=Paper=
{{Paper
|id=Vol-1752/paper41
|storemode=property
|title=
Unevenly Spaced Spatio-Temporal Time Series Analysis in Context of Volcanoes Eruptions
|pdfUrl=https://ceur-ws.org/Vol-1752/paper41.pdf
|volume=Vol-1752
|authors=Grigory Trifonov
|dblpUrl=https://dblp.org/rec/conf/rcdl/Trifonov16
}}
==
Unevenly Spaced Spatio-Temporal Time Series Analysis in Context of Volcanoes Eruptions
==
https://ceur-ws.org/Vol-1752/paper41.pdf
Unevenly Spaced Spatio-Temporal Time Series Analysis
in Context of Volcanoes Eruptions
Grigory Trifonov
Moscow State University, Moscow
trifonov.grigory@gmail.com
3. radar readings — lava flows and domes may be
Abstract observed as they change the landscape.
Paper presents a simplistic approach towards the This paper describes an approach towards infrared
detection and dynamics analysis of volcanic eruptions data analysis.
represented as unevenly spaced spatio-temporal time 1.2 Current problem state
series of satellite retrieved hot spots. The paper discusses
isolation and interpolation of hot spots data produced by There are at least two global monitoring systems of
Nightfire algorithm for the purposes of short-term volcanic activity based on hot spots detection in satellite
volcanic activity ARIMA based forecasting. The case data, namely: MODVOLC [4], MIROVA [3]. The oldest
study for Chirpoi Snow volcano is presented. one (MODVOLC) has been in service for more than a
The work is supported by RFBR (grants 14-07- decade by now [8]. Both systems are using MODIS
00548, 16-07-01028, 15-29-06045). sensor data as an input, which is provided by two
NASA's polar-orbiters Terra and Aqua, launched in 1999
1 Introduction and 2002 respectively. Each service is using hot spots
detection algorithm of its own. Essentially any such
Volcanic eruptions are one of well-known types of algorithm is based on the Plank curves fitting with some
natural hazard. Some volcanoes are better studied than variations and modifications, book “Thermal Remote
the others, this mostly depends on their location, and Sensing of Active Volcanoes” by Andrew Harris [2]
those located on uninhabited islands may erupt without provides a good introduction on how does it work. Both
people in field observing them, while the others may services provide real time and historical hot spots
erupt nearby cities and attract thousands of people. There attributed to volcanoes and alerts based on some radiant
are different kinds of volcanic activity such as: gas heat threshold value. Neither of services does any
emissions, ash plumes, lava flows and domes, etc. These additional hot spot analysis.
events may accompany one another. Some volcanoes
demonstrate regular patterns in their activity others not. 1.3 Suggested approach
Events listed may be tracked by instrumental networks This paper suggests an alternative approach towards
consisting of different instruments like seismographs, volcanic activity monitoring and dynamics analysis.
regular and thermal cameras, gas analyzers and others. Instead of just tracking hot spots it is suggested to
Such networks sometimes are impossible to deploy due analyze hot spots as time series for each volcano. Such
to various reasons. However it is possible to utilize an approach will let to better adjust alert thresholds as
satellites based instruments; such instruments do not well as to look up behavioral patterns and anomalies for
require any special onsite installation and provide all the existing volcanoes rather than just to detect
coverage for the entire planet. potential eruptions.
1.1 Volcanoes satellite observations
2 Data
As of 2016 there is no single satellite developed
specifically for volcanology purposes. Fortunately there This study is using hot spots detected by a Nightfire
are a lot of meteorological satellites suitable for algorithm [1]. Hot spots come in a form of a separate csv
volcanology purposes. There are basically three kinds of file for each 24 hours; each csv file contains around 100
satellite data which has a widespread use for volcanology fields out of which the most important and suitable for
purposes, these are: analysis are: pixel longitude and latitude, radiant heat,
1. visual data — which is basically just an image; estimated black body temperature, estimated black body
2. infrared data — most of volcanic events are area, cloud conditions, satellite angles, detection quality
accompanied with heat emission, hence they are flags and original image geometry. Due to its nature the
visible in infrared spectra; data used have some specificity, which are worth
consideration.
Proceedings of the XVIII International Conference
«Data Analytics and Management in Data Intensive 2.1 Satellite imaging
Domains» (DAMDID/RCDL’2016), Ershovo, Russia, Nightfire is using VIIRS sensor nighttime data to detect
October 11 - 14, 2016 hot spots. VIIRS sensor is basically a next improved
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generation of MODIS sensor, as of April 2016 there is set of hot-spots with varying coordinates, scan
one polar-orbiting satellite carrying VIIRS sensor time, radiant heat and temperature.
operating (Suomi-NPP launched in 2011). Satellite The three key points mentioned allowed to classify
continuously goes from one Earth pole to another data as a set of unevenly spaced spatio-temporal time
following sun terminator. Every full circle satellite is series.
crossing equator once in a day time and once in a night
time. Satellite is constantly reading pixels in a line 3 Analysis
orthogonal to its path, each pixel size at Nadir (directly
under the satellite) is 742x776 m, this size is non To observe volcano as a process it is first necessary to
linearly growing towards the edge of scan, scan width is bisect the data related to the volcano in question. The
3040 km, the satellite does 14 full revolutions each 24 simplest method to attribute hot spot to a volcano is to
hours, which essentially means that every point at check how far it is from it. Basically the largest thermal
equator is seen at least once every day and once every anomalies, which can be seen from space, are lava
night. However for higher latitudes due to a flows and these typically would not reach further than
considerable swath overlap locations are seen several 20 km from the volcano summit, hence distance based
times each day and each night. hot spots filtering leaves out most of the hot spots of
2.2 Hot spot sources non-volcanic origins. This simplistic approach does not
There are several major sources of hot spots, protect from false attribution of forest fires to a volcanic
anthropogenic ones, such as: gas flares over oil fields, activity, however as it has been already mentioned
high temperature manufacturing, thermal power stations forest fires temperature range closely overlaps with that
as well as natural ones of which the most significant are of volcanic events, hence such discrimination is a
forest fires and volcanic activity. Coincidentally hot subject of future research.
spots of volcanic and forest fire origins have closely
overlapping temperature ranges. 3.1 Interpolating data
Nightfire has been originally geared towards the To interpolate time series for a specific volcano it is
detection and tracking of gas flares over oil fields. Gas first necessary to somehow regularize the data presented
flares are smaller than VIIRS pixel (they either lay within a single reading. As was already mentioned each
inside one pixel or between several neighboring pixels); reading may consist of several hot spots of varying
hence Nightfire performs subpixel analysis, to estimate radiant heat, temperature, area, cloud conditions all of
heat source size and energy. In the case of volcanic them with different coordinates and satellite angles.
events it is no rare occasion to have dozens of hot-spots There could be no more than a single hot spot for each
per image, which are all part of the same lava field for pixel of the original satellite image. Knowing satellite
instance [7]. Thus it is crucial to somehow group such altitude, nadir and azimuth angles as well as how does
hot spots as the ones attributed to a single event. internally VIIRS sensor work [6] it is possible to
2.3 Missing data calculate the area of the original pixel for each hot spot.
Another problem apart from separation of hot spots of A pixel area may be calculated with the following
volcanic and non-volcanic origins is a high number of formula:
missing or incomplete readings. There are several
reasons for volcanic hot spots to become corrupted or
even missing:
• clouds – may cover the area of interest, this leads
to either missing hot spots or hot spots with a
lower radiant heat than it should be;
• volcanic gasses and ash – these act more or less
the same as clouds;
• volcano being too far off nadir – cauldron like
volcanoes with lava lake inside crater may produce
hot spots only at angles close to nadir, since
otherwise satellite's sensor can't see lava lake;
• polar day – since Nightfire works with nighttime
Where – earth radius, – satellite zenith angle,
data only there will be no hot spots detected for
the entire duration of polar day. – satellite height, – pixel along scan size at nadir
2.4 Data specifics summary (776m), – pixel along track size at nadir (742m),
To summarize, there are three key points about data – aggregation group which is if , if
involved: and 1 otherwise.
1. there are hot spots readings spanning since the This formula produces an upper boundary area
early 2012 available for each volcano; estimate, while hot spot area calculated by Nightfire
2. readings are unevenly spaced in time with a itself could be used as a lower boundary estimate. Next
distance varying between 2-24 hours (discounting step would be to aggregate both boundaries within any
polar day/night cases); given reading:
3. each day of the observations comes in a form of a
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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
Where – reading active area estimated upper it possible to forecast eruption power output, at least for
bound, – hot spot area upper bound, - reading some volcanoes?” Power and radiant heat are
active area estimated lower bound, - hot spot area interchangeable in this context. Power poses the most
lower bound, – reading's aggregate radiant interest since there is a direct relation between radiant
heat, – hot spot radiant heat, – estimated reading heat observed and the volume of lava being erupted.
temperature, – estimated pixel temperature. Radiant heat readings Figure 1 exhibit non
The majority of the time series analysis theory is stationary behavior, however after differencing step
geared towards the analysis of regularly spaced time Ошибка! Источник ссылки не найден. situation
series; hence there are essentially two ways to analyze gets better. For a difference time series mean is 0
an unevenly spaced time series. The first one would be standard deviation is 11.38. In fact early weeks of
to interpolate an unevenly spaced time series and eruption impact standard deviation. Trimming first 6
proceed with analysis of a regularly spaced time series. weeks off time series brings standard deviation to about
The second method would be to analyze unevenly 8 and this value is valid for almost every segment of
spaced time series without performing such a time series. Thus after differencing step process shows
transformation. For this paper the first approach as the strong signs of being near stationary, which means that
simpler one has been chosen. Thus the resulting d parameter of ARIMA model will be 1 in this case. For
unevenly-spaced time series are linearly interpolated p and q start parameters 3 will be taken.
into their evenly-spaced form.
3.2 Analyzing interpolated time series
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 Figure 1 Chirpoi Snow Radiant Heat (MW) December
data combined with both autoregressive and moving- 2012 - February 2016
average models. Model is usually denoted as
where – the order of autoregressive To perform ARIMA forecast Pythons StastModels
model, – is the degree of differencing, – is the order [5] package has been used. Model has been fit on 100
of moving-average model. model is readings and attempted to predict the next 24 hours,
given by: next the closest to 101 reading hour prediction has been
used to cross validate. One hundred retrains in the
middle of the data set were made. Even though in most
cases ARIMA managed to perform forecast sometimes
it was impossible due to random shocks, which
disrupted data strong enough to make data set non
stationary, hence
3.3 Forecasting Chirpoi Snow activity
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
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ARMA step is not applicable. improve its temporal resolution and shorten the gaps
between readings.
Future work
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
Figure 2 Chirpoi Snow Radiant Heat increment (MW) been very promising;
December 2012 - February 2016 4. better insight – via neural networks based
algorithms application, such an approach seem to
Conclusion 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.
References
[1] Christopher D. Elvidge et. al., VIIRS Nightfire:
Satellite Pyrometry at Night, ISSN 2072-4292,
http://www.mdpi.com/2072-4292/5/9/4423/pdf
[2] Andrew Harris, Thermal Remote Sensing of Active
Volcanoes A USER'S MANUAL, ISBN 978-0-521-
85945-5
[3] MIROVA Near Real Time Volcanic HotSpot
Detection System http://www.mirovaweb.it
Figure 3 Relative error of ARIMA forecast [4] MODVOLC Near-real-time thermal monitoring of
Unfortunately due to persistently poor weather global hot-spots http://modis.higp.hawaii.edu/
conditions, there were too many gaps in data with a [5] Skipper Seabold, Jonathan Taylor, StatsModels
temporal distance between two readings coming up to statistical package, Josef Perktold,
several weeks. Thus, ARIMA did not manage to do http://statsmodels.sourceforge.net/devel/index.html
reasonably accurate forecasts. As it could be seen on [6] Curtis Seaman, Beginner’s Guide to VIIRS Imagery
Fugure 3 relative error comes up to hundreds of percent. Data, http://rammb.cira.colostate.edu/
The situation could’ve been improved via introduction of projects/npp/Beginner_Guide_to_VIIRS_Imagery_
new data sources, however many volcanoes are not easily Data.pdf
accessible leaving little to no choice but to use satellite [7] Grigory Trifonov (1), Mikhail Zhizhin (2), and
data only. For instance, Chirpoi volcano reviewed in this Dmitry Melnikov, Nightfire method to track
article is located at an uninhabited island. Moreover even volcanic eruptions from multispectral satellite
if there does exist an instrumental network for a specific images, http://meetingorganizer.copernicus.org/
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from different classes and generations of satellites to geol_soc_426.pdf
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