Total Systematic Error Research Articles

Calibration system for OH radicals based on differential optical absorption spectroscopy

In the present paper, we describe a calibration system for OH radicals based on differential optical absorption spectroscopy (DOAS). In the system OH radicals can be produced by photolysis of H2O which is irradiated by the 185 nm light in a cavity. The produced OH radicals with a certain concentration can be detected exactly. The system consists of a xenon lamp as light source in which the light has been collimated, a 1.25 m multiple-reflection cell in which the light can reflect 60 times to achieve 75.0 m whole path-length, and a double pass high resolution echelle spectrometer that is suitable for the measurement of OH radicals (best resolution: 3.3 pm). Utilizing the system the measurement spectra and lamp spectra can be obtained for OH concentration retrieval. OH concentration can be calculated by DOAS retrieval and during the DOAS retrieval the reference absorption cross section is obtained by applying the Voigt broadening method to the absorption lines. By changing water vapor concentration, the system accurately detects OH concentration ranging from 5×108 molecules/cm3 to 1.8×1010 molecules/cm3. In the concentration range, OH concentration fluctuation is very small. For example, when the volume ratio between water vapor and pure N2 reaches 0.3 L:24.7 L, the fluctuation is just ± 4%. Taking into account the effects of absorption cross section, gas pressure in the cavity and other factors, the total systematic error of the instrument is less than 7.3%. According to the results in the paper, the system can be used for the fluorescence assay by gas expansion technology calibration in field experiments.

Observations of peroxyacetyl nitrate (PAN) in the upper troposphere by the Atmospheric Chemistry Experiment-Fourier Transform Spectrometer (ACE-FTS)

Abstract. Peroxyacetyl nitrate (CH3CO·O2NO2, abbreviated as PAN) is a trace molecular species present in the troposphere and lower stratosphere due primarily to pollution from fuel combustion and the pyrogenic outflows from biomass burning. In the lower troposphere, PAN has a relatively short lifetime and is principally destroyed within a few hours through thermolysis, but it can act as a reservoir and carrier of NOx in the colder temperatures of the upper troposphere, where UV photolysis becomes the dominant loss mechanism. Pyroconvective updrafts from large biomass burning events can inject PAN into the upper troposphere and lower stratosphere (UTLS), providing a means for the long-range transport of NOx. Given the extended lifetimes at these higher altitudes, PAN is readily detectable via satellite remote sensing. A new PAN data product is now available for the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) version 3.0 data set. We report observations of PAN in boreal biomass burning plumes recorded during the BORTAS (quantifying the impact of BOReal forest fires on Tropospheric oxidants over the Atlantic using Aircraft and Satellites) campaign (12 July to 3 August 2011). The retrieval method employed by incorporating laboratory-recorded absorption cross sections into version 3.0 of the ACE-FTS forward model and retrieval software is described in full detail. The estimated detection limit for ACE-FTS PAN is 5 pptv, and the total systematic error contribution to the ACE-FTS PAN retrieval is ~ 16%. The retrieved volume mixing ratio (VMR) profiles are compared to coincident measurements made by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) instrument on the European Space Agency (ESA) Environmental Satellite (ENVISAT). The MIPAS measurements demonstrated good agreement with the ACE-FTS VMR profiles for PAN, where the measured VMR values are well within the associated measurement errors for both instruments and comparative measurements differ no more than 70 pptv. The ACE-FTS PAN data set is used to obtain zonal mean distributions of seasonal averages from ~ 5–20 km. A strong seasonality is clearly observed for PAN concentrations in the global UTLS. Since the principal source of PAN in the UTLS is due to lofted biomass burning emissions from the pyroconvective updrafts created by large fires, the observed seasonality in enhanced PAN coincides with fire activity in different geographical regions throughout the year.

MAX-DOAS formaldehyde slant column measurements during CINDI: intercomparison and analysis improvement

Abstract. We present intercomparison results for formaldehyde (HCHO) slant column measurements performed during the Cabauw Intercomparison campaign of Nitrogen Dioxide measuring Instruments (CINDI) that took place in Cabauw, the Netherlands, in summer 2009. During two months, nine atmospheric research groups simultaneously operated MAX-DOAS (MultiAXis Differential Optical Absorption Spectroscopy) instruments of various designs to record UV-visible spectra of scattered sunlight at different elevation angles that were analysed using common retrieval settings. The resulting HCHO data set was found to be highly consistent, the mean difference between instruments generally not exceeding 15% or 7.5 × 1015 molec cm−2, for all viewing elevation angles. Furthermore, a sensitivity analysis was performed to investigate the uncertainties in the HCHO slant column retrieval when varying key input parameters such as the molecular absorption cross sections, correction terms for the Ring effect or the width and position of the fitting interval. This study led to the identification of potentially important sources of errors associated with cross-correlation effects involving the Ring effect, O4, HCHO and BrO cross sections and the DOAS closure polynomial. As a result, a set of updated recommendations was formulated for HCHO slant column retrieval in the 336.5–359 nm wavelength range. To conclude, an error budget is proposed which distinguishes between systematic and random uncertainties. The total systematic error is estimated to be of the order of 20% and is dominated by uncertainties in absorption cross sections and related spectral cross-correlation effects. For a typical integration time of one minute, random uncertainties range between 5 and 30%, depending on the noise level of individual instruments.

Validation of v1.022 mesospheric water vapor observed by the Solar Occultation for Ice Experiment instrument on the Aeronomy of Ice in the Mesosphere satellite

Water vapor measured by the Solar Occultation for Ice Experiment (SOFIE) instrument on the Aeronomy of Ice in the Mesosphere satellite has been validated in the vertical range 45–95 km. Precision estimates for SOFIE v1.022 H2O are ∼0.2%–2.5% up to 80 km and degrade to ∼20% at ∼90 km. The SOFIE total systematic error from the retrieval analysis remains at ∼3%–4% throughout the lower to middle mesosphere and increases from ∼9% at 85 km to ∼16% at 95 km. Comparisons with Atmospheric Chemistry Experiment‐Fourier Transform Spectrometer (ACE‐FTS) and Microwave Limb Sounder (MLS) H2O show excellent agreement (0%–2%) up to 80 km in the Northern Hemisphere with rare exceptions. Percentage differences above ∼85 km increase to ∼20% or worse due largely to the low H2O volume mixing ratios in the upper mesosphere. For the Southern Hemisphere SOFIE is consistently biased low by 10%–20% relative to both ACE‐FTS and MLS H2O. Slopes of SOFIE daily mean H2O isopleths on an altitude versus time cross section are used as an indicator of upwelling air motion. In the lower to middle mesosphere, the slope is the largest from mid‐May to mid‐June (maximum of ∼1.5 cm/s), and then in July and August, it is reduced significantly. Both SOFIE and MLS daily mean H2O volume mixing ratios at the polar mesospheric cloud height increase rapidly from ∼2.0 to ∼5.0 ppmv prior to the solstice and then approach a near‐constant but slightly increasing level (6.0–6.5 ppmv) throughout the season.

Keck telescope constraint on cosmological variation of the proton-to-electron mass ratio

Molecular transitions recently discovered at redshift z_abs=2.059 toward the bright background quasar J2123-0050 are analysed to limit cosmological variation in the proton-to-electron mass ratio, mu=m_p/m_e. Observed with the Keck telescope, the optical echelle spectrum has the highest resolving power and largest number (86) of H_2 transitions in such analyses so far. Also, (seven) HD transitions are used for the first time to constrain mu-variation. These factors, and an analysis employing the fewest possible free parameters, strongly constrain mu's relative deviation from the current laboratory value: dmu/mu =(+5.6+/-5.5_stat+/-2.9_sys)x10^{-6}, indicating an insignificantly larger mu in the absorber. This is the first Keck result to complement recent null constraints from three systems at z_abs>2.5 observed with the Very Large Telescope. The main possible systematic errors stem from wavelength calibration uncertainties. In particular, distortions in the wavelength solution on echelle order scales are estimated to contribute approximately half the total systematic error component, but our estimate is model dependent and may therefore under or overestimate the real effect, if present. To assist future mu-variation analyses of this kind, and other astrophysical studies of H_2 in general, we provide a compilation of the most precise laboratory wavelengths and calculated parameters important for absorption-line work with H_2 transitions redwards of the hydrogen Lyman limit.

Influence of heterogeneous profiles in carrier density measurements with respect to iron concentration measurements in silicon

Carrier density is a frequently examined parameter for silicon material characterization especially to determine carrier lifetime. Typically integrated values are obtained which ignore nonhomogeneities in the depth dependent carrier profile and result in mean values for lifetime and injection density. Due to the averaging together with nonlinear recombination processes, these values may be subjected to substantial systematic errors. This work demonstrates the effect on iron concentration measurements which are based on the comparison of carrier lifetime measurements before and after light induced splitting of FeB pairs. Although this technique has been proven to be very sensitive, simple, and thus attractive, systematic quantitative errors are revealed in this work which are inherent to this method. It is demonstrated that the errors, while small for certain conditions, may be substantial in many practical cases. Simulations based on the calculation of carrier profiles and virtual measurements provide a tool to estimate the influence of material and setup parameters to the total systematic error. A correction method is developed from this analysis.

SIM PlanetQuest white-light fringe modeling: picometer accuracy calibration and estimation algorithms

SIM PlanetQuest will perform narrow-angle astrometry with microarcsecond accuracy using starlight interferometry requiring tens of picometers accuracy in estimating the optical path difference change between observing two stars. One challenge is to accurately model the white-light fringes and calibrate the required model parameters. Previous studies have developed algorithms based on a CCD-pixel-level calibration scheme assuming slowly varying phase-dispersion functions. However, recent measurements from the SIM PlanetQuest Spectral Calibration Development Unit (SCDU) showed that wavefront aberrations caused the phase-dispersion functions to vary by tens of nanometers across the bandwidth of a CCD pixel, making the previous CCD-pixel-based calibration scheme inadequate. We present a white-light fringe model including the extra phase dispersions caused by the wavefront aberrations together with a calibration and estimation scheme using long-stroke fringe measurements to resolve the bandwidth of pixels. Using simulated data, we show that the total systematic errors in the calibration and estimation scheme are less than a picometer. With SCDU experimental data, we demonstrate that the end-to-end accuracy of the calibration and estimation algorithm is better than 20 pm, achieving the SIM PlanetQuest Engineering Milestone 4.

Prospects of improving accuracy of the hadronic cross section measurements to the 10 −3 level at the VEPP-2000 [formula omitted] collider: experimental and theoretical problems

The main sources of systematic errors of the hadronic cross section measurements at the CMD-2 and SND detectors at VEPP-2M are discussed. To push down a total systematic error to the per mille accuracy in forthcoming experiments at VEPP-2000 some theoretical calculations and detector parameters should be significantly improved. These are: trigger and detection efficiencies, determination of the fiducial volume and event selection procedure, radiative corrections and pion losses caused by nuclear interaction with detector material. New results expected in the nearest future are also mentioned.

Online Kilovoltage Cone-beam CT Guided Lung Cancer Radiation: Initial Clinical Experiences from Shanghai

To introduce the initial clinical experiences of online Kilovoltage Cone-beam CT (KVCBCT) guided lung cancer radiation in our department. From March 2007 to January 2008, 30 patients with pathologically confirmed lung cancer were included in this study. After patients were positioned using their skin marks, KVCBCT scans were performed before treatment and aligned to planning CT scans using the self-developed semi-automatic alignment method. Treatment table were repositioned according to the alignment results. A second KVCBCT scan was acquired immediately after the table correction. A total of 308 KVCBCT images from 154 fractions were analyzed. The reproducibility of the semi-automatic image alignment method, workflow of the online correction, translational and rotational setup error in three dimensional conditions and residual setup error after online correction were evaluated. The reproducibility of the semi-automatic alignment method was evaluated. The alignment difference was smaller in intraobserver evaluation than in interobserver. The reproducibility of different physicians was better than the physician and radiation therapist in anterior-posterior (AP) and left-right (LR) directions. In superior-inferior (SI) direction, the percentage of alignment difference larger than 3 mm between different physicians, the physician and radiation therapist were both near 15%. The online correction protocol adds 7.6 min to the total treatment time and the workflow proved to be feasible in clinical practice. The total systematic error (∑) before online correction was 3.5 mm, 3.5 mm and 3.0 mm, the overall random error (σ) was 2.7 mm, 2.9 mm and 3.0 mm in the LR, SI, and AP direction, respectively. After online correction, the total systematic error (∑) was 0.7 mm, 0.7 mm and 0.6 mm, the overall random error (σ) was 1.2 mm, 1.5 mm and 1.3 mm in three directions. The average rotational setup error (± 1 SD) was -0.3 ± 1.5°, 0.2 ± 0.9 ° and 0.3 ± 0.8 ° in pitch, roll and yaw, respectively. According to the formalisms suggested by van Herk et al, 3mm can apply to the margin of clinical target volume (CTV) to PTV, when using the online correction. The KVCBCT guided radiation system can be applied successfully in lung cancer patients with reproducible image alignment method. With the help of the system, we have an opportunity of new realization for patient setup error, including both translational and rotational. We can improve patient setup accuracy and reduce the CTV to PTV margin from 11 mm to 3 mm with limited workload.

Tangent height registration method for the Version 14 data retrieval algorithm of the solar occultation sensor ILAS-II

The Improved Limb Atmospheric Spectrometer-II (ILAS-II) is a satellite-borne solar occultation sensor onboard the Advanced Earth Observing Satellite-II (ADEOS-II). The ILAS-II succeeded the ILAS. The ILAS-II used four grating spectrometers to observe vertical profiles of gas volume mixing ratios of trace constituents and was also equipped with a Sun-edge sensor to determine tangent heights geometrically with high precision. The accuracy of gas volume mixing ratios depends on the accuracy of the tangent height determination. The combination method is a tangent height registration method that was developed to give appropriate tangent heights for the ILAS-II Version 1.4 data retrieval algorithm. This study describes the method used in the ILAS-II Version 1.4 retrieval algorithm to register tangent heights. The root-sum-square total random error is estimated to be 30 m, and the total systematic error is 180 m at an altitude of 30 km. The influence of the tangent height errors on the vertical profiles of gas volume mixing ratios in ILAS-II Version 1.4 is estimated by using the relative difference. The relative difference for each species is within 7% (20%) for an altitude shift of +/-100 m(+/-300 m).

Beam energy spread measurement at the VEPP-4M Electron-Positron Collider

The VEPP-4M electron-positron collider is now operating with the KEDR detectorfor the experiment of precise measurement of tau-lepton mass. In this experiment, monitoring ofbeam energy spread is important to know the energy spread contribution into the totalsystematic error. Information about the energy spread gives an opportunity to reduce the error ofthe tau-lepton mass measurement. Several techniques for energy spread measurement aredescribed in the paper. Width of the ψ′ resonance measured with the KEDR detector is used asa reference.

Systematic geometric rigid body error identification of 5-axis milling machines

A 5-axis milling machine has 39 independent geometric error components when the machine tool is considered as a set of five rigid bodies. The identification of the deterministic component of the systematic error is very important. It permits one to improve the accuracy close to the repeatability of the machine tool. This paper gives a new way to identify and compensate all the systematic angular errors separately and then use them further to identify the systematic translational error. Identification based on a new mathematical method and a stable numerical solution method is proposed. The model explains from first principles why some error components have no effect in a first order model. The identification of the total angular systematic errors can be done independently from the translation errors. However, the total translation error depends on the angular errors and the translation errors of each machine tool slide. The main problems solved are to find enough linear independent equations and avoid numerical instability in the computation. It is important to separate numerical problems and linear dependence. The very complex equations are first analyzed in symbolic form to eliminate the linear dependencies. The total of linear independent components in the model is reduced from 30 to 26 for the position dependent errors and from 9 to 3 for the position independent components. Secondly, the large system of linear equations is broken down in many smaller systems. The model is tested first with simulated errors modeled as cubic polynomials. An artifact-based identification is proposed and implemented based on drilling holes in various locations and orientations. New ways to measure the volumetric error directly are proposed. Direct measurement of the total volumetric error requires considerably less measurement than measuring all 6 components of each machine slide especially in the case of a 5-axis machine.

On the quality of the Nimbus 7 LIMS version 6 ozone for studies of the middle atmosphere

The Nimbus 7 Limb Infrared Monitor of the Stratosphere (LIMS) radiance profile dataset of 1978/79 was reconditioned and reprocessed to Version 6 (V6) profiles of temperature and species that are improved significantly over those from Version 5 (V5). The LIMS V6 dataset was archived for public use in 2002. Improvements for its ozone include: (1) a more accurate accounting for instrument and spacecraft motion effects in the radiances, (2) the use of better spectroscopic line parameters for its ozone forward model, (3) retrievals of all its scans, (4) more accurate and compatible temperature versus pressure profiles (or T( p)) that are needed for the registration of the ozone radiances and for the removal of temperature effects from them, and (5) a better accounting for interfering species in the lower stratosphere. The retrieved V6 ozone profiles extend from near cloud top altitudes to about 80 km and from 64S to 84N latitude with better sampling along the orbit than for the V5 dataset. Calculated estimates of the single-profile precision and accuracy are provided; precision estimates based on the data themselves are of order 3% or better from 1 to 30 hPa. Estimates of total systematic error are hard to generalize because the separate sources of error may not all be of the same sign, and they depend somewhat on the atmospheric state. It is estimated that the accuracy of the V6 zonal mean ozone distribution is within ±9% from 50–10 hPa, improving to ±7% in the uppermost stratosphere. Simulation studies show that the LIMS T( p) retrievals are underestimating slightly the small amplitudes of the atmospheric temperature tides, which affect the retrieved day/night ozone differences. There are also small biases in the middle to lower stratosphere for the ascending versus descending node LIMS ozone, due principally to not accounting for the asymmetric weighting of its radiance within the tangent layer. The total accuracy for the LIMS ozone was assessed by comparing its daily zonal mean, daytime distributions against those from the Nimbus 7 SBUV Version 8 (V8) dataset for the same period. The LIMS V6 ozone agrees well with SBUV, except between 2 and 5 hPa where the LIMS ozone is greater. That bias is related to the differing vertical resolutions and forward models for the two experiments. The accuracy for LIMS V6 ozone in the lower stratosphere is improved over that reported for V5, as indicated by a small set of V6 comparisons with ECC ozonesonde profiles. Comparisons of diurnal, photochemical model calculations with the monthly-averaged, upper stratospheric ozone obtained with LIMS V6 indicate only a slight ozone deficit for the model at about 2 hPa. However, that deficit exhibits little to no seasonal variation and is in good agreement with similar model comparisons for a seasonal time series of ozone obtained with ground-based microwave instruments. Because the LIMS V6 ozone has improved accuracy and sampling versus that of V5 for the lower stratosphere it should now be possible to conduct quantitative studies of ozone transport and chemistry for the northern hemisphere, polar winter/spring of 1978/79—a time period when the catalytic loss of ozone due to reactive chlorine should not have been a major factor for the Arctic stratosphere.

Search forT-violating transverse muon polarization in theK+→π0μ+νdecay

At the 12-GeV proton synchrotron of KEK, an experiment (KEK-PS-E246) was performed to measure the transverse muon polarization (${P}_{T}$) in ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\mu}}^{+}\ensuremath{\nu}$ decays as a direct search of violation of time reversal invariance ($T$-violation). ${P}_{T}$ is a very sensitive probe of $CP$ violation beyond the standard model. A stopped positive kaon beam was used. An elaborate high-acceptance detector, in conjunction with a 12-sector superconducting toroidal spectrometer, was utilized. The stopped kaon method provided several advantages in performing a high-precision experiment. The decay was identified by detecting a ${\ensuremath{\mu}}^{+}$ with the spectrometer and a ${\ensuremath{\pi}}^{0}$ with a CsI(Tl) calorimeter surrounding the target as two photons as well as one photon with high energy. For the ${P}_{T}$ measurement, ${\ensuremath{\pi}}^{0}$ events in the forward (fwd) and backward (bwd) regions in the calorimeter were relevant. Systematic errors were greatly suppressed by exploiting the rotational and fwd-bwd symmetry of the system. Polarization measurement was done in terms of asymmetry measurement of decay positrons of stopped muons in the polarimeter. A longitudinal field method was applied for the ${P}_{T}$ polarization component. In the data analysis a novel technique of the two-analysis method was employed. Two independent analyses were performed following their own policy and criteria and good events were selected. Then, the two analyses were combined. A data quality check was carefully done by looking at the null asymmetry ${A}_{0}$, the sensitivity function ${A}_{N}$, the kinematical attenuation coefficient, and the decay-plane distributions. The asymmetry measurement for finite-size muon stoppers was performed ``differentially'' using the position information by the chamber in front of the polarimeter. From the measurements during 1996--2000, we accumulated $11.8\ifmmode\times\else\texttimes\fi{}{10}^{6}$ good events after the two-analysis combination, and deduced ${P}_{T}=\ensuremath{-}0.0017\ifmmode\pm\else\textpm\fi{}0.0023(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.0011(\mathrm{syst})$, corresponding to the $T$-violating parameter $\mathrm{Im}\ensuremath{\xi}=\ensuremath{-}0.0053\ifmmode\pm\else\textpm\fi{}0.0071(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.0036(\mathrm{syst})$. From these results the upper limits of $|{P}_{T}|l0.0050$ (90% C.L.) and $|\mathrm{Im}\ensuremath{\xi}|l0.016$ (90% C.L.) were deduced. Systematic errors were carefully studied and estimated. Almost all of the errors were canceled by the 12-sector summation and/or fwd-bwd subtraction, and the total systematic error was concluded to be as a half of the statistical error. The present result set constraints on model parameters of several theoretical models. For the three-Higgs-doublet model, e.g., a limit $|\mathrm{Im}({\ensuremath{\alpha}}_{1}{\ensuremath{\gamma}}_{1}^{*})|l544({M}_{{H}_{1}}/\mathrm{GeV}{)}^{2}$ was obtained. Implications for several other models are discussed.

The impact of the new Earth gravity models on the measurement of the Lense–Thirring effect with a new satellite

In this paper we investigate the opportunities offered by the new Earth gravity models from the dedicated CHAMP and, especially, GRACE missions to the project of measuring the general relativistic Lense–Thirring effect with a new Earth’s artificial satellite. It turns out that it would be possible to abandon the stringent, and expensive, requirements on the orbital geometry of the originally prosed LARES mission (same semimajor axis a = 12,270 km of the existing LAGEOS and inclination i = 70°) by inserting the new spacecraft in a relatively low, and cheaper, orbit ( a = 7500–8000 km, i ∼ 70°) and suitably combining its node Ω with those of LAGEOS and LAGEOS II in order to cancel out the first two even zonal harmonic coefficients of the multipolar expansion of the terrestrial gravitational potential J 2, J 4 along with their temporal variations J ˙ 2 , J ˙ 4 . The total systematic error due to the mismodelling in the remaining even zonal harmonics would amount to ∼1% and would be insensitive to departures of the inclination from the originally proposed value of many degrees. No semisecular long-period perturbations would be introduced because the period of the node, which is also the period of the solar K 1 tidal perturbation, would amount to ∼10 2 days. Since the coefficient of the node of the new satellite would be smaller than 0.1 for such low altitudes, the impact of the non-gravitational perturbations of it on the proposed combination would be negligible. Then, a particular financial and technological effort for suitably building the satellite in order to minimize the non-conservative accelerations would be unnecessary.

Sensitivity of near infrared total water vapour estimate to calibration errors

Analysis of satellite data to estimate the precipitable water (also called the columnar water vapour) amount often leads to systematic errors in deduced precipitable water (PW). The causes of systematic errors are likely to be instrumental calibration errors rather than variability of atmospheric parameters. We use the MODTRAN 4.0 radiative transfer code to model effects of various calibration errors on the Multi-spectral Thermal Imager (MTI) daytime total water vapour estimate. From the considered sources of calibration errors (spectral band centre error, spectral bandwidth error and radiometric calibration error) the radiometric calibration error has the largest influence on the accuracy of total water vapour estimate. When the radiometric calibration error between 1% and 5% is combined with the estimated spectral band centre error of 1 nm and the bandwidth error of 0.5 nm, the total systematic error of the columnar water vapour estimate is expected to be between 8% and 26%. The accuracy of the retrieved PW using the MTI imagery over the NASA Stennis site and Oklahoma DOE (Department of Energy) ARM (Atmospheric Radiation Measurement program) site is about 17%, well within the estimated range due to calibration errors. A similarity between the MTI and the MODIS (Moderate Resolution Imaging Spectral-Radiometer) bands used for water vapour estimate suggests that a similar error analysis may be valid for the MODIS sensor. However, the narrow band instruments (with bandwidth around 10 nm) are much more sensitive to the band centre calibration error.

On the possibility of measuring the Lense–Thirring effect with a LAGEOS–LAGEOS II–OPTIS mission

A space mission, OPTIS, has been proposed for testing the foundations of special relativity and post-Newtonian gravitation in the field of the Earth. The constraints posed on the original OPTIS orbital geometry would allow for a rather wide range of possibilities for the final OPTIS orbital parameters. This freedom could be exploited for further tests of post-Newtonian gravity. In this paper, we wish to preliminarily investigate if it would be possible to use the orbital data from OPTIS together with those from the existing geodetic passive laser-ranged LAGEOS and LAGEOS II satellites in order to perform precise measurements of the Lense–Thirring effect. With regard to this possibility, it is important to note that the drag-free technology which should be adopted for the OPTIS mission would yield a lifetime of many years for this satellite. It turns out that the best choice would probably be to adopt the same orbital configuration as the proposed LAGEOS-like LARES satellite and, for testing, select a linear combination including the nodes of LAGEOS, LAGEOS II and OPTIS and the perigee of OPTIS. The total systematic error should be of the order of 1%. The LARES orbital geometry should not be too much in conflict with the original specifications of the OPTIS mission. However, a compromise solution could also be adopted. A comparison with the new perspectives of measuring the Lense–Thirring effect with the existing laser-tracked satellites opened by the new gravity models from CHAMP and, especially, GRACE is made. It turns out that an OPTIS/LARES mission would still be of great significance because the obtainable accuracy would be better than that offered by a reanalysis of the currently existing satellites.

The REFLEX galaxy cluster survey

For the first time the large-scale clustering and the mean abundance of galaxy clusters are analysed simultaneously to get precise constraints on the normalized cosmic matter density and the linear theory RMS fluctuations in mass . A self-consistent likelihood analysis is described which combines, in a natural and optimal manner, a battery of sensitive cosmological tests where observational data are represented by the (Karhunen-Loéve) eigenvectors of the sample correlation matrix. This method breaks the degeneracy between and . The cosmological tests are performed with the ROSAT ESO Flux-Limited X-ray (REFLEX) cluster sample. The computations assume cosmologically flat geometries and a non-evolving cluster population mainly over the redshift range . The REFLEX sample gives the cosmological constraints and their random errors of and . Possible systematic errors are evaluated by estimating the effects of uncertainties in the value of the Hubble constant, the baryon density, the spectral slope of the initial scalar fluctuations, the mass/X-ray luminosity relation and its intrinsic scatter, the biasing scheme, and the cluster mass density profile. All these contributions sum up to total systematic errors of and .

Tangent height registration for the solar occultation satellite sensor ILAS: A new technique for Version 5.20 products

The Improved Limb Atmospheric Spectrometer (ILAS) was a solar occultation satellite sensor that was developed by the Environment Agency of Japan to monitor the stratospheric ozone layer. This paper describes methods of registering tangent heights for ILAS vertical profiles of gas mixing ratio and aerosol extinction coefficient. Accurate tangent height registration is crucial for the retrieval of accurate gas mixing ratios from atmospheric absorption spectra. Three methods for tangent height registration have been applied to retrieved ILAS data. The first method is the transmittance spectrum method (TS‐M), which uses absorption spectra of oxygen molecules at around 760 nm (O2A band) measured by the ILAS visible channel and compares the average transmittance with that calculated theoretically from temperature and pressure using meteorological data. A tangent height is derived from these data. Version 3.10 ILAS data products use the TS‐M. A second method is the Sun‐edge sensor method (SES‐M). This method for registering tangent heights was in mind when ILAS was originally designed. The SES‐M geometrically determines the direction of the instantaneous field‐of‐view (IFOV) of the spectrometer from the angular difference between the top edge of the Sun determined with the SES and the spectrometer's IFOV. Information on the satellite's orbital position and solar position relative to the center of the Earth is used to register the tangent height. Version 4.20 ILAS data products use SES‐M. The third method is a hybrid method (Hybrid‐M) that was developed to correct for seasonal differences in tangent heights computed by the SES‐M. The Hybrid‐M assumes that the TS‐M can correctly determine the tangent height at 30 km. Version 5.20 ILAS data products (the latest version) use Hybrid‐M. Random and systematic errors in the Hybrid‐M tangent height registration were estimated. The root‐sum‐square (RSS) total random error is 30 m, while the total systematic error is +300 ± 360 m in tangent height. Actual errors in tangent height registration in Version 5.20 algorithm are considered to be small judging from the results of comparisons with independent validation data sets. The Hybrid‐M gives good estimates of tangent heights in Version 5.20 of the ILAS data processing algorithms.

A new algorithm for retrieving GPS radio occultation total electron content

A new algorithm for retrieving the relative ionospheric satellite‐to‐satellite total electron content during Global Positioning System (GPS) radio occultations is proposed. The algorithm consists of a linear combination of the L1 and L2 excess phase data using precise orbit information of the transmitter and receiver. The combination eliminates the effects of refractive bending and dispersion to first order. Simulations, representative of solar maximum conditions, show that using the “traditional” combination of the L1 and L2 phases, bending and dispersion may cause a systematic residual error of up to 20 TECU. Using only the L1 excess phase, the corresponding maximum residual error is about 7 TECU. The proposed combination results in a residual error due to bending and dispersion less than 0.1 TECU. Uncertainty in satellite orbit determination, as well as an unmodeled residual related to the geomagnetic field, result in a total systematic error of 1–2 TECU.