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Abstract. The reflection of the sunlight over the sea surface is called glitter pattern. In previous works where the one-dimensional case was analyzed, the glitter function was mathematically described by a rect function. This rect function has proven to be a very good representation of the glitter pattern. A Gaussian glitter function is used like a first approximation to the rect function. The statistical relationship between the variance and the correlation function of the intensities of the image, the glitter pattern, and the variance of the sea surface slopes are obtained and analyzed. The analytical solutions for these relationships are given by different equations; however, the graphic representations are very similar. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

A volcanic eruption can produce large ash clouds in the atmosphere around a volcano, affecting commercial aviation use of the airspace around the volcano. Encountering these ash clouds can cause severe damage to different parts of the aircraft, mainly the engines. This work seeks to contribute to the development of methods for observing the dispersion of volcanic ash and to complement computational methods that are currently used for the prediction of ash dispersion. The method presented here is based on the frequency of occurrence of the regions of airspace areas affected by ash emission during a volcanic eruption. Popocatepetl volcano, 60 km east of Mexico City is taken as a case study. A temporal wind analysis was carried out at different atmospheric levels, to identify the direction towards which the wind disperses ash at different times of the year. This information showed two different trends, related to seasons in the direction of dispersion: the first from November to May and the second from July to September. To identify the ash cloud and estimate its area, a set of 920 MODIS images that recorded Popocatepetl volcanic activity between 2000 and 2021 was used. These satellite images were subjected to a semi-automatic, digital pre-processing of binarization by thresholds, according to the level of the brightness temperature difference between band 31 (11 µm) and band 32 (12 µm), followed by manual evaluation of each binarized image. With the information obtained by the processing of the MODIS image, an information table was built with the geographical position of each pixel characterized by the presence of ash for each event. With these data, the areas around Popocatepetl volcano with the highest frequency of affectation by ash emissions were identified during the period analyzed. This study seeks to complement the results obtained by numerical models that make forecasts of ash dispersions and that are very important for the prevention of air navigation risks.

A volcanic eruption can affect large areas of the atmosphere around the volcano. Commercial aviation uses these zones the airspace as a navigation zone. Encountering these ash clouds can cause severe damage to different parts of the aircraft, mainly the engines. This work aims to generate a predictive tool based on the frequency of affectation of the airspace areas around a volcano with eruptive activity, taking the Popocatépetl volcano as a case study. Was carried temporal wind analysis at different atmosphere levels to identifying direction towards which wind disperses ash in year months. This information shown two representative seasons in the direction of dispersion: the first from November to May and the second from July to September, taking into account that June and October are transitional months and therefore do not present a predominant direction. To identify the ash cloud and estimate its area, a set of MODIS images was compiled that recorded the activity in the period 2000-2014. These satellite images were subjected to a semi-automatic digital pre-processing of binarization by thresholds according to the level of the Brightness Temperature Difference between band 31 and band 32, followed by manual evaluation of each binarized image. The result of those above pre-processing was a set of pixels with spatial (longitude and latitude) and temporal (date) description, from which the history of the areas affected by ash permanence was obtained. Additionally, a set of pixels evaluated and labeled in table form could be used as training data for future artificial intelligence applications to automatically detect and discriminate ash clouds.

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