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GPS Position Time Series @ JPL

Different flavors of GPS time series analysis at JPL - Use same GPS Precise Point Positioning Analysis raw time series - Variations in time series analysis/post-processing driven by different users. center dot JPL Global Time Series/Velocities - researchers studying reference frame, combining with VLBI/SLR/DORIS center dot JPL/SOPAC Combined Time Series/Velocities - crustal deformation for tectonic, volcanic, ground water studies center dot ARIA Time Series/Coseismic Data Products - Hazard monitoring and response focused center dot ARIA data system designed to integrate GPS and InSAR - GPS tropospheric delay used for correcting InSAR - Caltech's GIANT time series analysis uses GPS to correct orbital errors in InSAR - Zhen Liu's talking tomorrow on InSAR Time Series analysis

Precise Point Positioning (PPP)

Detection of chaotic determinism in time series from randomly forced maps

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center

Load Balancing Using Time Series Analysis for Soft Real Time Systems with Statistically Periodic Loads

This thesis provides design and analysis of techniques for global load balancing on ensemble architectures running soft-real-time object-oriented applications with statistically periodic loads. It focuses on estimating the instantaneous average load over all the processing elements. The major contribution is the use of explicit stochastic process models for both the loading and the averaging itself. These models are exploited via statistical time-series analysis and Bayesian inference to provide improved average load estimates, and thus to facilitate global load balancing. This thesis explains the distributed algorithms used and provides some optimality results. It also describes the algorithms' implementation and gives performance results from simulation. These results show that our techniques allow more accurate estimation of the global system load ing, resulting in fewer object migration than local methods. Our method is shown to provide superior performance, relative not only to static load-balancing schemes but also to many adaptive methods.

REAL TIME

A Preferences Corpus and Annotation Scheme for Human-Guided Alignment of Time-Series GPTs

The process of time-series forecasting such as predicting trajectories of silicon content in blast furnaces is a difficult task. Most time-series approaches today focus on scalar-type MSE loss optimization. This optimization approach, while widely common, could benefit from the use of human expert or process-level preferences. In this paper, we introduce a novel alignment and fine-tuning approach that involves learning from a corpus of preferred and dis-preferred time-series prediction trajectories. Our contributions include (1) a preference annotation pipeline for time-series forecasts, (2) the application of Score-based Preference Optimization (SPO) to train decoder-only transformers from preferences, and (3) results showing improvements in forecast quality. The approach is validated on both proprietary blast furnace data and the UCI Appliances Energy dataset. The proposed preference corpus and training strategy offer a new option for fine-tuning sequence models in industrial settings.

DPO

A Waveform Skewness Index for Measuring Time Series Nonlinearity and Its Applications to the ENSO-Indian Monsoon Relationship

Many geophysical time series possess nonlinear characteristics that reflect the underlying physics of the phenomena the time series describe. The nonlinear character of times series can change with time, so it is important to quantify time series nonlinearity without assuming stationarity. A common way of quantifying the time evolution of time series nonlinearity is to compute sliding skewness time series, but it is shown here that such an approach can be misleading when time series contain periodicities. To remedy this deficiency of skewness, a new waveform skewness index is proposed for quantifying local nonlinearities embedded in time series. A waveform skewness spectrum is proposed for determining the frequency components that are contributing to time series waveform skewness. The new methods are applied to the El Niño–Southern Oscillation (ENSO) and the Indian monsoon to test a recently proposed hypothesis that states that changes in the ENSO–Indian monsoon relationship are related to ENSO nonlinearity. We show that the ENSO–Indian rainfall relationship weakens during time periods of high ENSO waveform skewness. The results from two different analyses suggest that the breakdown of the ENSO–Indian monsoon relationship during time periods of high ENSO waveform skewness is related to the more frequent occurrence of strong central Pacific El Niño events, supporting arguments that changes in the ENSO–Indian rainfall relationship are not solely related to noise.

Justin Schulte

Time Series Analysis of Insar Data: Methods and Trends

Time series analysis of InSAR data has emerged as an important tool for monitoring and measuring the displacement of the Earth's surface. Changes in the Earth's surface can result from a wide range of phenomena such as earthquakes, volcanoes, landslides, variations in ground water levels, and changes in wetland water levels. Time series analysis is applied to interferometric phase measurements, which wrap around when the observed motion is larger than one-half of the radar wavelength. Thus, the spatio-temporal ''unwrapping" of phase observations is necessary to obtain physically meaningful results. Several different algorithms have been developed for time series analysis of InSAR data to solve for this ambiguity. These algorithms may employ different models for time series analysis, but they all generate a first-order deformation rate, which can be compared to each other. However, there is no single algorithm that can provide optimal results in all cases. Since time series analyses of InSAR data are used in a variety of applications with different characteristics, each algorithm possesses inherently unique strengths and weaknesses. In this review article, following a brief overview of InSAR technology, we discuss several algorithms developed for time series analysis of InSAR data using an example set of results for measuring subsidence rates in Mexico City.

InSAR

SigTime: Learning and Visually Explaining Time Series Signatures

Understanding and distinguishing temporal patterns in time series data is essential for scientific discovery and decision-making. For example, in biomedical research, uncovering meaningful patterns in physiological signals can improve diagnosis, risk assessment, and patient outcomes. However, existing methods for time series pattern discovery face major challenges, including high computational complexity, limited interpretability, and difficulty in capturing meaningful temporal structures. Here, to address these gaps, we introduce a novel learning framework that jointly trains two Transformer models using complementary time series representations: shapelet-based representations to capture localized temporal structures and traditional feature engineering to encode statistical properties. The learned shapelets serve as interpretable signatures that differentiate time series across classification labels. Additionally, we develop a visual analytics system—SigTime—with coordinated views to facilitate exploration of time series signatures from multiple perspectives, aiding in useful insights generation. We quantitatively evaluate our learning framework on eight publicly available datasets and one proprietary clinical dataset. Additionally, we demonstrate the effectiveness of our system through two usage scenarios along with the domain experts: one involving public ECG data and the other focused on preterm labor analysis.

97 MATHEMATICS AND COMPUTING

Deep learning for time series forecasting: a survey of recent advances

Time series forecasting plays a critical role in numerous real-world applications, such as finance, healthcare, transportation, and scientific computing. In recent years, deep learning has become a powerful tool for modeling complex temporal patterns and improving forecasting accuracy. This survey provides an overview of recent deep learning approaches for time series forecasting, involving various architectures including RNNs, CNNs, GNNs, transformers, large language models, MLP-based models, and diffusion models. We first identify key challenges in the field, such as temporal dependency, efficiency, and cross-variable dependency, which drive the development of forecasting techniques. Then, the general advantages and limitations of each architecture are discussed to contextualize their adaptation in time series forecasting. Furthermore, we highlight promising design trends like multi-scale modeling, decomposition, and frequency-domain techniques, which are shaping the future of the field. This paper serves as a compact reference for researchers and practitioners seeking to understand the current landscape and future trajectory of deep learning in time series forecasting.

97 MATHEMATICS AND COMPUTING

Simulation of Ground Winds Time Series for the NASA Crew Launch Vehicle (CLV)

Simulation of wind time series based on power spectrum density (PSD) and spectral coherence models for ground wind turbulence is described. The wind models, originally developed for the Shuttle program, are based on wind measurements at the NASA 150-m meteorological tower at Cape Canaveral, FL. The current application is for the design and/or protection of the CLV from wind effects during on-pad exposure during periods from as long as days prior to launch, to seconds or minutes just prior to launch and seconds after launch. The evaluation of vehicle response to wind will influence the design and operation of constraint systems for support of the on-pad vehicle. Longitudinal and lateral wind component time series are simulated at critical vehicle locations. The PSD model for wind turbulence is a function of mean wind speed, elevation and temporal frequency. Integration of the PSD equation over a selected frequency range yields the variance of the time series to be simulated. The square root of the PSD defines a low-pass filter that is applied to adjust the components of the Fast Fourier Transform (FFT) of Gaussian white noise. The first simulated time series near the top of the launch vehicle is the inverse transform of the adjusted FFT. Simulation of the wind component time series at the nearest adjacent location (and all other succeeding next nearest locations) is based on a model for the coherence between winds at two locations as a function of frequency and separation distance, where the adjacent locations are separated vertically and/or horizontally. The coherence function is used to calculate a coherence weighted FFT of the wind at the next nearest location, given the FFT of the simulated time series at the previous location and the essentially incoherent FFT of the wind at the selected location derived a priori from the PSD model. The simulated time series at each adjacent location is the inverse Fourier transform of the coherence weighted FFT. For a selected design case, the equations, the process and the simulated time series at multiple vehicle stations are presented.

Adelfang, Stanley I.

Assessing methods in fusion and fitting for time series construction in remote sensing-based earth observations

This study evaluates the comparative performance of spatiotemporal fusion and time-series fitting methods for constructing high-spatiotemporal-resolution remote sensing time-series data. Due to in-class similarity of fusion methods and fitting methods, we employ the Fit-FC (Fitting, spatial Filtering, and residual Compensation) model as a representative fusion method and the linear harmonic fitting model as a representative fitting method. Both Fit-FC and the linear harmonic fitting are widely used for high-spatiotemporal-resolution time-series data construction, and we modify the original Fit-FC model to enable automatic time-series fusion. To ensure data representativeness, we use 3 years (2019–2021) of Harmonized Landsat and Sentinel-2 surface reflectance datasets and Terra MCD43A4 products. Eight experimental regions are selected worldwide to guarantee generalization of the comparative performance between fusion and fitting methods, covering diverse land-use types (cropland, developed land, forest, and grassland) and varying climatological conditions. Time-series of NDVI and surface reflectance are analyzed under both actual observations and simulated data-missing scenarios. The constructed time-series data reveals that (1) the modified Fit-FC and linear harmonic fitting model achieve excellent performance in constructing high-resolution time-series images; (2) the fusion method outperforms the fitting method in constructing time-series of NDVI and surface reflectance images in cropland-, forest-, and grassland-dominated regions; (3) both methods achieve comparable performance in developed-dominated regions; (4) the fusion method is more robust to missing data, and better captures abrupt phenological transitions under conditions of continuous missing data; (5) the fitting method is computationally more efficient, making it suitable for large-scale time-series image reconstruction. This study provides valuable insights for selecting optimal strategies to generate high-resolution time-series images across diverse application scenarios and lays a foundation for extensions to other vegetation indices or land surface variables.

54 ENVIRONMENTAL SCIENCES

Fast and Flexible Multivariate Time Series Subsequence Search

Multivariate Time-Series (MTS) are ubiquitous, and are generated in areas as disparate as sensor recordings in aerospace systems, music and video streams, medical monitoring, and financial systems. Domain experts are often interested in searching for interesting multivariate patterns from these MTS databases which often contain several gigabytes of data. Surprisingly, research on MTS search is very limited. Most of the existing work only supports queries with the same length of data, or queries on a fixed set of variables. In this paper, we propose an efficient and flexible subsequence search framework for massive MTS databases, that, for the first time, enables querying on any subset of variables with arbitrary time delays between them. We propose two algorithms to solve this problem (1) a List Based Search (LBS) algorithm which uses sorted lists for indexing, and (2) a R*-tree Based Search (RBS) which uses Minimum Bounding Rectangles (MBR) to organize the subsequences. Both algorithms guarantee that all matching patterns within the specified thresholds will be returned (no false dismissals). The very few false alarms can be removed by a post-processing step. Since our framework is also capable of Univariate Time-Series (UTS) subsequence search, we first demonstrate the efficiency of our algorithms on several UTS datasets previously used in the literature. We follow this up with experiments using two large MTS databases from the aviation domain, each containing several millions of observations. Both these tests show that our algorithms have very high prune rates (>99%) thus needing actual disk access for only less than 1% of the observations. To the best of our knowledge, MTS subsequence search has never been attempted on datasets of the size we have used in this paper.

Bhaduri, Kanishka

Using NASA's Giovanni System to Simulate Time-Series Stations in the Outflow Region of California's Eel River

Oceanographic time-series stations provide vital data for the monitoring of oceanic processes, particularly those associated with trends over time and interannual variability. There are likely numerous locations where the establishment of a time-series station would be desirable, but for reasons of funding or logistics, such establishment may not be feasible. An alternative to an operational time-series station is monitoring of sites via remote sensing. In this study, the NASA Giovanni data system is employed to simulate the establishment of two time-series stations near the outflow region of California s Eel River, which carries a high sediment load. Previous time-series analysis of this location (Acker et al. 2009) indicated that remotely-sensed chl a exhibits a statistically significant increasing trend during summer (low flow) months, but no apparent trend during winter (high flow) months. Examination of several newly-available ocean data parameters in Giovanni, including 8-day resolution data, demonstrates the differences in ocean parameter trends at the two locations compared to regionally-averaged time-series. The hypothesis that the increased summer chl a values are related to increasing SST is evaluated, and the signature of the Eel River plume is defined with ocean optical parameters.

Acker, James G.

Remote-Sensing Time Series Analysis, a Vegetation Monitoring Tool

The Time Series Product Tool (TSPT) is software, developed in MATLAB , which creates and displays high signal-to- noise Vegetation Indices imagery and other higher-level products derived from remotely sensed data. This tool enables automated, rapid, large-scale regional surveillance of crops, forests, and other vegetation. TSPT temporally processes high-revisit-rate satellite imagery produced by the Moderate Resolution Imaging Spectroradiometer (MODIS) and by other remote-sensing systems. Although MODIS imagery is acquired daily, cloudiness and other sources of noise can greatly reduce the effective temporal resolution. To improve cloud statistics, the TSPT combines MODIS data from multiple satellites (Aqua and Terra). The TSPT produces MODIS products as single time-frame and multitemporal change images, as time-series plots at a selected location, or as temporally processed image videos. Using the TSPT program, MODIS metadata is used to remove and/or correct bad and suspect data. Bad pixel removal, multiple satellite data fusion, and temporal processing techniques create high-quality plots and animated image video sequences that depict changes in vegetation greenness. This tool provides several temporal processing options not found in other comparable imaging software tools. Because the framework to generate and use other algorithms is established, small modifications to this tool will enable the use of a large range of remotely sensed data types. An effective remote-sensing crop monitoring system must be able to detect subtle changes in plant health in the earliest stages, before the effects of a disease outbreak or other adverse environmental conditions can become widespread and devastating. The integration of the time series analysis tool with ground-based information, soil types, crop types, meteorological data, and crop growth models in a Geographic Information System, could provide the foundation for a large-area crop-surveillance system that could identify a variety of plant phenomena and improve monitoring capabilities.

McKellip, Rodney

Studies in astronomical time series analysis: Modeling random processes in the time domain

Random process models phased in the time domain are used to analyze astrophysical time series data produced by random processes. A moving average (MA) model represents the data as a sequence of pulses occurring randomly in time, with random amplitudes. An autoregressive (AR) model represents the correlations in the process in terms of a linear function of past values. The best AR model is determined from sampled data and transformed to an MA for interpretation. The randomness of the pulse amplitudes is maximized by a FORTRAN algorithm which is relatively stable numerically. Results of test cases are given to study the effects of adding noise and of different distributions for the pulse amplitudes. A preliminary analysis of the optical light curve of the quasar 3C 273 is given.

Scargle, J. D.

The Relationship Between El Nino/La Nina Oscillations and Recent Anomaly Time Series of OLR Determined by CERES and AIRS

This paper compares recent spatial anomaly time series of OLR (Outgoing Longwave Radiation) and OLRCLR (Clear Sky OLR) as determined using CERES and AIRS observations over the time period September 2002 through June 2010. We find excellent agreement in OLR anomaly time series of both data sets in almost every detail, down to the 1 x 1 spatial grid point level. This extremely close agreement of OLR anomaly time series derived from observations by two different instruments implies that both sets of results must be highly stable. This agreement also validates to some extent the anomaly time series of the AIRS derived products used in the computation of the AIRS OLR product. The paper then examines anomaly time series of AIRS derived products over the extended time period September 2002 through April 2011. We show that OLR anomalies during this period are closely in phase with those of an El Nino index, and that the recent global and tropical mean decreases in OLR and OLRCLR are a result of a transition from an El Nino condition at the beginning of the data record to La Nina conditions toward the end of the data period. We show that the relationship between global mean, and especially tropical mean, OLR anomalies to the El Nino index can be explained by temporal changes of the distribution of mid-tropospheric water vapor and cloud cover in two spatial regions that are in direct response to El Nino/La Nina activity which occurs outside these spatial regions.

Susskind, Joel

Short-Term Chromospheric Variability in alpha Tauri (K5 III): Results from IUE Time Series Observations

We evaluate time series observations of chromospheric lines (Mg II, Mg I, and C II) for the K giant alpha Tau obtained using the IUE LWP camera at high dispersion. These observations cover a time span of about 2 weeks in 1994 February-March and were designed to resolve variations occurring within hours, days, and weeks. We consider the observational results in relation to theoretical acoustic heating models, motivated by the fact that alpha Tau may exhibit a basal (i.e., minimum) level of chromospheric activity. The data reveal flux variations between the extremes of 8% in Mg II h+k and 15% in each emission component. These variations occur on timescales as short as 8 hr but not on timescales longer than approx.3 days. For the h and k components, flux variations occurring on a timescale as short as 1.5 hr are also found. These changes are often not correlated (and are sometimes even anticorrelated), leading to remarkable differences in the h/k ratios. We argue that these results are consistent with the presence of strong acoustic shocks, which can lead to variable Mg II line emission when only a small number of strong shocks are propagating through the atmosphere. We deduce the electron density in the C II lambda 2325 line formation region to be log(base e) of N. approx. equals 9.0, in agreement with previous studies. Our data provide evidence that the Mg II basal flux limit for K giants might be a factor of 4 higher than suggested by Rutten et al.

Cuntz, Manfred

Time‐Series Analysis: A Cautionary Tale

Time-series analysis has often been a useful tool in atmospheric science for deriving long-term trends in various atmospherically important parameters (e.g., temperature or the concentration of trace gas species). In particular, time-series analysis has been repeatedly applied to satellite datasets in order to derive the long-term trends in stratospheric ozone, which is a critical atmospheric constituent. However, many of the potential pitfalls relating to the non-uniform sampling of the datasets were often ignored and the results presented by the scientific community have been unknowingly biased. A newly developed and more robust application of this technique is applied to the Stratospheric Aerosol and Gas Experiment (SAGE) II version 7.0 ozone dataset and the previous biases and newly derived trends are presented.

Damadeo, Robert

Intercomparison of Recent Anomaly Time-Series of OLR as Observed by CERES and Computed Using AIRS Products

This paper compares recent spatial and temporal anomaly time series of OLR as observed by CERES and computed based on AIRS retrieved surface and atmospheric geophysical parameters over the 7 year time period September 2002 through February 2010. This time period is marked by a substantial decrease of OLR, on the order of +/-0.1 W/sq m/yr, averaged over the globe, and very large spatial variations of changes in OLR in the tropics, with local values ranging from -2.8 W/sq m/yr to +3.1 W/sq m/yr. Global and Tropical OLR both began to decrease significantly at the onset of a strong La Ni a in mid-2007. Late 2009 is characterized by a strong El Ni o, with a corresponding change in sign of both Tropical and Global OLR anomalies. The spatial patterns of the 7 year short term changes in AIRS and CERES OLR have a spatial correlation of 0.97 and slopes of the linear least squares fits of anomaly time series averaged over different spatial regions agree on the order of +/-0.01 W/sq m/yr. This essentially perfect agreement of OLR anomaly time series derived from observations by two different instruments, determined in totally independent and different manners, implies that both sets of results must be highly stable. This agreement also validates the anomaly time series of the AIRS derived products used to compute OLR and furthermore indicates that anomaly time series of AIRS derived products can be used to explain the factors contributing to anomaly time series of OLR.

Susskind, Joel