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Clustering, randomness and regularity in cloud fields. I - Theoretical considerations. II - Cumulus cloud fields

The current controversy existing in reference to the regularity vs. clustering in cloud fields is examined by means of analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics. It is shown that the Poisson representation of random point processes is superior to pseudorandom-number-generated models and that pseudorandom-number-generated models bias the observed nearest-neighbor statistics towards regularity. Interpretation of this nearest-neighbor statistics is discussed for many cases of superpositions of clustering, randomness, and regularity. A detailed analysis is carried out of cumulus cloud field spatial distributions based upon Landsat, AVHRR, and Skylab data, showing that, when both large and small clouds are included in the cloud field distributions, the cloud field always has a strong clustering signal.

Weger, R. C.

Manufacture of Regularly Shaped Sol-Gel Pellets

An extrusion batch process for manufacturing regularly shaped sol-gel pellets has been devised as an improved alternative to a spray process that yields irregularly shaped pellets. The aspect ratio of regularly shaped pellets can be controlled more easily, while regularly shaped pellets pack more efficiently. In the extrusion process, a wet gel is pushed out of a mold and chopped repetitively into short, cylindrical pieces as it emerges from the mold. The pieces are collected and can be either (1) dried at ambient pressure to xerogel, (2) solvent exchanged and dried under ambient pressure to ambigels, or (3) supercritically dried to aerogel. Advantageously, the extruded pellets can be dropped directly in a cross-linking bath, where they develop a conformal polymer coating around the skeletal framework of the wet gel via reaction with the cross linker. These pellets can be dried to mechanically robust X-Aerogel.

Leventis, Nicholas

Preparation of Regular Specimens for Atom Probes

A method of preparation of specimens of non-electropolishable materials for analysis by atom probes is being developed as a superior alternative to a prior method. In comparison with the prior method, the present method involves less processing time. Also, whereas the prior method yields irregularly shaped and sized specimens, the present developmental method offers the potential to prepare specimens of regular shape and size. The prior method is called the method of sharp shards because it involves crushing the material of interest and selecting microscopic sharp shards of the material for use as specimens. Each selected shard is oriented with its sharp tip facing away from the tip of a stainless-steel pin and is glued to the tip of the pin by use of silver epoxy. Then the shard is milled by use of a focused ion beam (FIB) to make the shard very thin (relative to its length) and to make its tip sharp enough for atom-probe analysis. The method of sharp shards is extremely time-consuming because the selection of shards must be performed with the help of a microscope, the shards must be positioned on the pins by use of micromanipulators, and the irregularity of size and shape necessitates many hours of FIB milling to sharpen each shard. In the present method, a flat slab of the material of interest (e.g., a polished sample of rock or a coated semiconductor wafer) is mounted in the sample holder of a dicing saw of the type conventionally used to cut individual integrated circuits out of the wafers on which they are fabricated in batches. A saw blade appropriate to the material of interest is selected. The depth of cut and the distance between successive parallel cuts is made such that what is left after the cuts is a series of thin, parallel ridges on a solid base. Then the workpiece is rotated 90 and the pattern of cuts is repeated, leaving behind a square array of square posts on the solid base. The posts can be made regular, long, and thin, as required for samples for atom-probe analysis. Because of their small volume and regularity, the amount of FIB-milling time can be much less than that of the method of sharp shards. Individual posts can be broken off for mounting in a manner similar to that of the method of sharp shards. Alternatively, the posts can be left intact on the base and the base can be cut to a small square (e.g., 3 by 3 mm) suitable for mounting in an atom probe of a type capable of accepting multiple-tip specimens. The advantage of multiple-tip specimens is the possibility of analyzing many tips without the time-consuming interchange of specimens.

Kuhlman, Kim

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-Norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients(called 1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a database of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field.

Hurricanes

Product of the SNPP VIIRS SD Screen Transmittance and the SD BRDF (RSB) From Both Yaw Maneuver and Regular On-Orbit Data

To assure data quality, the Earth-observing Visible Infrared Imaging Radiometer Suite (VIIRS) regularly performs on-orbit radiometric calibrations of its 22 spectral bands. The primary calibration radiance source for the reflective solar bands (RSBs) is a sunlit solar diffuser (SD). During the calibration process, sunlight goes through a perforated plate (the SD screen) and then strikes the SD. The SD scattered sunlight is used for the calibration, with the spectral radiance proportional to the product of the SD screen transmittance and the SD bidirectional reflectance distribution function (BRDF). The BRDF is decomposed to the product of its value at launch and a numerical factor quantifying its change since launch. Therefore, the RSB calibration requires accurate knowledge of the product of the SD screen transmittance and the BRDF (RSB; launch time). Previously, we calculated the product with yaw maneuver data and found that the product had improved accuracy over the prelaunch one. With both yaw maneuver and regular on orbit data, we were able to improve the accuracy of the SDSM screen transmittance and the product for the solar diffuser stability monitor SD view. In this study, we use both yaw maneuver and a small portion of regular on-orbit data to determine the product for the RSB SD view.

Lei, Ning

Regularization and Error Characterization of GRACE Mascons

We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.

B. D. Loomis

Regularization and Error Characterization of GRACE Mascons

We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.

Loomis, B. D.

Trajectory optimization using regularized variables

Regularized equations for a particular optimal trajectory are compared with unregularized equations with respect to computational characteristics, using perturbation type numerical optimization. In the case of the three dimensional, low thrust, Earth-Jupiter rendezvous, the regularized equations yield a significant reduction in computer time.

Lewallen, J. M.

The topology of the regularized integral surfaces of the 3-body problem.

A method is described by which the integral surface can be modified in such a way that Newton's equations of motion actually give a flow. The process of regularization of vector fields by surgery, as described by the author (1971) is reviewed. The planar 3-body problem and its regularization, and the topology of the integral surfaces are considered. The Lagrange-Jacobi identity is used to show that there exists an isolating block such that any orbit which ends in a triple collision must enter and remain in this block.

Easton, R.

Solar reflection from a regular array of horizontally finite clouds

The reflected flux from a regular array of 2- and 3-D clouds has been computed to estimate the effect of fractional cloud cover on albedos and the solar flux available to heat the earth's surface. The broken clouds are represented by a regular array of identical cuboids for the 3-D problem and equally spaced, infinitely long, bars for the 2-D problem. A diffusion approximation to the radiative transfer equation is used to compute the fluxes leaving each face of the cloud. Interaction between clouds is simulated by assuming diffuse exitance from the cloud faces and applying angle factors to obtain modified boundary conditions on each cloud face.

Weinman, J. A.

Application of the regular associated solution model to the Cd-Te and Hg-Te binary systems

The regular associated solution model is used to treat the phase diagrams of the binary II-VI semiconductor alloy systems Hg-Te and Cd-Te. The equations for the species activity coefficients are used without approximations regarding the magnitudes of the various binary interchange energies or the functional dependence on component mol fraction. The values of the four-adjustable parameters required for description of each system are fixed by fitting liquidus data, and the resulting activity coefficients are used to calculate component partial pressures, which are compared with experimental values as an indpendent check of the validity of the model. The results show that the regular associated solution model provides a usefully accurate, but not complete, description for both the Hg-Te and Cd-Te systems. The relationship of this work to previous investigations is discussed.

Kelley, J. D.

Autocorrelation and regularization in digital images. I - Basic theory

Spatial structure occurs in remotely sensed images when the imaged scenes contain discrete objects that are identifiable in that their spectral properties are more homogeneous within than between them and other scene elements. The spatial structure introduced is manifest in statistical measures such as the autocovariance function and variogram associated with the scene, and it is possible to formulate these measures explicitly for scenes composed of simple objects of regular shapes. Digital images result from sensing scenes by an instrument with an associated point spread function (PSF). Since there is averaging over the PSF, the effect, termed regularization, induced in the image data by the instrument will influence the observable autocovariance and variogram functions of the image data. It is shown how the autocovariance or variogram of an image is a composition of the underlying scene covariance convolved with an overlap function, which is itself a convolution of the PSF. The functional form of this relationship provides an analytic basis for scene inference and eventual inversion of scene model parameters from image data.

Jupp, David L. B.

Analysis of regularized Navier-Stokes equations, 2

A practically important regularization of the Navier-Stokes equations was analyzed. As a continuation of the previous work, the structure of the attractors characterizing the solutins was studied. Local as well as global invariant manifolds were found. Regularity properties of these manifolds are analyzed.

Ou, Yuh-Roung

Regular structure in the inner Cassini Division of Saturn's rings

Voyager imaging, radio occultation, and stellar occultation data for the regular structure of Saturn's inner Cassini Division are presently analyzed. The regular optical depth variation observed by the radio occultation experiment scan and the feature noted in Voyager images is the same structure, namely the gravitational wakes of two 10-km radius satellites orbiting within the division. The structure is azimuthally symmetric, and is judged to rule out the possibility that large moonlets may be responsible for the observed structure.

Flynn, Brian C.

Regular variability of the shape of the primary minimum of the orbital light curve of SS 433 with the phase of the precessional period

The regular variations of the shape of the primary minimum of the orbital 13.082-day light curve of SS 433 with the phase of the 162.5-day processional period were discovered by analysis of the photometrical databank. The regular variability of the shape of the primary minimum of the discovered light curve of SS 433 reflects displacement with the 26-day double orbital period of at least two hot bright spots on the surface of the processional accretional disk and their eclipse by a normal star. Other aspects of the investigation are further discussed.

Cherepashchuk, A. M.

A regularization method for extrapolation of solar potential magnetic fields

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

Gary, G. A.

Energy functions for regularization algorithms

Regularization techniques are widely used for inverse problem solving in computer vision such as surface reconstruction, edge detection, or optical flow estimation. Energy functions used for regularization algorithms measure how smooth a curve or surface is, and to render acceptable solutions these energies must verify certain properties such as invariance with Euclidean transformations or invariance with parameterization. The notion of smoothness energy is extended here to the notion of a differential stabilizer, and it is shown that to void the systematic underestimation of undercurvature for planar curve fitting, it is necessary that circles be the curves of maximum smoothness. A set of stabilizers is proposed that meet this condition as well as invariance with rotation and parameterization.

Delingette, H.

Tracking magnetogram proper motions by multiscale regularization

Long uninterrupted sequences of solar magnetograms from the global oscillations network group (GONG) network and from the solar and heliospheric observatory (SOHO) satellite will provide the opportunity to study the proper motions of magnetic features. The possible use of multiscale regularization, a scale-recursive estimation technique which begins with a prior model of how state variables and their statistical properties propagate over scale. Short magnetogram sequences are analyzed with the multiscale regularization algorithm as applied to optical flow. This algorithm is found to be efficient, provides results for all the spatial scales spanned by the data and provides error estimates for the solutions. It is found that the algorithm is less sensitive to evolutionary changes than correlation tracking.

Jones, Harrison P.