The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

Extended cusp-like regions and their dependence on the Polar orbit, seasonal variations, and interplanetary conditions

Extended cusp-like regions (ECRs) are surveyed, as observed by the Magnetospheric Ion Composition Sensor (MICS) of the Charge and Mass Magnetospheric Ion Composition Experiment (CAMMICE) instrument aboard Polar between 1996 and 1999. The first of these ECR events was observed on 29 May 1996, an event widely discussed in the literature and initially thought to be caused by tail lobe reconnection due to the coinciding prolonged interval of strong northward IMF. ECRs are characterized here by intense fluxes of magnetosheath-like ions in the energy-per-charge range of _1 to 10 keV e_1. We investigate the concurrence of ECRs with intervals of prolonged (lasting longer than 1 and 3 hours) orientations of the IMF vector and high solar wind dynamic pressure (PSW). Also investigated is the opposite concurrence, i.e., of the IMF and high PSW with ECRs. (Note that these surveys are asking distinctly different questions.) The former survey indicates that ECRs have no overall preference for any orientation of the IMF. However, the latter survey reveals that during northward IMF, particularly when accompanied by high PSW, ECRs are more likely. We also test for orbital and seasonal effects revealing that Polar has to be in a particular region to observe ECRs and that they occur more frequently around late spring. These results indicate that ECRs have three distinct causes and so can relate to extended intervals in (1) the cusp on open field lines, (2) the magnetosheath, and (3) the magnetopause indentation at the cusp, with the latter allowing magnetosheath plasma to approach close to the Earth without entering the magnetosphere.

Sampling uncertainties in surface radiation budget calculations in RADAGAST

In the Radiative Atmospheric Divergence Using ARM Mobile Facility GERB and AMMA Stations (RADAGAST) project we calculate the divergence of radiative flux across the atmosphere by comparing fluxes measured at each end of an atmospheric column above Niamey, in the African Sahel region. The combination of broadband flux measurements from geostationary orbit and the deployment for over 12 months of a comprehensive suite of active and passive instrumentation at the surface eliminates a number of sampling issues that could otherwise affect divergence calculations of this sort. However, one sampling issue that challenges the project is the fact that the surface flux data are essentially measurements made at a point, while the top-of-atmosphere values are taken over a solid angle that corresponds to an area at the surface of some 2500 km2. Variability of cloud cover and aerosol loading in the atmosphere mean that the downwelling fluxes, even when averaged over a day, will not be an exact match to the area-averaged value over that larger area, although we might expect that it is an unbiased estimate thereof. The heterogeneity of the surface, for example, fixed variations in albedo, further means that there is a likely systematic difference in the corresponding upwelling fluxes. In this paper we characterize and quantify this spatial sampling problem. We bound the root-mean-square error in the downwelling fluxes by exploiting a second set of surface flux measurements from a site that was run in parallel with the main deployment. The differences in the two sets of fluxes lead us to an upper bound to the sampling uncertainty, and their correlation leads to another which is probably optimistic as it requires certain other conditions to be met. For the upwelling fluxes we use data products from a number of satellite instruments to characterize the relevant heterogeneities and so estimate the systematic effects that arise from the flux measurements having to be taken at a single point. The sampling uncertainties vary with the season, being higher during the monsoon period. We find that the sampling errors for the daily average flux are small for the shortwave irradiance, generally less than 5 W m−2, under relatively clear skies, but these increase to about 10 W m−2 during the monsoon. For the upwelling fluxes, again taking daily averages, systematic errors are of order 10 W m−2 as a result of albedo variability. The uncertainty on the longwave component of the surface radiation budget is smaller than that on the shortwave component, in all conditions, but a bias of 4 W m−2 is calculated to exist in the surface leaving longwave flux.

Estimating surface CO2 fluxes from space-borne dry air mole fraction observations using an Ensemble Kalman filter

We have developed an ensemble Kalman Filter (EnKF) to estimate 8-day regional surface fluxes of CO2 from space-borne CO2 dry-air mole fraction observations (XCO2) and evaluate the approach using a series of synthetic experiments, in preparation for data from the NASA Orbiting Carbon Observatory (OCO). The 32-day duty cycle of OCO alternates every 16 days between nadir and glint measurements of backscattered solar radiation at short-wave infrared wavelengths. The EnKF uses an ensemble of states to represent the error covariances to estimate 8-day CO2 surface fluxes over 144 geographical regions. We use a 12×8-day lag window, recognising that XCO2 measurements include surface flux information from prior time windows. The observation operator that relates surface CO2 fluxes to atmospheric distributions of XCO2 includes: a) the GEOS-Chem transport model that relates surface fluxes to global 3-D distributions of CO2 concentrations, which are sampled at the time and location of OCO measurements that are cloud-free and have aerosol optical depths <0.3; and b) scene-dependent averaging kernels that relate the CO2 profiles to XCO2, accounting for differences between nadir and glint measurements, and the associated scene-dependent observation errors. We show that OCO XCO2 measurements significantly reduce the uncertainties of surface CO2 flux estimates. Glint measurements are generally better at constraining ocean CO2 flux estimates. Nadir XCO2 measurements over the terrestrial tropics are sparse throughout the year because of either clouds or smoke. Glint measurements provide the most effective constraint for estimating tropical terrestrial CO2 fluxes by accurately sampling fresh continental outflow over neighbouring oceans. We also present results from sensitivity experiments that investigate how flux estimates change with 1) bias and unbiased errors, 2) alternative duty cycles, 3) measurement density and correlations, 4) the spatial resolution of estimated flux estimates, and 5) reducing the length of the lag window and the size of the ensemble. At the revision stage of this manuscript, the OCO instrument failed to reach its orbit after it was launched on 24 February 2009. The EnKF formulation presented here is also applicable to GOSAT measurements of CO2 and CH4.

The Geostationary Earth Radiation Budget Project

This paper reports on a new satellite sensor, the Geostationary Earth Radiation Budget (GERB) experiment. GERB is designed to make the first measurements of the Earth's radiation budget from geostationary orbit. Measurements at high absolute accuracy of the reflected sunlight from the Earth, and the thermal radiation emitted by the Earth are made every 15 min, with a spatial resolution at the subsatellite point of 44.6 km (north–south) by 39.3 km (east–west). With knowledge of the incoming solar constant, this gives the primary forcing and response components of the top-of-atmosphere radiation. The first GERB instrument is an instrument of opportunity on Meteosat-8, a new spin-stabilized spacecraft platform also carrying the Spinning Enhanced Visible and Infrared (SEVIRI) sensor, which is currently positioned over the equator at 3.5°W. This overview of the project includes a description of the instrument design and its preflight and in-flight calibration. An evaluation of the instrument performance after its first year in orbit, including comparisons with data from the Clouds and the Earth's Radiant Energy System (CERES) satellite sensors and with output from numerical models, are also presented. After a brief summary of the data processing system and data products, some of the scientific studies that are being undertaken using these early data are described. This marks the beginning of a decade or more of observations from GERB, as subsequent models will fly on each of the four Meteosat Second Generation satellites.

Stray light analysis of SALEX instrument

Discrepancies between recent global earth albedo anomaly data obtained from the climate models, space and ground observations call for a new and better earth reflectance measurement technique. The SALEX (Space Ashen Light Explorer) instrument is a space-based visible and IR instrument for precise estimation of the global earth albedo by measuring the ashen light reflected off the shadowy side of the Moon from the low earth orbit. The instrument consists of a conventional 2-mirror telescope, a pair of a 3-mirror visible imager and an IR bolometer. The performance of this unique multi-channel optical system is sensitive to the stray light contamination due to the complex optical train incorporating several reflecting and refracting elements, associated mounts and the payload mechanical enclosure. This could be further aggravated by the very bright and extended observation target (i.e. the Moon). In this paper, we report the details of extensive stray light analysis including ghosts and cross-talks, leading to the optimum set of stray light precautions for the highest signal-to-noise ratio attainable.

Time-resolved gas-phase kinetic and quantum chemical studies of the reaction of silylene with oxygen

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reaction with O-2. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at five temperatures in the range 297-600 K. The second order rate constants at 10 Torr were fitted to the Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-11.08 +/- 0.04) + (1.57 +/- 0.32 kJ mol(-1))/RT ln10 The decrease in rate constant values with increasing temperature, although systematic is very small. The rate constants showed slight increases in value with pressure at each temperature, but this was scarcely beyond experimental uncertainty. From estimates of Lennard-Jones collision rates, this reaction is occurring at ca. 1 in 20 collisions, almost independent of pressure and temperature. Ab initio calculations at the G3 level backed further by multi-configurational (MC) SCF calculations, augmented by second order perturbation theory (MRMP2), support a mechanism in which the initial adduct, H2SiOO, formed in the triplet state (T), undergoes intersystem crossing to the more stable singlet state (S) prior to further low energy isomerisation processes leading, via a sequence of steps, ultimately to dissociation products of which the lowest energy pair are H2O + SiO. The decomposition of the intermediate cyclo-siladioxirane, via O-O bond fission, plays an important role in the overall process. The bottleneck for the overall process appears to be the T -> S process in H2SiOO. This process has a small spin orbit coupling matrix element, consistent with an estimate of its rate constant of 1 x 10(9) s(-1) obtained with the aid of RRKM theory. This interpretation preserves the idea that, as in its reactions in general, SiH2 initially reacts at the encounter rate with O-2. The low values for the secondary reaction barriers on the potential energy surface account for the lack of an observed pressure dependence. Some comparisons are drawn with the reactions of CH2 + O-2 and SiCl2 + O-2.

A variational method for the calculation of spin-rovibronic energy levels of any triatomic molecule in an electronic triplet state

The triatomic spin-rovibronic variational code RVIB3 has been extended to include the effect of two uncoupled electrons, for both (3)Sigma(-) and (3)Pi (Renner-Teller) electronic states. The spin-orbital-rotational kinetic energy is included in the usual way, via terms (J+L+S). The phenomenological terms AL.S and lambda 2/3(3S(z)(2)) are introduced to reproduce the 3 spin-orbit and spin-spin splittings, respectively. Calculations are performed to evaluate the spin-rovibronic energy levels of CCO (X) over tilde (3) Sigma(-) and CCO (A) over tilde (3) Pi for which the Born-Oppenheimer potentials are derived from high-accuracy ab initio calculations.

Design and fabrication of infrared filters for remote sounding instrumentation

Cooled infrared filters have been used in pressure modulation and filter radiometry to measure the dynamics, temperature distribution and concentrations of atmospheric elements in various satellite radiometers. Invariably such instruments use precision infrared bandpass filters and coatings for spectral selction, often operating at cryogenic temperatures. More recent developments in the use of spectrally-selective cooled detectors in focal plane arrays have simplified the optical layout and reduced the component count of radiometers but have placed additional demands on both the spectral and physical performance requirements of the filters. This paper describes and contrasts the more traditional radiometers using discrete detectors with those which use focal plane detector array technology, with particular emphasis on the function of the filters and coatings in the two cases. Additionally we discuss the spectral techniques and materials used to fabricate infrared coatings and filters for use in space optics, and give examples of their application in the fabrication of some demanding long wavelength dichroics and filters. We also discuss the effects of the space environment on the stability and durability of high performance infrared filters and materials exposed to low Earth orbit for 69 months on the NASA Long Duration Exposure Facility (LDEF).

Exposure to space radiation of high performance infrared multilayer filters and materials technology experiment

Infrared optical-multilayer filters and materials were exposed to the space environment of low Earth orbit on LDEF. This paper summarizes the effects of that environment on the physical and optical properties of the filters and materials flown.

Durability assessment of PbTe/II-IV infrared filters (Space Shuttle 1st LDEF)

Residual stress having been further reduced, selected infrared coatings composed of thin films of (PbTe/ ZnS (or ZnSe) can now be made which comply with the durability requirements of MIL-48616 whilst retaining transparency. Such improved durability is due to the sequence:- i) controlled deposition, followed by ii) immediate exposure to air, followed by iii) annealing in vacuo to relieve stress. (At the time of writing we assume the empiric procedure "exposure to air/annealing in vacuo" acts to relieve the inherent stresses of deposition). As part of their testing, representative sample filters prepared by the procedure are being assembled for the shuttle's 1st Long Duration Exposure Facility (to be placed in earth orbit for a considerable period and then recovered for analysis). The sample filters comprise various narrowband-designs to permit deduction of the constituent thin film optical properties. The Reading assembly also contains representative sample of the infrared crystals, glasses, thin-film absorbers and bulk absorbers, and samples of shorter-wavelength filters prepared similarly but made with Ge/SiO. Findings on durability and transparency after exposure will be reported.

The Heliospheric Imagers onboard the STEREO mission

Mounted on the sides of two widely separated spacecraft, the two Heliospheric Imager (HI) instruments onboard NASA’s STEREO mission view, for the first time, the space between the Sun and Earth. These instruments are wide-angle visible-light imagers that incorporate sufficient baffling to eliminate scattered light to the extent that the passage of solar coronal mass ejections (CMEs) through the heliosphere can be detected. Each HI instrument comprises two cameras, HI-1 and HI-2, which have 20° and 70° fields of view and are off-pointed from the Sun direction by 14.0° and 53.7°, respectively, with their optical axes aligned in the ecliptic plane. This arrangement provides coverage over solar elongation angles from 4.0° to 88.7° at the viewpoints of the two spacecraft, thereby allowing the observation of Earth-directed CMEs along the Sun – Earth line to the vicinity of the Earth and beyond. Given the two separated platforms, this also presents the first opportunity to view the structure and evolution of CMEs in three dimensions. The STEREO spacecraft were launched from Cape Canaveral Air Force Base in late October 2006, and the HI instruments have been performing scientific observations since early 2007. The design, development, manufacture, and calibration of these unique instruments are reviewed in this paper. Mission operations, including the initial commissioning phase and the science operations phase, are described. Data processing and analysis procedures are briefly discussed, and ground-test results and in-orbit observations are used to demonstrate that the performance of the instruments meets the original scientific requirements.

Accurate radiometry from space: an essential tool for climate studies

The Earth's climate is undoubtedly changing; however, the time scale, consequences and causal attribution remain the subject of significant debate and uncertainty. Detection of subtle indicators from a background of natural variability requires measurements over a time base of decades. This places severe demands on the instrumentation used, requiring measurements of sufficient accuracy and sensitivity that can allow reliable judgements to be made decades apart. The International System of Units (SI) and the network of National Metrology Institutes were developed to address such requirements. However, ensuring and maintaining SI traceability of sufficient accuracy in instruments orbiting the Earth presents a significant new challenge to the metrology community. This paper highlights some key measurands and applications driving the uncertainty demand of the climate community in the solar reflective domain, e.g. solar irradiances and reflectances/radiances of the Earth. It discusses how meeting these uncertainties facilitate significant improvement in the forecasting abilities of climate models. After discussing the current state of the art, it describes a new satellite mission, called TRUTHS, which enables, for the first time, high-accuracy SI traceability to be established in orbit. The direct use of a ‘primary standard’ and replication of the terrestrial traceability chain extends the SI into space, in effect realizing a ‘metrology laboratory in space’.