Paper presents a simplistic approach towards the detection and dynamics analysis of volcanic eruptions represented as unevenly spaced spatio-temporal time series of satellite retrieved hot spots. The paper discusses isolation and interpolation of hot spots data produced by Nightfire algorithm for the purposes of short-term volcanic activity ARIMA based forecasting. The case study for Chirpoi Snow volcano is presented. The work is supported by RFBR (grants 14-0700548, 16-07-01028, 15-29-06045).
Volcanic eruptions are one of well-known types of natural hazard. Some volcanoes are better studied than the others, this mostly depends on their location, and those located on uninhabited islands may erupt without people in field observing them, while the others may erupt nearby cities and attract thousands of people. There are different kinds of volcanic activity such as: gas emissions, ash plumes, lava flows and domes, etc. These events may accompany one another. Some volcanoes demonstrate regular patterns in their activity others not. Events listed may be tracked by instrumental networks consisting of different instruments like seismographs, regular and thermal cameras, gas analyzers and others. Such networks sometimes are impossible to deploy due to various reasons. However it is possible to utilize satellites based instruments; such instruments do not require any special onsite installation and provide coverage for the entire planet.
As of 2016 there is no single satellite developed specifically for volcanology purposes. Fortunately there are a lot of meteorological satellites suitable for volcanology purposes. There are basically three kinds of satellite data which has a widespread use for volcanology purposes, these are: 1. visual data — which is basically just an image; 2. infrared data — most of volcanic events are accompanied with heat emission, hence they are visible in infrared spectra; 3. radar readings — lava flows and domes may be observed as they change the landscape.
This paper describes an approach towards infrared data analysis.
There are at least two global monitoring systems of
volcanic activity based on hot spots detection in satellite
data, namely: MODVOLC [
This paper suggests an alternative approach towards volcanic activity monitoring and dynamics analysis. Instead of just tracking hot spots it is suggested to analyze hot spots as time series for each volcano. Such an approach will let to better adjust alert thresholds as well as to look up behavioral patterns and anomalies for all the existing volcanoes rather than just to detect potential eruptions.
This study is using hot spots detected by a Nightfire
algorithm [
Nightfire is using VIIRS sensor nighttime data to detect hot spots. VIIRS sensor is basically a next improved generation of MODIS sensor, as of April 2016 there is one polar-orbiting satellite carrying VIIRS sensor operating (Suomi-NPP launched in 2011). Satellite continuously goes from one Earth pole to another following sun terminator. Every full circle satellite is crossing equator once in a day time and once in a night time. Satellite is constantly reading pixels in a line orthogonal to its path, each pixel size at Nadir (directly under the satellite) is 742x776 m, this size is non linearly growing towards the edge of scan, scan width is 3040 km, the satellite does 14 full revolutions each 24 hours, which essentially means that every point at equator is seen at least once every day and once every night. However for higher latitudes due to a considerable swath overlap locations are seen several times each day and each night. 2.2 Hot spot sources There are several major sources of hot spots, anthropogenic ones, such as: gas flares over oil fields, high temperature manufacturing, thermal power stations as well as natural ones of which the most significant are forest fires and volcanic activity. Coincidentally hot spots of volcanic and forest fire origins have closely overlapping temperature ranges.
Nightfire has been originally geared towards the
detection and tracking of gas flares over oil fields. Gas
flares are smaller than VIIRS pixel (they either lay
inside one pixel or between several neighboring pixels);
hence Nightfire performs subpixel analysis, to estimate
heat source size and energy. In the case of volcanic
events it is no rare occasion to have dozens of hot-spots
per image, which are all part of the same lava field for
instance [
The three key points mentioned allowed to classify data as a set of unevenly spaced spatio-temporal time series. 3 Analysis To observe volcano as a process it is first necessary to bisect the data related to the volcano in question. The simplest method to attribute hot spot to a volcano is to check how far it is from it. Basically the largest thermal anomalies, which can be seen from space, are lava flows and these typically would not reach further than 20 km from the volcano summit, hence distance based hot spots filtering leaves out most of the hot spots of non-volcanic origins. This simplistic approach does not protect from false attribution of forest fires to a volcanic activity, however as it has been already mentioned forest fires temperature range closely overlaps with that of volcanic events, hence such discrimination is a subject of future research.
To interpolate time series for a specific volcano it is
first necessary to somehow regularize the data presented
within a single reading. As was already mentioned each
reading may consist of several hot spots of varying
radiant heat, temperature, area, cloud conditions all of
them with different coordinates and satellite angles.
There could be no more than a single hot spot for each
pixel of the original satellite image. Knowing satellite
altitude, nadir and azimuth angles as well as how does
internally VIIRS sensor work [
Where – earth radius, – satellite zenith angle, – satellite height, – pixel along scan size at nadir (776m), – pixel along track size at nadir (742m), – aggregation group which is if , if and 1 otherwise.
This formula produces an upper boundary area estimate, while hot spot area calculated by Nightfire itself could be used as a lower boundary estimate. Next step would be to aggregate both boundaries within any given reading:
Where – reading active area estimated upper bound, – hot spot area upper bound, - reading active area estimated lower bound, - hot spot area lower bound, – reading's aggregate radiant heat, – hot spot radiant heat, – estimated reading temperature, – estimated pixel temperature.
The majority of the time series analysis theory is geared towards the analysis of regularly spaced time series; hence there are essentially two ways to analyze an unevenly spaced time series. The first one would be to interpolate an unevenly spaced time series and proceed with analysis of a regularly spaced time series. The second method would be to analyze unevenly spaced time series without performing such a transformation. For this paper the first approach as the simpler one has been chosen. Thus the resulting unevenly-spaced time series are linearly interpolated into their evenly-spaced form.
It comes as no surprise that in the majority of cases it would be impossible to forecast eruption dynamics due to the lack of data and high irregularity of the processes involved. However some volcanoes may show some regularity in their activity, which may signalize an applicability of classic time series forecasting techniques. One such popular technique ARIMA model widely used in econometric will be used in the case study to attempt to forecast volcanic activity of a selected volcano.
ARIMA (autoregressive integrated moving average) is widely used in econometrics. The model uses an initial differencing step to reduce non-stationarity of data combined with both autoregressive and movingaverage models. Model is usually denoted as where – the order of autoregressive model, – is the degree of differencing, – is the order of moving-average model. model is given by:
Snow is a stratovolcano located on an uninhabited volcanic island Chirpoi. The island is located in the Sea of Okhotsk between Simushir and Urup in the Kuril island chain. Snow has been continuously erupting for a since April 2012, its eruption seems to follow a pattern, where periods of activity are interleaved with short periods of low to no activity. There is no other dedicated observing equipment but the only unmanned seismic station, which may be disabled for weeks due to battery discharge, located on the island. Nightfire has the full data for this eruption and there are no other potential sources of hot spots, which could have added additional noise. Factors mentioned make Snow a good candidate for a case study.
This case study attempts to answer the question: “Is it possible to forecast eruption power output, at least for some volcanoes?” Power and radiant heat are interchangeable in this context. Power poses the most interest since there is a direct relation between radiant heat observed and the volume of lava being erupted.
Radiant heat readings Figure 1 exhibit non stationary behavior, however after differencing step Ошибка! Источник ссылки не найден. situation gets better. For a difference time series mean is 0 standard deviation is 11.38. In fact early weeks of eruption impact standard deviation. Trimming first 6 weeks off time series brings standard deviation to about 8 and this value is valid for almost every segment of time series. Thus after differencing step process shows strong signs of being near stationary, which means that d parameter of ARIMA model will be 1 in this case. For p and q start parameters 3 will be taken.
Figure 1 Chirpoi Snow Radiant Heat (MW) December 2012 - February 2016
To perform ARIMA forecast Pythons StastModels
[
Unfortunately due to persistently poor weather conditions, there were too many gaps in data with a temporal distance between two readings coming up to several weeks. Thus, ARIMA did not manage to do reasonably accurate forecasts. As it could be seen on Fugure 3 relative error comes up to hundreds of percent. The situation could’ve been improved via introduction of new data sources, however many volcanoes are not easily accessible leaving little to no choice but to use satellite data only. For instance, Chirpoi volcano reviewed in this article is located at an uninhabited island. Moreover even if there does exist an instrumental network for a specific volcano it still requires a lot of work, both organizational and technical, to integrate its data, whereas satellite imagery serves as a universal data source. Hence the most reasonable approach seems to be to integrate data from different classes and generations of satellites to improve its temporal resolution and shorten the gaps between readings.
Satellite infrared imagery proves itself to be an interesting source of data for volcano research. Current plans involve, although not limited to: 1. data delivery latency improvements – via software installation at receiving station around the world (currently installed on Kamchatka); 2. data volume improvements – via incorporation of older satellites data and SAR satellites data; 3. better classification – via various clustering algorithms application and evaluation, preliminary results of a graph based hierarchical clustering have been very promising; 4. better insight – via neural networks based algorithms application, such an approach seem to be more stable in the presence of large data gaps.
This would not only allow better analysis of activity patterns in global volcanism, but will improve quality of neighboring data products such as the forest fire monitoring product.