Spatio-temporal Statistical Model Research Articles

Homogenized gridded dataset for drought and hydrometeorological modeling for the continental United States

We present a novel data set for drought in the continental US (CONUS) built to enable computationally efficient spatio-temporal statistical and probabilistic models of drought. We converted drought data obtained from the widely-used US Drought Monitor (USDM) from its native geo-referenced polygon format to a 0.5 degree regular grid. We merged known environmental drivers of drought, including those obtained from the North American Land Data Assimilation System (NLDAS-2), US Geological Survey (USGS) streamflow data, and National Oceanic and Atmospheric Administration (NOAA) teleconnections data. The resulting data set permits statistical and probabilistic modeling of drought with explicit spatial and/or temporal dependence. Such models could be used to forecast drought at short-range, seasonal to sub-seasonal, and inter-annual timescales with uncertainty, extending the reach and value of the current US Drought Outlook from the National Weather Service Climate Prediction Center. This novel data product provides the first common gridded dataset that includes critical variables used to inform hydrological and meteorological drought.

Bayesian spatio-temporal statistical modeling of violent-related fatality in western and central Africa

Fatality arising from violent events is a critical public health problem in Africa. Although numerous studies on crime and violent events have been conducted, adequate attention has not been given to the distribution of fatalities arising from these events. This study unraveled the spatio-temporal pattern of fatality from violent events in Western and Central Africa. A two-component spatio-temporal zero-inflated model on a continuous spatial domain within a Bayesian framework was adopted. The stochastic partial differential equation was used to quantify the continuous pattern and make projections in unsampled regions. Fatality data from 1997 to 2021 was obtained from the Armed Conflict Location and Event Data Project (ACLED). Findings from the result revealed a spatial and temporal divide in the prevalence of fatality in the study region. Between the years 1997 and 2010, fatality from violence was most prevalent in Central Africa, whereas in more recent years, it was most prevalent in Western Africa. The posterior predictive probabilities of fatality occurrence due to violent events in Nigeria and Cameroon were highest and above 0.6, and the probability of more than one death per violent event is highest in Angola and Chad with probability 0.2. On violent event type, findings showed that suicide bombs had the highest likelihood of fatality occurrence whereas the event of violent non-state actors overtaking territory had the highest impact on the likelihood of multiple fatality counts. Among the armed actors who participated in violent events, armed religious groups were linked to the highest likelihood of fatality occurrence whereas Military forces were linked to the highest likelihood of multiple fatality counts per event. The finding also revealed that there is a higher likelihood of multiple fatalities in the Winter temperate season. These findings could be used for planning and policy design geared towards mitigating fatality and providing a guide towards resource distribution to support the affected communities.

MODELING LAND DEFORMATIONS IN MOUNTAINS BY COMBINING TIME-SERIES L-BAND SAR IMAGES AND SPATIOTEMPORAL STATISTICAL MODELS

Abstract. Predicting land deformations using remote-sensing technology is extremely challenging because the simulation models that are involved have many parameters, including geological features, that must be calibrated against areas of interest, and no universal model is available. Instead, this paper proposes a method for modeling land deformations with time-series L-band synthetic aperture radar (SAR) images and spatiotemporal statistical models for prediction. First, time-series SAR analysis generates temporal land deformation. Then, water-related products are obtained from the Today’ Earth system of the Japan Aerospace Exploration Agency. The three-day consecutive maximum values are calculated and then interpolated spatially. Finally, a descriptive or dynamic spatiotemporal statistical model is applied. The low-rank Gaussian process model, a descriptive model, is found to be highly accurate for explaining land deformations, even for actual slid areas, as long as the areas of analysis are limited, e.g., 150 m × 50 m. It is concluded that the proposed method is effective for predicting land deformations spatially and temporally and so can be used to identify possible landslide locations.

Informing management of recovering predators and their prey with ecological diffusion models

The reintroduction and recovery of predators can be ecologically beneficial as well as socially and economically controversial. However, the growth and expansion of predator populations, and thus their ecological, social, and economic impacts, are not static but rather they vary in space and time. We propose a spatiotemporal statistical modeling framework based on ecological diffusion to better inform the ecology and management of recovering predators and their prey. We demonstrate its utility by applying it to a recovering sea otter (Enhydra lutris) population in Southeast Alaska, where sea otters were reintroduced in the late 1960s and have exhibited unprecedented population growth. Estimated parameters yield inferences about movement and population ecology, and our approach provides useful derived quantities, such as local abundance and carrying capacity as well as a quantity we term the equilibrium differential. We used our model to examine how density dependence and carrying capacity of sea otters vary spatially across a region. The diffusion modeling approach we present can be generalized for use in other instances of (re)colonization across taxa to inform management and conservation efforts.

Exploring Daily Activity Pattern Using Spatio-Temporal Statistics with R for Predicting Trip Production

Spatio-temporal data modelling is one of the methods in data analysis that uses space (spatial) and time (temporal) approaches. This study used Spatio-temporal statistical modelling to observe the daily activity patterns of people. Spatio-temporal modelling selected for support activity-based transportation demand. This research identifies community mobility patterns that will provide trip production data for transportation demand prediction. Using Spatio-temporal statistical modelling benefit this study because statistical this model can make model components in a physical system appearing to be random. Even if they are not, the models are helpful as they have accurate and precise predictions. In this study, descriptive analysis was used. Incorporating statistical distributions into the model is a natural way to solve the problem. This research collects daily activity data from 400 respondents recorded every 15 minutes. From this data, a pattern of respondents’ daily activities was formed, which was analyzed using R. Software R also visualizes data on daily activities of the community in Spatio-temporal modelling. This research aims to depict the daily activity patterns to predict trip production. This research found three clusters of trip production patterns with specific groups member and specific patterns between workdays and holidays.

Test and Visualization of Covariance Properties for Multivariate Spatio-Temporal Random Fields

The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance function plays a key role in modeling, inference, and prediction. For multivariate space-time data, understanding the spatio-temporal variability, within and across variables, is essential in employing a realistic covariance model. Meanwhile, the complexity of generic covariances often makes model fitting very challenging, and simplified covariance structures, including symmetry and separability, can reduce the model complexity and facilitate the inference procedure. However, a careful examination of these properties is needed in real applications. In the work presented here, we formally define these properties for multivariate spatio-temporal random fields and use functional data analysis techniques to visualize them, hence, providing intuitive interpretations. We then propose a rigorous rank-based testing procedure to conclude whether the simplified properties of covariance are suitable for the underlying multivariate space-time data. The good performance of our method is illustrated through synthetic data, for which we know the true structure. We also investigate the covariance of bivariate wind speed, a key variable in renewable energy, over a coastal and an inland area in Saudi Arabia. The supplementary material is available online, including the R code for our developed methods.

Spatial and seasonal determinants of Lyme borreliosis incidence in France, 2016 to 2021.

BackgroundLyme borreliosis (LB) is the most widespread hard tick-borne zoonosis in the northern hemisphere. Existing studies in Europe have focused mainly on acarological risk assessment, with few investigations exploring human LB occurrence.AimWe explored the determinants of spatial and seasonal LB variations in France from 2016 to 2021 by integrating environmental, animal, meteorological and anthropogenic factors, and then mapped seasonal LB risk predictions.MethodsWe fitted 2016-19 LB national surveillance data to a two-part spatio-temporal statistical model. Spatial and temporal random effects were specified using a Besag-York-Mollie model and a seasonal model, respectively. Coefficients were estimated in a Bayesian framework using integrated nested Laplace approximation. Data from 2020-21 were used for model validation.ResultsA high vegetation index (≥ 0.6) was positively associated with seasonal LB presence, while the index of deer presence (> 60%), mild soil temperature (15-22 °C), moderate air saturation deficit (1.5-5 mmHg) and higher tick bite frequency were associated with increased incidence. Prediction maps show a higher risk of LB in spring and summer (April-September), with higher incidence in parts of eastern, midwestern and south-western France.ConclusionWe present a national level spatial assessment of seasonal LB occurrence in Europe, disentangling factors associated with the presence and increased incidence of LB. Our findings yield quantitative evidence for national public health agencies to plan targeted prevention campaigns to reduce LB burden, enhance surveillance and identify further data needs. This approach can be tested in other LB endemic areas.

Constructing large nonstationary spatio-temporal covariance models via compositional warpings

Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance stationarity, which is unrealistic in many geophysical applications. In this article, we introduce a deep-learning-inspired approach to construct descriptive nonstationary spatio-temporal models by modeling stationary processes on warped spatio-temporal domains. The warping functions we use are constructed using several simple injective warping units which, when combined through composition, can induce complex warpings. A stationary spatio-temporal covariance function on the warped domain induces covariance nonstationarity on the original domain. Sparse linear algebraic methods are used to reduce the computational complexity when fitting the model in a big data setting. We show that our proposed nonstationary spatio-temporal model can capture covariance nonstationarity in both space and time, and provide better probabilistic predictions than conventional stationary models in both simulation studies and on a real-world data set.

Learning spatiotemporal statistical shape models for non-linear dynamic anatomies.

Numerous clinical investigations require understanding changes in anatomical shape over time, such as in dynamic organ cycle characterization or longitudinal analyses (e.g., for disease progression). Spatiotemporal statistical shape modeling (SSM) allows for quantifying and evaluating dynamic shape variation with respect to a cohort or population of interest. Existing data-driven SSM approaches leverage information theory to capture population-level shape variations by learning correspondence-based (landmark) representations of shapes directly from data using entropy-based optimization schemes. These approaches assume sample independence and thus are unsuitable for sequential dynamic shape observations. Previous methods for adapting entropy-based SSM optimization schemes for the spatiotemporal case either utilize a cross-sectional design (ignoring within-subject correlation) or impose other limiting assumptions, such as the linearity of shape dynamics. Here, we present a principled approach to spatiotemporal SSM that relaxes these assumptions to correctly capture population-level shape variation over time. We propose to incorporate modeling the underlying time dependency into correspondence optimization via a regularized principal component polynomial regression. This approach is flexible enough to capture non-linear temporal dynamics while encoding population-specific spatial regularity. We demonstrate our method's efficacy on synthetic data and left atrium segmented from cardiac MRI scans. Our approach better captures the population modes of variation and a statistically significant time dependency than existing methods.

Incorporating distribution shifts and spatio-temporal variation when estimating weight-at-age for stock assessments: a case study involving the Bering Sea pollock (Gadus chalcogrammus)

AbstractEnvironmental conditions can create spatial and temporal variability in growth and distribution processes, yet contemporary stock assessment methods often do not explicitly address the consequences of these patterns. For example, stock assessments often assume that body weight-at-age (i.e. size) is constant across the stocks’ range, and may thereby miss important spatio-temporal patterns. This is becoming increasingly relevant given climate-driven distributional shifts, because samples for estimating size-at-age can be spatially unbalanced and lead to biases when extrapolating into unsampled areas. Here, we jointly analysed data on the local abundance and size of walleye pollock (Gadus chalcogrammus) in the Bering Sea, to demonstrate a tractable first step in expanding spatially unbalanced size-at-age samples, while incorporating fine-scale spatial and temporal variation for inclusion in stock assessments. The data come from NOAA’s bottom trawl survey data and were evaluated using a multivariate spatio-temporal statistical model. We found extensive variation in size-at-age at fine spatial scales, though specific patterns differed between age classes. In addition to persistent spatial patterns, we also documented year-to-year differences in the spatial patterning of size-at-age. Intra-annual variation in the population-level size-at-age (used to generate the size-at-age matrix in the stock assessment) was largely driven by localized changes in fish size, while shifts in species distribution had a smaller effect. The spatio-temporal size-at-age matrix led to marginal improvement in the stock assessment fit to the survey biomass index. Results from our case study suggest that accounting for spatially unbalanced sampling improved stock assessment consistency. Additionally, it improved our understanding on the dynamics of how local and population-level demographic processes interact. As climate change affects fish distribution and growth, integrating spatiotemporally explicit size-at-age processes with anticipated environmental conditions may improve stock-assessment forecasts used to set annual harvest limits.

Spatio-temporal modeling of infectious diseases by integrating compartment and point process models.

The online version contains supplementary material available at 10.1007/s00477-022-02354-4.

Quantifying Spatio-temporal risk of Harmful Algal Blooms and their impacts on bivalve shellfish mariculture using a data-driven modelling approach

Harmful algal blooms (HABs) intoxicate and asphyxiate marine life, causing devastating environmental and socio-economic impacts, costing at least $8bn/yr globally. Accumulation of phycotoxins from HAB phytoplankton in filter-feeding shellfish can poison human consumers, prompting harvesting closures at shellfish production sites. To quantify long-term intoxication risk from Dinophysis HAB species, we used historical HAB monitoring data (2009–2020) to develop a new modelling approach to predict Dinophysis toxin concentrations in a range of bivalve shellfish species at shellfish sites in Western Scotland, South-West England and Northern France. A spatiotemporal statistical modelling framework was developed within the Generalized Additive Model (GAM) framework to quantify long-term HAB risks for different bivalve shellfish species across each region, capturing seasonal variations, and spatiotemporal interactions. In all regions spatial functions were most important for predicting seasonal HAB risk, offering the potential to inform optimal siting of new shellfish operations and safe harvesting periods for businesses. A 10-fold cross-validation experiment was carried out for each region, to test the models’ ability to predict toxin risk at harvesting locations for which data were withheld from the model. Performance was assessed by comparing ranked predicted and observed mean toxin levels at each site within each region: the correlation of ranks was 0.78 for Northern France, 0.64 for Western Scotland, and 0.34 for South-West England, indicating our approach has promise for predicting unknown HAB risk, depending on the region and suitability of training data.

A 5000-year record of relative sea-level change in New Jersey, USA

Stratigraphic data from salt marshes provide accurate reconstructions of Holocene relative sea-level (RSL) change and necessary constraints to models of glacial isostatic adjustment (GIA), which is the dominant cause of Late-Holocene RSL rise along the U.S. mid-Atlantic coast. Here, we produce a new Mid- to Late-Holocene RSL record from a salt marsh bordering Great Bay in southern New Jersey using basal peats. We use a multi-proxy approach (foraminifera and geochemistry) to identify the indicative meaning of the basal peats and produce sea-level index points (SLIPs) that include a vertical uncertainty for tidal range change and sediment compaction and a temporal uncertainty based on high precision Accelerator Mass Spectrometry radiocarbon dating of salt-marsh plant macrofossils. The 14 basal SLIPs range from 1211 ± 56 years BP to 4414 ± 112 years BP, which we combine with published RSL data from southern New Jersey and use with a spatiotemporal statistical model to show that RSL rose 8.6 m at an average rate of 1.7 ± 0.1 mm/year (1σ) from 5000 years BP to present. We compare the RSL changes with an ensemble of 1D (laterally homogenous) and site-specific 3D (laterally heterogeneous) GIA models, which tend to overestimate the magnitude of RSL rise over the last 5000 years. The continued discrepancy between RSL data and GIA models highlights the importance of using a wide array of ice model and viscosity model parameters to more precisely fit site-specific RSL data along the U.S. mid-Atlantic coast.

Spatiotemporal Characteristics and Statistical Model Prediction of Potential Evaporation during the Growing Season in Ningxia

Based on the daily data of 24 meteorological warfare points in Ningxia, the potential evaporation (ET0), the Mann–Kendall test (MK), and inverse distance weight interpolation were used to analyze the temporal and spatial changes in the potential evaporation at different scales, and the Pearson correlation coefficient was used to determine the growth rate in Ningxia. The atmospheric circulation influencing factors of seasonal potential evaporation were established, and the prediction model of potential evaporation in the growing season in Ningxia was established by stepwise linear regression, using mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE). The error test was carried out, and the results show the following: (1) The areas with larger potential evaporation during the growing season are mainly the central area of Ningxia and the northern side of the northern area. The presence on the north side tends to decrease. (2) On the monthly scale, the potential evaporation continued to increase from April to June, reached the maximum in June, continued to decrease from July to October, and was the smallest in October. (3) During the MK test in the growing season, the change in potential evaporation in the growing season showed an “increase–decrease” trend. The results of the monthly MK test show that the potential evaporation in April, May, and June has shown an increasing trend over the past 30 years, and the UF value in July, August, and October has been relatively high. The change trend of potential evaporation has been relatively stable, and the potential evaporation in September has shown a downward trend over the past 20 years. (4) The prediction model of potential evaporation in the growing season established by the circulation factor has shown a good effect in Ningxia and can be used to establish the scheduling prediction of irrigation water.

Source reconstruction for spatio-temporal physical statistical models

In many applications, a signal is deformed by well-understood dynamics before it can be measured. For example, when a pollutant enters a river, it immediately begins dispersing, flowing, settling, and reacting. If the pollutant enters at a single point, its concentration can be measured before it enters the complex dynamics of the river system. However, in the case of a non-point source pollutant, it is not clear how to efficiently measure its source. One possibility is to record concentration measurements in the river, but this signal is masked by the fluid dynamics of the river. Specifically, concentration is governed by the advection–diffusion–reaction PDE, with an unknown source term. We propose a method to statistically reconstruct a source term from these PDE-deformed measurements. Our method is general and applies to any linear PDE. This method has important applications in the study of environmental DNA and non-point source pollution.

Spatiotemporal Asymmetric Modeling of the Long Run Response of Corn Productivity to Environmental Variabilities

A spatiotemporal statistical model for the corn productivity of Bulacan using local and global variables was generated. The data from January 1995–September 2019 for a total of 99 quarters were used. Necessary imputations and conversions aside from a transformation technique were done to match the data and generate the best fitting model. The nonlinear autoregressive distributed lag was used to determine the asymmetric long-run effects on the corn production volume of the province to the potential positive and negative changes in the amount of rainfall, minimum temperature, maximum temperature, the water level of Angat Dam, atmospheric carbon dioxide concentration, and sea surface temperature anomaly. It also included the land area harvested as a deterministic factor. The findings show that the corn production of the selected area responds to both negative and positive shocks to the rainfall amount and availability of water supply in the dam in the long run. It also shows that the long-term effects of an increase in the minimum temperature are detrimental, whereas rising levels of carbon dioxide concentration in the environment could be profoundly contributory to the dependent variable, at least in a direct manner. Several diagnostic tests substantiated the fitness of the econometric model. The empirical findings of this study extend the generally collective results of existing literature. It may also be used as a basis for plans of action for sustainable production practices of the grain, as well as other crops in the uncertain future amidst the threat of environmental stresses.

Predictive Statistical Model of Early Cranial Development.

We present a data-driven method to build a spatiotemporal statistical shape model predictive of normal cranial growth from birth to the age of 2 years. The model was constructed using a normative cross-sectional computed tomography image dataset of 278 subjects. First, we propose a new standard representation of the calvaria using spherical maps to establish anatomical correspondences between subjects at the cranial sutures - the main areas of cranial bone expansion. Then, we model the cranial bone shape as a bilinear function of two factors: inter-subject anatomical variability and temporal growth. We estimate these factors using principal component analysis on the spatial and temporal dimensions, using a novel coarse-to-fine temporal multi-resolution approach to mitigate the lack of longitudinal images of the same patient. Our model achieved an accuracy of 1.54 ± 1.05 mm predicting development on an independent longitudinal dataset. We also used the model to calculate the cranial volume, cephalic index and cranial bone surface changes during the first two years of age, which were in agreement with clinical observations. To our knowledge, this is the first data-driven and personalized predictive model of cranial bone shape development during infancy and it can serve as a baseline to study abnormal growth patterns in the population.

Managing African Swine Fever: Assessing the Potential of Camera Traps in Monitoring Wild Boar Occupancy Trends in Infected and Non-infected Zones, Using Spatio-Temporal Statistical Models.

The recent spreading of African swine fever (ASF) over the Eurasian continent has been acknowledged as a serious economic threat for the pork industry. Consequently, an extensive body of research focuses on the epidemiology and control of ASF. Nevertheless, little information is available on the combined effect of ASF and ASF-related control measures on wild boar (Sus scrofa) population abundances. This is crucial information given the role of the remaining wild boar that act as an important reservoir of the disease. Given the high potential of camera traps as a non-invasive method for ungulate trend estimation, we assess the effectiveness of ASF control measures using a camera trap network. In this study, we focus on a major ASF outbreak in 2018–2020 in the South of Belgium. This outbreak elicited a strong management response, both in terms of fencing off a large infected zone as well as an intensive culling regime. We apply a Bayesian multi-season site-occupancy model to wild boar detection/non-detection data. Our results show that (1) occupancy rates at the onset of our monitoring period reflect the ASF infection status; (2) ASF-induced mortality and culling efforts jointly lead to decreased occupancy over time; and (3) the estimated mean total extinction rate ranges between 22.44 and 91.35%, depending on the ASF infection status. Together, these results confirm the effectiveness of ASF control measures implemented in Wallonia (Belgium), which has regained its disease-free status in December 2020, as well as the usefulness of a camera trap network to monitor these effects.

Analysis of atmospheric temperature data by 4D spatial\u2013temporal statistical model

The meteorological data such as temperature of the upper atmosphere is ssential for accurate weather forecasting. The Universal Rawinsonde Observation Program (RAOB) establishes an extensive radiosonde network worldwide to observe atmospheric meteorological data from the surface to the low stratosphere. The RAOB data data has very high accuracy but can offer a very limited spatial coverage. Meanwhile, ERA-Interim reanalysis data is widely available but with low-quality. We propose a 4D spatiotemporal statistical model which can make effective inferences from ERA-Interim reanalysis data to RAOB data. Finally, we can obtain a huge amount of RAOB data with high-quality and can offer a very wide spatial coverage. In empirical research, we collected data from 200 launch sites around the world in January 2015. The 4D spatiotemporal statistical model successfully analyzed the observation gaps at different pressure levels.

A spatio-temporal statistical model to analyze COVID-19 spread in the USA

Coronavirus pandemic has affected the whole world extensively and it is of immense importance to understand how the disease is spreading. In this work, we provide evidence of spatial dependence in the pandemic data and accordingly develop a new statistical technique that captures the spatio-temporal dependence pattern of the COVID-19 spread appropriately. The proposed model uses a separable Gaussian spatio-temporal process, in conjunction with an additive mean structure and a random error process. The model is implemented through a Bayesian framework, thereby providing a computational advantage over the classical way. We use state-level data from the United States of America in this study. We show that a quadratic trend pattern is most appropriate in this context. Interestingly, the population is found not to affect the numbers significantly, whereas the number of deaths in the previous week positively affects the spread of the disease. Residual diagnostics establish that the model is adequate enough to understand the spatio-temporal dependence pattern in the data. It is also shown to have superior predictive power than other spatial and temporal models. In fact, we show that the proposed approach can predict well for both short term (1 week) and long term (up to three months).