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System identification and model reduction using modulating function techniques

Weighted least squares (WLS) and adaptive weighted least squares (AWLS) algorithms are initiated for continuous-time system identification using Fourier type modulating function techniques. Two stochastic signal models are examined using the mean square properties of the stochastic calculus: an equation error signal model with white noise residuals, and a more realistic white measurement noise signal model. The covariance matrices in each model are shown to be banded and sparse, and a joint likelihood cost function is developed which links the real and imaginary parts of the modulated quantities. The superior performance of above algorithms is demonstrated by comparing them with the LS/MFT and popular predicting error method (PEM) through 200 Monte Carlo simulations. A model reduction problem is formulated with the AWLS/MFT algorithm, and comparisons are made via six examples with a variety of model reduction techniques, including the well-known balanced realization method. Here the AWLS/MFT algorithm manifests higher accuracy in almost all cases, and exhibits its unique flexibility and versatility. Armed with this model reduction, the AWLS/MFT algorithm is extended into MIMO transfer function system identification problems. The impact due to the discrepancy in bandwidths and gains among subsystem is explored through five examples. Finally, as a comprehensive application, the stability derivatives of the longitudinal and lateral dynamics of an F-18 aircraft are identified using physical flight data provided by NASA. A pole-constrained SIMO and MIMO AWLS/MFT algorithm is devised and analyzed. Monte Carlo simulations illustrate its high-noise rejecting properties. Utilizing the flight data, comparisons among different MFT algorithms are tabulated and the AWLS is found to be strongly favored in almost all facets.

Shen, Yan↗

A numerical study of viscous vortex rings using a spectral method

Viscous, axisymmetric vortex rings are investigated numerically by solving the incompressible Navier-Stokes equations using a spectral method designed for this type of flow. The results presented are axisymmetric, but the method is developed to be naturally extended to three dimensions. The spectral method relies on divergence-free basis functions. The basis functions are formed in spherical coordinates using Vector Spherical Harmonics in the angular directions, and Jacobi polynomials together with a mapping in the radial direction. Simulations are performed of a single ring over a wide range of Reynolds numbers (Re approximately equal gamma/nu), 0.001 less than or equal to 1000, and of two interacting rings. At large times, regardless of the early history of the vortex ring, it is observed that the flow approaches a Stokes solution that depends only on the total hydrodynamic impulse, which is conserved for all time. At small times, from an infinitely thin ring, the propagation speeds of vortex rings of varying Re are computed and comparisons are made with the asymptotic theory by Saffman. The results are in agreement with the theory; furthermore, the error is found to be smaller than Saffman's own estimate by a factor square root ((nu x t)/R squared) (at least for Re=0). The error also decreases with increasing Re at fixed core-to-ring radius ratio, and appears to be independent of Re as Re approaches infinity). Following a single ring, with Re=500, the vorticity contours indicate shedding of vorticity into the wake and a settling of an initially circular core to a more elliptical shape, similar to Norbury's steady inviscid vortices. Finally, we consider the case of leapfrogging vortex rings with Re=1000. The results show severe straining of the inner vortex core in the first pass and merging of the two cores during the second pass.

Stanaway, S. K.↗

Theory of wide-angle photometry from standard stars

Wide angle celestial structures, such as bright comet tails and nearby galaxies and clusters of galaxies, rely on photographic methods for quantified morphology and photometry, primarily because electronic devices with comparable resolution and sky coverage are beyond current technological capability. The problem of the photometry of extended structures and of how this problem may be overcome through calibration by photometric standard stars is examined. The perfect properties of the ideal field of view are stated in the guise of a radiometric paraxial approximation, in the hope that fields of view of actual telescopes will conform. Fundamental radiometric concepts are worked through before the issue of atmospheric attenuation is addressed. The independence of observed atmospheric extinction and surface brightness leads off the quest for formal solutions to the problem of surface photometry. Methods and problems of solution are discussed. The spectre is confronted in the spirit of standard stars and shown to be chimerical in that light, provided certain rituals are adopted. After a brief discussion of Baker-Sampson polynomials and the vexing issue of saturation, a pursuit is made of actual numbers to be expected in real cases. While the numbers crunched are gathered ex nihilo, they demonstrate the feasibility of Newton's method in the solution of this overdetermined, nonlinear, least square, multiparametric, photometric problem.

Usher, Peter D.↗

Rendering Three-Dimensional Solar Coronal Structures

An X-ray or EUV image of the corona or chromosphere is a 2D representation of an extended 3D complex for which a general inversion process is impossible. A specific model must be incorporated in order to understand the full 3D structure. We approach this problem by modeling a set of optically-thin 3D plasma flux tubes which we render these as synthetic images. The resulting images allow the interpretation of the X-ray/EUV observations to obtain information on (1) the 3D structure of X-ray images, i.e., the geometric structure of the flux tubes, and on (2) the internal structure using specific plasma characteristics, i.e., the physical structure of the flux tubes. The data-analysis technique uses magnetograms to characterize photospheric magnetic fields and extrapolation techniques to form the field lines. Using a new set of software tools, we have generated 3D flux tube structures around these field lines and integrated the plasma emission along the line of sight to obtain a rendered image. A set of individual flux-tube images is selected by a non-negative least-squares technique to Provide a match with an observed X-ray image. The scheme minimizes the squares of the differences between the synthesized image and the observed image with a non-negative constraint on the coefficients of the brightness of the individual flux-tube loops. The derived images are used to determine the specific photospheric foot points and physical data, i.e., scaling laws for densities and loop lengths. The development has led to Computer efficient integration and display software that is compatible for comparison with observations (e.g., Yohkoh SXT data, NIXT, or EIT). This analysis is important in determining directly the magnetic field configuration, which provides the structure of coronal loops, and indirectly the electric currents or waves, which provide the energy for the heating of the plasma. We have used very simple assumptions (i.e., potential magnetic fields and isothermal corona) to provide an initial test of the techniques before complex models are introduced. We have separated the physical and geometric contributions of the emission for a set of flux tubes and concentrated, in this initial study, on the geometric contributions by making approximations to the physical contributions. The initial results are consistent with the scaling laws derived from Yohkoh SXT data.

Gary, G. Allen↗

Sounding Rocket Microgravity Experiments Elucidating Diffusive and Radiative Transport Effects on Flame Spread over Thermally-Thick Solids

A series of 6-minute microgravity combustion experiments of opposed flow flame spread over thermally-thick PMMA has been conducted to extend data previously reported at high opposed flows to almost two decades lower in flow. The effect of flow velocity on flame spread shows a square root power law dependence rather than the linear dependence predicted by thermal theory. The experiments demonstrate that opposed flow flame spread is viable to very low velocities and more robust than expected from the numerical model, which predicts that at very low velocities (less than 5 centimeters per second), flame spread rates fall off more rapidly as flow is reduced. It is hypothesized that the enhanced flame spread observed in the experiments may be due to three- dimensional hydrodynamic effects, which are not included in the zero-gravity, two-dimensional hydrodynamic model. The effect of external irradiation was found to be more complex that the model predicted over the 0-2 Watts per square centimeter range. In the experiments, the flame compensated for the increased irradiation by stabilizing farther from the surface. A surface energy balance reveals that the imposed flux was at least partially offset by a reduced conductive flux from the increased standoff distance, so that the effect on flame spread was weaker than anticipated.

Olson, Sandra L.↗

The Satellite Passive-Microwave Record of Sea Ice in the Ross Sea Since Late 1978

Satellites have provided us with a remarkable ability to monitor many aspects of the globe day-in and day-out and sea ice is one of numerous variables that by now have quite substantial satellite records. Passive-microwave data have been particularly valuable in sea ice monitoring, with a record that extends back to August 1987 on daily basis (for most of the period), to November 1970 on a less complete basis (again for most of the period), and to December 1972 on a less complete basis. For the period since November 1970, Ross Sea sea ice imagery is available at spatial resolution of approximately 25 km. This allows good depictions of the seasonal advance and retreat of the ice cover each year, along with its marked interannual variability. The Ross Sea ice extent typically reaches a minimum of approximately 0.7 x 10(exp 6) square kilometers in February, rising to a maximum of approximately 4.0 x 10(exp 6) square kilometers in September, with much variability among years for both those numbers. The Ross Sea images show clearly the day-by-day activity greatly from year to year. Animations of the data help to highlight the dynamic nature of the Ross Sea ice cover. The satellite data also allow calculation of trends in the ice cover over the period of the satellite record. Using linear least-squares fits, the Ross Sea ice extent increased at an average rate of 12,600 plus or minus 1,800 square kilometers per year between November 1978 and December 2007, with every month exhibiting increased ice extent and the rates of increase ranging from a low of 7,500 plus or minus 5,000 square kilometers per year for the February ice extents to a high of 20,300 plus or minus 6,100 kilometers per year for the October ice extents. On a yearly average basis, for 1979-2007 the Ross Sea ice extent increased at a rate of 4.8 plus or minus 1.6 % per decade. Placing the Ross Sea in the context of the Southern Ocean as a whole, over the November 1978-December 2007 period the Ross Sea had the highest rate of increase in sea ice coverage of any of five standard divisions of the Southern Ocean, although the Weddell Sea, Indian Ocean, and Western Pacific Ocean all also had sea ice increases, while only the Bellingshausen/Smundsen Seas experienced overall sea ice decreases. Overall, the Southern Ocean sea ice cover increased at an average rate of 10,800 plus or minus 2,500 square kilometers per year between November 1978 and December 2007, with every month showing positive values although with some of these values not being statistically significant. The sea ice increase since November 1978 was preceded by a sharp decrease in Southern Ocean ice coverage in the 1970's and is in marked contrast to the decrease in Arctic sea ice coverage that has occurred both in the period since November 1978 and since earlier in the 1970's. On a yearly average bases, for 1979-2007 the Southern Ocean sea ice extent increased at a rate of 1.0 plus or minus 0.4% per decade, whereas the Arctic ice extent decreased at the much greater rate of 4.0 plus or minus 0.4 percent per decade (closer to the % per decade rate of increase in the Ross Sea). Considerable research is ongoing to explain the differences.

Parkinson, Claire L.↗

Stability and Heat Transfer Characteristics of Condensing Films

The overall objective of this research is to investigate the fundamental physics of film condensation in reduced gravity. The condensation of vapor on a cool surface is important in many engineering problems,including spacecraft thermal control and also the behavior of condensate films that may form on the interior surfaces of spacecraft. To examine the effects of body force on condensing films, two different geometries have been tested in the laboratory: (1) a stabilizing gravitational body force (+1g, or condensing surface facing 'upwards') and (2) de-stabilizing gravitational body force (-1g, or 'downwards'). For each geometry, different fluid configurations are employed to help isolate the fluid mechanical and thermal mechanisms operative in condensing films. The fluid configurations are (a) a condensing film, and (b) a non-condensing film with film growth by mass addition by through the plate surface. Condensation experiments are conducted in a test cell containing a cooled copper or brass plate with an exposed diameter of 12.7 cm. The metal surface is polished to allow for double-pass shadowgraph imaging, and the test surface is instrumented with imbedded heat transfer gauges and thermocouples. Representative shadowgraph images of a condensing, unstable (-1g) n-pentane film are shown. The interfacial disturbances associated with the de-stabilizing body force leading to droplet formation and break-off can be clearly seen. The heat transfer coefficient associated with the condensing film is shown. The heat transfer coefficient is seen to initially decrease, consistent with the increased thermal resistance due to layer growth. For sufficiently long time, a steady value of heat transfer is observed, accompanied by continuous droplet formation and break-off. The non-condensing cell consists of a stack of thin stainless steel disks 10 cm in diameter mounted in a brass enclosure. The disks are perforated with a regular pattern of 361 holes each 0.25 mm in diameter. Non-condensing experiments in -1g have employed 50 cSt and 125 cSt silicone oil pumped through the perforated disks at a specified rate by a syringe micropump. The time to droplet break-off and the disturbance wavelengths appear to decrease with increasing pumping rate. The ability to reliably perform multi-point, ultrasonic measurements of the film thickness has been demonstrated. A linear array of eight transducers of 6 mm diameter (with a beam footprint of comparable size) are pulsed with a square-wave signal at a frequency of 5 MHz and a pulse duration of approximately 0.3 s. For thin films (60 m to 2-3 mm in thickness) the layer thickness is determined by frequency analysis, where the received ultrasound pulse is Fourier transformed and the spacing between the peaks in the frequency spectrum is analyzed. For thicker layers (up to at least 1 cm in thickness), time-domain analysis is performed of the received ultrasound pulses to generate directly the layer thickness. A time-trace of the film thickness at a point using a single transducer in the linear array is shown for the case of an unstable (-1g) n-pentane film. The oscillations in film thickness are evidently due to the passage and/or shedding of droplets from the cooled plate surface. The entire transducer array was used to measure the changes in film thickness resulting from the passage of gravity waves generated either by an oscillating wall or the impact of a single droplet on the free surface of a film. The enclosure in both cases was 14 cm square and the transducer spacing was 12 mm. Best results were obtained using as test fluid a mixture of 50% glycerol and 50% water with a fluid layer thickness of 3-5 mm. In both cases the measured wavelengths and wave propagation speeds using the ultrasound technique compared reasonably well with those observed by optical imaging. Additional information can be found in the original extended abstract.

Hermanson, J. C.↗

SEDS: The Spitzer Extended Deep Survey. Survey Design, Photometry, and Deep IRAC Source Counts

The Spitzer Extended Deep Survey (SEDS) is a very deep infrared survey within five well-known extragalactic science fields: the UKIDSS Ultra-Deep Survey, the Extended Chandra Deep Field South, COSMOS, the Hubble Deep Field North, and the Extended Groth Strip. SEDS covers a total area of 1.46 deg(exp 2) to a depth of 26 AB mag (3sigma) in both of the warm Infrared Array Camera (IRAC) bands at 3.6 and 4.5 micron. Because of its uniform depth of coverage in so many widely-separated fields, SEDS is subject to roughly 25% smaller errors due to cosmic variance than a single-field survey of the same size. SEDS was designed to detect and characterize galaxies from intermediate to high redshifts (z = 2-7) with a built-in means of assessing the impact of cosmic variance on the individual fields. Because the full SEDS depth was accumulated in at least three separate visits to each field, typically with six-month intervals between visits, SEDS also furnishes an opportunity to assess the infrared variability of faint objects. This paper describes the SEDS survey design, processing, and publicly-available data products. Deep IRAC counts for the more than 300,000 galaxies detected by SEDS are consistent with models based on known galaxy populations. Discrete IRAC sources contribute 5.6 +/- 1.0 and 4.4 +/- 0.8 nW / square m/sr at 3.6 and 4.5 micron to the diffuse cosmic infrared background (CIB). IRAC sources cannot contribute more than half of the total CIB flux estimated from DIRBE data. Barring an unexpected error in the DIRBE flux estimates, half the CIB flux must therefore come from a diffuse component.

Spitzer↗

A New Approach to using a Cloud-Resolving Model to Study the Interactions between Clouds, Precipitation and Aerosols

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-kilometer scales are resolved in horizontal domains as large as 10,000 kilometers in two dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically-based parameterizations for climate models and numerical weather prediction models. A review of developments and applications of cloud models in the past, present and future will be presented in this talk. In particular, a new approach to using cloud-resolving models to study the interactions between clouds, precipitation and aerosols will be presented.

Tao, Wei-Kuo↗

A New Approach to using a Cloud-Resolving Model to Study the Interactions between Clouds, Precipitation and Aerosols

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 km, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-km scales are resolved in horizontal domains as large as 10,000 km in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically-based parameterizations for climate models and numerical weather prediction models. A review of developments and applications of cloud models in the past, present and future will be presented in this talk. In particular, a new approach to using cloud-resolving models to study the interactions between clouds, precipitation and aerosols will be presented.

Tao, Wei-Kuo↗

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial 1-kilometer scales are resolved in horizontal domains as large as 10,000 kilometers in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard will be presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo↗

Using Multi-scale Modeling System to Study the Interactions between Clouds, Precipitation, Aerosols, Radiation and Land Surface

Numerical cloud models, which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Because cloud-scale dynamics are treated explicitly, uncertainties stemming from convection that have to be parameterized in (hydrostatic) large-scale models are obviated, or at least mitigated, in cloud models. Global models will use the non-hydrostatic framework when their horizontal resolution becomes about 10 kilometers, the theoretical limit for the hydrostatic approximation. This juncture will be reached one to two decades from now. Over the past generation, voluminous datasets on atmospheric convection have been accumulated from radar, instrumented aircraft, satellites, and rawinsonde measurements in field campaigns, enabling the detailed evaluation of models. Improved numerical methods have resulted in more accurate and efficient dynamical cores in models. Improvements have been made in the parameterizations of microphysical processes, radiation, boundary-layer effects, and turbulence; however, microphysical parameterizations remain a major source of uncertainty in all classes of atmospheric models. In recent years, exponentially increasing computer power has extended cloud-resolving-model integrations from hours to months, the number of computational grid points from less than a thousand to close to ten million. Three-dimensional models are now more prevalent. Much attention is devoted to precipitating cloud systems where the crucial-lkm scales are resolved in horizontal domains as large as 10,000 kilometers in two-dimensions, and 1,000 x 1,000 square kilometers in three-dimensions. Cloud models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that NWP and mesoscale model can be run in grid size similar to cloud resolving model through nesting technique. A review of developments, improvements and applications of cloud models (GCE and WRF) at Goddard wlll be is presented in this talk. In particular, a new approach to using multi-scale modeling system to study the interactions between clouds, precipitation, aerosols and land will be presented.

Tao, Wei-Kuo↗

UV testing of INTELSAT-7, 7A, and 8 solar cells

A 4000 hour experiment, conducted in late 1992 through mid 1993, confirmed earlier results on the ultraviolet damage effects in covered solar cells of various types being used, or proposed for use, in INTELSAT programs. Two different UV test systems were used to identify systematic errors and to study the effects of UV source-bulb age on degradation rate. After correction for contamination and UV source-bulb aging, the extrapolated degradation rates for irradiated and unirradiated INTELSAT-5, -6 single AR(SAR) coated cells and INTELSAT-7, -7A, -8 double layer AR(DAR) coated cells in both the 1993 tests confirm the following hypotheses resulting from the 1992 experiment. (a) Irradiated cells display significantly more UV degradation than do the unirradiated cells for tests exceeding 2000 hours. The new data indicates that degradation effects from electron irradiation are proportional to t(exp 2) (the square of the UV hours), at least for times less than or equal to 3000 hours. (b) This difference does not depend upon entire reflective coating, cell resistivity, or manufacturer within the sensitivity and reproducibility of the experiment. (c) There is a clear difference in degradation rate between single AR coated cells (TiO(x)) and double layer AR coated cells (SiO(x) and Al2O3?). At 100,000 hours (11.4 years) the DAR coated cells display more degradation than do the SAR coated cells, even though at 1,000 hours the DAR cells display less degradation. (d) UV degradation rates, to modern covered silicon solar cells, at the beginning of bulb life drop from approximately 2 times the average rate to near zero after 2000 hours (average end-of-life for the xenon short-arc lamps used in the tests). The effects of 1 MeV electron irradiation (10(exp 15) e(-)/sq cm) prior to UV exposure are clearly indicated in the plot of percent change in cell open circuit voltage (Voc) versus percent change in short circuit current (Isc) during the UV test and post-test cleanup of the cells. Clearly, extended UV testing produces a permanent photo-induced redegradation of previously irradiated cells. However, this photo-induced redegradation may be caused by the long-wavelength light, not the UV light.

Meulenberg, A.↗

Baseline Observations of Hemispheric Sea Ice with the Nimbus 7 Scanning Multichannel Microwave Radiometer

The Scanning Multichannel Microwave Radiometer (SMMR) on board the NASA Nimbus 7 satellite was designed to obtain data for sea surface temperatures (SSTs), near-surface wind speeds, sea ice coverage and type, rainfall rates over the oceans, cloud water content, snow water equivalent, and soil moisture. In this paper, I shall emphasize the sea ice observations and mention briefly some important SST observations. A prime factor contributing to the importance of SMMR sea ice observations lies in their successful integration into a long-term time series, presently being extended by observations from the series of Special Sensor Microwave/Imager (SSMI) on board the DOD/DMSP F8, Fl1, and F12 satellites. This currently constitutes a 19-year data set. Almost half of this was provided by the SMMR. Unfortunately, the 4-year data set produced earlier by the single-channel Electrically Scanned Microwave Radiometer (ESMR) was not successfully integrated into the SMMR/SSMI data set. This resulted primarily from the lack of an overlap period to provide intersensor adjustment, but also because of the large difference between the algorithms to produce ice concentrations and large temporal gaps in the ESMR data. The lack of overlap between the SeaSat and Nimbus 7 SMMR data sets was an important consideration for also excluding the SeatSat one, but the spatial gaps especially in the Southern Hemisphere daily SeaSat observations was another. The sea ice observations will continue into the future by means of the Advanced Microwave Scanning Radiometer (AMSR) on board the ADEOS II and EOS satellites due to be launched in mid- and late-2000, respectively. Analysis of the sea ice data has been carried out by a number of different techniques. Long-term trends have been examined by means of ordinary least squares and band-limited regression. Oscillations in the data have been examined by band-limited Fourier analysis. Here, I shall present results from a novel combination of Principal Component analysis and the recently-developed Empirical Mode Decomposition (EMD). In this method, the data are first separated into spatial and temporal parts, and then the temporal parts of the first few PCs are broken into intrinsic modes by the EMD method.

Gloersen, Per↗

Observer-Based Magnetic Bearing Controller Developed for Aerospace Flywheels

A prototype of a versatile, observer-based magnetic bearing controller for aerospace flywheels was successfully developed and demonstrated on a magnetic bearing test rig (see the photograph) and an actual flywheel module. The objective of this development included a fast, yet low risk, control development process, and a robust, high-performance controller for a large variety of flywheels. This required a good system model, an efficient development procedure, and a model-based controller that addressed the key problems associated with flywheel and bearing imbalance, sensor error, and vibration. The model used in this control development and tuning procedure included the flexible rotor dynamics and motor-induced vibrations. Such a model was essential for low-risk scheduling of speed-dependent control parameters and for reliable evaluation of novel control strategies. The successfully tested control prototype utilized an extended Kalman filter to estimate the true rotor principal-axis motion from the raw sensor position feedback. For control refinement, the extended Kalman filter also estimated and eliminated the combined effects of mass-imbalance and sensor runouts from the input data. A key advantage of the design based on the extended Kalman filter is its ability to accurately estimate both the rotor's principal-axis position and gyroscopic rates with the least amount of phase lag. This is important for control parameter scheduling to dampen the gyroscopic motions. Because of large uncertainties in the magnetic bearing and imbalance characteristics, this state-estimation scheme alone is insufficient for containing the rotor motion within the desired 1-mil excursion radius. A nonlinear gain adjustment based on an estimation of the principal-axis orbit size was needed to provide a coarse (nonoptimal), but robust, control of the orbit growth. Control current minimization was achieved with a (steepest gradient) search of synchronous errors in the principal-axis position input data. Actual flywheel tests of this observer-based controller (developed entirely in-house) at the NASA Glenn Research Center showed that the model correctly predicted the rotor orbit growth as a function of rotational speed, and it demonstrated the capability of gain adjustments to arrest this growth. Data from these tests on an actual flywheel module spun to 26,000 rpm proved that the controller was able to contain the shaft motion to within much less than 0.5 mils of radial excursion with axis currents less than 300 mA in root-mean-square estimate. The test speed range was limited because of thermal expansion concerns for this particular flywheel unit, not because of any deficiency in the controller. Simulations for this unit indicated that the controller should be robust up to its top operating speed of 60,000 rpm. Aside from these important achievements, and most significantly, it took less than 1 week to adapt this controller from the simple test rig to the actual flywheel and to demonstrate full five-axis levitation and control. This demonstration showed that both the controller and the model-based development and tuning framework are easily adaptable to a wide range of rotors and bearing configurations and, hence, are capable of reducing design risks and costs for many future flywheel technology developments.

Le, Dzu K.↗

Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models

Abstract. Strongly coupled nonlinear phenomena such as those described by Earth system models (ESMs) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESMs is to remap or interpolate component solution fields defined on their computational mesh to another mesh with a different combinatorial structure and decomposition, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESMs. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations is conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid (Hill et al., 2004), TempestRemap (Ullrich and Taylor, 2015), generalized moving least squares (GMLS) (Trask and Kuberry, 2020) with post-processing filters, and WLS-ENOR (Li et al., 2020). By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless GMLS and hybrid mesh-based WLS-ENOR schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh-invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations, thereby allowing for a more complete analysis of production-ready remapping packages.

58 GEOSCIENCES↗

ACCRUE—An Integral Index for Measuring Experimental Relevance in Support of Neutronic Model Validation

A key challenge for the introduction of any design changes, e.g., advanced fuel concepts, first-of-a-kind nuclear reactor designs, etc., is the cost of the associated experiments, which are required by law to validate the use of computer models for the various stages, starting from conceptual design, to deployment, licensing, operation, and safety. To achieve that, a criterion is needed to decide on whether a given experiment, past or planned, is relevant to the application of interest. This allows the analyst to select the best experiments for the given application leading to the highest measures of confidence for the computer model predictions. The state-of-the-art methods rely on the concept of similarity or representativity, which is a linear Gaussian-based inner-product metric measuring the angle—as weighted by a prior model parameters covariance matrix—between two gradients, one representing the application and the other a single validation experiment. This manuscript emphasizes the concept of experimental relevance which extends the basic similarity index to account for the value accrued from past experiments and the associated experimental uncertainties, both currently missing from the extant similarity methods. Accounting for multiple experiments is key to the overall experimental cost reduction by prescreening for redundant information from multiple equally-relevant experiments as measured by the basic similarity index. Accounting for experimental uncertainties is also important as it allows one to select between two different experimental setups, thus providing for a quantitative basis for sensor selection and optimization. The proposed metric is denoted by ACCRUE, short for Accumulative Correlation Coefficient for Relevance of Uncertainties in Experimental validation. Using a number of criticality experiments for highly enriched fast metal systems and low enriched thermal compound systems with accident tolerant fuel concept, the manuscript will compare the performance of the ACCRUE and basic similarity indices for prioritizing the relevance of a group of experiments to the given application.

97 MATHEMATICS AND COMPUTING↗

Assessment of Postflight Locomotor Performance Utilizing a Test of Functional Mobility: Strategic and Adaptive Responses

Space flight induces adaptive modification in sensorimotor function, allowing crewmembers to operate in the unique microgravity environment. This adaptive state, however, is inappropriate for a terrestrial environment. During a re-adaptation period upon their return to Earth, crewmembers experience alterations in sensorimotor function, causing various disturbances in perception, spatial orientation, posture, gait, and eye-head coordination. Following long duration space flight, sensorimotor dysfunction would prevent or extend the time required to make an emergency egress from the vehicle; compromising crew safety and mission objectives. We are investigating two types of motor learning that may interact with each other and influence a crewmember's ability to re-adapt to Earth's gravity environment. In strategic learning, crewmembers make rapid modifications in their motor control strategy emphasizing error reduction. This type of learning may be critical during the first minutes and hours after landing. In adaptive learning, long-term plastic transformations occur, involving morphological changes and synaptic modification. In recent literature these two behavioral components have been associated with separate brain structures that control the execution of motor strategies: the strategic component was linked to the posterior parietal cortex and the adaptive component was linked to the cerebellum (Pisella, et al. 2004). The goal of this paper was to demonstrate the relative contributions of the strategic and adaptive components to the re-adaptation process in locomotor control after long duration space flight missions on the International Space Station (ISS). The Functional Mobility Test (FMT) was developed to assess crewmember s ability to ambulate postflight from an operational and functional perspective. Sixteen crewmembers were tested preflight (3 sessions) and postflight (days 1, 2, 4, 7, 25) following a long duration space flight (approx 6 months) on the ISS. We have further analyzed the FMT data to characterize strategic and adaptive components during the postflight readaptation period. Crewmembers walked at a preferred pace through an obstacle course set up on a base of 10 cm thick medium density foam (Sunmate Foam, Dynamic Systems, Inc., Leicester, NC). The 6.0m X 4.0m course consisted of several pylons made of foam; a Styrofoam barrier 46.0cm high that crewmembers stepped over; and a portal constructed of two Styrofoam blocks, each 31cm high, with a horizontal bar covered by foam and suspended from the ceiling which was adjusted to the height of the crewmember s shoulder. The portal required crewmembers to bend at the waist and step over a barrier simultaneously. All obstacles were lightweight, soft and easily knocked over. Crewmembers were instructed to walk through the course as quickly and as safely as possible without touching any of the objects on the course. This task was performed three times in the clockwise direction and three times in the counterclockwise direction that was randomly chosen. The dependent measures for each trial were: time to complete the course (seconds) and the number of obstacles touched or knocked down. For each crewmember, the time to complete each FMT trial from postflight days 1, 2, 4, 7 and 25 were further analyzed. A single logarithmic curve using a least squares calculation was fit through these data to produce a single comprehensive curve (macro). This macro curve composed of data spanning 25 days, illustrates the re-adaptive learning function over the longer time scale term. Additionally, logarithmic curves were fit to the 6 data trials within each individual post flight test day to produce 5 separate daily curves. These micro curves, produced from data obtained over the course of minutes, illustrates the strategic learning function exhibited over a relative shorter time scale. The macro curve for all subjects exhibited adaptive motor learning patterns over the 25 day period. Howev, 9/16 crewmembers exhibited significant strategic motor learning patterns in their micro curves, as defined by m > 1 in the equation of the line y=m*LN(x) +b. These data indicate that postflight recovery in locomotor function involves both strategic and adaptive mechanisms. Future countermeasures will be designed to enhance both recovery processes.

Warren, L. E.↗