Search NASA⌕ Search

SEARCH · Search NASA

Results for “ill-posed problems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Site B - NREL ASSIST (SN11) Thermodynamic Retrievals TROPoe / Derived Data

This dataset contains daily files with thermodynamic profiles retrieved with the optimal estimation physical retrieval TROPoe v0.12 (Turner and Löhnert 2014; Turner and Blumberg 2019; Turner and Löhnert 2021). The profiles are retrieved every 10 minutes from instantaneous observations from the NREL ASSIST-II (SN 11) infrared spectrometer. Observations are noise-filtered but not averaged in time to minimize errors due to non-uniform clouds. Additional input data in TROPoe are cloud base height (CBH), which is a combined data product that uses data from ceilometers at sites A1 and H and scanning lidars from ARM sites C1 and E37. The CBH is weighted inversely proportionally to the distance to the respective site to take into account the spatial variability of clouds (see https://github.com/StefanoWind/ASSIST_analysis/blob/main/awaken_processing/combine_cbh.py). The full pipeline for running the retrieval is available at https://github.com/StefanoWind/TROPoe_processor. Met data was not ingested. In addition to these temporally resolved input data, TROPoe requires an a priori dataset (prior) that provides mean climatological estimates of thermodynamic profiles and specifies how temperature and humidity covary with height as an input (for details see, e.g., Djalalova et al. 2022). The prior is a key component of the retrieval and provides a constraint on the ill-posed inversion problem. A monthly prior was computed from operational radiosonde launches at ARM SGP, OK.

17 WIND ENERGY↗
DOE OSTI2025

Site G - NREL ASSIST (SN10) Thermodynamic Retrievals TROPoe / Derived Data

This dataset contains daily files with thermodynamic profiles retrieved with the optimal estimation physical retrieval TROPoe v0.12 (Turner and Löhnert 2014; Turner and Blumberg 2019; Turner and Löhnert 2021). The profiles are retrieved every 10 minutes from instantaneous observations from the NREL ASSIST-II (SN 10) infrared spectrometer. Observations are noise-filtered but not averaged in time to minimize errors due to non-uniform clouds. Additional input data in TROPoe are cloud base height (CBH), which is a combined data product that uses data from ceilometers at sites A1 and H and scanning lidars from ARM sites C1 and E37. The CBH is weighted inversely proportionally to the distance to the respective site to take into account the spatial variability of clouds (see https://github.com/StefanoWind/ASSIST_analysis/blob/main/awaken_processing/combine_cbh.py). The full pipeline for running the retrieval is available at https://github.com/StefanoWind/TROPoe_processor. Met data was not ingested. In addition to these temporally resolved input data, TROPoe requires an a priori dataset (prior) that provides mean climatological estimates of thermodynamic profiles and specifies how temperature and humidity covary with height as an input (for details see, e.g., Djalalova et al. 2022). The prior is a key component of the retrieval and provides a constraint on the ill-posed inversion problem. A monthly prior was computed from operational radiosonde launches at ARM SGP, OK.

17 WIND ENERGY↗
DOE OSTI2025

Site C1a - NREL ASSIST (SN12) Thermodynamic Retrievals TROPoe / Derived Data

This dataset contains daily files with thermodynamic profiles retrieved with the optimal estimation physical retrieval TROPoe v0.12 (Turner and Löhnert 2014; Turner and Blumberg 2019; Turner and Löhnert 2021). The profiles are retrieved every 10 minutes from instantaneous observations from the NREL ASSIST-II (SN 12) infrared spectrometer. Observations are noise-filtered but not averaged in time to minimize errors due to non-uniform clouds. Additional input data in TROPoe are cloud base height (CBH), which is a combined data product that uses data from ceilometers at sites A1 and H and scanning lidars from ARM sites C1 and E37. The CBH is weighted inversely proportionally to the distance to the respective site to take into account the spatial variability of clouds (see https://github.com/StefanoWind/ASSIST_analysis/blob/main/awaken_processing/combine_cbh.py). The full pipeline for running the retrieval is available at https://github.com/StefanoWind/TROPoe_processor. Met data was not ingested. In addition to these temporally resolved input data, TROPoe requires an a priori dataset (prior) that provides mean climatological estimates of thermodynamic profiles and specifies how temperature and humidity covary with height as an input (for details see, e.g., Djalalova et al. 2022). The prior is a key component of the retrieval and provides a constraint on the ill-posed inversion problem. A monthly prior was computed from operational radiosonde launches at ARM SGP, OK.

17 WIND ENERGY↗
DOE OSTI2025

Rhode Island Site - NREL ASSIST Thermodynamic Retrievals TROPoe v0.19 / Derived Data

This dataset contains daily files with thermodynamic profiles retrieved with the optimal estimation physical retrieval TROPoe v0.19 (Turner and Löhnert, 2014; Turner and Blumberg, 2019; Turner and Löhnert, 2021). The profiles are retrieved every 10 minutes from instantaneous observations from the NREL ASSIST-II (SN 12) infrared spectrometer. Observations are noise-filtered but not averaged in time to minimize errors due to non-uniform clouds. Additional input data in TROPoe are cloud base height from the collocated NREL upgraded Galion lidar (Newsom et al., 2019), and surface temperature, relative humidity, and pressure from the collocated PNNL met tower. The full pipeline to run the retrieval is available at https://github.com/StefanoWind/TROPoe_processor. In addition to these temporally resolved input data, TROPoe requires an a priori dataset (prior) that provides mean climatological estimates of thermodynamic profiles and specifies how temperature and humidity covary with height as an input (for details see, e.g., Djalalova et al., 2022). The prior is a key component of the retrieval and provides a constraint on the ill-posed inversion problem. A monthly prior was computed from operational radiosonde launches at Upton, NY.

17 WIND ENERGY↗
DOE OSTI2026

BLOC Site - ASSIST Thermodynamic Retrievals TROPoe v0.18 / Derived Data

This dataset contains daily files with thermodynamic profiles retrieved with the optimal estimation physical retrieval TROPoe (Turner and Löhnert 2014; Turner and Blumberg 2019; Turner and Löhnert 2021). This is a post-processed dataset and recommended for use. The profiles are retrieved every 10 minutes from instantaneous radiances observed with an Atmospheric Sounder Spectrometer by Infrared Spectral Technology (ASSIST, Michaud-Belleau et al. 2025) operated by NOAA Physical Sciences Laboratory (PSL) on Block Island for WFIP3. The spectral bands used in the retrieval are in the wavenumber range from 612 - 905.4 cm-1 and are specified in Turner and Löhnert (2021). Additional input data in TROPoe are cloud base height from a collocated ceilometer operated by NOAA GML and temperature, water vapor mixing ratio, and pressure from a collocated surface tower operated by NOAA PSL. In addition to these temporally resolved input data, TROPoe requires an a priori dataset (prior) that provides mean climatological estimates of thermodynamic profiles and specifies how temperature and humidity covary with height as an input (for details see, e.g., Djalalova et al. 2022). The prior is a key component of the retrieval and provides a constraint on the ill-posed inversion problem. A monthly prior was computed from operational radiosonde launches at Upton, NY. The TROPoe docker container (version 0.18) is available from Docker Hub at https://hub.docker.com/r/davidturner53/tropoe/tags, and the source code code is available in the GitHub repository https://github.com/OAR-atmospheric-observations/TROPoe.

17 WIND ENERGY↗
DOE OSTI2026

NANT Site - ASSIST Thermodynamic Retrievals TROPoe v0.18 / Derived Data

This dataset contains daily files with thermodynamic profiles retrieved with the optimal estimation physical retrieval TROPoe (Turner and Löhnert 2014; Turner and Blumberg 2019; Turner and Löhnert 2021). This is a post-processed dataset and recommended for use. The profiles are retrieved every 10 minutes from instantaneous radiances observed with an Atmospheric Sounder Spectrometer by Infrared Spectral Technology (ASSIST, Michaud-Belleau et al. 2025) operated by NOAA Physical Sciences Laboratory (PSL) on Nantucket Island for WFIP3. The spectral bands used in the retrieval are in the wavenumber range from 612 - 905.4 cm-1 and are specified in Turner and Löhnert (2021). Additional input data in TROPoe are cloud base height from a collocated ceilometer operated by NOAA GML and temperature, water vapor mixing ratio, and pressure from a collocated surface tower operated by NOAA PSL. In addition to these temporally resolved input data, TROPoe requires an a priori dataset (prior) that provides mean climatological estimates of thermodynamic profiles and specifies how temperature and humidity covary with height as an input (for details see, e.g., Djalalova et al. 2022). The prior is a key component of the retrieval and provides a constraint on the ill-posed inversion problem. A monthly prior was computed from operational radiosonde launches at Upton, NY. The TROPoe docker container (version 0.18) is available from Docker Hub at https://hub.docker.com/r/davidturner53/tropoe/tags, and the source code code is available in the GitHub repository https://github.com/OAR-atmospheric-observations/TROPoe.

17 WIND ENERGY↗
DOE OSTI2026

FC Site 4.0 - NLR Thermodynamic profiler (ASSIST II-11) Thermodynamic Retrievals TROPoe

This dataset contains daily files with thermodynamic profiles retrieved with the optimal estimation physical retrieval TROPoe v0.19 (Turner and Löhnert 2014; Turner and Blumberg 2019; Turner and Löhnert 2021). The profiles are retrieved every 10 minutes from instantaneous observations from the NLR ASSIST II infrared spectrometer. Observations are noise-filtered but not averaged in time to minimize errors due to non-uniform clouds. Additional input data in TROPoe are cloud base height (CBH) from co-located scanning lidar. The full pipeline for running the retrieval is available at https://github.com/StefanoWind/TROPoe_processor. Met data was not ingested. In addition to these temporally resolved input data, TROPoe requires an a priori dataset (prior) that provides mean climatological estimates of thermodynamic profiles and specifies how temperature and humidity covary with height as an input (for details see, e.g., Djalalova et al. 2022). The prior is a key component of the retrieval and provides a constraint on the ill-posed inversion problem. A monthly prior was computed from operational radiosonde launches in Denver, CO.

17 WIND ENERGY↗
DOE OSTI2026

Microwave Radiometer

This dataset contains daily files with thermodynamic profiles retrieved with the optimal estimation physical retrieval TROPoe (Turner and Löhnert 2014; Turner and Blumberg 2019; Turner and Löhnert 2021). The profiles are retrieved every 10 minutes from instantaneous brightness temperature measurements at 35 channels observed with a microwave radiometer MP3000A operated by UND on the Barge for WFIP3. Additional input data in TROPoe are cloud base height from a collocated ceilometer operated by NOAA GML and temperature, water vapor mixing ratio, and pressure from a sensor attached to the MWR housing. In addition to these temporally resolved input data, TROPoe requires an a priori dataset (prior) that provides mean climatological estimates of thermodynamic profiles and specifies how temperature and humidity covary with height as an input (for details see, e.g., Djalalova et al. 2022). The prior is a key component of the retrieval and provides a constraint on the ill-posed inversion problem. A monthly prior was computed from operational radiosonde launches at Upton, NY.

17 WIND ENERGY↗
DOE OSTI2026

NREL ASSIST Rhode Island / Thermodynamic retrievals TROPoe

This dataset contains daily files with thermodynamic profiles retrieved with the optimal estimation physical retrieval TROPoe (Turner and Löhnert 2014; Turner and Blumberg 2019; Turner and Löhnert 2021). The profiles are retrieved every 10 minutes from instantaneous observations from the NREL ASSIST-II (SN 11) infrared spectrometer. Observations are noise-filtered but not averaged in time to minimize errors due to non-uniform clouds. Additional input data in TROPoe are cloud base height from a collocated NREL Upgraded Galion lidar #1212-60 and temperature, RH, and pressure from collocated PNNL met station. The lidar beta is used to estimate the cloud base height through a modified algorithm by Newsom et al., 2019 used at ARM SGP. The full pipeline for running the retrieval is available at https://github.com/StefanoWind/TROPoe_processor. In addition to these temporally resolved input data, TROPoe requires an a priori dataset (prior) which provides mean climatological estimates of thermodynamic profiles and specifies how temperature and humidity covary with height as an input (for details see e.g. Djalalova et al. 2022). The prior is a key component of the retrieval and provides a constraint on the ill-posed inversion problem. A monthly prior was computed from operational radiosonde launches at Upton, NY.

17 WIND ENERGY↗
DOE OSTI2025

Propagating information content: an example with advection

The mathematical algorithm to derive geophysical information from remote sensing observations is called a retrieval. The mathematics of many retrieval problems are ill-posed, and thus a priori information is used to help constrain the derived geophysical variable to realistic values. One quantity of interest, therefore, is the information content of the observation. Perfect information content in the observation would be achieved if the retrieval were able to capture any perturbation in the desired geophysical variable with the proper magnitude. Many new data products can be derived by combining geophysical variables retrieved from multiple different remote sensors. This paper explores, for the first time, how to derive the information content of these derived products. The approach uses traditional error propagation techniques to derive the uncertainty of the derived field twice, both when the observations are used in the retrieval and also when only the a priori information from each remote sensor is propagated. These two uncertainties are then used to provide an estimate of the information content of the derived geophysical variable. This study demonstrates how to propagate the uncertainties from six different instruments to provide the information content for water vapor and temperature advection. A multi-month analysis demonstrates that, in a mean sense, the information content for temperature advection is nearly unity for all heights below 700 m while, the information content for water vapor advection is somewhat more variable but still larger than 0.6 in the convective boundary layer.

Turner, David D. [National Oceanic and Atmospheric↗
NASA NTRS1986

The ill-posed nature of the satellite temperature retrieval problem and the limits of retrievability

The inverse problem of satellite temperature profile retrieval is well known to be ill-posed. This means that not only is a vertical temperature profile solution not unique, but that two solutions can be very different from each other. A set of atmosphere-like, and true atmospheric examples of significantly dissimilar inverse solutions, were sought and found, using an 11-channel simulated HIRS sounding radiometer. Using the Riemann-Lebesgue Lemma for guidance, it is shown that simultaneous, numerical solutions of an atmospheric character may differ by as much as 10 K between 10-1000 mb. However, an empirical search for dissimilar solutions in the natural atmosphere reveals an extremely low probability of finding two significantly different RAOBs which produce radiance measurements whose differences cannot be resolved by the satellite radiometer. The empirical results are used to derive a first estimate of the limits of retrievability, analogous to the limits of predictability derivable from the ill-posed nature of the numerical weather prediction problem.

Thompson, Owen E.↗
NASA NTRS1986

History matching by spline approximation and regularization in single-phase areal reservoirs

An automatic history matching algorithm is developed based on bi-cubic spline approximations of permeability and porosity distributions and on the theory of regularization to estimate permeability or porosity in a single-phase, two-dimensional real reservoir from well pressure data. The regularization feature of the algorithm is used to convert the ill-posed history matching problem into a well-posed problem. The algorithm employs the conjugate gradient method as its core minimization method. A number of numerical experiments are carried out to evaluate the performance of the algorithm. Comparisons with conventional (non-regularized) automatic history matching algorithms indicate the superiority of the new algorithm with respect to the parameter estimates obtained. A quasioptimal regularization parameter is determined without requiring a priori information on the statistical properties of the observations.

Lee, T. Y.↗
NASA NTRS1988

Computing motion using resistive networks

Recent developments in the theory of early vision are described which lead from the formulation of the motion problem as an ill-posed one to its solution by minimizing certain 'cost' functions. These cost or energy functions can be mapped onto simple analog and digital resistive networks. It is shown how the optical flow can be computed by injecting currents into resistive networks and recording the resulting stationary voltage distribution at each node. These networks can be implemented in cMOS VLSI circuits and represent plausible candidates for biological vision systems.

Koch, Christof↗
NASA NTRS1983

PAN AIR modeling studies

PAN AIR is a computer program that predicts subsonic or supersonic linear potential flow about arbitrary configurations. The code's versatility and generality afford numerous possibilities for modeling flow problems. Although this generality provides great flexibility, it also means that studies are required to establish the dos and don'ts of modeling. The purpose of this paper is to describe and evaluate a variety of methods for modeling flows with PAN AIR. The areas discussed are effects of panel density, internal flow modeling, forebody modeling in subsonic flow, propeller slipstream modeling, effect of wake length, wing-tail-wake interaction, effect of trailing-edge paneling on the Kutta condition, well- and ill-posed boundary-value problems, and induced-drag calculations. These nine topics address problems that are of practical interest to the users of PAN AIR.

Towne, M. C.↗
NASA NTRS1979

Calculated global conditions for the unsteady Euler's flow equations

This paper considers the numerical solution of a fluid dynamical system with time-dependent oscillating boundaries. The problem detailed, a compressible and inviscid flow in a one-dimensional pipe with vibrating ends, is examined to develop techniques needed to solve the more complex unsteady flows in turbomachine cascades. The problem is shown to be mathematically ill-posed but by complementing the governing equations with energy conservation, a unique solution is obtained. An artificial damping term is introduced into the governing equations to improve the performance of the time-marching integration.

Kuzo, D. M.↗
NASA NTRS1984

Neutrino tomography - Tevatron mapping versus the neutrino sky

The feasibility of neutrino tomography of the earth's interior is discussed, taking the 80-GeV W-boson mass determined by Arnison (1983) and Banner (1983) into account. The opacity of earth zones is calculated on the basis of the preliminary reference earth model of Dziewonski and Anderson (1981), and the results are presented in tables and graphs. Proposed tomography schemes are evaluated in terms of the well-posedness of the inverse-Radon-transform problems involved, the neutrino generators and detectors required, and practical and economic factors. The ill-posed schemes are shown to be infeasible; the well-posed schemes (using Tevatrons or the neutrino sky as sources) are considered feasible but impractical.

Wilson, T. L.↗
NASA NTRS1984

CREKID: A computer code for transient, gas-phase combustion of kinetics

A new algorithm was developed for fast, automatic integration of chemical kinetic rate equations describing homogeneous, gas-phase combustion at constant pressure. Particular attention is paid to the distinguishing physical and computational characteristics of the induction, heat-release and equilibration regimes. The two-part predictor-corrector algorithm, based on an exponentially-fitted trapezoidal rule, includes filtering of ill-posed initial conditions, automatic selection of Newton-Jacobi or Newton iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm was found to compare favorably with LSODE on two representative test problems drawn from combustion kinetics.

Pratt, D. T.↗
NASA NTRS1986

Fast algorithm for calculating chemical kinetics in turbulent reacting flow

This paper addresses the need for a fast batch chemistry solver to perform the kinetics part of a split operator formulation of turbulent reacting flows, with special attention focused on the solution of the ordinary differential equations governing a homogeneous gas-phase chemical reaction. For this purpose, a two-part predictor-corrector algorithm which incorporates an exponentially fitted trapezoidal method was developed. The algorithm performs filtering of ill-posed initial conditions, automatic step-size selection, and automatic selection of Jacobi-Newton or Newton-Raphson iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm, termed CREK1D (combustion reaction kinetics, one-dimensional), compared favorably with the code LSODE when tested on two representative problems drawn from combustion kinetics, and is faster than LSODE.

Radhakrishnan, K.↗