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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Adaptive Error Estimation in Linearized Ocean General Circulation Models

Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large representation error, i.e. the dominance of the mesoscale eddies in the T/P signal, which are not part of the 21 by 1" GCM. Therefore, the impact of the observations on the assimilation is very small even after the adjustment of the error statistics. This work demonstrates that simult&neous estimation of the model and measurement error statistics for data assimilation with global ocean data sets and linearized GCMs is possible. However, the error covariance estimation problem is in general highly underdetermined, much more so than the state estimation problem. In other words there exist a very large number of statistical models that can be made consistent with the available data. Therefore, methods for obtaining quantitative error estimates, powerful though they may be, cannot replace physical insight. Used in the right context, as a tool for guiding the choice of a small number of model error parameters, covariance matching can be a useful addition to the repertory of tools available to oceanographers.

Chechelnitsky, Michael Y.↗
NASA NTRS2013

The Role of Model and Initial Condition Error in Numerical Weather Forecasting Investigated with an Observing System Simulation Experiment

A series of experiments that explore the roles of model and initial condition error in numerical weather prediction are performed using an observing system simulation experiment (OSSE) framework developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASA/GMAO). The use of an OSSE allows the analysis and forecast errors to be explicitly calculated, and different hypothetical observing networks can be tested with ease. In these experiments, both a full global OSSE framework and an 'identical twin' OSSE setup are utilized to compare the behavior of the data assimilation system and evolution of forecast skill with and without model error. The initial condition error is manipulated by varying the distribution and quality of the observing network and the magnitude of observation errors. The results show that model error has a strong impact on both the quality of the analysis field and the evolution of forecast skill, including both systematic and unsystematic model error components. With a realistic observing network, the analysis state retains a significant quantity of error due to systematic model error. If errors of the analysis state are minimized, model error acts to rapidly degrade forecast skill during the first 24-48 hours of forward integration. In the presence of model error, the impact of observation errors on forecast skill is small, but in the absence of model error, observation errors cause a substantial degradation of the skill of medium range forecasts.

Model Error↗
NASA NTRS1992

Error analysis of optical correlators

With the growing interest in using binary phase only filters (BPOF) in optical correlators that are implemented on magnetooptic spatial light modulators, an understanding of the effect of errors in system alignment and optical components is critical in obtaining optimal system performance. We present simulations of optical correlator performance degradation in the presence of eight errors. We break these eight errors into three groups: 1) alignment errors, 2) errors due to a combination of component imperfections and alignment errors, and 3) errors which result solely from non-ideal components. Under the first group, we simulate errors in the distance from the object to the first principle plane of the transform lens, the distance from the second principle plane of the transform lens to the filter plane, and rotational misalignment of the input mask with the filter mask. Next we consider errors which result from a combination of alignment and component imperfections. These include errors in the transform lens, the phase compensation lens, and the inverse Fourier transform lens. Lastly we have the component errors resulting from the choice of spatial light modulator. These include contrast error and phase errors caused by the non-uniform flatness of the masks. The effects of each individual error are discussed, and the result of combining all eight errors under assumptions of reasonable tolerances and system parameters is also presented. Conclusions are drawn as to which tolerances are most critical for optimal system performance.

Ma, Paul W.↗
NASA NTRS2003

Estimation of Model Error Variances During Data Assimilation

Data assimilation is all about understanding the error characteristics of the data and models that are used in the assimilation process. Reliable error estimates are needed to implement observational quality control, bias correction of observations and model fields, and intelligent data selection. Meaningful covariance specifications are obviously required for the analysis as well, since the impact of any single observation strongly depends on the assumed structure of the background errors. Operational atmospheric data assimilation systems still rely primarily on climatological background error covariances. To obtain error estimates that reflect both the character of the flow and the current state of the observing system, it is necessary to solve three problems: (1) how to account for the short-term evolution of errors in the initial conditions; (2) how to estimate the additional component of error caused by model defects; and (3) how to compute the error reduction in the analysis due to observational information. Various approaches are now available that provide approximate solutions to the first and third of these problems. However, the useful accuracy of these solutions very much depends on the size and character of the model errors and the ability to account for them. Model errors represent the real-world forcing of the error evolution in a data assimilation system. Clearly, meaningful model error estimates and/or statistics must be based on information external to the model itself. The most obvious information source is observational, and since the volume of available geophysical data is growing rapidly, there is some hope that a purely statistical approach to model error estimation can be viable. This requires that the observation errors themselves are well understood and quantifiable. We will discuss some of these challenges and present a new sequential scheme for estimating model error variances from observations in the context of an atmospheric data assimilation system.

Dee, Dick↗
DOE OSTI2026

Concatenated dual displacement code for continuous-variable quantum error correction

The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors. However, when the displacement magnitude becomes large, inevitable lattice-crossing errors arise beyond the correctable range of the GKP state. To address this issue, we concatenate the Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Contrary to conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against displacement errors at different scales: The inner GKP layer employs non-Gaussian resources to suppress continuous Gaussian noise and reduce residual variance, while the outer analog Steane code corrects discrete lattice-crossing events that exceed the GKP correctable range. It is precisely this separation of error-mitigation roles that enables CV error correction. In contrast to prior work on concatenating GKP and repetition codes to establish error correction for discrete qubit/qudit encoding, we provide correction in the continuous encoding space. Analytical studies show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors acting on all qumodes by up to 50%, while enabling unbiased correction of lattice-crossing errors with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture still provides Gaussian-error suppression and lattice-crossing correction. Moreover, the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides insight into the design of concatenated CV error-correcting architectures.

quantum error correction↗
NASA NTRS2018

An Accurate Method for Correcting Spectral Convolution Errors in Intercalibration of Broadband and Hyperspectral Sensors

The intercalibration between a broadband and a hyperspectral satellite Earth observation system requires the convolution of the hyperspectral data with the spectral response functions (SRFs) of the corresponding broadband channels. There are two potential issues associated with the convolution procedure. First, the finite resolution of a hyperspectral spectrum, that is, the deviation from the highly accurate line-by-line monochromatic radiances, will contribute to convolution errors. The magnitude of the errors depends on the spectral resolution and the SRF shape of the hyperspectral instrument. This type of the convolution error has not been well recognized, and there is a lack of corresponding discussion in most published papers. Although it is small as compared with the instrument accuracy of existing hyperspectral sounders, the error is deemed to be signicant when it is compared with the stringent calibration requirement imposed by future climate missions like the Climate Absolute Radiance and Refractivity Observatory (CLARREO). Second, some broadband channels are insufficiently covered by the hyperspectral data, causing spectral gaps that lead to convolution errors. Although several methods have been developed to fill the spectral gaps and hence compensate for the second type of convolution error, the correction accuracy may still need improvement especially when a large spectral gap needs to be lled. This paper presents a methodology to accurately quantify and compensate for both types of convolution errors. This methodology utilizes the available hyperspectral information to correct the scene-dependent convolution errors due to either the limited spectral resolution or spectral gaps. We use simulations to characterize the intercalibration errors between the Moderate resolution Imaging Spectroradiometer (MODIS) and current operational infrared sounders. We demonstrate that convolution errors can be effectively removed to meet the highly accurate intersatellite calibration requirement proposed by the Climate Absolute Radiance and Refractivity Observatory. Our methodology is also validated using real satellite data for the intercalibration between Aqua MODIS and Aqua Atmospheric Infrared Sounders (AIRS). Our study demonstrates that the accurate characterization and correction for the convolution errors greatly reduces the scene-dependent and spectrally dependent errors, being critical to the consistency check between Infrared Atmospheric Sounding Interferometer (IASI) and AIRS using the double-difference method. The convolution correction also facilitates the evaluation for other intercalibration errors (e.g., the drift of MODIS SRFs). Our derived SRF shift values from MODIS-AIRS (after convolution error corrections) and from MODIS-IASI intercalibration are consistent with each other. We further extend the methodology to study the calibration of a broadband channel which is either completely or largely uncovered bya hyperspectral measurement.The large spectral gap-filling methodology is validated by demonstrating the accurate prediction of the MODIS radiance of band 29 using the Cross-track Infrared Sounder spectra, with the real IASI spectral data being used as the reference.

Correction Method↗
DOE OSTI2022

Bayesian estimation of cross-section and errors of experiment and calculation for accurate prediction of neutronic characteristics

In some experiments, there might be a correlation of experimental errors such as an error caused by fabrication. The correlation of calculation errors also might exist among analyses of experiments. In the present study, considering these correlations, the cross-section and errors of experiment and calculation are adjusted for the accurate prediction of neutronic characteristics. The adjustment method is derived based on Bayesian theory. The 'a posteriori' distributions of cross-section and errors of experiment and calculation are obtained by the derivation. The case study is performed by using the benchmarks of light-water moderated experiments reported in ICSBEP. The error from fuel rod fabrication and measurement are included in the experiment error, and the error from the simplification of the benchmark model is included in the calculation error. Since these errors have a positive correlation among the benchmarks, the prediction accuracy is expected to be improved by considering these correlations. For the sensitivity analysis of the correlation among benchmarks, the correlation coefficient of experiment error and that of calculation error is assumed from 0.0 to 0.9. The results indicate that the prediction accuracy of the multiplication factor can be improved by increasing the correlation coefficient of experiment error and that of calculation error. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Attribution of Snowpack Errors to Simulated Temperature and Precipitation in E3SMv1 Over the Contiguous United States

Abstract Snow water equivalent (SWE), temperature, and precipitation biases and trends are evaluated in the atmosphere‐land simulations of the Energy Exascale Earth System Model version 1 (E3SMv1) in comparison to the Community Earth System Model version 2 (CESM2) and two other models using the ground measurement‐based University of Arizona (UA) snow product. SWE, temperature, and precipitation biases are highest in magnitude in the Western contiguous United States (CONUS). SWE errors are attributed to temperature and precipitation through multiple linear regressions of normalized errors, the coefficients of which represent the sensitivities to temperature and precipitation errors. SWE errors are more sensitive to temperature errors throughout the CONUS. Model SWE and temperature trends are generally opposite from UA product trends in the Western CONUS. SWE trend errors are also attributed to temperature and precipitation trend errors using multiple linear regressions of normalized trend errors. SWE trend errors are more sensitive to those of precipitation at higher elevations (>1,500 m) in the Western CONUS in these simulations. Thus, the sensitivity to temperature and precipitation differ for SWE errors and its trend errors. Furthermore, the SWE trend errors are more sensitive to temperature and precipitation in the atmosphere‐ocean coupled simulations in which the atmosphere‐land is coupled to an active ocean model. These results suggest that both errors in simulated temperature and precipitation contribute to SWE errors.

Meteorology & Atmospheric Sciences↗
DOE OSTI2022

Numerical error analysis of SOLPS-ITER simulations of EAST

Abstract Plasma edge simulations with codes like SOLPS-ITER are widely employed to interpret fusion experiments. However, numerical errors appearing in such simulations are rarely investigated, despite their potential large impact on simulation results. These errors consist of the statistical error and the bias, both resulting from the finite number of employed EIRENE Monte Carlo particles and incomplete convergence, and the discretization error due to the finite resolution of the computational grids. In this contribution, the resulting numerical errors on simulations of pure deuterium and neon seeded H-mode EAST discharges are examined. The statistical error can be kept small compared to other numerical error contributions by averaging the plasma profiles. This allows investigating the bias and discretization errors using Richardson extrapolation. It is shown that grid refinement and the number of employed Monte Carlo particles have the largest influence on the result, in agreement with similar studies of an ITER deuterium case. For the first time, numerical error bars on the entire simulated target profiles are determined showing that the largest numerical error is 17.9%, mainly due to the plasma grid discretization. On top, also numerical errors on simulated neutral pressures are investigated in detail, for which the statistical error is dominant. The analysis demonstrates which setup is needed to keep numerical errors limited: the SOLPS-ITER averaging procedure should be employed including enough EIRENE particles, and the involved grids should be sufficiently refined to reduce discretization errors.

Boeyaert, Dieter (ORCID:0000000309208660)↗
DOE OSTI2024

Characterizing non-Markovian and coherent errors in quantum simulation

Quantum simulation of many-body systems, particularly using ultracold atoms and trapped ions, presents a unique form of quantum control—it is a direct implementation of a multi-qubit gate generated by the Hamiltonian. As a consequence, it also faces a unique challenge in terms of benchmarking, because the well-established gate benchmarking techniques are unsuitable for this form of quantum control. Here we show that the symmetries of the target many-body Hamiltonian can be used not only to benchmark but to characterize experimental errors in the quantum simulation. We use our results to develop protocols to characterize these errors, which can be implemented using state-of-the-art technology. We consider two forms of errors: (i) unitary errors arising out of systematic errors in the applied Hamiltonian and (ii) canonical non-Markovian errors arising out of random shot-to-shot fluctuations in the applied Hamiltonian. We show that the dynamics of the expectation value of the target Hamiltonian itself, which is ideally constant in time, can be used to characterize these errors. In the presence of errors, the expectation value of the target Hamiltonian shows a characteristic thermalization dynamics, when it satisfies the operator thermalization hypothesis (OTH). That is, an oscillation in the short time followed by relaxation to a steady-state value in the long time limit. We show that while the steady-state value can be used to characterize the coherent errors, the amplitude of the oscillations can be used to estimate the non-Markovian errors. We prove a sandwich theorem to establish a linear relation between the amplitude of the oscillations and the magnitude of the non-Markovian errors. Moreover, by varying the initial state, we show that the steady state values can be used to completely construct the generator of the coherent errors. Using these results, we develop two experimental protocols to characterize the unitary errors based on these results, one of which requires single-qubit addressing and the other one doesn't. We also develop a protocol to characterize non-Markovian errors. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Measurements and Model Improvement: Insight into NWP Model Error Using Doppler Lidar and Other WFIP2 Measurement Systems

Abstract Doppler-lidar wind-profile measurements at three sites were used to evaluate NWP model errors from two versions of NOAA’s 3-km-grid HRRR model, to see whether updates in the latest version 4 reduced errors when compared against the original version 1. Nested (750-m grid) versions of each were also tested to see how grid spacing affected forecast skill. The measurements were part of the field phase of the Second Wind Forecasting Improvement Project (WFIP2), an 18-month deployment into central Oregon–Washington, a major wind-energy-producing region. This study focuses on errors in simulating marine intrusions, a summertime, 600–800-m-deep, regional sea-breeze flow found to generate large errors. HRRR errors proved to be complex and site dependent. The most prominent error resulted from a premature drop in modeled marine-intrusion wind speeds after local midnight, when lidar-measured winds of greater than 8 m s −1 persisted through the next morning. These large negative errors were offset at low levels by positive errors due to excessive mixing, complicating the interpretation of model “improvement,” such that the updates to the full-scale versions produced mixed results, sometimes enhancing but sometimes degrading model skill. Nesting consistently improved model performance, with version 1’s nest producing the smallest errors overall. HRRR’s ability to represent the stages of sea-breeze forcing was evaluated using radiation budget, surface-energy balance, and near-surface temperature measurements available during WFIP2. The significant site-to-site differences in model error and the complex nature of these errors mean that field-measurement campaigns having dense arrays of profiling sensors are necessary to properly diagnose and characterize model errors, as part of a systematic approach to NWP model improvement. Significance Statement Dramatic increases in NWP model skill will be required over the coming decades. This paper describes the role of major deployments of accurate profiling sensors in achieving that goal and presents an example from the Second Wind Forecast Improvement Program (WFIP2). Wind-profile data from scanning Doppler lidars were used to evaluate two versions of HRRR, the original and an updated version, and nested versions of each. This study focuses on the ability of updated HRRR versions to improve upon predicting a regional sea-breeze flow, which was found to generate large errors by the original HRRR. Updates to the full-scale HRRR versions produced mixed results, but the finer-mesh versions consistently reduced model errors.

Meteorology & Atmospheric Sciences↗
NASA NTRS1994

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON altimetry

In order to facilitate the use of satellite-derived sea surface topography and velocity oceanographic models, methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from the TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10-day period is found tio be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm root mean square (RMS). This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east-west and north-south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions. For both variables the largest errors caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data.

Tsaoussi, Lucia S.↗
NASA NTRS2011

Determination of Barometric Altimeter Errors for the Orion Exploration Flight Test-1 Entry

The EFT-1 mission is the unmanned flight test for the upcoming Multi-Purpose Crew Vehicle (MPCV). During entry, the EFT-1 vehicle will trigger several Landing and Recovery System (LRS) events, such as parachute deployment, based on onboard altitude information. The primary altitude source is the filtered navigation solution updated with GPS measurement data. The vehicle also has three barometric altimeters that will be used to measure atmospheric pressure during entry. In the event that GPS data is not available during entry, the altitude derived from the barometric altimeter pressure will be used to trigger chute deployment for the drogues and main parachutes. Therefore it is important to understand the impact of error sources on the pressure measured by the barometric altimeters and on the altitude derived from that pressure. There are four primary error sources impacting the sensed pressure: sensor errors, Analog to Digital conversion errors, aerodynamic errors, and atmosphere modeling errors. This last error source is induced by the conversion from pressure to altitude in the vehicle flight software, which requires an atmosphere model such as the US Standard 1976 Atmosphere model. There are several secondary error sources as well, such as waves, tides, and latencies in data transmission. Typically, for error budget calculations it is assumed that all error sources are independent, normally distributed variables. Thus, the initial approach to developing the EFT-1 barometric altimeter altitude error budget was to create an itemized error budget under these assumptions. This budget was to be verified by simulation using high fidelity models of the vehicle hardware and software. The simulation barometric altimeter model includes hardware error sources and a data-driven model of the aerodynamic errors expected to impact the pressure in the midbay compartment in which the sensors are located. The aerodynamic model includes the pressure difference between the midbay compartment and the free stream pressure as a function of altitude, oscillations in sensed pressure due to wake effects, and an acoustics model capturing fluctuations in pressure due to motion of the passive vents separating the barometric altimeters from the outside of the vehicle.

Brown, Denise L.↗
DOE OSTI2022

Analytic error analysis of cross section interpolation methods in nodal diffusion codes - II: Numerical results

This paper is the second part of a two-part paper that documents the numerical results for the partial derivatives model presented in part I. In this paper, we derive the error bounds for the analytical point-wise error expression and verify our bounds with numerical experiments. The point-wise error expressions make available, and bound, the sources that contribute to the total error of the interpolated cross section in terms of the Lagrange interpolation errors and the model form error. MPACT is used to generate two-group homogenized cross sections for Westinghouse's AP1000 Region 4 lattice to evaluate the accuracy of the bounds. Error bounds calculated over a grid are compared to numerical data for uni-variate and multi-variate interpolation. The point-wise error bounds of a typical case matrix - two branches in each state variable - are displayed for bi-variate interpolation in the state variables: moderator density, fuel temperature, and boron concentration. The error bounds are shown to be highly accurate compared to numerical results, and in accordance with the underlying physics. We then discuss and show how the sources of error contribute to the total error, and consider the improvement of each error source. Finally, we mention future work such as propagating our cross section error bounds through a reactivity calculation. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1985

An experimental evaluation of error seeding as a program validation technique

A previously reported experiment in error seeding as a program validation technique is summarized. The experiment was designed to test the validity of three assumptions on which the alleged effectiveness of error seeding is based. Errors were seeded into 17 functionally identical but independently programmed Pascal programs in such a way as to produce 408 programs, each with one seeded error. Using mean time to failure as a metric, results indicated that it is possible to generate seeded errors that are arbitrarily but not equally difficult to locate. Examination of indigenous errors demonstrated that these are also arbitrarily difficult to locate. These two results support the assumption that seeded and indigenous errors are approximately equally difficult to locate. However, the assumption that, for each type of error, all errors are equally difficult to locate was not borne out. Finally, since a seeded error occasionally corrected an indigenous error, the assumption that errors do not interfere with each other was proven wrong. Error seeding can be made useful by taking these results into account in modifying the underlying model.

Knight, J. C.↗
NASA NTRS2000

Global Warming Estimation from MSU: Correction for Drift and Calibration Errors

Microwave Sounding Unit (MSU) radiometer observations in Ch 2 (53.74 GHz), made in the nadir direction from sequential, sun-synchronous, polar-orbiting NOAA morning satellites (NOAA 6, 10 and 12 that have approximately 7am/7pm orbital geometry) and. afternoon satellites (NOAA 7, 9, 11 and 14 that have approximately 2am/2pm orbital geometry) are analyzed in this study to derive global temperature trend from 1980 to 1998. In order to remove the discontinuities between the data of the successive satellites and to get a continuous time series, first we have used shortest possible time record of each satellite. In this way we get a preliminary estimate of the global temperature trend of 0.21 K/decade. However, this estimate is affected by systematic time-dependent errors. One such error is the instrument calibration error eo. This error can be inferred whenever there are overlapping measurements made by two satellites over an extended period of time. From the available successive satellite data we have taken the longest possible time record of each satellite to form the time series during the period 1980 to 1998 to this error eo. We find eo can decrease the global temperature trend by approximately 0.07 K/decade. In addition there are systematic time dependent errors ed and ec present in the data that are introduced by the drift in the satellite orbital geometry. ed arises from the diurnal cycle in temperature and ec is the drift related change in the calibration of the MSU. In order to analyze the nature of these drift related errors the multi-satellite Ch 2 data set is partitioned into am and pm subsets to create two independent time series. The error ed can be assessed in the am and pm data of Ch 2 on land and can be eliminated. Observation made in the MSU Ch 1 (50.3 GHz) support this approach. The error ec is obvious only in the difference between the pm and am observations of Ch 2 over the ocean. We have followed two different paths to assess the impact of the error ec on the global temperature trend. In one path the entire error ec is placed in the am data while in the other it is placed in the pm data. Global temperature trend is increased or decreased by approximately 0.03 K/decade depending upon this placement. Taking into account all random errors and systematic errors our analysis of MSU observations leads us to conclude that a conservative estimate of the global warming is 0. 11 (+/-) 0.04 K/decade during 1980 to 1998.

Prabhakara, C.↗
NASA NTRS2000

Global Warming Estimation from MSU: Correction for Drift and Calibration Errors

Microwave Sounding Unit (MSU) radiometer observations in Ch 2 (53.74 GHz), made in the nadir direction from sequential, sun-synchronous, polar-orbiting NOAA morning satellites (NOAA 6, 10 and 12 that have about 7am/7pm orbital geometry) and afternoon satellites (NOAA 7, 9, 11 and 14 that have about 2am/2pm orbital geometry) are analyzed in this study to derive global temperature trend from 1980 to 1998. In order to remove the discontinuities between the data of the successive satellites and to get a continuous time series, first we have used shortest possible time record of each satellite. In this way we get a preliminary estimate of the global temperature trend of 0.21 K/decade. However, this estimate is affected by systematic time-dependent errors. One such error is the instrument calibration error. This error can be inferred whenever there are overlapping measurements made by two satellites over an extended period of time. From the available successive satellite data we have taken the longest possible time record of each satellite to form the time series during the period 1980 to 1998 to this error. We find we can decrease the global temperature trend by about 0.07 K/decade. In addition there are systematic time dependent errors present in the data that are introduced by the drift in the satellite orbital geometry arises from the diurnal cycle in temperature which is the drift related change in the calibration of the MSU. In order to analyze the nature of these drift related errors the multi-satellite Ch 2 data set is partitioned into am and pm subsets to create two independent time series. The error can be assessed in the am and pm data of Ch 2 on land and can be eliminated. Observations made in the MSU Ch 1 (50.3 GHz) support this approach. The error is obvious only in the difference between the pm and am observations of Ch 2 over the ocean. We have followed two different paths to assess the impact of the errors on the global temperature trend. In one path the entire error is placed in the am data while in the other it is placed in the pm data. Global temperature trend is increased or decreased by about 0.03 K/decade depending upon this placement. Taking into account all random errors and systematic errors our analysis of MSU observations leads us to conclude that a conservative estimate of the global warming is 0. 11 (+-) 0.04 K/decade during 1980 to 1998.

Prabhakara, C.↗
NASA NTRS2011

Relative Effects of Trajectory Prediction Errors on the AAC Autoresolver

Trajectory prediction is fundamental to automated separation assurance. Every missed alert, false alert and loss of separation can be traced to one or more errors in trajectory prediction. These errors are a product of many different sources including wind prediction errors, inferred pilot intent errors, surveillance errors, navigation errors and aircraft weight estimation errors. This study analyzes the impact of six different types of errors on the performance of an automated separation assurance system composed of a geometric conflict detection algorithm and the Advanced Airspace Concept Autoresolver resolution algorithm. Results show that, of the error sources considered in this study, top-of-descent errors were the leading contributor to missed alerts and failed resolution maneuvers. Descent-speed errors were another significant contributor, as were cruise-speed errors in certain situations. The results further suggest that increasing horizontal detection and resolution standards are not effective strategies for mitigating these types of error sources.

Lauderdale, Todd↗