Spatio-temporal Geostatistical Model Research Articles

Spatio-Temporal Dual Kriging with Adaptive Coefficient Drift Function

Research on spatio-temporal geostatistical modeling remains a critical challenge in numerous scientific and engineering disciplines. This paper introduces a novel extension of dual kriging, called spatio-temporal dual kriging (ST-DK), in which drift functions with fixed and adaptive coefficients are established. The approach appears to be effective in modeling complex spatio-temporal dynamics, particularly when relevant auxiliary variables exert substantial influence on the target variable. To illustrate its performance, we compare the ST-DK model with the classical spatio-temporal regression kriging (ST-RK) and geographically and temporally weighted regression (GTWR) models for estimating temperature and air pressure data from Thailand in 2018. Our findings demonstrate that both the ST-DK and ST-RK models when utilizing adaptive coefficients outperform their fixed coefficient counterparts. Furthermore, the ST-DK method consistently exhibits superior performance compared to the ST-RK and GTWR methods.

Two decades of malaria control in Malawi: Geostatistical Analysis of the changing malaria prevalence from 2000-2022.

Malaria remains a public health problem in Malawi and has a serious socio-economic impact on the population. In the past two decades, available malaria control measures have been substantially scaled up, such as insecticide-treated bed nets, artemisinin-based combination therapies, and, more recently, the introduction of the malaria vaccine, the RTS,S/AS01. In this paper, we describe the epidemiology of malaria for the last two decades to understand the past transmission and set the scene for the elimination agenda. A collation of parasite prevalence surveys conducted between the years 2000 and 2022 was done. A spatio-temporal geostatistical model was fitted to predict the yearly malaria risk for children aged 2-10 years (PfPR 2-10) at 1×1 km spatial resolutions. Parameter estimation was done using the Monte Carlo maximum likelihood method. District-level prevalence estimates adjusted for population are calculated for the years 2000 to 2022. A total of 2,595 sampled unique locations from 2000 to 2022 were identified through the data collation exercise. This represents 70,565 individuals that were sampled in the period. In general, the PfPR2_10 declined over the 22 years. The mean modelled national PfPR2_10 in 2000 was 43.93 % (95% CI:17.9 to 73.8%) and declined to 19.2% (95%CI 7.49 to 37.0%) in 2022. The smoothened estimates of PfPR2_10 indicate that malaria prevalence is very heterogeneous with hotspot areas concentrated on the southern shores of Lake Malawi and the country's central region. The last two decades are associated with a decline in malaria prevalence, highly likely associated with the scale-up of control interventions. The country should move towards targeted malaria control approaches informed by surveillance data.

Hedonic real estate price estimation with the spatiotemporal geostatistical model

This study argues that the spatiotemporal geostatistical model for real estate prices, which accounts for and incorporates spatial autocorrelation, can be estimated successfully using the Bayesian Markov Chain Monte Carlo (MCMC) estimation. While this procedure often encounters difficulty in calculating probabilistic densities in the Metropolis–Hastings (MH) algorithm, this study introduces a feasible and practical estimation method, providing useful estimated parameters for the model. Using single-family house transaction data, we show that ordinary estimations of real estate prices, with respect to certain explanatory variables, may lead to the underestimation of standard errors of coefficients for explanatory variables with spatial effects unless spatial autocorrelation is controlled for. Our model also makes it possible to obtain accurate in-sample predictions and moderately improved out-of-sample predictions for real estate prices. This study further estimates a “decay rate:” a diminishing correlation between real estate prices and increasing distance, showing that geographical proximities are likely to have an important impact on real estate prices, especially at a range under 600 m.

Understanding the importance of spatial correlation in identifying spatio-temporal variation of disease risk, in the case of malaria risk mapping in southern Ethiopia

Malaria remains a major health problem in developing countries despite a significant reduction in incidence in the last few years. Disease mapping thus helps to understand the spatial pattern and identify areas characterized by unusual risks. Several spatial models have been used to analyze the incidence of malaria. We aim to compare the predictive performance of these models and investigate the effect of ignoring spatial correlation. The reported malaria case counts of genus P.falciparum in 149 districts of southern Ethiopia from January 2016 to May 2019 were analyzed using the spatial time series model (STS) that ignores spatial correlation, Spatio-temporal conditional autoregressive model (STCAR), Spatio-temporal geostatistical model (STG) and Spatio-temporal spatial discrete approximation to log Gaussian cox process (STSDALGCP). We assess the predictive performance of the models using root mean square error, mean absolute error, and coverage probability. We found that monthly average rainfall, temperature, humidity, and EVI are significantly associated with malaria risk. The spatial variation of malaria incidence changes with time, in particular, the high incidence was observed from November to December, months after heavy rainfall, and more pronounced in the southwest of the country. STSDALGCP gives a small prediction error in test set and captures the uncertainties better than other models, while the STS model gives a high prediction error. Accounting for spatial correlation is crucial for disease risk mapping and leads to better prediction of disease risk. Since malaria transmission operates in a spatially continuous manner, a spatially continuous model should be considered when it is computationally feasible.

Two decades of malaria control in Malawi: Geostatistical Analysis of the changing malaria prevalence from 2000-2022

Background Malaria remains a public health problem in Malawi and has a serious socio-economic impact on the population. In the past two decades, available malaria control measures have been substantially scaled up, such as insecticide-treated bed nets, artemisinin-based combination therapies, and, more recently, the introduction of the malaria vaccine, the RTS,S/AS01. In this paper, we describe the epidemiology of malaria for the last two decades to understand the past transmission and set the scene for the elimination agenda. Methods A collation of parasite prevalence surveys conducted between the years 2000 and 2022 was done. A spatio-temporal geostatistical model was fitted to predict the yearly malaria risk for children aged 2–10 years (PfPR 2–10) at 1×1 km spatial resolutions. Parameter estimation was done using the Monte Carlo maximum likelihood methods. District level prevalence estimates adjusted for population are calculated for the years 2000 to 2022. Results A total of 2,595 sampled unique locations from 2000 to 2022 were identified through the data collation exercise. This represents 70,565 individuals that were sampled in the period. In general, the PfPR2_10 declined over the 22 years. The mean modeled national PfPR2_10 in 2000 was 43.93 % (95% CI:17.9 to 73.8%) and declined to 19.2% (95%CI 7.49 to 37.0%) in 2022. The smoothened estimates of PfPR2_10 indicate that malaria prevalence is very heterogeneous with hotspot areas concentrated on the southern shores of Lake Malawi and the country's central region. Conclusions The last two decades are associated with a decline in malaria prevalence, highly likely associated with the scale up of control interventions. The country should move towards targeted malaria control approaches informed by surveillance data.

Applicability Assessment of a Spatiotemporal Geostatistical Fusion Model for Disaster Monitoring: Two Cases of Flood and Wildfire

A spatial time series geostatistical deconvolution/fusion model (STGDFM), as one of spatiotemporal data fusion model, combines Dense time series data with a Coarse-scale (i.e., DC data) and Sparse time series data with a Fine-scale (i.e., SF data) to generate Synthetic Dense time series data with a Fine-scale (i.e., SDF data). Specifically, STGDFM uses a geostatistics-based spatial time series modeling to capture the temporal trends included in time series DC data. This study evaluated the prediction performance of STGDFM for abrupt changes in reflectance due to disasters in spatiotemporal data fusion, and a spatial and temporal adaptive reflectance fusion model (STARFM) and an enhanced STARFM (ESTARFM) were selected as comparative models. For the applicability assessment, flood and wildfire were selected as case studies. In the case of flood, MODIS-like data (240 m) with spatial resolution converted from Landsat data and Landsat data (30 m) were used as DC and SF data, respectively. In the case of wildfire, MODIS and Landsat data were used as DC and SF data, respectively. The case study results showed that among the three spatiotemporal fusion models, STGDFM presented the best prediction performance with 0.894 to 0.979 at the structure similarity and 0.760 to 0.872 at the R-squared values in the flood- and wildfire-affected areas. Unlike STARFM and ESTARFM that adopt the assumptions for reflectance changes, STGDFM combines the temporal trends using time series DC data. Therefore, STGDFM could capture the abrupt changes in reflectance due to the flood and wildfire. These results indicate that STGDFM can be used for cases where satellite images of appropriate temporal and spatial resolution are difficult to acquire for disaster monitoring.

Spatio-Temporal Cross-Covariance Functions under the Lagrangian Framework with Multiple Advections

When analyzing the spatio-temporal dependence in most environmental and earth sciences variables such as pollutant concentrations at different levels of the atmosphere, a special property is observed: the covariances and cross-covariances are stronger in certain directions. This property is attributed to the presence of natural forces, such as wind, which cause the transport and dispersion of these variables. This spatio-temporal dynamics prompted the use of the Lagrangian reference frame alongside any Gaussian spatio-temporal geostatistical model. Under this modeling framework, a whole new class was birthed and was known as the class of spatio-temporal covariance functions under the Lagrangian framework, with several developments already established in the univariate setting, in both stationary and nonstationary formulations, but less so in the multivariate case. Despite the many advances in this modeling approach, efforts have yet to be directed to probing the case for the use of multiple advections, especially when several variables are involved. Accounting for multiple advections would make the Lagrangian framework a more viable approach in modeling realistic multivariate transport scenarios. In this work, we establish a class of Lagrangian spatio-temporal cross-covariance functions with multiple advections, study its properties, and demonstrate its use on a bivariate pollutant dataset of particulate matter in Saudi Arabia. Supplementary materials for this article are available online.

Spatiotemporal analysis of distribution of pest and predator in corn crops

ABSTRACT Crop pests have negative impacts on yield. This paper proposes a spatiotemporal geostatistical modeling to compare data of adult Syrphidae fly count and corn leaf aphid Rhopalosiphum maidis (Fitch, 1856) colonies in corn crops. The use of a geostatistical model that allows the space-time variation makes the approach more interesting because it is a more complete model. Multiple regression was used to model the trend component for the variable response adult Syrphidae fly count and corn leaf aphid colonies, with the coordinates serving as covariates and the spatiotemporal variations around the deviation are described by a random spacetime residual field. Finally, the prediction map obtained by kriging may be a biological indicator of possible corn leaf aphid colonies in the corn crop. It was possible to verify that the occurrence of the pest provided a significant increase in adult predators and seminatural habitats may favor populations of natural enemies.

Indirect effects of the COVID-19 pandemic on malaria intervention coverage, morbidity, and mortality in Africa: a geospatial modelling analysis

SummaryBackgroundSubstantial progress has been made in reducing the burden of malaria in Africa since 2000, but those gains could be jeopardised if the COVID-19 pandemic affects the availability of key malaria control interventions. The aim of this study was to evaluate plausible effects on malaria incidence and mortality under different levels of disruption to malaria control.MethodsUsing an established set of spatiotemporal Bayesian geostatistical models, we generated geospatial estimates across malaria-endemic African countries of the clinical case incidence and mortality of malaria, incorporating an updated database of parasite rate surveys, insecticide-treated net (ITN) coverage, and effective treatment rates. We established a baseline estimate for the anticipated malaria burden in Africa in the absence of COVID-19-related disruptions, and repeated the analysis for nine hypothetical scenarios in which effective treatment with an antimalarial drug and distribution of ITNs (both through routine channels and mass campaigns) were reduced to varying extents.FindingsWe estimated 215·2 (95% uncertainty interval 143·7–311·6) million cases and 386·4 (307·8–497·8) thousand deaths across malaria-endemic African countries in 2020 in our baseline scenario of undisrupted intervention coverage. With greater reductions in access to effective antimalarial drug treatment, our model predicted increasing numbers of cases and deaths: 224·1 (148·7–326·8) million cases and 487·9 (385·3–634·6) thousand deaths with a 25% reduction in antimalarial drug coverage; 233·1 (153·7–342·5) million cases and 597·4 (468·0–784·4) thousand deaths with a 50% reduction; and 242·3 (158·7–358·8) million cases and 715·2 (556·4–947·9) thousand deaths with a 75% reduction. Halting planned 2020 ITN mass distribution campaigns and reducing routine ITN distributions by 25%–75% also increased malaria burden to a total of 230·5 (151·6–343·3) million cases and 411·7 (322·8–545·5) thousand deaths with a 25% reduction; 232·8 (152·3–345·9) million cases and 415·5 (324·3–549·4) thousand deaths with a 50% reduction; and 234·0 (152·9–348·4) million cases and 417·6 (325·5–553·1) thousand deaths with a 75% reduction. When ITN coverage and antimalarial drug coverage were synchronously reduced, malaria burden increased to 240·5 (156·5–358·2) million cases and 520·9 (404·1–691·9) thousand deaths with a 25% reduction; 251·0 (162·2–377·0) million cases and 640·2 (492·0–856·7) thousand deaths with a 50% reduction; and 261·6 (167·7–396·8) million cases and 768·6 (586·1–1038·7) thousand deaths with a 75% reduction.InterpretationUnder pessimistic scenarios, COVID-19-related disruption to malaria control in Africa could almost double malaria mortality in 2020, and potentially lead to even greater increases in subsequent years. To avoid a reversal of two decades of progress against malaria, averting this public health disaster must remain an integrated priority alongside the response to COVID-19.FundingBill and Melinda Gates Foundation; Channel 7 Telethon Trust, Western Australia.

Tracking progress towards malaria elimination in China: Individual-level estimates of transmission and its spatiotemporal variation using a diffusion network approach.

In order to monitor progress towards malaria elimination, it is crucial to be able to measure changes in spatio-temporal transmission. However, common metrics of malaria transmission such as parasite prevalence are under powered in elimination contexts. China has achieved major reductions in malaria incidence and is on track to eliminate, having reporting zero locally-acquired malaria cases in 2017 and 2018. Understanding the spatio-temporal pattern underlying this decline, especially the relationship between locally-acquired and imported cases, can inform efforts to maintain elimination and prevent re-emergence. This is particularly pertinent in Yunnan province, where the potential for local transmission is highest. Using a geo-located individual-level dataset of cases recorded in Yunnan province between 2011 and 2016, we introduce a novel Bayesian framework to model a latent diffusion process and estimate the joint likelihood of transmission between cases and the number of cases with unobserved sources of infection. This is used to estimate the case reproduction number, Rc. We use these estimates within spatio-temporal geostatistical models to map how transmission varied over time and space, estimate the timeline to elimination and the risk of resurgence. We estimate the mean Rc between 2011 and 2016 to be 0.171 (95% CI = 0.165, 0.178) for P. vivax cases and 0.089 (95% CI = 0.076, 0.103) for P. falciparum cases. From 2014 onwards, no cases were estimated to have a Rc value above one. An unobserved source of infection was estimated to be moderately likely (p>0.5) for 19/ 611 cases and high (p>0.8) for 2 cases, suggesting very high levels of case ascertainment. Our estimates suggest that, maintaining current intervention efforts, Yunnan is unlikely to experience sustained local transmission up to 2020. However, even with a mean of 0.005 projected up to 2020, locally-acquired cases are possible due to high levels of importation.

Geostatistical analysis of Malawi's changing malaria transmission from 2010 to 2017.

Background: The prevalence of malaria infection in time and space provides important information on the likely sub-national epidemiology of malaria burdens and how this has changed following intervention. Model-based geostatitics (MBG) allow national malaria control programmes to leverage multiple data sources to provide predictions of malaria prevalance by district over time. These methods are used to explore the possible changes in malaria prevalance in Malawi from 2010 to 2017. Methods: Plasmodium falciparum parasite prevalence ( PfPR) surveys undertaken in Malawi between 2000 and 2017 were assembled. A spatio-temporal geostatistical model was fitted to predict annual malaria risk for children aged 2-10 years ( PfPR 2-10) at 1×1 km spatial resolutions. Parameter estimation was carried out using the Monte Carlo maximum likelihood methods. Population-adjusted prevalence and populations at risk by district were calculated for 2010 and 2017 to inform malaria control program priority setting. Results: 2,237 surveys at 1,834 communities undertaken between 2000 and 2017 were identified, geo-coded and used within the MBG framework to predict district malaria prevalence properties for 2010 and 2017. Nationally, there was a 47.2% reduction in the mean modelled PfPR 2-10 from 29.4% (95% confidence interval (CI) 26.6 to 32.3%) in 2010 to 15.2% (95% CI 13.3 to 18.0%) in 2017. Declining prevalence was not equal across the country, 25 of 27 districts showed a substantial decline ranging from a 3.3% reduction to 79% reduction. By 2017, 16% of Malawi's population still lived in areas that support PfPR 2-10 ≥ 25%. Conclusions: Malawi has made substantial progress in reducing the prevalence of malaria over the last seven years. However, Malawi remains in meso-endemic malaria transmission risk. To sustain the gains made and continue reducing the transmission further, universal control interventions need to be maintained at a national level.

Geostatistical analysis of Malawi’s changing malaria transmission from 2010 to 2017

Background: The prevalence of malaria infection in time and space provides important information on the likely sub-national epidemiology of malaria burdens and how this has changed following intervention. Model-based geostatitics (MBG) allow national malaria control programmes to leverage multiple data sources to provide predictions of malaria prevalance by district over time. These methods are used to explore the possible changes in malaria prevalance in Malawi from 2010 to 2017. Methods: Plasmodium falciparum parasite prevalence ( PfPR) surveys undertaken in Malawi between 2000 and 2017 were assembled. A spatio-temporal geostatistical model was fitted to predict annual malaria risk for children aged 2–10 years ( PfPR 2–10) at 1×1 km spatial resolutions. Parameter estimation was carried out using the Monte Carlo maximum likelihood methods. Population-adjusted prevalence and populations at risk by district were calculated for 2010 and 2017 to inform malaria control program priority setting. Results: 2,237 surveys at 1,834 communities undertaken between 2000 and 2017 were identified, geo-coded and used within the MBG framework to predict district malaria prevalence properties for 2010 and 2017. Nationally, there was a 47.2% reduction in the mean modelled PfPR 2-10 from 29.4% (95% confidence interval (CI) 26.6 to 32.3%) in 2010 to 15.2% (95% CI 13.3 to 18.0%) in 2017. Declining prevalence was not equal across the country, 25 of 27 districts showed a substantial decline ranging from a 3.3% reduction to 79% reduction. By 2017, 16% of Malawi’s population still lived in areas that support PfPR 2-10 ≥ 25%. Conclusions: Malawi has made substantial progress in reducing the prevalence of malaria over the last seven years. However, Malawi remains in meso-endemic malaria transmission risk. To sustain the gains made and continue reducing the transmission further, universal control interventions need to be maintained at a national level.

Spatiotemporal geostatistical modeling of groundwater levels under a Bayesian framework using means of physical background

The joint spatiotemporal modeling of aquifer level fluctuations provides a significant tool in the prediction of groundwater levels at unvisited locations. Two types of variogram functions, appropriately modified to incorporate physical information, are presented and compared under Space-time Residual kriging methodology using the Bayesian Bootstrap idea to quantify uncertainty. The spatiotemporal trend is approximated using a component of physical meaning. A recently developed Spartan type non-separable variogram function employs tools of physical meaning to enhance the efficiency and reliability of spatiotemporal geostatistical modeling in groundwater applications. In addition, the product-sum space-time variogram is applied and involves in the separable variogram functions a scale factor of hydraulic conductivity directional ratio. The proposed variogram functions involve a non-Euclidean distance metric and are mathematically valid (i.e., constitutes permissible models). Herein, the efficiency of the proposed tools is tested using groundwater level data from an alluvial unconfined aquifer. Both functions provide improved results compared to those of the Space-time Ordinary kriging. Between the two, the non-separable one has the most efficient performance.

Minimizing the uncertainties of RCMs climate data by using spatio-temporal geostatistical modeling

The spatio-temporal Κriging approach by using five different covariance models, has been applied into Regional Climate Model (RCM) simulated precipitation and temperature dataset in a coastal area. The results of the spatio-temporal technique were evaluated against the ERA-Interim reanalysis data during the period from 1981 to 2000. The reliability of the spatio-temporal interpolation results were estimated by using both the judgment of the wireframe plots, between the sample and the fitted covariance models, and the statistic metrics. Thus, Taylor diagrams were used and the Mean Square Error (MSE) was calculated. The analysis demonstrates that the sum-metric covariance model is highly superior to the other four covariance models as it is closer to the reanalysis data, having the highest correlation coefficient, as well as, the smallest standard deviation, resulting in the smallest Root Mean Square Error. The spatio-temporal interpolation approach improved the MPI and HadGEM2 climate model dataset. The largest enhancement is pointed out in the interpolated RCM precipitation during winter and autumn. Concerning the temperature, the interpolated MPI temperature data is negligibly improved, whereas the interpolated HadGEM2 temperature is particularly optimized during winter and autumn. The spatio-temporal interpolation technique led to the minimization of the uncertainties of the Regional Climate Models, (RCMs) simulations, and also to the best agreement between them and the ERA-Interim reanalysis data during the period from 1981 to 2000. Nevertheless, the MPI climate model is more reasonable compared to the HADGEM2 for the research area.

Spatio-temporal analysis of Plasmodium falciparum prevalence to understand the past and chart the future of malaria control in Kenya

BackgroundSpatial and temporal malaria risk maps are essential tools to monitor the impact of control, evaluate priority areas to reorient intervention approaches and investments in malaria endemic countries. Here, the analysis of 36 years data on Plasmodium falciparum prevalence is used to understand the past and chart a future for malaria control in Kenya by confidently highlighting areas within important policy relevant thresholds to allow either the revision of malaria strategies to those that support pre-elimination or those that require additional control efforts.MethodsPlasmodium falciparum parasite prevalence (PfPR) surveys undertaken in Kenya between 1980 and 2015 were assembled. A spatio-temporal geostatistical model was fitted to predict annual malaria risk for children aged 2–10 years (PfPR2–10) at 1 × 1 km spatial resolution from 1990 to 2015. Changing PfPR2–10 was compared against plausible explanatory variables. The fitted model was used to categorize areas with varying degrees of prediction probability for two important policy thresholds PfPR2–10 < 1% (non-exceedance probability) or ≥ 30% (exceedance probability).Results5020 surveys at 3701 communities were assembled. Nationally, there was an 88% reduction in the mean modelled PfPR2–10 from 21.2% (ICR: 13.8–32.1%) in 1990 to 2.6% (ICR: 1.8–3.9%) in 2015. The most significant decline began in 2003. Declining prevalence was not equal across the country and did not directly coincide with scaled vector control coverage or changing therapeutics. Over the period 2013–2015, of Kenya’s 47 counties, 23 had an average PfPR2–10 of < 1%; four counties remained ≥ 30%. Using a metric of 80% probability, 8.5% of Kenya’s 2015 population live in areas with PfPR2–10 ≥ 30%; while 61% live in areas where PfPR2–10 is < 1%.ConclusionsKenya has made substantial progress in reducing the prevalence of malaria over the last 26 years. Areas today confidently and consistently with < 1% prevalence require a revised approach to control and a possible consideration of strategies that support pre-elimination. Conversely, there remains several intractable areas where current levels and approaches to control might be inadequate. The modelling approaches presented here allow the Ministry of Health opportunities to consider data-driven model certainty in defining their future spatial targeting of resources.

Using non-exceedance probabilities of policy-relevant malaria prevalence thresholds to identify areas of low transmission in Somalia

BackgroundCountries planning malaria elimination must adapt from sustaining universal control to targeted intervention and surveillance. Decisions to make this transition require interpretable information, including malaria parasite survey data. As transmission declines, observed parasite prevalence becomes highly heterogeneous with most communities reporting estimates close to zero. Absolute estimates of prevalence become hard to interpret as a measure of transmission intensity and suitable statistical methods are required to handle uncertainty of area-wide predictions that are programmatically relevant.MethodsA spatio-temporal geostatistical binomial model for Plasmodium falciparum prevalence (PfPR) was developed using data from cross-sectional surveys conducted in Somalia in 2005, 2007–2011 and 2014. The fitted model was then used to generate maps of non-exceedance probabilities, i.e. the predictive probability that the region-wide population-weighted average PfPR for children between 2 and 10 years (PfPR2–10) lies below 1 and 5%. A comparison was carried out with the decision-making outcomes from those of standard approaches that ignore uncertainty in prevalence estimates.ResultsBy 2010, most regions in Somalia were at least 70% likely to be below 5% PfPR2–10 and, by 2014, 17 regions were below 5% PfPR2–10 with a probability greater than 90%. Larger uncertainty is observed using a threshold of 1%. By 2011, only two regions were more than 90% likely of being < 1% PfPR2–10 and, by 2014, only three regions showed such low level of uncertainty. The use of non-exceedance probabilities indicated that there was weak evidence to classify 10 out of the 18 regions as < 1% in 2014, when a greater than 90% non-exceedance probability was required.ConclusionUnlike standard approaches, non-exceedance probabilities of spatially modelled PfPR2–10 allow to quantify uncertainty of prevalence estimates in relation to policy relevant intervention thresholds, providing programmatically relevant metrics to make decisions on transitioning from sustained malaria control to strategies that encompass methods of malaria elimination.

Spatiotemporal geostatistical modelling of groundwater level variations at basin scale: a case study at Crete's Mires Basin

Abstract Spatiotemporal geostatistical analysis of groundwater levels is a significant tool for groundwater resources management. This work presents a valid spatiotemporal geostatistical model for the groundwater level variations of an aquifer in Crete, Greece. The goal of this approach is to accurately map the aquifer level at variable time-steps using joint space–time information. The proposed model applies the space–time ordinary kriging (STOK) methodology using joint space–time covariance functions. A space–time experimental variogram is determined from the monthly groundwater level time-series between the hydrological years 2009 and 2014 at 11 sampling stations. The experimental spatiotemporal variogram is successfully fitted by the product–sum model using a Matérn spatial and temporal function. STOK was used to predict the monthly groundwater level at each sampling station from January to May 2015. Validation results show low prediction errors that range from 0.95 to 1.45 m, while the kriging variance accurately determines the variability of predictions. Maps of groundwater level predictions and uncertainty are developed for significant months of the validation period to assess the aquifer spatiotemporal variability. This work demonstrates that space–time geostatistics can successfully model the spatial dynamic behaviour of an aquifer when the space–time dependencies are appropriately modelled, even for a sparse dataset.

A spatiotemporal geostatistical hurdle model approach for short-term deforestation prediction

This paper introduces and tests a geostatistical spatiotemporal hurdle approach for predicting the spatial distribution of future deforestation (one to three years ahead in time). The method accounts for neighborhood effects by modeling the auto-correlation of occurrence and intensity of deforestation, using a spatiotemporal geostatistical specification. Deforestation observations are modeled as a function of pertinent control variables, such as distance to roads and protected areas, and the model accounts for space–time autocorrelated residuals with non-stationary variance. Applied to the Brazilian Amazon, the model predicted the locations of new deforestation events with over 90% agreement. In addition, 100% of the deforestation intensity values were contained in the model’s confidence bounds. The features of the model and validation results qualify the model as a strong candidate for short-term deforestation modeling.

Identifying and characterizing hepatitis C virus hotspots in Massachusetts: a spatial epidemiological approach

BackgroundHepatitis C virus (HCV) infections have increased during the past decade but little is known about geographic clustering patterns.MethodsWe used a unique analytical approach, combining geographic information systems (GIS), spatial epidemiology, and statistical modeling to identify and characterize HCV hotspots, statistically significant clusters of census tracts with elevated HCV counts and rates. We compiled sociodemographic and HCV surveillance data (n = 99,780 cases) for Massachusetts census tracts (n = 1464) from 2002 to 2013. We used a five-step spatial epidemiological approach, calculating incremental spatial autocorrelations and Getis-Ord Gi* statistics to identify clusters. We conducted logistic regression analyses to determine factors associated with the HCV hotspots.ResultsWe identified nine HCV clusters, with the largest in Boston, New Bedford/Fall River, Worcester, and Springfield (p < 0.05). In multivariable analyses, we found that HCV hotspots were independently and positively associated with the percent of the population that was Hispanic (adjusted odds ratio [AOR]: 1.07; 95% confidence interval [CI]: 1.04, 1.09) and the percent of households receiving food stamps (AOR: 1.83; 95% CI: 1.22, 2.74). HCV hotspots were independently and negatively associated with the percent of the population that were high school graduates or higher (AOR: 0.91; 95% CI: 0.89, 0.93) and the percent of the population in the “other” race/ethnicity category (AOR: 0.88; 95% CI: 0.85, 0.91).ConclusionWe identified locations where HCV clusters were a concern, and where enhanced HCV prevention, treatment, and care can help combat the HCV epidemic in Massachusetts. GIS, spatial epidemiological and statistical analyses provided a rigorous approach to identify hotspot clusters of disease, which can inform public health policy and intervention targeting. Further studies that incorporate spatiotemporal cluster analyses, Bayesian spatial and geostatistical models, spatially weighted regression analyses, and assessment of associations between HCV clustering and the built environment are needed to expand upon our combined spatial epidemiological and statistical methods.

Spatiotemporal regression Kriging to predict precipitation using time-series MODIS data

Accurate prediction of the spatiotemporal distribution of precipitation is an important guide for more efficient agricultural production. However in the Xinjiang Uygur Autonomous Region, China, it is difficult to ensure accuracy due to sparse and unevenly distributed precipitation monitoring stations. The precipitation on raster grids must be predicted from point data. The combined China monthly mean meteorological data sets were used to build spatiotemporal geostatistical models to predict mean monthly precipitation in Xinjiang. Predictions in space and time were made for precipitation using spatiotemporal regression Kriging with some covariates. The Moderate Resolution Imaging Spectroradiometer 1-month images time series, topographic layers representing the normalized difference vegetation index and digital elevation model, and a temporal index to adjust for yearly periodic were used as covariates. The optimal covariates were selected by the all subset regression method to determine which predictor variables to be included in the multiple regression models. The accuracy of our mean monthly precipitation predictions was assessed by leave-one-out cross-validation. The prediction accuracy of the proposed spatiotemporal regression Kriging approach was compared with spatiotemporal multi-linear regression and spatiotemporal Kriging. These experimental results show that the normalized difference vegetation index, latitude, longitude, elevation, and time periodicity index are the optimal covariates for mean monthly precipitation prediction. The spatiotemporal distribution of precipitation in Xinjiang exhibits a distinctive pattern; in the north and west, there is more precipitation than in the south and east, respectively and more precipitation in the mountains than on the plains. Precipitation is closely related to topography. Annually, summer precipitation is the highest, followed by, spring and autumn, with winter the driest season in Xinjiang. Considering regression residuals the product---sum model was found to be suitable to fit the spatiotemporal variogram at higher accuracy. Precipitation maps generated by spatiotemporal regression Kriging were more accurate than those produced by the other tested methods, with lower MAE, RMSE, and BIAS values, and higher COR values for validation sampling sites. Spatiotemporal regression Kriging is an efficient method for accurate spatiotemporal prediction of precipitation in Xinjiang.