Search NASA⌕ Search

SEARCH · Search NASA

Results for “random variables”

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 1,063 records · Page 59

The Remarkable 2003--2004 Winter and Other Recent Warm Winters in the Arctic Stratosphere Since the Late 1990s

The 2003-2004 Arctic winter was remarkable in the approximately 50-year record of meteorological analyses. A major warming beginning in early January 2004 led to nearly 2 months of vortex disruption with high-latitude easterlies in the middle to lower stratosphere. The upper stratospheric vortex broke up in late December, but began to recover by early January, and in February and March was the strongest since regular observations began in 1979. The lower stratospheric vortex broke up in late January. Comparison with 2 previous years, 1984-1985 and 1986-1987, with prolonged midwinter warming periods shows unique characteristics of the 2003-2004 warming period: The length of the vortex disruption, the strong and rapid recovery in the upper stratosphere, and the slow progression of the warming from upper to lower stratosphere. January 2004 zonal mean winds in the middle and lower stratosphere were over 2 standard deviations below average. Examination of past variability shows that the recent frequency of major stratospheric warmings (7 in the past 6 years) is unprecedented. Lower stratospheric temperatures were unusually high during 6 of the past 7 years, with 5 having much lower than usual potential for polar stratospheric cloud (PSC) formation and ozone loss (nearly none in 1998-1999, 2001-2002, and 2003-2004, and very little in 1997-1998 and 2000-2001). Middle and upper stratospheric temperatures, however, were unusually low during and after February. The pattern of 5 of the last 7 years with very low PSC potential would be expected to occur randomly once every 850 years. This cluster of warm winters, immediately following a period of unusually cold winters, may have important implications for possible changes in interannual variability and for determination and attribution of trends in stratospheric temperatures and ozone.

ozone↗

Combined Effects of Stream Hydrology and Land Use on Basin‐Scale Hyporheic Zone Denitrification in the Columbia River Basin

Abstract Denitrification in the hyporheic zone (HZ) of river corridors is crucial to removing excess nitrogen in rivers from anthropogenic activities. However, previous modeling studies of the effectiveness of river corridors in removing excess nitrogen via denitrification were often limited to the reach‐scale and low‐order stream watersheds. We developed a basin‐scale river corridor model for the Columbia River Basin with random forest models to identify the dominant factors associated with the spatial variation of HZ denitrification. Our modeling results suggest that the combined effects of hydrologic variability in reaches and substrate availability influenced by land use are associated with the spatial variability of modeled HZ denitrification at the basin scale. Hyporheic exchange flux can explain most of spatial variation of denitrification amounts in reaches of different sizes, while among the reaches affected by different land uses, the combination of hyporheic exchange flux and stream dissolved organic carbon (DOC) concentration can explain the denitrification differences. Also, we can generalize that the most influential watershed and channel variables controlling denitrification variation are channel morphology parameters (median grain size (D50), stream slope), climate (annual precipitation and evapotranspiration), and stream DOC‐related parameters (percent of shrub area). The modeling framework in our study can serve as a valuable tool to identify the limiting factors in removing excess nitrogen pollution in large river basins where direct measurement is often infeasible.

54 ENVIRONMENTAL SCIENCES↗

The Remarkable 2003-2004 Winter and Other Recent Warm Winters in the Arctic Stratosphere Since the Late 1990s

The 2003-2004 Arctic winter was remarkable in the 40-year record of meteorological analyses. A major warming beginning in early January 2004 led to nearly two months of vortex disruption with high-latitude easterlies in the middle to lower stratosphere. The upper stratospheric vortex broke up in late December, but began to recover by early January, and in February and March was the strongest since regular observations began in 1979. The lower stratospheric vortex broke up in late January. Comparison with two previous years, 1984-1985 and 1986-1987, with prolonged mid-winter warming periods shows unique characteristics of the 2003-2004 warming period: The length of the vortex disruption, the strong and rapid recovery in the upper stratosphere, and the slow progression of the warming from upper to lower stratosphere. January 2004 zonal mean winds in the middle and lower stratosphere were over two standard deviations below average. Examination of past variability shows that the recent frequency of major stratospheric warmings (seven in the past six years) is unprecedented. Lower stratospheric temperatures were unusually high during six of the past seven years, with five having much lower than usual potential for PSC formation and ozone loss (nearly none in 1998-1999, 2001-2002 and 2003-2004, and very little in 1997-1998 and 2000-2001). Middle and upper stratospheric temperatures, however, were unusually low during and after February. The pattern of five of the last seven years with very low PSC potential would be expected to occur randomly once every approximately 850 years. This cluster of warm winters, immediately following a period of unusually cold winters, may have important implications for possible changes in interannual variability and for determination and attribution of trends in stratospheric temperatures and ozone.

Manney, Gloria L.↗

Predicting the reliability of an additively-manufactured metal part for the third Sandia fracture challenge by accounting for random material defects

We describe an approach to predict failure in a complex, additively-manufactured stainless steel part as defined by the third Sandia Fracture Challenge. A viscoplastic internal state variable constitutive model was calibrated to fit experimental tension curves in order to capture plasticity, necking, and damage evolution leading to failure. Defects such as gas porosity and lack of fusion voids were represented by overlaying a synthetic porosity distribution onto the finite element mesh and computing the elementwise ratio between pore volume and element volume to initialize the damage internal state variables. These void volume fraction values were then used in a damage formulation accounting for growth of these existing voids, while new voids were allowed to nucleate based on a nucleation rule. Blind predictions of failure are compared to experimental results. The comparisons indicate that crack initiation and propagation were correctly predicted, and that an initial porosity field superimposed as higher initial damage may provide a path forward for capturing material strength uncertainty. Here, the latter conclusion was supported by predicted crack face tortuosity beyond the usual mesh sensitivity and variability in predicted strain to failure; however, it bears further inquiry and a more conclusive result is pending compressive testing of challenge-built coupons to de-convolute materials behavior from the geometric influence of significant porosity.

36 MATERIALS SCIENCE↗

Remote Sensing of Droplet Number Concentration in Warm Clouds: A Review of the Current State of Knowledge and Perspectives

Abstract The cloud droplet number concentration ( N d ) is of central interest to improve the understanding of cloud physics and for quantifying the effective radiative forcing by aerosol‐cloud interactions. Current standard satellite retrievals do not operationally provide N d , but it can be inferred from retrievals of cloud optical depth ( τ c ) cloud droplet effective radius ( r e ) and cloud top temperature. This review summarizes issues with this approach and quantifies uncertainties. A total relative uncertainty of 78% is inferred for pixel‐level retrievals for relatively homogeneous, optically thick and unobscured stratiform clouds with favorable viewing geometry. The uncertainty is even greater if these conditions are not met. For averages over 1° ×1° regions the uncertainty is reduced to 54% assuming random errors for instrument uncertainties. In contrast, the few evaluation studies against reference in situ observations suggest much better accuracy with little variability in the bias. More such studies are required for a better error characterization. N d uncertainty is dominated by errors in r e , and therefore, improvements in r e retrievals would greatly improve the quality of the N d retrievals. Recommendations are made for how this might be achieved. Some existing N d data sets are compared and discussed, and best practices for the use of N d data from current passive instruments (e.g., filtering criteria) are recommended. Emerging alternative N d estimates are also considered. First, new ideas to use additional information from existing and upcoming spaceborne instruments are discussed, and second, approaches using high‐quality ground‐based observations are examined.

58 GEOSCIENCES↗

GraphAlign: Graph-Enabled Machine Learning for Seismic Event Filtering

This report summarizes results from a 2 year effort to improve the current automated seismic event processing system by leveraging machine learning models that can operated over the inherent graph data structure of a seismic sensor network. Specifically, the GraphAlign project seeks to utilize prior information on which stations are more likely to detect signals originating from particular geographic regions to inform event filtering. To date, the GraphAlign team has developed a Graphical Neural Network (GNN) model to filter out false events generated by the Global Associator (GA) algorithm. The algorithm operates directly on waveform data that has been associated to an event by building a variable sized graph of station waveforms nodes with edge relations to an event location node. This builds off of previous work where random forest models were used to do the same task using hand crafted features. The GNN model performance was analyzed using an 8 week IMS/IDC dataset, and it was demonstrated that the GNN outperforms the random forest baseline. We provide additional error analysis of which events the GNN model performs well and poorly against concluded by future directions for improvements.

58 GEOSCIENCES↗

Rossby waves in a fluctuating zonal mean flow

The effects of the zonal mean wind variability on the energy propagation of a stationary Rossby wave in a barotropic nondivergent atmosphere are studied. It is shown that the random nature of the zonal wind fluctuations do not allow Rossby wave energy to propagate from its energy source. The mechanism for this effect is strongly dependent on the spatial resolution at which the zonal mean flow is assumed to be known. Some speculations are offered on the relation between this mechanism and the systematic error of some low-resolution climate models.

Pandolfo, Lionel↗

Calibration of the COBE FIRAS instrument

The Far-Infrared Absolute Spectrophotometer (FIRAS) instrument on the Cosmic Background Explorer (COBE) satellite was designed to accurately measure the spectrum of the cosmic microwave background radiation (CMBR) in the frequency range 1-95/cm with an angular resolution of 7 deg. We describe the calibration of this instrument, including the method of obtaining calibration data, reduction of data, the instrument model, fitting the model to the calibration data, and application of the resulting model solution to sky observations. The instrument model fits well for calibration data that resemble sky condition. The method of propagating detector noise through the calibration process to yield a covariance matrix of the calibrated sky data is described. The final uncertainties are variable both in frequency and position, but for a typical calibrated sky 2.6 deg square pixel and 0.7/cm spectral element the random detector noise limit is of order of a few times 10(exp -7) ergs/sq cm/s/sr cm for 2-20/cm, and the difference between the sky and the best-fit cosmic blackbody can be measured with a gain uncertainty of less than 3%.

Fixsen, D. J.↗

Attitude Estimation Signal Processing: A First Report on Possible Algorithms and Their Utility

In this brief effort, time has been of the essence. The data had to be acquired from APL/Lincoln Labs, stored, and sorted out to obtain the pertinent streams. This has been a significant part of this effort and hardware and software problems have been addressed with the appropriate solutions to accomplish this part of the task. Passed this, some basic and important algorithms are utilized to improve the performance of the attitude estimation systems. These algorithms are an essential part of the signal processing for the attitude estimation problem as they are utilized to reduce the amount of the additive/multiplicative noise that in general may or may not change its structure and probability density function, pdf, in time. These algorithms are not currently utilized in the processing of the data, at least, we are not aware of their use in this attitude estimation problem. Some of these algorithms, like the variable thresholding, are new conjectures, but one would expect that someone somewhere must have utilized this kind of scheme before. The variable thresholding idea is a straightforward scheme to use in case of a slowly varying pdf, or statistical moments of the unwanted random process. The algorithms here are kept simple but yet effective for processing the data and removing the unwanted noise. For the most part, these algorithms can be arranged so that their consecutive and orderly execution would complement the preceding algorithm and improve the overall performance of the signal processing chain.

Riasati, Vahid R.↗

Accurate models of the added mass force of a uniform random distribution of spherical particles or bubbles

The added mass force resulting from the acceleration of a body in a fluid is of fundamental and practical interest in dispersed multiphase flows. Euler–Lagrange (EL) and Euler–Euler (EE) simulations require closure terms for the added mass force in order to accurately couple the conserved variables between phases. Presently, a more thorough understanding of the added mass force in a multi-particle system is developed based on potential flow resulting in a resistance matrix formulation analogous to Stokesian dynamics. This formulation is then used to generate a dataset of added mass resistance matrices for large systems of randomly generated particles. This methodology is used to create a volume fraction corrected binary model for predicting the added mass force in large systems as well as generate statistics of the added mass force in such systems. This work provides clarification to the theory of the added mass force for particle clouds, and modelling options that may be implemented in existing EL and EE codes.

42 ENGINEERING↗

A predictability study of Lorenz's 28-variable model as a dynamical system

The dynamics of error growth in a two-layer nonlinear quasi-geostrophic model has been studied to gain an understanding of the mathematical theory of atmospheric predictability. The growth of random errors of varying initial magnitudes has been studied, and the relation between this classical approach and the concepts of the nonlinear dynamical systems theory has been explored. The local and global growths of random errors have been expressed partly in terms of the properties of an error ellipsoid and the Liapunov exponents determined by linear error dynamics. The local growth of small errors is initially governed by several modes of the evolving error ellipsoid but soon becomes dominated by the longest axis. The average global growth of small errors is exponential with a growth rate consistent with the largest Liapunov exponent. The duration of the exponential growth phase depends on the initial magnitude of the errors. The subsequent large errors undergo a nonlinear growth with a steadily decreasing growth rate and attain saturation that defines the limit of predictability. The degree of chaos and the largest Liapunov exponent show considerable variation with change in the forcing, which implies that the time variation in the external forcing can introduce variable character to the predictability.

Krishnamurthy, V.↗

SU-F-T-113: Inherent Functional Dependence of Spinal Cord Doses of Variable Irradiated Volumes in Spine SBRT

Purpose: Spinal cord tolerance for SBRT has been recommended for the maximum point dose level or at irradiated volumes such as 0.35 mL or 10% of contoured volumes. In this study, we investigated an inherent functional relationship that associates these dose surrogates for irradiated spinal cord volumes of up to 3.0 mL. Methods: A hidden variable termed as Effective Dose Radius (EDR) was formulated based on a dose fall-off model to correlate dose at irradiated spinal cord volumes ranging from 0 mL (point maximum) to 3.0 mL. A cohort of 15 spine SBRT cases was randomly selected to derive an EDR-parameterized formula. The mean prescription dose for the studied cases was 21.0±8.0 Gy (range, 10–40Gy) delivered in 3±1 fractions with target volumes of 39.1 ± 70.6 mL. Linear regression and variance analysis were performed for the fitting parameters of variable EDR values. Results: No direct correlation was found between the dose at maximum point and doses at variable spinal cord volumes. For example, Pearson R{sup 2} = 0.643 and R{sup 2}= 0.491 were obtained when correlating the point maximum dose with the spinal cord dose at 1 mL and 3 mL, respectively. However, near perfect correlation (R{sup 2} ≥0.99) was obtained when corresponding parameterized EDRs. Specifically, Pearson R{sup 2}= 0.996 and R{sup 2} = 0.990 were obtained when correlating EDR (maximum point dose) with EDR (dose at 1 mL) and EDR(dose at 3 mL), respectively. As a result, high confidence level look-up tables were established to correlate spinal cord doses at the maximum point to any finite irradiated volumes. Conclusion: An inherent functional relationship was demonstrated for spine SBRT. Such a relationship unifies dose surrogates at variable cord volumes and proves that a single dose surrogate (e.g. point maximum dose) is mathematically sufficient in constraining the overall spinal cord dose tolerance for SBRT.

60 APPLIED LIFE SCIENCES↗

Remote Sensing and GIS data at 1km-grid over Chesapeake Bay used in “He et al. 2024, Effects of spatial variability in vegetation phenology, climate, landcover, biodiversity, topography, and soil property on soil respiration across a coastal ecosystem”

The package contains the data layers used in “He et al. 2024, Effects of spatial variability in vegetation phenology, climate, landcover, biodiversity, topography, and soil property on soil respiration across a coastal ecosystem”. The study aims to use multi-source remote sensing and GIS datasets to investigate the spatial heterogeneity and identify spatial zones with similar environmental characteristics and understand the primary driving factors affecting soil respiration within sub-ecosystems of the coastal ecosystem. We employed unsupervised hierarchical clustering analysis to identify spatial regions with distinct environmental characteristics, then determined the main driving factors using Random Forest regression and SHapley Additive exPlanations (SHAP). Spatial data layers include soil respiration, kernel Normalized Difference Vegetation Index (kNDVI) computed from Harmonized Landsat 8 and Sentinel-2 time series, climate variables from the Daymet dataset, land cover, biodiversity, topographical metrics, soil property, and tidal elevation.

54 ENVIRONMENTAL SCIENCES↗

Effects of sample design and landscape features on a measure of environmental heterogeneity

Environmental heterogeneity, an important influence on organisms and ecological processes, can be quantified by the variance of an environmental characteristic over all locations within a study extent. However on landscapes with autocorrelation and gradient patterns, estimating this variance from a sample of locations may lead to errors that cannot be corrected with statistical techniques. We analytically derived the relative expected sampling error of sample designs on landscapes with particular gradient pattern and autocorrelation features. We applied this closed-form approach to temperature observations from an existing study. The expected heterogeneity differed, both in magnitude and direction, amongst sample designs over the study site's likely range of autocorrelation and gradient features. We conducted a simulation study to understand the effects of (i) landscape variability and (ii) design variability on an average sampling error. On 10 000 simulated landscapes with varying gradient and autocorrelation features, we compared estimates of variance from a variety of structured and random sample designs. While gradient patterns and autocorrelation cause large errors for some designs, others yield near-zero average sampling error. Sample location spacing is a key factor in sample design performance. Random designs have larger range of possible sampling errors than structured designs due to the potential for sample arrangements that over- and under-sample certain areas of the landscape. Furthermore, when implementing a new sample design to quantify environmental heterogeneity via variance, we recommend using a simple structured design with appropriate sample spacing. For existing designs, we recommend calculating the relative expected sampling error via our analytical derivation.

54 ENVIRONMENTAL SCIENCES↗

Modeling Spatial Distribution of Snow Water Equivalent by Combining Meteorological and Satellite Data with Lidar Maps

Abstract An accurate characterization of the water content of snowpack, or snow water equivalent (SWE), is necessary to quantify water availability and constrain hydrologic and land surface models. Recently, airborne observations (e.g., lidar) have emerged as a promising method to accurately quantify SWE at high resolutions (scales of ∼100 m and finer). However, the frequency of these observations is very low, typically once or twice per season in the Rocky Mountains of Colorado. Here, we present a machine learning framework that is based on random forests to model temporally sparse lidar-derived SWE, enabling estimation of SWE at unmapped time points. We approximated the physical processes governing snow accumulation and melt as well as snow characteristics by obtaining 15 different variables from gridded estimates of precipitation, temperature, surface reflectance, elevation, and canopy. Results showed that, in the Rocky Mountains of Colorado, our framework is capable of modeling SWE with a higher accuracy when compared with estimates generated by the Snow Data Assimilation System (SNODAS). The mean value of the coefficient of determination R 2 using our approach was 0.57, and the root-mean-square error (RMSE) was 13 cm, which was a significant improvement over SNODAS (mean R 2 = 0.13; RMSE = 20 cm). We explored the relative importance of the input variables and observed that, at the spatial resolution of 800 m, meteorological variables are more important drivers of predictive accuracy than surface variables that characterize the properties of snow on the ground. This research provides a framework to expand the applicability of lidar-derived SWE to unmapped time points. Significance Statement Snowpack is the main source of freshwater for close to 2 billion people globally and needs to be estimated accurately. Mountainous snowpack is highly variable and is challenging to quantify. Recently, lidar technology has been employed to observe snow in great detail, but it is costly and can only be used sparingly. To counter that, we use machine learning to estimate snowpack when lidar data are not available. We approximate the processes that govern snowpack by incorporating meteorological and satellite data. We found that variables associated with precipitation and temperature have more predictive power than variables that characterize snowpack properties. Our work helps to improve snowpack estimation, which is critical for sustainable management of water resources.

54 ENVIRONMENTAL SCIENCES↗

The impact of SST resolution change in the ERA-Interim reanalysis on wintertime Gulf Stream frontal air-sea interaction: SST Resolution Change in ERA-Interim

This paper examines the sensitivity to a change in sea surface temperature (SST) resolution of the interaction between atmospheric and oceanic fronts in the Gulf Stream region in the ERA-Interim reanalysis data set. Two periods are considered, January 1979 to December 2001 (SST resolution 1° × 1°) and December 2010 to February 2016 (SST resolution 0.05° × 0.05°). The winter season from the latter 6 years of high-resolution SST is compared against six random periods of six wintertime seasons from the low-resolution SST period, to assess the robustness of the result against natural climate variability. In all comparisons, a significant change in frontal air-sea sensible heat flux exchange is found that is highly correlated to the change in mean SST gradient. This leads to both increases and decreases in occurrence of atmospheric fronts and mean precipitation of up to 30%. These results reemphasize the importance of high SST resolution in resolving the influence of oceanic fronts on weather and climate.

54 ENVIRONMENTAL SCIENCES↗

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen-Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen-Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log-predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Approximate Bayesian inference↗

State-Level Trends in Renewable Energy Procurement via Solar Installation versus Green Electricity

In recent years, options for procuring renewable energy have increased, ranging from rooftop solar installation to utility green pricing to Community Choice Aggregation. These options vary in terms of costs and benefits to the consumer as well as grid integration implications. However, little is known regarding how the presence of a wide range of voluntary utility-scale renewable procurement options as well as their growth could affect adoption of distributed residential solar. To examine this relationship, we fit a two-stage least squares random effects regression model on panel data from 2016 to 2019 for all fifty US states plus the District of Columbia, controlling for variables that measure state-level policies, economic factors, and resource availability. Although there was no evidence of a strong relationship between demand for utility-scale and distributed options across all states, the state-level correlations suggest a wide variation between states including a positive, zero or negative relationship between utility-scale and distributed generation.

consumer demand↗