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NASA NTRS1989

The GRADIO spaceborne gravity gradiometer: Development and accommodation

The European ARISTOTELES mission aims at the determination of the Earth's gravity field at short wavelength with a global coverage. Gravity gradient measurements will be achieved during six months by the GRADIO instrument onboard a dedicated satellite in a near dawn-dusk sun-synchronous orbit at an altitude of 200 km. The objective is an accuracy of better than 5 mgals for gravity anomalies, at ground level for blocks of 1 x 1 deg. According to present knowledge of the potential, the recovery of higher spherical harmonics (degree and order greater than 30) is of main importance. This leads to focus on the variations of the measured components T(sub ij) of the gravity gradient tensor, at frequencies greater than 5 x 10(exp -3) Hz. The resolution, required for the gradiometer is 10(exp -2) Eotvos (i.e., 10(exp -11)/s squared) with an averaging time of 4 s.

Bernard, A.↗

NASA NTRS2002

Progress Toward Generation of a Navier-Stokes Database for a Harrier in Ground Effect

The Harrier YAV-8B aircraft is capable of vertical and short-field take-off and landing (V/STOL) by directing its four exhaust nozzles toward the ground, or conventional flight by rotating its nozzles into a horizontal position. The British Royal Air Force and the United States Marine Corps have used this aircraft for more than 30 years to provide a quick reaction time for troop support, and reduce the need for long runways. The success of this powered-lift (PL) vehicle has also prompted the more recent design of the Joint Strike Fighter (JSF). However there are significant safety issues that must be addressed when operating a PL vehicle in close proximity to the ground. Hot Gas Ingestion (HGI) by the inlets can result in a rapid loss of powered lift; and high-speed jet flows along the ground plane can induce low pressures underneath the vehicle, causing a 'suck-down' effect. Under these conditions, departure from controlled flight may occur. Moreover, unsteady ground vortices and jet fountains can affect the aircraft,s controllability and its proximity to ground troops. The viscous, time-dependent flow fields of PL vehicles are difficult to accurately and efficiently predict using Computational Fluid Dynamics (CFD). A number of researchers have used the time-dependent Reynolds-averaged Navier-Stokes (RANS) equations to compute flows for single and multiple jets in a cross-flow. A few have added some geometric complexity to the problem by computing flows for jet-augmented delta wings near a ground plane. Smith et.al. computed for the first time a single RANS solution about a simplified Harrier. This geometry included a fuselage, wing, leading edge root extension (LERX), inlets, and exhaust nozzles. All of these investigations cite two practical problems with computing these flows: 1) the need for improved solution accuracy; and, 2) the need for faster solution methods. We view the need for faster solution methods as key to improving the solution accuracy and making this class of computation more routine. One can hardly refine grids, explore the use of advanced turbulence models, and generate databases when it takes weeks of dedicated computer time for a single solution. Chaderjian, Ahmad, Pandya, and Murman have focused on reducing the time-to-solution for this very difficult and complex problem through process automation and exploitation of parallel computing. They began with the Harrier geometry reported, and added a deflected wing flap and empennage for greater realism. To date more than 80 solutions have been carried out. This paper will describe this process and progress made in reducing the time required to generate a simple longitudinal force and moment database for a Harrier in ground effect. It shows a typical snap-shot from an unsteady streakline animation, where fluid particles are colored by temperature. The ground vortex and a jet-fountain vortex are highlighted. It also shows a similar streakline image, where HGI occurs due to the vehicle in close proximity to the ground. It is show the mean lift coefficient as a function of angle of attack and height. The angle of attack range was 4 deg less than or = alpha less than or = 10 deg with an increment of 1 degree, and the height range was 10 ft less than or = h less than or = 30ft with an increment of 5 feet. This 35 solution database was extended to over 2500 cases using a monotone cubic-spline interpolation procedure. The suck-down effect (reduction of lift near the ground) is highlighted in the figure. The "cushion effect," the conventional reduction of lift as the vehicle moves out of ground effect, is also indicated. All 35 RANS solutions were obtained using 952 Silicon Graphics Origin 2000 and 3000 processors in dedicated mode for one week. Typically, 112 processors were assigned to each case. Some other cases used fewer processors to utilize all available CPUS. The final paper will report on the automation of the solution process, including: grid generation, job monitoring, solution completion criteria, and post processing. Moreover, improvements in parallel efficiency for a dual time-step algorithm for the RANS equations will also be presented. Results will be discussed in detail using unsteady streakline flow visualization to correlate unsteady flow structures with dominant aerodynamic frequencies. The stability derivatives, CL, and CL, will also be presented.

Chaderjian, Neal M.↗

NASA NTRS2016

Analysis of Large Civil Tilt Rotor Wind Tunnel Blockage and Validation Using RotCFD

Ground based experiments are often used to understand and measure rotor and airframe aerodynamic performance; however, these experiments have certain limitations. The effects of these limitations are evaluated here using computational fluid dynamic (CFD) modeling techniques. Through this study, data from the 7- by 10-Foot Wind Tunnel experiments of the Large Civil Tilt Rotor (LCTR) at NASA Ames Research Center is validated using CFD. The Reynolds Averages Navier-Stokes solver, RotCFD, is used for the computations. In particular, the effect of the blockage generated by the test hardware on the walls is investigated. To study this problem, simplified geometries such as a flat plate, cube and cylinder are also investigated for blockage effects. This is done to explore if these different geometries can represent the LCTR as a simplified case to reduce computational time and get a quick first understanding of tunnel blockage effects. The focus of this research is to understand the limitations and accuracy of the recent small-scale Large Civil Tilt Rotor wind tunnel test campaigns.

Validation↗

NASA NTRS1986

Transonic Navier-Stokes wing solutions using a zonal approach. Part 2: High angle-of-attack simulation

A computer code is under development whereby the thin-layer Reynolds-averaged Navier-Stokes equations are to be applied to realistic fighter-aircraft configurations. This transonic Navier-Stokes code (TNS) utilizes a zonal approach in order to treat complex geometries and satisfy in-core computer memory constraints. The zonal approach has been applied to isolated wing geometries in order to facilitate code development. Part 1 of this paper addresses the TNS finite-difference algorithm, zonal methodology, and code validation with experimental data. Part 2 of this paper addresses some numerical issues such as code robustness, efficiency, and accuracy at high angles of attack. Special free-stream-preserving metrics proved an effective way to treat H-mesh singularities over a large range of severe flow conditions, including strong leading-edge flow gradients, massive shock-induced separation, and stall. Furthermore, lift and drag coefficients have been computed for a wing up through CLmax. Numerical oil flow patterns and particle trajectories are presented both for subcritical and transonic flow. These flow simulations are rich with complex separated flow physics and demonstrate the efficiency and robustness of the zonal approach.

Chaderjian, N. M.↗

NASA NTRS1998

Experimental Techniques Verified for Determining Yield and Flow Surfaces

Structural components in aircraft engines are subjected to multiaxial loads when in service. For such components, life prediction methodologies are dependent on the accuracy of the constitutive models that determine the elastic and inelastic portions of a loading cycle. A threshold surface (such as a yield surface) is customarily used to differentiate between reversible and irreversible flow. For elastoplastic materials, a yield surface can be used to delimit the elastic region in a given stress space. The concept of a yield surface is central to the mathematical formulation of a classical plasticity theory, but at elevated temperatures, material response can be highly time dependent. Thus, viscoplastic theories have been developed to account for this time dependency. Since the key to many of these theories is experimental validation, the objective of this work (refs. 1 and 2) at the NASA Lewis Research Center was to verify that current laboratory techniques and equipment are sufficient to determine flow surfaces at elevated temperatures. By probing many times in the axial-torsional stress space, we could define the yield and flow surfaces. A small offset definition of yield (10 me) was used to delineate the boundary between reversible and irreversible behavior so that the material state remained essentially unchanged and multiple probes could be done on the same specimen. The strain was measured with an off-the-shelf multiaxial extensometer that could measure the axial and torsional strains over a wide range of temperatures. The accuracy and resolution of this extensometer was verified by comparing its data with strain gauge data at room temperature. The extensometer was found to have sufficient resolution for these experiments. In addition, the amount of crosstalk (i.e., the accumulation of apparent strain in one direction when strain in the other direction is applied) was found to be negligible. Tubular specimens were induction heated to determine the flow surfaces at elevated temperatures. The heating system induced a large amount of noise in the data. By reducing thermal fluctuations and using appropriate data averaging schemes, we could render the noise inconsequential. Thus, accurate and reproducible flow surfaces (see the figure) could be obtained.

Lerch, Brad A.↗

NASA NTRS2006

Aeolian Shear Stress Ratio Measurements within Mesquite-Dominated Landscapes of the Chihuahuan Desert, New Mexico, USA

A field study was conducted to ascertain the amount of protection that mesquite-dominated communities provide to the surface from wind erosion. The dynamics of the locally accelerated evolution of a mesquite/coppice dune landscape and the undetermined spatial dependence of potential erosion by wind from a shear stress partition model were investigated. Sediment transport and dust emission processes are governed by the amount of protection that can be provided by roughness elements. Although shear stress partition models exist that can describe this, their accuracy has only been tested against a limited dataset because instrumentation has previously been unable to provide the necessary measurements. This study combines the use of meteorological towers and surface shear stress measurements with Irwin sensors to measure the partition of shear stress in situ. The surface shear stress within preferentially aligned vegetation (within coppice dune development) exhibited highly skewed distributions, while a more homogenous surface stress was recorded at a site with less developed coppice dunes. Above the vegetation, the logarithmic velocity profile deduced roughness length (based on 10-min averages) exhibited a distinct correlation with compass direction for the site with vegetation preferentially aligned, while the site with more homogenously distributed vegetation showed very little variation in the roughness length. This distribution in roughness length within an area, defines a distribution of a resolved shear stress partitioning model based on these measurements, ultimately providing potential closure to a previously uncorrelated model parameter.

King, James↗

NASA NTRS2013

Digitally Calibrated TR Modules Enabling Real-Time Beamforming SweepSAR Architectures

SweepSAR, a novel radar architecture that depends on a DBF (digital beamforming) array, requires calibration accuracies that are order(s) of magnitude greater than is possible with traditional techniques, such as a priori characterization of TR (transmit/receive) modules in thermal vacuum chambers, or simple loop-back of the calibration signal. The advantages of a SweepSAR architecture are so great that it is worth applying significant resources to calibration efforts. Due to the nature of the DBF, each channel contains a digitizer and very powerful digital processor. Each channel can independently digitize (with the digitizer) and analyze (with the processor) its channel's unique calibration signal, and extract the relevant calibration parameters, namely channel gain and channel phase delay commonly referred to as the gain (or amplitude) and phase of the channel. Using the processor, each channel's gain and phase can theoretically be estimated with arbitrary precision through averaging a sufficiently large number of samples. Systematic errors and the changing gain and phase of the channels, typically due to temperature drifts, limits how long the averaging can occur, which limits the precision of the calibration estimate. However, results indicate that calibration knowledge of both the transmit and receive chains of each TR module can be improved by one or two orders of magnitude. Due to the digital nature of the receiver data, the channel's gain and phase may be corrected by a similar amount, while the transmit chain can only be corrected in a traditional manner. To implement Sweep SAR, the order of magnitude improvement in the knowledge of the channel's gain and phase is needed, and the control of the receiver to a similar level is required. Inherent to the DBF array is the individual digitization of each of the array's receiver channels. Current systems typically combine all of the analog signals in the array into one or two analog channels, which are then digitized and processed. All signal conditioning performed prior to digitization is done using analog hardware (which is less precise than digital signal conditioning and dependent on temperature). The DBF digitizes every signal prior to combining, and can therefore analyze and correct received signals, as well as analyze signals that are being transmitted through analog hardware (by sampling a copy and digitizing). Each channel of a DBF also has a powerful processor. With this combination, one is able to digitize, analyze, and correct each channel prior to its being combined. A unique factor is the ability to digitize and analyze (in real time) each of the array's channels independently, allowing one to achieve unprecedented knowledge of each channel's performance (gain and phase), and since the combining is done digitally, each receive channel can be corrected prior to combining. This enables an unprecedented level of accuracy and control through onboard processing. SweepSAR promises significant increases in instrument capability for solid earth and biomass remote sensing, while reducing mission mass and cost. This new instrument concept requires new methods for calibrating the multiple channels, which must be combined onboard, in real time. New methods are being developed for digitally calibrating digital beam-forming arrays to reduce development time, risk, and cost of precision calibrated TR modules for array architectures by accurately tracking modules' characteristics through closed-loop digital calibration, thus tracking systematic changes regardless of temperature.-

Hoffman, James P.↗

NASA NTRS1981

The MSS control point location error filter for LANDSAT-D

The filter produces the maximum likelihood estimates for average values of the spacecraft position and attitude errors during a single scene. The quality of the filter performance is characterized by the maximal cross and along track residual errors for which probability distributions can be calculated analytically for a given pattern of control points. The filter with an automatic selection of the best set of estimates provides geodetic correction at 90% of pixels with residual errors less than 40 m for four or more control points and the mean squared measurement errors of the order of 20-25 m. The same accuracy can be preserved for eight or more control points and measurement errors of 30-35 m.

Levine, I.↗

NASA NTRS1986

Time dependent wind fields

Two tasks were performed: (1) determination of the accuracy of Seasat scatterometer, altimeter, and scanning multichannel microwave radiometer measurements of wind speed; and (2) application of Seasat altimeter measurements of sea level to study the spatial and temporal variability of geostrophic flow in the Antarctic Circumpolar Current. The results of the first task have identified systematic errors in wind speeds estimated by all three satellite sensors. However, in all cases the errors are correctable and corrected wind speeds agree between the three sensors to better than 1 ms sup -1 in 96-day 2 deg. latitude by 6 deg. longitude averages. The second task has resulted in development of a new technique for using altimeter sea level measurements to study the temporal variability of large scale sea level variations. Application of the technique to the Antarctic Circumpolar Current yielded new information about the ocean circulation in this region of the ocean that is poorly sampled by conventional ship-based measurements.

Chelton, D. B.↗

NASA NTRS1992

A computational study of advanced exhaust system transition ducts with experimental validation

The current study is an application of CFD to a 'real' design and analysis environment. A subsonic, three-dimensional parabolized Navier-Stokes (PNS) code is used to construct stall margin design charts for optimum-length advanced exhaust systems' circular-to-rectangular transition ducts. Computer code validation has been conducted to examine the capability of wall static pressure predictions. The comparison of measured and computed wall static pressures indicates a reasonable accuracy of the PNS computer code results. Computations have also been conducted on 15 transition ducts, three area ratios, and five aspect ratios. The three area ratios investigated are constant area ratio of unity, moderate contracting area ratio of 0.8, and highly contracting area ratio of 0.5. The degree of mean flow acceleration is identified as a dominant parameter in establishing the minimum duct length requirement. The effect of increasing aspect ratio in the minimum length transition duct is to increase the length requirement, as well as to increase the mass-averaged total pressure losses. The design guidelines constructed from this investigation may aid in the design and manufacture of advanced exhaust systems for modern fighter aircraft.

Wu, C.↗

NASA NTRS1995

Measurement of high-degree solar oscillation frequencies

We present m-averaged solar p- and f-mode oscillation frequencies over the frequency range nu greater than 1.8 and less than 5.0 mHz and the spherical harmonic degree range l greater than or equal to 100 and less than or equal to 1200 from full-disk, 1000 x 1024 pixel, Ca II intensity images collected 1993 June 22-25 with a temporal cadence of 60 s. We itemize the sources and magnitudes of statistical and systematic uncertainties and of small frequency corrections, and we show that our frequencies represent an improvement in accuracy and coverage over previous measurements. Our frequencies agree at the 2 micro Hz level with Mount Wilson frequencies determined for l less than or equal to 600 from full-disk images, and we find systematic offsets of 10-20 micro Hz with respect to frequencies measured from Big Bear and La Palma observations. We give evidence that these latter offsets are indicative of spatial scaling uncertainties associated with the analysis of partial-disk images. In comparison with theory, our p-mode frequencies agree within 10 micro Hz of frequencies predicted by the Los Alamos model but are as much as 100 micro Hz smaller than frequencies predicted by the Denmark and Yale models at degrees near 1000. We also find systematic differences between our n = 0 frequencies and the frequencies closely agreed upon by all three models.

Bachmann, K. T.↗

NASA NTRS2009

Re-evaluation of an Optimized Second Order Backward Difference (BDF2OPT) Scheme for Unsteady Flow Applications

Recent experience in the application of an optimized, second-order, backward-difference (BDF2OPT) temporal scheme is reported. The primary focus of the work is on obtaining accurate solutions of the unsteady Reynolds-averaged Navier-Stokes equations over long periods of time for aerodynamic problems of interest. The baseline flow solver under consideration uses a particular BDF2OPT temporal scheme with a dual-time-stepping algorithm for advancing the flow solutions in time. Numerical difficulties are encountered with this scheme when the flow code is run for a large number of time steps, a behavior not seen with the standard second-order, backward-difference, temporal scheme. Based on a stability analysis, slight modifications to the BDF2OPT scheme are suggested. The performance and accuracy of this modified scheme is assessed by comparing the computational results with other numerical schemes and experimental data.

Vatsa, Veer N.↗

NASA NTRS2021

Passive Ground-based Optical Techniques for Monitoring the On-Orbit ICESat-2 Altimeter Geolocation and Footprint Diameter

NASA launched its second Earth observing laser altimeter in 2018 with mission objectives of studying the changes in our climate by monitoring global elevations, particularly in the polar regions. Since the mission is focused on generating accurate elevations and elevation change, the geolocation (or geodetic position) of the measurements are of upmost importance to each of the scientific disciplines supported by these observations. Geolocation validation is required to ensure that the mission is meeting its objectives with the appropriate level of geolocation accuracy. One validation technique uses small optical reflectors placed in a specific pattern along one or more satellite ground-tracks. The optics provide a unique signal back to the satellite that can be used to compare the geolocation of these returns in the data to the known position on the surface. Results of the position comparison indicate the measurement locations are accurate to within 3.5 m with a standard deviation of 1.6 m. They also provide a method for determining a representative footprint diameter using geometric analysis, which resulted in an average value of 10.9 m +- 2.1 m.

ICESat-2↗

NASA NTRS2012

Recent Advances in Ozone Data Assimilation at the GMAO - Towards a New Reanalysis

This presentation summarized ongoing work on improving the representation of ozone in the GEOS Data Assimilation Systems. Data from two EOS Aura sensors was used: the total column ozone from the Ozone Monitoring Instrument (OMI) and high vertical resolution stratospheric profiles from Microwave Limb Sounder (MLS, version 3.3). As several previous studies have demonstrated, assimilation of this data can constrain the stratospheric and tropospheric ozone columns with relatively good accuracy. However, the representation of the vertical structures in the troposphere and near tropopause region is often deficient. Since both these layers of the atmosphere are critical to the understanding of the radiative forcing as well as the ozone budget in the troposphere, current work will focus on improving the assimilated product between the surface and the 50 hPa pressure level. The discussion included recent steps that have been taken towards refining the treatment of ozone in GEOS-5. Impacts of improved tropospheric chemistry model were discussed including the introduction of efficiency factors ("averaging kernels") for OMI total ozone, and direct assimilation of radiances from the MLS instrument. In particular, advantages and challenges involved in assimilating limb radiances rather than retrieved product were discussed. This work is, in part, a preparation for a planned reanalysis of the EOS Aura data from 2005 to present.

Krzysztof, Wargan↗

NASA NTRS2019

An Evaluation and Recommendations for Further CFD Research Based on the NASA Common Research Model (CRM) Analysis from the AIAA Drag Prediction Workshop (DPW) Series

The six Drag Prediction Workshops (DPW) have drawn a total of 125 participants submitting 225 data entries. Over half of these occurred in the last three workshops dealing with the NASA Common Research Model (CRM). Participants have ranged from North America, Europe, Asia, and South America, representing Government, Industry, Academia, and Commercial/Vendors. The DPW Series has generated a tremendous amount of CFD data, freely available to the public domain. A continuous improvement of the results as measured by: the reduction of the spread of drag predictions for the specified “nominal” cruise point, accuracy of drag increment, and the angle-of-attack sweep behavior, has been noted. Although it has been difficult separating out the parts and pieces that contribute to errors in CFD drag predictions, part of the improvements over the years can be attributed to grid resolution. The scatter in predicted drag in the continuum has been reduced dramatically from plus or minus 50 counts in DPW-I to around plus or minus 5 counts for DPW-V and - VI. During the six workshops, the grid size has grown dramatically. The average size of the medium wing-body meshes in DPW-I through DPW-IV have been 3.2, 5.4, 7.8 and 10.9 million, respectively. This represents a growth rate of approximately 17 percent per year during the eight years between DPW-I and DPW-IV. For DPW-VI, this number has grown from 25 to 50 million points for the various families of grids available. The finest level grids have increased steadily, from just over 3 million grid points in DPW-I to 225 million for the WBNP (Wing-Body-Nacelle-Pylon) in DPW-VI. While progress has been made, persistent problems with grid generation and separated flow prediction continue. The experiences and recommendations presented here are consistent with those espoused in the “CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences,” NASA/CR-2014-218178.

Tinoco, Edward N.↗

NASA NTRS2020

Improved Orbit Determination of the Cygnss Satellites and its Application to Gnss-R Ocean Altimetry

The accuracy of spaceborne ocean surface altimetry depends on precise knowledge of the altimeter satellite orbit. Previous studies of the potential utility of CYGNSS GNSS Reflectometry (GNSS-R) measurements for ocean altimetry have identified its orbit error as a limiting factor. To address this, a recent firmware upgrade to the CYGNSS satellites have enabled the downlink of additional GPS raw measurements from its navigation receiver and increased numerical precision in open-loop GNSS-R tracking information. In this paper, we present improvements to the accuracy of both the orbit determination and the ocean surface height retrievals as a result of these recent upgrades. JPL’s GipsyX software is used to process 120 days of GPS navigation measurements for one of the 8 CYGNSS satellites. Incorporating high fidelity dynamic models and antenna group delay correction, daily orbit overlaps throughout the period show mean RMS differences of 3 cm in height, 7 cm in cross-track, and 10 cm in along-track. Applying these new orbits reduced the standard deviation of retrieved surface height anomalies. When spatially averaged, the sea surface height anomalies were reduced from 1.0 m to 0.8 m. Further improvements are expected using new ionospheric corrections and re-tracking methods currently in development.

Conrad, Alex↗

NASA NTRS1990

Stratosphere chemistry in a 2-D model with residual circulation

The objective of this research was to examine the effects of chemical perturbations on the stratosphere using models which can incorporate fully interactive radiative, chemical, and dynamical responses, in the context of a zonally averaged model. Model runs for the unperturbed, chlorine-perturbed and simultaneously chlorine-and CO2-perturbed cases were completed using the JPL-87 chemical kinetics data. The base case was analyzed and submitted for publication. The perturbed cases show substantial sensitivity of the predicted column ozone depletion to the perturbations affecting lower stratosphere temperature, but less to far dynamical perturbations. The column ozone distribution changed substantially when the kinetics data was changed. This implies a greater-than-expected uncertainty in predicted latitude distributions of ozone depletion, due to uncertainty about the accuracy and completeness of the chemical kinetics data set.

Guthrie, Paul D.↗

NASA NTRS2004

Temporal Large-Eddy Simulation

In 1999, Stolz and Adams unveiled a subgrid-scale model for LES based upon approximately inverting (defiltering) the spatial grid-filter operator and termed .the approximate deconvolution model (ADM). Subsequently, the utility and accuracy of the ADM were demonstrated in a posteriori analyses of flows as diverse as incompressible plane-channel flow and supersonic compression-ramp flow. In a prelude to the current paper, a parameterized temporal ADM (TADM) was developed and demonstrated in both a priori and a posteriori analyses for forced, viscous Burger's flow. The development of a time-filtered variant of the ADM was motivated-primarily by the desire for a unifying theoretical and computational context to encompass direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds averaged Navier-Stokes simulation (RANS). The resultant methodology was termed temporal LES (TLES). To permit exploration of the parameter space, however, previous analyses of the TADM were restricted to Burger's flow, and it has remained to demonstrate the TADM and TLES methodology for three-dimensional flow. For several reasons, plane-channel flow presents an ideal test case for the TADM. Among these reasons, channel flow is anisotropic, yet it lends itself to highly efficient and accurate spectral numerical methods. Moreover, channel-flow has been investigated extensively by DNS, and a highly accurate data base of Moser et.al. exists. In the present paper, we develop a fully anisotropic TADM model and demonstrate its utility in simulating incompressible plane-channel flow at nominal values of Re(sub tau) = 180 and Re(sub tau) = 590 by the TLES method. The TADM model is shown to perform nearly as well as the ADM at equivalent resolution, thereby establishing TLES as a viable alternative to LES. Moreover, as the current model is suboptimal is some respects, there is considerable room to improve TLES.

Pruett, C. D.↗