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Dykes are magma-filled fractures propagating through the brittle crust. Understanding the physics of dyking process is essential to mitigate the volcanic hazard associated with the opening of new eruptive fissures at the surface. Often, physics-based models view either fracturing of the host rock or viscous flow of the magma as the dominating energy sink during dyke propagation. Here, we provide a numerical model that captures the coupling of fracturing at the crack tip and the transport of a viscous fluid. Built with the boundary element technique, our model allows for computation of the shape and velocity of a growing fluid-filled crack accounting for the viscosity of the fluid: The fluid flow induces a viscous pressure drop acting at the crack walls, and modifies the shape of the crack. The energy conservation equation provides the constraints to solve for the crack growth velocity, assuming that brittle fracturing and viscous flow are the main processes that dissipate energy. Using a parameter range that represents typical magmatic intrusions, we obtain crack shapes displaying some typical characteristics, including a tear-drop head and an open tail that depend on rock rigidity, magma viscosity and buoyancy. We show that viscous forces significantly contribute to the energy dissipated during the propagation of magmatic dykes. Applied to the 1998 intrusion at Piton de la Fournaise (La Réunion Island), we provide ranges of dyke lengths and openings by adjusting the numerical velocity to the one deduced from the migration of volcano-tectonic events. Key Points We present a new modeling scheme to compute the shape and velocity of a growing fluid-filled crack Our magmatic dykes show a tear drop head and open tail, on a wide range of propagation velocities We reproduce the velocity and fit important parameters for the 1998 Piton de la Fournaise intrusion

The physical processes that operate within, and beneath, a volcano control the frequency, duration, location and size of volcanic eruptions. Volcanotectonics focuses on such processes, combining techniques, data, and ideas from structural geology, tectonics, volcano deformation, physical volcanology, seismology, petrology, rock and fracture mechanics and classical physics. A central aim of volcanotectonics is to provide sufficient understanding of the internal processes in volcanoes so that, when combined with monitoring data, reliable forecasting of eruptions, vertical (caldera) and lateral (landslide) collapses and related events becomes possible. To gain such an understanding requires knowledge of the material properties of the magma and the crustal rocks, as well as the associated stress fields, and their evolution. The local stress field depends on the properties of the layers that constitute the volcano and, in particular, the geometric development of its shallow magma chamber. During this decade an increasing use of data from InSAR, pixel offset and structure-from-motion, as well as dense, portable seismic networks will provide further details on the mechanisms of volcanic unrest, magma-chamber rupture, the propagation of magma-filled fractures (dikes, inclined sheets and sills) and lateral and vertical collapse. Additionally, more use will be made of accurate quantitative data from fossil and active volcanoes, combined with realistic numerical, analytical and machine-learning studies, so as to provide reliable models on volcano behaviour and eruption forecasting.

[1] The Radiation Transfer Model Intercomparison ( RAMI) initiative benchmarks canopy reflectance models under well-controlled experimental conditions. Launched for the first time in 1999, this triennial community exercise encourages the systematic evaluation of canopy reflectance models on a voluntary basis. The first phase of RAMI focused on documenting the spread among radiative transfer (RT) simulations over a small set of primarily 1-D canopies. The second phase expanded the scope to include structurally complex 3-D plant architectures with and without background topography. Here sometimes significant discrepancies were noted which effectively prevented the definition of a reliable "surrogate truth,'' over heterogeneous vegetation canopies, against which other RT models could then be compared. The present paper documents the outcome of the third phase of RAMI, highlighting both the significant progress that has been made in terms of model agreement since RAMI-2 and the capability of/need for RT models to accurately reproduce local estimates of radiative quantities under conditions that are reminiscent of in situ measurements. Our assessment of the self-consistency and the relative and absolute performance of 3-D Monte Carlo models in RAMI-3 supports their usage in the generation of a "surrogate truth'' for all RAMI test cases. This development then leads ( 1) to the presentation of the "RAMI Online Model Checker'' (ROMC), an open-access web-based interface to evaluate RT models automatically, and ( 2) to a reassessment of the role, scope, and opportunities of the RAMI project in the future.