Spatial Time Series Data Research Articles

Spatial association measures for time series with fixed spatial locations

Spatial time series (STS), which refers to time-series data collected at fixed spatial locations, is crucial for understanding the spatiotemporal dynamics of geographical phenomena. Measuring the spatial association based on STS similarity provides valuable insights into the exploratory analysis of spatiotemporal data. However, existing methods are not effective in accurately quantifying such spatial association. To address this gap, this study proposes a conceptual model and a statistical method for identifying spatial clusters that exhibit significantly similar time-varying characteristics within a set of STS data. Conceptually, three representative patterns are defined: positive, negative, and no associations. A positive pattern occurs when spatially adjacent STSs show similar time-varying characteristics, while a negative pattern occurs when they show dissimilar ones. Technically, this study introduces a distance metric to measure similarities among STSs. The spatial association of STS at global and local scales is quantified according to the spatial concentration of these similarities. The validity and applicability of the proposed statistics are verified through synthetic and real-world examples, demonstrating their potential as effective tools for understanding spatiotemporal dynamics from a new perspective.

Insights into Boreal Forest Disturbance from Canopy Stability Index

The world’s forests are being increasingly disturbed from exposure to the compounding impacts of land use and climate change, in addition to natural disturbance regimes. Boreal forests have a lower level of deforestation compared to tropical forests, and while they have higher levels of natural disturbances, the accumulated impact of forest management for commodity production coupled with worsening fire weather conditions and other climate-related stressors is resulting in ecosystem degradation and loss of biodiversity. We used satellite-based time-series analysis of two canopy indices—canopy photosynthesis and canopy water stress—to calculate an index that maps the relative stability of forest canopies in the Canadian provinces of Ontario and Quebec. By drawing upon available spatial time-series data on logging, wildfire, and insect infestation impacts, we were able to attribute the causal determinants of areas identified as having unstable forest canopy. The slope of the two indices that comprise the stability index also provided information as to where the forest is recovering from prior disturbances. The stability analyses and associated spatial datasets are available in an interactive web-based mapping app. that can be used to map disturbed forest canopies and the attribution of disturbances to human or natural causes. This information can assist decision-makers in identifying areas that are potentially ecologically degraded and in need of restoration and those stable areas that are a priority for protection.

Advancing Process-Oriented Geographical Regionalization Model

Existing regionalization methods have largely overlooked the temporal dimension, leading to outcomes that predominantly reflect spatial differentiation of regional variables only at a singular temporal instance, rather than across their entire evolutionary process. In response, this research proposes a novel model for geographic process regionalization based on spatial time-series (STS) data. This model is designed to amalgamate adjacent entities exhibiting analogous trends in regional variable fluctuations, while segregating those with disparate trajectories. The study starts by establishing methodologies for the assessment of three distinct types of STS data similarities: value-based, shape-oriented, and periodic patterns. Following this, a tailored regionalization methodology specific to STS data is delineated. This methodology facilitates a quantitative analysis of time-series variables within each geographical region, leading to the development of a process-oriented geographic boundary model (GBM). The efficacy of this model is validated through empirical testing with synthetic data sets and further elucidated via case studies focusing on the dynamics of population and pollution levels, underscoring its substantial applicability in both human and physical geography. The proposed methodology is adaptable for any time-series data that incorporate locational information for regionalization.

Higher-Order Convolutional Neural Networks for Essential Climate Variables Forecasting

Earth observation imaging technologies, particularly multispectral sensors, produce extensive high-dimensional data over time, thus offering a wealth of information on global dynamics. These data encapsulate crucial information in essential climate variables, such as varying levels of soil moisture and temperature. However, current cutting-edge machine learning models, including deep learning ones, often overlook the treasure trove of multidimensional data, thus analyzing each variable in isolation and losing critical interconnected information. In our study, we enhance conventional convolutional neural network models, specifically those based on the embedded temporal convolutional network framework, thus transforming them into models that inherently understand and interpret multidimensional correlations and dependencies. This transformation involves recasting the existing problem as a generalized case of N-dimensional observation analysis, which is followed by deriving essential forward and backward pass equations through tensor decompositions and compounded convolutions. Consequently, we adapt integral components of established embedded temporal convolutional network models, like encoder and decoder networks, thus enabling them to process 4D spatial time series data that encompass all essential climate variables concurrently. Through the rigorous exploration of diverse model architectures and an extensive evaluation of their forecasting prowess against top-tier methods, we utilize two new, long-term essential climate variables datasets with monthly intervals extending over four decades. Our empirical scrutiny, particularly focusing on soil temperature data, unveils that the innovative high-dimensional embedded temporal convolutional network model-centric approaches markedly excel in forecasting, thus surpassing their low-dimensional counterparts, even under the most challenging conditions characterized by a notable paucity of training data.

Integrated surrogate framework for reactive transport simulation of uranium in situ leaching with generative models

The heterogeneity of uranium-bearing aquifers plays a crucial role in governing the migration and leaching of uranium. Uncertainty quantification (UQ) based on the Monte Carlo method is usually used to deal with the issue of aquifer heterogeneity. However, the substantial computational costs of this method arise from a large number of calls to the uranium reactive transport simulation; therefore, surrogate models are developed to reduce these costs. This study leverages a conditional deep convolutional generative adversarial network (cDC-GAN) and an adversarial autoencoder-based kriging regression (AAE-KRG) to develop an integrated surrogate framework for uranium reactive transport simulation. cDC-GAN and AAE-KRG are designed to achieve the cross-domain mapping of the permeability coefficient field to the uranium spatial distribution and leaching concentration over time, respectively. The results demonstrate a structural similarity exceeding 0.9 between the cDC-GAN and the numerical simulation, with a mean square error generally less than 0.002. These findings suggest that the cDC-GAN exhibits high accuracy and stability in terms of replacing the numerical simulation to obtain the spatial-temporal evolution of the uranium plume. Additionally, cDC-GAN is a dynamic surrogate model with the capability of interpolation because uranium spatial distributions with multiple time steps are used as training data during the training process. AAE-KRG also exhibits high accuracy and stability in terms of predicting the leaching concentration by permeability coefficient fields, as evidenced by determination coefficients generally exceeding 0.95. By comparing the computational costs, it is clear that cDC-GAN and AAE-KRG are suitable for processing spatial distribution and time series data, respectively. The trained surrogate models are used to undertake UQ of the uranium leaching area and leaching concentration. The results indicate that the uncertainty of the leaching area in the field-test model increases with time, and the increasing rate reaches a maximum in the middle period (201–300 d). The uncertainty of the leaching concentration increases with time in the early period, decreases after peaking at 137 d, and stabilizes in the middle and late periods. It is observed that the change characteristics of the uncertainty are consistent with the values of the leaching area or concentration. Furthermore, the spatial distribution pattern of uranium pollution is determined based on stochastic simulation results. The uncertainty intervals and the pollution risk status at multiple time steps are quickly obtained by surrogate models, which is helpful for scheme optimization in uranium mining. Owing to its characteristics of being data-driven and highly adaptable to nonlinear data, the integrated surrogate framework has applications beyond uranium in situ leaching.

Generation of Spatial Time Series Data

In the era of deep learning, global-local deep neural networks are gradually replacing statistical approaches for time-series forecasting, especially for the spatiotemporal modeling field. However, the development of such methods is hindered by the lack of open benchmark datasets in this research domain. Generating synthetic data is an alternative solution to data collection, but prior works focus mainly on generating uncorrelated independent time series. In this work, we present a method for spatially correlated time-series generation. It uses a set of parametric autoregressive models for univariate time series generation in combination with the approach for sampling model parameters which allows one to simulate spatial relationships. We describe its implementation and conduct experiments showing the validity of the data for spatiotemporal modeling.

SeeLevelViz: A simple data science tool for dynamic visualization of shoreline displacement caused by sea-level change

We present SeeLevelViz, a free, open-source program written in Python for making interactive visualizations of relative sea-level change in landscapes and shorelines. The accurate reconstruction of shoreline positions is a crucial factor in coastal palaeolandscape studies, particularly in areas where the coast is fronted by islands, since the separation of islands from the mainland drives important ecological and sociocultural outcomes. This program creates accurate time-slice reconstructions of shoreline positions and palaeolandscapes when the user provides two components: 1) a digital elevation model of the target region (including currently submerged areas), and 2) a simple spreadsheet of relative sea-level elevations at different dates derived either from a glacio isostatic adjustment model of relative sea-level change, or from observed past sea-level data points. The tool is presented using the eastern coast of the Adriatic Sea in the Mediterranean as a test case, since this region has a complex coastline articulation due to combined geological and geomorphological factors. In this area, like in many other Mediterranean coastal areas, the separation of islands from the mainland following the last glacial maximum and throughout the Holocene has occurred in connection with important phases of the development, particularly of Mesolithic and Neolithic cultures, influencing human migrations and the spread of seafaring techniques. Reliable palaeolandscape reconstructions at different time slices are thus crucial for supporting archaeological interpretation. Flexibile and user-friendly, SeeLevelViz can compliment reconstructions of coastal landscape changes either based on glacial isostatic adjustment models or on relative palaeo-sea- level evidence, since simple, interactive visualizations are a powerful technique for understanding spatial time-series data, both for the interpretation phase of research, and for presentation to colleagues and the public. The program can be modified or used freely for papers, presentations, etc. By crediting and citing this article.

Modeling in-process machining data using spatial point cloud vs. time series data structures

In-process machining data (e.g., cutting forces and vibrations) have been typically collected and structured as time-referenced measurements (i.e., time-series data) and utilized in this structure to develop statistical data models used in process monitoring and control methods. This paper argues that a time-only-referenced representation overlooks the 3D nature of the physical process generating the data, and that machining data can be represented alternatively as functions of the tool-workpiece relative position resulting in a spatial point cloud data structure. High-density measurements of such spatially refenced data could be highly correlated to surrounding measurements, resulting in spatial correlation structures that could be of physical meaning and value to preserve and leverage. Using a simulated data study, this paper shows that preserving the spatial correlation structure of the data clearly improves the relative modeling performance when utilizing machining data point clouds versus the traditional time-referenced data structure. Specifically, this simulation study investigated the hypothesis that “considering the Gaussian process model class, the best model among all possible models developed using the spatial point cloud data structure has smaller/equal modeling and prediction errors compared to the best model among all possible models developed using the time-referenced data structure.” While this investigation was limited to considering the case of stationary isotropic processes, it demonstrated that the performance gap was relatively large. This encourages further investigations using real-world data to better understand the types of spatial correlations that exist in machining data and the specific machining regimes and process variables that would benefit the most from the spatial point cloud representation of the data.

Histogram Anomaly Time Series: A Compact Graphical Representation of Spatial Time Series Data Sets

ABSTRACTWe introduce a simple method for detecting changes, both transient and persistent, in reanalysis and merged satellite products due to both natural climate variability and changes to the data sources/analyses used as input. This note demonstrates this Histogram Anomaly Time Series (HATS) method using tropical ocean daily precipitation from MERRA-2 and from GPCP One-Degree Daily (1DD) precipitation estimates. Rather than averaging over space or time, we create a time series display of histograms for each increment of data (such as a day or month). Regional masks such as land–ocean can be used to isolate particular domains. While the histograms reveal subtle structures in the time series, we can amplify the signal by computing the histogram’s anomalies from its climatological seasonal cycle. The qualitative analysis provided by this scheme can then form the basis for more quantitative analyses of specific features, both real and analysis induced. As an example, in the tropical oceans the analysis clearly identifies changes in the time series of both reanalysis and observations that may be related to changing inputs.

DeepCOVIDNet: An Interpretable Deep Learning Model for Predictive Surveillance of COVID-19 Using Heterogeneous Features and Their Interactions.

In this paper, we propose a deep learning model to forecast the range of increase in COVID-19 infected cases in future days and we present a novel method to compute equidimensional representations of multivariate time series and multivariate spatial time series data. Using this novel method, the proposed model can both take in a large number of heterogeneous features, such as census data, intra-county mobility, inter-county mobility, social distancing data, past growth of infection, among others, and learn complex interactions between these features. Using data collected from various sources, we estimate the range of increase in infected cases seven days into the future for all U.S. counties. In addition, we use the model to identify the most influential features for prediction of the growth of infection. We also analyze pairs of features and estimate the amount of observed second-order interaction between them. Experiments show that the proposed model obtains satisfactory predictive performance and fairly interpretable feature analysis results; hence, the proposed model could complement the standard epidemiological models for national-level surveillance of pandemics, such as COVID-19. The results and findings obtained from the deep learning model could potentially inform policymakers and researchers in devising effective mitigation and response strategies. To fast-track further development and experimentation, the code used to implement the proposed model has been made fully open source.

PEMODELAN GENERALIZED SPACE TIME AUTOREGRESSIVE (GSTAR) SEASONAL PADA DATA CURAH HUJAN EMPAT KABUPATEN DI PROVINSI JAWA TENGAH

In many applications, several time series data are recorded simultaneously at a number of locations. Time series data from nearby locations often to be related by spatial and time. This data is called spatial time series data. Generalized Space Time Autoregressive (GSTAR) model is one of space time models used to modeling and forecasting spatial time series data. This study applied GTSAR model to modeling volume of rainfall four locations in Jepara Regency, Kudus Regency, Pati Regency, and Grobogan Regency. Based on the smallest RMSE mean of forecasting result, the best model chosen by this study is GSTAR (11)-I(1)12 with the inverse distance weighted. Based on GSTAR(11)-I(1)12 with the inverse distance weighted, the relationship between the location shown on rainfall Pati Regency influenced by the rainfall in other regencies. Keywords: GSTAR, RMSE, Rainfall

Differential equations learning from spatial-time series data by the fast iterative shrinkage-thresholding algorithm

The numerical method of data-driven modeling is presented in this work. It can be used to find the corresponding governing equations in terms of differential equations from some provided spatial and time series data. The problem can be reduced to solve by sparse linear regression technique that can be referred to one of the powerful technique in machine learning algorithm. Here we propose to apply the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and then study the capability of its predictions. The environmental problem involves advection and diffusion effects are demonstrated to show the accuracy and the efficiency for finding all of the coefficients in the partial differential equation corresponding to the input data.

Using a holistic ecosystem-integrated approach to assess the environmental status of Saronikos Gulf, Eastern Mediterranean

The holistic Nested Environmental status Assessment Tool (NEAT), developed for the integrated assessment of the status of marine waters, was applied to Saronikos Gulf, in the Eastern Mediterranean. We used different spatial and decadal time series data covering 9 biological and chemical ecosystem components, 24 indicators and 8 descriptors of the Marine Strategy Framework Directive (MSFD), to test its performance under different ecosystem approaches. The results were evaluated in relation to the anthropogenic pressures affecting the study area as well as the management measures taken, and compared to the results from previous studies. NEAT has shown clear spatial gradients differentiating the impacted and slightly-impacted areas, as well as the response of the ecosystem towards the management measures taken, demonstrating the most responsive and early warning ecosystem components. The application of NEAT to Saronikos Gulf classified the whole basin into good status, with the pelagic habitat components (fish, water column and phytoplankton ecosystem components) contributing strongly to the overall environmental status of the gulf. Sediment, benthic fauna and vegetation, mammals and alien species were the most impacted ecological components in Saronikos Gulf. The most affected areas, Elefsis Bay and Psittalia (wastewater submarine outfall), were assessed as in poor and moderate status, respectively. We conclude that: (i) it is possible to integrate data from different sources, spatial and temporal scales; (ii) this integration has permitted to undertake a real ecosystem assessment; (iii) there is no loss of information, allowing full tracking of problems and cases in no good status that should be addressed at lower levels (e.g. species or species groups); (iv) the results are related with the pressures identified; (v) the assessment demonstrates the recovery of the system and the time needed to recovery; and (vi) these results could be very useful for managers, policy makers and scientists when deciding the method to use in assessing the environmental status under the MSFD.

The effect of conservation policy and varied open space on residential property values: A dynamic hedonic analysis

We investigate open space value in an ideal setting for a natural experiment between Riverside County, with an open space conservation policy, and neighboring San Bernardino County without the policy. With spatial econometrics, time series and spatial data, this study accounts for both spatial and temporal variation of open space values. The novelty of our paper is that we combine an investigation of the effect of open space proximity on residential property value with an analysis of the effect of endangered species habitat preservation policy distinguishing between types of open space (wild habitat for endangered species versus developed parks) in a two county study. We find that proximity to open space has a positive and statistically significant influence on increased value of residential real estate, with some distinction among type of open space between the counties. Conservation policy for open space with wild habitats contributes to increased value of this amenity in Riverside County.

Trend analysis of evapotranspiration over India: Observed from long-term satellite measurements

Owing to the lack of consistent spatial time series data on actual evapotranspiration (ET), very few studies have been conducted on the long-term trend and variability in ET at a national scale over the Indian subcontinent. The present study uses biome specific ET data derived from NOAA satellite’s advanced very high resolution radiometer to investigate the trends and variability in ET over India from 1983 to 2006. Trend analysis using the non-parametric Mann–Kendall test showed that the domain average ET decreased during the period at a rate of $$0.22\,\hbox {mm year}^{-1}$$ . A strong decreasing trend ( $$m = -1.75\, \hbox {mm year}^{-1}$$ , $$F = 17.41$$ , $$P$$ 0.01) was observed in forest regions. Seasonal analyses indicated a decreasing trend during southwest summer monsoon ( $$m= -0.320\, \hbox {mm season}^{-1}\,\hbox {year}^{-1})$$ and post-monsoon period ( $$m= -0.188\, \hbox {mm season}^{-1 }\,\hbox {year}^{-1})$$ . In contrast, an increasing trend was observed during northeast winter monsoon ( $$m = 0.156 \,\hbox {mm season}^{-1 }\,\hbox {year}^{-1})$$ and pre-monsoon ( $$m = 0.068\, \hbox {mm season}^{-1 }\,\hbox {year}^{-1})$$ periods. Despite an overall net decline in the country, a considerable increase ( $$4 \,\hbox {mm year}^{-1}$$ ) was observed over arid and semi-arid regions. Grid level correlation with various climatic parameters exhibited a strong positive correlation ( $$r \!>\!0.5$$ ) of ET with soil moisture and precipitation over semi-arid and arid regions, whereas a negative correlation ( $$r$$ $$-0.5$$ ) occurred with temperature and insolation in dry regions of western India. The results of this analysis are useful for understanding regional ET dynamics and its relationship with various climatic parameters over India. Future studies on the effects of ET changes on the hydrological cycle, carbon cycle, and energy partitioning are needed to account for the feedbacks to the climate.

Construction of smooth daily remote sensing time series data: a higher spatiotemporal resolution perspective

Research in time-series remote sensing data is receiving increasing attention. With the availability of relatively short repeat cycle and high spatial resolution satellite data, the construction and application of high spatiotemporal remote sensing time-series data is promising. In this paper, we proposed a method to construct complete spatial time series data, with Savitzky-Golay filter for smoothing and locally-adaptive linear interpolation for generating daily NDVI imagery. An IDL-based program was developed to achieve this goal. The China’s HJ-1 A/B satellite data were employed for this remote sensing time series construction. The results demonstrated that: (1) This method can generate smooth continuous time series image data successfully based on irregularly short-revisit remote sensing data; (2) HJ-1 A/B NDVI time-series were demonstrated to be successful in monitoring crop phenology and hyperspectral analysis was successfully applied on HJ-1 A/B time-series data to perform temporal endmember extraction. The IDL-based time-series construction program is generalizable for various kind of multi-temporal remote sensing data such as MODIS vegetation-index product. Discussion and concluding remarks are made to reveal the authors’ perspective on higher spatial resolution time-series analysis in the remote sensing community.

Estimation for semiparametric nonlinear regression of irregularly located spatial time-series data

Large spatial time-series data with complex structures collected at irregularly spaced sampling locations are prevalent in a wide range of applications. However, econometric and statistical methodology for nonlinear modeling and analysis of such data remains rare. A semiparametric nonlinear regression is thus proposed for modeling nonlinear relationship between response and covariates, which is location-based and considers both temporal-lag and spatial-neighboring effects, allowing data-generating process nonstationary over space (but turned into stationary series along time) while the sampling spatial grids can be irregular. A semiparametric method for estimation is also developed that is computationally feasible and thus enables application in practice. Asymptotic properties of the proposed estimators are established while numerical simulations are carried for comparisons between estimates before and after spatial smoothing. Empirical application to investigation of housing prices in relation to interest rates in the United States is demonstrated, with a nonlinear threshold structure identified.

Compressive Spatio-Temporal Forecasting of Meteorological Quantities and Photovoltaic Power

This paper presents a solar power forecasting scheme, which uses spatial and temporal time series data along with a photovoltaic (PV) power conversion model. The PV conversion model uses the forecast of three different variables, namely, irradiance on the tilted plane, ambient temperature, and wind speed, in order to estimate the power produced by a PV plant at the grid connection terminals. The forecast values are obtained using a spatio-temporal method that uses the data recorded from a target meteorological station as well as data of its surrounding stations. The proposed forecasting method exploits the sparsity of correlations between time series data in a collection of stations. The performance of both the PV conversion model and the spatio-temporal algorithm is evaluated using high-resolution real data recorded in various locations in Italy. Comparison with other benchmark methods illustrates that the proposed method significantly improves the solar power forecasts, particularly over short-term horizons.

Big city, small world: density, contact rates, and transmission of dengue across Pakistan

Macroscopic descriptions of populations commonly assume that encounters between individuals are well mixed; i.e. each individual has an equal chance of coming into contact with any other individual. Relaxing this assumption can be challenging though, due to the difficulty of acquiring detailed knowledge about the non-random nature of encounters. Here, we fitted a mathematical model of dengue virus transmission to spatial time-series data from Pakistan and compared maximum-likelihood estimates of ‘mixing parameters’ when disaggregating data across an urban–rural gradient. We show that dynamics across this gradient are subject not only to differing transmission intensities but also to differing strengths of nonlinearity due to differences in mixing. Accounting for differences in mobility by incorporating two fine-scale, density-dependent covariate layers eliminates differences in mixing but results in a doubling of the estimated transmission potential of the large urban district of Lahore. We furthermore show that neglecting spatial variation in mixing can lead to substantial underestimates of the level of effort needed to control a pathogen with vaccines or other interventions. We complement this analysis with estimates of the relationships between dengue transmission intensity and other putative environmental drivers thereof.

Evaluating an animated and static time series map of District Six: A visual and cognitive approach

Visualization of spatial information is an important aspect in the representation of map displays. Maps today are visually adapted to a variety of mediums in displaying spatial information temporally and as time series phenomena. GIS technology has incorporated tools for analysing these spatio-temporal trends. However map users are overwhelmed by the amount of information in these map displays and therefore experience cognitive overload. In this study we find that static and animated maps have their respective advantages in the visualization of the map reader by placing participants through a structured set of questions. All these facets exist in the visual and cognitive realm of the map reader. District Six is a unique area that has experienced significant spatial change in the last century, mainly attributed to its political history. This has been depicted in a conventional static and animated time series map representation which has been designed to facilitate the understanding of the spatial change that occurred during this unique period of history. In this paper a methodology has been investigated and implemented in the design of the map, by enhancing the map reader’s experience in visualising time series spatial data. We conclude further that visual intention and attention are cognitive facets that collectively strengthen the map reader’s ability in learning spatial information.