra that were under-or overexposed were removed from the evaluation. This was done in two steps: rst we removed all spectra for which the highest exposure was below 12 or above 92 % of the maximum number of counts in the complete spectrum (500 and 3800 of 4096 counts, respectively, for a single exposure).These limits refer to spectra corrected for dark current and offset. Limiting the maximum exposure over the complete spectrum (not just the part used for SO2 retrieval) served to prevent problems due to blooming effects. Second, after investigating the t quality for both retrieval methods we additionally excluded all spectra with a maximum intensity below 5 or above 85 % in the SO2 retrieval wavelength range from further processing. The latter maximum value was chosen since the ~2 of the retrieval largely increased at higher intensities due to detector non-linearity.

After a wavelength calibration (by comparing the spectrum with the Fraunhofer lines of the Chance and Kurucz, 2010, solar atlas spectrum), spectra were evaluated for SO2 using a DOAS t. The DOAS evaluation was performed in the wavelength range between 310 and 326.8 nm. In order to create the principal components (for which the input vectors need to have the same length), we chose the channels corresponding to these wavelengths once at the beginning and kept the channels of the t range xed throughout the entire evaluation process.

Based on the respective FRS, a Ring spectrum was calculated and included in the t in order to account for the Ring effect, the lling of the Fraunhofer lines of the solar spectrum (Shefov, 1959; Grainger and Ring, 1962). The Ring spectrum is calculated using a method that is implemented in DOASIS, which is based on Bussemer (1993).

The DOAS t approach was (except for the FRS and the additional pseudo-absorbers) identical for methods A and B:

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Deviating from the approach of Galle et al. (2010), we used the lowest SO2 CD of each scan as the SO2 CD offset instead of using the average over the SO2 CD of several spectra. As the offset value is based on only one single spectrum it is important to remove spectra where the SO2 t failed completely from the results before calculating the offset value.

We therefore only used viewing directions that were not inuenced by obstacles in the eld of view and where the intensity was adequate, for further evaluation. This meant, for example, that for instrument D2J2201 at Nevado del Ruiz only spectra with a scanning angle between 72 and 86

were allowed (the scan angle is dened from 90 to +90

clockwise for an observer looking from the instrument towards the volcano). If no viewing directions inuenced by obstacles were identied, we only excluded the two lowest viewing directions for these instruments (i.e. scan angle of

90 ). Limiting the viewing directions for the calculation of the offset is a trade-off. Viewing directions with obstacles (for example mountains or buildings) in the eld of view obviously lead to erroneous DOAS t results. However, excluding too many viewing directions could inuence the results, since we might in some cases exclude viewing directions which are interference free.

We also removed spectra from further evaluation, where the DOAS t from Method A clearly failed and had a ~2 above 0.05. ~2 was calculated for all pixels of the evaluation range and typically had values between 1 103 and

0.01. Therefore, this threshold only removed a small fraction below 1 % of the remaining spectra from further evaluation.Afterwards the lowest SO2 CD of each scan was chosen as the offset value and subtracted from all SO2 CDs of the respective scan.

3.3 Principal component analysis for Method B

PCA (Pearson, 1901; Smith, 2002) is a statistical technique that can be used to transform a set of vectors (in our case the remaining residual structure of the DOAS t) into a set of orthogonal vectors and also provides immediately time series for the magnitude of each of the vectors. These orthogonal vectors are chosen in such a way that a sequence of n principal components provides the best possible linear approximation of the residual data using an euclidean norm (Hastie et al., 2001). The PCA technique was rst applied in DOAS applications by Ferlemann (1998). Li et al. (2013) retrieved SO2 from OMI satellite data with help of PCA. The PCA was used by Lampel (2014) to identify problems in the spectral evaluation of multi-axis DOAS and cavity-enhanced DOAS measurements. We performed a PCA on the residuals of the initial DOAS t with the modelled FRS in order to take instrumental effects into account (see Eq. 3). Different from usual PCA applications, we did not remove the mean value from the spectra since we are interested in all systematic variations of the residual spectra from the zero value (which would be the ideal case).

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P. Lbcke et al.: DOAS evaluation with a solar atlas 5681

to account for trace gas absorption in the atmosphere one SO2 cross section (recorded at 298 K by Vandaele et al., 2009) and two O3 cross sections (recorded at 221 and 273 K by Burrows et al., 1999) were included in the DOAS t.The 334.15 nm peak of a mercury line spectrum recorded at room temperature was used as a representation of the ILF for the convolution. The O3 cross section with a temperature of 273 K was orthogonalised with respect to the lower temperature O3 cross section in the DOASIS software. To account for small inaccuracies in the wavelength calibration, the FRS and the Ring spectrum as one set and all trace gas reference cross sections as another set were allowed a wavelength shift and squeeze with respect to the measurement spectrum for Method A. A shift of 0.2 nm was allowed and the spectra

were allowed to be stretched/squeezed by 2 %. Since the

modelled FRS spectrum (Method B) is synthetic, the calibration is inherited from the solar atlas. Given the stated accuracy of the calibration of the solar atlas 3.2 104 nm

(Chance and Kurucz, 2010), we assume that it is correct for our purposes. Therefore the FRS, the Ring spectrum and all trace gas absorption cross sections were only allowed to be shifted and squeezed as one set in Method B. Some of the instruments had a hot detector pixel, a pixel which always showed a much higher signal. For Method A this was not a problem, since a similar signal is typically found in the FRS. To exclude these hot pixels from the t in Method B an additional absorber that is zero everywhere except at the location of the hot pixel (where its value was chosen as 1) was included in the t. A DOAS polynomial of third order was used to remove broadband variations in the spectrum. In order to take a possibly remaining offset into account (after the dark spectrum removal, for example due to instrumental stray light), an additional constant in intensity space was allowed in the retrieval.

After an initial DOAS t the retrieved trace gas CDs were used as input parameters for a saturation correction and the I0 correction of the SO2 and the O3 absorption cross sections. Both the I0 effect (for highly structured light sources) and the saturation effect (for absorbers with high optical densities) are due to narrow structures that cannot be resolved by the spectrometer and the fact that the exponential function in the BouguerBeerLambert law and the convolution do not commute (Wenig et al., 2005). The correction of both effects are standard procedures in DOAS evaluations (Platt et al., 1997; Platt and Stutz, 2008). Both O3 cross sections were corrected for the saturation effect using the CD of the (non-orthogonalised) O3 cross section recorded at 221 K.

3.2 Calculation of the SO2 offset value for Method A

As discussed above, it cannot be ruled out that the spectrum used as FRS in Method A is contaminated with SO2. One approach to (partially) correct for this contamination is to calculate an SO2 offset value. This value is calculated for each scan and subtracted from all SO2 CDs of the respective scan.

5682 P. Lbcke et al.: DOAS evaluation with a solar atlas

In order to nd mainly instrumental effects and exclude other problems in the residuals (e.g. large O3 CDs, objects in the light path), even more restrictive criteria had to be fullled by the spectra included in the PCA:

Only spectra with a scan angle in the range of 75

to +75 were included in order to avoid inuences by

very long atmospheric light paths and errors due to topographic features or buildings/vegetation in the light path.

Only spectra recorded at SZAs below 60 were used, to exclude spectra with large stratospheric O3 CDs.

Only spectra with a ~2 below 0.01 for Method A (using a spectrum recorded with the same instrument before the scan as FRS) were included in order to exclude spectra that are already problematic in a regular DOAS retrieval.

A more restrictive selection criterion for the intensity of the spectrum was chosen. Only spectra with a maximum number of counts between 32 and 78 % (1333 or 3200 counts for a single exposure after dark current correction) of the maximum possibly number of counts over the entire spectrum were allowed for the PCA.

Only spectra that were not inuenced by SO2 (i.e. SO2 CD below two times the DOAS retrieval error) were allowed for the PCA. This was assured by a DOAS t using a modelled spectrum as FRS without including additional PCA pseudo-absorbers.

There are some pitfalls which can make the application of the PCA non-trivial. The spectra that are analysed in the PCA should not include any real SO2 absorption features because this would introduce a potential negative SO2 offset.These features would show up in the residual structure and thus inuence the principal components and ultimately lead to unreliable t results. Li et al. (2013) assured this criterion by selecting an SO2-free reference sector. For our data set we have to use a different approach to only select spectra without SO2 structures for the PCA. We chose spectra from times with only little degassing activity to create the PCA. Since this was difcult (in particular at Nevado del Ruiz) rather than relying on guesses about the SO2 CD we used an additional SO2 t with a modelled FRS to select gas-free spectra.Only spectra where the absolute value of the SO2 CD was smaller than twice the DOAS t error were considered in the PCA. Using a similar argument, including an SO2 absorption cross section in the DOAS t used for the PCA can lead to problems. Inaccuracies in the DOAS t with a modelled FRS (due to the same detector structures that we want to nd with help of the PCA) might lead to a false SO2 signal (with positive or negative sign). The t might nd these structures and thus remove them from the residual spectrum. Thus they are missing in the principal component which is later included in

Figure 1. Time series of the residuals optical density (colour-coded) of a DOAS retrieval using a modelled background spectrum. The gure shows data from the 7 days (511 September 2010) used in the PCA (without SO2 included in the t) for instrument D2J2201 at Nevado del Ruiz. The residuals are shown in chronological order.

The discontinuities in horizontal direction are at the transition from one day to another.

-0.2

D2J2200 D2J2201 D2J2140 I2J8546 I2J8548

(a)

PC1

PC2

0.2

Optical density

0.1

0

-0.1

(b)

0.2

Optical density

0

-0.2

-0.4 310 315 320 325

Wavelength [nm]

Figure 2. The rst two principal components that were included in the solar atlas evaluation shown for all ve instruments at Nevado del Ruiz and Tungurahua. For Tungurahua the principal components from 2010 are shown.

the DOAS t. In this case the principal component would not only describe the instrumental effects but also add/subtract SO2 features from the spectrum and thus lead to an additional error of the SO2 CD. It is therefore crucial not to include SO2 in the DOAS t that is used to create the residual structures that are investigated with help of the PCA. Therefore, we made two DOAS ts with the modelled FRS. The rst t had an SO2 absorption cross sections included and was used to select spectra suited for the PCA. The second t did not include an SO2 absorption cross sections and was used to create the residuals.

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At Nevado del Ruiz we selected 7 days in September/October of 2010 as our training data set for the PCA; the increasing activity after this time made it difcult to nd gas-free days. At Tungurahua the situation was quite different: the volcano had periods of higher activity alternating with times with very low or no degassing at all. The instruments at Tungurahua also showed a drift of instrument calibration and we thus performed the PCA for each year individually. For each instrument and each year at Tungurahua we chose 10 days as our training data for the PCA. These 10 days were distributed over the year (at times of low volcanic degassing activity) in order to nd long-term variations of the principal components. For example in 2009 we chose 5 days in January and 5 days in October for the PCA. For each PCA (that means one for each instrument at Nevado del Ruiz and one per instrument and per year at Tungurahua) typically more than 10 000 residual spectra were evaluated. Choosing only a small set of a few days for the PCA has several advantages. For one, it allows us to investigate the performance on gas-free days that are not part of the training data. Using all gas-free days for the PCA would by denition shift the average SO2 CD to zero on these days. The second advantage is of a more practical nature; in real life it is not always feasible to manually investigate a large amount of data to nd gas-free days, and only a few days have to be sufcient.

4 Results

At Nevado del Ruiz the two original stations, Bruma (instrument D2J2200, installed at a 3100 m distance from the crater in NW direction) and Alfrombales (instrument D2J2201, installed at 4150 m distance in W direction from the crater), have been installed in 2009. We evaluated spectra recorded between 1 January 2010 and 30 June 2012 from these two NOVAC stations (see Garzon et al., 2013, and Lbcke et al., 2014, for maps of the stations and more information on NOVAC measurements at Nevado del Ruiz). After evaluating the spectra, we found that the instruments GPS antennas occasionally reported erroneous times, which led to offsets in the time stamps of spectra of up to 55 min. Before selecting spectra for the nal results (Sect. 4.24.4), we corrected for possible time offsets with help of a Langley plot of the O3 CDs (see Appendix A for details).

At Tungurahua there are currently four stations installed.

A map of the different NOVAC stations at Tungurahua can be found in Galle et al. (2010) and additional information on the gas emissions from Tungurahua is available in Hidalgo et al. (2015). We used data recorded between January 2009 and December 2011 from the three stations that are located in the main wind direction: Pillate, 8000 m W, Huayarapata, 9100 m NW, and Bayushig, 11900 m SW of the volcano.

Figure 3. Peak-to-peak apparent optical density (e.g. peak-to-peak optical depth of the principal component times the t coefcient) of the rst and second principal components for instrument D2J2201 at Nevado del Ruiz. In the left column the principal components are shown as a function of time and in the right column as a function of instrument temperature. It appears that PC1 describes a constant apparent spectral feature of the instrument while PC2 describes a temperature-dependent effect.

4.1 Structure and variation of the principal components

A time series of the residual structures for the spectra used in the PCA for instrument D2J2201 is shown in Fig. 1. It can be clearly seen that there is a dominating constant structure apparent in all spectra. This residual structure is quite similar for all instruments, as can be seen from Fig. 2, which shows the rst two principal components of the residual structures for all instruments included in this study. While the principal components are not exactly the same, similar broadband as well as narrowband features can be observed for all instruments, in particular for the rst principal component.

At Nevado del Ruiz, we observed that the rst principal component is mostly constant with only little temperature variations while the second principal component usually shows stronger temperature-dependent variations. This can be seen by looking at the peak-to-peak optical density of the rst and second principal component, shown in Fig. 3 for instrument D2J2201. For a better comparison with other absorbers the apparent optical density of the respective principal component (i.e. the t coefcient multiplied with the peak-to-peak optical density of the pseudo-absorber) is shown in Figs. 3 and 4.

The behaviour of the instruments at Tungurahua is more complex (see Fig. 4 for an example of instrument I2J8548).Both principal components show a time dependency for all three instruments at this volcano; a temperature dependency of the principal components can only be observed for some

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Figure 4. Peak-to-peak apparent optical density of the rst and second principal components, as Fig. 3, but for instrument I2J8548 at Tungurahua. The vertical dashed lines indicate the start of the intervals for which a new set of principal components was calculated. In contrast to the case shown in Fig. 3 here both PC1 and PC2 show a temporal drift but a rather chaotic temperature dependence. It is interesting to note that the instruments at Tungurahua show behaviour similar to this gure, while both spectrometers at Nevado del Ruiz both show a behaviour similar to the one shown in Fig. 3

of the instruments. The same kind of gure for the three other instruments can be found in the Appendix.

We interpret the rst principal component as the factor

log(Q( )) from Eq. (3), while the second principal component appears to take temperature-induced or time-dependent variations of the instrument into account.

4.2 Comparison of the SO2 column densities from methods A and B

Before directly comparing the SO2 CDs of the two methods, we rst investigate how well Method B performs if there is no absorbing gas in the light path (i.e. if the retrieval yields zero when no gas is present). We assessed this by manually choosing gas-free days and looking at the distribution of the SO2 CDs. Besides low SO2 CDs from both Method A and

B, another criterion to identify gas-free days are the variations of the SO2 CDs within one scan, which are typically less structured if no gas is present. At Nevado del Ruiz fewer days (73 or 137 days for D2J2200 or D2J2201, respectively) were available in the entire data set due to strong activity. At Tungurahua more data were available, since periods with volcanic activity or no degassing both occur frequently. Examples of the diurnal variation of the SO2 CDs for both instruments at Nevado del Ruiz during gas-free days are shown in Fig. 5. In contrast to the other instruments (at both volcanoes), instrument D2J2200 (Fig. 5 at the top) showed a clear variation of the SO2 CD (as derived by Method B) over the course of a day with enhanced CDs during the evening. However, the histogram on the right-hand side (which was

Figure 5. SO2 column densities for days with presumably no SO2 apparent in the light path for the two instruments at Nevado del

Ruiz. The histogram on the right side shows the distribution of the values of both methods for all gas-free days in the data set. An increase in SO2 CDs in the early morning and towards the evening can be observed. However, the histogram shows that this only inuences a small fraction of the data (typically for SZAs above 70 ).

created for all gas-free days) shows that even though the increase towards the evening is clearly visible it only inuences a very small fraction of the data set. The other instruments (an example is D2J2201 in Fig. 5, bottom) only show deviations from the zero value during the rst or last scan of each day. At these times Method A shows larger variation within one scan as well. The average SO2 CD for gas-free periods are between 71015 [molecules cm2]

and 1.5 1015 [molecules cm2], with a standard deviation

of 2.73.6 1016 [molecules cm2]. The values of the mean

SO2 CD and the standard deviation for all instruments are given in Table A1 in the Appendix.

As discussed in detail below, the SO2 CDs derived by Method B are frequently considerably larger than those derived by Method A. In order to study the ability of both methods to derive the variation of the SO2 CD within one scan we compared the dSCDs by subtracting an offset from the data derived by Method B as well and plotted the result in Fig. 6, which shows a two-dimensional histogram of the SO2 CDs from Method A (in y direction) and Method B (in x direction, after offset removal) for the complete data set (January 2010June 2012) for instrument D2J2201 at Nevado del Ruiz. We used a bin size of 5 1016 [molecules cm2] (in x as well as

in y direction); the colour denotes how often a certain SO2

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Figure 6. Two-dimensional histogram of the SO2 SCDs from the solar atlas method vs. the SCDs from the NOVAC evaluation for instrument D2J2201 at Nevado del Ruiz. For this gure an offset value was subtracted from the solar atlas SO2 CDs as well. The dSCDs of both methods show a good linear relationship with a slope close to 1 (0.956 in this case). The black-dashed line shows the identity line.

CD pair exists. The slope of this curve can be interpreted as the relationship between the dSCDs from the two methods. When an offset is removed for both methods, they show a linear relationship. The slope of this curve is not exactly unity, it varies between 0.88 and 1.14 for the different instruments (the values are given in Table A1 in the Appendix). It is not entirely clear, what causes the difference between the two methods. One possible explanation is that spectrometer stray light (that should be corrected for by an additional offset in intensity space during the t) is not corrected for in the same way for Method A and B. While the measurement spectrum is the same for both methods, only the FRS of Method A is inuenced by stray light while the FRS of Method B is not contaminated with stray light.

After making sure that Method B performs well for gas-free days and that both methods show similar SO2 dSCDs (within a certain error), we trust that Method B works and compare the absolute SO2 CDs from Method A with

Method B. One rather extreme example of the difference between the SO2 CDs derived for both methods is shown in Fig. 7. This gure shows data from instrument D2J2201 at Nevado del Ruiz recorded on 6 March 2012. It can be clearly observed that Method B retrieved much larger SO2 CDs, especially during the middle of the day. At this time the modelled FRS leads to SO2 CDs of up to 5

1018 [molecules cm2] while Method A only shows SO2 CDs around 11018 [molecules cm2]. The variations within

each scan (which can be identied by the small gaps between data points) show similar variations for both methods. However, for Method A each scan has one viewing direction with

Figure 7. SO2 CDs at Nevado del Ruiz on 6 March 2012 from instrument D2J2201. Method A (which is similar to the standard NO

VAC approach) leads to much lower SO2 CDs compared to Method B (modelled FRS). Many of the scans from this day would have been rejected by the standard NOVAC evaluation due to very low plume completeness values (see Galle et al., 2010, for details on plume completeness).

an SO2 CD of 0, since we subtracted an offset value for each scan (see Sect. 3.2). Additional criteria exist for the calculation of SO2 emission rates (e.g. the completeness value; see

Galle et al., 2010, for an exact denition) that would have led to discarding most measurements on the day presented in Fig. 7.

We also observed days in which both methods agreed nicely. One example is 11 January 2012, as shown in Fig. 8.Only a part of the day is shown for a better visibility of the variability of the SO2 CDs within each scan.

A more systematic way to compare the SO2 CDs of many measurements is shown in the histogram in Fig. 9. This gure again shows 2-D histograms of the SO2 CDs from Method

A (in y direction) and Method B (in x direction, this time without removing an offset) for the complete data set (January 2010June 2012) for instrument D2J2201 at Nevado del Ruiz. The same bin size as above was used. As can be seen in Fig. 9, Method B leads to larger SO2 CDs on a signi-cant number of spectra. When evaluated by Method A only a negligible number of spectra has larger SO2 column densities than given by Method B. The larger SO2 CDs of Method B are most likely caused by contamination of all viewing directions with SO2 absorption structures (the likely reasons for the contamination will be discussed in Sect. 5).

4.3 Fit quality and SO2 t error for Method B

An example of an SO2 t using a modelled background spectrum is shown in Fig. 10. The spectral signature of SO2 (SO2 CD of 1.631017 [molecules cm2]) can be easily identied

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in the t. The residual is unstructured and has a peak-to-peak value of roughly 1.5 102; this value is comparable to a

regular DOAS SO2 t using an FRS measured with the same instrument from the same scan. Note that the rst principal component was found in the t extraordinarily well while the second principal component does not contribute to the spectrum signicantly in this case, which is a spectrum recorded at 16.3 C.

The time series of the SO2 retrieval error (for instrument D2J2201) depicted in Fig. 11 shows a more or less constant distribution of the t error between March 2010 and February 2012, the majority of spectra have an t error below 2 1016 [molecules cm2]. Slightly larger t errors can be

observed in the beginning of 2010. Much larger SO2 t errors after March 2012 are caused by strong volcanic activity and large SO2 CDs that lead to non-linearities in the DOAS retrieval (Method A shows increased retrieval errors in this period as well).

For instrument I2J8548 (as one example from Tungurahua) the SO2 t errors in Fig. 12 are slightly larger and show some temporal variation. There are larger values of the SO2 t error at the border between 2 years. This indicates that variations of the instruments characteristics were not completely captured by the principal components. In these cases, performing the PCA on smaller time intervals can help to improve the performance.

The SO2 DOAS t error of Method B is shown as a function of instrument temperature in Fig. 13 and as a function of SZA in Fig. 14. In Fig. 13 the t error increases for temperatures below 10 C. This can be explained with the variation of the ILF with instrument temperature. The ILF used for the convolution of the Chance and Kurucz (2010) solar atlas spectrum and the absorption cross sections was recorded at room temperature. Pinardi et al. (2007) investigated the change of ILF with temperature and reported variations of the ILF of up to 0.1 nm, in particular at temperatures below room temperature.

In Fig. 14 we can observe that the SO2 retrieval error largely increases at solar zenith angles above 75 . This behaviour can be caused by a couple of reasons: for one less radiation is available at low SZAs, in particular in the low UV used for the SO2 evaluation, leading to a poor signal-to-noise ratio. Additionally, low SZAs coincide with lower temperatures, in particular in the morning hours. A third reason can be interferences between O3 and SO2 in the DOAS retrieval. Both trace gases have quite similar absorption structures in the UV, large O3 CDs at large SZAs can lead to nonlinearities in the absorption or in the photon light path and thus result in an increased residual structure.

4.4 Relative difference of the SO2 content from Method A and Method B

Section 4.2 showed that the more commonly applied Method A (removing an SO2 offset in order to correct for SO2 con-

taminated background spectra) sometimes leads to different SO2 CD than Method B. In order to identify how frequently a signicant difference of both methods can be observed, we look at the relative ratio R of the SO2 CDs determined with the two methods:

R =

SSO2(B) SSO2(A) SSO2(B)

, (4)

where SSO2(B) is the average SO2 CD for one scan from Method B and SSO2(A) is the average CD from Method A.

Since the slope of the linear t against the dSCDs of Method B and Method A was not exactly unity (see Sect. 4.3 and Fig. 6), we multiplied the SCDs from Method B with a correction factor (see Table 1). We only averaged over spectra in a scan that exceed a certain SO2 threshold (for Method B) in order to reduce inuences of possible retrieval inaccuracies and to avoid dividing by zero when calculating the relative difference R. Additionally, in order to reduce possible errors due to strong ozone absorption, we only used the following spectra for further investigation:

Only spectra with an SO2 CD above 5

1017 [molecules cm2] were taken into account for the averaging process. This ensures a robust relative ratio by preventing divisions with values close to zero in Eq. 4 and reducing the inuence of inaccuracies in the retrieval for low SO2 contents.

Only spectra with an SZA below 70 were taken into account in order to circumvent potential problems due to strong ozone absorption at lower SZAs.

Figure 15 shows histograms of the relative difference R for Nevado del Ruiz. For Tungurahua the results are shown in Fig. 16. The histogram plots show the relative difference for all data (top left) and for different wind speed intervals in the other plots. Wind speeds were taken from the ECMWF (European Centre for Medium-Range Weather Forecasts, Dee et al., 2011) database. Wind data are obtained from analysed data products from ECMWF at a spatial resolution of 0.75

and a time resolution of 6 h. Data are interpolated to the location of the crater and time of measurement (in this case the original time stamp from the instruments was used).

The distribution of the relative ratio in the top left of Fig. 15 has a peak at 0 (e.g. both methods give the same SO2 CD) and a tail that goes up to a relative ratio of 100 %

(i.e. Method A nds zero SO2 while Method B nds a signicant amount). The other histograms in Fig. 15 show the same as Fig. 15a; however, each histogram only shows data for a specic wind speed interval. For wind speeds above 10 m s1 (Fig. 15b) a dominant peak at a relative ratio of 0 %

can be observed with only few values at a higher relative ratio. This means that both methods essentially give the same result. For wind speeds between 5 and 10 m s1 we observe a slight increase of larger relative ratio values (c). For wind

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Figure 8. Zoom into the variation of the SO2 CD at Nevado del Ruiz from instrument D2J2201 on 11 January 2012. In this example both methods agree well.

of absolute SO2 CD is detected. One possible explanation for the larger number of contaminated spectra at Nevado del Ruiz is the distance of the instruments from the crater (see Table A1). The instruments at Nevado del Ruiz are installed

34 km from the crater, while the instruments at Tungurahua are installed at more than 8 km distance.

5 Conclusions

We developed a new evaluation scheme for volcanic SO2 relying not on any locally recorded Fraunhofer reference spectrum but rather on a FRS modelled based on a high-resolution solar atlas, which makes the retrieval immune against possibly contaminated reference spectra (i.e. FRS containing absorption structures due to SO2). Statistical methods were applied in order to identify instrumental effects. Using this evaluation scheme we investigated how frequently contaminated FRS occur for scanning-DOAS instruments from NOVAC at the volcanoes Nevado del Ruiz and Tungurahua.

We observed that the DOAS retrieval, which used the convolved Chance and Kurucz (2010) solar atlas spectrum as FRS, typically showed a similar residual structure for all spectra (before including principal components in the t). A PCA on the residual structures revealed that the rst principal component accounts for more than 88 % of the variation of the residual structures (for all instruments), while the combination of the rst two principal components typically accounts for even more than 90 % of the variation.Each of the further principal components only has an individual contribution below 1 % to the residual structure. We interpret the rst two principal components as instrumental effects. The rst principal component describes the quantum efciency and grating efciency of the spectrometer, while the second principal component takes temperature or time-dependent variations into account. However, we cannot completely rule out that these principal components also include structures that are inherent in the Chance and Kurucz (2010) solar atlas as suggested by Burton and Sawyer (2016), which should not affect the t results. After including the rst two principal components as pseudo-absorbers in the DOAS t we obtained a t quality comparable to a regular DOAS SO2 evaluation with an SO2 DOAS retrieval error as good as 11016 [molecules cm2] and typically below

21016 [molecules cm2]. The SO2 t error shows increased

values with low instrument temperatures and high SZA. The temperature dependency of the t error can be explained by temperature-induced variations of the ILF. Taking these effects into account could further improve the evaluation in the future.

We found that the SO2 evaluation based on a modelled FRS (Method B) nds the zero level well and that the dSCDs of this method typically lies within 15 % of the dSCDs of a standard DOAS retrieval using an FRS recorded with the same instrument (Method A). Furthermore, the new method

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Figure 9. Two-dimensional histogram of the SO2 SCDs from Method B vs. the SCDs from Method A for instrument D2J2201 at Nevado del Ruiz. Method B, which uses a modelled background spectrum, leads to larger SO2 column densities. The black-dashed line shows the identity line.

speeds below 5 m s1 (Fig. 15d) we see a homogeneous distribution with almost constant values between 0 and 100 %. This means that we can observe widespread plumes which cover the complete FOV of the scanning-DOAS instrument more frequently at low wind speeds.

When comparing the histograms for Nevado del Ruiz (Fig. 15) and Tungurahua (Fig. 16) we can observe that the relative difference is larger at Nevado del Ruiz. At Nevado del Ruiz 21.4 % of the scans containing signicant SO2 have a relative difference above 0.5, compared to only 7 % at Tungurahua. This indicates that contaminated reference spectra occur more frequently at Nevado del Ruiz. While the relative difference of 0.5 is an arbitrary value, it means only 50 %

5688 P. Lbcke et al.: DOAS evaluation with a solar atlas

Figure 10. Example SO2 DOAS t of instrument D2J2201 (Nevado del Ruiz). The measurement spectrum was recorded on 5 March 2010 at 16:01 (UTC). The model functions are shown in red while the model+the residual (i.e. the measurement) are shown in blue.

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allows us to retrieve absolute SO2 CDs. The comparison of the SO2 CDs of the two methods showed that Method A in a number of cases leads to smaller SO2 CD values than MethodB. We found that at Nevado del Ruiz 21.4 % of the scans

01-01-2009 01-01-2010 01-01-2011Day-Month-Year

Figure 12. Two-dimensional histogram of the SO2 DOAS t error from the solar atlas evaluation as a function time for instrument

I2J8548 at Tungurahua.

containing a signicant amount of SO2 in all viewing directions (according to Method B) show much lower SO2 CDs for Method A (factor of 2, which corresponds to a relative ratio R; see Eq. (4), of 0.5). At Tungurahua only 7 % of the

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1016

ent data sets is complex already for a single volcano, and additional error sources must be taken into account. The observation geometry needs to be controlled in a way that both instruments sample the same section of the plume and are subject to similar radiative transfer effects. The complexity of this can lead to an uncertainty that can be observed in Fig. 6a of Salerno et al. (2009a). Furthermore, the volcanoes studied here are not as easily accessible as Mt. Etna, and regularly conducted traverse measurements cannot be obtained.A direct comparison of the differences observed at the two volcanoes would suffer from additional error sources due to the different set-up locations of the instruments relative to each respective volcano and differences in local meteorological patterns (wind speeds and directions), terrain and subsequent dispersion patterns.

We interpret scans with a large relative ratio between the two methods as situations in which the recorded spectra show signatures of volcanic SO2 for all viewing directions. Removing an offset value (as for Method A) leads to lower SO2 CDs and therefore smaller uxes. It is important to question the reason for signatures of volcanic SO2 in all viewing directions and what the effect on the SO2 emission rate retrieval is. There are at least two possible explanations for this phenomenon:

1. It is due to radiative transfer effects; i.e. there is no SO2 present in the column dened by the instrument viewing direction. However, a fraction of the radiation passed the plume (and thus picked up an SO2 absorption signature) and then was scattered into the instruments FOV.

2. There is actually SO2 in the instrument FOV.

Model calculations to investigate the inuence of radiative transfer on SO2 emission rates at volcanoes were made by Bigge (2015). These radiative transfer model calculations indicate that it is possible to obtain an SO2 signal in viewing directions that should be gas free according to a geometric approach. This means that radiation passes the volcanic plume before being scattered into the eld of view of the spectrometer from a direction that should be gas free. The results of Bigge (2015) showed that the magnitude of these signal depends on the measurement geometry (distance plume instrument, SZA, extent of the volcanic plume). At Nevado del Ruiz the situation gets further complicated, since clouds are present at the volcano almost throughout the entire year.If the difference between methods A and B is caused by a radiative transfer effect, it is difcult to judge which one of the methods leads to more accurate results.

For the second explanation, that actual SO2 is present in all viewing directions of the particular scan we have to distinguish further between a broadly dispersed (and moving) plume or SO2 that sits around the instrument without actually moving. The case of an actually broadly dispersed volcanic plume describes a situation in which the volcanic gas plume disperses after being released from the volcano (e.g. due to

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D2J2201.

scans have a relative ratio above 0.5. The relative ratio between the two methods shows large values in particular for low wind speeds at both volcanoes. The difference between the two volcanoes might be due to the fact that the stations at Nevado del Ruiz are placed on the anks of the volcano, at higher altitude and closer to the crater. The enhanced activity and low wind speeds contribute to the occurrence of wide plumes covering all viewing directions of the scanners.

Further validation of the results presented here, e.g. with traverse measurements as in Salerno et al. (2009a), would be advantageous. The authors of Salerno et al. (2009a) found good agreement between their specic FRS evaluation for scanning spectrometers and car traverse measurements at Mt. Etna. However, comparing measurements from such differ-

5690 P. Lbcke et al.: DOAS evaluation with a solar atlas

Figure 15. Histograms of the relative ratio R 100 % (see Eq. 4)

between the SO2 CDs derived by Method A and Method B for different wind speeds at Nevado del Ruiz. The different histograms show the results for both instruments. In the top left the results for all spectra are shown. The top right shows only spectra where the wind speed was above 10 m s1. The results for lower wind speeds are shown in the lower part of this gure.

Figure 16. Histograms of the underestimation for different wind speeds at Tungurahua. The results show data from all three instruments.

low wind speeds and thus more time to disperse). In this situation Method A would lead to an underestimation of the SO2 emission rate, while Method B would give a more accurate picture. However, it is difcult to obtain an SO2 emission rate from the SO2 column densities in the case of a dispersed plume with the current integration schemes used in NOVAC since the plume cross section cannot be dened accurately in this situation. Another possibility is that volcanic SO2 hovers in the vicinity of the instrument (without actually moving). In this (less likely) case Method A would still lead to accurate SO2 emission rates. Method B would fail to give us a reasonable emission ux since it would add SO2 that is just sitting around the instrument to the real SO2 emission rate.

Finally there is the possibility that the SO2 contamination originates from background SO2 due to air pollution or other nearby volcanoes. Method A in this case would also would give the more precise result for the SO2 ux of the volcano under consideration. In summary, however, we believe that a dispersed plume may be the most likely cause for FRS contamination at least in the cases we investigated and that the results of Method B give results which are closer to the

true SO2 column density than those of Method A. However, there may be situations in which Method A would in fact provide more correct data. In any case we recommend performing both evaluations in order to have a warning for contaminated FRS.

The approach presented was developed with the aim to implement it into the operational monitoring of spectroscopic networks. Its great advantage is reduction of manual labour (eld measurements and calibration) at the expense of a more elaborate statistical evaluation. The main challenge for the implementation is the availability of a training set of eld-spectra, which is guaranteed to be gas free (the importance of such a data set was also suggested in Burton and Sawyer, 2016). Additionally, the end user has to set a number of instrument-specic parameters, which can potentially inuence the performance of the retrieval. These parameters are mainly connected to the PCA and include the ~2 cut-off value determining which spectra are excluded from PCA, accounting for hot pixels of the detector (which leave a dominant structure in the residual) and a well-chosen number of principal components to include in the DOAS retrieval.

At present, the algorithm can easily be applied to any other volcano of the NOVAC network ofine, but it is not yet part of the standard software used by the observatories in the network. The main advantage of implementing this method in the future will be the possibility to identify plume scans not having an SO2-free spectrum that gives the baseline zero SO2 level. Currently, lack of a SO2-free reference spectrum will in some cases result in the standard NOVAC software not calculating the emission rate for such measurements.

In these cases, applying our new method yields the important information that the SO2 emission rate from the volcano is non-zero if one of the following conditions prevails: (1) the plume is extending at low altitude towards the spectrometer site and/or (2) the plume is elevated but sufciently extended to ll the entire range of scan angles. Even if those cases only occur rarely at some volcanoes, it is highly advantageous to obtain information on gas emissions in these cases to complement monitored time series. Last but not least, the presented method conrms SO2 emission rate measurements with low or no degassing present because it eliminates the chance that those are resulting from contaminated FRS.

6 Data availability

Raw spectral data used to obtain the results presented in this study have been acquired within the NOVAC collaboration. Access to these data is permitted with consent of the respective volcanological observatories owning the source instruments, according to their internal policies for data administration. Please refer the author list for contact details.

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Appendix A: Calculation of the time offset at Nevado del Ruiz

The instruments at Nevado del Ruiz had minor problems with the GPS antennas, which led to occasionally wrong time stamps in the spectra during complete days. Under the assumption of a constant daily time offset it is possible to identify time offsets with help of a Langley plot of the O3 CDs.

O3 is mainly distributed in the stratosphere and the light path through the stratosphere largely depends on the SZA. The so-called air mass factor (AMF) can be used to compare the O3

SCD with the vertical column density (VCD). For small values of the SZA # below 75 the AMF can be approximated by (Platt and Stutz, 2008):

AMF =

In order to calculate the time shift we applied a time offset and recalculated the SZAs according to Reda and Andreas (2004)1. For each offset value a polynomial of second order was tted to the Langley plot and the time offset that maximised R2 was used for this day.

1cos(#). (A1)

Since the diurnal O3 VCD variation is small compared to the inuence of the SZA, the O3 SCDs for the morning and evening with the same SZA should be similar. We used this property to determine the time of the instrument. We used the O3 CD of the O3 cross section recorded at 221 K from

Method B and investigated the Langley plot (a plot of the O3 SCD as a function of AMF). For correct time settings we observed a smooth line with slight curvature, while for incorrect time settings the Langley plot is not a smooth curve but shows two distinguishable branches for the morning and afternoon.

Table A1. Table showing data for the instruments at Nevado del Ruiz and Tungurahua. (a) Retrieved SO2 CDs from Method B, their variation and how many gas-free spectra were taken into account for this statistic. (b) Results of a linear t when plotting Method B offset vs. Method A (see Fig. 6). (c) Comparison the SO2 DOAS retrieval errors and (d) locations of the instrument and statistics on how frequently contaminated spectra exist.

Volcano Nevado del Ruiz Tungurahua

station Bruma Alfrombrales Pillate Bayushig Huayarapata serial number D2J2200 D2J2201 D2J2140 I2J8546 I2J8548

(a) Gas-free spectra Mean : SO2 : CD : S (molecules cm

2) 1.0 10

15 1.4 10

15 1.8 10

15 1.4 10

15

15 6.9 10

(S) (molecules cm2) 3.6 10

16 2.7 10

16 3.2 10

16 3.6 10

16 3.5 10

16

Number of spectra 3.3 10

5 3.5 10

5 1.8 10

6 1.6 10

6 2.5 10

6

(b) Plot: SO2 CD (B offset) Slope 1.14 0.95 0.91 0.95 0.88 vs. SO2 CD A offset (molecules cm2) 3.0 10

15 5.2 10

15 7.7 10

15 6.8 10

15 8.7 10

15

(c) Mean SO2 t error Method A (molecules cm2) 1.43 10

16 1.38 10

16 1.81 10

16 1.89 10

16 1.89 10

16

Method B molecules cm2] 1.55 10

16 1.46 10

16 1.84 10

16 1.94 10

16 1.85 10

16

(d) Statistics Distance from crater (m) 3100 4150 8000 11900 9100 Altitude (m a.s.l.) 4865 4500 2550 2750 2850 Scanner geometry at conical at conical conical Time frame covered (mm/yy) 01/1006/12 01/1006/12 01/0912/11 01/0911/10 01/0911/11 Number of scans 12826 7935 4442 2331 3538 Relative ratio 50 % (%) 22.4 20.0 4.2 7.0 10.0

1We used a MatLab implementation of the Reda and Andreas (2004) algorithm by Vincent Roy.

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Appendix B: SO2 CD time series for all instruments

Time series of the SO2 column density for all instruments are shown in Figs. B1 and B2 (for Nevado del Ruiz) and Figs. B35 (for Tungurahua). While Nevado del Ruiz has constantly high activity from the end of 2010, there are different phases with higher and lower activity at Tungurahua.

Figure B1. SO2 CD time series for instrument D2J2200 at Nevado del Ruiz. The blue dots show a NOVAC-type evaluation while the red dots show the SO2 CDs from a modelled FRS.

Figure B2. SO2 CD time series for instrument D2J2201 at Nevado del Ruiz.

Figure B3. SO2 CD time series for instrument D2J2140 at Tungurahua. The blue dots show a NOVAC-type evaluation while the red dots show the SO2 CDs from a modelled FRS.

Figure B4. SO2 CD time series for instrument I2J8546 at Tungurahua.

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Figure B5. SO2 CD time series for instrument I2J8548 at Tungurahua.

Appendix C: Implementation of the new algorithm

In summary the evaluation of data in this study encompassed the following steps (which are also shown in Fig. C1):

1. Preparation of the modelled FRS and the gas absorption cross sections:

a. A gas-free spectrum, recorded with a small SZA, was wavelength-calibrated by comparing it with the Fraunhofer lines of the Chance and Kurucz (2010) solar atlas spectrum. This spectrum was subsequently used as the wavelength grid for this instrument; i.e. all trace gas cross sections and the Ring spectrum were sampled at the wavelength points where this spectrum was sampled.

b. The Chance and Kurucz (2010) spectrum was convolved using the ILF of the instrument and interpolated to match the wavelength grid from step 1a; this is our modelled FRS for Method B. The Ring spectrum for Method B was calculated from the modelled FRS.

c. Two O3 and the SO2 absorption cross sections were convolved using the ILF of the instrument and the same wavelength grid as above. In order to speed up the evaluation all cross sections were pre-convolved with saturation and I0 correction using different input SCDs and saved.

2. Spectra were evaluated using two t scenarios which both use the modelled FRS. The rst t scenario includes the SO2 cross section; this t scenario is used to select spectra with negligible SO2 content for the PCA in Step 3. The second t scenario does not contain SO2;

it is used to create the residual structures, which are later used in the PCA. After an initial round to determine estimates of the O3 and SO2 CDs for the I0 and saturation correction the I0 and saturation corrected absorption cross sections (from step 1c) were loaded and a second DOAS t was performed using I0 and saturation corrected cross sections (the SO2 CDs and residual structures from these corrected ts were used in Step 3).

3. The residual structures of the DOAS t (without SO2 in the t scenario) were examined using the PCA as described in Sect. 3.3. The spectra which were analysed with the PCA were selected with help of the DOAS t that included SO2 (from Step 2).

4. All spectra were evaluated using the DOAS method as described in Step 2 for a second time. This time two different FRS were used. For Method A, a spectrum that was measured with the same instrument directly before the scan (recorded with minimal scan angle) was used as FRS; a Ring spectrum for Method A was calculated from this FRS. All trace gas cross sections (two O3 as well as one SO2) were included in the t. For Method A an offset value was calculated for each scan and subtracted from the SO2 CDs of each viewing direction (see

Sect. 3.2 for details). Method B used the modelled FRS. All trace gas cross sections (O3 and SO2) and the rst two principal components from Step 3 were included in the t scenario. For instruments with a hot pixel this was included for Method B as well. I0 and saturation corrected cross sections were used for Method A and Method B.

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Preparation of model FRS and convolution of trace gas absorption cross-sections

1.

2.

First iteration DOAS evaluation:

DOAS fit - solar atlas without SO2

DOAS fit - solar atlas with SO2

Residual structures

SO2 column densities

DOAS fit routine

First SO2 fit with uncorrected cross sections

SCDs

Second SO2 fit withI0 and saturation corrected cross sections

Results, residuals

3.

Principal component analysisCreate additional pseudo-absorbers for solar atlas SO2 fit from residual structures

Second iteration DOAS evaluation :

DOAS fit SO 2

NOVAC type

DOAS fit SO 2

- Solar atlas

Remove SO2 offset

SO2 column densities

SO2 column densities

Method A Method B

4.

Figure C1. Flow chart of the evaluation steps that were used in order to create the SO2 column densities from methods A and B.

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Appendix D: Variation of the principal components

These gures show the variation of the t coefcient of the rst two principal components for the three instruments that were not shown in the text. Figure D1 shows data for instrument D2J2200 at Nevado del Ruiz while Figs. D2 and D3 show data from instruments D2J2140 and I2J8546, respectively.

Figure D1. Peak-to-peak apparent optical density (e.g. peak-to-peak optical depth of the principal component times the t coefcient) of the rst and second principal components for instrument D2J2200 at Nevado del Ruiz.

Figure D2. Peak-to-peak apparent optical density (e.g. peak-to-peak optical depth of the principal component times the t coefcient) of the rst and second principal components for instrument D2J2140 at Tungurahua. The vertical dashed lines indicate the start of new time intervals for which a new set of principal components was calculated.

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Figure D3. Peak-to-peak apparent optical density (e.g. peak-to-peak optical depth of the principal component times the t coefcient) of the rst and second principal components for instrument I2J8546 at Tungurahua. The two distinct values at the end of 2009 might be due to calibration issues due to a drift of the instrument calibration. Creating the principal components more frequently might help in such cases as can be observed at the beginning of 2010.

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Acknowledgements. The authors thank Michel Van Roozendael for editing this paper and Andrew McGonigle, Keith Horton and three anonymous reviewers for their comments on the manuscript.We would like to thank the European Commission Framework6 Research Program for funding of the NOVAC project. We kindly acknowledge the NOVAC partners from the Colombian Geological Survey (formerly INGEOMINAS), especially the FISQUIM Research Group and the technical staff at the Manizales Volcanological Observatory as well as the staff at Observatorio del Volcn Tungurahua (IGEPN) for keeping the instruments running for almost a decade at Nevado del Ruiz and Tungurahua. Nicole Bobrowski thanks for nancial support from DFG BO 3611/1-1 and the VAMOS project. We thank the Deutsche Forschungsgemeinschaft for supporting this work within the project DFG PL193/14-1. We thank the German ministry of education and research (BMBF) for supporting this work within the SOPRAN (Surface Ocean Processes in the Anthropocene) project (Frderkennzeichen: FKZ 03F0662F). Peter Lbcke would like to thank Vincent Roy for providing the MatLab script that was used for calculating the Suns position.

Edited by: M. Van RoozendaelReviewed by: A. J. S. McGonigle, D. Horton, and three anonymous referees

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