Virginie Pinel

Modeling radiative transfer in heterogeneous 3-D vegetation canopies

Abstract The DART (discrete anisotropic radiative transfer) model simulates radiative transfer in heterogeneous 3-D scenes that may comprise different landscape features, i.e., leaves, grass, trunks, water, soil. The scene is divided into a rectangular cell matrix, i.e., building block for simulating larger scenes. Cells are parallelipipedic. Their optical properties are represented by individual scattering phase functions that are directly input into the model or are computed with optical and structural characteristics of elements within the cell. Radiation scattering and propagation are simulated with the exact kernel and discrete ordinate approaches; any set of discrete direction can be selected. In addition to topography and hot spot, leaf specular and first-order polarization mechanisms are modeled. Two major iterative steps are distinguished: 1) Cell illumination with direct sun radiation: Within cell multiple scattering is accurately simulated. 2) Interception and scattering of previously scattered radiation: Atmospheric radiation, possibly anisotropic, is input at this stage. Multiple scattering is stored as spherical harmonics expansions, for reducing computer memory constraints. The model iterates on step 2, for all cells, and stops with the energetic equilibrium. Two simple accelerating techniques can be used: 1) Gauss Seidel method, i.e., simulation of scattering with radiation already scattered at the iteration stage, and (2) decrease of the spherical harmonics expansion order with the iteration order. Moreover, convergence towards the energetic equilibrium is accelerated with an exponential fitting technique. This model predicts the bidirectional reflectance distribution function of 3-D canopies. Radiation components associated with leaf volume and surface mechanisms are distinguished. It gives also the radiation regime within canopies, for further determination of 3-D photosynthesis rates and primary production. Accurate modeling of multiple scattering within cells, combined with the fact that cells can have different x,y,z dimensions, is well adapted to remote sensing based studies, i.e., scenes with large dimensions. The model was successfully tested with homogeneous covers. Preliminary comparisons of simulated reflectance images with remotely acquired spectral images of a 3-D heterogeneous forest cover stressed the usefulness of the DART model for conducting studies with remotely acquired information.

The effect of edifice load on magma ascent beneath a volcano

A volcanic edifice exerts a large load at Earths surface and modifies the stress field at depth. We investigate how this affects upward dyke propagation towards the surface. For given edifice dimensions and pressure conditions in the deep magma source, there is a critical density threshold above which magmas cannot reach the surface. This density threshold is a decreasing function of edifice height. For edifice heights in the range 0-3000 m, the density threshold spans the density range of common natural magmas (between 2700 and 2300 kg m−3). With time, differentiation in a magma chamber generates increasingly evolved magmas with decreasing densities, which favours eruption. However, the edifice grows simultaneously at the surface, which counterbalances this effect. The general tendency is to gradually prevent more and more evolved magmas from reaching the surface. A volcanic edifice acts as a magma filter which prevents eruption and affects the chemical evolution of the chamber through its control on magma withdrawal. Thus, one may not consider that eruption products are random samples of an evolving magma reservoir. The partial destruction of an edifice may lead to renewed eruption of primitive and dense magmas.

Icelandic rhythmics: Annual modulation of land elevation and plate spreading by snow load

] We find strong correlation between seasonal variationin CGPS time series and predicted response to annual snowload in Iceland. The load is modeled using Green’sfunctions for an elastic halfspace and a simple sinusoidalload history on Iceland’s four largest ice caps. We deriveE = 40 ± 15 GPa as a minimum value for the effectiveYoung’s modulus in Iceland, increasing with distance fromthe Eastern Volcanic Zone. We calculate the elastic responseover all of Iceland to maximum snow load at the ice capsusing E = 40 GPa. Predicted annual vertical displacementsare largest under the Vatnajo¨kull ice cap with a peak-to-peakseasonal displacement of 37 mm. CGPS stations closest tothe ice cap experience a peak-to-peak seasonal displacementof 16 mm, consistent with our model. East and north ofVatnajo¨kull we find the maximum of annual horizontaldisplacements of 6 mm resulting in apparent modulationof plate spreading rates in this area.

Climate effects on volcanism: influence on magmatic systems of loading and unloading from ice mass variations, with examples from Iceland

Pressure influences both magma production and the failure of magma chambers. Changes in pressure interact with the local tectonic settings and can affect magmatic activity. Present-day reduction in ice load on subglacial volcanoes due to global warming is modifying pressure conditions in magmatic systems. The large pulse in volcanic production at the end of the last glaciation in Iceland suggests a link between unloading and volcanism, and models of that process can help to evaluate future scenarios. A viscoelastic model of glacio-isostatic adjustment that considers melt generation demonstrates how surface unloading may lead to a pulse in magmatic activity. Iceland’s ice caps have been thinning since 1890 and glacial rebound at rates exceeding 20 mm yr−1 is ongoing. Modelling predicts a significant amount of ‘additional’ magma generation under Iceland due to ice retreat. The unloading also influences stress conditions in shallow magma chambers, modifying their failure conditions in a manner that depends critically on ice retreat, the shape and depth of magma chambers as well as the compressibility of the magma. An annual cycle of land elevation in Iceland, due to seasonal variation of ice mass, indicates an annual modulation of failure conditions in subglacial magma chambers.

Seismicity and deformation induced by magma accumulation at three basaltic volcanoes

We analyzed the evolution of volcano-tectonic (VT) seismicity and deformation at three basaltic volcanoes (Kilauea, Mauna Loa, Piton de la Fournaise) during phases of magma accumulation. We observed that the VT earthquake activity displays an accelerating evolution at the three studied volcanoes during the time of magma accumulation. At the same times, deformation rates recorded at the summit of Kilauea and Mauna Loa volcanoes were not accelerating but rather tend to decay. To interpret these observations, we propose a physical model describing the evolution of pressure produced by the accumulation of magma into a reservoir. This variation of pressure is then used to force a simple model of damage, where damage episodes are equivalent to earthquakes. This model leads to an exponential increase of the VT activity and to an exponential decay of the deformation rate during accumulation phases. Seismicity and deformation data are well fitted by such an exponential model. The time constant, deduced from the exponential increase of the seismicity, is in agreement with the time constant predicted by the model of magma accumulation. This VT activity can thus be a direct indication of the accumulation of magma at depth, and therefore can be seen as a long-term precursory phenomenon, at least for the three studied basaltic volcanoes. Unfortunately, it does not allow the prediction of the onset of future eruptions, as no diverging point (i.e., critical time) is present in the model.

Mexico City Subsidence Measured by InSAR Time Series: Joint Analysis Using PS and SBAS Approaches

In multi-temporal InSAR processing, both the Permanent Scatterer (PS) and Small BAseline Subset (SBAS) approaches are optimized to obtain ground displacement rates with a nominal accuracy of millimeters per year. In this paper, we investigate how applying both approaches to Mexico City subsidence validates the InSAR time series results and brings complementary information to the subsidence pattern. We apply the PS approach (Gamma-IPTA chain) and an ad-hoc SBAS approach on 38 ENVISAT images from November 2002 to March 2007 to map the Mexico City subsidence. The subsidence rate maps obtained by both approaches are compared quantitatively and analyzed at different steps of the PS processing. The inter-comparison is done separately for low-pass (LP) and high-pass (HP) filtered difference maps to take the complementarity of both approaches at different scales into account. The inter-comparison shows that the differential subsidence map obtained by the SBAS approach describes the local features associated with urban constructions and infrastructures, while the PS approach quantitatively characterizes the motion of individual targets. The latter information, once related to the type of building foundations, should be essential to quantify the relative importance of surface loads, surface drying and drying due to aquifer over-exploitation, in subsoil compaction.

A two‐magma chamber model as a source of deformation at Grímsvötn Volcano, Iceland

Grimsvotn Volcano is the most active volcano in Iceland, and its last three eruptions were in 1998, 2004, and 2011. Here we analyze the displacement around Grimsvotn during these last three eruptive cycles using 10 GPS stations. The observed displacements in this region generally contain a linear component of tectonic and glacio-isostatic origin, in agreement with the previously estimated values of plate motions and vertical rebound. Larger amplitude deformation observed close to Grimsvotn at the GFUM continuous GPS station clearly reflects a major volcanic contribution superimposed on a tectonic component. We estimate and subtract the tectonic trend at this station using regional observed displacement. The direction and pattern of the residual volcanic displacement (for coeruptive and intereruptive periods) are consistent for all three of these eruptive cycles. The posteruptive inflation is characterized by an exponential trend, followed by a linear trend. In this study, we explain this temporal behavior using a new analytic model that has two connected magma chambers surrounded by an elastic medium and fed by a constant basal magma inflow. During the early posteruptive phase, pressure readjustment occurs between the two reservoirs, with replenishment of the shallow chamber from the deep chamber. Afterward, due to the constant inflow of magma into the deep reservoir, the pressurization of the system produces linear uplift. A large deep reservoir favors magma storage rather than surface emission. Based on displacement measured at GFUM station, we estimate an upper limit for the radius of the deep reservoir of ∼10 km.

Cointrusive shear displacement by sill intrusion in a detachment: A numerical approach

Sheared sills are observed at Piton des Neiges (the eroded basaltic volcano of La Reunion) and are a suspected cause of the coeruptive flank displacement of Piton de la Fournaise in 2007. We performed a 2-D numerical study to quantify the perturbation induced by sill injection within a volcanic edifice. Magma is considered as an inviscid and pressurized fluid injected in an initially stable edifice under gravity-controlled extension. Two cases of injection are tested, in an elastic homogeneous edifice or along a detachment controlled by a friction law. We show that sill injection induces tangential displacements. This effect is strongly increased when sills are emplaced along a detachment, producing extension behind the injection and potentially ending in a large-scale flank collapse. Sill injections can thus explain the cointrusive shear deformation observed at Piton des Neiges and the tangential displacements measured at Piton de la Fournaise in 2007.

Large‐scale inflation of Tungurahua volcano (Ecuador) revealed by Persistent Scatterers SAR interferometry

The Tungurahua volcano, in Ecuador, has been experiencing a substantial activity period since 1999, with several eruptions, including those of 2006 and 2008. We use a persistent scatterers approach to analyze a time series of Envisat synthetic aperture radar (SAR) data over the period 2003–2009, to investigate surface deformation in the region of the volcano. We measure a continuous large-scale uplift with a maximum line of sight displacement rate of about 8 mm/yr, which is the first evidence of a sustained inflation in the Andes for an active volcano encompassing several eruptions. We model this signal as magma emplacement in a permanent storage zone at 11.5 km below sea level, with a net inflow rate of 7 million m3/yr. The paroxysmal eruptions in 2006 and 2008 did not seem to disrupt this long-term signal. However, we observe significant deformation during the 2006 eruption consistent with an additional intrusion of 4.5 million m3 of magma.

Fusion of D-InSAR and sub-pixel image correlation measurements for coseismic displacement field estimation: Application to the Kashmir earthquake (2005)

In geophysics, the uncertainty associated with model parameters or displacement measurements plays a crucial role in the understanding of geophysical phenomenon. An emerging way to reduce the geodetic parameter uncertainty is to combine a large number of data provided by SAR images. However, the measurements by radar imagery are subject to both random and epistemic uncertainties. Probability theory is known as the appropriate theory for random uncertainty, but questionable for epistemic uncertainty. Fuzzy theory is more adapted to epistemic uncertainty. Moreover, in a context of random and epistemic uncertainties, the conventional joint inversion in the least squares sense cannot be considered any more as the best scheme to reduce uncertainty. Therefore, in this article, in addition to joint inversion, two other fusion schemes, pre-fusion and post-fusion, are proposed. We consider here the conventional approach and an original fuzzy approach for handling random and epistemic uncertainties of D-InSAR and sub-pixel image correlation measurements. Joint inversion and pre-fusion are then applied to the measurement of displacement field due to the 2005 Kashmir earthquake by fusion of these data. The behaviours of these two fusion schemes versus uncertainty reduction are highlighted through comparisons of results.