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Comparison and testing of extended Kalman filters for attitude estimation of the Earth Radiation Budget Satellite

This paper presents the testing and comparison of two extended Kalman filters (EKFs) developed for the Earth Radiation Budget Satellite (ERBS). One EKF updates the attitude quaternion using a four-component additive error quaternion. This technique is compared to that of a second EKF, which uses a multiplicative error quaternion. Brief developments of the algorithms are included. The convergence properties, singularity problems, and normalization techniques of the two filters are addressed. Both filters are tested with simulated ERBS sensor data in addition to real ERBS sensor data. The results of the two filters are also compared to those from the ERBS operational ground support software, which uses a batch differential correction algorithm to estimate attitude and gyro biases.

Bar-Itzhack, Itzhack Y.↗

Comparison and testing of extended Kalman filters for attitude estimation of the Earth radiation budget satellite

The testing and comparison of two Extended Kalman Filters (EKFs) developed for the Earth Radiation Budget Satellite (ERBS) is described. One EKF updates the attitude quaternion using a four component additive error quaternion. This technique is compared to that of a second EKF, which uses a multiplicative error quaternion. A brief development of the multiplicative algorithm is included. The mathematical development of the additive EKF was presented in the 1989 Flight Mechanics/Estimation Theory Symposium along with some preliminary testing results using real spacecraft data. A summary of the additive EKF algorithm is included. The convergence properties, singularity problems, and normalization techniques of the two filters are addressed. Both filters are also compared to those from the ERBS operational ground support software, which uses a batch differential correction algorithm to estimate attitude and gyro biases. Sensitivity studies are performed on the estimation of sensor calibration states. The potential application of the EKF for real time and non-real time ground attitude determination and sensor calibration for future missions such as the Gamma Ray Observatory (GRO) and the Small Explorer Mission (SMEX) is also presented.

Deutschmann, Julie↗

A new look at Wolf sunspot numbers in the late 1700's

A procedure is described for the derivation of the Wolf sunspot number from the number of sunspot groups, and the approach is used to obtain a 'Group Wolf number'. It is shown that this technique is superior to the classical method of determining the Wolf number, because corrections for differences due to the observers' bias are reduced and self-consistent long-term time series can be developed; the level of solar activity can be calculated with an accuracy of +/- 5 percent. The procedure was used to determine Wolf sunspot numbers for the solar cycles 1, 2, and 3 (1761-1777). It is found that the standard Wolf numbers are nearly homogeneous with sunspot numbers measured from 1875 to 1976, but the peak of solar cycle 2 is too low by 30 percent.

Hoyt, Douglas V.↗

A deep x ray survey in the Lockman hole and the soft x ray log N - log S

The longest pointed observation (152 ksec) with the Rosat position sensitive proportional counter in the direction of the absolutely lowest neutral hydrogen column density is discussed. 26 shallower fields from the Rosat medium sensivity survey are analyzed. 1176 X-ray sources were detected in at least one Rosat energy band in these fields covering a total solid angle of 9.3 deg; 661 of these sources constitute a statistically complete sample detected in the hard band with 0.5 to 2 keV fluxes greater than 2.5 times 10 to the power of minus 15 erg/sq cm s. The faintest limiting flux of the survey is analyzed. Detailed simulations show that confusion effects and other selection biases are relatively small and can be corrected for in the sample. From an analysis in the Lockman field, a best fit slope of approximately 1.8 is found for the extrapolation of the differential X-ray counts below 2.5 times 10 to the power of minus 15 erg/sq cm s. On the basis of this analysis an upper limit of approximately 25% can be found for a truly diffuse background component in the Rosat hard band.

Hasinger, G.↗

Estimates of Ground Temperature and Atmospheric Moisture from CERES Observations

A method is developed to retrieve surface ground temperature (Tg) and atmospheric moisture using clear sky fluxes (CSF) from CERES-TRMM observations. In general, the clear sky outgoing long-wave radiation (CLR) is sensitive to upper level moisture (q(sub h)) over wet regions and Tg over dry regions The clear sky window flux from 800 to 1200 /cm (RadWn) is sensitive to low level moisture (q(sub j)) and Tg. Combining these two measurements (CLR and RadWn), Tg and q(sub h) can be estimated over land, while q(sub h) and q(sub t) can be estimated over the oceans. The approach capitalizes on the availability of satellite estimates of CLR and RadWn and other auxiliary satellite data. The basic methodology employs off-line forward radiative transfer calculations to generate synthetic CSF data from two different global 4-dimensional data assimilation products. Simple linear regression is used to relate discrepancies in CSF to discrepancies in Tg, q(sub h) and q(sub t). The slopes of the regression lines define sensitivity parameters that can be exploited to help interpret mismatches between satellite observations and model-based estimates of CSF. For illustration, we analyze the discrepancies in the CSF between an early implementation of the Goddard Earth Observing System Data Assimilation System (GEOS-DAS) and a recent operational version of the European Center for Medium-Range Weather Prediction data assimilation system. In particular, our analysis of synthetic total and window region SCF differences (computed from two different assimilated data sets) shows that simple linear regression employing (Delta)Tg and broad layer (Delta)q(sub l) from 500 hPa to surface and (Delta)q(sub h) from 200 to 500 hPa provides a good approximation to the full radiative transfer calculations, typically explaining more than 90% of the 6-hourly variance in the flux differences. These simple regression relations can be inverted to "retrieve" the errors in the geophysical parameters. Uncertainties (normalized by standard deviation) in the monthly mean retrieved parameters range from 7% for (Delta)T to about 20% for (Delta)q(sub t). Our initial application of the methodology employed an early CERES-TRMM data set (CLR and Radwn) to assess the quality of the GEOS2 data. The results showed that over the tropical and subtropical oceans GEOS2 is, in general, too wet in the upper troposphere (mean bias of 0.99 mm) and too dry in the lower troposphere (mean bias of -4.7 mm). We note that these errors, as well as a cold bias in the Tg, have largely been corrected in the current version of GEOS-2 with the introduction of a land surface model, a moist turbulence scheme and the assimilation of SSTM/I total precipitable water.

Wu, Man Li C.↗

High Frequency, Long Time Series Measurements from the Bermuda Testbed Mooring in Support of SIMBIOS

It has been recognized that optical moorings are important platforms for the validation of Sea-Viewing Wide Field-of-view Sensor (SeaWiFS). It was recommended that optical moorings be maintained in order to: (1) provide long-term time series comparisons between in situ and SeaWIFS measurements of normalized water-leaving radiance; (2) develop and test algorithms for pigment biomass and phytoplankton primary productivity; and (3) provide long-term, virtually continuous in situ observations which can be used to determine and optimize the accuracy of derived satellite products. These applications require the use of in situ radiometers for long periods of time to evaluate and correct for inherent satellite undersampling (aliasing and biasing) and degradation of satellite color sensors (e.g., drifts as experienced by the Coastal Zone Color Scanner). The Bermuda Testbed Mooring (BTM) program was initiated in 1994 at a site located about 80km southeast of Bermuda in waters of about 4530 m depth. In August 1997, with NASA's support, we started to provide the Sensor Intercomparison and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS) program with large volumes of high frequency, long-term time-series bio-optical data from the BTM for SeaWiFS satellite ocean color groundtruthing and algorithm development. This NASA supported portion of the BTM activity spanned three years and covered five BTM deployments. During these three years, the quality of radiometric data has improved dramatically. Excellent agreement between BTM moored data and both SeaWiFS and nearby ship profile radiometric data demonstrate that technical advances in the moored optical observations have reduced the major difficulties that moored platforms face: biofouling and less frequent calibration.

Dickey, Tommy↗

View angle dependence of cloud optical thicknesses retrieved by MODIS

This study examines whether cloud inhomogeneity influences the view angle dependence of MODIS cloud optical thickness (tau) retrieval results. The degree of cloud inhomogeneity is characterized through the local gradient in 11 microns brightness temperature. The analysis of liquid phase clouds in a one year long global dataset of Collection 4 MODIS data reveals that while optical thickness retrievals give remarkably consistent results for all view directions if clouds are homogeneous, they give much higher tau-values for oblique views than for overhead views if clouds are inhomogeneous and the sun is fairly oblique. For solar zenith angles larger than 55deg, the mean optical thickness retrieved for the most inhomogeneous third of cloudy pixels is more than 30% higher for oblique views than for overhead views. After considering a variety of possible scenarios, the paper concludes that the most likely reason for the increase lies in three-dimensional radiative interactions that are not considered in current, one-dimensional retrieval algorithms. Namely, the radiative effect of cloud sides viewed at oblique angles seems to contribute most to the enhanced tau-values. The results presented here will help understand cloud retrieval uncertainties related to cloud inhomogeneity. They complement the uncertainty estimates that will start accompanying MODIS cloud products in Collection 5 and may eventually help correct for the observed view angle dependent biases.

Marshak, Alexander↗

Validation of SO2 Retrievals from the Ozone Monitoring Instrument over NE China

The Dutch-Finnish Ozone Monitoring Instrument (OMI) launched on the NASA Aura satellite in July 2004 offers unprecedented spatial resolution, coupled with contiguous daily global coverage, for space-based UV measurements of sulfur dioxide (SO2). We present a first validation of the OMI SO2 data with in situ aircraft measurements in NE China in April 2005. The study demonstrates that OMI can distinguish between background SO2 conditions and heavy pollution on a daily basis. The noise (expressed as the standard deviation,sigma) is approximately 1.5 DU (Dobson units; 1 DU = 2.69 10 (exp 16) molecules/cm (exp 2)) for instantaneous field of view boundary layer (PBL) SO2 data. Temporal and spatial averaging can reduce the noise to sigma approximetly 0.3 DU over a remote region of the South Pacific; the long-term average over this remote location was within 0.1 DU of zero. Under polluted conditions collection 2 OMI data are higher than aircraft measurements by a factor of two. Improved calibrations of the radiance and irradiance data (collection 3) result in better agreement with aircraft measurements on polluted days. The air mass corrected collection 3 data still show positive bias and sensitivity to UV absorbing aerosols. The difference between the in situ data and the OMI SO2 measurements within 30 km of the aircraft profiles was about 1 DU, equivalent to approximately 5 ppb from 0 to 3000 m altitude. Quantifying the SO2 and aerosol profiles and spectral dependence of aerosol absorption between 310 and 330 nm are critical for an accurate estimate of SO2 from satellite UV measurements.

Krotkov, Nickolay A.↗

Constraining Black Carbon Aerosol over Asia using OMI Aerosol Absorption Optical Depth and the Adjoint of GEOS-Chem

Accurate estimates of the emissions and distribution of black carbon (BC) in the region referred to here as Southeastern Asia (70degE-l50degE, 11degS-55degN) are critical to studies of the atmospheric environment and climate change. Analysis of modeled BC concentrations compared to in situ observations indicates levels are underestimated over most of Southeast Asia when using any of four different emission inventories. We thus attempt to reduce uncertainties in BC emissions and improve BC model simulations by developing top-down, spatially resolved, estimates of BC emissions through assimilation of OMI observations of aerosol absorption optical depth (AAOD) with the GEOS-Chem model and its adjoint for April and October of 2006. Overwhelming enhancements, up to 500%, in anthropogenic BC emissions are shown after optimization over broad areas of Southeast Asia in April. In October, the optimization of anthropogenic emissions yields a slight reduction (1-5%) over India and parts of southern China, while emissions increase by 10-50% over eastern China. Observational data from in situ measurements and AERONET observations are used to evaluate the BC inversions and assess the bias between OMI and AERONET AAOD. Low biases in BC concentrations are improved or corrected in most eastern and central sites over China after optimization, while the constrained model still underestimates concentrations in Indian sites in both April and October, possibly as a. consequence of low prior emissions. Model resolution errors may contribute up to a factor of 2.5 to the underestimate of surface BC concentrations over northern India. We also compare the optimized results using different anthropogenic emission inventories and discuss the sensitivity of top-down constraints on anthropogenic emissions with respect to biomass burning emissions. In addition, the impacts of brown carbon, the formulation of the observation operator, and different a priori constraints on the optimization are investigated. Overall, despite these limitations and uncertainties, using OMI AAOD to constrain BC sources improves model representation of BC distributions, particularly over China.

Aerosols↗

Four Problematic Methods in Reliability Analysis

Some basic methods used in reliability analysis are problematic because they produce incorrect and overoptimistic predictions. Initially gratifying forecasts are often invalidated by testing and operational experience. The problematic methods in reliability analysis include estimating the system failure rate as the sum of component failure rates, assuming that reliability growth continues indefinitely during testing, overestimating the benefits of redundancy, and using the fault tolerance count instead of a detailed reliability analysis. Reliability analysis can produce more optimism than accuracy. This bug may now be a feature. The optimistic bias inevitable in project planning should be corrected by realistic reliability analysis that reflects relevant experience. That the repeated poor performance of reliability analysis is found to be surprising suggests willful blindness. Rigorous methods and impartial critical review are necessary to improve reliability analysis.

Reliability analysis↗

Four Problematic Methods in Reliability Analysis

Some basic methods used in reliability analysis are problematic because they produce incorrect and overoptimistic predictions. Initially gratifying forecasts are often invalidated by testing and operational experience. The problematic methods in reliability analysis include estimating the system failure rate as the sum of component failure rates, assuming that reliability growth continues indefinitely during testing, overestimating the benefits of redundancy, and using the fault tolerance count instead of a detailed reliability analysis. Reliability analysis can produce more optimism than accuracy. This bug may now be a feature. The optimistic bias inevitable in project planning should be corrected by realistic reliability analysis that reflects relevant experience. That the repeated poor performance of reliability analysis is found to be surprising suggests willful blindness. Rigorous methods and impartial critical review are necessary to improve reliability analysis.

Reliability analysis↗

Cosmological constraints from the Planck cluster catalogue with DES shear profiles and Chandra observations

We present cosmological constraints from the Planck PSZ2 cosmological cluster sample, using weak-lensing shear profiles from Dark Energy Survey (DES) data and X-ray observations from the Chandra telescope for the mass calibration. We compute hydrostatic mass estimates for all clusters in the PSZ2 sample with a scaling relation between their Sunyaev-Zeldovich signal and X-ray derived hydrostatic mass, calibrated with the Chandra data. We introduce a method to correct these masses with a hydrostatic mass bias using shear profiles from wide-field galaxy surveys. We simultaneously fit the number counts of the PSZ2 sample and the mass calibration with the DES data, finding $Ω_\text{m}=0.312^{+0.018}_{-0.024}$, $σ_8=0.777\pm 0.024$, $S_8\equiv σ_8 \sqrt{Ω_\text{m} / 0.3}=0.791^{+0.023}_{-0.021}$, and $(1-b)=0.844^{+0.055}_{-0.062}$ for our baseline analysis when combined with BAO data. When considering a hydrostatic mass bias evolving with mass, we find $Ω_\text{m}=0.353^{+0.025}_{-0.031}$, $σ_8=0.751\pm 0.023$, and $S_8=0.814^{+0.019}_{-0.020}$. We verify the robustness of our results by exploring a variety of analysis settings, with a particular focus on the definition of the halo centre used for the extraction of shear profiles. We compare our results with a number of other analyses, in particular two recent analyses of cluster samples obtained from SPT and eROSITA data that share the same mass calibration data set. We find that our results are in overall agreement with most late-time probes, in very mild tension with CMB results (1.6$σ$), and in significant tension with results from eROSITA clusters (2.9$σ$). We confirm that our mass calibration is consistent with the eROSITA analysis by comparing masses for clusters present in both Planck and eROSITA samples, eliminating it as a potential cause of tension.

Aymerich, G. [Orsay, IAS; AIM, Saclay] (ORCID:0009↗

Model-observation discrepancies in Arctic moisture intrusions: causes and pathways for improved simulation

Arctic moisture intrusions (MIs), narrow filaments of strong moisture transport, are key drivers of poleward moisture flux and Arctic weather extremes, yet their representation in climate models is poorly understood. Using a new Arctic MI detection algorithm, we document persistent biases across three CMIP generations (CMIP3–CMIP6): models overestimate MI occurrence over the Pacific sector and underestimate it over the Atlantic sector. These errors stem from misrepresented midlatitude westerly jets, with an equatorward North Atlantic jet associated with too few Atlantic MIs, and a poleward, weakened North Pacific jet linked to too many Pacific MIs. Experiments that correct sea surface temperature and sea ice concentration biases and increase atmospheric resolution improve jet structure and MI statistics, while a cloud-locking simulation indicates that better high-frequency cloud–radiation–circulation interactions can yield further gains. Our results clarify pathways to reducing long-standing MI and jet biases, providing guidance for improving simulations of Arctic and midlatitude climate.

54 ENVIRONMENTAL SCIENCES↗

Can We Fix It Automatically? Development of Fault Auto-Correction Algorithms for HVAC and Lighting Systems

A fault detection and diagnostics (FDD) tool is a type of energy management and information system designed to continuously identify the presence of faults and efficiency improvement opportunities through a one-way interface to the building automation system and application of automated analytics. Building owners and operators at the leading edge of technology adoption are using FDD tools to enable average whole-building portfolio savings of 8 percent. Although FDD tools can inform building operators of operational faults, currently a manual action is always required to correct faults and generate the associated energy savings. A subset of faults, however, such as biased sensors and manual override, can be addressed automatically, removing the need for operations and maintenance staff intervention. Automating this fault “correction” can significantly increase the savings generated by FDD tools and reduce the reliance on human intervention. Doing so is expected to advance the usability, as well as the technical and economic performance, of FDD technologies. In this paper, we present the development of 10 innovative fault auto-correction algorithms for HVAC and lighting systems. When the auto-correction routine is triggered, it will overwrite the control setpoints or other variables (via BACnet or other protocol) to implement the intended changes. These algorithms are able to automatically correct the faults or improve the operation associated with an incorrectly programmed schedule, override manual control, sensor bias, control hunting, rogue zone, and less aggressive setpoints/setpoints setback. The paper will also discuss the implementation of the auto-correction algorithms in FDD software products.

Lin, Guanjing↗

System Dynamic Analysis of a Wind Tunnel Model with Applications to Improve Aerodynamic Data Quality

The research investigates the effect of wind tunnel model system dynamics on measured aerodynamic data. During wind tunnel tests designed to obtain lift and drag data, the required aerodynamic measurements are the steady-state balance forces and moments, pressures, and model attitude. However, the wind tunnel model system can be subjected to unsteady aerodynamic and inertial loads which result in oscillatory translations and angular rotations. The steady-state force balance and inertial model attitude measurements are obtained by filtering and averaging data taken during conditions of high model vibrations. The main goals of this research are to characterize the effects of model system dynamics on the measured steady-state aerodynamic data and develop a correction technique to compensate for dynamically induced errors. Equations of motion are formulated for the dynamic response of the model system subjected to arbitrary aerodynamic and inertial inputs. The resulting modal model is examined to study the effects of the model system dynamic response on the aerodynamic data. In particular, the equations of motion are used to describe the effect of dynamics on the inertial model attitude, or angle of attack, measurement system that is used routinely at the NASA Langley Research Center and other wind tunnel facilities throughout the world. This activity was prompted by the inertial model attitude sensor response observed during high levels of model vibration while testing in the National Transonic Facility at the NASA Langley Research Center. The inertial attitude sensor cannot distinguish between the gravitational acceleration and centrifugal accelerations associated with wind tunnel model system vibration, which results in a model attitude measurement bias error. Bias errors over an order of magnitude greater than the required device accuracy were found in the inertial model attitude measurements during dynamic testing of two model systems. Based on a theoretical modal approach, a method using measured vibration amplitudes and measured or calculated modal characteristics of the model system is developed to correct for dynamic bias errors in the model attitude measurements. The correction method is verified through dynamic response tests on two model systems and actual wind tunnel test data.

Buehrle, Ralph David↗

Dynamic response tests of inertial and optical wind-tunnel model attitude measurement devices

Results are presented for an experimental study of the response of inertial and optical wind-tunnel model attitude measurement systems in a wind-off simulated dynamic environment. This study is part of an ongoing activity at the NASA Langley Research Center to develop high accuracy, advanced model attitude measurement systems that can be used in a dynamic wind-tunnel environment. This activity was prompted by the inertial model attitude sensor response observed during high levels of model vibration which results in a model attitude measurement bias error. Significant bias errors in model attitude measurement were found for the measurement using the inertial device during wind-off dynamic testing of a model system. The amount of bias present during wind-tunnel tests will depend on the amplitudes of the model dynamic response and the modal characteristics of the model system. Correction models are presented that predict the vibration-induced bias errors to a high degree of accuracy for the vibration modes characterized in the simulated dynamic environment. The optical system results were uncorrupted by model vibration in the laboratory setup.

Buehrle, R. D.↗

Development and Implementation of Fault-Correction Algorithms in Fault Detection and Diagnostics Tools

A fault detection and diagnostics (FDD) tool is a type of energy management and information system that continuously identifies the presence of faults and efficiency improvement opportunities through a one-way interface to the building automation system and the application of automated analytics. Building operators on the leading edge of technology adoption use FDD tools to enable median whole-building portfolio savings of 8%. Although FDD tools can inform operators of operational faults, currently an action is always required to correct the faults to generate energy savings. A subset of faults, however, such as biased sensors, can be addressed automatically, eliminating the need for staff intervention. Automating this fault “correction” can significantly increase the savings generated by FDD tools and reduce the reliance on human intervention. Doing so is expected to advance the usability and technical and economic performance of FDD technologies. This paper presents the development of nine innovative fault auto-correction algorithms for Heating, Ventilation, and Air Conditioning pi(HVAC) systems. When the auto-correction routine is triggered, it overwrites control setpoints or other variables to implement the intended changes. It also discusses the implementation of the auto-correction algorithms in commercial FDD software products, the integration of these strategies with building automation systems and their preliminary testing.

field testing↗