The Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission will provide a calibration laboratory in orbit for the purpose of accurately measuring and attributing climate change. CLARREO measurements establish new climate change benchmarks with high absolute radiometric accuracy and high statistical confidence across a wide range of essential climate variables. CLARREO's inherently high absolute accuracy will be verified and traceable on orbit to Système Internationale (SI) units. The benchmarks established by CLARREO will be critical for assessing changes in the Earth system and climate model predictive capabilities for decades into the future as society works to meet the challenge of optimizing strategies for mitigating and adapting to climate change. The CLARREO benchmarks are derived from measurements of the Earth's thermal infrared spectrum (5–50 μm), the spectrum of solar radiation reflected by the Earth and its atmosphere (320–2300 nm), and radio occultation refractivity from which accurate temperature profiles are derived. The mission has the ability to provide new spectral fingerprints of climate change, as well as to provide the first orbiting radiometer with accuracy sufficient to serve as the reference transfer standard for other space sensors, in essence serving as a “NIST [National Institute of Standards and Technology] in orbit.” CLARREO will greatly improve the accuracy and relevance of a wide range of space-borne instruments for decadal climate change. Finally, CLARREO has developed new metrics and methods for determining the accuracy requirements of climate observations for a wide range of climate variables and uncertainty sources. These methods should be useful for improving our understanding of observing requirements for most climate change observations

Kane's method is a well-established approach to the formulation of the equations of motions of complex multibody mechanical systems. This method is systematic and clearly presented in the now famous book, Dynamics: Theory and Applications, by Kane and Levinson [1]. The present book, Dynamics: Theory and Application of Kane's Method, borrows material mostly from the original book of Kane and Levinson [1] and to a lesser extent, from the book, Spacecraft Dynamics, by Kane et al. [2]. New material and minor revisions contributed by Roithmayr and Hodges are distributed throughout the text. The book is a timely and welcome update of the work of Kane and Levinson, provides coverage of a broader class of problems, and presents recent advances in the field.The book's layout follows closely that of the original work of Kane and Levinson. Special emphasis is given to the topic of constraints because classical approaches and Kane's method treat this topic differently. Furthermore, the treatment of motion constraints has been expanded to focus on the forces and torques required to enforce such constraints exactly. The chapter dealing with the extraction of information from the equation of motion has also been augmented to include the checking function, which can be constructed even when an energy integral does not exist. The material presented in the last chapter, which deals with the manipulation of finite rotation, is largely drawn from the book Spacecraft Dynamics [2] with the exception of the first two sections that present the Wiener-Milenković parameters.This book covers material presented in graduate-level courses in physics or mechanical and aerospace engineering. A typical course could be either a first-year graduate course in dynamics or a follow-up course, if the first-year introductory course is based on the classical treatment of dynamics. The coverage focuses on rigid multibody systems, such as spacecraft, robotic manipulators, or articulated mechanisms. From the onset of the presentation, a specific notation is introduced that emphasizes frames of reference, regarded as massless rigid bodies. Constraints are introduced early on: both holonomic and nonholonomic constraints are treated in a unified manner. Rather than enforcing constraints via the classical Lagrange multiplier technique, Kane's equations are used as the basis of the formulation.The book addresses the relevant topics in a sequential manner. After a review of basic calculus techniques in the first chapter, the kinematics of rigid bodies is presented, followed by the discussion of configuration and motion constraints. Mass distribution and generalized forces are presented next. Constraint forces and torques are discussed in an independent chapter. After a discussion of energy functions, the derivation of the equations of motion is presented, and the procedures for extracting information from these equations of motion are developed. The final chapter of the book is devoted to the representation of finite rotation.Over one-quarter of the book is devo...

A concise method has been formulated for identifying a set of forces needed to constrain the behavior of a mechanical system, modeled as a set of particles and rigid bodies, when it is subject to motion constraints described by nonholonomic equations that are inherently nonlinear in velocity. An expression in vector form is obtained for each force; a direction is determined, together with the point of application. This result is a consequence of expressing constraint equations in terms of dot products of vectors rather than in the usual way, which is entirely in terms of scalars and matrices. The constraint forces in vector form are used together with two new analytical approaches for deriving equations governing motion of a system subject to such constraints. If constraint forces are of interest they can be brought into evidence in explicit dynamical equations by employing the well-known nonholonomic partial velocities associated with Kane's method; if they are not of interest, equations can be formed instead with the aid of vectors introduced here as nonholonomic partial accelerations. When the analyst requires only the latter, smaller set of equations, they can be formed directly; it is not necessary to expend the labor to form the former, larger set first and subsequently perform matrix multiplications.

The implementation of the Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission was recommended by the National Research Council in 2007 to provide an on-orbit intercalibration standard with accuracy of 0.3% (k = 2) for relevant Earth observing sensors. The goal of reference intercalibration, as established in the Decadal Survey, is to enable rigorous high-accuracy observations of critical climate change parameters, including reflected broadband radiation [Clouds and Earth's Radiant Energy System (CERES)], cloud properties [Visible Infrared Imaging Radiometer Suite (VIIRS)], and changes in surface albedo, including snow and ice albedo feedback. In this paper, we describe the CLARREO approach for performing intercalibration on orbit in the reflected solar (RS) wavelength domain. It is based on providing highly accurate spectral reflectance and reflected radiance measurements from the CLARREO Reflected Solar Spectrometer (RSS) to establish an on-orbit reference for existing sensors, namely, CERES and VIIRS on Joint Polar Satellite System satellites, Advanced Very High Resolution Radiometer and follow-on imagers on MetOp,Landsat imagers, and imagers on geostationary platforms. One of two fundamental CLARREO mission goals is to provide sufficient sampling of high-accuracy observations that are matched in time, space, and viewing angles with measurements made by existing instruments, to a degree that overcomes the random error sources from imperfect data matching and instrument noise. The data matching is achieved through CLARREO RSS pointing operations on orbit that align its line of sight with the intercalibrated sensor. These operations must be planned in advance; therefore, intercalibration events must be predicted by orbital modeling. If two competing opportunities are identified, one target sensor must be given priority over the other. The intercalibration method is to monitor changes in targeted sensor response function parameters: effective offset, gain, nonlinearity, optics spectral response, and sensitivity to polarization. In this paper, we use existing satellite data and orbital simulation methods to determine mission requirements for CLARREO, its instrument pointing ability, methodology, and needed intercalibration sampling and data matching for accurate intercalibration of RS radiation sensors on orbit.

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