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Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 2: Algorithmic developments and implementation

This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present second part of the report, we focus on the specific details of the numerical schemes, and associated computer algorithms, for the finite-element implementation of GVIPS and NAV models.

Li, Wei

Utilization of Ancillary Data Sets for Conceptual SMAP Mission Algorithm Development and Product Generation

The planned Soil Moisture Active Passive (SMAP) mission is one of the first Earth observation satellites being developed by NASA in response to the National Research Council's Decadal Survey, Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond [1]. Scheduled to launch late in 2014, the proposed SMAP mission would provide high resolution and frequent revisit global mapping of soil moisture and freeze/thaw state, utilizing enhanced Radio Frequency Interference (RFI) mitigation approaches to collect new measurements of the hydrological condition of the Earth's surface. The SMAP instrument design incorporates an L-band radar (3 km) and an L band radiometer (40 km) sharing a single 6-meter rotating mesh antenna to provide measurements of soil moisture and landscape freeze/thaw state [2]. These observations would (1) improve our understanding of linkages between the Earth's water, energy, and carbon cycles, (2) benefit many application areas including numerical weather and climate prediction, flood and drought monitoring, agricultural productivity, human health, and national security, (3) help to address priority questions on climate change, and (4) potentially provide continuity with brightness temperature and soil moisture measurements from ESA's SMOS (Soil Moisture Ocean Salinity) and NASA's Aquarius missions. In the planned SMAP mission prelaunch time frame, baseline algorithms are being developed for generating (1) soil moisture products both from radiometer measurements on a 36 km grid and from combined radar/radiometer measurements on a 9 km grid, and (2) freeze/thaw products from radar measurements on a 3 km grid. These retrieval algorithms need a variety of global ancillary data, both static and dynamic, to run the retrieval models, constrain the retrievals, and provide flags for indicating retrieval quality. The choice of which ancillary dataset to use for a particular SMAP product would be based on a number of factors, including its availability and ease of use, its inherent error and resulting impact on the overall soil moisture or freeze/thaw retrieval accuracy, and its compatibility with similar choices made by the SMOS mission. All decisions regarding SMAP ancillary data sources would be fully documented by the SMAP Project and made available to the user community.

freeze/thaw

Ocean observations with EOS/MODIS: Algorithm Development and Post Launch Studies

Significant accomplishments made during the present reporting period: (1) We expanded our "spectral-matching" algorithm (SMA), for identifying the presence of absorbing aerosols and simultaneously performing atmospheric correction and derivation of the ocean's bio-optical parameters, to the point where it could be added as a subroutine to the MODIS water-leaving radiance algorithm; (2) A modification to the SMA that does not require detailed aerosol models has been developed. This is important as the requirement for realistic aerosol models has been a weakness of the SMA; and (3) We successfully acquired micro pulse lidar data in a Saharan dust outbreak during ACE-2 in the Canary Islands.

Gordon, Howard R.

Ocean Observations with EOS/MODIS: Algorithm Development and Post Launch Studies

The following accomplishments were made during the present reporting period: (1) We expanded our new method, for identifying the presence of absorbing aerosols and simultaneously performing atmospheric correction, to the point where it could be added as a subroutine to the MODIS water-leaving radiance algorithm; (2) We successfully acquired micro pulse lidar (MPL) data at sea during a cruise in February; (3) We developed a water-leaving radiance algorithm module for an approximate correction of the MODIS instrument polarization sensitivity; and (4) We participated in one cruise to the Gulf of Maine, a well known region for mesoscale coccolithophore blooms. We measured coccolithophore abundance, production and optical properties.

Gordon, Howard R.

Ocean Observations with EOS/MODIS: Algorithm Development and Post Launch Studies

Significant accomplishments made during the present reporting period include: 1) Installed spectral optimization algorithm in the SeaDas image processing environment and successfully processed SeaWiFS imagery. The results were superior to the standard SeaWiFS algorithm (the MODIS prototype) in a turbid atmosphere off the US East Coast, but similar in a clear (typical) oceanic atmosphere; 2) Inverted ACE-2 LIDAR measurements coupled with sun photometer-derived aerosol optical thickness to obtain the vertical profile of aerosol optical thickness. The profile was validated with simultaneous aircraft measurements; and 3) Obtained LIDAR and CIMEL measurements of typical maritime and mineral dust-dominated marine atmosphere in the U.S. Virgin Islands. Contemporaneous SeaWiFS imagery were also acquired.

Gordon, Howard R.

Ice surface temperature retrieval from AVHRR, ATSR, and passive microwave satellite data: Algorithm development and application

One essential parameter used in the estimation of radiative and turbulent heat fluxes from satellite data is surface temperature. Sea and land surface temperature (SST and LST) retrieval algorithms that utilize the thermal infrared portion of the spectrum have been developed, with the degree of success dependent primarily upon the variability of the surface and atmospheric characteristics. However, little effort has been directed to the retrieval of the sea ice surface temperature (IST) in the Arctic and Antarctic pack ice or the ice sheet surface temperature over Antarctica and Greenland. The reason is not one of methodology, but rather our limited knowledge of atmospheric temperature, humidity, and aerosol vertical, spatial and temporal distributions, the microphysical properties of polar clouds, and the spectral characteristics of snow, ice, and water surfaces. Over the open ocean the surface is warm, dark, and relatively homogeneous. This makes SST retrieval, including cloud clearing, a fairly straightforward task. Over the ice, however, the surface within a single satellite pixel is likely to be highly heterogeneous, a mixture of ice of various thicknesses, open water, and snow cover in the case of sea ice. Additionally, the Arctic is cloudy - very cloudy - with typical cloud cover amounts ranging from 60-90 percent. There are few observations of cloud cover amounts over Antarctica. The goal of this research is to increase our knowledge of surface temperature patterns and magnitudes in both polar regions, by examining existing data and improving our ability to use satellite data as a monitoring tool. Four instruments are of interest in this study: the AVHRR, ATSR, SMMR, and SSM/I. Our objectives are as follows. Refine the existing AVHRR retrieval algorithm defined in Key and Haefliger (1992; hereafter KH92) and applied elsewhere. Develop a method for IST retrieval from ATSR data similar to the one used for SST. Further investigate the possibility of estimating surface temperature from passive microwave data (in conjunction with AVHRR clear sky samples) through the use of 'effective emissivities' and physical relationships between skin temperature and subsurface temperature. Use the general method outlined in MK93 to calculate a 12-year record of clear sky equivalent surface temperatures, or possibly all-sky snow-ice interface physical temperatures, from SMMR and SSM/I, compare these temperatures to climatologies, ECMWF modeled surface temperatures, and surface temperatures predicted by a 2-D ice model. And intercompare several ice surface retrieval methods and validate them against ground measurements from the Swiss Camp on the Greenland ice sheet. Additionally, we intend to develop a surface temperature product based on AVHRR data and possibly blended with drifting buoy and meteorological station temperatures.

Key, Jeff

Scheduling language and algorithm development study. Appendix: Study approach and activity summary

The approach and organization of the study to develop a high level computer programming language and a program library are presented. The algorithm and problem modeling analyses are summarized. The approach used to identify and specify the capabilities required in the basic language is described. Results of the analyses used to define specifications for the scheduling module library are presented.

Source record

Ocean observations with EOS/MODIS: Algorithm development and post launch studies

An investigation of the influence of stratospheric aerosol on the performance of the atmospheric correction algorithm is nearly complete. The results indicate how the performance of the algorithm is degraded if the stratospheric aerosol is ignored. Use of the MODIS 1380 nm band to effect a correction for stratospheric aerosols was also studied. Simple algorithms such as subtracting the reflectance at 1380 nm from the visible and near infrared bands can significantly reduce the error; however, only if the diffuse transmittance of the aerosol layer is taken into account. The atmospheric correction code has been modified for use with absorbing aerosols. Tests of the code showed that, in contrast to non absorbing aerosols, the retrievals were strongly influenced by the vertical structure of the aerosol, even when the candidate aerosol set was restricted to a set appropriate to the absorbing aerosol. This will further complicate the problem of atmospheric correction in an atmosphere with strongly absorbing aerosols. Our whitecap radiometer system and solar aureole camera were both tested at sea and performed well. Investigation of a technique to remove the effects of residual instrument polarization sensitivity were initiated and applied to an instrument possessing (approx.) 3-4 times the polarization sensitivity expected for MODIS. Preliminary results suggest that for such an instrument, elimination of the polarization effect is possible at the required level of accuracy by estimating the polarization of the top-of-atmosphere radiance to be that expected for a pure Rayleigh scattering atmosphere. This may be of significance for design of a follow-on MODIS instrument. W.M. Balch participated on two month-long cruises to the Arabian sea, measuring coccolithophore abundance, production, and optical properties. A thorough understanding of the relationship between calcite abundance and light scatter, in situ, will provide the basis for a generic suspended calcite algorithm.

Gordon, Howard R.

Data inversion algorithm development for the hologen occultation experiment

The successful retrieval of atmospheric parameters from radiometric measurement requires not only the ability to do ideal radiometric calculations, but also a detailed understanding of instrument characteristics. Therefore a considerable amount of time was spent in instrument characterization in the form of test data analysis and mathematical formulation. Analyses of solar-to-reference interference (electrical cross-talk), detector nonuniformity, instrument balance error, electronic filter time-constants and noise character were conducted. A second area of effort was the development of techniques for the ideal radiometric calculations required for the Halogen Occultation Experiment (HALOE) data reduction. The computer code for these calculations must be extremely complex and fast. A scheme for meeting these requirements was defined and the algorithms needed form implementation are currently under development. A third area of work included consulting on the implementation of the Emissivity Growth Approximation (EGA) method of absorption calculation into a HALOE broadband radiometer channel retrieval algorithm.

Gordley, Larry L.

Ocean observations with EOS/MODIS: Algorithm development and post launch studies

During CY 1994 there are five objectives under this task: (1) investigate the effects of stratospheric aerosol on the proposed correction algorithm, and investigate the use of the 1380 nm MODIS band to remove the stratospheric aerosol perturbation; (2) investigate the effect of vertical structure in aerosol concentration and type on the behavior of the proposed correction algorithm; (3) investigate the effects of polarization on the accuracy of the algorithm; (4) improve the accuracy and speed of the existing algorithm; and (5) investigate removal of the O2 'A' absorption band at 762 nm from the 765 nm SeaWiFS band so the latter can be used in atmospheric correction of SeaWiFS. The importance of this to MODIS is that SeaWiFS data will be used extensively to test and improve the MODIS algorithm. Thus it is essential that the O2 absorption be adequately dealt with for SeaWiFS.

Gordon, Howard R.

Ocean observations with EOS/MODIS: Algorithm development and post launch studies

Several significant accomplishments were made during the present reporting period. (1) Initial simulations to understand the applicability of the MODerate Resolution Imaging Spectrometer (MODIS) 1380 nm band for removing the effects of stratospheric aerosols and thin cirrus clouds were completed using a model for an aged volcanic aerosol. The results suggest that very simple procedures requiring no a priori knowledge of the optical properties of the stratospheric aerosol may be as effective as complex procedures requiring full knowledge of the aerosol properties, except the concentration which is estimated from the reflectance at 1380 nm. The limitations of this conclusion will be examined in the next reporting period; (2) The lookup tables employed in the implementation of the atmospheric correction algorithm have been modified in several ways intended to improve the accuracy and/or speed of processing. These have been delivered to R. Evans for implementation into the MODIS prototype processing algorithm for testing; (3) A method was developed for removal of the effects of the O2 'A' absorption band from SeaWiFS band 7 (745-785 nm). This is important in that SeaWiFS imagery will be used as a test data set for the MODIS atmospheric correction algorithm over the oceans; and (4) Construction of a radiometer, and associated deployment boom, for studying the spectral reflectance of oceanic whitecaps at sea was completed. The system was successfully tested on a cruise off Hawaii on which whitecaps were plentiful during October-November. This data set is now under analysis.

Gordon, Howard R.

Fast Radiative Transfer Model and Retrieval Algorithm Development for Satellite Remote Sensing Applications

The radiative transfer model (RTM) has a wide range of applications in satellite remote sensing and atmospheric radiation studies. For example, it can be used as a forward model for an inversion algorithm and a satellite data assimilation system, or as a L1 data simulator for pre-launch end-to-end satellite sensor performance studies. However, millions of line-by-line (LBL) radiative transfer calculations at fine monochromatic frequencies are needed in order to properly calculate spectral contributions of water vapor and trace gases in the atmosphere in infrared and solar spectral regions. Therefore, fast, and accurate radiative transfer models are needed. A Principal Component-based radiative transfer model (PCRTM) was developed at NASA Langley to fulfil this need. The PCRTM can simulate the top-of-atmosphere (TOA) radiance or reflectance spectra from 250 nm to 2000 micrometers with several orders of magnitude faster speed as compared to a LBL RTM. It is also extremely accurate compared to LBL RTM benchmarks. The PCRTM model has been developed for hyperspectral sensors such as AIRS, CrIS, IASI, NAST-I, SHIS, CPF, TEMPO, EMIT, OMI, and SCIAMACHY. By using the PCRTM as forward model for an inversion algorithm, one can reduce the data dimension significantly while maintaining original information content by compressing the TOA radiance spectrum into PC-scores. The PCRTM can directly compute the PC-scores and their derivatives with respect to retrieved parameters. Examples of using various PCRTM inversion algorithms to retrieve atmospheric temperature, water vapor, and trace gas profiles, as well as cloud and surface properties from satellite hyperspectral remote sensors will be given. Some of the algorithms have been transitioned to NASA's Goddard Earth Sciences Data and Information Services Center (GES DISC) for public access of high-quality L2 and L3 data.

Xu Liu

Motion Cueing Algorithm Development: New Motion Cueing Program Implementation and Tuning

A computer program has been developed for the purpose of driving the NASA Langley Research Center Visual Motion Simulator (VMS). This program includes two new motion cueing algorithms, the optimal algorithm and the nonlinear algorithm. A general description of the program is given along with a description and flowcharts for each cueing algorithm, and also descriptions and flowcharts for subroutines used with the algorithms. Common block variable listings and a program listing are also provided. The new cueing algorithms have a nonlinear gain algorithm implemented that scales each aircraft degree-of-freedom input with a third-order polynomial. A description of the nonlinear gain algorithm is given along with past tuning experience and procedures for tuning the gain coefficient sets for each degree-of-freedom to produce the desired piloted performance. This algorithm tuning will be needed when the nonlinear motion cueing algorithm is implemented on a new motion system in the Cockpit Motion Facility (CMF) at the NASA Langley Research Center.

Houck, Jacob A.

SeaWiFS Technical Report Series: Satellite Primary Productivity Data and Algorithm Development: A Science Plan for Mission to Planet Earth - Volume 42

Two issues regarding primary productivity, as it pertains to the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Program and the National Aeronautics and Space Administration (NASA) Mission to Planet Earth (MTPE) are presented in this volume. Chapter 1 describes the development of a science plan for deriving primary production for the world ocean using satellite measurements, by the Ocean Primary Productivity Working Group (OPPWG). Chapter 2 presents discussions by the same group, of algorithm classification, algorithm parameterization and data availability, algorithm testing and validation, and the benefits of a consensus primary productivity algorithm.

Falkowski, Paul G.

Multifunction Sensor Algorithm Development

A multifunction sensor has been developed in the Sensors and Electronics Technology Branch. It is capable of measuring heat flux, surface temperature, and, in principle, strain magnitude & direction, while compensating for the apparent strain due to changes in operating temperature. In order to achieve this strain measuring capability, Mr. Zeller will work on improving the signal processing algorithm to include several special cases, such as when the principal strain axis lies either parallel to or perpendicular to one of the arms of the sensor. In addition, he will implement a GUI to make the sensor more user friendly.

Zeller, Donald F.

Algorithm development for the control design of flexible structures

The critical problems associated with the control of highly damped flexible structures are outlined. The practical problems include: high performance; assembly in space, configuration changes; on-line controller software design; and lack of test data. Underlying all of these problems is the central problem of modeling errors. To justify the expense of a space structure, the performance requirements will necessarily be very severe. On the other hand, the absence of economical tests precludes the availability of reliable data before flight. A design algorithm is offered which: (1) provides damping for a larger number of modes than the optimal attitude controller controls; (2) coordinates the rate of feedback design with the attitude control design by use of a similar cost function; and (3) provides model reduction and controller reduction decisions which are systematically connected to the mathematical statement of the control objectives and the disturbance models.

Skelton, R. E.