Lava flows impact prediction at Mount Etna by Cellular Automata

ADVANCES in CLIMATE CHANGES, GLOBAL WARMING, BIOLOGICAL PROBLEMS and NATURAL HAZARDS Lava flows impact prediction at Mount Etna by Cellular Automata ...
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Lava flows impact prediction at Mount Etna by Cellular Automata VALERIA LUPIANO, ROCCO RONGO Department of Earth Sciences University of Calabria Ponte Bucci, Arcavacata di Rende (CS) – I-87036 ITALY [email protected] MARIA VITTORIA AVOLIO, WILLIAM SPATARO Department of Mathematics University of Calabria Ponte Bucci, Arcavacata di Rende (CS) – I-87036 ITALY [email protected] Abstract: - Millions of people live either on or in the surrounding areas of about six hundred worldwide volcanoes, which are known to be capable of renewed activity. The individuation of those areas that are more likely to be interested by new events is of fundamental relevance for mitigating possible consequences, both in terms of loss of human lives and material properties. Here we show a new methodology for defining flexible high-detailed lava invasion susceptibility maps. It relies on both an adequate knowledge of the volcano, assessed by an accurate analysis of its past behaviour, together with a reliable computational model for simulating lava flows on present topographic data and on High Performance Parallel Computing for increasing computational efficiency. The application of the methodology to the case of Mt Etna, the most active volcano in Europe, makes it appropriate for land use planning and Civil Defence applications in practice. Key-Words: - Lava flows, Hazard Assessment, Land Use Planning, Cellular Automata, Modeling and Simulation, Mt Etna.

1 Introduction Many volcanic areas around the world are densely populated and urbanized. In Italy, Mt Etna is home to approximately one million people, though being the most active volcano in Europe ([1]). More than half of the events occurred in the last four centuries report damage to human properties in numerous towns on the volcano flanks. In particular, eruptions in 1669 and 1928 destroyed entire villages and, in the earlier case, portions of Catania, the main city of the region ([2]). In last decades, the vulnerability of the Etnean area has increased exponentially due to continued, sometimes wild, urbanization ([3]), with the consequence that new eruptions may involve even greater risks. In recent crises, countermeasures based on embankments or channels were adopted to stop or deflect lava ([4], [5]). In some cases, even exceptional actions were necessary which, for instance, involved the adoption of explosive and/or cement tapping inside the active craters in order to reduce lava emission. Such kind of interventions are generally performed while the eruption is in progress, by both not guarantying their effectiveness, and by inevitably putting into danger the safety of involved persons. Lava flows forecasting could significantly change this scenario. A modern and widely adopted approach is the application of algorithms that permit numerical simulations of lava flows ([6], [7]), for the purpose of individuating affected areas in advance. For instance, in 2001 the path of the eruption that

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threatened the town of Nicolosi on Mt Etna was correctly predicted by means of a lava flows simulation model ([8]), providing useful information to Civil Defense authorities. However, this modus operandi can be difficult to be replicated and an a priori knowledge of the degree of exposure of the volcano surrounding areas desirable, in order to allow both the realization of preventive countermeasures, and a more rational land use planning. This paper illustrates a new methodology for the definition of flexible high-resolution lava invasion susceptibility maps, and show results related to the South-Eastern flank of Mt Etna, the most densely populated sector of the volcano.

2 An integrated methodology for lava flows impact prediction The methodology here proposed relies on the application of a lava flows computational model for simulating new events on present topographic data, and on a new criterion for evaluating the impact of performed simulations in terms of spatial hazard. In general, a lava flow computational model should be well calibrated and validated and thus able to reproduce the events which characterise the considered volcano with a high level of accuracy. Furthermore, it should be as much efficient as possible since, depending on the extent of the

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considered area, a great number of simulations could be required ([9]). In order to significantly apply the model, the methodology provides for the analysis of the past behaviour of the volcano, for the purpose of classifying the events that historically interested the region. By assuming that the volcano’s behaviour will not dramatically change in the near future, a representative case is selected for each of the individuated classes and triggered from each crater of a set which opportunely covers the area. In such a way, a meaningful database of plausible simulated lava flows can be obtained, by characterising the study area both in terms of areal coverage, and lava flows typologies. Subsequently, such data is processed by considering a proper criterion of evaluation. It is worth to note that a first solution could simply consist in considering lava flows overlapping, by assigning a greater hazard to those sites interested by a higher number of simulations. However, a similar choice could be misleading. In fact, depending on their particular traits (such as the location of the main crater, the duration and the amount of emitted lava, or the effusion rate trend), different events can occur with different probabilities, which should be taken into account in evaluating the actual contribution of performed simulations with respect to the definition of the overall susceptibility of the study area. In most cases, such probabilities can be properly inferred from the statistical analysis of past eruptions, allowing for the definition of a more refined evaluation criterion. Accordingly, in spite of a simple hitting frequency, a measure of lava invasion susceptibility can be obtained in probabilistic terms. In the following, we show how such approach was applied to the South-Eastern flank of Mt Etna.

Cellular Automata paradigm have demonstrated to be valid and efficient for the modelling of geological processes ([15]). In order to execute a simulation, SCIARA requires a hexagonal discretisation (for the purpose of minimising the intrinsic anisotropic effects of discrete modelling of continuous systems – cf. [16], [17]) of the topography over which the event will be simulated, the craters coordinates and the emission rate history, besides the specification of a set of parameters related to the magma rheology ([18]). Accordingly, the considered Etnean sector was digitalised as a DEM (Digital Elevation Model) of 22721790 hexagonal cells, each with a 5 m apothem, by considering the GIS vectorization of good-quality 1:10000 scale topographic maps. Thanks to proper calibration and validation phases, a suitable set of model’s parameters was determined, by allowing the model to reproduce Etnean lava flows with a high level of accuracy ([8]). At the same time, many computational refinements were implemented, by significantly speeding up the model ([11]). Eventually, even a sensitivity analysis study was performed, by excluding unpredictable changes in simulation outcomes when small changes are considered in input data, thus demonstrating the overall robustness of the computational algorithm.

2.1 The computational model Concerning the choice of a reliable and efficient lava flows simulation model, many notable examples can be found in literature, including models that have been applied in practice to the simulation of real events ([10], [11]). Our research group is experienced in this field since 1982, when a first computational model of basaltic lava flows was proposed ([12]). In recent years we enriched the SCIARA family of lava flows simulation models, by proposing improved releases and applying them to the simulation of diverse Etnean cases of study. For the purposes of this work, being the South-Eastern flank of mount Etna a vast area of about 237 km2 (cf. Fig. 1), a great number of simulation were planned to be executed (cf. below) and thus a computational model that is at the same time accurate and efficient seemed the best choice. For this reason, the SCIARA-fv release (simply SCIARA in the following) ([11]), based on the Cellular Automata computational paradigm ([13]) and, specifically, on the Macroscopic Cellular Automata approach for the modelling of spatially extended dynamical systems ([14]), was chosen as the reference computational algorithm. Models based on the

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Figure 1: The South-Eastern flank of Mt Etna. Grey colouring indicate crater activation probability, in decreasing order, corresponding to 0.645, 0.33, 0.02, 0.005 and 0, respectively; dots represent the grid of 208 craters considered in this work.

Eventually, it is worth to note that, with the exception of few isolated cases (cf. the 1981 event - [19]), a typical effusive behaviour was strongly evidenced by the analysis of the volcano past activity ([20]). As a consequence, it is not a hasty judgement to suppose that such behaviour will not dramatically change in the near future and thus that the SCIARA lava flows simulation model, calibrated and validated on a set of effusive eruptions, be adequate for simulating new events on Mt Etna.

2.2 The volcano behaviour As specified above, the proposed methodology involves a preliminary study of the past activity of the volcano for the purpose of characterising the study area in terms of eruptive

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study area in terms of probability of activation of new craters by statistically analysing historical eruptions in terms of spatial distribution of eruptive fractures, vent density and their concentration in rift zones, tectonic structures and proximity to the summit area of the volcano (where eruptions are statistically more frequent). 12

m3 /sec

behaviour. Accordingly, such study was performed by analysing a significant set of 64 events occurred on Mt Etna since 1600 AD, from which information is quite reliable ([20]). Historical events were classified on the basis of both their duration and the amount of emitted lava, by considering ranges of 30 days and 32106 m3, respectively (cf. [20]). Nevertheless, since the majority of analysed events dropped in the first temporal class (i.e. 0–30 days), this latter was further split into two sub-classes, in order to better characterise the statistical distribution. Unfortunately, considered events were not sufficient to obtain at least a representative for each of the considered classes. Therefore, available data was further elaborated by means of bivariate analysis in order to gather information on the events for which no quantitative records were available. Some events were in any case discarded, since they represent unrealistic cases in the study area. A total of 50 not empty classes were thus obtained. For each of them, values were normalized into the range [0,1], obtaining the probability, pc, that a new hypothetical event can occur, depending on which class it belongs to. Eventually, 50 representative cases were selected, one for each of the individuated classes. In particular, the representative characterised by the maximum lava emission and temporal duration inside its membership class was considered. As regards the effusion rate trend to be considered, it is well-known that different types of distribution of emitted magma can generate quite different lava areal distributions (cf. [2]). For instance, if an initial low flow rate is considered, the lava solidification of the front magma layers can hamper successive lava flowing from the main crater, while an initial high flow rate can favour the elongation of the lava flow. Consequently, the individuation of proper effusion rate trends is a crucial aspect for properly characterising the volcano behaviour. Nevertheless, performed analysis of past eruptions evidenced two typical effusion rate trends for Etnean lava flows. In particular, both typologies can be considered equi-probable and well approximated by Gaussian-like distributions with maximum flow rate values at 1/3 and 1/6 of the total duration, as shown in Fig. 2. Accordingly, a trend probability, pt, was defined and imposed to the constant value of 0.5 for both the individuated trends. Consequently, by considering the combination of the 50 representative events in terms of emitted-lava/duration and the two representative effusion rate trends, a total of 100 representative typologies of lava flows were obtained which we assumed adequate for representing all the possible behaviour of the volcano from the emissive point of view. Further, depending on their position, different sites can have different probability to trigger new lava flows. Many volcanological and geo-structural (sometimes conflicting) studies attempted to individuate Etnean sectors that are more prone to generate new eruptive events. Among these, Behncke et al. ([20]) proposed a characterisation of the

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Figure 2: An example of the representative evolution of the effusion rate during a typical Etnean eruption, referred to an event lasting 90 days, with a peak in the effusion rate of ~10 m3s-1 located at ~1/3 of the overall duration. Note that the trend was obtained by uniting randomly chosen points between two Gaussian curves (in dotted lines)

The result of such study is shown in Fig. 1, where the Southern-East flank of Mt Etna is subdivided into five sectors, representing areas characterised by different probabilities of activation of new craters. For the purpose of this study, in agreement with the authors of the original research, such probabilities were assumed to be 0.645, 0.33, 0.02, 0.005 and 0, respectively, by considering a quadratic trend between the higher and the lower value. Accordingly, a probability of activation for a generic crater in the study area, ps, was defined, which assumes one of the above specified values depending on which sector it is located in (cf. Fig. 1). In short, we made the fundamental assumption that events on Mt Etna can be classified on the basis of the following peculiar features: the amount of emitted lava and the event duration, the emission rate trend, as well as the source position. Moreover, for each of the above cited features, characteristic probabilities were defined on the basis of the statistical analysis of past eruptions. Consequently, if a new event is conjectured to be triggered in the study area, an overall (conditioned) probability of occurrence, pe, can be defined by simply considering the product of the individual probabilities of its characteristic features: pe = pc· pt· ps

(1)

2.3 Lava flow hazard susceptibility at Mt Etna Once representative lava flows were devised in terms of both emitted-volume/duration and effusion rate trend, a set of simulations were planned to be executed in the study area by means of the SCIARA lava flows simulation model. At this purpose, a grid composed by 208 craters was defined on the considered SE flank of Mt Etna, as shown in Fig. 1. It is composed by two 1 km spaced sub grids, the latter

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displaced by 500 m along South and East directions with respect to the former. This choice allowed to both adequately and uniformly cover the study area, besides considering a relatively small number of craters. It is worth to note that, as well as representative lava flows can be characterised by the conditioned probability pc· pt (being pc the probability related to the event’s membership class, and pt the probability related to the event’s emission rate trend), still a crater in the grid can be characterised by the probability of activation ps, depending on in which sector it belongs to (cf. Fig. 1). In this way, a representative lava flow on Mt Etna can be simulated by considering a given point of the defined grid as source location, by evaluating its probability of occurrence by simply applying equation 1. Therefore, all the 100 representative lava flows were simulated for each of the 208 craters of the grid, thus obtaining a set of N=20800 simulations. By considering the extent of the study area and the duration of the events to be simulated computing times would have resulted in the order of about one year on standard sequential architectures, in spite of the high computational efficiency of the employed lava flow simulation model. Accordingly, the simulation phase was performed on two high performance parallel machines, namely a 16 Itanium processor NEC TX7 NUMA super computer and a 4 bi-quadcore Xeon processor Apple Xserve cluster, thus reducing the overall execution to less than one month (cf. [11]). Lava flow invasion susceptibility was then punctually evaluated by considering the contributions of all the simulations which affected a generic site in terms of their probability of occurrence, with a resulting detail which exclusively depends on the resolution of the considered DEM. Thus, if a given DEM cell of co-ordinates x,y was affected by nx,y ≤ N simulations, its susceptibility was defined as the sum of the probabilities of occurrence of involved lava flows, pe(i) (i=1, 2, ..., nx,y): nx , y

s x , y   p e( i )

(2)

i 1

N

s max   p e(i )

Note that, if

denotes the maximum

i 1

obtainable value, i.e. that resulting from the contribution of all the N performed simulations, the susceptibility in the study area can also be expressed in probabilistic terms by simply considering the following equation: nx , y

p x, y 

p i 1 N

(i ) e

 pe(i )

overall information about the vulnerability of the entire study area with respect to the occurrence of new lava flows, independently from their effective source locations and emissive behaviours.

Figure 3: Hazard map of the study area based on the 20,800 executed simulations. As a compromise between map readability and reliability, 5 classes are reported (grey colouring), in increasing order of susceptibility (probability of lava invasion).

Note that, depending on the number of performed simulations and morphological conditions, the susceptibility of interested areas may range in a quasi-continuous manner, allowing to compile maps with a high level of description. However, in general, a limited number of hazard classes are considered adequate for many practical applications. Accordingly, and also for a better readability, Fig. 3 just reports 5 susceptibility classes. Eventually, it is worth to note that, since the obtained results are strongly related to morphological conditions, they could require to be updated each time topographic alterations occur. In this case, it will be sufficient to consider a DEM representing the actual topography, and re-simulate only the (generally few) representative events which involve the modified areas. A new susceptibility map can then be obtained by simply reprocessing the new set of simulations, which is a quite rapid procedure even on sequential computers. At the contrary, if a certain number of events will occur on Mt. Etna, whose characteristics determine a modification of the previously individuated representative set of lava flows, a new overall simulation phase will be required in order to obtain a correct susceptibility scenario.

3 Further applications 

s x, y s max

(3)

i 1

The resulting lava invasion susceptibility map, shown in Fig. 3, represents the probability that future events will affect the study area. A similar map results particularly suitable for land use planning purposes, since it gives an

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Besides the definition of overall lava invasion susceptibility maps, the above described methodology lends itself to further Civil Defense oriented applications. For instance, in case of a new event, one can identify all the areas that are more likely to be affected. For simplicity, let suppose that it is originated by a single crater, which coincides with a crater of the simulation grid. In this case, the map shown in Fig. 3 could not be adequate for assessing

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do not affect the area of interest and by circumscribing source locations of the remaining ones.

the exposure scenario as, depending on morphological conditions, it could account for the contribution of simulations originated also by other craters in the grid. Nevertheless, it is possible to assign a probability equal to 1 to the crater and only consider the contribution of the simulations originated from it, still by considering equation 3. The main advantage of this approach is that results can be obtained without any information about the emission rate that will characterize the actual lava flow, being such information embedded in the subset of analysed simulations. Moreover, since just the analysis of already available data is involved, the susceptibility scenario can be rapidly obtained, making such method suitable for real-time Civil Defence applications. If the position of the crater which originates the lava flow does not coincide with a point of the simulation grid, it is always possible to consider a minimum source area, e.g. defined by the three craters that are next to the actual one (cf. Fig. 4).

Figure 5: Map showing a total of 34 vents belonging to the simulation grid of Fig. 1 that produce lava flows affecting the town of Nicolosi, together with the corresponding susceptibility scenario.

Fig. 5 shows an example of this application for the individuation of all the source areas that can trigger events able to affect the town of Nicolosi. This kind of application, assessing if new events have to be considered dangerous for a given area in advance, could represent a useful tool for decision support.

4 Conclusions The fundamental problem of assessing the impact of future eruptions of Etna lies mostly in the uncertainty concerning their duration, effusion rate, and location. The approach presented in this paper tackles this problem from two directions. It allows to attribute to any given location on Etna a statistical likelihood (a) to give rise to new eruptive vents and (b) to be impacted by lava flows of future eruptions. A novel element of the model is that the simulation data base does not only permit to produce general susceptibility maps in unprecedented detail, but it contains each single scenario out of a total of over 20,000 simulated cases. It is therefore no longer necessary to wait for the next eruption and know its eruptive parameters and location in order to run ad-hoc simulations, as has been the practice until now. Instead, virtually all possible eruption scenarios can be simulated a priori, and from as dense a network of hypothetical vent locations as possible, and extracted in real time as soon as the need arises, as in the case of an imminent or incipient flank eruption. This approach has been recently extended to the entire Etnean area and can be applied to all other volcanoes where there is a risk of lava flow invasion.

Figure 4: Hazard map related to a single hypothetical event of unknown emission rate. In grey the probability (in percentage terms) of lava invasion. Key: 1) real lava source crater 2) the 3 nearest craters to the considered lava source point.

Similarly, any type of lava sources (e.g. multiple craters or even fractures) can be inscribed in a minimum source area by individuating an appropriate set of carters in the simulation grid, allowing to cover all the possible triggering situations. In the last two cases, as an overestimation of the source area is considered, a prudential estimation of the spatial susceptibility is obtained. Such approximation becomes even more smaller the denser the simulation grid is, since it allows for a more precise definition of the minimum source area. As a further example, it is possible to individuate all the source areas that could generate lava flows able to affect a given area of interest. Analogously as before, this application could be rapidly accomplished by a reprocessing of the simulation set, by simply eliminating the events that

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using the magflow cellular automata model, Bull. Volcanol., No. 70, 2008, pp. 805–812. [8] Crisci G.M., Rongo R., Di Gregorio S., Spataro W., The simulation model SCIARA: the 1991 and 2001 lava flows at Mount Etna, J. Volcanol. Geotherm. Res., No. 132, 2004, pp. 253–267. [9] D'Ambrosio D., Rongo R., Spataro W., Avolio M.V., Lupiano V., Lava Invasion Susceptibility Hazard Mapping Through Cellular Automata, 7th International Conference on Cellular Automata for Research and Industry, ACRI, LNCS 4173, 2006, pp. 452–461. [10] Vicari A., Herault A., Del Negro C., Coltelli M., Marsella M., Proietti C., Modeling of the 2001 lava flow at Etna volcano by a Cellular Automata approach, Environmental Modelling & Software, No. 22, 2007, pp. 1465-1471. [11] Rongo R., Spataro W., D’Ambrosio D., Avolio M.V., Trunfio G.A., Di Gregorio S., Lava Flow Hazard Evaluation Through Cellular Automata and Genetic Algorithms: an Application to Mt Etna Volcano, Fundamenta Informaticae, No.87, 2008, pp. 247-268. [12] Crisci G.M., Di Gregorio S., Ranieri G., A cellular space model of basaltic lava flow, Proceedings International AMSE Conference Modelling & Simulation, 1982 (Paris, France, Jul.1-3, 1982). [13] Von Neumann J. Theory of self reproducing automata, Univ. Illinois Press, Urbana, 1966. [14] Di Gregorio S., Serra R., An empirical method for modelling and simulating some complex macroscopic phenomena by cellular automata, Future Generation Computer Systems, No. 16, 1999, pp. 259–271. [15] D’Ambrosio D., Spataro W., Parallel evolutionary modelling of geological processes, Parallel Computing, 33, 2007, pp. 186–212. [16] Miyamoto H., Sasaki S., Simulating lava flows by an improved cellular automata method, Computer & Geosciences, No. 23, 1997, pp. 283-292. [17] D'Ambrosio D., Di Gregorio S., Iovine G., Simulating debris flows through a hexagonal Cellular Automata model: Sciddica S3-hex, Natural Hazards and Earth System Sciences, No. 3, 2003, pp. 545-559. [18] Giordano D., Dingwell D., Viscosity of hydrous Etna basalt: implications for Plinian-style basaltic eruptions, Bulletin of Volcanology, No. 65(1), 2003, pp. 8-14. [19] Guest J.E., Kilburn C.R.J., Pinkerton H., Duncan A.M. The evolution of lava flow-fields: observations of the 1981 and 1983 eruptions of Mount Etna, Sicily, Bull. Volcanol., No. 49, 1987, pp. 527–540. [20] Behncke B., Neri M., Nagay A., New data from a GIS-based study, Kinematics and dynamics of lava flows (Geol. Soc. Am. Spec. Pap.), No. 396, 2005, pp. 189-208.

Since the obtained results are strongly related to the morphology of the study area, each new eruption will require the creation of an updated DEM incorporating the morphostructural changes induced by the eruption. Resimulation would be necessary only for those events affecting the modified area, and a new, updated susceptibility map can then be obtained by simply reprocessing the new set of simulations, which is a quite rapid procedure even on sequential computers. On the contrary, if Etna were to produce eruptions whose characteristics imply a modification of the previously determined representative set of lava flows, a new overall simulation phase would be required in order to obtain a correct susceptibility scenario. Nevertheless, even if a more rigorous assessment of the reliability of the methodology here presented is certainly desirable for effective usage in Civil Defense - such as the compilation of the map on a subset of sample events (e.g. occurred in the first 300 years) and validating it over the remaining ones – the proposed method seems to be more reliable when compared with a more classical criterion of hazard mapping. Current work regards the application of the methodology to other areas of the volcano and a more rigorous study on a map validation procedure. References: [1] Behncke B., Neri M., Cycles and Trends in the recent eruptive behaviour of Mount Etna (Italy). Can. J. Earth Sci., No. 40, 2003, pp. 1405–1411. [2] Crisci G.M., Di Gregorio S., Rongo R., Scarpelli M., Spataro W., Calvari S., Revisiting the 1669 Etnean eruptive crisis using a cellular automata model and implications for volcanic hazard in the Catania area. J. Volcanol. Geotherm. Res., No. 123, 2003, pp. 211– 230. [3] Dibben C.J.L., Leaving the city for the suburbs – The dominance of ‘ordinary’ decision making over volcanic risk perception in the production of volcanic risk on Mt Etna, Sicily. J. Volcanol. Geotherm. Res. No. 172, 2008, pp. 288–299. [4] Barberi F., Carapezza M. L., Valenza M., Villari L., The control of lava flow during the 1991-1992 eruption of Mt. Etna., J. Volcanol. Geotherm. Res., No. 56, 1993, pp. 1–34. [5] Barberi F., Brondi F., Carapezza M.L., Cavarra L., Murgia C., Earthen barriers to control lava flows in the 2001 eruption of Mt. Etna. J. Volcanol. Geotherm. Res., No. 123, 2003, pp. 231–243 (2003). [6] Ishihara K., Iguchi M., Kamo K., Numerical simulation of lava flows on some volcanoes in Japan, Lava flows and domes: emplacement mechanisms and hazard implications, pp. 174–207, Springer, Berlin Heidelberg New York, 1990. [7] Del Negro C., Fortuna L., Herault A., Vicari A., Simulations of the 2004 lava flow at Etna volcano

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