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Multi-Scale Hydrometeorological Modeling, Land Data Assimilation and Parameter Estimation with the Land Information System

The Land Information System (LIS; http://lis.gsfc.nasa.gov; Kumar et al., 2006; Peters- Lidard et al.,2007) is a flexible land surface modeling framework that has been developed with the goal of integrating satellite- and ground-based observational data products and advanced land surface modeling techniques to produce optimal fields of land surface states and fluxes. As such, LIS represents a step towards the next generation land component of an integrated Earth system model. In recognition of LIS object-oriented software design, use and impact in the land surface and hydrometeorological modeling community, the LIS software was selected ase co-winner of NASA's 2005 Software of the Year award. LIS facilitates the integration of observations from Earth-observing systems and predictions and forecasts from Earth System and Earth science models into the decision-making processes of partnering agency and national organizations. Due to its flexible software design, LIS can serve both as a Problem Solving Environment (PSE) for hydrologic research to enable accurate global water and energy cycle predictions, and as a Decision Support System (DSS) to generate useful information for application areas including disaster management, water resources management, agricultural management, numerical weather prediction, air quality and military mobility assessment. LIS has evolved from two earlier efforts North American Land Data Assimilation System (NLDAS; Mitchell et al. 2004) and Global Land Data Assimilation System (GLDAS; Rodell al. 2004) that focused primarily on improving numerical weather prediction skills by improving the characterization of the land surface conditions. Both of GLDAS and NLDAS now use specific configurations of the LIS software in their current implementations. In addition, LIS was recently transitioned into operations at the US Air Force Weather Agency (AFWA) to ultimately replace their Agricultural Meteorology (AGRMET) system, and is also used routinely by NOAA's National Centers for Environmental Prediction (NCEP)/Environmental Modeling Center (EMC) for their land data assimilation systems to support weather and climate modeling. LIS not only consolidates the capabilities of these two systems, but also enables a much larger variety of configurations with respect to horizontal spatial resolution, input datasets and choice of land surface model through "plugins,". As described in Kumar et al., 2007, and demonstrated in Case et al., 2008, and Santanello et al., 2009, LIS has been coupled to the Weather Research and Forecasting (WRF) model to support studies of land-atmosphere coupling the enabling ensembles of land surface states to be tested against multiple representations of the atmospheric boundary layer. LIS has also been demonstrated for parameter estimation as described in Peters-Lidard et al. (2008) and Santanello et al. (2007), who showed that the use of sequential remotely sensed soil moisture products can be used to derive soil hydraulic and texture properties given a sufficient dynamic range in the soil moisture retrievals and accurate precipitation inputs. LIS has also recently been demonstrated for multi-model data assimilation (Kumar et al., 2008) using an Ensemble Kalman Filter for sequential assimilation of soil moisture, snow, and temperature. Ongoing work has demonstrated the value of bias correction as part of the filter, and also that of joint calibration and assimilation. Examples and case studies demonstrating the capabilities and impacts of LIS for hydrometeoroogical modeling, assimilation and parameter estimation will be presented as advancements towards the next generation of integrated observation and modeling systems.

Peters-Lidard, Christa D.

Parameter estimation for the Euler-Bernoulli-beam

An approximation involving cubic spline functions for parameter estimation problems in the Euler-Bernoulli-beam equation (phrased as an optimization problem with respect to the parameters) is described and convergence is proved. The resulting algorithm was implemented and several of the test examples are documented. It is observed that the use of penalty terms in the cost functional can improve the rate of convergence.

Graif, E.

Thermal Property Parameter Estimation of TPS Materials

Accurate knowledge of the thermophysical properties of TPS (thermal protection system) materials is necessary for pre-flight design and post-flight data analysis. Thermal properties, such as thermal conductivity and the volumetric specific heat, can be estimated from transient temperature measurements using non-linear parameter estimation methods. Property values are derived by minimizing a functional of the differences between measured and calculated temperatures. High temperature thermal response testing of TPS materials is usually done in arc-jet or radiant heating facilities which provide a quasi one-dimensional heating environment. Last year, under the NASA-ASEE-Stanford Fellowship Program, my work focused on developing a radiant heating apparatus. This year, I have worked on increasing the fidelity of the experimental measurements, optimizing the experimental procedures and interpreting the data.

Maddren, Jesse

Characterization, parameter estimation, and aircraft response statistics of atmospheric turbulence

A nonGaussian three component model of atmospheric turbulence is postulated that accounts for readily observable features of turbulence velocity records, their autocorrelation functions, and their spectra. Methods for computing probability density functions and mean exceedance rates of a generic aircraft response variable are developed using nonGaussian turbulence characterizations readily extracted from velocity recordings. A maximum likelihood method is developed for optimal estimation of the integral scale and intensity of records possessing von Karman transverse of longitudinal spectra. Formulas for the variances of such parameter estimates are developed. The maximum likelihood and least-square approaches are combined to yield a method for estimating the autocorrelation function parameters of a two component model for turbulence.

Mark, W. D.

The Accuracy of Parameter Estimation in System Identification of Noisy Aircraft Load Measurement

This thesis focuses on the subject of the accuracy of parameter estimation and system identification techniques. Motivated by a complicated load measurement from NASA Dryden Flight Research Center, advanced system identification techniques are needed. The objective of this problem is to accurately predict the load experienced by the aircraft wing structure during flight determined from a set of calibrated load and gage response relationship. We can then model the problem as a black box input-output system identification from which the system parameter has to be estimated. Traditional LS (Least Square) techniques and the issues of noisy data and model accuracy are addressed. A statistical bound reflecting the change in residual is derived in order to understand the effects of the perturbations on the data. Due to the intrinsic nature of the LS problem, LS solution faces the dilemma of the trade off between model accuracy and noise sensitivity. A method of conflicting performance indices is presented, thus allowing us to improve the noise sensitivity while at the same time configuring the degredation of the model accuracy. SVD techniques for data reduction are studied and the equivalence of the Correspondence Analysis (CA) and Total Least Squares Criteria are proved. We also looked at nonlinear LS problems with NASA F-111 data set as an example. Conventional methods are neither easily applicable nor suitable for the specific load problem since the exact model of the system is unknown. Neural Network (NN) does not require prior information on the model of the system. This robustness motivated us to apply the NN techniques on our load problem. Simulation results for the NN methods used in both the single load and the 'warning signal' problems are both useful and encouraging. The performance of the NN (for single load estimate) is better than the LS approach, whereas no conventional approach was tried for the 'warning signals' problems. The NN design methodology is also presented. The use of SVD, CA and Collinearity Index methods are used to reduce the number of neurons in a layer.

Kong, Jeffrey

Parameter estimation supplement to the Mission Analysis Evaluation and Space Trajectory Operations program (MAESTRO)

This Parameter Estimation Supplement describes the PEST computer program and gives instructions for its use in determination of lunar gravitation field coefficients. PEST was developed for use in the RAE-B lunar orbiting mission as a means of lunar field recovery. The observations processed by PEST are short-arc osculating orbital elements. These observations are the end product of an orbit determination process obtained with another program. PEST's end product it a set of harmonic coefficients to be used in long-term prediction of the lunar orbit. PEST employs some novel techniques in its estimation process, notably a square batch estimator and linear variational equations in the orbital elements (both osculating and mean) for measurement sensitivities. The program's capabilities are described, and operating instructions and input/output examples are given. PEST utilizes MAESTRO routines for its trajectory propagation. PEST's program structure and subroutines which are not common to MAESTRO are described. Some of the theoretical background information for the estimation process, and a derivation of linear variational equations for the Method 7 elements are included.

Bjorkman, W. S.

Formulation and implementation of a practical algorithm for parameter estimation with process and measurement noise

A new formulation is proposed for the problem of parameter estimation of dynamic systems with both process and measurement noise. The formulation gives estimates that are maximum likelihood asymptotically in time. The means used to overcome the difficulties encountered by previous formulations are discussed. It is then shown how the proposed formulation can be efficiently implemented in a computer program. A computer program using the proposed formulation is available in a form suitable for routine application. Examples with simulated and real data are given to illustrate that the program works well.

Maine, R. E.

Formulation of a practical algorithm for parameter estimation with process and measurement noise

A new formulation is proposed for the problem of parameter estimation in dynamic systems with both process and measurement noise. The formulation applies to continuous-time state space system models with discrete-time measurements. Previous formulations of this problem encountered several theoretical and practical difficulties which are overcome by the new formulation. The most important element of the new formulation is a reparameterization of the unknown noise covariances. A computer program that implements the new formulation is available.

Maine, R. E.

Single-tone parameter estimation from discrete-time observations

Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramer-Rao bounds and maximum-likelihood (ML) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practial algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.

Rife, D. C.

Use of Dual-wavelength Radar for Snow Parameter Estimates

Use of dual-wavelength radar, with properly chosen wavelengths, will significantly lessen the ambiguities in the retrieval of microphysical properties of hydrometeors. In this paper, a dual-wavelength algorithm is described to estimate the characteristic parameters of the snow size distributions. An analysis of the computational results, made at X and Ka bands (T-39 airborne radar) and at S and X bands (CP-2 ground-based radar), indicates that valid estimates of the median volume diameter of snow particles, D(sub 0), should be possible if one of the two wavelengths of the radar operates in the non-Rayleigh scattering region. However, the accuracy may be affected to some extent if the shape factors of the Gamma function used for describing the particle distribution are chosen far from the true values or if cloud water attenuation is significant. To examine the validity and accuracy of the dual-wavelength radar algorithms, the algorithms are applied to the data taken from the Convective and Precipitation-Electrification Experiment (CaPE) in 1991, in which the dual-wavelength airborne radar was coordinated with in situ aircraft particle observations and ground-based radar measurements. Having carefully co-registered the data obtained from the different platforms, the airborne radar-derived size distributions are then compared with the in-situ measurements and ground-based radar. Good agreement is found for these comparisons despite the uncertainties resulting from mismatches of the sample volumes among the different sensors as well as spatial and temporal offsets.

Liao, Liang

Earth-moon system: Dynamics and parameter estimation; numerical considerations and program documentation

Major activities included coding and verifying equations of motion for the earth-moon system. Some attention was also given to numerical integration methods and parameter estimation methods. Existing analytical theories such as Brown's lunar theory, Eckhardt's theory for lunar rotation, and Newcomb's theory for the rotation of the earth were coded and verified. These theories serve as checks for the numerical integration. Laser ranging data for the period January 1969 - December 1975 was collected and stored on tape. The main goal of this research is the development of software to enable physical parameters of the earth-moon system to be estimated making use of data available from the Lunar Laser Ranging Experiment and the Very Long Base Interferometry experiment of project Apollo. A more specific goal is to develop software for the estimation of certain physical parameters of the moon such as inertia ratios, and the third and fourth harmonic gravity coefficients.

Breedlove, W. J., Jr.

Observation model and parameter partials for the JPL VLBI parameter estimation software MODEST, 19 94

This report is a revision of the document Observation Model and Parameter Partials for the JPL VLBI Parameter Estimation Software 'MODEST'---1991, dated August 1, 1991. It supersedes that document and its four previous versions (1983, 1985, 1986, and 1987). A number of aspects of the very long baseline interferometry (VLBI) model were improved from 1991 to 1994. Treatment of tidal effects is extended to model the effects of ocean tides on universal time and polar motion (UTPM), including a default model for nearly diurnal and semidiurnal ocean tidal UTPM variations, and partial derivatives for all (solid and ocean) tidal UTPM amplitudes. The time-honored 'K(sub 1) correction' for solid earth tides has been extended to include analogous frequency-dependent response of five tidal components. Partials of ocean loading amplitudes are now supplied. The Zhu-Mathews-Oceans-Anisotropy (ZMOA) 1990-2 and Kinoshita-Souchay models of nutation are now two of the modeling choices to replace the increasingly inadequate 1980 International Astronomical Union (IAU) nutation series. A rudimentary model of antenna thermal expansion is provided. Two more troposphere mapping functions have been added to the repertoire. Finally, corrections among VLBI observations via the model of Treuhaft and lanyi improve modeling of the dynamic troposphere. A number of minor misprints in Rev. 4 have been corrected.

Sovers, O. J.

Application of Model Based Parameter Estimation for RCS Frequency Response Calculations Using Method of Moments

An implementation of the Model Based Parameter Estimation (MBPE) technique is presented for obtaining the frequency response of the Radar Cross Section (RCS) of arbitrarily shaped, three-dimensional perfect electric conductor (PEC) bodies. An Electric Field Integral Equation (EFTE) is solved using the Method of Moments (MoM) to compute the RCS. The electric current is expanded in a rational function and the coefficients of the rational function are obtained using the frequency derivatives of the EFIE. Using the rational function, the electric current on the PEC body is obtained over a frequency band. Using the electric current at different frequencies, RCS of the PEC body is obtained over a wide frequency band. Numerical results for a square plate, a cube, and a sphere are presented over a bandwidth. Good agreement between MBPE and the exact solution over the bandwidth is observed.

Reddy, C. J.

Parameter Estimation of Actuators for Benchmark Active Control Technology (BACT) Wind Tunnel Model with Analysis of Wear and Aerodynamic Loading Effects

This report describes the development of transfer function models for the trailing-edge and upper and lower spoiler actuators of the Benchmark Active Control Technology (BACT) wind tunnel model for application to control system analysis and design. A simple nonlinear least-squares parameter estimation approach is applied to determine transfer function parameters from frequency response data. Unconstrained quasi-Newton minimization of weighted frequency response error was employed to estimate the transfer function parameters. An analysis of the behavior of the actuators over time to assess the effects of wear and aerodynamic load by using the transfer function models is also presented. The frequency responses indicate consistent actuator behavior throughout the wind tunnel test and only slight degradation in effectiveness due to aerodynamic hinge loading. The resulting actuator models have been used in design, analysis, and simulation of controllers for the BACT to successfully suppress flutter over a wide range of conditions.

Waszak, Martin R.

A distributed fault-detection and diagnosis system using on-line parameter estimation

The development of a model-based fault-detection and diagnosis system (FDD) is reviewed. The system can be used as an integral part of an intelligent control system. It determines the faults of a system from comparison of the measurements of the system with a priori information represented by the model of the system. The method of modeling a complex system is described and a description of diagnosis models which include process faults is presented. There are three distinct classes of fault modes covered by the system performance model equation: actuator faults, sensor faults, and performance degradation. A system equation for a complete model that describes all three classes of faults is given. The strategy for detecting the fault and estimating the fault parameters using a distributed on-line parameter identification scheme is presented. A two-step approach is proposed. The first step is composed of a group of hypothesis testing modules, (HTM) in parallel processing to test each class of faults. The second step is the fault diagnosis module which checks all the information obtained from the HTM level, isolates the fault, and determines its magnitude. The proposed FDD system was demonstrated by applying it to detect actuator and sensor faults added to a simulation of the Space Shuttle Main Engine. The simulation results show that the proposed FDD system can adequately detect the faults and estimate their magnitudes.

Guo, T.-H.

Parameter estimation in truss beams using Timoshenko beam model with damping

Truss beams with members having viscous damping are modeled with a Timoshenko beam. Procedures for deriving the equivalent bending rigidity, transverse shear rigidity, and damping are presented. Explicit expressions for these equivalent beam properties are obtained for a specific truss beam. The beam model thus established is then used to investigate the effect of damping in free vibration. Finally, the beam is employed in the estimation of structural parameters in a simply-supported truss beam using a random search algorithm.

Sun, C. T.

An investigation of surface parameter estimation from surface models

In surface scattering problems, scattering models are used to estimate the surface parameters by comparing model predictions to data. The meaning of such a procedure is examined using computer simulated scattering data from statistically known surfaces. Numerically exact scattering computations based on the moment method are conducted, and standard surface scattering models are applied to these simulated data. It is shown that such an approach usually leads to effective surface parameters as opposed to real surface parameters, except for a limited frequency region. It is also shown that if a surface scattering model is valid over all frequencies, then it is possible to recover the real surface parameters regardless of whether the surface is single scale or two scale.

Fung, A. K.