Multiband radar characterization of forest biomes

The utility of airborne and orbital SAR in classification, assessment, and monitoring of forest biomes is investigated through analysis of orbital synthetic aperature radar (SAR) and multifrequency and multipolarized airborne SAR imagery relying on image tone and texture. Preliminary airborne SAR experiments and truck-mounted scatterometer observations demonstrated that the three dimensional structural complexity of a forest, and the various scales of temporal dynamics in the microwave dielectric properties of both trees and the underlying substrate would severely limit empirical or semi-empirical approaches. As a consequence, it became necessary to develop a more profound understanding of the electromagnetic properties of a forest scene and their temporal dynamics through controlled experimentation coupled with theoretical development and verification. The concatenation of various models into a physically-based composite model treating the entire forest scene became the major objective of the study as this is the key to development of a series of robust retrieval algorithms for forest biophysical properties. In order to verify the performance of the component elements of the composite model, a series of controlled laboratory and field experiments were undertaken to: (1) develop techniques to measure the microwave dielectric properties of vegetation; (2) relate the microwave dielectric properties of vegetation to more readily measured characteristics such as density and moisture content; (3) calculate the radar cross-section of leaves, and cylinders; (4) improve backscatter models for rough surfaces; and (5) relate attenuation and phase delays during propagation through canopies to canopy properties. These modeling efforts, as validated by the measurements, were incorporated within a larger model known as the Michigan Microwave Canopy Scattering (MIMICS) Model

SIR-B measurements and modeling of vegetation

A summary is presented of the results derived from analysis of six SIR-B data takes over an agricultural test site in west central Illinois. The first part describes the procedure used to calibrate the SIR-B imagery, the second part pertains to the observed radar response to soil moisture content, and the last part examines the information derivable from multiangle observations

Long-time behaviour of degenerate diffusions: UFG-type SDEs and time-inhomogeneous hypoelliptic processes

We study the long time behaviour of a large class of diffusion processes on $R^N$, generated by second order differential operators of (possibly) degenerate type. The operators that we consider {\em need not} satisfy the H\"ormander condition. Instead, they satisfy the so-called UFG condition, introduced by Herman, Lobry and Sussman in the context of geometric control theory and later by Kusuoka and Stroock, this time with probabilistic motivations. In this paper we study UFG diffusions and demonstrate the importance of such a class of processes in several respects: roughly speaking i) we show that UFG processes constitute a family of SDEs which exhibit multiple invariant measures and for which one is able to describe a systematic procedure to determine the basin of attraction of each invariant measure (equilibrium state). ii) We use an explicit change of coordinates to prove that every UFG diffusion can be, at least locally, represented as a system consisting of an SDE coupled with an ODE, where the ODE evolves independently of the SDE part of the dynamics. iii) As a result, UFG diffusions are inherently "less smooth" than hypoelliptic SDEs; more precisely, we prove that UFG processes do not admit a density with respect to Lebesgue measure on the entire space, but only on suitable time-evolving submanifolds, which we describe. iv) We show that our results and techniques, which we devised for UFG processes, can be applied to the study of the long-time behaviour of non-autonomous hypoelliptic SDEs and therefore produce several results on this latter class of processes as well. v) Because processes that satisfy the (uniform) parabolic H\"ormander condition are UFG processes, our paper contains a wealth of results about the long time behaviour of (uniformly) hypoelliptic processes which are non-ergodic, in the sense that they exhibit multiple invariant measures.Comment: 66 page

Maximum Mass-Radius Ratio for Compact General Relativistic Objects in Schwarzschild- de Sitter Geometry

Upper limits for the mass-radius ratio are derived for arbitrary general relativistic matter distributions in the presence of a cosmological constant. General restrictions for the red shift and total energy (including the gravitational contribution) for compact objects in the Schwarzschild-de Sitter geometry are also obtained in terms of the cosmological constant and of the mean density of the star.Comment: 8 pages, no figure

Assessment of radar resolution requirements for soil moisture estimation from simulated satellite imagery

Radar simulations were performed at five-day intervals over a twenty-day period and used to estimate soil moisture from a generalized algorithm requiring only received power and the mean elevation of a test site near Lawrence, Kansas. The results demonstrate that the soil moisture of about 90% of the 20-m by 20-m pixel elements can be predicted with an accuracy of + or - 20% of field capacity within relatively flat agricultural portions of the test site. Radar resolutions of 93 m by 100 m with 23 looks or coarser gave the best results, largely because of the effects of signal fading. For the distribution of land cover categories, soils, and elevation in the test site, very coarse radar resolutions of 1 km by 1 km and 2.6 km by 3.1 km gave the best results for wet moisture conditions while a finer resolution of 93 m by 100 m was found to yield superior results for dry to moist soil conditions

A simulation study of scene confusion factors in sensing soil moisture from orbital radar

Simulated C-band radar imagery for a 124-km by 108-km test site in eastern Kansas is used to classify soil moisture. Simulated radar resolutions are 100 m by 100 m, 1 km by 1km, and 3 km by 3 km. Distributions of actual near-surface soil moisture are established daily for a 23-day accounting period using a water budget model. Within the 23-day period, three orbital radar overpasses are simulated roughly corresponding to generally moist, wet, and dry soil moisture conditions. The radar simulations are performed by a target/sensor interaction model dependent upon a terrain model, land-use classification, and near-surface soil moisture distribution. The accuracy of soil-moisture classification is evaluated for each single-date radar observation and also for multi-date detection of relative soil moisture change. In general, the results for single-date moisture detection show that 70% to 90% of cropland can be correctly classified to within +/- 20% of the true percent of field capacity. For a given radar resolution, the expected classification accuracy is shown to be dependent upon both the general soil moisture condition and also the geographical distribution of land-use and topographic relief. An analysis of cropland, urban, pasture/rangeland, and woodland subregions within the test site indicates that multi-temporal detection of relative soil moisture change is least sensitive to classification error resulting from scene complexity and topographic effects

Mesoscale monitoring of the soil freeze/thaw boundary from orbital microwave radiometry

The fundamental objectives are to test the feasibility of delineating the lateral boundary between frozen and thawed condition in the surface layer of soil from orbital microwave radiometry and secondly to examine the sensitivity of general circulation models to an explicit parameterization of the boundary condition. Physical models were developed to relate emissivity to scene properties and a simulation package was developed to predict brightness temperature as a function of emissivity and physical temperature in order to address issues of heterogeneity, scaling, and scene dynamics. Radiative transfer models were develped for both bare soil surfaces and those obscured by an intervening layer of vegetation or snow. These models relate the emissivity to the physical properties of the soil and to those of the snow or vegetation cover. A SMMR simulation package was developed to evaluate the adequacy of the emission models and the limiting effects of scaling for realistic scenarios incorporating spatially heterogeneous scenes with dynamic moisture and temperature gradients at the pixel scale

External calibration of SIR-B imagery with area-extended and point targets

Data-takes on two ascending orbits of the Shuttle Imaging Radar-B (SIR-B) over an agricultural test site in west-central Illinois were used to establish end-to-end transfer functions for conversion of the digital numbers on the 8-bit image to values of the radar backscattering coefficient sigma sup 0 (sq m/sq. m) in dB. The transfer function for each data-take was defined by the SIR-B response to an array of six calibrated point targets of known radar cross-section (transponders) and to a large number of area-extended targets also with known radar cross-section as measured by externally calibrated, truck-mounted scatterometers. The radar cross-section of each transponder at the SIR-B center frequency was measured on an antenna range as a function of local angle of incidence. Two truck-mounted scatterometers observed 20 to 80 agricultural fields daily at 1.6 GHz with HH polarization and at azimuth viewing angles and incidence angles equivalent to those of the SIR-B. The form of the transfer function is completely defined by the SIR-B receiver and the incoherent averaging procedure incorporated into production of the standard SIR-B image product

Kohn-Sham Exchange Potential for a Metallic Surface

The behavior of the surface barrier that forms at the metal-vacuum interface is important for several fields of surface science. Within the Density Functional Theory framework, this surface barrier has two non-trivial components: exchange and correlation. Exact results are provided for the exchange component, for a jellium metal-vacuum interface, in a slab geometry. The Kohn-Sham exact-exchange potential $V_{x}(z)$ has been generated by using the Optimized Effective Potential method, through an accurate numerical solution, imposing the correct boundary condition. It has been proved analytically, and confirmed numerically, that $V_{x}(z\to \infty)\to - e^{2}/z$; this conclusion is not affected by the inclusion of correlation effects. Also, the exact-exchange potential develops a shoulder-like structure close to the interface, on the vacuum side. The issue of the classical image potential is discussed.Comment: Phys. Rev. Lett. (to appear

Multipole strength function of deformed superfluid nuclei made easy

We present an efficient method for calculating strength functions using the finite amplitude method (FAM) for deformed superfluid heavy nuclei within the framework of the nuclear density functional theory. We demonstrate that FAM reproduces strength functions obtained with the fully self-consistent quasi-particle random-phase approximation (QRPA) at a fraction of computational cost. As a demonstration, we compute the isoscalar and isovector monopole strength for strongly deformed configurations in $^{240}$Pu by considering huge quasi-particle QRPA spaces. Our approach to FAM, based on Broyden's iterative procedure, opens the possibility for large-scale calculations of strength distributions in well-bound and weakly bound nuclei across the nuclear landscape.Comment: 5 pages, 3 figure