Evaluating skills and issues of quantile-based bias adjustment for climate change scenarios

Daily meteorological data such as temperature or precipitation from climate models are needed for many climate impact studies, e.g., in hydrology or agriculture, but direct model output can contain large systematic errors. A large variety of methods exist to adjust the bias of climate model outputs. Here we review existing statistical bias-adjustment methods and their shortcomings, and compare quantile mapping (QM), scaled distribution mapping (SDM), quantile delta mapping (QDM) and an empiric version of PresRAT (PresRATe). We then test these methods using real and artificially created daily temperature and precipitation data for Austria. We compare the performance in terms of the following demands: (1) the model data should match the climatological means of the observational data in the historical period; (2) the long-term climatological trends of means (climate change signal), either defined as difference or as ratio, should not be altered during bias adjustment; and (3) even models with too few wet days (precipitation above 0.1 mm) should be corrected accurately, so that the wet day frequency is conserved. QDM and PresRATe combined fulfill all three demands. For (2) for precipitation, PresRATe already includes an additional correction that assures that the climate change signal is conserved.</p

AMR, stability and higher accuracy

Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the combination, that is a higher order accurate adaptive scheme. This combines the power that adaptive gridding techniques provide to resolve fine scales (in addition to a more efficient use of resources) together with the higher accuracy furnished by higher order schemes when the solution is adequately resolved. To define a convenient higher order adaptive mesh refinement scheme, we discuss a few different modifications of the standard, second order accurate approach of Berger and Oliger. Applying each of these methods to a simple model problem, we find these options have unstable modes. However, a novel approach to dealing with the grid boundaries introduced by the adaptivity appears stable and quite promising for the use of high order operators within an adaptive framework

The discrete energy method in numerical relativity: Towards long-term stability

The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete system can be used to construct stable finite difference equations for these problems at the linear level. In this paper we apply these techniques to some test problems commonly used in numerical relativity and observe that while we obtain convergent schemes, fast growing modes, or ``artificial instabilities,'' contaminate the solution. We find that these growing modes can partially arise from the lack of a Leibnitz rule for discrete derivatives and discuss ways to limit this spurious growth.Comment: 18 pages, 22 figure

Hamiltonian Relaxation

Due to the complexity of the required numerical codes, many of the new formulations for the evolution of the gravitational fields in numerical relativity are not tested on binary evolutions. We introduce in this paper a new testing ground for numerical methods based on the simulation of binary neutron stars. This numerical setup is used to develop a new technique, the Hamiltonian relaxation (HR), that is benchmarked against the currently most stable simulations based on the BSSN method. We show that, while the length of the HR run is somewhat shorter than the equivalent BSSN simulation, the HR technique improves the overall quality of the simulation, not only regarding the satisfaction of the Hamiltonian constraint, but also the behavior of the total angular momentum of the binary. The latest quantity agrees well with post-Newtonian estimations for point-mass binaries in circular orbits.Comment: More detailed description of the numerical implementation added and some typos corrected. Version accepted for publication in Class. and Quantum Gravit

First Results From The Taiwanese-American Occultation Survey (TAOS)

Results from the first two years of data from the Taiwanese-American Occultation Survey (TAOS) are presented. Stars have been monitored photometrically at 4 Hz or 5 Hz to search for occultations by small (~3 km) Kuiper Belt Objects (KBOs). No statistically significant events were found, allowing us to present an upper bound to the size distribution of KBOs with diameters 0.5 km < D < 28 km.Comment: 5 pages, 5 figure, accepted in Ap

The Taiwanese-American Occultation Survey: The Multi-Telescope Robotic Observatory

The Taiwanese-American Occultation Survey (TAOS) operates four fully automatic telescopes to search for occultations of stars by Kuiper Belt Objects. It is a versatile facility that is also useful for the study of initial optical GRB afterglows. This paper provides a detailed description of the TAOS multi-telescope system, control software, and high-speed imaging.Comment: 11 pages, 11 figure

On "many black hole" space-times

We analyze the horizon structure of families of space times obtained by evolving initial data sets containing apparent horizons with several connected components. We show that under certain smallness conditions the outermost apparent horizons will also have several connected components. We further show that, again under a smallness condition, the maximal globally hyperbolic development of the many black hole initial data constructed by Chrusciel and Delay, or of hyperboloidal data of Isenberg, Mazzeo and Pollack, will have an event horizon, the intersection of which with the initial data hypersurface is not connected. This justifies the "many black hole" character of those space-times.Comment: several graphic file

The TAOS Project: Statistical Analysis of Multi-Telescope Time Series Data

The Taiwanese-American Occultation Survey (TAOS) monitors fields of up to ~1000 stars at 5 Hz simultaneously with four small telescopes to detect occultation events from small (~1 km) Kuiper Belt Objects (KBOs). The survey presents a number of challenges, in particular the fact that the occultation events we are searching for are extremely rare and are typically manifested as slight flux drops for only one or two consecutive time series measurements. We have developed a statistical analysis technique to search the multi-telescope data set for simultaneous flux drops which provides a robust false positive rejection and calculation of event significance. In this paper, we describe in detail this statistical technique and its application to the TAOS data set.Comment: 15 pages, 14 figures. Submitted to PAS

Towards absorbing outer boundaries in General Relativity

We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations on a subset of flat spacetime of the form [0,T] x B_R, where B_R is a ball of radius R, and analyze different kinds of boundary conditions on \partial B_R. Our main results are: i) We give an explicit analytic example showing that boundary conditions obtained from freezing the incoming characteristic fields to their initial values are not compatible with the constraints. ii) With the help of the exact solutions constructed, we determine the amount of artificial reflection of gravitational radiation from constraint-preserving boundary conditions which freeze the Weyl scalar Psi_0 to its initial value. For monochromatic radiation with wave number k and arbitrary angular momentum number l >= 2, the amount of reflection decays as 1/(kR)^4 for large kR. iii) For each L >= 2, we construct new local constraint-preserving boundary conditions which perfectly absorb linearized radiation with l <= L. (iv) We generalize our analysis to a weakly curved background of mass M, and compute first order corrections in M/R to the reflection coefficients for quadrupolar odd-parity radiation. For our new boundary condition with L=2, the reflection coefficient is smaller than the one for the freezing Psi_0 boundary condition by a factor of M/R for kR > 1.04. Implications of these results for numerical simulations of binary black holes on finite domains are discussed.Comment: minor revisions, 30 pages, 6 figure