K-ProtoDiff: Key Prototypes-Guided Diffusion for Time Series Generation

I investigated the ability of statistical tests to detect delayed density dependence in series of abundances per generation. I generated time series containing delayed density dependence using two simple population models (a host-parasitoid model and a version of the Ricker equation) and analysed these using the tests for delayed density dependence of Turchin (1990), the lag 2 partial autocorrelation coefficient (PACF) and a novel modification of Pollard et al's (1987) test. All tests of delayed density dependence are of low statistical power, and so any delayed density dependence that is present may frequently be overlooked, particularly with short (< 25 generation) time series. The modification of Pollard et al's test was the best test for detecting delayed density dependence

Quantifying and comparing the performance of methods that detect abrupt changes in climate time series remains challenging due to limited ground-truth data and the complex, nonlinear and stochastic dynamics of the climate system. To address this gap, we present PONDS (Perturbed Observables in Noisy Dynamics Synthesiser), a new software package designed to generate synthetic, climate-like time series for benchmarking and methodological development. PONDS serves three core purposes: (1) mimicking real-world climate shift events through configurable perturbations applied to synthetic or observationally informed dynamical systems; (2) enabling evaluation of abrupt-shift detectors by providing standardized benchmark datasets with known structural and statistical properties; and (3) offering a flexible framework for incorporating alternative time-series generators within a climate-data context.PONDS provides a controlled environment for exploring the detectability of regime shifts under varying assumptions about noise characteristics and complexity of the shift events. This includes the generation of spatio-temporal clusters and time series of customizable configurations. For example, a user can generate shift cluster events that spatially overlap and shift event properties propagate. This bridging tool supports systematic sensitivity analysis and promotes reproducible comparison across detection algorithms.PONDS aims to contribute to the session by offering a modular tool that is able to enhance data-driven abrupt shift detection tools and potential climate tipping points, by providing a benchmark oriented data synthesizer. It further helps to understand the various appearances of practically observed and theoretically expected shift events.

Time series generated from remotely sensed data are important for regional to global monitoring, estimating long-term trends, and analysis of variations due to droughts or other extreme events such as El Nintildeo. Temporal vegetation patterns including phenological states, photosynthetic activity, or biomass estimations are an essential input for climate modeling or the analysis of the carbon cycle. However, long-term analysis requires accurate calibration and error estimation, i.e., the quality of the time series determines its usefulness. Although previous attempts of quality assessment have been made with NOAA-AVHRR data, a first rigorous concept of data quality and validation was introduced with the MODIS sensors. This paper presents the time-series generator (TiSeG), which analyzes the pixel-level quality-assurance science data sets of all gridded MODIS land (MODLand) products suitable for time-series generation. According to user-defined settings, the tool visualizes the spatial and temporal data availability by generating two indices, the number of invalid pixels and the maximum gap length. Quality settings can be modified spatially and temporally to account for regional and seasonal variations of data quality. The user compares several quality settings and masks or interpolates the data gaps. This paper describes the functionality of TiSeG and shows an example of enhanced vegetation index time-series generation with numerous settings for Germany. The example indicates the improvements of time series when the quality information is employed with a critical weighting between data quality and the necessary quantity for meaningful interpolation.

The Dansgaard-Oeschger (DO) events are characteriszed by pronounced abrupt changes in climatic conditions in high northern latitudes. While they have first been discovered in Greenland ice core records, their imprints are global and can be deteced in proxy archives across the globe. They can be considered as the archetype of abrupt climate changes for which empirical evidence exists, but have not yet been fully explained. In this talk I will present some recent results from analyzing ice-core derived time series with a focus on dating uncertainties, from concentual models proposing unerling physical mechanisms, and from comparing spatial patterns of the impacts of the DO events on global atmospheric circulation patterns.&amp;#160;

Effectiveness of the BFAST algorithm for detecting vegetation response patterns in a semi-arid region

Effect of noise and filtering on largest Lyapunov exponent of time series associated with human walking

Addresses the identification of nonlinear systems from output time series, which we have called dynamic modeling. We start by providing the mathematical basis for dynamic modeling and show that it is equivalent to a multivariate nonlinear prediction problem in the reconstructed space. We address the importance of dynamic reconstruction for dynamic modeling. Recognizing that dynamic reconstruction is an ill-defined inverse problem, we describe a regularized radial basis function network for solving the dynamic reconstruction problem. Prior knowledge in the form of smoothness of the mapping is imposed on the solution via regularization. We also show that, in time-series analysis, some form of regularization can be accomplished by using the structure of the time series instead of imposing a smoothness constraint on the cost function. We develop a methodology based on iterated prediction to train the network weights with an error derived through trajectory learning. This method provides a robust performance because during learning the weights are constrained to follow a trajectory. The dynamic invariants estimated from the generated time series are similar to the ones estimated from the original time series, which means that the properties of the attractor have been captured by the neural network. We finally raise the question that generalized delay operators may have advantages in dynamic reconstruction, primarily in cases where the time series is corrupted by noise. We show how to set the recursive parameter of the gamma operator to attenuate noise and preserve the dynamics.

We generate time series from scale-free networks based on a finite-memory random walk traversing the network. These time series reveal topological and functional properties of networks via their temporal correlations. Remarkably, networks with different node-degree mixing patterns exhibit distinct self-similar characteristics. In particular, assortative networks are transformed into time series with long-range correlation, while disassortative networks are transformed into time series exhibiting anticorrelation. These relationships are consistent across a diverse variety of real networks. Moreover, we show that multiscale analysis of these time series can describe and classify various physical networks ranging from social and technological to biological networks according to their functional origin. These results suggest that there is a unified dynamical mechanism that governs the structural organization of many seemingly different networks.

Field observations and time series of vegetation greenness data from satellites provide evidence of changes in terrestrial vegetation activity over the past decades for several regions in the world. Changes in vegetation greenness over time may consist of an alternating sequence of greening and/or browning periods. This study examined this effect using detection of trend changes in normalized difference vegetation index (NDVI) satellite data between 1982 and 2008. Time series of 648 fortnightly images were analyzed using a trend breaks analysis (BFAST) procedure. Both abrupt and gradual changes were detected in large parts of the world, especially in (semi‐arid) shrubland and grassland biomes where abrupt greening was often followed by gradual browning. Many abrupt changes were found around large‐scale natural influences like the Mt Pinatubo eruption in 1991 and the strong 1997/98 El Niño event. The net global figure – considered over the full length of the time series – showed greening since the 1980s. This is in line with previous studies, but the change rates for individual short‐term segments were found to be up to five times higher. Temporal analysis indicated that the area with browning trends increased over time while the area with greening trends decreased. The Southern Hemisphere showed the strongest evidence of browning. Here, periods of gradual browning were generally longer than periods of gradual greening. Net greening was detected in all biomes, most conspicuously in croplands and least conspicuously in needleleaf forests. For 15% of the global land area, trends were found to change between greening and browning within the analysis period. This demonstrates the importance of accounting for trend changes when analyzing long‐term NDVI time series.

Earth observation (EO) data play a crucial role in monitoring ecosystems and environmental processes. Time series of satellite data are essential for long-term studies in this context. Working with large volumes of satellite data, however, can still be a challenge, as the computational environment with respect to storage, processing and data handling can be demanding, which sometimes can be perceived as a barrier when using EO data for scientific purposes. In particular, open-source developments which comprise all components of EO data handling and analysis are still scarce. To overcome this difficulty, we present Tools for Analyzing Time Series of Satellite Imagery (TATSSI), an open-source platform written in Python that provides routines for downloading, generating, gap-filling, smoothing, analyzing and exporting EO time series. Since TATSSI integrates quality assessment and quality control flags when generating time series, data quality analysis is the backbone of any analysis made with the platform. We discuss TATSSI’s 3-layered architecture (data handling, engine and three application programming interfaces (API)); by allowing three APIs (a native graphical user interface, some Jupyter Notebooks and the Python command line) this development is exceptionally user-friendly. Furthermore, to demonstrate the application potential of TATSSI, we evaluated MODIS time series data for three case studies (irrigation area changes, evaluation of moisture dynamics in a wetland ecosystem and vegetation monitoring in a burned area) in different geographical regions of Mexico. Our analyses were based on methods such as the spatio-temporal distribution of maxima over time, statistical trend analysis and change-point decomposition, all of which were implemented in TATSSI. Our results are consistent with other scientific studies and results in these areas and with related in-situ data.

Atmospheric propagation channels of satellite-to-ground optical links are hard to model and are rather represented with time series generated using complex emulators. In this paper, we propose a simple framework which, from an arbitrary time series, generates rapidly similar series that exhibit the same system-level performance. The goal of such generated time series is not to model differently the channel but rather to assist in analysing the system performance (synchronization, error correction code, interleaving . . . ) and also in evaluating equipment behavior for free-space laser propagation through atmospheric turbulence.

The lack of data samples of performance degradation often makes it difficult to accurately determine the timing of maintenance for electromechanical device. To tackle the issue, A multi-scale fusion prediction method for time series using Transfer Learning-Generative Adversarial Nets (TL-GAN) is proposed. TL-GAN is employed to generate time series of performance degradation, and the migratable sample of the source domain is then superimposed on the domain difference of the generative time series to obtain the sample of the target domain. The wavelet decomposition is utilized to divide the time series into trend series and detailed series. Consequently, the multiscale fusion is performed to reconstruct the synthetic time series, which is used for the prediction process. The results demonstrate that the multi-scale fusion prediction model reduces the prediction error by approximately 10% compared to traditional prediction models such as Gate Recurrent Unit (GRU) model and thus supports the effectiveness of the proposed method in small sample conditions.

In this paper, time series of length T are seen as frequency distributions. Each distribution is defined with respect to a statistical variable having T observed values. A methodological system based on Gini’s approach is put forward, so the statistical model through which time series are handled is a frequency distribution studied inside a linear system. In addition to the starting frequency distributions that are observed, other frequency distributions are treated. Thus, marginal distributions based on the notion of proportionality are introduced together with joint distributions. Both distributions are statistical models. A fundamental invariance property related to marginal distributions is made explicit in this research work, so one can focus on collections of marginal frequency distributions, identifying multiple frequency distributions. For this reason, the latter is studied via a tensor. As frequency distributions are practical realizations of nonparametric probability distributions over R, one passes from frequency distributions to discrete random variables. In this paper, a mathematical model that generates time series is put forward. It is a stochastic process based on subjective previsions of random variables. A subdivision of the exchangeability of variables of a statistical nature is shown, so a reinterpretation of principal component analysis that is based on the notion of proportionality also characterizes this research work.

The analysis of annual precipitation evolution characteristics is of great value and significance for revealing the spatial and temporal variation patterns of regional precipitation, water resources development and utilization, short-term climate, drought, flood disaster prediction, etc. The Mann-Kendall (MK) mutation test, cumulative distance level method, and Morlet wavelet analysis were used to analyze the precipitation evolution in Anhui Province from 1961 to 2020. The results showed that the average annual temperature and precipitation in Anhui Province showed a significant increasing trend during 1961–2020, with warming and humidification. 1994 was the year of abrupt climate change in Anhui Province, and the temperature after the abrupt change was 2.10 times that before the abrupt change. El Niño-Southern Oscillation (ENSO) has a synchronized resonance cycle with droughts and floods in Anhui Province at 5.8 a. The annual scale of ENSO events is an important theoretical support for regional drought and flood warnings. The chance of drought and flooding in Anhui Province is greater than 50% in the year of ENSO event or two years after the event, and the year of ENSO event or the year after is prone to drought and flooding, so we should strengthen the flood and drought warning, disaster prevention and mitigation.

The successful launch of the Sentinel-2 constellation satellite, along with advanced cloud detection algorithms, has enabled the generation of continuous time series at high spatial and temporal resolutions, which is in turn expected to enable the classification of salt marsh vegetation over larger spatiotemporal scales. This study presents a critical comparison of vegetation index (VI) and curve fitting methods—two key factors for time series construction that potentially influence vegetation classification performance. To accomplish this objective, the stability of five different VI time series, namely Normalized Difference Vegetation Index (NDVI), Soil-Adjusted Vegetation Index (SAVI), Enhanced Vegetation Index (EVI), Green Normalized Difference Vegetation Index (GNDVI), and Water-Adjusted Vegetation Index (WAVI), was compared empirically; the suitability between three curve fitting methods, namely Asymmetric Gaussian (AG), Double Logistic (DL), and Two-term Fourier (TF), and VI time series was measured using the coefficient of determination, and the salt marsh vegetation separability among different combinations of VI time series and curve fitting methods (i.e., VI time series-based curve fitting model) was quantified using overall the Jeffries–Matusita distance. Six common types of salt marsh vegetation from three typical coastal sites in China were used to validate these findings, which demonstrate: (1) the SAVI performed best in terms of time series stability, while the EVI exhibited relatively poor time series stability with conspicuous outliers induced by the sensitivity to omitted clouds and shadows; (2) the DL method commonly resulted in the most accurate classification of different salt marsh vegetation types, especially when combined with the EVI time series, followed by the TF method; and (3) the SAVI/NDVI-based DL/TF model demonstrated comparable efficiency for classifying salt marsh vegetation. Notably, the SAVI/NDVI-based DL model performed most strongly for high latitude regions with a continental climate, whilst the SAVI/NDVI-based TF model appears to be better suited to mid- to low latitude regions dominated by a monsoonal climate.