The Formal Underpinnings of the Response Functions used in X-Ray Spectral Analysis

This work provides an in-depth mathematical description of the response functions that are used for spatial and spectral analysis of X-ray data. The use of such functions is well-known to anyone familiar with the analysis of X-ray data where they may be identified with the quantities contained in the Ancillary Response File (ARF), the Redistribution Matrix File (RMF), and the Exposure Map. Starting from first-principles, explicit mathematical expressions for these functions, for both imaging and dispersive modes, are arrived at in terms of the underlying instrumental characteristics of the telescope including the effects of pointing motion. The response functions are presented in the context of integral equations relating the expected detector count rate to the source spectrum incident upon the telescope. Their application to the analysis of several source distributions is considered. These include multiple, possibly overlapping, and spectrally distinct point sources, as well as extended sources. Assumptions and limitations behind the usage of these functions, as well as their practical computation are addressed.Comment: 22 pages, 3 figures (LaTeX

Res Ipsa Loquitur: Reducing Confusion of Creating Bias?

The so-called doctrine of res ipsa loquitur has been a mystery since its birth more than a century ago. This Article helps solve the mystery. In practical effect, res ipsa loquirtur, though usually thought of as a tort doctrine, functions as a rule of trial practice that allows jurors to rely on circumstantial evidence surrounding an accident to find the defendant liable. Standard jury instructions in negligence cases, however, fail to inform jurors that they are permitted to rely upon circumstantial evidence in reaching a verdict. Why, then, is another, more specific circumstantial evidence charge necessary or desirable? We describe and evaluate the arguments that have been made in support of and in opposition to the res ipsa instruction. One theory is that jurors are confused in performing their task when given only standard instructions; the charge, therefore, clarifies their task, thereby improving the quality of their decisionmaking. A competing theory is that the instruction biases jurors in favor of plaintiffs, thereby degrading the quality of the decisionmaking. Our theoretical analysis concludes that the boas explanation is stronger. We reach this conclusion by applying for the first-time modern learning on cognition to the res ipsa instruction. To support our theoretical conclusion, we report the results of experiments designed o determine the effects of the instruction. All these experiments were intended first to confirm that the res ipsa instruction has an effect and second to confirm or refute our theoretical conclusion that the instruction biases rather than clarifies. While the empirical results did not demonstrate bias, they also failed to show the absence of bias. Moreover, we found no evidence that the instruction reduces confusion. Our conclusion is that the charge has no positive effect, and either may create a bias or, at best, is meaningless

Demand for Environmental Goods: Evidence from Voting Patterns on California Initiatives

This paper studies voting behavior on 16 environmental ballot propositions in California in order to characterize the demand for environmental goods. The environment is found to be a normal good for people with mean incomes, but some environmental goods are inferior for people with high incomes, at least when supplied collectively. An important "price" of environmental goods is reduced income in the construction, farming, forestry, and manufacturing industries. In most cases, income and price can explain most of the variation in voting; it is not essential to introduce non-economic concepts such as ideology and politics

Environmental snapshots from ACE‐Asia

On five occasions spanning the Asian Pacific Regional Aerosol Characterization Experiment (ACE‐Asia) field campaign in spring 2001, the Multiangle Imaging Spectroradiometer spaceborne instrument took data coincident with high‐quality observations by instruments on two or more surface and airborne platforms. The cases capture a range of clean, polluted, and dusty aerosol conditions. With a three‐stage optical modeling process, we synthesize the data from over 40 field instruments into layer‐by‐layer environmental snapshots that summarize what we know about the atmospheric and surface states at key locations during each event. We compare related measurements and discuss the implications of apparent discrepancies, at a level of detail appropriate for satellite retrieval algorithm and aerosol transport model validation. Aerosols within a few kilometers of the surface were composed primarily of pollution and Asian dust mixtures, as expected. Medium‐ and coarse‐mode particle size distributions varied little among the events studied; however, column aerosol optical depth changed by more than a factor of 4, and the near‐surface proportion of dust ranged between 25% and 50%. The amount of absorbing material in the submicron fraction was highest when near‐surface winds crossed Beijing and the Korean Peninsula and was considerably lower for all other cases. Having simultaneous single‐scattering albedo measurements at more than one wavelength would significantly reduce the remaining optical model uncertainties. The consistency of component particle microphysical properties among the five events, even in this relatively complex aerosol environment, suggests that global, satellite‐derived maps of aerosol optical depth and aerosol mixture (air‐mass‐type) extent, combined with targeted in situ component microphysical property measurements, can provide a detailed global picture of aerosol behavior

Scientific Objectives, Measurement Needs, and Challenges Motivating the PARAGON Aerosol Initiative

Aerosols are involved in a complex set of processes that operate across many spatial and temporal scales. Understanding these processes, and ensuring their accurate representation in models of transport, radiation transfer, and climate, requires knowledge of aerosol physical, chemical, and optical properties and the distributions of these properties in space and time. To derive aerosol climate forcing, aerosol optical and microphysical properties and their spatial and temporal distributions, and aerosol interactions with clouds, need to be understood. Such data are also required in conjunction with size-resolved chemical composition in order to evaluate chemical transport models and to distinguish natural and anthropogenic forcing. Other basic parameters needed for modeling the radiative influences of aerosols are surface reflectivity and three-dimensional cloud fields. This large suite of parameters mandates an integrated observing and modeling system of commensurate scope. The Progressive Aerosol Retrieval and Assimilation Global Observing Network (PARAGON) concept, designed to meet this requirement, is motivated by the need to understand climate system sensitivity to changes in atmospheric constituents, to reduce climate model uncertainties, and to analyze diverse collections of data pertaining to aerosols. This paper highlights several challenges resulting from the complexity of the problem. Approaches for dealing with them are offered in the set of companion papers

Environmental snapshots from ACE-Asia

On five occasions spanning the Asian Pacific Regional Aerosol Characterization Experiment (ACE-Asia) field campaign in spring 2001, the Multiangle Imaging Spectroradiometer spaceborne instrument took data coincident with high-quality observations by instruments on two or more surface and airborne platforms. The cases capture a range of clean, polluted, and dusty aerosol conditions. With a three-stage optical modeling process, we synthesize the data from over 40 field instruments into layer-by-layer environmental snapshots that summarize what we know about the atmospheric and surface states at key locations during each event. We compare related measurements and discuss the implications of apparent discrepancies, at a level of detail appropriate for satellite retrieval algorithm and aerosol transport model validation. Aerosols within a few kilometers of the surface were composed primarily of pollution and Asian dust mixtures, as expected. Medium- and coarse-mode particle size distributions varied little among the events studied; however, column aerosol optical depth changed by more than a factor of 4, and the near-surface proportion of dust ranged between 25% and 50%. The amount of absorbing material in the submicron fraction was highest when near-surface winds crossed Beijing and the Korean Peninsula and was considerably lower for all other cases. Having simultaneous single-scattering albedo measurements at more than one wavelength would significantly reduce the remaining optical model uncertainties. The consistency of component particle microphysical properties among the five events, even in this relatively complex aerosol environment, suggests that global, satellite-derived maps of aerosol optical depth and aerosol mixture (air-mass-type) extent, combined with targeted in situ component microphysical property measurements, can provide a detailed global picture of aerosol behavior