Asymmetric Hillslope Erosion Following Wildfire in Fourmile Canyon, Colorado

Infrequent, high-magnitude events cause a disproportionate amount of sediment transport on steep hillslopes, but few quantitative data are available that capture these processes. Here we study the influence of wildfire and hillslope aspect on soil erosion in Fourmile Canyon, Colorado. This region experienced the Fourmile Fire of 2010, strong summer convective storms in 2011 and 2012, and extreme flooding in September 2013. We sampled soils shortly after these events and use fallout radionuclides to trace erosion on polar- and equatorial-facing burned slopes and on a polar-facing unburned slope. Because these radionuclides are concentrated in the upper decimeter of soil, soil inventories are sensitive to erosion by surface runoff. The polar-facing burned slope had significantly lower cesium-137 (137Cs) and lead-210 (210Pb) inventories (p \u3c 0.05) than either the polar-facing unburned slope or equatorial-facing burned slope. Local slope magnitude does not appear to control the erosional response to wildfire, as relatively gently sloping (~20%) polar-facing positions were severely eroded in the most intensively burned area. Field evidence and soil profile analyses indicate up to 4 cm of local soil erosion on the polar-facing burned slope, but radionuclide mass balance indicates that much of this was trapped nearby. Using a 137Cs-based erosion model, we find that the burned polar-facing slope had a net mean sediment loss of 2 mm (~1 kg m−2) over a one to three year period, which is one to two orders of magnitude higher than longer-term erosion rates reported for this region. In this part of the Colorado Front Range, strong hillslope asymmetry controls soil moisture and vegetation; polar-facing slopes support significantly denser pine and fir stands, which fuels more intense wildfires. We conclude that polar-facing slopes experience the most severe surface erosion following wildfires in this region, indicating that landscape-scale aridity can control the geomorphic response of hillslopes to wildfires. Copyright © 2018 John Wiley & Sons, Ltd

The Evolution of Distorted Rotating Black Holes II: Dynamics and Analysis

We have developed a numerical code to study the evolution of distorted, rotating black holes. This code is used to evolve a new family of black hole initial data sets corresponding to distorted ``Kerr'' holes with a wide range of rotation parameters, and distorted Schwarzschild black holes with odd-parity radiation. Rotating black holes with rotation parameters as high as $a/m=0.87$ are evolved and analyzed in this paper. The evolutions are generally carried out to about $t=100M$, where $M$ is the ADM mass. We have extracted both the even- and odd-parity gravitational waveforms, and find the quasinormal modes of the holes to be excited in all cases. We also track the apparent horizons of the black holes, and find them to be a useful tool for interpreting the numerical results. We are able to compute the masses of the black holes from the measurements of their apparent horizons, as well as the total energy radiated and find their sum to be in excellent agreement with the ADM mass.Comment: 26 pages, LaTeX with RevTeX 3.0 macros. 27 uuencoded gz-compressed postscript figures. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/ Submitted to Physical Review

Adaptive computation of gravitational waves from black hole interactions

We construct a class of linear partial differential equations describing general perturbations of non-rotating black holes in 3D Cartesian coordinates. In contrast to the usual approach, a single equation treats all radiative $\ell -m$ modes simultaneously, allowing the study of wave perturbations of black holes with arbitrary 3D structure, as would be present when studying the full set of nonlinear Einstein equations describing a perturbed black hole. This class of equations forms an excellent testbed to explore the computational issues of simulating black spacetimes using a three dimensional adaptive mesh refinement code. Using this code, we present results from the first fully resolved 3D solution of the equations describing perturbed black holes. We discuss both fixed and adaptive mesh refinement, refinement criteria, and the computational savings provided by adaptive techniques in 3D for such model problems of distorted black holes.Comment: 16 Pages, RevTeX, 13 figure

Dynamics of Gravitational Waves in 3D: Formulations, Methods, and Tests

The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge degrees of freedom. Using gravitational waves with amplitudes low enough that one has a good understanding of the physics involved, but large enough to enable non-linear effects to emerge, we study the coupling between numerical errors, coordinate effects, and the nonlinearities of the theory. We discuss the various strategies used in identifying specific features of the evolution. We show the importance of the flexibility of being able to use different numerical schemes, different slicing conditions, different formulations of the Einstein equations (standard ADM vs. first order hyperbolic), and different sets of equations (linearized vs. full Einstein equations). A non-linear scalar field equation is presented which captures some properties of the full Einstein equations, and has been useful in our understanding of the coupling between finite differencing errors and non-linearites. We present a set of monitoring devices which have been crucial in our studying of the waves, including Riemann invariants, pseudo-energy momentum tensor, hamiltonian constraint violation, and fourier spectrum analysis.Comment: 34 pages, 14 figure

Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity

We study the stability properties of the standard ADM formulation of the 3+1 evolution equations of general relativity through linear perturbations of flat spacetime. We focus attention on modes with zero speed of propagation and conjecture that they are responsible for instabilities encountered in numerical evolutions of the ADM formulation. These zero speed modes are of two kinds: pure gauge modes and constraint violating modes. We show how the decoupling of the gauge by a conformal rescaling can eliminate the problem with the gauge modes. The zero speed constraint violating modes can be dealt with by using the momentum constraints to give them a finite speed of propagation. This analysis sheds some light on the question of why some recent reformulations of the 3+1 evolution equations have better stability properties than the standard ADM formulation.Comment: 15 pages, 9 figures. Added a new section, plus incorporated many comments made by refere

The Head-On Collision of Two Equal Mass Black Holes Peter Anninos

We study the head-on collision of two equal mass, nonrotating black holes. Various initial configurations are investigated, including holes which are initially surrounded by a common apparent horizon to holes that are separated by about $20M$, where $M$ is the mass of a single black hole. We have extracted both $\ell = 2$ and $\ell=4$ gravitational waveforms resulting from the collision. The normal modes of the final black hole dominate the spectrum in all cases studied. The total energy radiated is computed using several independent methods, and is typically less than $0.002 M$. We also discuss an analytic approach to estimate the total gravitational radiation emitted in the collision by generalizing point particle dynamics to account for the finite size and internal dynamics of the two black holes. The effects of the tidal deformations of the horizons are analysed using the membrane paradigm of black holes. We find excellent agreement between the numerical results and the analytic estimates.Comment: 33 pages, NCSA 94-048, WUGRAV-94-

The Evolution of Distorted Rotating Black Holes III: Initial Data

In this paper we study a new family of black hole initial data sets corresponding to distorted ``Kerr'' black holes with moderate rotation parameters, and distorted Schwarzschild black holes with even- and odd-parity radiation. These data sets build on the earlier rotating black holes of Bowen and York and the distorted Brill wave plus black hole data sets. We describe the construction of this large family of rotating black holes. We present a systematic study of important properties of these data sets, such as the size and shape of their apparent horizons, and the maximum amount of radiation that can leave the system during evolution. These data sets should be a very useful starting point for studying the evolution of highly dynamical black holes and can easily be extended to 3D.Comment: 16 page

Event Horizons in Numerical Relativity II: Analyzing the Horizon

We present techniques and methods for analyzing the dynamics of event horizons in numerically constructed spacetimes. There are three classes of analytical tools we have investigated. The first class consists of proper geometrical measures of the horizon which allow us comparison with perturbation theory and powerful global theorems. The second class involves the location and study of horizon generators. The third class includes the induced horizon 2-metric in the generator comoving coordinates and a set of membrane-paradigm like quantities. Applications to several distorted, rotating, and colliding black hole spacetimes are provided as examples of these techniques.Comment: 23 double column pages including 28 figures. Higher quality figures (big size!) available upon request (jmasso OR [email protected]