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Conceived and designed the experiments: GM PP LP. Performed the experiments: GM PP LP FMG. Analyzed the data: GM PP LP FMG. Wrote the paper: GM PP LP.
The evaluation of mortality of pyroclastic surges and flows (PDCs) produced by explosive eruptions is a major goal in risk assessment and mitigation, particularly in distal reaches of flows that are often heavily urbanized. Pompeii and the nearby archaeological sites preserve the most complete set of evidence of the 79 AD catastrophic eruption recording its effects on structures and people.
Here we investigate the causes of mortality in PDCs at Pompeii and surroundings on the bases of a multidisciplinary volcanological and bio-anthropological study. Field and laboratory study of the eruption products and victims merged with numerical simulations and experiments indicate that heat was the main cause of death of people, heretofore supposed to have died by ash suffocation. Our results show that exposure to at least 250°C hot surges at a distance of 10 kilometres from the vent was sufficient to cause instant death, even if people were sheltered within buildings. Despite the fact that impact force and exposure time to dusty gas declined toward PDCs periphery up to the survival conditions, lethal temperatures were maintained up to the PDCs extreme depositional limits.
This evidence indicates that the risk in flow marginal zones could be underestimated by simply assuming that very thin distal deposits, resulting from PDCs with poor total particle load, correspond to negligible effects. Therefore our findings are essential for hazard plans development and for actions aimed to risk mitigation at Vesuvius and other explosive volcanoes.
Pyroclastic density currents (PDCs), turbulent hot mixtures of fine ash and gas flowing down volcano slopes at high speeds, are common in volcanic explosive eruptions. They can devastate large areas and cause numerous fatalities by exposure to mechanical impact, extreme heat and dusty gas .
In proximal and intermediate PDCs emplacement zone, all these factors commonly exceed the critical threshold for human survival, thus indicating that none mitigation strategy is suitable except for the timely evacuation . However, since the lethality of PDCs may decline up to human survival conditions with increasing distance, the evaluation of PDCs effects near the flow termination is widely debated being crucial for risk mitigation management, particularly for distal areas often densely inhabited. Nevertheless, these aspects are documented only in a few modern eruptions and difficult to retrieve from historical record, due to scarce availability of data on thin distal layers.
A unique, although poorly-investigated, record of the far-reaching lethal effects of PDCs on people and the environment is well preserved at the distal archaeological site of Pompeii, ca. 10 kilometres southeast of Vesuvius. Here, the remains of hundreds human victims were discovered within the pyroclastic surges of the 79 AD eruption , . In order to evaluate the potential effects of a future Plinian eruption at Vesuvius we have assessed the PDCs overall impact by combining volcanological and bio-anthropological studies with experiments and numerical modeling.
No ethics approval was required to the Ethics Committee (Comitato Etico per le Attività Biomediche dell'Università degli Studi Federico II di Napoli”, Azienda Ospedaliera Universitaria della Seconda Università degli Studi di Napoli, Naples, Italy) because human and animal (Equus caballus) bone samples used in this work are Institute certified specimens (sample inventory N. 14083/880/71 of the Department of Structural and Functional Biology and sample inventory N. 2408/Z653/50 of the Museum of Zoology) at the University of Naples “Federico II”. Samples were officially provided for our study by informed written consent from the University of Naples “Federico II”.
The steady, uniform velocity profile for a Bingham flow in infinitely wide channels is given by:
where z≥Dc is the height (measured from the bottom of the channel), k is yield strength, ρ is the density of flow material, g is acceleration due to of gravity, θ is the slope of ground, η is the viscosity, D the total flow depth, and Dc is the plug thickness,
The acceleration of the plug in a wide channel is :
where vp is plug velocity and |a| is the modulus of the gravity contribution to the flow motion.
Resistance terms in the equation describing a Bingham flow unit depends on several factors. For a Bingham flow, the transition from laminar to turbulent flow depends upon two dimensionless numbers, the Reynolds number Re=ρv D/η, and the Bingham number Bi=k D/η v. From empirical relations, Middleton and Southard  observed that, when Bi exceeds about 1.0 the onset of turbulence occurs for Re/Bi≥1000. According to McEwen and Malin , we the frontal air drag is assumed to be negligible, so that the deceleration due to air drag on the upper surface  of the flow is:
with ca ranging between 0.1 and 1.
We examined undecalcified and unstained ground sections, and decalcified and stained cryostat sections of bone samples. Ground sections (80–100 µm thick) were prepared after embedding in LY-554 araldite resin (Vantico) and observed under light microscopy, in ordinary and polarized light. Bone cryostat sections (7 µm thick) were obtained after decalcification in 3% nitric acid from 2 to 4 h, depending on the size of bone samples and their brittleness. These sections were stained by thionin (Sigma) and 4′,6′-diamidino-2-phenylindole (DAPI, Sigma) to investigate the persistence of DNA within osteocyte lacunae . DAPI-stained sections were observed under fluorescence light microscopy. Concerning SEM study a bone slice, adjacent to that used for light microscopy, was examined using Cambridge 250 Mark 3 scanning electron microscope, working at 20 kV beam voltage.
Recent human bone samples were exposed at temperatures progressively ranging from 100°C to 800°C, using a Linkam TS 1500 system, at a constant rate of 100°C/min. For each test, the specimen was maintained at a first rate temperature of 60″ and the final one of 30″. As further control, fresh femur bone samples of recent horse (Equus caballus) were also tested, with rates temperature of 60″ to 180″. Bone colours of the experimentally heated specimens were assessed by comparison to Munsell  soil color chart.
The 79 AD Vesuvius eruption generated a sequence of six distinctive pyroclastic surges (S1 to S6) and flows with increasing power, which caused landscape modification as well widespread building collapse and fatalities . The resulting ash deposits have thicknesses ranging from tens of metres near the vent to few millimetres at the flow periphery. In particular, the early three surges (S1 to S3) stopped ahead the northwestern walls of Pompeii, while the later ones (S4 to S6) over passed the town. The last two surges traveled up to a distance even exceeding 15 kilometres from the vent, whereas the S4 surge deposit least traces are confined within a few hundred of metres next to the south and southeastern walls.
The S4 pyroclastic surge is definitely relevant, since caused most of the fatalities in Pompeii in spite of the only 3 centimetres thick resulting deposit, a covered area of ca. 80 km2 and a modest total mass that we estimate in the order of 2×109 kg, at least one order of magnitude less than the overlying S5 and S6 surges. Textural and granulometric analyses of S4 deposit reveal absence of vertical grain-size grading with a graphic mean of 175 microns (Md=2.5) and graphical standard deviation of 300 microns (σ=1.9). This indicates that ash emplaced suddenly in a single depositional event resulting from dusty gas mixture deflation in response to horizontal velocity and turbulence dumping at the flow termination.
In order to investigate dynamics and emplacement mechanisms of S4 PDC at Pompeii, we have developed a numerical model (Figure 1). It has been retrieved by a Bayesian data inversion  of a set of 300 numerical simulations on a Somma-Vesuvius and surrounding plains Digital Elevation Model, produced by sampling a wide matrix of input parameters typical of Vesuvius PDCs . Field data such as flow depositional limits as well as the computed PDC velocity, density and thickness relative to the outcrops of Osservatorio Vesuviano (northern Herculaneum district), Oplontis and Pompeii, at ca. 3, 7 and 10 kilometres from the vent respectively, have been used to constrain the inversion. These parameters have been computed from the measured deposits thickness, grain size distributions and components density by developing an original code using Matlab environment for sedimentation mechanisms of stratified pyroclastic flows .
We calculated that in Herculaneum, Oplontis and Pompeii the PDC advanced with average density of ca. 10, 5 e 1.5 kg/m3 and as thick as ca. 60, 25, 18 metres, with velocity of ca. 45, 28, 29 m/s, respectively. The best PDC model obtained with the above constrains is a flow with Newtonian rheology, with a velocity at the vent of 50÷100 m/s, front thickness of 30÷130 metres, density of 1.5÷50 kg/m3 and average run-out within 10 kilometres. The inferred PDC mass of ca. 7.5×107 kg which emplaced behind Pompeii, divided by the total mass flow rate through the town ranging from 1.5×105 to 7.4×106 kg/s (equivalent to 26÷240 kg/s/m2, of ca. 110 kg/s/m2 in average) computed from the above results, provides the passage time of PDC cloud between ca. 30 and ca. 1.5×102 seconds.
These results indicate that the pyroclastic surge advanced as a dilute turbulent poorly-energetic deflating cloud and emplaced suddenly, also lead by town buildings and walls and trench barrier effect. Such behavior accounts for the lack of evidence of mechanical impact on structures and of engulfment and transport in the S4 deposit of stuff such as tiles and bricks.
In order to recognize the effects on people of the S4 surge, we analyzed the human victims remains from the Pompeii archeological site. Here, within the lapilli bed were found 394 skeletons of victims of the early fallout eruptive phase, 90% of whom died within buildings probably due to roof and floor collapse. Deposits of the later S4 surge preserved the remains of 650 victims heretofore supposed to have died by ash suffocation , , .
We studied the body postures of 93 well-preserved plaster casts of the surge victims at Pompeii (Table 1). For comparison we also examined 37 additional corpses of surge fatalities at Oplontis (Table 2), a Roman seaside suburban site located ca. 2 kilometres west-northwest of Pompeii, and 78 skeletons of surge victims unearthed at Herculaneum (Table 3) . The body postures assumed at the time of PDC emplacement were assessed by both direct analysis of casts and skeletons as well as by archive photographs, to search for evidence of PDCs lethal effects caused by mechanical impact, heat exposure and dusty gas inhalation in victims found inside as well outside buildings.
In Pompeii, most of the groups of victims display a variety of postures that can be arranged as 1) primary postures assumed at the time of death or 2) secondary, post-mortem postures.
The primary postures include:
Postures types e. and f. are generally observed as secondary effects in victims exposed to extreme heat (at least 200–300°C) ,  (Figure 3b). The pugilistic attitude was erroneously thought to be the victim's attempt for self-defence by previous authors .
Similarly in Pompeii and surroundings most of the victims are typically frozen in suspended actions (73% life-like stance, 27% sleep-like stance), showing as well as limb contraction (76%) and a large number of corpses presenting the pugilistic attitude (64%). Even if different postures often coexist in the same victims group, the prevalence of people frozen in suspended actions (life-like stance) is univocally indicative of a condition known as cadaveric spasm. In contrast, postures indicative of mechanical impact effects on victims both inside and outside buildings are extremely rare (2.1%). These evidence confirm that dynamic overpressure was generally below the human lethal threshold as well as their partial or total entrapment into the current (about 2000 Pa), according with the results of our numerical modeling of PDC.
Cadaveric spasm is a rare but diagnostic form of instantaneous muscular stiffening associated with instant violent death, which crystallizes the last activity one did prior to death . Such instant rigor prevents the ordinary onset of muscular relaxation immediately after death, thus avoiding any further substantial body posture modification. The presence of this stance is indicative that people was alive at the time of posture arrest and its widespread occurrence is a key evidence that all victims groups were exposed to the same lethal conditions. Cadaveric spasm commonly involves groups of muscles and only exceptionally the entire body. This last condition is described in battle situations , due to the exposure of victims to extreme heat. The predominance of this rare feature in Pompeii victims points to an instant death due to heat exposure.
However, since thermal human survival threshold for death has been inferred at 200°C , in order to verify if such condition affected the Vesuvius victims we investigated the evidence of thermally induced modifications in bones of human victims as well of a group of horses found within the Pompeii ash deposits. Therefore, we carried out macroscopic, light microscopy, histochemical and scanning electron microscopy (SEM) analyses to assess the importance of thermal effects of pyroclastic surges on casualties.
The bones of the Pompeii victims show colour variations ranging from natural bone colour to pale yellow as well as evidence of linear microcracking at the interosteonic level (Figure 4a1). All these features are indicative of exposure to high temperature , . Additionally, our analyses by thionin staining and SEM observations reveal DNA preservation (Figure 5a1) and an intact bone ultrastructure (Figure 4a2).
To better constrain the range of temperature of bone modification, we heated recent human and horse (Equus caballus) bone samples to temperatures that range from 100° to 800°C (see data in Table 4), which are typical conditions for PDCs. At 200°C, 300°C, 400–500°C, 600–700°C and 800°C bones progressively exhibit pale yellow, bright brown, black, dark-brownish grey and light grey-white colour  (Figure 6), respectively, and structural microcracks increase from a linear to a polygonal pattern (Figure 7). At 500–800°C the basic bone structure recrystallizes into irregular globules (Figure 4b3, c3).
Our comparative histochemical analyses on the DNA within osteocyte lacunae of heated human (Figure 5b1–b4) and horse (Figure 5c1–c4) bones reveal that DNA is persistent up to 300°C, whereas it is undetectable at higher temperatures. A comparison of macroscopic, microscopic and ultrastructural bone features of Pompeii victims (Figure 4a1, a2) with results of our laboratory experiments (Figure 4a3–c3, Figure 7) suggest that the ancient bones were exposed to temperatures of 250–300°C . Thus indicating that these values likely correspond to minumum pyroclastic surge temperature due to the buffering effects of soft tissues.
A parallel analysis was conducted on victims from the town of Herculaneum and the suburban Oplontis, both of which lie at about 7 kilometres from Vesuvius. The remains of victims here consist exclusively of skeletons (Herculaneum) or skeletons with only partial body imprint in the ash (Oplontis, Figure 3c). The analyzed specimens from Herculaneum and Oplontis show bone colours ranging from black to grey-white, linear to polygonal microcracks (Figure 4a1–c1) and incipient to high recrystallization (Figure 4b2, c2), as well as complete DNA degradation (Figure 5a2, a3). In contrast to Pompeii but similar to Herculaneum  several victims at Oplontis show skull explosion, as testified by clear-cut fractures resulting from intracranial overpressure induced by exposure of the corpses to very high temperature. These features suggest temperatures of ca 500°C in Herculaneum, which matches well with previous supporting evidence , and a temperature of ca 600°C in Oplontis .
The total thermal energy, which is directly related to the deposit thickness and the emplacement temperature, is then lower at Pompeii than in Oplontis and Herculaneum. Therefore heat was enough for sudden and complete vaporization of soft tissues of the victims at Herculaneum and Oplontis, where the flesh was suddenly replaced by the ash, but was insufficient at Pompeii. This account for the nearly perfect preservation of the entire body imprint (plaster casts) in the ash as a consequence of the delayed disappearance of flesh of these bodies.
Our overall results indicate that S4 pyroclastic surge crossed Pompeii as a dilute poorly-energetic dusty gas cloud and emplaced suddenly in response to horizontal velocity decay and turbulence dumping, approaching its termination just next the southern town walls. Due to low density and velocity, its dynamic overpressure was low with negligible effects on the structures and people. The PDC had a concentration of inhalable ash particles (<100 microns) in the order of 0.1÷0.7 kg/m3, the lower values commonly observed at the head of dilute PDCs, and temperature range between 250 and 600°C. These values are consistent with the pyroclastic surge temperatures computed for the marginal zone of PDCs derived from general numerical modeling of Plinian column collapse .
An independent verification that PDC temperatures in Pompeii exceeded 250°C is the melting of silverware solder . In Roman times this material was made with a lead/tin alloy like Tertiarium (Pb-Sn 21) , which has a melting point of ca 250°C. A temperature of 250°–300°C was also high enough to char wood objects, vegetal material and food  but was unable to affect glass , that is preserved intact in the ash deposits.
Nevertheless, the exposure time of the victims to high temperature and dusty gas was very short as resulting from lasting passage of S4 surge in the range of 30÷1.5×102 seconds. This result is crucial being the capability of PDCs to cause death and injury not only depending on their physical conditions but also on the exposure time. The passage time is consistent with the inferred lethal time for temperatures in the range of 250°–600°C evaluated from ca 10 to ca 102 seconds . Notably, such a time lapse is insufficient to cause asphyxia that would require an exposure time of several minutes, thus indicating that people would be able to survive to suffocation in 0.5 to 2.5 minutes of the S4 surge cloud passage . Nevertheless, the calculated concentration of inhalable ash in the PDC approached the survival condition in the order of ca. 0.1 kg/m3. Consistently, the widespread occurrence of primary life-like postures (cadaveric spasm) in the victims is only compatible with an instantaneous death, while exclude the longer agony and the final floppy posture that characterize suffocation.
Finally, contrary to previous hypotheses, our findings based on the interdisciplinary volcanological and bio-anthropological study of the deposits and victims of the 79 AD Plinian eruption reveal that even at the extreme periphery of the S4 surge neither asphyxia nor impact force but heat caused the deaths. Actually, while impact force and exposure time to dusty gas dropped below lethal conditions, the pyroclastic cloud retained its high temperature thus being the main cause of instantaneous mortality for the Vesuvius area inhabitants, including people who were sheltered within buildings as far as in Pompeii. Definitely, a group of indoor victims found at Muregine, within the S4 PDC limit about half kilometer south-east of Pompeii walls, suggests that even an extremely short exposure to the pyroclastic surge in the order of seconds to a few tents of seconds was lethal.
These facts and the evidence that the late, most powerful 79 AD PDCs reached distance exceeding 20 kilometres from the vent and the findings of several scattered groups of victims in Roman villas even as far as at least 15 kilometres in Stabiae highlight the need to strengthen the emergency plans for Vesuvius and other similar explosive volcanoes considering long-distance thermal effects even at the extreme PDCs periphery as primary cause of fatalities.
We thank Grete Stefani and Lorenzo Fergola of the Superintendence of Pompeii and Mario Pagano Executive Archaeologist at the Ministero per i Beni e le Attività Culturali for providing suggestions and access to archaeological documentation and materials. We are grateful to dott. Andrea Panizza and dott. Sergio Rossano for their crucial collaboration in the numerical modeling and code developing. Helpful and constructive comments from Prof. Francesco Maria Guadagno and an anonymous reviewer are gratefully acknowledged, as are the Editor's helpful comments and manuscript revision handling.
Competing Interests: The authors have declared that no competing interests exist.
Funding: The authors have no support or funding to report.