Sensitivity of the Amazon biome to high resolution climate change projections

ABSTRACT: Despite the reduction in deforestation rate in recent years, the impact of global warming by itself can cause changes in vegetation cover. The objective of this work was to investigate the possible changes on the major Brazilian biome, the Amazon Rainforest, under different climate change scenarios. The dynamic vegetation models may simulate changes in vegetation distribution and the biogeochemical processes due to climate change. Initially, the Inland dynamic vegetation model was forced with initial and boundary conditions provided by CFSR and the Eta regional climate model driven by the historical simulation of HadGEM2-ES. These simulations were validated using the Santarém tower data. In the second part, we assess the impact of a future climate change on the Amazon biome by applying the Inland model forced with regional climate change projections. The projections show that some areas of rainforest in the Amazon region are replaced by deciduous forest type and grassland in RCP4.5 scenario and only by grassland in RCP8.5 scenario at the end of this century. The model indicates a reduction of approximately 9% in the area of tropical forest in RCP4.5 scenario and a further reduction in the RCP8.5 scenario of about 50% in the eastern region of Amazon. Although the increase of CO2 atmospheric concentration may favour the growth of trees, the projections of Eta-HadGEM2-ES show increase of temperature and reduction of rainfall in the Amazon region, which caused the forest degradation in these simulations.

Conformal symmetry of the critical 3D Ising model inside a sphere

We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our results for one and two point functions in this geometry are consistent with the predictions from the conjectured conformal symmetry of the critical Ising model.

Evaluation of temperature influence on embedded kinematic system

Dissertação de mestrado integrado em Engenharia Mecânica

Adaptive facade systems - review of performance requirements, design approaches, use cases and market needs

The paper reflects the work of COST Action TU1403 Workgroup 3/Task group 1. The aim is to identify research needs from a review of the state of the art of three aspects related to adaptive façade systems: (1) dynamic performance requirements; (2) façade design under stochastic boundary conditions and (3) experiences with adaptive façade systems and market needs.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Magnetic resonance coronary lumen and vessel wall imaging.

Coronary magnetic resonance angiography (MRA) is a technique aimed at establishing a noninvasive test for the assessment of significant coronary stenoses. There are certain boundary conditions that have hampered the clinical success of coronary MRA and coronary vessel wall imaging. Recent advances in hardware and software allow for consistent visualization of the proximal and mid portions of the native coronary arteries. Current research focuses on the use of intravascular MR contrast agents and black blood coronary angiography. One common goal is to create a noninvasive test which might allow for screening for major proximal and mid coronary artery disease. These novel approaches will represent a major step forward in diagnostic cardiology.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

Stoneley wave modeling in heterogeneous porous media with viscous pore fluids

We implemented Biot-type porous wave equations in a pseudo-spectral numerical modeling algorithm for the simulation of Stoneley waves in porous media. Fourier and Chebyshev methods are used to compute the spatial derivatives along the horizontal and vertical directions, respectively. To prevent from overly short time steps due to the small grid spacing at the top and bottom of the model as a consequence of the Chebyshev operator, the mesh is stretched in the vertical direction. As a large benefit, the Chebyshev operator allows for an explicit treatment of interfaces. Boundary conditions can be implemented with a characteristics approach. The characteristic variables are evaluated at zero viscosity. We use this approach to model seismic wave propagation at the interface between a fluid and a porous medium. Each medium is represented by a different mesh and the two meshes are connected through the above described characteristics domain-decomposition method. We show an experiment for sealed pore boundary conditions, where we first compare the numerical solution to an analytical solution. We then show the influence of heterogeneity and viscosity of the pore fluid on the propagation of the Stoneley wave and surface waves in general.

Weak approximations. A Malliavin calculus approach

We introduce a variation of the proof for weak approximations that issuitable for studying the densities of stochastic processes which areevaluations of the flow generated by a stochastic differential equation on a random variable that maybe anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore if the inverse of the Malliavin covariance matrix associated with the process under consideration is sufficiently integrable then approximations fordensities and distributions can also be achieved. We apply theseideas to the case of stochastic differential equations with boundaryconditions and the composition of two diffusions.

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

Quantitative comparison of simulations of seismic wave propagation in heterogeneous poro-elastic media involving fluid-solid interfaces and in equivalent visco-elastic solids

There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes the predominant attenuation mechanism at seismic frequencies. As a consequence, centimeter-scale perturbations of the subsurface physical properties should be taken into account for seismic modeling whenever detailed and accurate responses of the target structures are desired. This is, however, computationally prohibitive since extremely small grid spacings would be necessary. A convenient way to circumvent this problem is to use an upscaling procedure to replace the heterogeneous porous media by equivalent visco-elastic solids. In this work, we solve Biot's equations of motion to perform numerical simulations of seismic wave propagation through porous media containing mesoscopic heterogeneities. We then use an upscaling procedure to replace the heterogeneous poro-elastic regions by homogeneous equivalent visco-elastic solids and repeat the simulations using visco-elastic equations of motion. We find that, despite the equivalent attenuation behavior of the heterogeneous poro-elastic medium and the equivalent visco-elastic solid, the seismograms may differ due to diverging boundary conditions at fluid-solid interfaces, where there exist additional options for the poro-elastic case. In particular, we observe that the seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an interesting result, which has potentially important implications for wave-equation-based algorithms in exploration geophysics involving fluid-solid interfaces, such as, for example, wave field decomposition.

Impacto de la circulación ecuatorial en la zona mínima de oxógeno presente en el norte del Ecosistema de la Corriente del Humboldt

El Norte del Ecosistema de la Corriente Humboldt (NECH) constituye una de las mayores zonas de afloramiento, localizada en el borde oriental del Pacifico Sur, la cual presenta características particulares, entre las que destacan una alta producción primaria y la presencia de una de las zonas mínimas de oxigeno (ZMO) más intensas en el océano abierto. La ZMO presente en esta zona es producto de la alta demanda de oxígeno durante la remineralización de la materia orgánica, el largo tiempo de residencia de sus aguas y su poca ventilación. En el presente estudio nos enfocamos en estudiar la influencia de cambios en la ventilación en la ZMO del NECH, tomando como las principales fuentes de aporte de oxígeno en esta zona a la Corriente Sub-superficial Ecuatorial (EUC) y las Contracorrientes Sub-superficiales del Sur (SSCCs) o también conocidas como los Jets de Tsuchiya. Utilizamos el modelo acoplado físico-biogeoquímico ROMS-PISCES, para observar la sensibilidad de la ZMO a diferentes condiciones de la circulación ecuatorial provenientes de dos modelos oceánicos de circulación general (SODA y MERCATOR). Los resultados muestran que el flujo de oxígeno a los 88ºW disminuye latitudinalmente de la EUC a los SSCCs; además, se observa que la ZMO desaparece de los 4ºN - 4ºS en la simulación que presenta una circulación más intensa (RPSoda) por lo que se puede concluir que una intensificación de la circulación ecuatorial afectaría principalmente a la zona ecuatorial y no frente a Perú, debido a que una mayor ventilación sería compensada con un mayor consumo de oxigeno durante la remineralización, producto de una alta productividad generada por un mayor flujo de nutrientes.