Anthony B. Davis

Hyperspectral remote sensing of foliar nitrogen content

A strong positive correlation between vegetation canopy bidirectional reflectance factor (BRF) in the near infrared (NIR) spectral region and foliar mass-based nitrogen concentration (%N) has been reported in some temperate and boreal forests. This relationship, if true, would indicate an additional role for nitrogen in the climate system via its influence on surface albedo and may offer a simple approach for monitoring foliar nitrogen using satellite data. We report, however, that the previously reported correlation is an artifact—it is a consequence of variations in canopy structure, rather than of %N. The data underlying this relationship were collected at sites with varying proportions of foliar nitrogen-poor needleleaf and nitrogen-rich broadleaf species, whose canopy structure differs considerably. When the BRF data are corrected for canopy-structure effects, the residual reflectance variations are negatively related to %N at all wavelengths in the interval 423–855 nm. This suggests that the observed positive correlation between BRF and %N conveys no information about %N. We find that to infer leaf biochemical constituents, e.g., N content, from remotely sensed data, BRF spectra in the interval 710–790 nm provide critical information for correction of structural influences. Our analysis also suggests that surface characteristics of leaves impact remote sensing of its internal constituents. This further decreases the ability to remotely sense canopy foliar nitrogen. Finally, the analysis presented here is generic to the problem of remote sensing of leaf-tissue constituents and is therefore not a specific critique of articles espousing remote sensing of foliar %N.

Multi sky-view 3D aerosol distribution recovery

Aerosols affect climate, health and aviation. Currently, their retrieval assumes a plane-parallel atmosphere and solely vertical radiative transfer. We propose a principle to estimate the aerosol distribution as it really is: a three dimensional (3D) volume. The principle is a type of tomography. The process involves wide angle integral imaging of the sky on a very large scale. The imaging can use an array of cameras in visible light. We formulate an image formation model based on 3D radiative transfer. Model inversion is done using optimization methods, exploiting a closed-form gradient which we derive for the model-fit cost function. The tomography model is distinct, as the radiation source is unidirectional and uncontrolled, while off-axis scattering dominates the images.

Linearization of Markov chain formalism for vector radiative transfer in a plane-parallel atmosphere/surface system.

The Markov chain formalism for polarized radiative transfer through a vertically inhomogeneous atmosphere is linearized comprehensively with respect to the aerosol and polarizing surface properties. For verification, numerical results are compared to those obtained by the finite difference method. We demonstrate the use of the linearized code as part of a retrieval of aerosol and surface properties for an atmosphere overlying a black and Fresnel-reflecting ocean surface.

Airborne Three-Dimensional Cloud Tomography

We seek to sense the three dimensional (3D) volumetric distribution of scatterers in a heterogenous medium. An important case study for such a medium is the atmosphere. Atmospheric contents and their role in Earths radiation balance have significant uncertainties with regards to scattering components: aerosols and clouds. Clouds, made of water droplets, also lead to local effects as precipitation and shadows. Our sensing approach is computational tomography using passive multi-angular imagery. For light-matter interaction that accounts for multiple-scattering, we use the 3D radiative transfer equation as a forward model. Volumetric recovery by inverting this model suffers from a computational bottleneck on large scales, which include many unknowns. Steps taken make this tomography tractable, without approximating the scattering order or angle range.

Markov chain formalism for vector radiative transfer in a plane-parallel atmosphere overlying a polarizing surface

We report on a way of building bidirectional surface reflectivity into the Markov chain formalism for polarized radiative transfer through a vertically inhomogeneous atmosphere. Numerical results are compared to those obtained by the Monte Carlo method, showing the accuracy of the Markov chain method when 90 streams are used to compute the radiation from a Rayleigh-plus-aerosol atmosphere that overlies a surface with a bidirectional reflection function consisting of both depolarizing and polarizing parts.

Markov chain formalism for polarized light transfer in plane-parallel atmospheres, with numerical comparison to the Monte Carlo method.

Building on the Markov chain formalism for scalar (intensity only) radiative transfer, this paper formulates the solution to polarized diffuse reflection from and transmission through a vertically inhomogeneous atmosphere. For verification, numerical results are compared to those obtained by the Monte Carlo method, showing deviations less than 1% when 90 streams are used to compute the radiation from two types of atmospheres, pure Rayleigh and Rayleigh plus aerosol, when they are divided into sublayers of optical thicknesses of less than 0.03.

A Generalized Linear Transport Model for Spatially Correlated Stochastic Media

We formulate a new model for transport in stochastic media with long-range spatial correlations where exponential attenuation (controlling the propagation part of the transport) becomes power law. Direct transmission over optical distance τ(s), for fixed physical distance s, thus becomes (1 + τ(s)/a)− a, with standard exponential decay recovered when a → ∞. Atmospheric turbulence phenomenology for fluctuating optical properties rationalizes this switch. Foundational equations for this generalized transport model are stated in integral form for d = 1, 2, 3 spatial dimensions. A deterministic numerical solution is developed in d = 1 using Markov Chain formalism, verified with Monte Carlo, and used to investigate internal radiation fields. Standard two-stream theory, where diffusion is exact, is recovered when a = ∞. Differential diffusion equations are not presently known when a < ∞, nor is the integro-differential form of the generalized transport equation. Monte Carlo simulations are performed in d = 2, as a model for transport on random surfaces, to explore scaling behavior of transmittance T when transport optical thickness τt ≫ 1. Random walk theory correctly predicts T∝τ− minu2009{1, a/2}t in the absence of absorption. Finally, single scattering theory in d = 3 highlights the model’s violation of angular reciprocity when a < ∞, a desirable property at least in atmospheric applications. This violation is traced back to a key trait of generalized transport theory, namely, that we must distinguish more carefully between two kinds of propagation: one that ends in a virtual or actual detection and the other in a transition from one position to another in the medium.

A hybrid (Monte Carlo/deterministic) approach for multi-dimensional radiation transport

Abstract A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or a airplane). It uses a deterministic approximation of an adjoint transport solution to reduce variance, computed quickly by ignoring atmospheric interactions. This allows significant variance and computational cost reductions when the atmospheric scattering and absorption coefficient are small. When combined with an atmospheric photon-redirection scheme, significant variance reduction (equivalently acceleration) is achieved in the presence of atmospheric interactions.

Multiple-Scattering Microphysics Tomography

Scattering effects in images, including those related to haze, fog and appearance of clouds, are fundamentally dictated by microphysical characteristics of the scatterers. This work defines and derives recovery of these characteristics, in a three-dimensional (3D) heterogeneous medium. Recovery is based on a novel tomography approach. Multi-view (multi-angular) and multi-spectral data are linked to the underlying microphysics using 3D radiative transfer, accounting for multiple-scattering. Despite the nonlinearity of the tomography model, inversion is enabled using a few approximations that we describe. As a case study, we focus on passive remote sensing of the atmosphere, where scatterer retrieval can benefit modeling and forecasting of weather, climate and pollution.

Space-time Green functions for diffusive radiation transport, in application to active and passive cloud probing

Clouds are a feast for the eye but, when contemplating their fluid beauty, it is important — at least for scientists — to bear in mind that they are also key elements of the Earth’s climate system. They are indeed the first-order regulators of the intake in solar energy: What portion goes back to space? What reaches the surface (then warms the ground, drives photosynthesis, etc.)? Clouds also contribute strongly to the vertical distribution of solar heating and, from there, the thermal balance of the atmosphere. These are well-known and relatively well-understood/modeled climate roles of clouds, as can be expected for such naturally occurring components of the atmosphere. We note that these roles involve radiative transfer across the electromagnetic spectrum. What is far less understood about clouds is how they interact microphysically, chemically and thermo-hydrodynamically, with other natural and anthropogenic constituents, especially aerosols. These are known as cloud feedback mechanisms in the parlance of climate science, and have been identified as the single most resilient roadblock in the way of reducing uncertainty in future climate prediction [1], an enterprise that relies heavily on models to explore various scenarios in global greenhouse gas emissions.