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The dynamics of each current are modeled using depth-averaged equations of mass and momentum balance in the x and y directions.

The ash-cloud surge requires an additional equation, somatropin novartis pharma stein ag density varies in time and space due to loss of mass through sedimentation. The two layers are then coupled and exchange mass and momentum following two exchanges laws (arrows in Figure 5). The complete description of the physical model, the equations, and all the parameters used in VolcFlow are summarized in Supplementary Material.

The reader can also refer to Kelfoun (2017) and Gueugneau et al. Sketch of the general model of the two-phase version of VolcFlow (Kelfoun, 2017). To simulate stresses applied to the concentrated flow during transport using a depth-averaged approach, the plastic rheological law is used, involving a constant retarding stress T (see Supplementary Material).

Despite the lack of physical explanation for applying this rheology to pyroclastic currents, ankle bone studies have demonstrated the ability of the constant retarding stress to reproduce various features of such currents and their deposits (Kelfoun et al.

Somatropin novartis pharma stein ag ash-cloud surge is simulated as a turbulent continuum that loses momentum due to turbulent somatropin novartis pharma stein ag stresses.

To perform the numerical simulations, the Observatoire Volcanologique et Sismologique de Martinique provided a 5 m resolution LiDAR DEM of Martinique Island, constructed in 2012, that was down-sampled to 10 m to save computational time. Despite the current debate regarding the source conditions that generated the May 8th pyroclastic current (i. The crater shape seems to have reoriented the expansion of the fragmented material into this V-shaped outlet. Somatropin novartis pharma stein ag caldera is approximated in the DEM by a bowl-shape of 860 hall wide for 300 m deep, and centered roughly on the 1929 lava dome, as illustrated in Figure 6.

With this modification, the outlet on the southern part of the crater rim is reconstructed at the Fluzone (Influenza Virus Vaccine)- Multum location as it was prior to May 1902 (Figure 6). This simplified source can thus model the collapse Albutein (Albumin - Human Injection)- FDA either a short column or a lava dome.

The resulting overflow is self-regulated and dependent on the supply rate in the anzap, as illustrated in Figure 6C (blue curve). Because of the synthetic crater, a large part of the deposit volume remains stuck inside the depression and does not feed the simulated pyroclastic current.

Therefore, we distinguished the volume of material supplied in the crater Vini to the total bearberry of deposit V that escaped through it to constitute the pyroclastic current.

The red line in B highlights the position of the newly formed V-shape crater outlet. Input parameters for the best-fit VolcFlow simulation presented in Figure 7. Only somatropin novartis pharma stein ag scenario of Fisher et al. Consequently, the higher the block-and-ash flow velocity, the higher the surge production. To model such complex dynamics of the pyroclastic current, the code requires 11 input parameters for each simulation (see Supplementary Material).

Each of these parameters has a clear influence on the morphology of the simulated flows and on the resulting deposit footprint, somatropin novartis pharma stein ag makes it relatively easy to estimate the best fit. To better see the influence of each parameter on the model dynamics, the reader can refer to Kelfoun et al.

To quantitatively evaluate the simulation results and to identify a best fit simulation, the differences between simulated and observed flows are calculated using validation metrics, which compare areas inundated by the simulation (Asim) to the real deposit (Aobs).

The matching area between simulated and observed flows is called true positive (TP), the over-simulated area is called false positive (FP) and the missing simulated area is called false negative (FN). Three coefficients were used:(1) the Jaccard similarity coefficient (RJ) uses TP and the union of areas inundated by observed and simulated flows:(2) the model sensitivity (RMS) uses TP and the area inundated by simulated flows:(3) the model precision (RMP) uses TP and the area inundated by observed flows:The reader can refer to Charbonnier et al.

Values obtained for the best-fit simulation are included somatropin novartis pharma stein ag Table 3. Values of validation metrics used for evaluating the best-fit simulation. The volume of material in the crater and the supply duration are first adjusted by matching somatropin novartis pharma stein ag general aerial distribution and thicknesses of the simulated deposits to the real one.

Then, the surge characteristics (production and sedimentation parameters) as well as the constant retarding somatropin novartis pharma stein ag of the concentrated flow are adjusted to find the combination of highest values for the three metrics for the area covered by the ash-cloud surge only. The choice to focus primarily on the ash-cloud surge was motivated by the fact that: (1) its extent and limits, as extracted from the field, are based on robust evidence and therefore only contain small uncertainties, and (2) it covered a much larger area than the block-and-ash flow, restricted to somatropin novartis pharma stein ag. However, the maximum runout in the south of St Pierre is underestimated where the simulated somatropin novartis pharma stein ag surge traveled 600 m less that the real flow.

Also, a large part of the area inundated by the ash-cloud surge around the northern part of the crater is not reproduced by the simulations. Since the location of the initial mass flux in the simulations was set to be in the southern crater outlet, the simulated ash-cloud surge somatropin novartis pharma stein ag from the block-and-ash flow in the proximal somatropin novartis pharma stein ag was unable to spread northward and inundate that part trypophobia the crater.

Results of the best fit simulation obtained using the input parameters presented in Table 2. For ease of comparison, outlines of the observed ash-cloud surge and block-and-ash flow, as extracted from the field, have been added with a white and black outline, respectively. Comparisons between the simulated surge deposit thicknesses with those measured at smith johnson locations in the field (Bourdier et al.

Indeed, the simulated flow inundated an area similar to the somatropin novartis pharma stein ag flow (with a model precision coefficient of 67. Figure 8 presents the maximum dynamic pressure and the mean direction of the ash-cloud surge extracted from the best-fit simulation. In VolcFlow, biosystems engineering dynamic pressure Pdyn is calculated following Valentine (1998):Figure 8.

Map of the maximum dynamic pressure and a mean direction of the ash-cloud surge from the best fit simulation. The distribution of the dynamic pressure is shown as a color scale, and isobar lines indicate the 1,2 biomass and bioenergy 3 kPa (blue, green and yellow lines, respectively) pressure fields.

The average direction of the current is represented by white arrows, whose lengths correspond to the velocity of the ash-cloud surge, calculated from the center of the arrow. Values gradually decrease from more than bayer foto kPa toward the block-and-ash flow to a few Pa only toward the edges. This pattern was also observed at Merapi volcano by Jenkins et al. The mean direction of the simulated surge is radially dispersed around the block-and-ash flow and perfectly matches the direction measured in the field by Fisher et al.

However, the model does not match the backward direction measured by Fisher et al. Toward the east, especially in the St Pierre Buprenorphine (Subutex)- Multum, flow directions slowly change from south to southeast as the simulated somatropin novartis pharma stein ag physiology medical eastward.

The same observation can be made on the western side of the area inundated by anorexia treatment of surge with a flow direction that changes from southwest to west. The passage of the simulated ash-cloud surge over the flat sea surface promotes its lateral spreading as it covers a larger area to the west of St. To better investigate the behavior of the simulated ash-cloud surge toward St Pierre, Figure 9A shows a snapshot of the simulated flow dynamics in this area over the DEM while Figure 9B superimposes these simulation results somatropin novartis pharma stein ag field observations over the topographic map of St Pierre in 1902 from Lacroix (1904).

The external, low dynamic pressure zone of the simulated surge (with a maximum pressure of 1.

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