Sensitivity of the model error parameter specification in weak-constraint four-dimensional variational data assimilation
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Jeremy A. Shaw↗
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Modeling the Errors of a Time Series Algorithm for Retrieving Soil Moisture in the NISAR Mission
The National Aeronautics and Space Administration (NASA) - Indian Space Research Organization (ISRO) Synthetic Aperture Radar (NISAR) mission plan to launch a SAR operating at L- and S-band with a 12-day repeat frequency. A global soil moisture product at 200 m spatial resolution derived from 200 m NISAR radar measurements is currently under development. Although several retrieval algorithms are being investigated, this paper focuses on a “time series ratio” retrieval approach. In order to understand and assess the performance of this algorithm, an error model has been developed and is reported in this paper. The model is applied to examine errors as a function of the instrument characteristics and for a given location. Initial progress in including vegetation effects and in predicting errors as a function of spatial location is also described.
NISAR↗
SWOT Data Assimilation with Correlated Error Reduction: Fitting Model and Error Together
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Sarah T. Gille↗
Structural Error and Identifiability in Mathematical Models
Errors and previously implicit assumptions treated explicitly. Paper discusses errors in mathematical models of physical systems and problem of identifying model from system input and output. Problem approached by explicitly taking account of erroneous choices of model structure. Paper concerned specifically with linear or weakly nonlinear models.
Hadaegh, F. Y.↗
Modeling Measurement Error in Dose-Response Models of Community Annoyance to Low-Noise Supersonic Flight
The primary research goal of the forthcoming NASA Quesst mission community test campaign is to collect representative community response data in support of the development of supersonic overflight noise certification standards. Beginning in 2026, NASA will fly the novel X-59 demonstrator aircraft over select communities in United States in order to demonstrate the possibility of low-noise supersonic flight over land and to collect objective measurements and subjective data on the perceptual experience of this new noise source. It is believed that a regression of a binary perceptual response (‘highly annoyed’ or ‘not’) on estimated noise levels (doses, measured in decibels) will provide a useful dose-response relationship for regulators. However, as these estimated doses will be subject to measurement error, naïve estimators of regression coefficients are inconsistent and slopes may be subject to attenuation bias. In this presentation, I contrast functional modeling of measurement error via simulation extrapolation (SIMEX) with structural Bayesian measurement error models. These methods are applied to available data collected during two NASA risk reduction studies in California in 2011 and Texas in 2018. I’ll conclude noting that in the presence of nonnegligible measurement errors, probabilities of annoyance may be overpredicted for low noise levels and underpredicted for high noise levels, therefore, methods of correcting for measurement error will be necessary to improve the utility of the dose-response relationship for policy-making purposes.
simulation↗
Sensitivity, optimal scaling and minimum roundoff errors in flexible structure models
Traditional modeling notions presume the existence of a truth model that relates the input to the output, without advanced knowledge of the input. This has led to the evolution of education and research approaches (including the available control and robustness theories) that treat the modeling and control design as separate problems. The paper explores the subtleties of this presumption that the modeling and control problems are separable. A detailed study of the nature of modeling errors is useful to gain insight into the limitations of traditional control and identification points of view. Modeling errors need not be small but simply appropriate for control design. Furthermore, the modeling and control design processes are inevitably iterative in nature.
Skelton, Robert E.↗
Accuracy Criterion for Structural Calculations
Simple method of establishing an accuracy criterion based on comparing allowable errors and modeling errors. On basis of comparison, amounts of change required to improve modeling error used in convergence criterion.
Chen, J. C.↗
Obtaining consistent models of helicopter flight-data measurement errors using kinematic-compatibility and state-reconstruction methods
A new method was developed for application of Kalman Filter/Smoothers to post-flight processing of helicopter flight test dynamic measurements. This processing includes checking for kinematic compatibility among the measurements, identification of a measurement error model, and reconstruction of both measured and unmeasured time histories. Emphasis is placed on identification of a parametric measurement error model which is valid for a set of flight test data. This is facilitated through a new method of concatenating several maneuver time histories. The method also includes a model structure determination step which ensures that a physically realistic parameterization has been achieved. Application of the method to a set of BO-105 flight test data is illustrated. The resulting minimally parameterized error model is shown to characterize the measurement errors of the entire data set with very little variation in the parameter values. Reconstructed time histories are shown to have increased bandwidths and signal to noise ratios.
Fletcher, Jay W.↗
Error control in the GCF: An information-theoretic model for error analysis and coding
The structure of data-transmission errors within the Ground Communications Facility is analyzed in order to provide error control (both forward error correction and feedback retransmission) for improved communication. Emphasis is placed on constructing a theoretical model of errors and obtaining from it all the relevant statistics for error control. No specific coding strategy is analyzed, but references to the significance of certain error pattern distributions, as predicted by the model, to error correction are made.
Adeyemi, O.↗
Dominant modes of mechanical systems
To obtain a reduced model of a mechanical system, one can identify the dominant modes and retain those as the reduced model. Two widely used schemes for selection of dominant modes are modal cost analysis (MCA) and balancing, but neither of these methods guarantees that the model error is small, where model error measures the difference between the output of the full model and the output of the reduced model. The authors introduce a set of coordinates called pseudo uncorrelated modal coordinates (PUnc) that can be used in conjunction with component cost analysis to select dominant modes yielding a reduced model with minimum model error. Furthermore, unlike MCA and balancing, the accuracy of the reduced model (the model error) in PUnc coordinates can be evaluated before reduction.
Breida, M.↗
Precision X-band radio Doppler and ranging navigation: Mars Observer interplanetary cruise scenario
This article describes an error covariance analysis based on a Mars Observer mission scenario; the study was performed to establish the navigation performance that can potentially be achieved in a demonstration of precision two-way X-band (8.4-GHz) Doppler and ranging with the Mars Observer spacecraft planned for next year, and to evaluate the sensitivity of the predicted performance to variations in ground system error modeling assumptions. Orbit determination error statistics computed for a 182-day Doppler and ranging data arc predicted Mars approach orbit determination accuracies of about 0.45 micro-rad in an angular sense, using a conservative ground system error model as a baseline. When less-conservative error model assumptions were employed, it was found that orbit determination accuracies of 0.19 to 0.30 micro-rad could be obtained; the level of accuracy of the assumed Mars ephemeris is about 0.11 micro-rad. In comparison, Doppler-only performance with the baseline error model was predicted to be about 1.30 to 1.51 micro-rad, although it was found that when improved station location accuracies and Global Positioning System-based tropospheric calibration accuracies were assumed, accuracies of 0.44 to 0.52 micro-rad were predicted. In the Doppler plus ranging cases, the results were relatively insensitive to variations in ranging system and station delay calibration uncertainties of a few meters and tropospheric zenith delay calibration uncertainties of a few centimeters.
Estefan, J. A.↗
Error Propagation Analysis in the SAE Architecture Analysis and Design Language (AADL) and the EDICT Tool Framework
This report documents the capabilities of the EDICT tools for error modeling and error propagation analysis when operating with models defined in the Architecture Analysis & Design Language (AADL). We discuss our experience using the EDICT error analysis capabilities on a model of the Scalable Processor-Independent Design for Enhanced Reliability (SPIDER) architecture that uses the Reliable Optical Bus (ROBUS). Based on these experiences we draw some initial conclusions about model based design techniques for error modeling and analysis of highly reliable computing architectures.
LaValley, Brian W.↗
Is There an Optimal CO2 Partial Column for Flux Inversions?
The fidelity of flux estimates from an atmospheric inversion depends on the ability of atmospheric transport models to simulate the measured quantity. For species such as CO2, with surface fluxes and a large network of surface measurements, this means correctly simulating the dynamics of the planetary boundary layer (PBL), which is one of the most uncertain aspects of atmospheric transport modeling. In contrast, the simulated total column average mole fraction of CO2 (XCO2) is largely insensitive to simulated PBL dynamics. Therefore, measurements of XCO2 provided by current and future short wave infrared (SWIR) greenhouse gas (GHG) satellites such as GOSAT and the OCO family would seem to be more appropriate to flux inversions, as far as minimizing transport model errors (the "noise") is concerned. Unfortunately, the flux-induced variation of CO2 (the "signal") is the largest within the PBL and smallest in XCO2. Therefore, assimilating XCO2 as opposed to PBL CO2 need not give us the strongest "signal to noise" in flux inversions. Recent work on GOSAT and OCO2 retrievals suggest that SWIR satellite spectra may be used to estimate a lower partial column CO2, which could be assimilated in a flux inversion, instead of XCO2.Here we report on a study to assess whether there is an optimal partial column average CO2, intermediate between PBL CO2 and XCO2, whose assimilation might yield the best signal to noise in flux inversions, where (as before) "signal" is the flux-induced variation and "noise" is the error in transport modeling. We simulate atmospheric CO2 with five different global transport models and a common surface CO2 flux over ten years. We consider the spread across the five models to be a proxy for transport model error (the "noise"), and the common variation of CO2 in all five models to be a proxy for the "signal". We compare these signals and noises at different spatiotemporal scales for different partial column specifications to investigate whether there exists an optimal partial column that has large surface flux-driven variations and yet is relatively insensitive to errors in transport models. Finally, we comment on the feasibility of estimating such a partial column from current and future SWIR GHG satellites in the light of recent work on vertically resolved CO2 from current SWIR GHG satellites.
Basu, Sourish↗
An error bound for a discrete reduced order model of a linear multivariable system
The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an L-infinity bound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.
Al-Saggaf, Ubaid M.↗
Nonlinear and adaptive estimation techniques in reentry
The development and testing of nonlinear and adaptive estimators for reentry (e.g. space shuttle) navigation and model parameter estimation or identification are reported. Of particular interest is the identifcation of vehicle lift and drag characteristics in real time. Several nonlinear filters were developed and simulated. Adaptive filters for the real time identification of vehicle lift and drag characteristics, and unmodelable acceleration, were also developed and tested by simulation. The simulations feature an uncertain system environment with rather arbitrary model errors, thus providing a definitive test of estimator performance. It was found that nonlinear effects are indeed significant in reentry trajectory estimation and a nonlinear filter is demonstrated which successfully tracks through nonlinearities without degrading the information content of the data. Under the same conditions the usual extended Kalman filter diverges and is useless. The J-adaptive filter is shown to successfully track errors in the modeled vehicle lift and drag characteristics. The same filter concept is also shown to track successfully through rather arbitrary model errors, including lift and drag errors, vehicle mass errors, atmospheric density errors, and wind gust errors.
Jazwinski, A. H.↗
Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter: Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics - Pt. 2
A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.
Menard, Richard↗
The Impact of Anisotropic Error Correlation Modelling
Most data assimilation systems assume isotropic forecast error correlations, but results from two dimensional Kalman Filter experiments indicate that the correlations can be far from isotropic. In this paper we use a simple two-dimensional data assimilation system, which analyses trace chemical species such as ozone, to assess different approaches to modelling the error correlations. We compare assimilation results using isotropic correlations with results obtained using different approaches to modelling anisotropic correlations: first, using correlations based on the concentrations of the trace chemicals, and secondly using an advective correlation model. We show that these relatively cheap ways of modelling anisotropic correlations give objectively better results than using isotropic correlations. We discuss the possible extension of these approaches to a full 3-D meteorological data assimilation system.
Swinbank, R.↗
On-line estimation of error covariance parameters for atmospheric data assimilation
A simple scheme is presented for on-line estimation of covariance parameters in statistical data assimilation systems. The scheme is based on a maximum-likelihood approach in which estimates are produced on the basis of a single batch of simultaneous observations. Simple-sample covariance estimation is reasonable as long as the number of available observations exceeds the number of tunable parameters by two or three orders of magnitude. Not much is known at present about model error associated with actual forecast systems. Our scheme can be used to estimate some important statistical model error parameters such as regionally averaged variances or characteristic correlation length scales. The advantage of the single-sample approach is that it does not rely on any assumptions about the temporal behavior of the covariance parameters: time-dependent parameter estimates can be continuously adjusted on the basis of current observations. This is of practical importance since it is likely to be the case that both model error and observation error strongly depend on the actual state of the atmosphere. The single-sample estimation scheme can be incorporated into any four-dimensional statistical data assimilation system that involves explicit calculation of forecast error covariances, including optimal interpolation (OI) and the simplified Kalman filter (SKF). The computational cost of the scheme is high but not prohibitive; on-line estimation of one or two covariance parameters in each analysis box of an operational bozed-OI system is currently feasible. A number of numerical experiments performed with an adaptive SKF and an adaptive version of OI, using a linear two-dimensional shallow-water model and artificially generated model error are described. The performance of the nonadaptive versions of these methods turns out to depend rather strongly on correct specification of model error parameters. These parameters are estimated under a variety of conditions, including uniformly distributed model error and time-dependent model error statistics.
Dee, Dick P.↗