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Distorted stationary Gaussian process can be used to provide computer-generated imitations of experimental time series. A method of analyzing a source time series and synthesizing an imitation is shown, and an example using X-band radiometer data is given.
A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.
In passive microwave remote sensing of soil moisture, the tau-omega (τ-ω) model has often been used to provide soil moisture estimates at a spatial scale representative of the satellite footprint dimensions. For modeling simplicity, model parameters such as the single scattering albedo (ω) and vegetation opacity (τ) that go into the geophysical inversion process are often assumed to be independent of polarizations. Although this absence of polarization dependence can often be justified in special cases as in low-frequency remote sensing or under dense vegetation conditions, it is not a robust assumption in general. Additional model parameterization errors arising from this assumption are possible, leading to degradation in soil moisture estimation accuracy. In this paper, we propose a time series approach to try to resolve the polarization dependence of several τ-ω model parameters as well as the temperature bias arising from the ancillary temperature data. The Version 4 of the Soil Moisture Active Passive (SMAP) Level 1B brightness temperature time series observations were used to illustrate the mechanics of this approach, with an emphasis on a comparison between resulting satellite soil moisture retrievals and in situ data collected at several core validation sites. It was found that this time series approach resulted in significant reduction of the dry bias exhibited in the current SMAP passive soil moisture data products, while retaining the same performance in other metrics of the current baseline passive soil moisture retrieval algorithm.
The availability of a nearly-continuous record of remotely-sensed chlorophyll a data (chl a) from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) mission, now longer than ten years, enables examination of time-series trends for multiple global locations. Innovative data analysis technology available on the World Wide Web facilitates such analyses. In coastal regions influenced by river outflows, chl a is not always indicative of actual trends in phytoplankton chlorophyll due to the interference of colored dissolved organic matter and suspended sediments; significant chl a timeseries trends for coastal regions influenced by river outflows may nonetheless be indicative of important alterations of the hydrologic and coastal environment. Chl a time-series analysis of nine marine regions influenced by river outflows demonstrates the simplicity and usefulness of this technique. The analyses indicate that coastal time-series are significantly influenced by unusual flood events. Major river systems in regions with relatively low human impact did not exhibit significant trends. Most river systems with demonstrated human impact exhibited significant negative trends, with the noteworthy exception of the Pearl River in China, which has a positive trend.
This work deals with the challenge of online adaptive data collection in a time series. A remote sensor or explorer agent adapts its rate of data collection in order to track anomalous events while obeying constraints on time and power. This problem is challenging because the agent has limited visibility (all its datapoints lie in the past) and limited control (it can only decide when to collect its next datapoint). This problem is treated from an information-theoretic perspective, fitting a probabilistic model to collected data and optimizing the future sampling strategy to maximize information gain. The performance characteristics of stationary and nonstationary Gaussian process models are compared. Self-throttling sensors could benefit environmental sensor networks and monitoring as well as robotic exploration. Explorer agents can improve performance by adjusting their data collection rate, preserving scarce power or bandwidth resources during uninteresting times while fully covering anomalous events of interest. For example, a remote earthquake sensor could conserve power by limiting its measurements during normal conditions and increasing its cadence during rare earthquake events. A similar capability could improve sensor platforms traversing a fixed trajectory, such as an exploration rover transect or a deep space flyby. These agents can adapt observation times to improve sample coverage during moments of rapid change. An adaptive sampling approach couples sensor autonomy, instrument interpretation, and sampling. The challenge is addressed as an active learning problem, which already has extensive theoretical treatment in the statistics and machine learning literature. A statistical Gaussian process (GP) model is employed to guide sample decisions that maximize information gain. Nonsta tion - ary (e.g., time-varying) covariance relationships permit the system to represent and track local anomalies, in contrast with current GP approaches. Most common GP models are stationary, e.g., the covariance relationships are time-invariant. In such cases, information gain is independent of previously collected data, and the optimal solution can always be computed in advance. Information-optimal sampling of a stationary GP time series thus reduces to even spacing, and such models are not appropriate for tracking localized anomalies. Additionally, GP model inference can be computationally expensive.
Forests contain a majority of the aboveground carbon (C) found in ecosystems, and understanding biomass lost from disturbance is essential to improve our C-cycle knowledge. Our study region in the Wisconsin and Minnesota Laurentian Forest had a strong decline in Normalized Difference Vegetation Index (NDVI) from 1982 to 2007, observed with the National Ocean and Atmospheric Administration's (NOAA) series of Advanced Very High Resolution Radiometer (AVHRR). To understand the potential role of disturbances in the terrestrial C-cycle, we developed an algorithm to map forest disturbances from either harvest or insect outbreak for Landsat time-series stacks. We merged two image analysis approaches into one algorithm to monitor forest change that included: (1) multiple disturbance index thresholds to capture clear-cut harvest; and (2) a spectral trajectory-based image analysis with multiple confidence interval thresholds to map insect outbreak. We produced 20 maps and evaluated classification accuracy with air-photos and insect air-survey data to understand the performance of our algorithm. We achieved overall accuracies ranging from 65% to 75%, with an average accuracy of 72%. The producer's and user's accuracy ranged from a maximum of 32% to 70% for insect disturbance, 60% to 76% for insect mortality and 82% to 88% for harvested forest, which was the dominant disturbance agent. Forest disturbances accounted for 22% of total forested area (7349 km2). Our algorithm provides a basic approach to map disturbance history where large impacts to forest stands have occurred and highlights the limited spectral sensitivity of Landsat time-series to outbreaks of defoliating insects. We found that only harvest and insect mortality events can be mapped with adequate accuracy with a non-annual Landsat time-series. This limited our land cover understanding of NDVI decline drivers. We demonstrate that to capture more subtle disturbances with spectral trajectories, future observations must be temporally dense to distinguish between type and frequency in heterogeneous landscapes.
Sixty days of Doppler images from the Solar and Heliospheric Observatory (SOHO) / Michelson Doppler Imager (MDI) investigation during the 1996 and 2008 solar minima have been analyzed to show that certain supergranule characteristics (size, size range, and horizontal velocity) exhibit fluctuations of three to five days. Cross-correlating parameters showed a good, positive correlation between supergranulation size and size range, and a moderate, negative correlation between size range and velocity. The size and velocity do exhibit a moderate, negative correlation, but with a small time lag (less than 12 hours). Supergranule sizes during five days of co-temporal data from MDI and the Solar Dynamics Observatory (SDO) / Helioseismic Magnetic Imager (HMI) exhibit similar fluctuations with a high level of correlation between them. This verifies the solar origin of the fluctuations, which cannot be caused by instrumental artifacts according to these observations. Similar fluctuations are also observed in data simulations that model the evolution of the MDI Doppler pattern over a 60-day period. Correlations between the supergranule size and size range time-series derived from the simulated data are similar to those seen in MDI data. A simple toy-model using cumulative, uncorrelated exponential growth and decay patterns at random emergence times produces a time-series similar to the data simulations. The qualitative similarities between the simulated and the observed time-series suggest that the fluctuations arise from stochastic processes occurring within the solar convection zone. This behavior, propagating to surface manifestations of supergranulation, may assist our understanding of magnetic-field-line advection, evolution, and interaction.
Procedure for estimating mean square prediction error for stationary Gaussian time series of unknown covariance
Analysis of ambient aerosols provides valuable insight into particle sources and formation chemistry. However, due to the complexity of atmospheric data and the dynamic nature of aerosol composition, a substantial fraction of data often become discarded by conventional analysis methods. Furthermore, a large fraction of chemical species within those data are unidentifiable due to a lack of matching spectral information, resulting in suboptimal characterization of chemical composition. Previous work has demonstrated techniques for cataloging analytes in a chromatographic dataset by deconvolution of mass spectra, but integration of these analytes throughout a large dataset remains time consuming. Here, we present a method to automatically identify an ion for quantitation for single-ion chromatogram based peak fitting and integration, enabling comprehensive integration of analytes with minimal user interaction. The resulting time series are clustered with a machine-learning based dimensionality reduction technique to systematically investigate the underlying characteristics of the categorized analytes and gain new insights into the chemical composition and physicochemical properties of the unidentifiable analytes. We apply these methods to existing atmospheric datasets collected in Manacapuru, Brazil during the GoAmazon2014/5 campaign to identify new analytes and interpret their variability and transformations in the atmosphere. The analysis results generate 408 time series from cataloged analytes of interest, and the clustering of those time series with spherical k-means results in 8 distinct clusters. We find the analytes form clusters based on their distinct physicochemical properties, demonstrating the method’s ability to systematically identify and selectively filter contaminants and instrumental analytes and characterize the unidentifiable analytes.
Understory fires in Amazon forests alter forest structure, species composition, and the likelihood of future disturbance. The annual extent of fire-damaged forest in Amazonia remains uncertain due to difficulties in separating burning from other types of forest damage in satellite data. We developed a new approach, the Burn Damage and Recovery (BDR) algorithm, to identify fire-related canopy damages using spatial and spectral information from multi-year time series of satellite data. The BDR approach identifies understory fires in intact and logged Amazon forests based on the reduction and recovery of live canopy cover in the years following fire damages and the size and shape of individual understory burn scars. The BDR algorithm was applied to time series of Landsat (1997-2004) and MODIS (2000-2005) data covering one Landsat scene (path/row 226/068) in southern Amazonia and the results were compared to field observations, image-derived burn scars, and independent data on selective logging and deforestation. Landsat resolution was essential for detection of burn scars less than 50 ha, yet these small burns contributed only 12% of all burned forest detected during 1997-2002. MODIS data were suitable for mapping medium (50-500 ha) and large (greater than 500 ha) burn scars that accounted for the majority of all fire-damaged forest in this study. Therefore, moderate resolution satellite data may be suitable to provide estimates of the extent of fire-damaged Amazon forest at a regional scale. In the study region, Landsat-based understory fire damages in 1999 (1508 square kilometers) were an order of magnitude higher than during the 1997-1998 El Nino event (124 square kilometers and 39 square kilometers, respectively), suggesting a different link between climate and understory fires than previously reported for other Amazon regions. The results in this study illustrate the potential to address critical questions concerning climate and fire risk in Amazon forests by applying the BDR algorithm over larger areas and longer image time series.
Concepts of cerebral organization arising from time series analysis of neurophysiological data related to problems of EEG wave process origin
Advancing the capabilities of earthquake nowcasting, the real-time forecasting of seismic activities, remains crucial for reducing casualties. This multifaceted challenge has recently gained attention within the deep learning domain, facilitated by the availability of extensive earthquake datasets. Despite significant advancements, the existing literature on earthquake nowcasting lacks comprehensive evaluations of pre-trained foundation models and modern deep learning architectures; each focuses on a different aspect of data, such as spatial relationships, temporal patterns, and multi-scale dependencies. This paper addresses the mentioned gap by analyzing different architectures and introducing two innovative approaches called Multi Foundation Quake and GNNCoder. We formulate earthquake nowcasting as a time series forecasting problem for the next 14 days within 0.1-degree spatial bins in Southern California. Earthquake time series are generated using the logarithm energy released by quakes, spanning 1986 to 2024. Our comprehensive evaluations demonstrate that our introduced models outperform other custom architectures by effectively capturing temporal-spatial relationships inherent in seismic data. The performance of existing foundation models varies significantly based on the pre-training datasets, emphasizing the need for careful dataset selection. However, we introduce a novel method, Multi Foundation Quake, that achieves the best overall performance by combining a bespoke pattern with Foundation model results handled as auxiliary streams.
Modeling electric power systems with high shares of weather-dependent resources requires tradeoffs between temporal, spatial, and operational resolution. Many studies perform time series aggregation using clustering algorithms to reduce the temporal dimension, but when modeling continent-scale electricity systems that are large enough to contain multiple independent weather systems, this approach requires large numbers of representative periods to minimize errors in regional wind and solar capacity factors. Here, a new optimization-based approach for representative period selection and weighting is introduced that minimizes regional errors in average renewable capacity factors and electricity demand. The method delivers higher regional fidelity with fewer representative periods than alternative clustering methods when applied to wind, solar, and demand profiles for the contiguous United States. When representative periods are selected from multiple weather years, the optimized method reproduces regional averages with lower error than a complete 365-day time series from any single weather year. The method identifies only representative (as opposed to outlying) periods but can be combined with an iterative "stress period" identification approach to guide efficient decision-making considering both average and high-risk weather conditions.
The application of time-series radar measurements to accurately invert the thickness of saline ice is presented in this study. We describe briefly some experimental observations from the CRRELEX 93 campaign of sea ice.
The mathematical structure of the programs written to construct a nonlinear predictive model to forecast solar flux directly from its time series without reference to any underlying solar physics is presented. This method and the programs are written so that one could apply the same technique to forecast other chaotic time series, such as geomagnetic data, attitude and orbit data, and even financial indexes and stock market data. Perhaps the most important application of this technique to flight dynamics is to model Goddard Trajectory Determination System (GTDS) output of residues between observed position of spacecraft and calculated position with no drag (drag flag = off). This would result in a new model of drag working directly from observed data.
Adaptive technique determination of optimum operations for pure prediction of discrete time series with respect to mean square error cost function
Changepoint detection is a vital tool in the application of climate data analysis. Numerous types of climate observation data are most properly represented by functional time series, implying a need for accurate changepoint detection methods applicable to functional time series data. Such data taken at a global scale often contain both spatial heterogeneity and dependence as well as phase (time) misalignment. In this report, we present methods which can detect spatially-dependent changepoints while allowing different estimates of change time and change strength depending on location. Additionally, we provide extensions to this spatially-predicted model which controls for phase variability among observations. Our methods provide the ability to detect a single change, or control for epidemic changes (where a “return-to-normal” change is more likely to be detected than the initial change). We showcase results analyzing the June 1991 eruption of Mt. Pinatubo, where our methods demonstrate the ability to accurately detect both single and epidemic changepoints even in the presence of strong seasonal variability. We find that our spatially-predicted model improves the detection of relevant changepoints versus methods which do not take spatial information into account, and we find that controlling for phase variability helps to control the false discovery rate during the detection process.
A modeling method for the quantitative description of remotely sensed cloud field images is presented. A two-dimensional texture modeling scheme based on one-dimensional time series procedures is adopted for this purpose. The time series procedure used is the seasonal autoregressive, moving average (ARMA) process in Box and Jenkins. Cloud field properties such as directionality, clustering and cloud coverage can be retrieved by this method. It has been demonstrated that a cloud field image can be quantitatively defined by a small set of parameters and synthesized surrogates can be reconstructed from these model parameters. This method enables cloud climatology to be studied quantitatively.