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NASA NTRS1994

MODIS. Volume 2: MODIS level 1 geolocation, characterization and calibration algorithm theoretical basis document, version 1

The EOS Moderate Resolution Imaging Spectrometer (MODIS) is being developed by NASA for flight on the Earth Observing System (EOS) series of satellites, the first of which (EOS-AM-1) is scheduled for launch in 1998. This document describes the algorithms and their theoretical basis for the MODIS Level 1B characterization, calibration, and geolocation algorithms which must produce radiometrically, spectrally, and spatially calibrated data with sufficient accuracy so that Global change research programs can detect minute changes in biogeophysical parameters. The document first describes the geolocation algorithm which determines geodetic latitude, longitude, and elevation of each MODIS pixel and the determination of geometric parameters for each observation (satellite zenith angle, satellite azimuth, range to the satellite, solar zenith angle, and solar azimuth). Next, the utilization of the MODIS onboard calibration sources, which consist of the Spectroradiometric Calibration Assembly (SRCA), Solar Diffuser (SD), Solar Diffuser Stability Monitor (SDSM), and the Blackbody (BB), is treated. Characterization of these sources and integration of measurements into the calibration process is described. Finally, the use of external sources, including the Moon, instrumented sites on the Earth (called vicarious calibration), and unsupervised normalization sites having invariant reflectance and emissive properties is treated. Finally, algorithms for generating utility masks needed for scene-based calibration are discussed. Eight appendices are provided, covering instrument design and additional algorithm details.

Barker, John L.↗

NASA NTRS1994

A new algorithm for attitude-independent magnetometer calibration

A new algorithm is developed for inflight magnetometer bias determination without knowledge of the attitude. This algorithm combines the fast convergence of a heuristic algorithm currently in use with the correct treatment of the statistics and without discarding data. The algorithm performance is examined using simulated data and compared with previous algorithms.

Alonso, Roberto↗

NASA NTRS1993

The gust-front detection and wind-shift algorithms for the Terminal Doppler Weather Radar system

The Federal Aviation Administration's (FAA) Terminal Doppler Weather Radar (TDWR) system was primarily designed to address the operational needs of pilots in the avoidance of low-altitude wind shears upon takeoff and landing at airports. One of the primary methods of wind-shear detection for the TDWR system is the gust-front detection algorithm. The algorithm is designed to detect gust fronts that produce a wind-shear hazard and/or sustained wind shifts. It serves the hazard warning function by providing an estimate of the wind-speed gain for aircraft penetrating the gust front. The gust-front detection and wind-shift algorithms together serve a planning function by providing forecasted gust-front locations and estimates of the horizontal wind vector behind the front, respectively. This information is used by air traffic managers to determine arrival and departure runway configurations and aircraft movements to minimize the impact of wind shifts on airport capacity. This paper describes the gust-front detection and wind-shift algorithms to be fielded in the initial TDWR systems. Results of a quantitative performance evaluation using Doppler radar data collected during TDWR operational demonstrations at the Denver, Kansas City, and Orlando airports are presented. The algorithms were found to be operationally useful by the FAA airport controllers and supervisors.

Hermes, Laurie G.↗

NASA NTRS1994

On the utility of the multi-level algorithm for the solution of nearly completely decomposable Markov chains

Recently the Multi-Level algorithm was introduced as a general purpose solver for the solution of steady state Markov chains. In this paper, we consider the performance of the Multi-Level algorithm for solving Nearly Completely Decomposable (NCD) Markov chains, for which special-purpose iteractive aggregation/disaggregation algorithms such as the Koury-McAllister-Stewart (KMS) method have been developed that can exploit the decomposability of the the Markov chain. We present experimental results indicating that the general-purpose Multi-Level algorithm is competitive, and can be significantly faster than the special-purpose KMS algorithm when Gauss-Seidel and Gaussian Elimination are used for solving the individual blocks.

Leutenegger, Scott T.↗

NASA NTRS1994

A new algorithm for five-hole probe calibration, data reduction, and uncertainty analysis

A new algorithm for five-hole probe calibration and data reduction using a non-nulling method is developed. The significant features of the algorithm are: (1) two components of the unit vector in the flow direction replace pitch and yaw angles as flow direction variables; and (2) symmetry rules are developed that greatly simplify Taylor's series representations of the calibration data. In data reduction, four pressure coefficients allow total pressure, static pressure, and flow direction to be calculated directly. The new algorithm's simplicity permits an analytical treatment of the propagation of uncertainty in five-hole probe measurement. The objectives of the uncertainty analysis are to quantify uncertainty of five-hole results (e.g., total pressure, static pressure, and flow direction) and determine the dependence of the result uncertainty on the uncertainty of all underlying experimental and calibration measurands. This study outlines a general procedure that other researchers may use to determine five-hole probe result uncertainty and provides guidance to improve measurement technique. The new algorithm is applied to calibrate and reduce data from a rake of five-hole probes. Here, ten individual probes are mounted on a single probe shaft and used simultaneously. Use of this probe is made practical by the simplicity afforded by this algorithm.

Reichert, Bruce A.↗

NASA NTRS1994

An algorithm for extraction of periodic signals from sparse, irregularly sampled data

Temporal gaps in discrete sampling sequences produce spurious Fourier components at the intermodulation frequencies of an oscillatory signal and the temporal gaps, thus significantly complicating spectral analysis of such sparsely sampled data. A new fast Fourier transform (FFT)-based algorithm has been developed, suitable for spectral analysis of sparsely sampled data with a relatively small number of oscillatory components buried in background noise. The algorithm's principal idea has its origin in the so-called 'clean' algorithm used to sharpen images of scenes corrupted by atmospheric and sensor aperture effects. It identifies as the signal's 'true' frequency that oscillatory component which, when passed through the same sampling sequence as the original data, produces a Fourier image that is the best match to the original Fourier space. The algorithm has generally met with succession trials with simulated data with a low signal-to-noise ratio, including those of a type similar to hourly residuals for Earth orientation parameters extracted from VLBI data. For eight oscillatory components in the diurnal and semidiurnal bands, all components with an amplitude-noise ratio greater than 0.2 were successfully extracted for all sequences and duty cycles (greater than 0.1) tested; the amplitude-noise ratios of the extracted signals were as low as 0.05 for high duty cycles and long sampling sequences. When, in addition to these high frequencies, strong low-frequency components are present in the data, the low-frequency components are generally eliminated first, by employing a version of the algorithm that searches for non-integer multiples of the discrete FET minimum frequency.

Wilcox, J. Z.↗

NASA NTRS1994

Ocean observations with EOS/MODIS: Algorithm development and post launch studies

During CY 1994 there are five objectives under this task: (1) investigate the effects of stratospheric aerosol on the proposed correction algorithm, and investigate the use of the 1380 nm MODIS band to remove the stratospheric aerosol perturbation; (2) investigate the effect of vertical structure in aerosol concentration and type on the behavior of the proposed correction algorithm; (3) investigate the effects of polarization on the accuracy of the algorithm; (4) improve the accuracy and speed of the existing algorithm; and (5) investigate removal of the O2 'A' absorption band at 762 nm from the 765 nm SeaWiFS band so the latter can be used in atmospheric correction of SeaWiFS. The importance of this to MODIS is that SeaWiFS data will be used extensively to test and improve the MODIS algorithm. Thus it is essential that the O2 absorption be adequately dealt with for SeaWiFS.

Gordon, Howard R.↗

NASA NTRS1995

Passive microwave algorithm development and evaluation

The scientific objectives of this grant are: (1) thoroughly evaluate, both theoretically and empirically, all available Special Sensor Microwave Imager (SSM/I) retrieval algorithms for column water vapor, column liquid water, and surface wind speed; (2) where both appropriate and feasible, develop, validate, and document satellite passive microwave retrieval algorithms that offer significantly improved performance compared with currently available algorithms; and (3) refine and validate a novel physical inversion scheme for retrieving rain rate over the ocean. This report summarizes work accomplished or in progress during the first year of a three year grant. The emphasis during the first year has been on the validation and refinement of the rain rate algorithm published by Petty and on the analysis of independent data sets that can be used to help evaluate the performance of rain rate algorithms over remote areas of the ocean. Two articles in the area of global oceanic precipitation are attached.

Petty, Grant W.↗

NASA NTRS1995

SeaWiFS technical report series. Volume 28: SeaWiFS algorithms, part 1

This document provides five brief reports that address several algorithm investigations sponsored by the Calibration and Validation Team (CVT) within the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Project. This volume, therefore, has been designated as the first in a series of algorithm volumes. Chapter 1 describes the initial suite of masks, used to prevent further processing of contaminated radiometric data, and flags, which are employed to mark data whose quality (due to a variety of factors) may be suspect. In addition to providing the mask and flag algorithms, this chapter also describes the initial strategy for their implementation. Chapter 2 evaluates various strategies for the detection of clouds and ice in high latitude (polar and sub-polar regions) using Coastal Zone Color Scanner (CZCS) data. Chapter 3 presents an algorithm designed for detecting and masking coccolithosphore blooms in the open ocean. Chapter 4 outlines a proposed scheme for correcting the out-of-band response when SeaWiFS is in orbit. Chapter 5 gives a detailed description of the algorithm designed to apply sensor calibration data during the processing of level-1b data.

Hooker, Stanford B.↗

NASA NTRS1993

A comparison of three-dimensional nonequilibrium solution algorithms applied to hypersonic flows with stiff chemical source terms

Three solution algorithms, explicit underrelaxation, point implicit, and lower upper symmetric Gauss-Seidel (LUSGS), are used to compute nonequilibrium flow around the Apollo 4 return capsule at 62 km altitude. By varying the Mach number, the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness. The performance of the solution algorithms degraded as the Mach number and stiffness of the flow increased. At Mach 15, 23, and 30, the LUSGS method produces an eight order of magnitude drop in the L2 norm of the energy residual in 1/3 to 1/2 the Cray C-90 computer time as compared to the point implicit and explicit under-relaxation methods. The explicit under-relaxation algorithm experienced convergence difficulties at Mach 23 and above. At Mach 40 the performance of the LUSGS algorithm deteriorates to the point it is out-performed by the point implicit method. The effects of the viscous terms are investigated. Grid dependency questions are explored.

Palmer, Grant↗

NASA NTRS1994

A splitting algorithm for Vlasov simulation with filamentation filtration

A Fourier-Fourier transformed version of the splitting algorithm for simulating solutions of the Vlasov-Poisson system of equations is introduced. It is shown that with the inclusion of filamentation filtration in this transformed algorithm it is both faster and more stable than the standard splitting algorithm. It is further shown that in a scalar computer environment this new algorithm is approximately equal in speed and far less noisy than its particle-in-cell counterpart. It is conjectured that in a multiprocessor environment the filtered splitting algorithm would be faster while producing more precise results.

Klimas, A. J.↗

NASA NTRS1994

Passive microwave remote sensing of rainfall with SSM/I: Algorithm development and implementation

A physically based algorithm sensitive to emission and scattering is used to estimate rainfall using the Special Sensor Microwave/Imager (SSM/I). The algorithm is derived from radiative transfer calculations through an atmospheric cloud model specifying vertical distributions of ice and liquid hydrometeors as a function of rain rate. The algorithm is structured in two parts: SSM/I brightness temperatures are screened to detect rainfall and are then used in rain-rate calculation. The screening process distinguishes between nonraining background conditions and emission and scattering associated with hydrometeors. Thermometric temperature and polarization thresholds determined from the radiative transfer calculations are used to detect rain, whereas the rain-rate calculation is based on a linear function fit to a linear combination of channels. Separate calculations for ocean and land account for different background conditions. The rain-rate calculation is constructed to respond to both emission and scattering, reduce extraneous atmospheric and surface effects, and to correct for beam filling. The resulting SSM/I rain-rate estimates are compared to three precipitation radars as well as to a dynamically simulated rainfall event. Global estimates from the SSM/I algorithm are also compared to continental and shipboard measurements over a 4-month period. The algorithm is found to accurately describe both localized instantaneous rainfall events and global monthly patterns over both land and ovean. Over land the 4-month mean difference between SSM/I and the Global Precipitation Climatology Center continental rain gauge database is less than 10%. Over the ocean, the mean difference between SSM/I and the Legates and Willmott global shipboard rain gauge climatology is less than 20%.

Ferriday, James G.↗

NASA NTRS1994

A Coulomb collision algorithm for weighted particle simulations

A binary Coulomb collision algorithm is developed for weighted particle simulations employing Monte Carlo techniques. Charged particles within a given spatial grid cell are pair-wise scattered, explicitly conserving momentum and implicitly conserving energy. A similar algorithm developed by Takizuka and Abe (1977) conserves momentum and energy provided the particles are unweighted (each particle representing equal fractions of the total particle density). If applied as is to simulations incorporating weighted particles, the plasma temperatures equilibrate to an incorrect temperature, as compared to theory. Using the appropriate pairing statistics, a Coulomb collision algorithm is developed for weighted particles. The algorithm conserves energy and momentum and produces the appropriate relaxation time scales as compared to theoretical predictions. Such an algorithm is necessary for future work studying self-consistent multi-species kinetic transport.

Miller, Ronald H.↗

NASA NTRS1996

A Simplified Pattern Match Algorithm for Star Identification

A true pattern matching star algorithm similar in concept to the Van Bezooijen algorithm is implemented using an iterative approach. This approach allows for a more compact and simple implementation which can be easily adapted to be either an all-sky, no a priori algorithm or a follow on to a direct match algorithm to distinguish between ambiguous matches. Some simple analysis is shown to indicate the likelihood of mis-identifications. The performance of the algorithm for the all-sky, no a priori situation is detailed assuming he SKYMAP star catalog describes the true sky. The impact of errors and omissions in the SKYMAP catalog on performance are investigated. In addition, differing levels of noise in the star observations are assumed and results shown. The implications for possible implementation on-board spacecraft are discussed.

Lee, Michael H.↗

NASA NTRS1995

Examination of a Practical Aerobraking Guidance Algorithm

A practical real time guidance algorithm has been developed for aerobraking vehicles that minimizes the post-aeropass Delta V requirements for orbit insertion while nearly minimizing the maximum heating rate and the maximum structural loads. The algorithm is general in the sense that a minimum of assumptions is made, thus greatly reducing the number of parameters that must be determined prior to a given mission. An interesting feature is that in-plane guidance performance is tuned by adjusting one mission-dependent parameter, the bank margin; similarly, the out-of-plane guidance performance is tuned by adjusting a plane controller time constant. Other features of the algorithm are simplicity, efficiency, and ease of use. The algorithm is designed for, but not restricted to, a trimmed vehicle with bank angle modulation as the method of trajectory control. Performance of this guidance algorithm during flight in Earth's atmosphere is examined by its use in an aerobraking testbed program. The performance inquiry extends to a wide range of entry speeds covering a number of potential mission applications. Favorable results have been obtained with a minimum of development effort, and directions for improvement of performance are indicated.

Evans, Steven W.↗

NASA NTRS1995

Comparison of Nonequilibrium Solution Algorithms Applied to Chemically Stiff Hypersonic Flows

Three solution algorithms, explicit under-relaxation, point implicit, and lower-upper symmetric Gauss-Seidel, are used to compute nonequilibrium flow around the Apollo 4 return capsule at the 62-km altitude point in its descent trajectory. By varying the Mach number, the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness.The performance of the solution algorithms degraded as the Mach number and stiffness of the flow increased. At Mach 15 and 30, the lower-upper symmetric Gauss-Seidel method produces an eight order of magnitude drop in the energy residual in one-third to one-half the Cray C-90 computer time as compared to the point implicit and explicit under-relaxation methods. The explicit under-relaxation algorithm experienced convergence difficulties at Mach 30 and above. At Mach 40 the performance of the lower-upper symmetric Gauss-Seidel algorithm deteriorates to the point that it is out performed by the point implicit method. The effects of the viscous terms are investigated. Grid dependency questions are explored.

Palmer, Grant↗

NASA NTRS1996

SSM/I Rain Retrievals Within a Unified All-Weather Ocean Algorithm

A new method for the physical retrieval of rain rates from satellite microwave radiometers is presented and compared to two other rainfall climatologies derived from satellites. The method is part of a unified ocean parameter retrieval algorithm that is based on the fundamental principles of radiative transfer. The algorithm simultaneously finds near-surface wind speed W, columnar water vapor V, columnar cloud liquid water L, rain rate R, and effective radiating temperature T(sub U) for the upwelling radiation. The performance of the algorithm in the absence of rain is discussed in Wentz, and this paper focuses on the rain component of the algorithm. A particular strength of the unified algorithm is its ability to 'orthogonalize' the retrievals so that there is minimum cross-talk between the retrieved parameters. For example, comparisons of the retrieved water vapor with radiosonde observations show that there is very little correlation between the water vapor retrieval error and rain rate. For rain rates from 1 to 15 mm/h, the rms difference between the retrieved water vapor and the radiosonde value is 5 mm. A novel feature of the rain retrieval method is a beamfilling correction that is based upon the ratio of the retrieved liquid water absorption coefficients at 37 GHz and 19.35 GHz. This ratio decreases by about 40% when heavy and light rain co-exist within the SSM/I footprint as compared to the case of uniform rain. This correction has the effect of increasing the rain rate when the spectral ratio of the absorption coefficients is small. Even with this beamfilling correction, tropical rainfall is still unrealistically low when the freezing level in the tropics (approx. 5 km) is used to specify the rain layer thickness. We restore realism by reducing the assumed averaged tropical rain layer thickness to 3 km, thereby accounting for the existence of warm rain processes in which the rain layer does not extend to the freezing level. Global rain rates are produced for the 1991 through 1994 period from observations taken by microwave radiometers (SSM/I) that are aboard two polar-orbiting satellites. We find that approximately 6% of the SSM/I observations detect measurable rain rates (R greater than 0.2 mm/h). Zonal averages of the rain rates show the peak at the intertropical convergence zone (ITCZ) is quite narrow in meridional extent and varies from about 7 mm/day in the winter to a maximum 11 mm/day in the summer. Very low precipitation rates (less than 0.3 mm/day) are observed in those areas of subsidence influenced by the large semipermanent anticyclones. In general, these features are similar to those reported in previously published rain climatologies. However, significant differences do exists between our rain rates and those produced by Spencer. These differences seem to be related to non-precipitating cloud water.

Wentz, Frank J.↗

NASA NTRS1980

Fast, Conservative Algorithm for Solving the Transonic Full-Potential Equation

A fast, fully implicit approximate factorization algorithm designed to solve the conservative, transonic, full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., rotated differencing), thereby greatly enhancing the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted, finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line over-relaxation algorithms.

Holst, Terry L.↗