Multi-layer perceptrons are used in many fields of science and technology. From the perspective of pattern recognition, they can be regarded as an extension of the many conventional statistical techniques which have been developed over several decades [1] . More extensive treatments of these topics can be found in the many textbooks on statistical pattern recognition, including [2] - [5] . Articles [6] and [7] have also emphasized the sta- tistical underpinnings of neural networks.

The main application of ANN to remote sense data analysis is scene classification, more commonly land cover classification, namely the process in which pixels are grouped according to the similarities of their spectral properties. If a pixel satisfies a certain set of criteria then it is assigned to the land cover class that corresponds to those criteria. This is the most common task achieved with remote sensing, and applications that involve both supervised and unsupervised ANNs are numerous. Due to the absence of any assumption about the data, many land cover classifications use data from different sensors such as optical and radar data [8] [9] , texture and ancillary data. Texture is incorporated in different ways: 1) precomputed per pixel texture information that is fed to the ANN together with the spectral information [10] or 2) incorporating neighbouring spectral information using a sliding window [11] .

It was reported that ANNs have more accurate performance than other techniques such as statistical classifiers, especially when the functional space is particularly complex and the source of data presents different statistical distributions [12] - [15] .

An additional advantage of the ANN approach is that they can perform supervised classification using fewer training data than those with maximum probability, because rules of recognition of a given category are based on the attributes, not only of training data of that particular category class, but also of other classes [16] .

The IASI instrument is used for operational measurements of meteorological parameters for numerical weather prediction. However, the high density of spectral information available and good signal-to-noise characteristics mean that the instrument can also provide measurements of many chemical species. The high density of spectral information and low instrument noise means that IASI could potentially provide very sensitive detection of SO₂, especially for plumes in the upper-troposphere and lower-stratosphere, where the thermal contrast with the layers below is maximized. Usually full retrievals are time-consuming when searching for a sporadic event such as a volcanic eruption within a large data set. Detection methods do not require on-line radiative transfer cal- culations and can therefore be used to provide atmospheric measurements quickly, for example to help with volcanic hazard avoidance.

A commonly used method for the fast detection of trace atmospheric species is to calculate the difference in brightness temperature (BTD) between a small number of channels which are sensitive to the target species and others which are insensitive. The BTD between channels is then compared against a threshold which indicates a positive detection.

Simple BTD filters for the detection of SO₂ are applied operationally to provide an early warning of volcanic activity and to help track volcanic plumes in near-real-time [17] - [19] . Although fast and robust, current BTD methods do not fully exploit the spectral range and resolution of hyperspectral instruments, and the noise associated with the measurements remains high. SO₂ can be tracked from IASI using the difference in signal between two channels located at 1371.50 and 1371.75 cm⁻¹ in the SO₂ v₃ vibrational band and two background channels at 1407.25 and 1408.75 cm⁻¹ outside the SO₂ band [20] . Recently the detection method of Walker [21] , uses channels between 1300 and 1410 cm⁻¹ (441 channels). It is a fast method which uses many spectral channels to separate the contribution of SO₂ from the contribution of other parameters affecting the measure- ment.

To date, no significant studies involving volcanic SO₂ detection using ANNs have been carried out. The main aim of this study is to verify if such a technique may be useful and give substantial improvements for real time monitoring of SO₂, representing a reliable ANN monitoring tool during preliminary detection phase.

The challenge was to assess a classification problem by using ANN in order to detect the presence in the atmosphere of volcanic SO₂ using IASI hyperspectral data as input and the corresponding SO₂ retrievals by [22] as target outputs.

Beside its fast usage in the real time application, the advantage of ANN approach is in the ability to model the non-linearity in the variable space and in exploiting all the spectral information contained in hyperspectral data, and it does not need to select any target and background channels for implementing detection filters.

In this study, we first provide in Section 2.1. an overview of the IASI sensor characteristics and description of SO₂ total column estimation (Section 2.2.), then we discuss the neural network approach for SO₂ detection (Section 2.3.). In Section 3, the scenario where the ANN approach has been applied is introduced and the results obtained are discussed. Finally the conclusions are reported in section 4.

The neural network must first be “trained” by having it process a large number of input patterns and their as- sociated reference output patterns. Once trained, the neural network is able to recognize similarities when presented with a new input pattern, resulting in a predicted output pattern [23] .

After completion of the training process, the ANN classifier algorithm has been proposed for a remote sensing application such as the monitoring of two volcanic eruptions that occurred in Iceland in 2010 and 2011. The 14 April to 24 May 2010 Eyjafjallajökull eruption caused widespread impacts [29] .

It was an explosive eruption with an injection of volcanic ash into the atmosphere and plumes that affected many regions of Europe. Plumes reached altitudes of 9 km, and the ash was transported across Europe and to the Atlantic Ocean. Despite its impact, the explosive phase was modest in size and the amount of SO₂ released was low.

The Grímsvötn eruption occurred from May 21 to May 23 2011. It injected into the atmosphere a higher concentration of SO₂ than Eyjafjallajökull. The height reached by the plume was 20 km [30] .

In order to evaluate the performance of neural network classifier in terms of its generalization capability and accuracy in detecting SO₂ presence in the atmosphere from IASI datasets, we applied the trained ANN classifier to two independent IASI datasets from the May 2010 Eyjafjallajökull eruption and to two independent IASI datasets from the Grímsvötn eruption which occurred the following year. Note that ANN has been validated on datasets which include all IASI orbits, not only on SO₂ plume data, with a significant number of pixels not affected by SO₂ (more than 40%). Performance was assessed in terms of overall accuracy and Producer accuracy. The former represents the percentage of correct classifications, with respect to the total number of pixels analysed, considering all classes (i.e. SO₂ and not SO₂). The Producer accuracy instead represents the percentage of correct classifications with respect to the total obtained for that output class and it is an omission error indicator.

Tables 1-4 describe the confusion matrices obtained by applying the NN classifier to these independent datasets. Figures 1-4 show comparisons between classification maps obtained from the ANN classifier and from the SO₂ retrieved by Carboni [22] for all validation dates.

In Table 1, Table 2, which summarize the results related to the Eyjafjallajökull eruptions of April 30 2010 and May 15 2010, the neural network classifier achieves an accuracy of 100%. This is a very good result, considering the ANN classifier has been applied to the entire IASI orbits. In fact, looking at Figure 1, despite most of the pixels not being affected by SO₂, the ANN classifier perfectly detects SO₂ plume. The same result is obtained when ANN is applied to May 2010 (Figure 2). Table 2 describes the confusion matrix and shows an overall accuracy of 100% for detecting the plume, despite the fact that it extends from 45˚ to 75˚N. Again, neither commission nor omission errors are present.

The results of applying the ANN classifier to the IASI datasets during the Grímsvötn eruption are described by confusion matrices depicted in Table 3 and Table 4 and depicted in Figure 3 and Figure 4, for May, 22 2011, at 12:00 and 20:00 UTC, respectively.

In the case of the morning orbit depicted in Table 3, the overall accuracy obtained is 99.1%. The producer accuracy, which measures the probability that the classifier correctly labels a pixel as SO₂, is 70.3%. The lower accuracy obtained is due to the presence of an omission error, because 29.7% of pixels with SO₂ have been

labelled as not affected by SO₂.

Looking at the histograms in Figure 5 (top), representing the statistical distribution of false negatives for the 22 May 2011 date, we notice that most of the false negatives have values lower than 3 DU, which is around the SO₂ detection threshold for a plume height between 2 and 4 km [21] . Looking at the maps depicted in Figure 6 we notice that they belong to a portion of the plume located close to the vent and are characterized by a height of between 2 - 4 km [30] . Considering that the SO₂ detection threshold at these altitudes is 3.3 DU, we can assert that the ANN classifier shows a sensitivity in accord with the model for low SO₂ amounts in the lower troposphere. Furthermore it puts in evidence the absorption band limit at 7.3 μm when observing SO₂ in low troposhere.

For total SO₂ column amounts of less than 0.2 DU concentrated in the boundary layer between 0 - 2 km the signal falls below the noise level of the instrument [21] . Instead, when SO₂ is higher into the atmosphere due to an explosive volcanic event it is possible to discern very low concentrations. As shown in Figure 7, showing only positive detections for both Grímsvötn validation’s datasets, ANN classifier well detect low amount of SO₂ when they are located at higher altitudes (low stratosphere) [30] .

The same assertion can be made for the afternoon orbit of the May, 22, 2011, 20:00 UTC: looking at Table 4, an overall accuracy of 98.5% is shown. Producer accuracy is 57% and, once again, this is due to false negatives related to pixels of plume at lower altitudes, as in the previous validation. In fact, looking at the histogram representing SO₂ distribution (Figure 5, bottom) most of the values are around the detection threshold used for SO₂ discrimination, but not higher than 3 DU, which characterizes the detection threshold for the part of the plume in the lower troposphere. Instead, when SO₂ is higher into the atmosphere due to an explosive volcanic event it may be possible to discern very low concentrations.

The retrieval methodology of [22] establishes that for measurements in the thermal infrared spectral range the sensitivity is better for plume injected at high altitudes where the air is colder and the thermal contrast is higher,

while at lower altitudes (e.g. the troposphere) the lower thermal contrast reduces the sensitivity of the detection method, so we can assert that the ANN classifier is in accord with the sensitivity of the model.

What can be underlined is that no commission errors are present at the validation stage (pixels erroneously labelled as affected by SO₂) for both 2010 and 2011 eruptions, and the method shows the same accuracy when applied to IASI images with different illumination conditions (morning and afternoon orbits) and in cloudy sky conditions. Furthermore, it is noticeable that most of the training samples are from the Eyjafjallajökull eruption and only a low percentage from the Grímsvötn one (26%), which represents an event statistically not well known at the training stage. This can explain why the ANN classifier reveals a loss of accuracy when applied to Grímsvötn eruption.

This work proves the detection capability of volcanic SO₂ by means of an algorithm neural network based classifier, applied to the thermal channels of the IASI hyperspectral sensor. SO₂ amounts estimated by [22] were used as training target outputs.

The resulting confusion matrices associated with application to independent datasets spanning two Eyjafjalla- jökull volcanic eruptions revealed an accuracy of 100% on both tested images.

The results of applying the ANN classifier to the Grímsvötn eruption reveals an accuracy lower in detecting SO₂ plume, but these cases included: a) The data-sets belonging to the Grímsvötn eruption represented a minor percentage of IASI time-series used as training samples; b) the presence of false negatives, i.e. pixels affected by SO₂ not detected. In this case an analysis carried out on false negatives for both validation dates revealed that those pixel belonged to the portion of the plume at tropospheric altitudes where the sensitivity of the method is lower.

Nevertheless, the neural network classifier has been shown to work well both on daytime and night-time images and in cloudy sky conditions, and it successfully overcame the detection of false positives present in the validation dataset images, whose presence in multispectral or hyperspectral images can often undermine the performance of traditional classification algorithms. Therefore the proposed method represents a reliable new approach for volcanic SO₂ detection and demonstrates also its usefulness in near real time volcanic monitoring activities, due to its fast application in the operational stage.