Search NASASearch

SEARCH · Search NASA

Results for “error bars”

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

Stratospheric N2O5, CH4, and N2O Profiles from IR Solar Occultation Spectra

Stratospheric volume mixing ratio profiles of N2O5, CH4, and N2O have been retrieved from a set of 0.052/ cm resolution (FWHM) solar occultation spectra recorded at sunrise during a balloon flight from Aire sur I'Adour, France (44 deg N latitude) on 12 October 1990. The N2O5 results have been derived from measurements of the integrated absorption by the 1246/ cm band. Assuming a total intensity of 4.32 x 10(exp 17)cm(exp -1) molecule sq cm(exp -2) independent of temperature, the retrieved N2O5 volume mixing ratios in ppbv (parts per billion by volume, 10(exp -9)), interpolated to 2 km height spacings, are 1.64 +/- 0.49 at 37.5 km, 1.92 +/- 0.56 at 35.5 km, 2.06 +/- 0.47 at 33.5 km, 1.95 +/- 0.42 at 31.5 km, 1.60 +/- 0.33 at 29.5 km, 1.26 +/- 0.28 at 27.5 km, and 0.85 +/- 0.20 at 25.5 km. Error bars indicate the estimated I-sigma uncertainty including the error in the total band intensity (+/- 20% has been assumed). The retrieved profiles are compared with previous measurements and photochemical model results.

Peyeret, C. Camy

An accurate ab initio quartic force field for ammonia

The quartic force field of ammonia is computed using basis sets of spdf/spd and spdfg/spdf quality and an augmented coupled cluster method. After correcting for Fermi resonance, the computed fundamentals and nu 4 overtones agree on average to better than 3/cm with the experimental ones except for nu 2. The discrepancy for nu 2 is principally due to higher-order anharmonicity effects. The computed omega 1, omega 3, and omega 4 confirm the recent experimental determination by Lehmann and Coy (1988) but are associated with smaller error bars. The discrepancy between the computed and experimental omega 2 is far outside the expected error range, which is also attributed to higher-order anharmonicity effects not accounted for in the experimental determination. Spectroscopic constants are predicted for a number of symmetric and asymmetric top isotopomers of NH3.

Martin, J. M. L.

Hubble Space Telescope secondary mirror vertex radius/conic constant test

The Hubble Space Telescope backup secondary mirror was tested to determine the vertex radius and conic constant. Three completely independent tests (to the same procedure) were performed. Similar measurements in the three tests were highly consistent. The values obtained for the vertex radius and conic constant were the nominal design values within the error bars associated with the tests. Visual examination of the interferometric data did not show any measurable zonal figure error in the secondary mirror.

Parks, Robert

Highlights of TOMS Version 9 Total Ozone Algorithm

The fundamental basis of TOMS total ozone algorithm was developed some 45 years ago by Dave and Mateer. It was designed to estimate total ozone from satellite measurements of the backscattered UV radiances at few discrete wavelengths in the Huggins ozone absorption band (310-340 nm). Over the years, as the need for higher accuracy in measuring total ozone from space has increased, several improvements to the basic algorithms have been made. They include: better correction for the effects of aerosols and clouds, an improved method to account for the variation in shape of ozone profiles with season, latitude, and total ozone, and a multi-wavelength correction for remaining profile shape errors. These improvements have made it possible to retrieve total ozone with just 3 spectral channels of moderate spectral resolution (approx. 1 nm) with accuracy comparable to state-of-the-art spectral fitting algorithms like DOAS that require high spectral resolution measurements at large number of wavelengths. One of the deficiencies of the TOMS algorithm has been that it doesn't provide an error estimate. This is a particular problem in high latitudes when the profile shape errors become significant and vary with latitude, season, total ozone, and instrument viewing geometry. The primary objective of the TOMS V9 algorithm is to account for these effects in estimating the error bars. This is done by a straightforward implementation of the Rodgers optimum estimation method using a priori ozone profiles and their error covariances matrices constructed using Aura MLS and ozonesonde data. The algorithm produces a vertical ozone profile that contains 1-2.5 pieces of information (degrees of freedom of signal) depending upon solar zenith angle (SZA). The profile is integrated to obtain the total column. We provide information that shows the altitude range in which the profile is best determined by the measurements. One can use this information in data assimilation and analysis. A side benefit of this algorithm is that it is considerably simpler than the present algorithm that uses a database of 1512 profiles to retrieve total ozone. These profiles are tedious to construct and modify. Though conceptually similar to the SBUV V8 algorithm that was developed about a decade ago, the SBUV and TOMS V9 algorithms differ in detail. The TOMS algorithm uses 3 wavelengths to retrieve the profile while the SBUV algorithm uses 6-9 wavelengths, so TOMS provides less profile information. However both algorithms have comparable total ozone information and TOMS V9 can be easily adapted to use additional wavelengths from instruments like GOME, OMI and OMPS to provide better profile information at smaller SZAs. The other significant difference between the two algorithms is that while the SBUV algorithm has been optimized for deriving monthly zonal means by making an appropriate choice of the a priori error covariance matrix, the TOMS algorithm has been optimized for tracking short-term variability using month and latitude dependent covariance matrices.

Bhartia, Pawan

Ozone intercomparisons from the Balloon Intercomparison Campaign

Intercomparisons of remote and in-situ techniques used to measure stratospheric ozone are made using results obtained on the Balloon Intercomparison Campaign of 1982 and 1983. Two in-situ and four remote instruments participated. These included ECC ozonesondes, a UV absorption photometer, and microwave emission, IR emission, and absorption spectrometers. Differences are generally less than 15 percent, and are within the quoted error bars. Flights which involved different sets of instruments were made on four separate days, and results are intercompared in plots of ozone density versus altitude. A careful assessment of errors was made for each instrument, and a plot of absolute errors versus altitude is given.

Robbins, D.

Influence of 3D Radiative Effects on Satellite Retrievals of Cloud Properties

When cloud properties are retrieved from satellite observations, the calculations apply 1D theory to the 3D world: they only consider vertical structures and ignore horizontal cloud variability. This presentation discusses how big the resulting errors can be in the operational retrievals of cloud optical thickness. A new technique was developed to estimate the magnitude of potential errors by analyzing the spatial patterns of visible and infrared images. The proposed technique was used to set error bars for optical depths retrieved from new MODIS measurements. Initial results indicate that the 1 km resolution retrievals are subject to abundant uncertainties. Averaging over 50 by 50 km areas reduces the errors, but does not remove them completely; even in the relatively simple case of high sun (30 degree zenith angle), about a fifth of the examined areas had biases larger than ten percent. As expected, errors increase substantially for more oblique illumination.

Varnai, Tamas

VLBI tracking of the TDRS

The use of radio interferometry is being investigated by NASA/Goddard Space Flight Center as a means to track the TDRS geostationary satellites. This technique offers the advantages of very high accuracy using a ground network confined to the continental U.S. and minimal (or no) impact on spacecraft systems as the downlink transmissions can be used passively. A demonstration experiment was performed using very long baseline interferometry (VLBI). The TDRS-E was observed at S-band over a 28-hour definitive period together with dual X/S-band calibration observations of quasars. An orbit was determined for TDRS-E which agrees within estimated error bars with the orbit solution from NASA's operational tracking system but with about half the uncertainty. It was found that, for S-band tracking, the ionosphere is the largest source of orbit error. Use of Ku-band tracking instead would permit geostationary orbits accurate at the 10-m level.

Ray, J.

Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This proposal describes an approach to validate the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft. The research described here is absolutely cutting edge. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional"validation by test only'' mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computationaf Fluid Dynamics can be used to veritY these requirements; however, the model must be validated by test data. The proposed research project includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT and OPEN FOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid . . . Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. To date, the author is the only person to look at the uncertainty in the entire computational domain. For the flow regime being analyzed (turbulent, threedimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Groves, Curtis E.

Dissertation Defense Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional "validation by test only" mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

CFD

Dissertation Defense: Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional validation by test only mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions.Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations. This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System spacecraft system.Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Fluid Dynamics

Surface Reflectance of Mars Observed by CRISM-MRO: 1. Multi-angle Approach for Retrieval of Surface Reflectance from CRISM Observations (mars-reco)

This article addresses the correction for aerosol effects in near-simultaneous multiangle observations acquired by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) aboard the Mars Reconnaissance Orbiter. In the targeted mode, CRISM senses the surface of Mars using 11 viewing angles, which allow it to provide unique information on the scattering properties of surface materials. In order to retrieve these data, however, appropriate strategies must be used to compensate the signal sensed by CRISM for aerosol contribution. This correction is particularly challenging as the photometric curve of these suspended particles is often correlated with the also anisotropic photometric curve of materials at the surface. This article puts forward an innovative radiative transfer based method named Multi-angle Approach for Retrieval of Surface Reflectance from CRISM Observations (MARS-ReCO). The proposed method retrieves photometric curves of surface materials in reflectance units after removing aerosol contribution. MARS-ReCO represents a substantial improvement regarding previous techniques as it takes into consideration the anisotropy of the surface, thus providing more realistic surface products. Furthermore, MARS-ReCO is fast and provides error bars on the retrieved surface reflectance. The validity and accuracy of MARS-ReCO is explored in a sensitivity analysis based on realistic synthetic data. According to experiments, MARS-ReCO provides accurate results (up to 10 reflectance error) under favorable acquisition conditions. In the companion article, photometric properties of Martian materials are retrieved using MARS-ReCO and validated using in situ measurements acquired during the Mars Exploration Rovers mission.

CRISM/MRO

The TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI). Part III: Simulated Observables - The Return of the Spectrum

The TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI) is a community project that aims to quantify how differences in general circulation models (GCMs) could impact the climate prediction for TRAPPIST-le and, subsequently its atmospheric characterization in transit. Four GCMs have participated in THAI so far: ExoCAM, LMD-Generic, ROCKE-3D and the UM. This paper, focused on the simulated observations, is the third part of a trilogy, following the analysis of two land planet scenarios (part I) and two aquaplanet scenarios (part II). Here, we show a robust agreement between the simulated spectra and the number of transits estimated to detect the land planet atmospheres. For the cloudy aquaplanet ones, a 5-σ detection of CO2 could be achieved in about 10 transits if the atmosphere contains at least 1 bar of CO2. That number can vary by 41- 56% depending on the GCM used to predict the terminator profiles, principally due to differences in the cloud deck altitude, with ExoCAM and LMD-G producing higher clouds than ROCKE-3D and UM. Therefore, for the first time, this work provides "GCM uncertainty error bars" of ~ 50% that need to be considered in future analyses of transmission spectra. We also analyzed the inter-transit variability induced by weather patterns and changes of terminator cloudiness between transits. Its magnitude differs significantly between the GCMs but its impact on the transmission spectra is within the measurement uncertainties. THAI has demonstrated the importance of model intercomparison for exoplanets and also paved the way for a larger project to develop an intercomparison meta-framework, namely the Climates Using Interactive Suites of Intercomparisons Nested for Exoplanet Studies (CUISINES).

Exoplanet atmospheres

Results from observations of the 15 June 1983 occultation by the Neptune system

Observations of eight Neptune occultations from six sites in the southwestern Pacific on June 15, 1983. The data were used to search for evidence of rings around Neptune down to a distance of 0.03 Neptune radii from the planetary surface, but the results were negative. An astrometric analysis of the timings yielded solution for the equatorial radius a(0) of Neptune at 1 microbar pressure and the oblatness e at this level. The results are: a(0) = 25,295 + or - 50 km; e = 0.022 + or - 0.004, from which a value for a(1) (equatorial radius at 1 bar pressure) of 24,830 + or - 100 km; and a rotation period of P = 15 h (+3, -2 h) is derived. These results are based on a recent determination of Neptune's pole position and mass quadruple moment, and are consistent with the hypothesis that Neptune and Uranus have homologous mass distributions, although the constraint on interior structure is a weak one. If the probable uncertainty of the pole position is taken into account, error bars on e and derived quantities should be increased by about 50 percent. The present determinations of Neptune atmospheric temperatures at 1 microbar are consistent with earlier results and when combined with all previous data give an average value of 156 + or - 10 K. There is only slight evidence for any latitude dependence in the temperatures. Profiles with a high signal-to-noise ratio suggest the possible presence of an absorbing layer at altitudes higher than the 1-microbar level.

Hubbard, W. B.

Predicting Li-Ion Battery Capacity Fade Using Early-Life Data and a Hybrid Data-Driven Gaussian Process-Bayesian Regression Approach

Accurately predicting Li-ion battery capacity trajectories using early-life data can dramatically improve battery-life understandings and be used to rapidly evaluate design/cost/performance trade-offs when developing new battery materials. Accurate early-life predictions enable researchers to quickly iterate over cell designs and material precursor properties without consistently cycling cells to failure. To this end, we present a toolbox that uses a combined Gaussian Process and Bayesian regression approach that capitalizes on signals other than just capacity (e.g., dQ/dV, voltage drops) to rapidly predict capacity-fade trajectories. The prediction tool uses Bayesian regression to fit functional forms, e.g., power law, sigmoids, etc., to predict capacity-fade dynamics. By fitting functional forms, the capacity fade can be interrogated at any point in the future, allowing for early cell-failure prediction. Additionally, Bayesian regression allows for accurate uncertainty estimates that account for cell-to-cell variability (aleatoric uncertainty) and the lack of observation data (epistemic uncertainty). By only using early cycle data to predict the capacity fade trajectory, uncertainty bounds at end-of-life can be extremely large. The large uncertainty bounds are further exacerbated because there is no systematic way to define the prior distribution of the functional forms' parameters. We improve our the predicted trajectory confidence interval of our predicted trajectory using two methods. First, we shows that a small amount of held-out cycling data is sufficientuse some train cells, that have been cycled to failure to derive information regarding the appropriate prior distributions for the functional forms' parameters of the functional form, effectively leading to data-driven priors.. We propose constructing the data-driven priors by first running a Bayesian regression starting with uninformed priors to generate intermediate cell-specific posterior parameter distributions. These posterior distributions are combined using a Ggaussian mixture model for each parameter to create the data-driven priors. These mixture models serve as the data-driven prior distributions for the parameters for. Second, we derive multiple features, e.g., C_dchg 0.5 DoD 0.5, log (|mean(dQ/dV_(w_3-w_0 ) (V)|), etc., from the train cellsheld-out cycling data, identify which the features are that best predicting capacity at early/mid-life cycles, and then create Ggaussian process regression models that are used for predicting capacity at early/mid-life cycles for the test cells (see blue dots with error bars in Fig 1b). Finally, these predicted data-points are used in addition to the actual early cycle data capacity fade to construct the Bayesian regression trajectory for the test cell s. Notably. We note that these two methods are complementary and can be combined with each other. We evaluate the performance of our proposed method on an testing open-source dataset from Iowa State University and Iowa Lakes Community College (ISU-ILCC). This dataset comprises of 251 nickel-manganese-cobalt/graphite Lithium-ion cells that are cycled under 63 different conditions. We compute the mean average percentage error (MAPE) and negative log predictive density (NLPD) to quantify the efficacy of our method. Our initial findings suggest that, when only few observations are available, for test cells, when using only Bayesian regression with uninformed priors, a power law functional provides the most accurate predictions. with very few data points. However, asHowever, a the number of data points increases, a twin sigmoidal function becomes more accurate as the number of observations further increases. We also find that using as little as 10% of the data set towards generating data-driven priors can lead to significant improvement in prediction accuracy when using early cycle data. Lastly, we found that augmenting early-cycle data with Gaussian process-predicted capacity data for Bayesian regression greatly improves the prediction accuracy. We will present a comprehensive comparison of our methods to other methods available in the literature and apply this method to additional battery datasets.

42 ENGINEERING

A Treatment of Measurements of Heptane Droplet Combustion Aboard MSL-1

Results of measurements on the burning of free n-heptane droplets (that is, droplets without fiber supports) performed in Spacelab during the flights of the first Microgravity Science Laboratory (MSL-1) are presented. The droplet combustion occurred in oxidizing atmospheres which were at an ambient temperature within a few degrees of 300 K. A total of 34 droplets were burned in helium-oxygen atmospheres having oxygen mole fractions ranging from 20 to 50 percent, at pressures from 0.25 to 1.00 bar. In addition, four droplets were burned in air at 1.00 bar, bringing the total number of droplets for which combustion data were secured to 38; two of these four air tests were fiber-supported to facilitate comparisons with other fiber-support experiments, results of which also are given here. Initial diameters of free droplets ranged from about 1 to 4 mm. The primary data obtained were histories of droplet diameters, recorded in backlight on 35 mm film at 80 frames per second, and histories of flame diameters, inferred from emissions through a narrow-band interference filter centered at the 310 micron OH chemiluminescent ultraviolet band, recorded at 30 frames per second by a intensified-array camera. These data are reported here both in raw form and in a smoothed form with estimated error bars. In addition, summaries are presented of measured burning-rate constants, final droplet diameters, and final flame diameters. Both diffusive and radiative extinctions were exhibited under different conditions. Although some interpretations are reported and conclusions drawn concerning the combustion mechanisms, the principal intent of this report is to provide a complete, documented data set for future analysis.

Ackerman, M. D.

SAGE 2-Umkehr case study of ozone differences and aerosol effects from October 1984 to April 1989

A comparison of 1262 cases of coincident ozone profiles derived from 666 Umkehrs at 17 different stations and 901 SAGE 2 profiles within 1000 km and 12 hours between October 1984 and April 1989 indicates the following layer percentage differences with 2-sigma error bars: layer three 14.6 plus/minus 3.3 percent, layer four 17.6 plus/minus 1.1 percent, layer five -1.3 plus/minus 0.5 percent, layer six -5.7 plus/minus 0.7 percent, layer seven -1.0 plus/minus 0.7 percent, layer eight 4.2 plus/minus 0.7 percent, and layer nine 6.8 plus/minus 1.2 percent. Comparing SAGE 2-Umkehr differences to SAGE 1 version 5.5-Umkehr differences shows SAGE 2 higher than or equal to SAGE 1 relative to Umkehr in all layers except layer three. Adjustment for this bias would produce trends derived from SAGE 2-SAGE 1 differences and Umkehr observations in the 1980s more nearly equal to each other in layers six, seven, and eight. A possible explanation of these differences is a systematic shift in the reference altitude between SAGE 1 and SAGE 2, but there is no independent evidence of this. While the shape of the vertical profile of differences at 17 individual Umkehr stations (mostly in mid-latitudes) is generally consistent at all stations except at Poker Flat, Seoul, and Lauder, significant variation does exists among the stations. The profile of mean difference is similar to previously observed differences between Umkehr and both SAGE 2 and SBUV and also to an eigenvector analysis, but with site-dependent amplitude discrepancies. Because of the close correspondence of stratospheric aerosol optical depth at the SAGE 2-measured 0.525 micron wavelength and the extrapolated 0.32 Umkehr wavelength determined in this study, we use the 0.525 micron data to determine the aerosol effect of Umkehr profiles. The aerosol errors to the Umkehr ozone amounts in percent ozone amount per 0.01 stratospheric aerosol optical depth range from plus 2 percent in layer six to minus 3 percent in layer nine. These results agree with previous theoretical and empirical studies within their respective error bounds in layers nine, eight, and five. The result in layer six differs significantly from previous works. In view of the fact that SAGE 2 and Umkehr produce different ozone retrievals in layers eight and nine and because the intra-layer correlation of SAGE 2 ozone and aerosol in layers eight and nine in non-zero, one must exercise some caution in attributing the entire SAGE 2-Umkehr differences in the upper layers to an aerosol effect.

Newchurch, M. J.

Ensemble Monte Carlo calculations with five novel moves

We introduce five novel types of Monte Carlo (MC) moves that brings the number of moves of ensemble MC calculations from three to eight. So far such calculations have relied on affine invariant stretch moves that were originally introduced by Christen (2007), walk moves by Goodman and Weare (2010) and quadratic moves by Militzer (2023). Ensemble MC methods have been very popular because they harness information about the fitness landscape from a population of walkers rather than relying on expert knowledge. Here we modified the affine method and employed a simplex of points to set the stretch direction. We adopt the simplex concept to quadratic moves. We also generalize quadratic moves to arbitrary order. Finally, we introduce directed moves that employ the values of the probability density while all other types of moves rely solely on the location of the walkers. We apply all algorithms to the Rosenbrock density in 2 and 20 dimensions and to the ring potential in 12 and 24 dimensions. We evaluate their efficiency by comparing error bars, autocorrelation time, travel time, and the level of cohesion that measures whether any walkers were left behind. Our code is open source.

97 MATHEMATICS AND COMPUTING

Generalized framework for likelihood-based field-level inference of growth rate from velocity and density fields

Measuring the growth rate of large-scale structures ( f ) as a function of redshift has the potential to break degeneracies between modified gravity and dark energy models, when combined with expansion-rate probes. Direct estimates of peculiar velocities of galaxies have attracted interest as a means of estimating fσ 8 . In particular, field-level methods can be used to fit the field nuisance parameter along with cosmological parameters simultaneously. This article aims to provide the community with a unified framework for the theoretical modeling of the likelihood-based field-level inference by performing fast field covariance calculations for velocity and density fields. Our purpose is to lay the foundations for a nonlinear extension of the likelihood-based method at the field level. We have developed a generalized framework, implemented in the dedicated software flip to perform a likelihood-based inference of fσ 8 . We derived a new field covariance model, which includes wide-angle corrections. We also included the models previously described in the literature inside our framework. We compared their performance against ours, and we validated our model by comparing it with the two-point statistics of a recent N-body simulation. The tests we performed have allowed us to validate our software and determine the appropriate wavenumber range to integrate our covariance model and its validity in terms of separation. Our framework allows for a wider wavenumber coverage to be used in our calculations than in previous works, which is particularly interesting for nonlinear model extensions. Finally, our generalized framework allows us to efficiently perform a survey geometry-dependent Fisher forecast of the fσ 8 parameter. We show that the Fisher forecast method we developed gives an error bar that is 30% closer to a full likelihood-based estimation than a standard volume Fisher forecast.

Ravoux, Corentin