Comparing Methods for Interpolation to Improve Raster Digital Elevation Models

Digital elevation models (DEMs) are available as raster files at 100m, 30m, and 10m resolutions for the contiguous United States and are used in a variety of geographic analyses. Some projects may require a finer resolution. GIS software offers many options for interpolating data to higher resolutions. We compared ten interpolation methods using 10m sample data from the Ouachita Mountains in central Arkansas. We interpolated the 10m DEM to 5m, 2.5m, and 1m resolutions and compared the absolute mean difference (AMD) for each using surveyed control points. Overall, there was little difference in the accuracy between interpolation methods at the resolutions tested and minimal departure from the original 10m raster

Two-moment scheme for general-relativistic radiation hydrodynamics: a systematic description and new applications

We provide a systematic description of the steps necessary -- and of the potential pitfalls to be encountered -- when implementing a two-moment scheme within an Implicit-Explicit (IMEX) scheme to include radiative-transfer contributions in numerical simulations of general-relativistic (magneto-)hydrodynamics. We make use of the M1 closure, which provides an exact solution for the optically thin and thick limit, and an interpolation between these limits. Special attention is paid to the efficient solution of the emerging set of implicit conservation equations. In particular, we present an efficient method for solving these equations via the inversion of a $4\times 4$-matrix within an IMEX scheme. While this method relies on a few approximations, it offers a very good compromise between accuracy and computational efficiency. After a large number of tests in special relativity, we couple our new radiation code, \texttt{FRAC}, with the general-relativistic magnetohydrodynamics code \texttt{BHAC} to investigate the radiative Michel solution, namely, the problem of spherical accretion onto a black hole in the presence of a radiative field. By performing the most extensive exploration of the parameter space for this problem, we find that the accretion's efficiency can be expressed in terms of physical quantities such as temperature, $T$, luminosity, $L$, and black-hole mass, $M$, via the expression $\varepsilon=(L/L_{\rm Edd})/(\dot{M}/\dot{M}_{\rm Edd})= 7.41\times 10^{-7}\left(T/10^6\,\mathrm{K}\right)^{0.22} \left(L/L_\odot\right)^{0.48} \left(M/M_\odot\right)^{0.48}$, where $L_{\mathrm{Edd}}$ and $\dot{M}_{\mathrm{Edd}}$ are the Eddington luminosity and accretion rate, respectively. Finally, we also consider the accretion problem away from spherical symmetry, finding that the solution is stable under perturbations in the radiation field.Comment: 22 pages, 15 figures, matches version accepted to MNRA

Impervious Surface Area Change in Arkansas from 2001 to 2006

Impervious Surface Area (ISA) is a measurement used to determine stream quality as well as urban sprawl. ISA was calculated as part of the National Land Cover Dataset (NLCD) using Landsat imagery by the Multi-Resolution Land Characteristics Consortium (MRLC) in both 2001 and 2006. ISA for each of the 75 counties in Arkansas was taken from the NLCD for both 2001 and 2006. Using the ISA data, percent imperviousness was determined for each county in each time period as well as the difference between the two periods. These data were also compared to census projections for the two time periods as well as the difference between them. The differences between percent ISA change and census change were compared to determine consistency

Accuracy and User Variation Associated with Slope Measurement Using a Laser Hypsometer

Slope measurements are often necessary for assessing features and processes within the natural environment. Land managers often use handheld equipment rather than more complicated surveying equipment in order to measure slopes and to conduct field work efficiently. One type of handheld device used to measure slope is a laser clinometer. In order to determine the accuracy and user error associated with this type of clinometer, slope measurements were taken at multiple locations using two types of equipment: 1) a Haglof Sweden Vertex III Hypsometer with a laser clinometer function and 2) a Topcon GTS-603/AF electronic survey total station which can measure elevations and distances to an accuracy of ± 2mm. Slope measurements were compared among the four Vertex III clinometer users in order to determine the variation associated with each user. Also slopes determined by the clinometer were compared to those determined by Topcon GTS-603/AF in order to assess the accuracy of the clinometer. Slopes measured by the laser clinometer users were not significantly different (=0.05) than those measured using the total station, and the differences on average between the laser clinometer and the total station slopes were less than one percent slope for all clinometer observers

Beyond moments: relativistic Lattice-Boltzmann methods for radiative transport in computational astrophysics

We present a new method for the numerical solution of the radiative-transfer equation (RTE) in multidimensional scenarios commonly encountered in computational astrophysics. The method is based on the direct solution of the Boltzmann equation via an extension of the Lattice Boltzmann (LB) equation and allows to model the evolution of the radiation field as it interacts with a background fluid, via absorption, emission, and scattering. As a first application of this method, we restrict our attention to a frequency independent ("grey") formulation within a special-relativistic framework, which can be employed also for classical computational astrophysics. For a number of standard tests that consider the performance of the method in optically thin, optically thick and intermediate regimes with a static fluid, we show the ability of the LB method to produce accurate and convergent results matching the analytic solutions. We also contrast the LB method with commonly employed moment-based schemes for the solution of the RTE, such as the M1 scheme. In this way, we are able to highlight that the LB method provides the correct solution for both non-trivial free-streaming scenarios and the intermediate optical-depth regime, for which the M1 method either fails or provides inaccurate solutions. When coupling to a dynamical fluid, on the other hand, we present the first self-consistent solution of the RTE with LB methods within a relativistic-hydrodynamic scenario. Finally, we show that besides providing more accurate results in all regimes, the LB method features smaller or comparable computational costs compared to the M1 scheme.Comment: 22 pages, 16 figures, matches version accepted in MNRA