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NASA NTRS1994

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Coutsias, Evangelos A.↗

NASA NTRS1994

Atmospheric Infrared Sounder

The microwave 'first-guess' algorithm was run on the cloudy test simulations. Eight datasets were considered in the cloudy test, comprising approximately 360 retrievals, of which one failed to converge. Retrievals were done on the AMSU-A grid. Examination of the true profiles (provided for the A, C and D tracks) showed numerous cases of very pronounced temperature inversion layers in the troposphere which the retrieval does not have enough vertical resolution to reproduce. A typical example with an inversion layer near 700 mbar is shown in Figure 1. The inversion layers also exhibit strong vertical gradients of water vapor which are not resolved in the retrieval. (Water vapor volume density is given in g/sq cm per layer. Layer thickness is 20 mb from 200 to 400 mb, and 25 mb from 400 to 1,000 mb.) The retrievals do reproduce the overall smoothed shape of the profiles, and therefore as a first guess should be within the range of linear methods for IR retrievals using AIRS.

Rosenkranz, Philip W.↗

NASA NTRS1995

Feedback control laws for highly maneuverable aircraft

During this year, we concentrated our efforts on the design of controllers for lateral/directional control using mu synthesis. This proved to be a more difficult task than we anticipated and we are still working on the designs. In the lateral-directional control problem, the inputs are pilot lateral stick and pedal commands and the outputs are roll rate about the velocity vector and side slip angle. The control effectors are ailerons, rudder deflection, and directional thrust vectoring vane deflection which produces a yawing moment about the body axis. Our math model does not contain any provision for thrust vectoring of rolling moment. This has resulted in limitations of performance at high angles of attack. During 1994-95, the following tasks for the lateral-directional controllers were accomplished: (1) Designed both inner and outer loop dynamic inversion controllers. These controllers are implemented using accelerometer outputs rather than an a priori model of the vehicle aerodynamics; (2) Used classical techniques to design controllers for the system linearized by dynamics inversion. These controllers acted to control roll rate and Dutch roll response; (3) Implemented the inner loop dynamic inversion and classical controllers on the six DOF simulation; (4) Developed a lateral-directional control allocation scheme based on minimizing required control effort among the ailerons, rudder, and directional thrust vectoring; and (5) Developed mu outer loop controllers combined with classical inner loop controllers.

Garrard, William L.↗

NASA NTRS1995

Measuring soil moisture with imaging radars

An empirical model was developed to infer soil moisture and surface roughness from radar data. The accuracy of the inversion technique is assessed by comparing soil moisture obtained with the inversion technique to in situ measurements. The effect of vegetation on the inversion is studied and a method to eliminate the areas where vegetation impairs the algorithm is described.

Dubois, Pascale C.↗

NASA NTRS1994

Tectonic plates, D (double prime) thermal structure, and the nature of mantle plumes

It is proposed that subducting tectonic plates can affect the nature of thermal mantle plumes by determining the temperature drop across a plume source layer. The temperature drop affects source layer stability and the morphology of plumes emitted from it. Numerical models are presented to demonstrate how introduction of platelike behavior in a convecting temperature dependent medium, driven by a combination of internal and basal heating, can increase the temperature drop across the lower boundary layer. The temperature drop increases dramatically following introduction of platelike behavior due to formation of a cold temperature inversion above the lower boundary layer. This thermal inversion, induced by deposition of upper boundary layer material to the system base, decays in time, but the temperature drop across the lower boundary layer always remains considerably higher than in models lacking platelike behavior. On the basis of model-inferred boundary layer temperature drops and previous studies of plume dynamics, we argue that generally accepted notions as to the nature of mantle plumes on Earth may hinge on the presence of plates. The implication for Mars and Venus, planets apparently lacking plate tectonics, is that mantle plumes of these planets may differ morphologically from those of Earth. A corollary model-based argument is that as a result of slab-induced thermal inversions above the core mantle boundary the lower most mantle may be subadiabatic, on average (in space and time), if major plate reorganization timescales are less than those acquired to diffuse newly deposited slab material.

Lenardic, A.↗

NASA NTRS1994

Mirages and the nature of Pluto's atmosphere

We present model occultation lightcurves demonstrating that a strong thermal inversion layer at the base of Pluto's stratosphere can reproduce the minimum flux measured by the Kuiper Airborne Observatory (KAO) during the 1988 occultation of a star by Pluto. The inversion layer also forms the occultation equivalent of a mirage at a radius of 1198 km, which is capable of hiding tropospheres of significant depth. Pluto's surface lies below 1198 km, its radius depending on the depth of the troposphere. We begin by computing plausible temperature structures for Pluto's lower atmosphere, constrained by a calculation of the temperature of the atmosphere near the surface. We then trace rays from the occulted star through the model atmosphere, computing the resultant bending of the ray. Model light curves are obtained by summing the contribution of individual rays within the shadow of Pluto on Earth. We find that we can reproduce the KAO lightcurve using model atmospheres with a temperature inversion and no haze. We have explored models with tropospheres as deep as 40 km (implying a Pluto radius of 1158 km) that reproduce the suite of occultation data. Deeper tropospheres can be fitted to the data, but the mutual event radius of 1150 km probably provides a lower bound. If Pluto has a shallow or nonexistent troposphere, its density is consistent with formation in the solar nebula with modest water loss due to impact ejection. If the troposhere is relatively deep, implying a smaller radius and larger density, significant amounts of water loss are required.

Stansberry, J. A.↗

NASA NTRS1995

Error in predicting hydrosol backscattering from remotely sensed reflectance

Monte Carlo simulations are carried out to determine the error in the inversion of backscattering from remotely sensed reflectance when geometrical shape factors of the light field are assumed to be unity. The results show that error in backscattering inversion can vary from a 40% overestimation to a 20% underestimation and is dependent on the solar angle and the hydrosol consituents contributing to backscattering. The simulations also demostrate that for chlorophyll concentrations ranging from 0.05 to 20 mg/cu m the most dramatic change in the geometrical shape factors occurs near 1.0 to 1.5 mg/cu m chlorophyll. The potential importance of bacteria in influencing the shape factor and the subsequent effect of bacteria on the retrieval of the backscattering from remote sensing reflectance are shown. Quartzlike material's strong impact on geometrical shape factors and errors of retrieval of backscattering at low chlorophyll concentrations are also demonstrated. Remote sensing reflectance inversion schemes must include information about the backscattering function to be successful.

Weidemann, A. D.↗

NASA NTRS1996

Output Tracking for Systems with Non-Hyperbolic and Near Non-Hyperbolic Internal Dynamics: Helicopter Hover Control

A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics is presented. This approach integrates stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics is used (1) to remove non-hyperbolicity which an obstruction to applying stable inversion techniques and (2) to reduce large pre-actuation time needed to apply stable inversion for near non-hyperbolic cases. The method is applied to an example helicopter hover control problem with near non-hyperbolic internal dynamic for illustrating the trade-off between exact tracking and reduction of pre-actuation time.

Devasia, Santosh↗

NASA NTRS1996

Optimal Output Trajectory Redesign for Invertible Systems

Given a desired output trajectory, inversion-based techniques find input-state trajectories required to exactly track the output. These inversion-based techniques have been successfully applied to the endpoint tracking control of multi-joint flexible manipulators and to aircraft control. The specified output trajectory uniquely determines the required input and state trajectories that are found through inversion. These input-state trajectories exactly track the desired output; however, they might not meet acceptable performance requirements. For example, during slewing maneuvers of flexible structures, the structural deformations, which depend on the required state trajectories, may be unacceptably large. Further, the required inputs might cause actuator saturation during an exact tracking maneuver for example, in the flight control of conventional takeoff and landing aircraft. In such situations, a compromise is desired between the tracking requirement and other goals such as reduction of internal vibrations and prevention of actuator saturation; the desired output trajectory needs to be redesigned.

Devasia, Santosh↗

NASA NTRS1997

Retrieval of Soil Moisture and Roughness from the Polarimetric Radar Response

The main objective of this investigation was the characterization of soil moisture using imaging radars. In order to accomplish this task, a number of intermediate steps had to be undertaken. In this proposal, the theoretical, numerical, and experimental aspects of electromagnetic scattering from natural surfaces was considered with emphasis on remote sensing of soil moisture. In the general case, the microwave backscatter from natural surfaces is mainly influenced by three major factors: (1) the roughness statistics of the soil surface, (2) soil moisture content, and (3) soil surface cover. First the scattering problem from bare-soil surfaces was considered and a hybrid model that relates the radar backscattering coefficient to soil moisture and surface roughness was developed. This model is based on extensive experimental measurements of the radar polarimetric backscatter response of bare soil surfaces at microwave frequencies over a wide range of moisture conditions and roughness scales in conjunction with existing theoretical surface scattering models in limiting cases (small perturbation, physical optics, and geometrical optics models). Also a simple inversion algorithm capable of providing accurate estimates of soil moisture content and surface rms height from single-frequency multi-polarization radar observations was developed. The accuracy of the model and its inversion algorithm is demonstrated using independent data sets. Next the hybrid model for bare-soil surfaces is made fully polarimetric by incorporating the parameters of the co- and cross-polarized phase difference into the model. Experimental data in conjunction with numerical simulations are used to relate the soil moisture content and surface roughness to the phase difference statistics. For this purpose, a novel numerical scattering simulation for inhomogeneous dielectric random surfaces was developed. Finally the scattering problem of short vegetation cover above a rough soil surface was considered. A general scattering model for grass-blades of arbitrary cross section was developed and incorporated in a first order random media model. The vegetation model and the bare-soil model are combined and the accuracy of the combined model is evaluated against experimental observations from a wheat field over the entire growing season. A complete set of ground-truth data and polarimetric backscatter data were collected. Also an inversion algorithm for estimating soil moisture and surface roughness from multi-polarized multi-frequency observations of vegetation-covered ground is developed.

Sarabandi, Kamal↗

NASA NTRS1997

ERBE Geographic Scene and Monthly Snow Data

The Earth Radiation Budget Experiment (ERBE) is a multisatellite system designed to measure the Earth's radiation budget. The ERBE data processing system consists of several software packages or sub-systems, each designed to perform a particular task. The primary task of the Inversion Subsystem is to reduce satellite altitude radiances to fluxes at the top of the Earth's atmosphere. To accomplish this, angular distribution models (ADM's) are required. These ADM's are a function of viewing and solar geometry and of the scene type as determined by the ERBE scene identification algorithm which is a part of the Inversion Subsystem. The Inversion Subsystem utilizes 12 scene types which are determined by the ERBE scene identification algorithm. The scene type is found by combining the most probable cloud cover, which is determined statistically by the scene identification algorithm, with the underlying geographic scene type. This Contractor Report describes how the geographic scene type is determined on a monthly basis.

Coleman, Lisa H.↗

NASA NTRS1996

Radioactive Transfer Models for Saturn and Titan

The infrared spectra of the earth's atmosphere and planetary atmospheres contains information about atmospheric physical and chemical processes. Atmospheric molecular constituents absorb and emit infrared radiation by rotational and vibrational transition. Observed spectra exhibit characteristic features in the electromagnetic spectrum region. Observation of the absorption or thermal emission spectra may be obtained with space-borne high resolution infrared spectrometers in the 10-5000 cm(exp -1) (2-1000 micro-m) spectral region. Information about the atmospheric thermal structure, composition, and the chemical and physical processes of the observed spectral was accomplished. A preliminary version of a P-T retrieval algorithm for Saturn using all three modes for temperature inversion, e.g., CH4-limb, and H2-nadir spectra was completed and tested for accuracy. Radiative transfer and inversion programs were studied and analyzed for applications to infrared limb thermal emission observations of Saturn and Titan from the Cassini Orbiter, as well as Earth's atmosphere. Analysis and modification of the existing radiative transfer and inversion programs for Earth and planetary atmospheres are being made. Data analysis and retrieval of information form the observations by digital calculations were carried out at UAH and MSFC computer. The working program for generating and reading g-k arrays for using the c-k arrays via the c-k method for radiative transfer calculations for desired atmospheric and instrumental parameters was completed, tested for accuracy and resides at the MSFC computer.

Wu, S. T.↗

NASA NTRS1996

SSME Condition Monitoring Using Neural Networks and Plume Spectral Signatures

For a variety of reasons, condition monitoring of the Space Shuttle Main Engine (SSME) has become an important concern for both ground tests and in-flight operation. The complexities of the SSME suggest that active, real-time condition monitoring should be performed to avoid large-scale or catastrophic failure of the engine. In 1986, the SSME became the subject of a plume emission spectroscopy project at NASA's Marshall Space Flight Center (MSFC). Since then, plume emission spectroscopy has recorded many nominal tests and the qualitative spectral features of the SSME plume are now well established. Significant discoveries made with both wide-band and narrow-band plume emission spectroscopy systems led MSFC to develop the Optical Plume Anomaly Detection (OPAD) system. The OPAD system is designed to provide condition monitoring of the SSME during ground-level testing. The operational health of the engine is achieved through the acquisition of spectrally resolved plume emissions and the subsequent identification of abnormal emission levels in the plume indicative of engine erosion or component failure. Eventually, OPAD, or a derivative of the technology, could find its way on to an actual space vehicle and provide in-flight engine condition monitoring. This technology step, however, will require miniaturized hardware capable of processing plume spectral data in real-time. An objective of OPAD condition monitoring is to determine how much of an element is present in the SSME plume. The basic premise is that by knowing the element and its concentration, this could be related back to the health of components within the engine. For example, an abnormal amount of silver in the plume might signify increased wear or deterioration of a particular bearing in the engine. Once an anomaly is identified, the engine could be shut down before catastrophic failure occurs. Currently, element concentrations in the plume are determined iteratively with the help of a non-linear computer code called SPECTRA, developed at the USAF Arnold Engineering Development Center. Ostensibly, the code produces intensity versus wavelength plots (i.e., spectra) when inputs such as element concentrations, reaction temperature, and reaction pressure are provided. However, in order to provide a higher-level analysis, element concentration is not specified explicitly as an input. Instead, two quantum variables, number density and broadening parameter, are used. Past experience with OPAD data analysis has revealed that the region of primary interest in any SSME plume spectrum lies in the wavelength band of 3300 A to 4330 A. Experience has also revealed that some elements, such as iron, cobalt and nickel, cause multiple peaks over the chosen wavelength range whereas other elements (magnesium, for example) have a few, relatively isolated peaks in the chosen wavelength range. Iteration with SPECTRA as a part of OPAD data analysis is an incredibly labor intensive task and not one to be performed by hand. What is really needed is the "inverse" of the computer code but the mathematical model for the inverse mapping is tenuous at best. However, building generalized models based upon known input/output mappings while ignoring details of the governing physical model is possible using neural networks. Thus the objective of the research project described herein was to quickly and accurately predict combustion temperature and element concentrations (i.e., number density and broadening parameter) from a given spectrum using a neural network. In other words, a neural network had to be developed that would provide a generalized "inverse" of the computer code SPECTRA.

Hopkins, Randall↗

NASA NTRS1999

A Neural Network Aero Design System for Advanced Turbo-Engines

An inverse design method calculates the blade shape that produces a prescribed input pressure distribution. By controlling this input pressure distribution the aerodynamic design objectives can easily be met. Because of the intrinsic relationship between pressure distribution and airfoil physical properties, a Neural Network can be trained to choose the optimal pressure distribution that would meet a set of physical requirements. Neural network systems have been attempted in the context of direct design methods. From properties ascribed to a set of blades the neural network is trained to infer the properties of an 'interpolated' blade shape. The problem is that, especially in transonic regimes where we deal with intrinsically non linear and ill posed problems, small perturbations of the blade shape can produce very large variations of the flow parameters. It is very unlikely that, under these circumstances, a neural network will be able to find the proper solution. The unique situation in the present method is that the neural network can be trained to extract the required input pressure distribution from a database of pressure distributions while the inverse method will still compute the exact blade shape that corresponds to this 'interpolated' input pressure distribution. In other words, the interpolation process is transferred to a smoother problem, namely, finding what pressure distribution would produce the required flow conditions and, once this is done, the inverse method will compute the exact solution for this problem. The use of neural network is, in this context, highly related to the use of proper optimization techniques. The optimization is used essentially as an automation procedure to force the input pressure distributions to achieve the required aero and structural design parameters. A multilayered feed forward network with back-propagation is used to train the system for pattern association and classification.

Sanz, Jose M.↗

NASA NTRS1999

Optical Properties of Aerosols from Long Term Ground-Based Aeronet Measurements

AERONET is an optical ground-based aerosol monitoring network and data archive supported by NASA's Earth Observing System and expanded by federation with many non-NASA institutions including AEROCAN (AERONET CANada) and PHOTON (PHOtometrie pour le Traiteinent Operatonnel de Normalisation Satellitaire). The network hardware consists of identical automatic sun-sky scanning spectral radiometers owned by national agencies and universities purchased for their own monitoring and research objectives. Data are transmitted hourly through the data collection system (DCS) on board the geostationary meteorological satellites GMS, GOES and METEOSAT and received in a common archive for daily processing utilizing a peer reviewed series of algorithms thus imposing a standardization and quality control of the product data base. Data from this collaboration provides globally distributed near real time observations of aerosol spectral optical depths, aerosol size distributions, and precipitable water in diverse aerosol regimes. Access to the AERONET data base has shifted from the interactive program 'demonstrat' (reserved for PI's) to the AERONET homepage allowing faster access and greater development for GIS object oriented retrievals and analysis with companion geocoded data sets from satellites, LIDAR and solar flux measurements for example. We feel that a significant yet under utilized component of the AERONET data base are inversion products made from hourly principal plane and almucanter measurements. The current inversions have been shown to retrieve aerosol volume size distributions. A significant enhancement to the inversion code has been developed and is presented in these proceedings.

Holben, B. N.↗

NASA NTRS1999

The Thin Oil Film Equation

A thin film of oil on a surface responds primarily to the wall shear stress generated on that surface by a three-dimensional flow. The oil film is also subject to wall pressure gradients, surface tension effects and gravity. The partial differential equation governing the oil film flow is shown to be related to Burgers' equation. Analytical and numerical methods for solving the thin oil film equation are presented. A direct numerical solver is developed where the wall shear stress variation on the surface is known and which solves for the oil film thickness spatial and time variation on the surface. An inverse numerical solver is also developed where the oil film thickness spatial variation over the surface at two discrete times is known and which solves for the wall shear stress variation over the test surface. A One-Time-Level inverse solver is also demonstrated. The inverse numerical solver provides a mathematically rigorous basis for an improved form of a wall shear stress instrument suitable for application to complex three-dimensional flows. To demonstrate the complexity of flows for which these oil film methods are now suitable, extensive examination is accomplished for these analytical and numerical methods as applied to a thin oil film in the vicinity of a three-dimensional saddle of separation.

Brown, James L.↗

NASA NTRS1999

[Global Atmospheric Chemistry/Transport Modeling and Data-Analysis]

This grant supported a global atmospheric chemistry/transport modeling and data- analysis project devoted to: (a) development, testing, and refining of inverse methods for determining regional and global transient source and sink strengths for trace gases; (b) utilization of these inverse methods which use either the Model for Atmospheric Chemistry and Transport (MATCH) which is based on analyzed observed winds or back- trajectories calculated from these same winds for determining regional and global source and sink strengths for long-lived trace gases important in ozone depletion and the greenhouse effect; (c) determination of global (and perhaps regional) average hydroxyl radical concentrations using inverse methods with multiple "titrating" gases; and (d) computation of the lifetimes and spatially resolved destruction rates of trace gases using 3D models. Important ultimate goals included determination of regional source strengths of important biogenic/anthropogenic trace gases and also of halocarbons restricted by the Montreal Protocol and its follow-on agreements, and hydrohalocarbons now used as alternatives to the above restricted halocarbons.

Prinn, Ronald G.↗

NASA NTRS1999

Icehouse Effect: A Polar Autumn and Winter Cooling Trend

The icehouse effect is a hypothesized polar climate trend toward cooling (or lack of warming) in response to greenhouse warming of adjacent lower latitudes. When greenhouse warmed air from lower latitudes moves over ice and snow, it generates a stronger, more stable, cappino, inversion than in a parallel case without greenhouse warming. Because the degree of decoupling between vertically adjacent air masses is directly dependent on the strength of the inversion, the capping inversion acts somewhat analogously to the walls and roof of the icehouse of generations past. What is inside the icehouse, namely the cold polar atmospheric boundary layer (ABL) air, is preserved by the "insulation" or decoupling, provided by the warm air aloft. Observations over the Arctic Ocean have shown an unexpected lack of any detectable surface warming trend over the past 40 years. This finding strongly contradicts climate model predictions that polar regions should show the strongest effect of greenhouse warming. It also stands in contrast to the consensus reached by the Intergovernmental Panel on Climate Change (IPCC), that human caused greenhouse warming is now detectable globally. One might ask: Are these Arctic observations wrong? Or, if right, is there a plausible physical explanation for them? The published observations mentioned above used about 50,000 soundings over the Arctic Ocean. Here I present a novel analysis of ALL available Arctic rawinsonde data north of 65N--a total of more than 1.1 million soundings. The analysis confirms the previously published result: There is indeed a slight climate-cooling trend in the vast majority of the data. Importantly, there are also select conditions (very strong and very weak stability of the ABL) which show a consistent, strong Arctic warming trend. It is the juxtaposition of these warming and cooling trends which defines a unique "icehouse signature" for which an explanation can be sought.

Wetzel, Peter J.↗