The Utility of Infrequent Snow Depth Images for Deriving Continuous Space‐Time Estimates of Seasonal Snow Water Equivalent
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Steven A. Margulis↗
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Construction of Covariance Functions with Variable Length Fields
This article focuses on construction, directly in physical space, of three-dimensional covariance functions parametrized by a tunable length field, and on an application of this theory to reproduce the Quasi-Biennial Oscillation (QBO) in the Goddard Earth Observing System, Version 4 (GEOS-4) data assimilation system. These Covariance models are referred to as multi-level or nonseparable, to associate them with the application where a multi-level covariance with a large troposphere to stratosphere length field gradient is used to reproduce the QBO from sparse radiosonde observations in the tropical lower stratosphere. The multi-level covariance functions extend well-known single level covariance functions depending only on a length scale. Generalizations of the first- and third-order autoregressive covariances in three dimensions are given, providing multi-level covariances with zero and three derivatives at zero separation, respectively. Multi-level piecewise rational covariances with two continuous derivatives at zero separation are also provided. Multi-level powerlaw covariances are constructed with continuous derivatives of all orders. Additional multi-level covariance functions are constructed using the Schur product of single and multi-level covariance functions. A multi-level powerlaw covariance used to reproduce the QBO in GEOS-4 is described along with details of the assimilation experiments. The new covariance model is shown to represent the vertical wind shear associated with the QBO much more effectively than in the baseline GEOS-4 system.
Gaspari, Gregory↗
Construction of Response Surface with Higher Order Continuity and Its Application to Reliability Engineering
The usefulness of piecewise polynomials with C1 and C2 derivative continuity for response surface construction method is examined. A Moving Least Squares (MLS) method is developed and compared with four other interpolation methods, including kriging. First the selected methods are applied and compared with one another in a two-design variables problem with a known theoretical response function. Next the methods are tested in a four-design variables problem from a reliability-based design application. In general the piecewise polynomial with higher order derivative continuity methods produce less error in the response prediction. The MLS method was found to be superior for response surface construction among the methods evaluated.
Krishnamurthy, T.↗
Characterization of shallow ocean sediments using the airborne electromagnetic method
Experimental airborne electromagnetic (AEM) survey data collected in Cape Cod Bay are used to derive continuous profiles of water depth, electrical depth, water conductivity, and bottom sediment conductivity. Through a few well-known empirical relationships, the conductivities are used, in turn, to derive density, porosity, sound speed, and acoustic reflectivity of the ocean bottom. A commercially available Dighem III AEM system was used for the survey without any significant modification. The helicopter-borne system operated at 385 and 7200 Hz; both were in a horizontal coplanar configuration. The interpreted profiles show good agreement with available ground truth data. Where no such data are available, the results appear to be very reasonable. Compared with the shipborne electrode array method, the AEM method can determine the necessary parameters at a much higher speed with a better lateral resolution over a wide range of water depths from 0 to perhaps 100 m. The bottom sediment conductivity that can be measured by the AEM method is closely related to physical properties of sediments, such as porosity, density, sound speed, and, indirectly, sediment types that might carry broad implications for various offshore activities.
Won, I. J.↗
Combined Microwave and Sferics Measurements as a Continuous Proxy for Latent Heating in Mesoscale Model Predictions
Planar rainfall distributions were retrieved from data provided by the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and Special Sensor Microwave/Imager (SSM/I) radiometers. Lightning generates Very Low Frequency (VLF) radio noise pulses called sferics. Those pulses propagate over large distances so that they can be continuously monitored with a network of ground based radio receivers. An empirical relationship between the sferics rate and the convective rainfall permitted maps of convective latent heating profiles to be derived continuously from the sferics distributions. Those inferred latent heating rates were assimilated into the Penn State/NCAR Mesoscale Model (MM5) that depicted an intense winter cyclone that passed over Florida on 2 February 1998. When compared to a 14 hour MM5 rainfall forecast using conventional data, the use of lightning data improved the forecast.
Chang, D.-E.↗
Combined Microwave and Sferics Measurements as a Continuous Proxy for Latent Heating in Mesoscale Model Predictions
Planar rainfall distributions were retrieved from data provided by the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and Special Sensor Microwave Imager (SSM/I) radiometers. Lightning generates Very Low Frequency (VLF) radio noise pulses called sferics. Those pulses propagate over large distances so that they can be continuously monitored with a network of ground based radio receivers. An empirical relationship between the sferics rate and the convective rainfall permitted maps of convective latent heating profiles to be derived continuously from the sferics distributions. Those inferred latent heating rates were assimilated into the Penn State/NCAR Mesoscale Model (MM5) that depicted an intense winter cyclone that passed over Florida on 2 February 1998. When compared to a 14 hour MM5 rainfall forecast using conventional data, the use of lightning data improved the forecast.
Chang, D. -E.↗
Asteroids - Spectral reflectance and color characteristics
We present visible and near-infrared spectral reflectance curves for 35 asteroids, making a total sample of 67 including our previous work. Several previously unknown spectral types have been discovered. Absorption bands and other features, from which information about the surface composition of the asteroids can be derived, continue to appear. Sampling statistics suggest we have observed about half of the significantly different mineralogical assemblages present in the asteroid belt. There is a general, but imperfect, correlation between spectral type and semimajor axis, which is consistent with the hypothesis that meteorites are derived from the asteroid belt. The color-frequency histogram for the 67 objects is bimodal, probably associated with 'stony' objects and 'carbonaceous' objects. Hirayama family pairs usually show disparate spectral types. 19 Fortuna may show strikingly different photometric properties on opposite sides.
Mccord, T. B.↗
A representation of Jacchia's thermospheric models in spherical harmonic functions
The Jacchia models are represented in terms of spherical harmonic functions. This representation has the advantage of ease of comparison with other global theoretical and empirical models that use this mathematical form. Furthermore, it is analytic, continuous, and has continuous derivatives all over the globe. The representation of the exospheric temperatures shows clearly the amplitudes of the various periodic terms and uses relatively few constants. An example of a similar representation for the total mass density at a particular height and level of solar activity is given as well.
Blum, P.↗
A structural model of the adaptive human pilot
A compensatory tracking model of the human pilot is offered which attempts to provide a more realistic representation of the human's signal processing structure than that which is exhibited by pilot models currently in use. Two features of the model distinguish it from other representations of the human pilot. First, proprioceptive information from the control stick or manipulator constitutes one of the major feedback paths in the model, providing feedback of vehicle output rate due to control activity. Implicit in this feedback loop is a model of the vehicle dynamics which is valid in and beyond the region of crossover. Second, error-rate information is continuously derived and independently but intermittently controlled. An output injected remnant model is offered and qualitatively justified on the basis of providing a measure of the effect of inaccuracies such as time variations in the pilot's internal model of the controlled element dynamics. The data from experimental tracking tasks involving five different controlled element dynamics and one nonideal viewing condition were matched with model generated describing functions and remnant power spectral densities.
Hess, R. A.↗
Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion
To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1 deg-averaged surface free-air gravity anomalies of POGO satellite magnetometer data for the United States, Mexico, and Central America illustrate the capabilities of the method.
Von Frese, R. R. B.↗
Geodetic and geophysical results from Lageos
Seven years of laser tracking of the Lageos spacecraft have been used to derive geodetic quantities describing the earth and its rotational motion. The dynamical motions of the solid-earth on its axis have been derived continuously since launch and changes in the length-of-day show very high correlation with variations in the atmospheric zonal winds between 1000 and 50 mbars. A significant improvement in the determination of the product of the earth's mass and the gravitational constant has been made. The high accuracy of the orbit determination of Lageos over the 7 years since launch has permitted the identification of a small deceleration in the nodal precession of the orbit. This deceleration is being caused by a small reduction in the flattening of the earth arising from the rebound of the earth after the last ice age. Measurements of the distances between the tracking stations over several years are showing changes consistent with tectonic plate motion and with general ideas of vertical movements.
Smith, D. E.↗
Systematic methods for calculation of the dielectric properties of arbitrary plasmas
In the novel approach presented for calculating the dispersion integrals needed for determining plasma dielectric properties, the dispersion integrals for an arbitrary distortion function with a continuous derivative are systematically expanded in terms of a set of orthogonal functions whose corresponding dispersion functions are already known. This general approach is, on the one hand, implemented for unmagnetized plasmas, and on the other generalized to treat relativistic and magnetized plasmas. The method allows the systematic and efficient calculation of dispersion integrals, for the cases of either real or complex arguments.
Robinson, P. A.↗
Shuttle Debris Impact Tool Assessment Using the Modern Design of Experiments
Computational tools have been developed to estimate thermal and mechanical reentry loads experienced by the Space Shuttle Orbiter as the result of cavities in the Thermal Protection System (TPS). Such cavities can be caused by impact from ice or insulating foam debris shed from the External Tank (ET) on liftoff. The reentry loads depend on cavity geometry and certain Shuttle state variables, among other factors. Certain simplifying assumptions have been made in the tool development about the cavity geometry variables. For example, the cavities are all modeled as shoeboxes , with rectangular cross-sections and planar walls. So an actual cavity is typically approximated with an idealized cavity described in terms of its length, width, and depth, as well as its entry angle, exit angle, and side angles (assumed to be the same for both sides). As part of a comprehensive assessment of the uncertainty in reentry loads estimated by the debris impact assessment tools, an effort has been initiated to quantify the component of the uncertainty that is due to imperfect geometry specifications for the debris impact cavities. The approach is to compute predicted loads for a set of geometry factor combinations sufficient to develop polynomial approximations to the complex, nonparametric underlying computational models. Such polynomial models are continuous and feature estimable, continuous derivatives, conditions that facilitate the propagation of independent variable errors. As an additional benefit, once the polynomial models have been developed, they require fewer computational resources to execute than the underlying finite element and computational fluid dynamics codes, and can generate reentry loads estimates in significantly less time. This provides a practical screening capability, in which a large number of debris impact cavities can be quickly classified either as harmless, or subject to additional analysis with the more comprehensive underlying computational tools. The polynomial models also provide useful insights into the sensitivity of reentry loads to various cavity geometry variables, and reveal complex interactions among those variables that indicate how the sensitivity of one variable depends on the level of one or more other variables. For example, the effect of cavity length on certain reentry loads depends on the depth of the cavity. Such interactions are clearly displayed in the polynomial response models.
DeLoach, R.↗
Summary of Terra and Aqua MODIS Long-Term Performance
Since launch in December 1999, the MODIS ProtoFlight Model (PFM) onboard the Terra spacecraft has successfully operated for more than 11 years. Its Flight Model (FM) onboard the Aqua spacecraft, launched in May 2002, has also successfully operated for over 9 years. MODIS observations are made in 36 spectral bands at three nadir spatial resolutions and are calibrated and characterized regularly by a set of on-board calibrators (OBC). Nearly 40 science products, supporting a variety of land, ocean, and atmospheric applications, are continuously derived from the calibrated reflectances and radiances of each MODIS instrument and widely distributed to the world-wide user community. Following an overview of MODIS instrument operation and calibration activities, this paper provides a summary of both Terra and Aqua MODIS long-term performance. Special considerations that are critical to maintaining MODIS data quality and beneficial for future missions are also discussed.
Xiong, Xiaoxiong (Jack)↗
Mapping the Daily Progression of Large Wildland Fires Using MODIS Active Fire Data
High temporal resolution information on burned area is a prerequisite for incorporating bottom-up estimates of wildland fire emissions in regional air transport models and for improving models of fire behavior. We used the Moderate Resolution Imaging Spectroradiometer (MODIS) active fire product (MO(Y)D14) as input to a kriging interpolation to derive continuous maps of the evolution of nine large wildland fires. For each fire, local input parameters for the kriging model were defined using variogram analysis. The accuracy of the kriging model was assessed using high resolution daily fire perimeter data available from the U.S. Forest Service. We also assessed the temporal reporting accuracy of the MODIS burned area products (MCD45A1 and MCD64A1). Averaged over the nine fires, the kriging method correctly mapped 73% of the pixels within the accuracy of a single day, compared to 33% for MCD45A1 and 53% for MCD64A1.
Aqua↗
Error analysis of finite element solutions for postbuckled cylinders
A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.
Sistla, Rajaram↗
Coordinate generation with precise controls over mesh properties
Powerful local controls have been developed for mesh generation with the class of multisurface coordinate transformations. The controls come from local piecewise linear interpolants, and the resulting coordinates have continuous first derivatives. At the boundaries, the mesh controls provide the capability of joining distinct coordinate systems together with continuous derivatives. Away from boundaries, a local region can be given a particular mesh form to model internal objects or to simplify a problem. Applications of the controls are illustrated with a sequence of two-dimensional examples. For simplicity, each is generated about a NACA0012 airfoil which is of unit length and with leading edge pointed in a negative x-direction.
Eiseman, P. R.↗
Simultaneous integration of n-bodies by analytic continuation with recursively formed derivatives.
Motion equations of sun, moon, earth and lunar probe integrated by power series solution and analytic continuation with recursively formed derivatives
Hartwell, J. G.↗