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NASA NTRS2004

Parameter Estimation in Atmospheric Data Sets

In this study the structure tensor technique is used to estimate dynamical parameters in atmospheric data sets. The structure tensor is a common tool for estimating motion in image sequences. This technique can be extended to estimate other dynamical parameters such as diffusion constants or exponential decay rates. A general mathematical framework was developed for the direct estimation of the physical parameters that govern the underlying processes from image sequences. This estimation technique can be adapted to the specific physical problem under investigation, so it can be used in a variety of applications in trace gas, aerosol, and cloud remote sensing. As a test scenario this technique will be applied to modeled dust data. In this case vertically integrated dust concentrations were used to derive wind information. Those results can be compared to the wind vector fields which served as input to the model. Based on this analysis, a method to compute atmospheric data parameter fields will be presented. .

Wenig, Mark↗
NASA NTRS1999

Real-Time Parameter Estimation in the Frequency Domain

A method for real-time estimation of parameters in a linear dynamic state space model was developed and studied. The application is aircraft dynamic model parameter estimation from measured data in flight for indirect adaptive or reconfigurable control. Equation error in the frequency domain was used with a recursive Fourier transform for the real-time data analysis. Linear and nonlinear simulation examples and flight test data from the F-18 High Alpha Research Vehicle HARV) were used to demonstrate that the technique produces accurate model parameter estimates with appropriate error bounds. Parameter estimates converged in less than 1 cycle of the dominant dynamic mode natural frequencies, using control surface inputs measured in flight during ordinary piloted maneuvers. The real-time parameter estimation method has low computational requirements, and could be implemented aboard an aircraft in real time.

Morelli, Eugene A.↗
NASA NTRS2003

Comparison of mode estimation methods and application in molecular clock analysis

BACKGROUND: Distributions of time estimates in molecular clock studies are sometimes skewed or contain outliers. In those cases, the mode is a better estimator of the overall time of divergence than the mean or median. However, different methods are available for estimating the mode. We compared these methods in simulations to determine their strengths and weaknesses and further assessed their performance when applied to real data sets from a molecular clock study. RESULTS: We found that the half-range mode and robust parametric mode methods have a lower bias than other mode methods under a diversity of conditions. However, the half-range mode suffers from a relatively high variance and the robust parametric mode is more susceptible to bias by outliers. We determined that bootstrapping reduces the variance of both mode estimators. Application of the different methods to real data sets yielded results that were concordant with the simulations. CONCLUSION: Because the half-range mode is a simple and fast method, and produced less bias overall in our simulations, we recommend the bootstrapped version of it as a general-purpose mode estimator and suggest a bootstrap method for obtaining the standard error and 95% confidence interval of the mode.

Evolution, Molecular↗
NASA NTRS2003

Estimation and Simulation of Slow Crack Growth Parameters from Constant Stress Rate Data

Closed form, approximate functions for estimating the variances and degrees-of-freedom associated with the slow crack growth parameters n, D, B, and A(sup *) as measured using constant stress rate ('dynamic fatigue') testing were derived by using propagation of errors. Estimates made with the resulting functions and slow crack growth data for a sapphire window were compared to the results of Monte Carlo simulations. The functions for estimation of the variances of the parameters were derived both with and without logarithmic transformation of the initial slow crack growth equations. The transformation was performed to make the functions both more linear and more normal. Comparison of the Monte Carlo results and the closed form expressions derived with propagation of errors indicated that linearization is not required for good estimates of the variances of parameters n and D by the propagation of errors method. However, good estimates variances of the parameters B and A(sup *) could only be made when the starting slow crack growth equation was transformed and the coefficients of variation of the input parameters were not too large. This was partially a result of the skewered distributions of B and A(sup *). Parametric variation of the input parameters was used to determine an acceptable range for using closed form approximate equations derived from propagation of errors.

Salem, Jonathan A.↗
NASA NTRS2001

Estimation of diastolic intraventricular pressure gradients by Doppler M-mode echocardiography

Previous studies have shown that small intraventricular pressure gradients (IVPG) are important for efficient filling of the left ventricle (LV) and as a sensitive marker for ischemia. Unfortunately, there has previously been no way of measuring these noninvasively, severely limiting their research and clinical utility. Color Doppler M-mode (CMM) echocardiography provides a spatiotemporal velocity distribution along the inflow tract throughout diastole, which we hypothesized would allow direct estimation of IVPG by using the Euler equation. Digital CMM images, obtained simultaneously with intracardiac pressure waveforms in six dogs, were processed by numerical differentiation for the Euler equation, then integrated to estimate IVPG and the total (left atrial to left ventricular apex) pressure drop. CMM-derived estimates agreed well with invasive measurements (IVPG: y = 0.87x + 0.22, r = 0.96, P < 0.001, standard error of the estimate = 0.35 mmHg). Quantitative processing of CMM data allows accurate estimation of IVPG and tracking of changes induced by beta-adrenergic stimulation. This novel approach provides unique information on LV filling dynamics in an entirely noninvasive way that has previously not been available for assessment of diastolic filling and function.

Non-NASA Center↗
NASA NTRS2004

How Well are Recent Climate Variability Signals Resolved by Satellite Radiative Flux Estimates?

One notable aspect of Earth s climate is that although the planet appears to be very close to radiative balance at top-of-atmosphere (TOA), the atmosphere itself and underlying surface are not. Profound exchanges of energy between the atmosphere and oceans, land and cryosphere occur over a range of time scales. Recent evidence from broadband satellite measurements suggests that even these TOA fluxes contain some detectable variations. Our ability to measure and reconstruct radiative fluxes at the surface and at the top of atmosphere is improving rapidly. Understanding the character of radiative flux estimates and relating them to variations in other energy fluxes and climate state variables is key to improving our understanding of climate. In this work we will evaluate several recently released estimates of radiative fluxes, focusing primarily on surface estimates. The International Satellite Cloud Climatology Project FD radiative flux profiles are available from rnid-1983 to near present and have been constructed by driving the radiative transfer physics from the Goddard Institute for Space Studies (GISS) global model with ISCCP clouds and HlRS operational soundings profiles. Full and clear sky SW and LW fluxes are produced. A similar product from the NASA/GEWEX Surface Radiation Budget Project using different radiative flux codes and thermodynamics from the NASA/Goddard Earth Observing System assimilation model makes a similar calculation of surface fluxes. However this data set currently extends only through 1995. Several estimates of downward LW flux at the surface inferred from microwave data are also examined. Since these products have been evaluated with Baseline Surface Radiation Network data over land we focus over ocean regions and use the DOE/NOAA/NASA Shipboard Ocean Atmospheric Radiation (SOAR) surface flux measurements to characterize performance of these data sets under both clear and cloudy conditions. Some aspects of performance are stratified according to SST and vertical motion regimes. Comparisons to the TRMM/CERES SRB data in 1998 are also interpreted. These radiative fluxes are then analyzed to determine how surface (and TOA) radiative exchanges respond to interannual signals of ENS0 warm and cold events. Our analysis includes regional changes as well as integrated signals over land, ocean and various latitude bands. Changes in water vapor and cloud forcing signatures are prominent on interannual time scales. Prominent signals are also found in the SW fluxes for the Pinatubo volcanic event. These systematic changes in fluxes are related to changes in large-scale circulations and energy transport in the atmosphere and ocean. Some estimates of signal-to-noise and reliability are discussed to place our results in context.

Robertson, Franklin R.↗
NASA NTRS2004

A Geomagnetic Estimate of Mean Paleointensity

To test a statistical hypothesis about Earth's magnetic field against paleomagnetism, the present field is used to estimate time averaged paleointensity. The estimate uses the modem magnetic multipole spectrum R(n), which gives the mean square induction represented by spherical harmonics of degree n averaged over the sphere of radius a = 6371.2 km. The hypothesis asserts that the low degree multipole powers of the core-source field are distributed as chi-squared with 2n+l degrees of freedom and expectation values {R(n)} = K[(n+l/2)/n(n+l](c/a)(sup 2n+4), where c is the 3480 km radius of Earth's core. (This is compatible with a usually mainly geocentric axial dipolar field). Amplitude K is estimated by fitting theoretical to observational spectra through degree 12. The resulting calibrated expectation spectrum is summed through degree 12 to estimate expected square intensity {F(sup 2)}. The sum also estimates {F(sup 2)} averaged over geologic time, in so far as the present magnetic spectrum is a fair sample of that generated in the past by core geodynamic processes.

Voorhies, Coerte↗
NASA NTRS2004

Top-of-Atmosphere Shortwave Broadband Observed Radiance and Estimated Irradiance over Polar Regions from Clouds and the Earth's Radiant Energy System (CERES) Instruments on Terra

Empirical angular distribution models for estimating top-of-atmosphere shortwave irradiances from radiance measurements over permanent snow, fresh snow and sea ice are developed using CERES measurements on Terra. Permanent snow angular distribution models depend on cloud fraction, cloud optical thickness, and snow brightness. Fresh snow and sea ice angular distribution models depend on snow and sea ice fraction, cloud fraction, cloud optical thickness, and snow and ice brightness. These classifications lead to 10 scene types for permanent snow and 25 scene types for fresh snow and sea ice. The average radiance over clear-sky permanent snow is more isotropic with satellite viewing geometry than that over overcast permanent snow. On average, the albedo of clear-sky permanent snow varies from 0.65 to 0.68 for solar zenith angles between 60$logical and\circ$ and 80 deg, while the corresponding albedo of overcast scenes varies from 0.70 to 0.73. Clear-sky permanent snow albedos over Antarctica estimated from two independent angular distribution models are consistent to within 0.6%, on average. Despite significant variability in sea ice optical properties with season, the estimated mean relative albedo error is -1 % for very dark sea ice and 0.1% for very bright sea ice when albedos derived from different viewing angles are averaged. The estimated regional root-mean-square (RMS) relative albedo error is 5.6% and 2.6% when the sea ice angular distribution models are applied to a region that contains very dark and very bright sea ice, respectively. Similarly, the estimated relative albedo bias error for fresh snow is -0.1% for very dark snow.

Kato, S.↗
NASA NTRS2005

Lightning Contribution to Improvement of Passive Microwave Vertical Structure and Rainfall Estimation

Joint observations from the TRMM mission are used to examine the contribution which lightning observations can make towards estimation of vertical structure and rainfall from passive microwave data. Passive microwave (TMI) observations are binned into distinct vertical structure categories based on cluster analysis of radar (PR) vertical profiles and convective/stratiform (C/S) classifiers. TMI rain estimates are high-biased relative to radar for stratiform and mixed convective/stratiform vertical structures and low-biased relative to radar for convective structures. Significant ambiguity exists in the TMI brightness temperature space between midlevel stratiform and convective profile types which are primary contributors to tropical rainfall. The ambiguity is worst for convective profile types with radar echo tops within and just above the mixed-phase region. The ability of TMI data (including all low and high frequency polarized brightness temperatures; 19V, 19H, 21V, 37V, 37H, 85V, 85H) to predict vertical structure is assessed. The incremental benefit of including TMI convective/stratiform (C/S) classifiers (both 85 GHz polarization and 19, 37 and 85 GHz texture-based) and LZS lightning observations is then considered. The use of all parameters (brightness temperatures, TMI C/S classifiers, lightning data, predicted vertical structure) to reduce TMI/PR rainfall estimate scatter is demonstrated. For both vertical structure and rainfall estimation, inclusion of C/S classifiers and lightning observations provide statistical skill improvements but do not completely alleviate critical midlevel profile C/S ambiguity and related rain estimate errors.

Boccippio, Dennis↗
NASA NTRS2004

A Geomagnetic Estimate of Mean Paleointensity

To test a statistical hypothesis about Earth's magnetic field against paleomagnetism, the present field is used to estimate time averaged paleointensity. The estimate used the modern magnetic multipole spectrum R(n), which gives the mean square induction represented by spherical harmonics of degree n averaged over the sphere of radius a = 6371.2 km. The hypothesis asserts that low degree multi-pole powers of the coresource field are distributed as chi-squared with 2n+1 degrees of freedom and expectation values, where c is the 3480 km radius of the Earth's core. (This is compatible with a usually mainly geocentric axial dipolar field). Amplitude K is estimated by fitting theoretical to observational spectra through degree 12. The resulting calibrated expectation spectrum is summed through degree 12 to estimate expected square intensity F(exp 2). The sum also estimates F(exp 2) averaged over geologic time, in so far as the present magnetic spectrum is a fair sample of that generated in the past by core geodynamic processes. Additional information is included in the original extended abstract.

Voorhies, Coerte V.↗
NASA NTRS2005

Aerodynamic Parameter Estimation for the X-43A (Hyper-X) from Flight Data

Aerodynamic parameters were estimated based on flight data from the third flight of the X-43A hypersonic research vehicle, also called Hyper-X. Maneuvers were flown using multiple orthogonal phase-optimized sweep inputs applied as simultaneous control surface perturbations at Mach 8, 7, 6, 5, 4, and 3 during the vehicle descent. Aerodynamic parameters, consisting of non-dimensional longitudinal and lateral stability and control derivatives, were estimated from flight data at each Mach number. Multi-step inputs at nearly the same flight conditions were also flown to assess the prediction capability of the identified models. Prediction errors were found to be comparable in magnitude to the modeling errors, which indicates accurate modeling. Aerodynamic parameter estimates were plotted as a function of Mach number, and compared with estimates from the pre-flight aerodynamic database, which was based on wind-tunnel tests and computational fluid dynamics. Agreement between flight estimates and values computed from the aerodynamic database was excellent overall.

Morelli, Eugene A.↗
NASA NTRS2006

The Potential of Water Vapor & Precipitation Estimation with a Differential-frequency Radar

In the presence of rain, the radar return powers from a three-frequency radar, with center frequency at 22.235 GHz and upper and lower frequencies chosen with equal water vapor absorption coefficients, can be used to estimate water vapor density and parameters of the precipitation. A linear combination of differential measurements between the center and lower frequencies on one hand and the upper and lower frequencies on the other provide an estimate of differential water vapor absorption. Conversely, the difference in radar reflectivity factors (in dB) between the upper and lower frequencies is independent of water vapor absorption and can be used to estimate the median mass diameter of the hydrometeors. For a down-looking radar, path-integrated estimates of water vapor absorption may be possible under rain-free as well as raining conditions by using the surface returns at the three frequencies. Cross-talk or interference between the precipitation and water vapor estimates depends on the frequency separation of the channels as well as on the phase state and the median mass diameter of the hydrometeors. Simulations of the retrieval of water vapor absorption show that the largest source of variability arises from the variance in the measured radar return powers while the largest biases occur in the mixed-phase region. Use of high pulse repetition frequencies and signal whitening methods may be needed to obtain the large number of independent samples required. Measurements over a fractional bandwidth, defined as the ratio of the difference between the upper and lower frequencies to the center frequency, up to about 0.2 should be passible in a differential frequency mode, where a single transceiver and antenna are used. Difficulties in frequency allocation may require alternative choices of frequency where the water vapor absorptions at the low and high frequencies are unequal. We consider the degradation in the retrieval accuracy when the frequencies are not optimum.

Meneghini, Robert↗
NASA NTRS2007

Estimating Rain Rates from Tipping-Bucket Rain Gauge Measurements

This paper describes the cubic spline based operational system for the generation of the TRMM one-minute rain rate product 2A-56 from Tipping Bucket (TB) gauge measurements. Methodological issues associated with applying the cubic spline to the TB gauge rain rate estimation are closely examined. A simulated TB gauge from a Joss-Waldvogel (JW) disdrometer is employed to evaluate effects of time scales and rain event definitions on errors of the rain rate estimation. The comparison between rain rates measured from the JW disdrometer and those estimated from the simulated TB gauge shows good overall agreement; however, the TB gauge suffers sampling problems, resulting in errors in the rain rate estimation. These errors are very sensitive to the time scale of rain rates. One-minute rain rates suffer substantial errors, especially at low rain rates. When one minute rain rates are averaged to 4-7 minute or longer time scales, the errors dramatically reduce. The rain event duration is very sensitive to the event definition but the event rain total is rather insensitive, provided that the events with less than 1 millimeter rain totals are excluded. Estimated lower rain rates are sensitive to the event definition whereas the higher rates are not. The median relative absolute errors are about 22% and 32% for 1-minute TB rain rates higher and lower than 3 mm per hour, respectively. These errors decrease to 5% and 14% when TB rain rates are used at 7-minute scale. The radar reflectivity-rainrate (Ze-R) distributions drawn from large amount of 7-minute TB rain rates and radar reflectivity data are mostly insensitive to the event definition.

Wang, Jianxin↗
NASA NTRS2007

Using Remotely-Sensed Estimates of Soil Moisture to Infer Soil Texture and Hydraulic Properties across a Semi-arid Watershed

Near-surface soil moisture is a critical component of land surface energy and water balance studies encompassing a wide range of disciplines. However, the processes of infiltration, runoff, and evapotranspiration in the vadose zone of the soil are not easy to quantify or predict because of the difficulty in accurately representing soil texture and hydraulic properties in land surface models. This study approaches the problem of parameterizing soils from a unique perspective based on components originally developed for operational estimation of soil moisture for mobility assessments. Estimates of near-surface soil moisture derived from passive (L-band) microwave remote sensing were acquired on six dates during the Monsoon '90 experiment in southeastern Arizona, and used to calibrate hydraulic properties in an offline land surface model and infer information on the soil conditions of the region. Specifically, a robust parameter estimation tool (PEST) was used to calibrate the Noah land surface model and run at very high spatial resolution across the Walnut Gulch Experimental Watershed. Errors in simulated versus observed soil moisture were minimized by adjusting the soil texture, which in turn controls the hydraulic properties through the use of pedotransfer functions. By estimating a continuous range of widely applicable soil properties such as sand, silt, and clay percentages rather than applying rigid soil texture classes, lookup tables, or large parameter sets as in previous studies, the physical accuracy and consistency of the resulting soils could then be assessed. In addition, the sensitivity of this calibration method to the number and timing of microwave retrievals is determined in relation to the temporal patterns in precipitation and soil drying. The resultant soil properties were applied to an extended time period demonstrating the improvement in simulated soil moisture over that using default or county-level soil parameters. The methodology is also applied to an independent case at Walnut Gulch using a new soil moisture product from active (C-band) radar imagery with much lower spatial and temporal resolution. Overall, results demonstrate the potential to gain physically meaningful soils information using simple parameter estimation with few but appropriately timed remote sensing retrievals.

Santanello, Joseph A.↗
NASA NTRS2005

Multidecadal Changes in Near-Global Cloud Cover and Estimated Cloud Cover Radiative Forcing

The first paper was Multidecadal changes in near-global cloud cover and estimated cloud cover radiative forcing, by J. R. Norris (2005, J. Geophys. Res. - Atmos., 110, D08206, doi: lO.l029/2004JD005600). This study examined variability in zonal mean surface-observed upper-level (combined midlevel and high-level) and low-level cloud cover over land during 1971-1 996 and over ocean during 1952-1997. These data were averaged from individual synoptic reports in the Extended Edited Cloud Report Archive (EECRA). Although substantial interdecadal variability is present in the time series, long-term decreases in upper-level cloud cover occur over land and ocean at low and middle latitudes in both hemispheres. Near-global upper-level cloud cover declined by 1.5%-sky-cover over land between 1971 and 1996 and by 1.3%-sky-cover over ocean between 1952 and 1997. Consistency between EECRA upper-level cloud cover anomalies and those from the International Satellite Cloud Climatology Project (ISCCP) during 1984-1 997 suggests the surface-observed trends are real. The reduction in surface-observed upper-level cloud cover between the 1980s and 1990s is also consistent with the decadal increase in all-sky outgoing longwave radiation reported by the Earth Radiation Budget Satellite (EMS). Discrepancies occur between time series of EECRA and ISCCP low-level cloud cover due to identified and probable artifacts in satellite and surface cloud data. Radiative effects of surface-observed cloud cover anomalies, called "cloud cover radiative forcing (CCRF) anomalies," are estimated based on a linear relationship to climatological cloud radiative forcing per unit cloud cover. Zonal mean estimated longwave CCRF has decreased over most of the globe. Estimated shortwave CCRF has become slightly stronger over northern midlatitude oceans and slightly weaker over northern midlatitude land areas. A long-term decline in the magnitude of estimated shortwave CCRF occurs over low-latitude land and ocean, but comparison with EMS all-sky reflected shortwave radiation during 1985-1997 suggests this decrease may be underestimated.

Norris, Joel↗
NASA NTRS2007

Real-time Signal-to-noise Ratio (SNR) Estimation for BPSK and QPSK Modulation Using the Active Communications Channel

Method and apparatus for estimating signal-to-noise ratio (SNR) gamma of a composite input signal e(t) on a phase modulated (e.g., BPSK) communications link. A first demodulator receives the composite input signal and a stable carrier signal and outputs an in-phase output signal; a second demodulator receives the composite input signal and a phase-shifted version of the carrier signal and outputs a quadrature-phase output signal; and phase error theta(sub E)(t) contained within the composite input signal e(t) is calculated from the outputs of the first and second demodulators. A time series of statistically independent phase error measurements theta(sub E)(t(sub 1)), theta (sub E)(t(sub 2)),..., theta (sub E)(t(sub k)) is obtained from the composite input signal subtending a time interval delta t = t(sub k) - t(sub 1) whose value is small enough such that gamma(t) and sigma(t) can be taken to be constant in delta t. A biased estimate gamma(sup *) for the signal-to-noise ratio (SNR) gamma if the composite input signal is calculated using maximum likelihood (ML) estimation techniques, and an unbiased estimate gamma(sup ^) for the signal-to-noise ratio (SNR) gamma of the composite input signal is determined from the biased estimate gamma(sup *), such as by use of a look-up table.

Manning, Robert M.↗
NASA NTRS2006

Classes of Split-Plot Response Surface Designs for Equivalent Estimation

When planning an experimental investigation, we are frequently faced with factors that are difficult or time consuming to manipulate, thereby making complete randomization impractical. A split-plot structure differentiates between the experimental units associated with these hard-to-change factors and others that are relatively easy-to-change and provides an efficient strategy that integrates the restrictions imposed by the experimental apparatus. Several industrial and scientific examples are presented to illustrate design considerations encountered in the restricted randomization context. In this paper, we propose classes of split-plot response designs that provide an intuitive and natural extension from the completely randomized context. For these designs, the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. This property provides best linear unbiased estimators and simplifies model estimation. The design conditions that allow for equivalent estimation are presented enabling design construction strategies to transform completely randomized Box-Behnken, equiradial, and small composite designs into a split-plot structure.

Parker, Peter A.↗
NASA NTRS2008

Estimating the Effect of Gypsy Moth Defloiation Using MODIS

The area of North American forests affected by gypsy moth defoliation continues to expand despite efforts to slow the spread. With the increased area of infestation, ecological, environmental and economic concerns about gypsy moth disturbance remain significant, necessitating coordinated, repeatable and comprehensive monitoring of the areas affected. In this study, our primary objective was to estimate the magnitude of defoliation using Moderate Resolution Imaging Spectroradiometer (MODIS) imagery for a gypsy moth outbreak that occurred in the US central Appalachian Mountains in 2000 and 2001. We focused on determining the appropriate spectral MODIS indices and temporal compositing method to best monitor the effects of gypsy moth defoliation. We tested MODIS-based Normalized Difference Vegetation Index (NDVI), Enhanced Vegetation Index (EVI), Normalized Difference Water Index (NDWI), and two versions of the Normalized Difference Infrared index (NDIIb6 and NDIIb7, using the channels centered on 1640 nm and 2130 nm respectively) for their capacity to map defoliation as estimated by ground observations. In addition, we evaluated three temporal resolutions: daily, 8-day and 16-day data. We validated the results through quantitative comparison to Landsat based defoliation estimates and traditional sketch maps. Our MODIS based defoliation estimates based on NDIIb6 and NDIIb7 closely matched Landsat defoliation estimates derived from field data as well as sketch maps. We conclude that daily MODIS data can be used with confidence to monitor insect defoliation on an annual time scale, at least for larger patches (greater than 0.63 km2). Eight-day and 16-day MODIS composites may be of lesser use due to the ephemeral character of disturbance by the gypsy moth.

deBeurs, K. M.↗