Vegetation Angular Signatures of Equatorial Forests From DSCOVR EPIC and Terra MISR Observations

In vegetation canopies cross-shading between finite dimensional leaves leads to a peak in reflectance in the retro-illumination direction. This effect is called the hot spot in optical remote sensing. The hotspot region in reflectance of vegetated surfaces represents the most information-rich directions in the angular distribution of canopy reflected radiation. This paper presents a new approach for generating hot spot signatures of equatorial forests from synergistic analyses of multiangle observations from the Multiangle Imaging SpectroRadiometer (MISR) on Terra platform and near backscattering reflectance data from the Earth Polychromatic Imaging Camera (EPIC) onboard NOAA’s Deep Space Climate Observatory (DSCOVR). A canopy radiation model parameterized in terms of canopy spectral invariants underlies the theoretical basis for joining Terra MISR and DSCOVR EPIC data. The proposed model can accurately reproduce both MISR angular signatures acquired at 10:30 local solar time and diurnal courses of EPIC reflectance (NRMSE < 9%, R2 > 0.8). Analyses of time series of the hot spot signature suggest its ability to unambiguously detect seasonal changes of equatorial forests.

Anisotropic stress softening of residually stressed solids

Residual stress in purely elastic solids has been extensively studied in the literature. However, to the best of the author’s knowledge, the influence of residual stresses on anisotropic Mullins materials has not been studied. Hence, the aim of this paper is to propose an anisotropic phenomenological model to describe the Mullins phenomena for residually stressed elastomers; taking note that most materials are not purely elastic and some of them exhibit an anisotropic stress-softening phenomenon widely known as the Mullins effect. The anisotropic model is based on the use of direction-dependent damage parameters and a set of anisotropic spectral invariants presented recently in the literature by the author. The spectral invariants have a clear physical meaning that is useful in aiding the design of a rigorous experiment to construct a specific form of constitutive equation. Since boundary value results for residually stressed Mullins material are not found in the literature, the effect of residual stresses on the Mullins phenomena in simple tension, torsion and equibiaxial deformations is discussed in this paper.

The geometric invariants for the spectrum of the Stokes operator

For a bounded domain $$\Omega \subset {\mathbb {R}}^n$$ Ω ⊂ R n with smooth boundary, we explicitly calculate the first two coefficients of the asymptotic expansion for the integral of the trace of the Stokes semigroup $$e^{-t S}$$ e - t S as $$t\rightarrow 0^+$$ t → 0 + . These coefficients (i.e., spectral invariants) provide precise information for the volume of the domain $$\Omega $$ Ω and the surface area of the boundary $$\partial \Omega $$ ∂ Ω by the spectrum of the Stokes problem. As an application, we show that an n-dimensional ball is uniquely determined by its Stokes spectrum among all Euclidean bounded domains with smooth boundary.

Simulation-Based Evaluation of the Estimation Methods of Far-Red Solar-Induced Chlorophyll Fluorescence Escape Probability in Discontinuous Forest Canopies

The escape probability of Solar-induced chlorophyll fluorescence (SIF) can be remotely estimated using reflectance measurements based on spectral invariants theory. This can then be used to correct the effects of canopy structure on canopy-leaving SIF. However, the feasibility of these estimation methods is untested in heterogeneous vegetation such as the discontinuous forest canopy layer under evaluation here. In this study, the Discrete Anisotropic Radiative Transfer (DART) model is used to simulate canopy-leaving SIF, canopy total emitted SIF, canopy interceptance, and the fraction of absorbed photosynthetically active radiation (fAPAR) in order to evaluate the estimation methods of SIF escape probability in discontinuous forest canopies. Our simulation results show that the normalized difference vegetation index (NDVI) can be used to partly eliminate the effects of background reflectance on the estimation of SIF escape probability in most cases, but fails to produce accurate estimations if the background is partly or totally covered by vegetation. We also found that SIF escape probabilities estimated at a high solar zenith angle have better estimation accuracy than those estimated at a lower solar zenith angle. Our results show that additional errors will be introduced to the estimation of SIF escape probability with the use of satellite products, especially when the product of leaf area index (LAI) and clumping index (CI) was underestimated. In other results, fAPAR has comparable estimation accuracy of SIF escape probability when compared to canopy interceptance. Additionally, fAPAR for the entire canopy has better estimation accuracy of SIF escape probability than fPAR for leaf only in sparse forest canopies. These results help us to better understand the current estimation results of SIF escape probability based on spectral invariants theory, and to improve its estimation accuracy in discontinuous forest canopies.

Sub-Riemannian Limit of the Differential Form Heat Kernels of Contact Manifolds

We study the behavior of the heat kernel of the Hodge Laplacian on a contact manifold endowed with a family of Riemannian metrics that blow-up the directions transverse to the contact distribution. We apply this to analyze the behavior of global spectral invariants such as the $\eta $-invariant and the determinant of the Laplacian. In particular, we prove that contact versions of the relative $\eta $-invariant and the relative analytic torsion are equal to their Riemannian analogues and hence topological.