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NASA NTRS2003

Ozone Climatological Profiles for Version 8 TOMS and SBUV Retrievals

A new altitude dependent ozone climatology has been produced for use with the latest Total Ozone Mapping Spectrometer (TOMS) and Solar Backscatter Ultraviolet (SBUV) retrieval algorithms. The climatology consists of monthly average profiles for ten degree latitude zones covering from 0 to 60 km. The climatology was formed by combining data from SAGE II (1988 to 2000) and MLS (1991-1999) with data from balloon sondes (1988-2002). Ozone below about 20 km is based on balloons sondes, while ozone above 30 km is based on satellite measurements. The profiles join smoothly between 20 and 30 km. The ozone climatology in the southern hemisphere and tropics has been greatly enhanced in recent years by the addition of balloon sonde stations under the SHADOZ (Southern Hemisphere Additional Ozonesondes) program. A major source of error in the TOMS and SBUV retrieval of total column ozone comes from their reduced sensitivity to ozone in the lower troposphere. An accurate climatology for the retrieval a priori is important for reducing this error on the average. The new climatology follows the seasonal behavior of tropospheric ozone and reflects its hemispheric asymmetry. Comparisons of TOMS version 8 ozone with ground stations show an improvement due in part to the new climatology.

McPeters, R. D.↗

NASA NTRS2012

Causal Correlation Functions and Fourier Transforms: Application in Calculating Pressure Induced Shifts

By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.

correlation function↗

NASA NTRS2012

Determination of Ice Cloud Models Using MODIS and MISR Data

Representation of ice clouds in radiative transfer simulations is subject to uncertainties associated with the shapes and sizes of ice crystals within cirrus clouds. In this study, we examined several ice cloud models consisting of smooth, roughened, homogeneous and inhomogeneous hexagonal ice crystals with various aspect ratios. The sensitivity of the bulk scattering properties and solar reflectances of cirrus clouds to specific ice cloud models is investigated using the improved geometric optics method (IGOM) and the discrete ordinates radiative transfer (DISORT) model. The ice crystal habit fractions in the ice cloud model may significantly affect the simulations of cloud reflectances. A new algorithm was developed to help determine an appropriate ice cloud model for application to the satellite-based retrieval of ice cloud properties. The ice cloud particle size retrieved from Moderate Resolution Imaging Spectroradiometer (MODIS) data, collocated with Multi-angle Imaging Spectroradiometer (MISR) observations, is used to infer the optical thicknesses of ice clouds for nine MISR viewing angles. The relative differences between view-dependent cloud optical thickness and the averaged value over the nine MISR viewing angles can vary from −0.5 to 0.5 and are used to evaluate the ice cloud models. In the case for 2 July 2009, the ice cloud model with mixed ice crystal habits is the best fit to the observations (the root mean square (RMS) error of cloud optical thickness reaches 0.365). This ice cloud model also produces consistent cloud property retrievals for the nine MISR viewing configurations within the measurement uncertainties.

MODIS↗

NASA NTRS1995

Development of an automatic block generation algorithm

A method for automatic multiblock grid generation is described. The method combines the modified advancing front method as a predictor with an elliptic scheme as a corrector. It advances a collection of cells by one cell height in the outward direction using modified advancing front method, and then corrects newly-obtained cell positions by solving elliptic equations. This predictor-corrector type scheme is repeatedly applied until the field of interest is filled with hexahedral grid cells. Given the configuration surface grid, the scheme produces block layouts as well as grid cells with overall smoothness as its output. The method saves human-time and reduces the burden on the user in generating grids for general 3D configurations. It is used to generate multiblock grids for wings in their high-lift configuration.

Eberhardt, Scott↗

NASA NTRS2013

First Evaluation of the Climatological Calibration Algorithm in the Real-time TMPA Precipitation Estimates over Two Basins at High and Low Latitudes

The TRMM Multi-satellite Precipitation Analysis (TMPA) system underwent a crucial upgrade in early 2009 to include a climatological calibration algorithm (CCA) to its realtime product 3B42RT, and this algorithm will continue to be applied in the future Global Precipitation Measurement era constellation precipitation products. In this study, efforts are focused on the comparison and validation of the Version 6 3B42RT estimates before and after the climatological calibration is applied. The evaluation is accomplished using independent rain gauge networks located within the high-latitude Laohahe basin and the low-latitude Mishui basin, both in China. The analyses indicate the CCA can effectively reduce the systematic errors over the low-latitude Mishui basin but misrepresent the intensity distribution pattern of medium-high rain rates. This behavior could adversely affect TMPA's hydrological applications, especially for extreme events (e.g., floods and landslides). Results also show that the CCA tends to perform slightly worse, in particular, during summer and winter, over the high-latitude Laohahe basin. This is possibly due to the simplified calibration-processing scheme in the CCA that directly applies the climatological calibrators developed within 40 degrees latitude to the latitude belts of 40 degrees N-50 degrees N. Caution should therefore be exercised when using the calibrated 3B42RT for heavy rainfall-related flood forecasting (or landslide warning) over high-latitude regions, as the employment of the smooth-fill scheme in the CCA bias correction could homogenize the varying rainstorm characteristics. Finally, this study highlights that accurate detection and estimation of snow at high latitudes is still a challenging task for the future development of satellite precipitation retrievals.

TMPA-RT Precipitation Estimates↗

NASA NTRS1988

Measuring the topology of large-scale structure in the universe

An algorithm for quantitatively measuring the topology of large-scale structure has now been applied to a large number of observational data sets. The present paper summarizes and provides an overview of some of these observational results. On scales significantly larger than the correlation length, larger than about 1200 km/s, the cluster and galaxy data are fully consistent with a sponge-like random phase topology. At a smoothing length of about 600 km/s, however, the observed genus curves show a small shift in the direction of a meatball topology. Cold dark matter (CDM) models show similar shifts at these scales but not generally as large as those seen in the data. Bubble models, with voids completely surrounded on all sides by wall of galaxies, show shifts in the opposite direction. The CDM model is overall the most successful in explaining the data.

Gott, J. Richard, III↗

NASA NTRS2011

Multiangle Implementation of Atmospheric Correction (MAIAC):: Radiative Transfer Basis and Look-up Tables - 1

This paper describes a radiative transfer basis of the algorithm MAIAC which performs simultaneous retrievals of atmospheric aerosol and bidirectional surface reflectance from the Moderate Resolution Imaging Spectroradiometer (MODIS). The retrievals are based on an accurate semianalytical solution for the top-of-atmosphere reflectance expressed as an explicit function of three parameters of the Ross-Thick Li-Sparse model of surface bidirectional reflectance. This solution depends on certain functions of atmospheric properties and geometry which are precomputed in the look-up table (LUT). This paper further considers correction of the LUT functions for variations of surface pressure/height and of atmospheric water vapor, which is a common task in the operational remote sensing. It introduces a new analytical method for the water vapor correction of the multiple ]scattering path radiance. It also summarizes the few basic principles that provide a high efficiency and accuracy of the LUT ]based radiative transfer for the aerosol/surface retrievals and optimize the size of LUT. For example, the single-scattering path radiance is calculated analytically for a given surface pressure and atmospheric water vapor. The same is true for the direct surface-reflected radiance, which along with the single-scattering path radiance largely defines the angular dependence of measurements. For these calculations, the aerosol phase functions and kernels of the surface bidirectional reflectance model are precalculated at a high angular resolution. The other radiative transfer functions depend rather smoothly on angles because of multiple scattering and can be calculated at coarser angular resolution to reduce the LUT size. At the same time, this resolution should be high enough to use the nearest neighbor geometry angles to avoid costly three ]dimensional interpolation. The pressure correction is implemented via linear interpolation between two LUTs computed for the standard and reduced pressure levels. A linear mixture and a modified linear mixture methods are used to represent different aerosol types in the aerosol/surface retrievals from several base models of the fine and coarse aerosol fractions. In summary, the developed LUT algorithm allows fast high-accuracy simulations of the outgoing radiance with full variability of the atmospheric and surface bidirectional reflectance properties for the aerosol/surface remote sensing.

Lyapustin, Alexei↗

NASA NTRS1999

Remote Sensing of Rain

The first problem addressed concerns passive-microwave rain retrievals. Most current approaches start by building off-line a cloud-model-derived database. Given data, the retrieval algorithms search the database for the microwave temperatures "closest" to the observed data, then after some fine-tuning (performed in different ways by different implementations) the rain is estimated to be that which corresponds to the selected (and fine-tuned) set of database temperatures. These approaches have three drawbacks: they cannot properly take into account the ambiguities which arise from the fact that several rain scenarios can produce the same observed temperatures; they are quite inefficient since they require manipulating a large database along with often complex "fine-tuning" procedures; and they cannot refine their estimates if additional data is available. This past year we have derived closed formulae relating observed microwave brightness temperatures, T(sub b), and the underlying rain rates, R: average T(sub b) =f (rain) and average rain = g (T(sub b)), along with the corresponding covariance matrices. These results are sufficient to describe the conditional probabilities p(R/T(sub b)) and p(T(sub b)/R) to second order. Progress has also been made towards deriving a robust description of the rain drop size distribution (DSD). The widespread approach consisting in parameterizing the DSD as a gamma-distribution in terms of the drop diameter D suffers from the facts that, in reality, the DSD is not a smooth function of D and that the largely arbitrary Gamma model imposes unintended behavior, which has implications on any quantities derived from the DSD model. We have therefore developed a non-parametric yet practical description of the DSD, which is particularly well-suited for use in remote-sensing applications. The diagram on the left shows a comparison between an actual DSD sample and the truncated non-parametric representation. One figure shows the relation between radar reflectivity and rain rate derived using this representation. Validation of the Tropical Rainfall Measuring Mission (TRMM) radar-radiometer combined R and DSD algorithm is underway. This algorithm was designed to make optimal use of the instantaneous reflectivity profiles measured by the TRMM radar and the microwave brightness temperatures measured by the TRMM passive radiometer. So far, it appears to be the most reliable TRMM rain algorithm.

Haddad, Ziad S.↗

NASA NTRS2006

Spatial Variability of Barrow-Area Shore-Fast Sea Ice and Its Relationships to Passive Microwave Emissivity

Aircraft-acquired passive microwave data, laser radar height observations, RADARSAT synthetic aperture radar imagery, and in situ measurements obtained during the AMSR-Ice03 experiment are used to investigate relationships between microwave emission and ice characteristics over several space scales. The data fusion allows delineation of the shore-fast ice and pack ice in the Barrow area, AK, into several ice classes. Results show good agreement between observed and Polarimetric Scanning Radiometer (PSR)-derived snow depths over relatively smooth ice, with larger differences over ridged and rubbled ice. The PSR results are consistent with the effects on snow depth of the spatial distribution and nature of ice roughness, ridging, and other factors such as ice age. Apparent relationships exist between ice roughness and the degree of depolarization of emission at 10,19, and 37 GHz. This depolarization .would yield overestimates of total ice concentration using polarization-based algorithms, with indications of this seen when the NT-2 algorithm is applied to the PSR data. Other characteristics of the microwave data, such as effects of grounding of sea ice and large contrast between sea ice and adjacent land, are also apparent in the PSR data. Overall, the results further demonstrate the importance of macroscale ice roughness conditions such as ridging and rubbling on snow depth and microwave emissivity.

Maslanik, J. A.↗

NASA NTRS2014

A Semiautomated Multilayer Picking Algorithm for Ice-sheet Radar Echograms Applied to Ground-Based Near-Surface Data

Snow accumulation over an ice sheet is the sole mass input, making it a primary measurement for understanding the past, present, and future mass balance. Near-surface frequency-modulated continuous-wave (FMCW) radars image isochronous firn layers recording accumulation histories. The Semiautomated Multilayer Picking Algorithm (SAMPA) was designed and developed to trace annual accumulation layers in polar firn from both airborne and ground-based radars. The SAMPA algorithm is based on the Radon transform (RT) computed by blocks and angular orientations over a radar echogram. For each echogram's block, the RT maps firn segmented-layer features into peaks, which are picked using amplitude and width threshold parameters of peaks. A backward RT is then computed for each corresponding block, mapping the peaks back into picked segmented-layers. The segmented layers are then connected and smoothed to achieve a final layer pick across the echogram. Once input parameters are trained, SAMPA operates autonomously and can process hundreds of kilometers of radar data picking more than 40 layers. SAMPA final pick results and layer numbering still require a cursory manual adjustment to correct noncontinuous picks, which are likely not annual, and to correct for inconsistency in layer numbering. Despite the manual effort to train and check SAMPA results, it is an efficient tool for picking multiple accumulation layers in polar firn, reducing time over manual digitizing efforts. The trackability of good detected layers is greater than 90%.

Antarctic Ice-Sheet↗

NASA NTRS1984

Computational problems on composite grids

Most currently used algorithms for the numerical solution of the partial differential equations encountered in fluid flow problems can be implemented on composite grid systems. Finite volume formulations are easier to derive on composite grids, and may in principle be derived for partial differential equations of all types. Except when using Alternating Difference Implicit-type schemes, the overlapping of grids is an alternative to the more common grid construction procedure where grid lines continue smoothly from one subregion to the next. In the solution of model problems, the correct choice of an interpolation formula has been found able to reduce errors by a factor of two.

Mastin, C. W.↗

NASA NTRS1991

Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms

A micron n+ - n - n+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the non-steady case, and a limiting process is used to reach steady state. The simulation employs shock capturing algorithms, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially nonoscillatory, were successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws in fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge-Kutta methods allow one to achieve higher accuracy in time if desired. The spatial accuracy is of high order in regions of smoothness.

Fatemi, Emad↗

NASA NTRS2013

RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers

RUSHMAPS is a new onboard data reduction scheme that gives real-time access to key science parameters (e.g. moments) of a class of heliophysics science and/or solar system exploration investigation that includes plasma particle spectrometers (PPS), but requires moments reporting (density, bulk-velocity, temperature, pressure, etc.) of higher-level quality, and tolerates a lowpass (variable quality) spectral representation of the corresponding particle velocity distributions, such that telemetry use is minimized. The proposed methodology trades access to the full-resolution velocity distribution data, saving on telemetry, for real-time access to both the moments and an adjustable-quality (increasing quality increases volume) spectral representation of distribution functions. Traditional onboard data storage and downlink bandwidth constraints severely limit PPS system functionality and drive cost, which, as a consequence, drives a limited data collection and lower angular energy and time resolution. This prototypical system exploit, using high-performance processing technology at GSFC (Goddard Space Flight Center), uses a SpaceCube and/or Maestro-type platform for processing. These processing platforms are currently being used on the International Space Station as a technology demonstration, and work is currently ongoing in a new onboard computation system for the Earth Science missions, but they have never been implemented in heliospheric science or solar system exploration missions. Preliminary analysis confirms that the targeted processor platforms possess the processing resources required for realtime application of these algorithms to the spectrometer data. SpaceCube platforms demonstrate that the target architecture possesses the sort of compact, low-mass/power, radiation-tolerant characteristics needed for flight. These high-performing hybrid systems embed unprecedented amounts of onboard processing power in the CPU (central processing unit), FPGAs (field programmable gate arrays), and DSP (digital signal processing) elements. The fundamental computational algorithm de constructs 3D velocity distributions in terms of spherical harmonic spectral coefficients (which are analogous to a Fourier sine-cosine decomposition), but uses instead spherical harmonics Legendre polynomial orthogonal functions as a basis for the expansion, portraying each 2D angular distribution at every energy or, geometrically, spherical speed-shell swept by the particle spectrometer. Optionally, these spherical harmonic spectral coefficients may be telemetered to the ground. These will provide a smoothed description of the velocity distribution function whose quality will depend on the number of coefficients determined. Successfully implemented on the GSFC-developed processor, the capability to integrate the proposed methodology with both heritage and anticipated future plasma particle spectrometer designs is demonstrated (with sufficiently detailed design analysis to advance TRL) to show specific science relevancy with future HSD (Heliophysics Science Division) solar-interplanetary, planetary missions, sounding rockets and/or CubeSat missions.

Figueroa-Vinas, Adolfo↗

NASA NTRS1988

Vortex methods for separated flows

The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented and includes the relationship with traditional point-vortex studies, convergence to smooth solutions of the Euler equations, and the essential differences between two and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. Two-dimensional flows around bluff bodies are emphasized. Robustness of the method and the assessment of accuracy, vortex-core profiles, time-marching schemes, numerical dissipation, and efficient programming are treated. Operation counts for unbounded and periodic flows are given, and two algorithms designed to speed up the calculations are described.

Spalart, Philippe R.↗

NASA NTRS1989

Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms

A micron n+ - n - n+ silicon diode is simulated via the hydrodynamic model for carrier transport. The numerical algorithms employed are for the non-steady case, and a limiting process is used to reach steady state. The simulation employs shock capturing algorithms, and indeed shocks, or very rapid transition regimes, are observed in the transient case for the coupled system, consisting of the potential equation and the conservation equations describing charge, momentum, and energy transfer for the electron carriers. These algorithms, termed essentially non-oscillatory, were successfully applied in other contexts to model the flow in gas dynamics, magnetohydrodynamics, and other physical situations involving the conservation laws in fluid mechanics. The method here is first order in time, but the use of small time steps allows for good accuracy. Runge-Kutta methods allow one to achieve higher accuracy in time if desired. The spatial accuracy is of high order in regions of smoothness.

Fatemi, Emad↗

NASA NTRSDate not supplied

Using the Diurnal Variability in GeoNEX TOA Reflectances for Earth Monitoring

Observations from the third-generation geostationary satellite instruments (GOES 16/17 ABI, Himawari 8/9 AHI, and etc.) have spatial resolution and spectral band configurations comparable to flagship LEO sensors (e.g., MODIS/VIIRS). More importantly, these data are acquired at very high temporal resolution, faithfully recording the variations of the full disk of Earth at every 5-10 minutes. They thus provide unique information about Earth’s atmosphere and surface. In order to explore the unique information content of geostationary data, this study systematically analyzes the diurnal variability in the GeoNEX L1G TOA reflectance products and compares them to simulated results by state-of-the-art radiative transfer codes. Our results show that • The smoothness of the TOA reflectance diurnal cycle provides a convenient and reliable way to identify stable atmospheric conditions and filter out passing clouds/shadows. • The diurnal variability of the blue band (0.47µm) reflectance is regulated mainly by atmospheric optical conditions over a majority of land cover types. As such, the diurnal variability of the blue band data allows us to retrieve AOD without invoking the use of spectral band ratios (SRC) as in previous algorithms. • In comparison, the diurnal variability of the short-wave infrared band (2.2µm) BRFs is mainly regulated by surface reflectance and the sun-target-satellite geometry. This information allows us to test and, if suitable, retrieve surface BRDF parameters. • Spectral band ratios, especially those between the 2.2µm and 0.47µm bands, are not constant but vary by locations and sun-target-satellite geometries. Our analysis clearly demonstrates that the information provided in high-frequent geostationary observations is unique and complementary to LEO sensors. Therefore, a synergy of GEO and LEO (and other) sensors has the great potential to improve existing remote sensing models and algorithms for better Earth monitoring.

Diurnal Variability↗

NASA NTRS1972

Nonlinear estimation theory applied to the interplanetary orbit determination problem.

Martingale theory and appropriate smoothing properties of Loeve (1953) have been used to develop a modified Gaussian second-order filter. The performance of the filter is evaluated through numerical simulation of a Jupiter flyby mission. The observations used in the simulation are on-board measurements of the angle between Jupiter and a fixed star taken at discrete time intervals. In the numerical study, the influence of each of the second-order terms is evaluated. Five filter algorithms are used in the simulations. Four of the filters are the modified Gaussian second-order filter and three approximations derived by neglecting one or more of the second-order terms in the equations. The fifth filter is the extended Kalman-Bucy filter which is obtained by neglecting all of the second-order terms.

Tapley, B. D.↗

NASA NTRS2003

Computational Aeroacoustics: An Overview

An overview of recent advances in computational aeroacoustics (CAA) is presented. CAA algorithms must not be dispersive and dissipative. It should propagate waves supported by the Euler equations with the correct group velocities. Computation domains are inevitably finite in size. To avoid the reflection of acoustic and other outgoing waves at the boundaries of the computation domain, it is required that special boundary conditions be imposed at the boundary region. These boundary conditions either absorb all the outgoing waves without reflection or allow the waves to exit smoothly. High-order schemes, invariably, supports spurious short waves. These spurious waves tend to pollute the numerical solution. They must be selectively damped or filtered out. All these issues and relevant computation methods are briefly reviewed. Jet screech tones are known to have caused structural fatigue in military combat aircrafts. Numerical simulation of the jet screech phenomenon is presented as an example of a successful application of CAA.

Tam, Christopher K. W.↗