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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.↗

Directional models for analysis of earth radiation budget measurements

The determination of the radiation heat flux densities at the top of the atmosphere (30 km) for spatial scales ranging from global to regional is necessary for the conversion of satellite irradiance measurements into useful earth radiation budget information. Data reduction algorithms are required which contain assumed directional characteristics of radiation emitted and scattered from the earth-atmosphere system. The directional characteristics are defined by models which express, for a given surface element at the top of the atmosphere, the exiting flux per unit solid angle for each direction out to space as a fraction of the total hemispheric flux exiting the surface element. Both longwave and shortwave directional radiation models are analyzed. It is found that the validity of the Nimbus 2-based limb darkening curves has generally been verified for the longwave data with the exception of the Antarctic snow fields where limb brightening was noticed in the earth radiation budget data.

Suttles, J. T.↗

Validation of clear-sky fluxes for tropical oceans from the Earth Radiation Budget Experiment

The existence and magnitude of a systematic bias in the clear-sky longwave fluxes from the Earth Radiation Budget Experiment (ERBE) is investigated. The bias is apparently introduced because the ERBE method for scene identification does not account for large zonal gradients in longwave absorption by water vapor. The ERBE fluxes are compared to fluxes calculated with a radiative transfer model from ship radiosonde measurements. The comparison is based upon an analysis of 5 yr of coincident satellite and radiosonde observations for equatorial ocean regions. The differences between the ERBE and model fluxes are examined as functions of sea surface temperature (SST) and relative humidity. The authors use height-mean relative humidity bar-RH as an index of atmospheric moisture. The average offset between and model ERBE fluxes ranges between +2 and +6 W/sq m for SSTs above 295 K, and the gradients with respect to SST are nearly identical. However, the difference between the model and ERBE depends significantly on the tropospheric relative humidity. ERBE fluxes exceed model fluxes for bar-RH above 70%, and the maximum offset of +9 to +12 W/sq m is consistent with previous estimates. There are also indications that the clear-sky fluxes for bar-RH below 25% may be underestimated by about 10-15 W/sq m. Since extreme values of height-mean humidity are relatively infrequent, the net bias introduced in the ERBE monthly mean clear-sky fluxes is generally less than the systematic error in estimates introduced in the ERBE monthly mean clear-sky fluxes is generally less than the systematic error in estimates of the instantaneous fluxes. These findings support earlier work on the coupling between SST and the atmospheric greenhouse effect, in particular the existence of a super greenhouse effect for oceans warmer than 300 K. Recent reports of much larger systematic differences are not supported by this analysis. The results indicate that comparison of general circulation model (GCM) and ERBE clear-sky longwave fluxes will depend explicitly on atmospheric humidity.

Collins, W. D.↗

The Earth Radiation Budget (ERB) experiment

The radiation budget of the earth on both synoptic and planetary scales by simultaneous measurement of incoming solar radiation and outgoing earth reflected (shortwave) and emitted (longwave) radiation was determined. Both fixed wide angle sampling of terrestrial fluxes at the satellite altitude, and scanned narrow-angle sampling of the radiance components, dependent on angle are used to determine outgoing radiation. Measurements of radiation are obtained in 22 different optical channels.

Jacobowitz, H.↗

Sampling analysis for the Earth Radiation Budget Satellite System mission based on orbital coverage and cloud variability

It is pointed out that accurate computation of the earth's radiation budget from satellite measurements requires spatial and temporal sampling which accounts for variations in cloud and surface conditions. It is in this connection important that cloud radiative properties and areal cloud cover be accurately determined for the desired time period. The reported investigation represents an extension of a study by Harrison et al. (1976). The time and space coverage capabilities of various sampling schemes are analyzed for the proposed Earth Radiation Budget Satellite System. The effects of cloud cover variability on the measured monthly mean reflected shortwave (0.2-5.0 micrometers) irradiance are also analyzed for several spatial scales.

Harrison, E. F.↗

Evaluating the design of an earth radiation budget instrument with system simulations. Part 2: Minimization of instantaneous sampling errors for CERES-I

Much of the new record of broadband earth radiation budget satellite measurements to be obtained during the late 1990s and early twenty-first century will come from the dual-radiometer Clouds and Earth's Radiant Energy System Instrument (CERES-I) flown aboard sun-synchronous polar orbiters. Simulation studies conducted in this work for an early afternoon satellite orbit indicate that spatial root-mean-square (rms) sampling errors of instantaneous CERES-I shortwave flux estimates will range from about 8.5 to 14.0 W/m on a 2.5 deg latitude and longitude grid resolution. Rms errors in longwave flux estimates are only about 20% as large and range from 1.5 to 3.5 W/sq m. These results are based on an optimal cross-track scanner design that includes 50% footprint overlap to eliminate gaps in the top-of-the-atmosphere coverage, and a 'smallest' footprint size to increase the ratio in the number of observations lying within to the number of observations lying on grid area boundaries. Total instantaneous measurement error also depends on the variability of anisotropic reflectance and emission patterns and on retrieval methods used to generate target area fluxes. Three retrieval procedures from both CERES-I scanners (cross-track and rotating azimuth plane) are used. (1) The baseline Earth Radiaton Budget Experiment (ERBE) procedure, which assumes that errors due to the use of mean angular dependence models (ADMs) in the radiance-to-flux inversion process nearly cancel when averaged over grid areas. (2) To estimate N, instantaneous ADMs are estimated from the multiangular, collocated observations of the two scanners. These observed models replace the mean models in computation of satellite flux estimates. (3) The scene flux approach, conducts separate target-area retrievals for each ERBE scene category and combines their results using area weighting by scene type. The ERBE retrieval performs best when the simulated radiance field departs from the ERBE mean models by less than 10%. For larger perturbations, both the scene flux and collocation methods produce less error than the ERBE retrieval. The scene flux technique is preferable, however, because it involves fewer restrictive assumptions.

Stowe, Larry↗

Atlas of wide-field-of-view outgoing longwave radiation derived from Nimbus 7 Earth radiation budget data set, November 1985 to October 1987

An atlas of monthly outgoing longwave radiation global contour maps and associated spherical harmonic coefficients is presented. The atlas contains 23 months of data from November 1985 to October 1987 . The data were derived from the second Earth Radiation Budget (ERB) package, which was flown on the Nimbus 7 Sun-synchronous satellite in 1987. This data set is a companion set and extension to similar atlases that documented 10 years of outgoing longwave radiation results from Nimbus 6 and Nimbus 7 satellites. This atlas and the companion atlases give a data set covering a 12-year time period and will be very useful in studying different aspects of our changing climate. The data set also provides a 3-year overlap with the current Earth Radiation Budget Experiment (ERBE).

Bess, T. Dale↗

Earth Radiation Budget Experiment (ERBE) scanner instrument anomaly investigation

The results of an ad-hoc committee investigation of in-Earth orbit operational anomalies noted on two identical Earth Radiation Budget Experiment (ERBE) Scanner instruments on two different spacecraft busses is presented. The anomalies are attributed to the bearings and the lubrication scheme for the bearings. A detailed discussion of the pertinent instrument operations, the approach of the investigation team and the current status of the instruments now in Earth orbit is included. The team considered operational changes for these instruments, rework possibilities for the one instrument which is waiting to be launched, and preferable lubrication considerations for specific space operational requirements similar to those for the ERBE scanner bearings.

Watson, N. D.↗

Spatial autocorrelation of radiation measured by the Earth Radiation Budget Experiment: Scene inhomogeneity and reciprocity violation

The spatial autocorrelation functions of broad-band longwave and shortwave radiances measured by the Earth Radiation Budget Experiment (ERBE) are analyzed as a function of view angle in an investigation of the general effects of scene inhomogeneity on radiation. For nadir views, the correlation distance of the autocorrelation function is about 900 km for longwave radiance and about 500 km for shortwave radiance, consistent with higher degrees of freedom in shortwave reflection. Both functions rise monotonically with view angle, but there is a substantial difference in the relative angular dependence of the shortwave and longwave functions, especially for view angles less than 50 deg. In this range, the increase with angle of the longwave functions is found to depend only on the expansion of pixel area with angle, whereas the shortwave functions show an additional dependence on angle that is attributed to the occlusion of inhomogeneities by cloud height variations. Beyond a view angle of about 50 deg, both longwave and shortwave functions appear to be affected by cloud sides. The shortwave autocorrelation functions do not satisfy the principle of directional reciprocity, thereby proving that the average scene is horizontally inhomogeneous over the scale of an ERBE pixel (1500 sq km). Coarse stratification of the measurements by cloud amount, however, indicates that the average cloud-free scene does satisfy directional reciprocity on this scale.

Davies, Roger↗

Human factors analysis of workstation design: Earth Radiation Budget Satellite Mission Operations Room

A human factors analysis addressed three related yet distinct issues within the area of workstation design for the Earth Radiation Budget Satellite (ERBS) mission operation room (MOR). The first issue, physical layout of the MOR, received the most intensive effort. It involved the positioning of clusters of equipment within the physical dimensions of the ERBS MOR. The second issue for analysis was comprised of several environmental concerns, such as lighting, furniture, and heating and ventilation systems. The third issue was component arrangement, involving the physical arrangement of individual components within clusters of consoles, e.g., a communications panel.

Stewart, L. J.↗

Daily earth radiation budget results from the Nimbus-7 scanning radiometer

Nimbus-7 broadband narrow-field-of-view scanning-radiometer data obtained in the Earth Radiation Budget Experiment on three days in 1979 (one with a blocking situation over the Northern Hemisphere, one with normal zonal flow, and one with two mature hurricanes over the Caribbean), are presented graphically and discussed. Both blocking and hurricane situations are characterized by anomalies (relative to the zonal-flow condition) in the zonally averaged emitted flux and albedo, with decreased tropical and midlatitude gradients in the case of blocking.

Randel, D. L.↗

Extended Kalman filter for attitude estimation of the earth radiation budget satellite

The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the Sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.

Deutschmann, Julie↗

Investigating ocean surface solar irradiance using Nimbus-7 Earth Radiation Budget data

A new estimation technique is introduced, using a surface solar irradiance database with advanced climate monitoring capabilities. Incorporating the Nimbus-7 Earth Radiation Budget (ERB) planetary albedo data obtained from wide-field-of-view radiometer measurements, the new solar irradiance model uses plane-parallel theory and assumes the isotropy of radiance reflected by the clouds and ocean surface. A brief description of the data, a treatment of the model verification, and a discussion of surface solar irradiance variability are presented. The results demonstrate the model's sensitivity to large-scale seasonal and interannual phenomena. A summary of the investigation is also presented, along with a perspective on potential uses and future development.

Chertock, Beth↗

Extended Kalman Filter for attitude estimation of the Earth Radiation Budget Satellite

The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.

Deutschmann, Julie↗

Comparison of general circulation models to Earth Radiation Budget Experiment data - Computation of clear-sky fluxes

A clear-sky flux computation method is described which is representative of the Earth Radiation Budget Experiment data processing, while at the same time being enough straightforward for implementation in a general circulation model (GCM). The method is a hybrid version of Cess and Potter (1987) Method I and Method II clear-sky top-of-the-atmosphere flux computations for GCMs. The procedure is demonstrated using the ECMWF GCM.

Cess, Robert D.↗

User's guide: Nimbus-7 Earth radiation budget narrow-field-of-view products. Scene radiance tape products, sorting into angular bins products, and maximum likelihood cloud estimation products

The archived Earth radiation budget (ERB) products produced from the Nimbus-7 ERB narrow field-of-view scanner are described. The principal products are broadband outgoing longwave radiation (4.5 to 50 microns), reflected solar radiation (0.2 to 4.8 microns), and the net radiation. Daily and monthly averages are presented on a fixed global equal area (500 sq km), grid for the period May 1979 to May 1980. Two independent algorithms are used to estimate the outgoing fluxes from the observed radiances. The algorithms are described and the results compared. The products are divided into three subsets: the Scene Radiance Tapes (SRT) contain the calibrated radiances; the Sorting into Angular Bins (SAB) tape contains the SAB produced shortwave, longwave, and net radiation products; and the Maximum Likelihood Cloud Estimation (MLCE) tapes contain the MLCE products. The tape formats are described in detail.

Kyle, H. Lee↗

Earth Radiation Budget Experiment (ERBE) Data Sets for Global Environment and Climate Change Studies

For a number of years there has been considerable interest in the earth's radiation budget (ERB) or energy balance, and entails making the best measurements possible of absorbed solar radiation, reflected shortwave radiation (RSW), thermal outgoing longwave radiation (OLR), and net radiation. ERB data are fundamental to the development of realistic climate models and studying natural and anthropogenic perturbations of the climate. Much of the interest and investigations in the earth's energy balance predated the age of earth-orbiting satellites (Hunt et al., 1986). Beginning in the mid 1960's earth-orbiting satellites began to play an important role in making measurements of the earth's radiation flux although much effort had gone into measuring ERB parameters prior to 1960 (House et al., 1986). Beginning in 1974 and extending until the present time, three different satellite experiments (not all operating at the same time) have been making radiation budget measurements almost continually in time. Two of the experiments were totally dedicated to making radiation budget measurements of the earth, and the other experiment flown on NOAA sun-synchronous AVHRR weather satellites produced radiation budget parameters as a by-product. The heat budget data from the AVHRR satellites began collecting data in June 1974 and have operated almost continuously for 23 years producing valuable data for long term climate monitoring.

Bess, T. Dale↗