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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Mitigation of spatial nonstationarity with vision transformers

Spatial nonstationarity, the location variance of features’ statistical distributions, is ubiquitous in many natural settings. For example, in geological reservoirs rock matrix porosity varies vertically due to geomechanical compaction trends, in mineral deposits grades vary due to sedimentation and concentration processes, in hydrology rainfall varies due to the atmosphere and topography interactions, and in metallurgy crystalline structures vary due to differential cooling. Conventional geostatistical modeling workflows rely on the assumption of stationarity to be able to model spatial features for geostatistical inference. Nevertheless, this is often not a realistic assumption when dealing with nonstationary spatial data and this has motivated a variety of nonstationary spatial modeling workflows such as trend and residual decomposition, cosimulation with secondary features, and spatial segmentation and independent modeling over stationary subdomains. The advent of deep learning technologies has enabled new workflows for modeling spatial relationships. However, there is a paucity of demonstrated best practice and general guidance on mitigation of spatial nonstationarity with deep learning in the geospatial context. We demonstrate the impact of two common types of geostatistical spatial nonstationarity on deep learning model prediction performance and propose the mitigation of such impacts using self-attention (vision transformer) models. We demonstrate the utility of vision transformers for the mitigation of nonstationarity with relative errors as low as 10%, exceeding the performance of alternative deep learning methods such as convolutional neural networks. We establish best practice by demonstrating the ability of self-attention networks for modeling large-scale spatial relationships in the presence of commonly observed geospatial nonstationarity.

58 GEOSCIENCES↗
DOE OSTI2024

Nonstationarity in the global terrestrial water cycle and its interlinkages in the Anthropocene

Climate change and human activities alter the global freshwater cycle, causing nonstationary processes as its distribution shifting over time, yet a comprehensive understanding of these changes remains elusive. Here, we develop a remote sensing–informed terrestrial reanalysis and assess the nonstationarity of and interconnections among global water cycle components from 2003 to 2020. We highlight 20 hotspot regions where terrestrial water storage exhibits strong nonstationarity, impacting 35% of the global population and 45% of the area covered by irrigated agriculture. Emerging long-term trends dominate the most often (48.2%), followed by seasonal shifts (32.8%) and changes in extremes (19%). Notably, in mid-latitudes, this encompasses 34% of Asia and 27% of North America. The patterns of nonstationarity and their dominant types differ across other water cycle components, including precipitation, evapotranspiration, runoff, and gross primary production. These differences also manifest uniquely across hotspot regions, illustrating the intricate ways in which each component responds to climate change and human water management. Our findings emphasize the importance of considering nonstationarity when assessing water cycle information toward the development of strategies for sustainable water resource usage, enhancing resilience to extreme events, and effectively addressing other challenges associated with climate change.

Science & Technology - Other Topics↗
NASA NTRS1994

Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated

Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient-related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, 'roughness' and 'sparseness', respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from approximately 60 m to approximately 60 km. Finally, we define the 'mean multifractal plane' and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.

Davis, Anthony↗
DOE OSTI2019

Incorporating Climate Nonstationarity and Snowmelt Processes in Intensity–Duration–Frequency Analyses with Case Studies in Mountainous Areas

In this work, downscaled high-resolution climate simulations were used to provide inputs to the physics-based Distributed Hydrology Soil Vegetation Model (DHSVM), which accounts for the combined effects of snowmelt and rainfall processes, to determine spatially distributed available water for runoff (AWR). After quasi-stationary time windows were identified based on model outputs extracted for two different mountainous field sites in Colorado and California, intensity–duration–frequency (IDF) curves for precipitation and AWR were generated and evaluated at each numerical grid to provide guidance on hydrological infrastructure design. Impacts of snowmelt are found to be spatially variable due to spatial heterogeneity associated with topography according to geostatistical analyses. AWR extremes have stronger spatial continuity compared to precipitation. Snowmelt impacts on AWR are more pronounced at the wet California site than at the semiarid Colorado site. The sensitivities of AWR and precipitation IDFs to increasing greenhouse gas emissions are found to be localized and spatially variable. In subregions with significant snowfall, snowmelt can result in an AWR (e.g., 6-h 100-yr events) that is 70% higher than precipitation. For comparison, future greenhouse gas emissions may increase 6-h 100-yr precipitation and AWR by up to 50% and 80%, respectively, toward the end of this century.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1985

The influence of nonstationarity of the solar activity and general solar field on modulation of cosmic rays

A numerical model of the propagation of galactic cosmic rays in interplanetary space was constructed for the case when the modulation depth determined by the level of solar activity changed in time. Also the contribution of particle drift in the regular field was calculated, and the agreement with experimental data concerning the ratio of protons and electrons in two solar activity minima is shown.

Zusmanovich, A. G.↗
NASA NTRS1998

Flux Sampling Errors for Aircraft and Towers

Various errors and influences leading to differences between tower- and aircraft-measured fluxes are surveyed. This survey is motivated by reports in the literature that aircraft fluxes are sometimes smaller than tower-measured fluxes. Both tower and aircraft flux errors are larger with surface heterogeneity due to several independent effects. Surface heterogeneity may cause tower flux errors to increase with decreasing wind speed. Techniques to assess flux sampling error are reviewed. Such error estimates suffer various degrees of inapplicability in real geophysical time series due to nonstationarity of tower time series (or inhomogeneity of aircraft data). A new measure for nonstationarity is developed that eliminates assumptions on the form of the nonstationarity inherent in previous methods. When this nonstationarity measure becomes large, the surface energy imbalance increases sharply. Finally, strategies for obtaining adequate flux sampling using repeated aircraft passes and grid patterns are outlined.

Mahrt, Larry↗
NASA NTRS2016

Rippled Quasiperpendicular Shock Observed by the Magnetospheric Multiscale Spacecraft

Collisionless shock nonstationarity arising from microscale physics influences shock structure and particle acceleration mechanisms. Nonstationarity has been difficult to quantify due to the small spatial and temporal scales. We use the closely spaced (subgyroscale), high-time-resolution measurements from one rapid crossing of Earths quasiperpendicular bow shock by the Magnetospheric Multiscale (MMS) spacecraft to compare competing nonstationarity processes. Using MMSs high-cadence kinetic plasma measurements, we show that the shock exhibits nonstationarity in the form of ripples.

Johlander, A.↗
DOE OSTI2021

Flexible nonstationary spatiotemporal modeling of high-frequency monitoring data

Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of nonstationarity in space and time and demonstrate that this method provides a natural and tractable way to incorporate complex behaviors into a covariance model. Further, we use this method with fully time-domain computations to obtain bona fide maximum likelihood estimators—as opposed to using Whittle-type likelihood approximations, for example—that can still be computed conveniently. Additionally, we apply this method to very high-frequency Doppler LIDAR vertical wind velocity measurements, demonstrating that the model can expressively capture the extreme nonstationarity of dynamics above and below the atmospheric boundary layer and, more importantly, the interaction of the process dynamics across it.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A Nonstationary and Non-Gaussian Moving Average Model for Solar Irradiance

Historically, power has flowed from large power plants to customers. Increasing penetration of distributed energy resources such as solar power from rooftop photovoltaic has made the distribution network a two-way-street with power being generated at the customer level. The incorporation of renewables introduces additional uncertainty and variability into the power grid. Distribution network operation studies are being adapted to include renewables; however, such studies require high quality solar irradiance data that adequately reflect realistic meteorological variability. Data from satellite-based products are spatially complete, but temporally coarse, whereas solar irradiances exhibit high frequency variation at very fine timescales. We propose a new stochastic method for temporally downscaling global horizontal irradiance (GHI) to 1 min resolution, but we do not consider the spatial aspect due to limited availability of the in situ irradiance measurements. Solar irradiance's first and second-order structures vary diurnally and seasonally, and our model adapts to such nonstationarity. Empirical irradiance data exhibits highly non-Gaussian behavior; we develop a nonstationary and non-Gaussian moving average model that is shown to capture realistic solar variability at multiple timescales. We also propose a new estimation scheme based on Cholesky factors of empirical autocovariance matrices, bypassing difficult and inaccessible likelihood-based approaches. The model is demonstrated for a case study of three locations that are located in diverse climates through the United States. The model is compared against competitors from the literature and is shown to provide better uncertainty and variability quantification on testing data.

Cholesky factor↗
NASA NTRS2002

Evaluation of Standard Gear Metrics in Helicopter Flight Operation

Each false alarm made by a machine monitoring system carries a high price tag. The machine must be taken out of service, thoroughly inspected with possible disassembly, and then made ready for service. Loss of use of the machine and the efforts to inspect it are costly. In addition, if a monitoring system is prone to false alarms, the system will soon be turned off or ignored. For aircraft applications, one growing concern is that the dynamic flight environment differs from the laboratory environment where fault detection methods are developed and tested. Vibration measurements made in flight are less stationary than those made in a laboratory, or test facility, and thus a given fault detection method may produce more false alarms in flight than might be anticipated. In 1977. Stewart introduced several metrics, including FM0 and FM4, for evaluating the health of a gear. These metrics are single valued functions of the vibration signal that indicate if the signal deviates from an ideal model of the signal. FM0 is a measure of the ratio of the peak-to-peak level to the harmonic energy in the signal. FM4 is the kurtosis of the signal with the gear mesh harmonics and first order side bands removed. The underlying theory is that a vibration signal from a gear in good condition is expected to be dominated by a periodic signal at the gear mesh frequency. If one or a small number of gear teeth contain damage or faults, the signal will change, possibly showing increased amplitude, local phase changes or both near the damaged region of the gear. FM0 increases if a signal contains a local increase in amplitude. FM4 increases if a signal contains a local increase in amplitude or local phase change in a periodic signal. Over the years, other single value metrics were also introduced to detect the onset and growth of damage in gears. These various metrics have detected faults in several gear tests in experimental test rigs. Conditions in these tests have been steady state in the sense that the rpm, torque and forces on the gear have been held steady. For gears used in a dynamic environment such as that occurring in aircraft, the rpm, torque and forces on the gear are constantly changing. The authors have measured significant variation in rpm and torque in the transmissions of helicopters in controlled steady flight conditions flown by highly proficient test pilots. Statistical analyses of the data taken in flight show significant nonstationarity in the vibration measurements. These deviations from stationarity may increase false alarms in gear monitoring during aircraft flight. In the proposed paper, the authors will study vibration measurements made in flight on an AH- 1 Cobra and an OH-58C Kiowa helicopters. The primary focus will be the development of a methodology to assess the impact of nonstationarity on false alarms. Issues to be addressed include how time synchronous averages are constructed from raw data as well as how lack of stationarity effects the behavior of single value metrics. Emphasis will be placed on the occurrence of false alarms with the use of standard metrics. In order to maintain an acceptable level of false alarms in the flight environment, this study will also address the determination of appropriate threshold levels, which may need to be higher than for test rigs.

Mosher, M.↗
DOE OSTI2025

Compactly‐Supported Nonstationary Kernels for Computing Exact Gaussian Processes on Big Data

The Gaussian process (GP) is a widely used method for analyzing large-scale data sets, including spatio-temporal measurements of nonlinear processes that are now commonplace in the environmental sciences. Traditional implementations of GPs involve stationary kernels (also termed covariance functions) that limit their flexibility, and exact methods for inference that prevent application to data sets with more than about 10,000 points. Modern approaches to address stationarity assumptions generally fail to accommodate large data sets, while all attempts to address scalability focus on approximating the Gaussian likelihood, which can involve subjectivity and lead to inaccuracies. In this work, we explicitly derive an alternative kernel that can discover and encode both sparsity and nonstationarity. We embed the kernel within a fully Bayesian GP model and leverage high-performance computing resources to enable the analysis of massive data sets. We demonstrate the favorable performance of our novel kernel relative to existing exact and approximate GP methods across a variety of synthetic data examples. Furthermore, we conduct space–time prediction based on more than 1 million measurements of daily maximum temperature and verify that our results outperform state-of-the-art methods in the Earth sciences. More broadly, having access to exact GPs that use ultra-scalable, sparsity-discovering, nonstationary kernels allows GP methods to truly compete with a wide variety of machine learning methods.

Gaussian processes↗
DOE OSTI2024

Monitoring covariance in multivariate time series: Comparing machine learning and statistical approaches

Abstract In complex systems with multiple variables monitored at high‐frequency, variables are not only temporally autocorrelated, but they may also be nonlinearly related or exhibit nonstationarity as the inputs or operation changes. One approach to handling such variables is to detrend them prior to monitoring and then apply control charts that assume independence and stationarity to the residuals. Monitoring controlled systems is even more challenging because the control strategy seeks to maintain variables at prespecified mean levels, and to compensate, correlations among variables may change, making monitoring the covariance essential. In this paper, a vector autoregressive model (VAR) is compared with a multivariate random forest (MRF) and a neural network (NN) for detrending multivariate time series prior to monitoring the covariance of the residuals using a multivariate exponentially weighted moving average (MEWMA) control chart. Machine learning models have an advantage when the data's structure is unknown or may change. We design a novel simulation study with nonlinear, nonstationary, and autocorrelated data to compare the different detrending models and subsequent covariance monitoring. The machine learning models have superior performance for nonlinear and strongly autocorrelated data and similar performance for linear data. An illustration with data from a reverse osmosis process is given.

Weix, Derek↗
DOE OSTI2020

Target Detection via Cognitive Radars Using Change-Point Detection, Learning, and Adaptation

Many radar detection algorithms that assume a stationary environment (clutter) have been proposed and analyzed over the years. However, in practice, changes in the nonstationary environment can perturb the parameters of the clutter distribution, or even alter the clutter distribution family, which can greatly deteriorate the target detection capability. To avoid such potential performance degradation, cognitive radar systems are envisioned which are required to rapidly realize the nonstationarity, accurately learn the new characteristics of the environments, and adaptively update the detector. In this paper, aiming to develop a fully cognitive radar for target detection in nonstationary environments, we propose a unifying framework that integrates (i) change-point detection of clutter distributions by using a data-driven cumulative sum (CUSUM) algorithm and its extended version, (ii) learning/identification of clutter distribution by applying sparse theory and kernel density estimation methods, and (iii) adaptive target detection by automatically modifying the likelihood-ratio test and corresponding detection threshold. Further, with extensive numerical examples, we demonstrate the achieved improvements in detection performance due to the proposed framework in comparison to a nonadaptive case, an adaptive matched filter (AMF) method, and the clairvoyant case. Herein, we also use Wilcoxon rank-sum tests to evaluate the statistical significance of the performance improvements

42 ENGINEERING↗
DOE OSTI2024

Emergent Trends Complicate the Interpretation of the United States Drought Monitor (USDM)

Abstract Effective drought management must be informed by an understanding of whether and how current drought monitoring and assessment practices represent underlying nonstationary climate conditions, either naturally occurring or forced by climate change. Here we investigate the emerging climatology and associated trends in drought classes defined by the United States Drought Monitor (USDM), a weekly product that, since 2000, has been used to inform drought management in the United States. The USDM classifies drought intensity based in part on threshold percentiles in key hydroclimate quantities. Here we assess how those USDM‐defined drought threshold percentiles have changed over the last 23 years, examining precipitation, runoff, soil moisture (SM), terrestrial water storage (TWS), vapor pressure deficit (VPD), and near‐surface air temperature. We also assess underlying trends in the frequency of drought classifications across the U.S. Our analysis suggests that the frequency of drought class occurrence is exceeding the threshold percentiles defined by the USDM in a number of regions in the United States, particularly in the American West, where the last 23 years have emerged as a prolonged dry period. These trends are also reflected in percentile‐based thresholds in precipitation, runoff, SM, TWS, VPD, and temperature. Our results emphasize that while the USDM appears to be accurately reflecting observed nonstationarity in the physical climate, such trends raise critical questions about whether and how drought diagnosis, classification, and monitoring should address long‐term intervals of wet and dry periods or trends.

Geology↗
DOE OSTI2025

Deep Koopman operators for causal discovery

Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. Thus, applying these methods to study causal dynamics in real-world systems, such as the Earth, is a major challenge. Addressing this shortcoming, we leverage deep learning and a Koopman operator-theoretic formalism to present a class of causal discovery algorithms. Kausal uses deep Koopman operator methods to approximate nonlinear dynamics in a linearized vector space in which traditional causal inference methods such as Granger causality can be more easily applied. Our idealized experiments demonstrate Kausal’s superior ability in discovering and characterizing causal signals compared to existing deep learning and non-deep learning state-of-the-art approaches. Finally, the successful identification of major El Niño and La Niña events in observations showcases Kausal’s skill to handle real-world applications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Mechanism of electron bunching by an ultrarelativistically intense laser pulse when crossing a nonuniform-plasma boundary

Numerical simulations were used to investigate the electron bunching induced by a laser pulse in its penetration into a plasma that has a nonuniform density profile at the vacuum – plasma boundary, which reaches a plateau. A mechanism was found to exist for this plasma which fosters a denser electron grouping in the generated bunch in comparison with the plasma with a sharp boundary. This mechanism is related to the nonstationarity of the wake wave produced by the laser pulse at the beginning of the plasma density plateau. (paper)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Structure of Offshore Low-Level Jet Turbulence and Implications to Mesoscale-to-Microscale Coupling

This paper explores realistic nonstationary atmospheric boundary layer (ABL) turbulence arising from nonstationarity at the mesoscale, particularly within offshore low-level jets with implications to offshore wind farms, using high-fidelity multiscale large-eddy simulations (LES). To this end, we analyzed the single-point turbulence statistical structure of a North-Atlantic offshore LLJ event simulated using high-resolution LES (AMR-Wind). The nonstationary LLJ is simulated using a mesoscale-to-microscale coupled (MMC) simulation procedure involving data assimilation of mesoscale velocity and temperature data from the Weather Research and Forecasting (WRF) model. Unlike the assimilation of mesoscale velocity data into the LES, the direct assimilation of temperature profiles had a strong impact on turbulence stratification, thereby causing erroneous predictions of turbulence both above and within the jet layer. Various approaches to mitigate this effect have resulted in multiple (four) variants of this MMC strategy. Outcomes from this work clearly show that the turbulence within the low-level jet is a strong function of the MMC approach as the turbulence structure within the low-level jet is dependent on the flux of residual turbulence from outside the jet, which in turn depends on the temperature forcing history. Additionally, the turbulence predicted by all these different methods (as well as the observation data) show similar deviations from equilibrium as evidenced by comparisons with idealized atmospheric turbulence structure obtained using the same numerical method. In general, we observe that the predicted LLJ turbulence tends to differ from canonical ABL turbulence with comparable shear. Particularly, the combination of shear and turbulence observed in such nonstationary low-level turbulence cannot be matched using equilibrium settings and therefore, represents a critical use-case for both testing and leveraging meso–micro coupling strategies.

17 WIND ENERGY↗