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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

A fast, uncoupled, compressible, two-dimensional, unsteady boundary layer algorithm with separation for engine inlets

A finite difference boundary layer algorithm was developed to model viscous effects when an inviscid core flow solution is given. This algorithm solved each boundary layer equation separately, then iterated to find a solution. Solving the boundary layer equations sequentially was 2.4 to 4.0 times faster than solving the boundary layer equations simultaneously. This algorithm used a modified Baldwin-Lomax turbulence model, a weighted average of forward and backward differencing of the pressure gradient, and a backward sweep of the pressure. With these modifications, the boundary layer algorithm was able to model flows with and without separation. The number of grid points used in the boundary layer algorithm affected the stability of the algorithm as well as the accuracy of the predictions of friction coefficients and momentum thicknesses. Results of this boundary layer algorithm compared well with experimental observations of friction coefficients and momentum thicknesses. In addition, when used interactively with an inviscid flow algorithm, this boundary layer algorithm corrected for viscous effects to give a good match with experimental observations for pressures in a supersonic inlet.

Roach, Robert L.↗
NASA NTRS1996

A Fast parallel tridiagonal algorithm for a class of CFD applications

The parallel diagonal dominant (PDD) algorithm is an efficient tridiagonal solver. This paper presents for study a variation of the PDD algorithm, the reduced PDD algorithm. The new algorithm maintains the minimum communication provided by the PDD algorithm, but has a reduced operation count. The PDD algorithm also has a smaller operation count than the conventional sequential algorithm for many applications. Accuracy analysis is provided for the reduced PDD algorithm for symmetric Toeplitz tridiagonal (STT) systems. Implementation results on Langley's Intel Paragon and IBM SP2 show that both the PDD and reduced PDD algorithms are efficient and scalable.

Moitra, Stuti↗
NASA NTRS1998

A Polynomial Time, Numerically Stable Integer Relation Algorithm

Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.

Ferguson, Helaman R. P.↗
NASA NTRS2002

Use of Collocated KWAJEX Satellite, Aircraft, and Ground Measurements for Understanding Ambiguities in TRMM Radiometer Rain Profile Algorithm

Coordinated ground, aircraft, and satellite observations are analyzed from the 1999 TRMM Kwajalein Atoll field experiment (KWAJEX) to better understand the relationships between cloud microphysical processes and microwave radiation intensities in the context of physical evaluation of the Level 2 TRMM radiometer rain profile algorithm and uncertainties with its assumed microphysics-radiation relationships. This talk focuses on the results of a multi-dataset analysis based on measurements from KWAJEX surface, air, and satellite platforms to test the hypothesis that uncertainties in the passive microwave radiometer algorithm (TMI 2a12 in the nomenclature of TRMM) are systematically coupled and correlated with the magnitudes of deviation of the assumed 3-dimensional microphysical properties from observed microphysical properties. Re-stated, this study focuses on identifying the weaknesses in the operational TRMM 2a12 radiometer algorithm based on observed microphysics and radiation data in terms of over-simplifications used in its theoretical microphysical underpinnings. The analysis makes use of a common transform coordinate system derived from the measuring capabilities of the aircraft radiometer used to survey the experimental study area, i.e., the 4-channel AMPR radiometer flown on the NASA DC-8 aircraft. Normalized emission and scattering indices derived from radiometer brightness temperatures at the four measuring frequencies enable a 2-dimensional coordinate system that facilities compositing of Kwajalein S-band ground radar reflectivities, ARMAR Ku-band aircraft radar reflectivities, TMI spacecraft radiometer brightness temperatures, PR Ku-band spacecraft radar reflectivities, bulk microphysical parameters derived from the aircraft-mounted cloud microphysics laser probes (including liquid/ice water contents, effective liquid/ice hydrometeor radii, and effective liquid/ice hydrometeor variances), and rainrates derived from any of the individual ground, aircraft, or satellite algorithms applied to the radar or radiometer measurements, or their combination. The results support the study's underlying hypothesis, particularly in context of ice phase processes, in that the cloud regions where the 2a12 algorithm's microphysical database most misrepresents the microphysical conditions as determined by the laser probes, are where retrieved surface rainrates are most erroneous relative to other reference rainrates as determined by ground and aircraft radar. In reaching these conclusions, TMI and PR brightness temperatures and reflectivities have been synthesized from the aircraft AMPR and ARMAR measurements with the analysis conducted in a composite framework to eliminate measurement noise associated with the case study approach and single element volumes obfuscated by heterogeneous beam filling effects. In diagnosing the performance of the 2a12 algorithm, weaknesses have been found in the cloud-radiation database used to provide microphysical guidance to the algorithm for upper cloud ice microphysics. It is also necessary to adjust a fractional convective rainfall factor within the algorithm somewhat arbitrarily to achieve satisfactory algorithm accuracy.

Smith, Eric A.↗
NASA NTRS2001

Algorithms and Application of Sparse Matrix Assembly and Equation Solvers for Aeroacoustics

An algorithm for symmetric sparse equation solutions on an unstructured grid is described. Efficient, sequential sparse algorithms for degree-of-freedom reordering, supernodes, symbolic/numerical factorization, and forward backward solution phases are reviewed. Three sparse algorithms for the generation and assembly of symmetric systems of matrix equations are presented. The accuracy and numerical performance of the sequential version of the sparse algorithms are evaluated over the frequency range of interest in a three-dimensional aeroacoustics application. Results show that the solver solutions are accurate using a discretization of 12 points per wavelength. Results also show that the first assembly algorithm is impractical for high-frequency noise calculations. The second and third assembly algorithms have nearly equal performance at low values of source frequencies, but at higher values of source frequencies the third algorithm saves CPU time and RAM. The CPU time and the RAM required by the second and third assembly algorithms are two orders of magnitude smaller than that required by the sparse equation solver. A sequential version of these sparse algorithms can, therefore, be conveniently incorporated into a substructuring for domain decomposition formulation to achieve parallel computation, where different substructures are handles by different parallel processors.

Watson, W. R.↗
NASA NTRS2007

A Comparison of Two Skip Entry Guidance Algorithms

The Orion capsule vehicle will have a Lift-to-Drag ratio (L/D) of 0.3-0.35. For an Apollo-like direct entry into the Earth's atmosphere from a lunar return trajectory, this L/D will give the vehicle a maximum range of about 2500 nm and a maximum crossrange of 216 nm. In order to y longer ranges, the vehicle lift must be used to loft the trajectory such that the aerodynamic forces are decreased. A Skip-Trajectory results if the vehicle leaves the sensible atmosphere and a second entry occurs downrange of the atmospheric exit point. The Orion capsule is required to have landing site access (either on land or in water) inside the Continental United States (CONUS) for lunar returns anytime during the lunar month. This requirement means the vehicle must be capable of flying ranges of at least 5500 nm. For the L/D of the vehicle, this is only possible with the use of a guided Skip-Trajectory. A skip entry guidance algorithm is necessary to achieve this requirement. Two skip entry guidance algorithms have been developed: the Numerical Skip Entry Guidance (NSEG) algorithm was developed at NASA/JSC and PredGuid was developed at Draper Laboratory. A comparison of these two algorithms will be presented in this paper. Each algorithm has been implemented in a high-fidelity, 6 degree-of-freedom simulation called the Advanced NASA Technology Architecture for Exploration Studies (ANTARES). NASA and Draper engineers have completed several monte carlo analyses in order to compare the performance of each algorithm in various stress states. Each algorithm has been tested for entry-to-target ranges to include direct entries and skip entries of varying length. Dispersions have been included on the initial entry interface state, vehicle mass properties, vehicle aerodynamics, atmosphere, and Reaction Control System (RCS). Performance criteria include miss distance to the target, RCS fuel usage, maximum g-loads and heat rates for the first and second entry, total heat load, and control system saturation. The comparison of the performance criteria has led to a down select and guidance merger that will take the best ideas from each algorithm to create one skip entry guidance algorithm for the Orion vehicle.

Rea, Jeremy R.↗
NASA NTRS2006

Quantifying Global Uncertainties in a Simple Microwave Rainfall Algorithm

While a large number of methods exist in the literature for retrieving rainfall from passive microwave brightness temperatures, little has been written about the quantitative assessment of the expected uncertainties in these rainfall products at various time and space scales. The latter is the result of two factors: sparse validation sites over most of the world's oceans, and algorithm sensitivities to rainfall regimes that cause inconsistencies against validation data collected at different locations. To make progress in this area, a simple probabilistic algorithm is developed. The algorithm uses an a priori database constructed from the Tropical Rainfall Measuring Mission (TRMM) radar data coupled with radiative transfer computations. Unlike efforts designed to improve rainfall products, this algorithm takes a step backward in order to focus on uncertainties. In addition to inversion uncertainties, the construction of the algorithm allows errors resulting from incorrect databases, incomplete databases, and time- and space-varying databases to be examined. These are quantified. Results show that the simple algorithm reduces errors introduced by imperfect knowledge of precipitation radar (PR) rain by a factor of 4 relative to an algorithm that is tuned to the PR rainfall. Database completeness does not introduce any additional uncertainty at the global scale, while climatologically distinct space/time domains add approximately 25% uncertainty that cannot be detected by a radiometer alone. Of this value, 20% is attributed to changes in cloud morphology and microphysics, while 5% is a result of changes in the rain/no-rain thresholds. All but 2%-3% of this variability can be accounted for by considering the implicit assumptions in the algorithm. Additional uncertainties introduced by the details of the algorithm formulation are not quantified in this study because of the need for independent measurements that are beyond the scope of this paper. A validation strategy for these errors is outlined.

Kummerow, Christian↗
NASA NTRS2007

An Improved Algorithm for Retrieving Surface Downwelling Longwave Radiation from Satellite Measurements

Zhou and Cess [2001] developed an algorithm for retrieving surface downwelling longwave radiation (SDLW) based upon detailed studies using radiative transfer model calculations and surface radiometric measurements. Their algorithm linked clear sky SDLW with surface upwelling longwave flux and column precipitable water vapor. For cloudy sky cases, they used cloud liquid water path as an additional parameter to account for the effects of clouds. Despite the simplicity of their algorithm, it performed very well for most geographical regions except for those regions where the atmospheric conditions near the surface tend to be extremely cold and dry. Systematic errors were also found for scenes that were covered with ice clouds. An improved version of the algorithm prevents the large errors in the SDLW at low water vapor amounts by taking into account that under such conditions the SDLW and water vapor amount are nearly linear in their relationship. The new algorithm also utilizes cloud fraction and cloud liquid and ice water paths available from the Cloud and the Earth's Radiant Energy System (CERES) single scanner footprint (SSF) product to separately compute the clear and cloudy portions of the fluxes. The new algorithm has been validated against surface measurements at 29 stations around the globe for Terra and Aqua satellites. The results show significant improvement over the original version. The revised Zhou-Cess algorithm is also slightly better or comparable to more sophisticated algorithms currently implemented in the CERES processing and will be incorporated as one of the CERES empirical surface radiation algorithms.

Zhou, Yaping↗
NASA NTRS2006

An Improved Algorithm for Retrieving Surface Downwelling Longwave Radiation from Satellite Measurements

Retrieving surface longwave radiation from space has been a difficult task since the surface downwelling longwave radiation (SDLW) are integrations from radiation emitted by the entire atmosphere, while those emitted from the upper atmosphere are absorbed before reaching the surface. It is particularly problematic when thick clouds are present since thick clouds will virtually block all the longwave radiation from above, while satellites observe atmosphere emissions mostly from above the clouds. Zhou and Cess developed an algorithm for retrieving SDLW based upon detailed studies using radiative transfer model calculations and surface radiometric measurements. Their algorithm linked clear sky SDLW with surface upwelling longwave flux and column precipitable water vapor. For cloudy sky cases, they used cloud liquid water path as an additional parameter to account for the effects of clouds. Despite the simplicity of their algorithm, it performed very well for most geographical regions except for those regions where the atmospheric conditions near the surface tend to be extremely cold and dry. Systematic errors were also found for areas that were covered with ice clouds. An improved version of the algorithm was developed that prevents the large errors in the SDLW at low water vapor amounts. The new algorithm also utilizes cloud fraction and cloud liquid and ice water paths measured from the Cloud and the Earth's Radiant Energy System (CERES) satellites to separately compute the clear and cloudy portions of the fluxes. The new algorithm has been validated against surface measurements at 29 stations around the globe for the Terra and Aqua satellites. The results show significant improvement over the original version. The revised Zhou-Cess algorithm is also slightly better or comparable to more sophisticated algorithms currently implemented in the CERES processing. It will be incorporated in the CERES project as one of the empirical surface radiation algorithms.

Zhou, Yaping↗
NASA NTRS2011

Advancements in the Development of an Operational Lightning Jump Algorithm for GOES-R GLM

Rapid increases in total lightning have been shown to precede the manifestation of severe weather at the surface. These rapid increases have been termed lightning jumps, and are the current focus of algorithm development for the GOES-R Geostationary Lightning Mapper (GLM). Recent lightning jump algorithm work has focused on evaluation of algorithms in three additional regions of the country, as well as, markedly increasing the number of thunderstorms in order to evaluate the each algorithm s performance on a larger population of storms. Lightning characteristics of just over 600 thunderstorms have been studied over the past four years. The 2 lightning jump algorithm continues to show the most promise for an operational lightning jump algorithm, with a probability of detection of 82%, a false alarm rate of 35%, a critical success index of 57%, and a Heidke Skill Score of 0.73 on the entire population of thunderstorms. Average lead time for the 2 algorithm on all severe weather is 21.15 minutes, with a standard deviation of +/- 14.68 minutes. Looking at tornadoes alone, the average lead time is 18.71 minutes, with a standard deviation of +/-14.88 minutes. Moreover, removing the 2 lightning jumps that occur after a jump has been detected, and before severe weather is detected at the ground, the 2 lightning jump algorithm s false alarm rate drops from 35% to 21%. Cold season, low topped, and tropical environments cause problems for the 2 lightning jump algorithm, due to their relative dearth in lightning as compared to a supercellular or summertime airmass thunderstorm environment.

Shultz, Chris↗
NASA NTRS2011

Analysis of the Dryden Wet Bulb GLobe Temperature Algorithm for White Sands Missile Range

In locations where workforce is exposed to high relative humidity and light winds, heat stress is a significant concern. Such is the case at the White Sands Missile Range in New Mexico. Heat stress is depicted by the wet bulb globe temperature, which is the official measurement used by the American Conference of Governmental Industrial Hygienists. The wet bulb globe temperature is measured by an instrument which was designed to be portable and needing routine maintenance. As an alternative form for measuring the wet bulb globe temperature, algorithms have been created to calculate the wet bulb globe temperature from basic meteorological observations. The algorithms are location dependent; therefore a specific algorithm is usually not suitable for multiple locations. Due to climatology similarities, the algorithm developed for use at the Dryden Flight Research Center was applied to data from the White Sands Missile Range. A study was performed that compared a wet bulb globe instrument to data from two Surface Atmospheric Measurement Systems that was applied to the Dryden wet bulb globe temperature algorithm. The period of study was from June to September of2009, with focus being applied from 0900 to 1800, local time. Analysis showed that the algorithm worked well, with a few exceptions. The algorithm becomes less accurate to the measurement when the dew point temperature is over 10 Celsius. Cloud cover also has a significant effect on the measured wet bulb globe temperature. The algorithm does not show red and black heat stress flags well due to shorter time scales of such events. The results of this study show that it is plausible that the Dryden Flight Research wet bulb globe temperature algorithm is compatible with the White Sands Missile Range, except for when there are increased dew point temperatures and cloud cover or precipitation. During such occasions, the wet bulb globe temperature instrument would be the preferred method of measurement. Out of the 30 dates examined, 23 fell under the category of having good accuracy.

LaQuay, Ryan Matthew↗
NASA NTRS2012

An Enhanced TIMESAT Algorithm for Estimating Vegetation Phenology Metrics from MODIS Data

An enhanced TIMESAT algorithm was developed for retrieving vegetation phenology metrics from 250 m and 500 m spatial resolution Moderate Resolution Imaging Spectroradiometer (MODIS) vegetation indexes (VI) over North America. MODIS VI data were pre-processed using snow-cover and land surface temperature data, and temporally smoothed with the enhanced TIMESAT algorithm. An objective third derivative test was applied to define key phenology dates and retrieve a set of phenology metrics. This algorithm has been applied to two MODIS VIs: Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI). In this paper, we describe the algorithm and use EVI as an example to compare three sets of TIMESAT algorithm/MODIS VI combinations: a) original TIMESAT algorithm with original MODIS VI, b) original TIMESAT algorithm with pre-processed MODIS VI, and c) enhanced TIMESAT and pre-processed MODIS VI. All retrievals were compared with ground phenology observations, some made available through the National Phenology Network. Our results show that for MODIS data in middle to high latitude regions, snow and land surface temperature information is critical in retrieving phenology metrics from satellite observations. The results also show that the enhanced TIMESAT algorithm can better accommodate growing season start and end dates that vary significantly from year to year. The TIMESAT algorithm improvements contribute to more spatial coverage and more accurate retrievals of the phenology metrics. Among three sets of TIMESAT/MODIS VI combinations, the start of the growing season metric predicted by the enhanced TIMESAT algorithm using pre-processed MODIS VIs has the best associations with ground observed vegetation greenup dates.

Tan, Bin↗
NASA NTRS2011

A Universal Tare Load Prediction Algorithm for Strain-Gage Balance Calibration Data Analysis

An algorithm is discussed that may be used to estimate tare loads of wind tunnel strain-gage balance calibration data. The algorithm was originally developed by R. Galway of IAR/NRC Canada and has been described in the literature for the iterative analysis technique. Basic ideas of Galway's algorithm, however, are universally applicable and work for both the iterative and the non-iterative analysis technique. A recent modification of Galway's algorithm is presented that improves the convergence behavior of the tare load prediction process if it is used in combination with the non-iterative analysis technique. The modified algorithm allows an analyst to use an alternate method for the calculation of intermediate non-linear tare load estimates whenever Galway's original approach does not lead to a convergence of the tare load iterations. It is also shown in detail how Galway's algorithm may be applied to the non-iterative analysis technique. Hand load data from the calibration of a six-component force balance is used to illustrate the application of the original and modified tare load prediction method. During the analysis of the data both the iterative and the non-iterative analysis technique were applied. Overall, predicted tare loads for combinations of the two tare load prediction methods and the two balance data analysis techniques showed excellent agreement as long as the tare load iterations converged. The modified algorithm, however, appears to have an advantage over the original algorithm when absolute voltage measurements of gage outputs are processed using the non-iterative analysis technique. In these situations only the modified algorithm converged because it uses an exact solution of the intermediate non-linear tare load estimate for the tare load iteration.

balance calibration analysis↗
NASA NTRS2017

Computationally Efficient Motion Planning Algorithms for Agile Autonomous Vehicles in Cluttered Environments

Fast, real-time motion planning of an agile, autonomous vehicle in a cluttered environment, with many geometrically-fixed obstacles, is a very complex problem, especially because of the vehicle dynamics constraints and resource constrained computational capabilities onboard the vehicle. In this paper, we present computationally-efficient versions of our novel motion planning algorithm called the Spherical Expansion and Sequential Convex Programming (SE–SCP) algorithm. The SE–SCP algorithm first uses a spherical-expansion-based randomized sampling algorithm to explore the workspace. Oncea path is found from the start position to the goal position, the algorithm computes a locally optimal trajectory, within its homotopy class for a desired cost function, by solving a sequence of convex optimization problems. Thus, the SE–SCP algorithm is anytime locally optimal and the trajectory is globally optimal if the number of samples tends to infinity. In this paper, we further enhance the computational efficiency of the SE–SCP algorithm using uni-directional and bi-directional rewiring techniques. We also present a detailed proof of the local optimality characteristics of the new SE–SCP algorithms for aspecial case of vehicle dynamics. Simulation examples involving quadrotor and spacecraft help demonstrate the effectiveness of our new algorithms.

Bandyopadhyay, Saptarshi↗
NASA NTRS2022

Merging of the Case 2 Regional Coast Colour and Maximum‑Peak Height Chlorophyll‑a Algorithms: Validation and Demonstration of Satellite‑derived Retrievals Across US Lakes

Water quality monitoring is relevant for protecting the designated, or beneficial uses, of water such as drinking, aquatic life, recreation, irrigation, and food supply that support the economy, human well-being, and aquatic ecosystem health. Managing finite water resources to support these designated uses requires information on water quality so that managers can make sustainable decisions. Chlorophyll-a (chl-a, µg L−1) concentration can serve as a proxy for phytoplankton biomass and may be used as an indicator of increased anthropogenic nutrient stress. Satellite remote sensing may present a complement to in situ measures for assessments of water quality through the retrieval of chl-a with in-water algorithms. Validation of chl-a algorithms across US lakes improves algorithm maturity relevant for monitoring applications. This study compares performance of the Case 2 Regional Coast Colour (C2RCC) chl-a retrieval algorithm, a revised version of the Maximum-Peak Height (MPH(P)) algorithm, and three scenarios merging these two approaches. Satellite data were retrieved from the MEdium Resolution Imaging Spectrometer (MERIS) and the Ocean and Land Colour Instrument (OLCI), while field observations were obtained from 181 lakes matched with U.S. Water Quality Portal chl-a data. The best performance based on mean absolute multiplicative error (MAEmult) was demonstrated by the merged algorithm referred to as C15−M10 (MAEmult = 1.8, biasmult = 0.97, n = 836). In the C15−M10 algorithm, the MPH(P) chl-a value was retained if it was > 10 µg L−1; if the MPH(P) value was ≤ 10 µg L−1, the C2RCC value was selected, as long as that value was < 15 µg L−1. Time-series and lake-wide gradients compared against independent assessments from Lake Champlain and long-term ecological research stations in Wisconsin were used as complementary examples supporting water quality reporting requirements. Trophic state assessments for Wisconsin lakes provided examples in support of inland water quality monitoring applications. This study presents and assesses merged adaptations of chl-a algorithms previously reported independently. Additionally, it contributes to the transition of chl-a algorithm maturity by quantifying error statistics for a number of locations and times.

Satellite↗
NASA NTRSDate not supplied

A NASA Perspective on Quantum Computing: Algorithmic Opportunities and Challenges

In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can provide an advantage, and if so how to design quantum algorithms that realize such advantages. Today, classical heuristics are used to solve many of the most challenging computational problems arising in the practical world, algorithms that have been shown to be effective empirically but have not been mathematically proven to outperform other approaches. With the advent of quantum advantage, the ability of current quantum hardware to do certain computations beyond the ability of even that largest supercomputers, we have an unprecedented opportunity to explore heuristic quantum algorithms. The next few years will be exciting as empirical testing of quantum heuristic algorithms becomes more and more feasible. The talk will begin overview of the NASA QuAIL team’s ongoing quantum computing investigations, and then focus on both near-term and longer term algorithms for optimization, including distributed algorithms.

quantum computing↗
NASA NTRS2012

Generating Global Leaf Area Index from Landsat: Algorithm Formulation and Demonstration

This paper summarizes the implementation of a physically based algorithm for the retrieval of vegetation green Leaf Area Index (LAI) from Landsat surface reflectance data. The algorithm is based on the canopy spectral invariants theory and provides a computationally efficient way of parameterizing the Bidirectional Reflectance Factor (BRF) as a function of spatial resolution and wavelength. LAI retrievals from the application of this algorithm to aggregated Landsat surface reflectances are consistent with those of MODIS for homogeneous sites represented by different herbaceous and forest cover types. Example results illustrating the physics and performance of the algorithm suggest three key factors that influence the LAI retrieval process: 1) the atmospheric correction procedures to estimate surface reflectances; 2) the proximity of Landsatobserved surface reflectance and corresponding reflectances as characterized by the model simulation; and 3) the quality of the input land cover type in accurately delineating pure vegetated components as opposed to mixed pixels. Accounting for these factors, a pilot implementation of the LAI retrieval algorithm was demonstrated for the state of California utilizing the Global Land Survey (GLS) 2005 Landsat data archive. In a separate exercise, the performance of the LAI algorithm over California was evaluated by using the short-wave infrared band in addition to the red and near-infrared bands. Results show that the algorithm, while ingesting the short-wave infrared band, has the ability to delineate open canopies with understory effects and may provide useful information compared to a more traditional two-band retrieval. Future research will involve implementation of this algorithm at continental scales and a validation exercise will be performed in evaluating the accuracy of the 30-m LAI products at several field sites. ©

Landsat↗
NASA NTRS2016

Soil Moisture Active Passive (SMAP) Project Algorithm Theoretical Basis Document SMAP L1B Radiometer Data Product: L1B_TB

The purpose of the Soil Moisture Active Passive (SMAP) radiometer calibration algorithm is to convert Level 0 (L0) radiometer digital counts data into calibrated estimates of brightness temperatures referenced to the Earth's surface within the main beam. The algorithm theory in most respects is similar to what has been developed and implemented for decades for other satellite radiometers; however, SMAP includes two key features heretofore absent from most satellite borne radiometers: radio frequency interference (RFI) detection and mitigation, and measurement of the third and fourth Stokes parameters using digital correlation. The purpose of this document is to describe the SMAP radiometer and forward model, explain the SMAP calibration algorithm, including approximations, errors, and biases, provide all necessary equations for implementing the calibration algorithm and detail the RFI detection and mitigation process. Section 2 provides a summary of algorithm objectives and driving requirements. Section 3 is a description of the instrument and Section 4 covers the forward models, upon which the algorithm is based. Section 5 gives the retrieval algorithm and theory. Section 6 describes the orbit simulator, which implements the forward model and is the key for deriving antenna pattern correction coefficients and testing the overall algorithm.

microwave radiometers↗