Spatiotemporal Kriging Research Articles

Spatio-temporal Kriging for spatial irradiance estimation with short-term forecasting in a thermosolar power plant

This article proposes a method to improve the efficiency of solar power plants by estimating and forecasting the spatial distribution of direct normal irradiance (DNI) using a sensor network and anemometer data. For this purpose, the proposed approach employs spatio-temporal kriging with an anisotropic spatio-temporal variogram that depends on wind speed to accurately estimate the distribution of DNI in real-time, making it useful for short-term forecast and nowcast of DNI. Finally, the method is validated using synthetic data from varying sky conditions, outperforming another state-of-the-art technique.

Satellite-Based Reconstruction of Atmospheric CO2 Concentration over China Using a Hybrid CNN and Spatiotemporal Kriging Model

Although atmospheric CO2 concentrations collected by satellites play a crucial role in understanding global greenhouse gases, the sparse geographic distribution greatly affects their widespread application. In this paper, a hybrid CNN and spatiotemporal Kriging (CNN-STK) model is proposed to generate a monthly spatiotemporal continuous XCO2 dataset over China at 0.25° grid-scale from 2015 to 2020, utilizing OCO-2 XCO2 and geographic covariates. The validations against observation samples, CAMS XCO2 and TCCON measurements indicate the CNN-STK model is effective, robust, and reliable with high accuracy (validation set metrics: R2 = 0.936, RMSE = 1.3 ppm, MAE = 0.946 ppm; compared with TCCON: R2 = 0.954, RMSE = 0.898 ppm and MAE = 0.741 ppm). The accuracy of CNN-STK XCO2 exhibits spatial inhomogeneity, with higher accuracy in northern China during spring, autumn, and winter and lower accuracy in northeast China during summer. XCO2 in low-value-clustering areas is notably influenced by biological activities. Moreover, relatively high uncertainties are observed in the Qinghai-Tibet Plateau and Sichuan Basin. This study innovatively integrates deep learning with the geostatistical method, providing a stable and cost-effective approach for other countries and regions to obtain regional scales of atmospheric CO2 concentrations, thereby supporting policy formulation and actions to address climate change.

Estimating the Amount of the Wild Artemisia annua in China Based on the MaxEnt Model and Spatio-Temporal Kriging Interpolation.

In order to determine the distribution area and amount of Artemisia annua Linn. (A. annua) in China, this study estimated the current amount of A. annua specimens based on the field survey sample data obtained from the Fourth National Census of Chinese Medicinal Resources. The amount was calculated using the maximum entropy model (MaxEnt model) and spatio-temporal kriging interpolation. The influencing factors affecting spatial variations in the amount were studied using geographic probes. The results indicated that the amount of A. annua in China was about 700 billion in 2019. A. annua was mainly distributed in the circular coastal belt of Shandong Peninsula, central Hebei, Tianjin, western Liaoning, and along the Yangtze River and in the middle and lower reaches of Jiangsu, Anhui, and the northern Chongqing provinces. The main factors affecting the amount are the precipitation in the wettest and the warmest seasons, the average annual precipitation, and the average temperature in the coldest and the driest seasons. The results show that the amount of A. annua is strongly influenced by precipitation and temperature.

A comparative evaluation of spatial interpolation techniques for maximum temperature series in the Montreal region, Canada

This study aims to provide a comparative analysis of two of the most used methods of spatial interpolation – Thiessen Polygons (TP) and Inverse Distance Weighting (IDW) with a spatio-temporal approach – Spatio-temporal kriging (STK) on a data series from Canada. The IDW parameter is optimized to obtain the best fitting for the studied series, based on the Root Mean Squared Errors (RMSE) and Mean Absolute Percentage Error (MAPE). The advantages and disadvantages of each algorithm are emphasized. Although TP registered the lowest RMSE and a MAPE, the analysis favors the STK use for modeling Montreal’s maximum temperature series.

Simultaneous monitoring of the limited area ionosphere with the use of GPS and ionosonde

The importance of this study lies in its contribution to the field of ionospheric science, particularly in the monitoring and prediction of ionospheric parameters. This study focuses on comparing two techniques for spatio-temporal kriging of critical ionospheric parameters, namely the F2 layer critical frequency (foF2) and Total Electron Content (TEC), under both quiet and disturbed ionospheric conditions. The first technique, Ordinary Kriging (OK), relies solely on foF2 data, while the second technique, Kriging with External Drift (KED), incorporates the dynamic relationship between foF2 and TEC data to improve the interpolation process. This study demonstrates how KED, which utilizes dynamic secondary information, offers advantages over OK. By simultaneously monitoring the ionosphere from a single ionosonde station and collecting data from visible GPS satellites, KED enhances the accuracy of spatial structural analysis, enabling more precise estimations of ionospheric characteristics across interpolation grid nodes. The research highlights that the non-uniform distribution of ionosonde stations, especially in regions with limited foF2 data, can benefit from KED's incorporation of TEC data. Additionally, the study reveals the potential for improving TEC maps by assimilating foF2 data located at the periphery of the observation area. Furthermore, the paper discusses the determination of semivariogram structures for both foF2 and TEC data, emphasizing the spatial correlations between data points. These findings contribute to a better understanding of ionospheric behavior and the potential for enhanced ionospheric modeling.

Downscaling MERRA-2 Reanalysis PM2.5 Series over the Arabian Gulf by Inverse Distance Weighting, Bicubic Spline Smoothing, and Spatio-Temporal Kriging.

This study offers a detailed analysis of the fine particulate matter (PM2.5) series in the Arabian Gulf zone, employing three interpolation models, Inverse Distance Weighting (IDW), Bicubic Spline Smoothing (BSS) and Spatio-Temporal Kriging (STK). Unique advancements include the use of complete temporal records in IDW, the management of edge effects in S with synthetic buffer points, and the application of STK to detrended data residuals. The results indicated that the BBS, particularly adept at handling boundary conditions, significantly outperformed the other methods. Compared to IDW, the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) decreased by 21%, 15%, and 21%, respectively, in BSS. Compared to STK, MAE, RMSE, and MAPE were lower with around 60%, 61%, and 58%, respectively in BSS. These findings underscore the efficacy of the BSS method in spatial interpolation for environmental monitoring, contributing to enhanced PM2.5 analysis and public health management in the region.

Understanding the Propagation of Meteorological Drought to Groundwater Drought: A Case Study of the North China Plain

As extreme climate events become more common with global warming, groundwater is increasingly vital for combating long-term drought and ensuring socio-economic and ecological stability. Currently, the mechanism of meteorological drought propagation to groundwater drought is still not fully understood. This study focuses on the North China Plain (NCP), utilizing statistical theories, spatiotemporal kriging interpolation, and the Mann–Kendall trend test to examine the spatial and temporal distribution characteristics of groundwater from 2005 to 2021. Based on drought theory, the characteristics and propagation process of drought are further quantified. Key findings reveal the following: (1) Shallow groundwater depths in the NCP follow a zonal pattern from the western mountains to the eastern plains and coastal areas. Over two-thirds of this region showed an increase in groundwater depth at a rate of 0–0.05 m/a; (2) Groundwater drought frequency typically ranges from 3 to 6 times, with an average duration of 10 to 30 months and average severity between 10 and 35; (3) Delayed effects last between 0 to 60 months, with attenuation effects varying from 0 to 3 and prolonged effects extending from 0 to 16. Additionally, delayed effects intensify with increasing time scales, while prolonged effects weaken. Notably, both delayed and prolonged effects in the north of the NCP are more pronounced than in the south of the region. This study quantifies the process by which meteorological drought propagates to groundwater drought, offering a new perspective for understanding the interaction between groundwater and meteorological drought. It holds significant scientific importance for monitoring drought and managing water resources in the context of global climate change.

Spatiotemporal modelling of PM2.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {PM}_{2.5}$$\\end{document} concentrations in Lombardy (Italy): a comparative study

This study presents a comparative analysis of three predictive models with an increasing degree of flexibility: hidden dynamic geostatistical models (HDGM), generalised additive mixed models (GAMM), and the random forest spatiotemporal kriging models (RFSTK). These models are evaluated for their effectiveness in predicting PM2.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {PM}_{2.5}$$\\end{document} concentrations in Lombardy (North Italy) from 2016 to 2020. Despite differing methodologies, all models demonstrate proficient capture of spatiotemporal patterns within air pollution data with similar out-of-sample performance. Furthermore, the study delves into station-specific analyses, revealing variable model performance contingent on localised conditions. Model interpretation, facilitated by parametric coefficient analysis and partial dependence plots, unveils consistent associations between predictor variables and PM2.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {PM}_{2.5}$$\\end{document} concentrations. Despite nuanced variations in modelling spatiotemporal correlations, all models effectively accounted for the underlying dependence. In summary, this study underscores the efficacy of conventional techniques in modelling correlated spatiotemporal data, concurrently highlighting the complementary potential of Machine Learning and classical statistical approaches.

A Novel Hybrid Spatiotemporal Missing Value Imputation Approach for Rainfall Data: An Application to the Ratnapura Area, Sri Lanka

Meteorological time series, such as rainfall data, show spatiotemporal characteristics and are often faced with the problem of containing missing values. Discarding missing values or modeling data with missing values causes negative impacts on the accuracy of the final predictions. Hence, accurately estimating missing values by considering the spatiotemporal variations in data has become a crucial step in eco-hydrological modeling. The multi-layer perceptron (MLP) is a promising tool for modeling temporal variation, while spatial kriging (SK) is a promising tool for capturing spatial variations. Therefore, in this study, we propose a novel hybrid approach combining the multi-layer perceptron method and spatial kriging to impute missing values in rainfall data. The proposed approach was tested using spatiotemporal data collected from a set of nearby rainfall gauging stations in the Ratnapura area, Sri Lanka. Missing values are present in collected rainfall data consecutively for a considerably longer period. This pattern has scattered among stations discontinuously over five years. The proposed hybrid model captures the temporal variability and spatial variability of the rainfall data through MLP and SK, respectively. It integrates predictions obtained through both MLP and SK with a novel optimal weight allocation method. The performance of the model was compared with individual approaches, MLP, SK, and spatiotemporal kriging. The results indicate that the novel hybrid approach outperforms spatiotemporal kriging and the other two pure approaches.

Lightning forecast from chaotic and incomplete time series using wavelet de-noising and spatiotemporal kriging

PurposePresent a method to impute missing data from a chaotic time series, in this case lightning prediction data, and then use that completed dataset to create lightning prediction forecasts.Design/methodology/approachUsing the technique of spatiotemporal kriging to estimate data that is autocorrelated but in space and time. Using the estimated data in an imputation methodology completes a dataset used in lightning prediction.FindingsThe techniques provided prove robust to the chaotic nature of the data, and the resulting time series displays evidence of smoothing while also preserving the signal of interest for lightning prediction.Research limitations/implicationsThe research is limited to the data collected in support of weather prediction work through the 45th Weather Squadron of the United States Air Force.Practical implicationsThese methods are important due to the increasing reliance on sensor systems. These systems often provide incomplete and chaotic data, which must be used despite collection limitations. This work establishes a viable data imputation methodology.Social implicationsImproved lightning prediction, as with any improved prediction methods for natural weather events, can save lives and resources due to timely, cautious behaviors as a result of the predictions.Originality/valueBased on the authors’ knowledge, this is a novel application of these imputation methods and the forecasting methods.

Spatiotemporal estimation of nutrient data from the northwest pacific and east asian seas

Nutrient data obtained from field observations have the potential to enhance our understanding of oceanic biogeochemical cycling and productivity changes. In particular, long-term nutrient data can provide valuable information on the links between climate change and biogeochemical changes. However, unlike other observational variables such as sea surface temperature, nutrient data are limited in terms of their broad-scale observations and automated sensor-based measurements. In this study, we analyzed nitrate and phosphate data obtained from coastal regions in Northeast Asia and the northwest Pacific from 1980 to 2019 using the spatiotemporal kriging technique and provide results in a spatiotemporal grid format. The data are available at monthly intervals and may be attractive to researchers in the fields of oceanography, marine ecology, and marine biogeochemistry at the climate change scale. Furthermore, sharing the source code of the data production process can contribute to better long-term data reproduction in the future.

Reconstructing High-Frequency Radar Derived Ocean Surface-Current Fields Using Spatio-Temporal Kriging

Reconstructing High-Frequency Radar Derived Ocean Surface-Current Fields Using Spatio-Temporal Kriging

Évaluation des changements dans les niveaux régionaux des eaux souterraines par krigeage spatio-temporel : application au système aquifère du sud du bassin de Mexico

AbstractA common approach for calculating the spatial distribution of groundwater level changes consists in choosing a set of different times, interpolating the groundwater level data available at each time over a spatial grid, and then calculating changes in each period by subtracting the interpolated values for these times. However, this can produce misleading results when the data are available in different positions for consecutive times. This paper presents an alternative procedure based on the interpolation of the groundwater level with spatio-temporal kriging, the assessment of the temporal groundwater elevation changes over a regional semiconfined aquifer, and the estimation of their error standard deviations. A comparative analysis of cross-validation results and error standard deviations provides a quantitative measure of the superiority of the introduced approach with respect to the one given in the literature. Moreover, the spatio-temporal case produces more reasonable estimates than the spatial kriging, notably fewer extreme recoveries and drawdowns, in an area under high water stress, such as the upper aquifer of the southern part of the Basin of Mexico aquifer system.

Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach

Traffic speed is central to characterizing the fluidity of the road network. Many transportation applications rely on it, such as real-time navigation, dynamic route planning, and congestion management. Rapid advances in sensing and communication techniques make traffic speed detection easier than ever. However, due to sparse deployment of static sensors or low penetration of mobile sensors, speeds detected are incomplete and far from network-wide use. In addition, sensors are prone to error or missing data due to various kinds of reasons, speeds from these sensors can become highly noisy. These drawbacks call for effective techniques to recover credible estimates from the incomplete data. In this work, we first identify the issue as a spatiotemporal kriging problem and propose a Laplacian enhanced low-rank tensor completion (LETC) framework featuring both low-rankness and multi-dimensional correlations for large-scale traffic speed kriging under limited observations. To be specific, three types of speed correlation including temporal continuity, temporal periodicity, and spatial proximity are carefully chosen and simultaneously modeled by three different forms of graph Laplacian, named temporal graph Fourier transform, generalized temporal consistency regularization, and diffusion graph regularization. We then design an efficient solution algorithm via several effective numeric techniques to scale up the proposed model to network-wide kriging. By performing experiments on two public million-level traffic speed datasets, we finally draw the conclusion and find our proposed LETC achieves the state-of-the-art kriging performance even under low observation rates, while at the same time saving more than half computing time compared with baseline methods. Some insights into spatiotemporal traffic data modeling and kriging at the network level are provided as well.

Optimal redesign of coastal groundwater quality monitoring networks under uncertainty: application of the theory of belief functions.

This paper presents a new methodology for the optimal redesign of water quality monitoring networks in coastal aquifers. The GALDIT index is used to evaluate the extent and magnitude of seawater intrusion (SWI) in coastal aquifers. The weights of the GALDIT parameters are optimized using the genetic algorithm (GA). A SEAWAT-based simulation model, a spatiotemporal Kriging interpolation technique, and an artificial neural network surrogate model are then implemented to simulate total dissolved solids (TDS) concentration in coastal aquifers. To obtain more precise estimations, an ensemble meta-model is developed using the Dempster-Shafer's belief function theory (D-ST) to combine the results obtained from the three individual simulation models. The combined meta-model is then used for calculating more precise TDS concentration. Some plausible scenarios are defined for variation of water elevation and water salinity at the coastline to incorporate uncertainty through the concept of value of information (VOI). Finally, the potential wells with the highest values of information are taken into consideration to redesign coastal groundwater quality monitoring network under uncertainty. The performance of the proposed methodology is evaluated by applying it to the Qom-Kahak aquifer, north-central Iran, which is threatened by SWI. At first, the individual and ensemble simulation models are developed and validated. Then, several scenarios are defined regarding the plausible changes in TDS concentration and water level at the coastline. In the next step, the scenarios, the GALDIT-GA vulnerability map, and the VOI concept are used for redesigning the existing monitoring network. The results illustrate that the revised groundwater quality monitoring network containing 10 new sampling locations outperforms the existing one based on the VOI criterion.

Spatiotemporal interpolation of surface chloride content for marine RC structures based on non-uniform spatiotemporal Kriging interpolation method

Chloride-induced corrosion of marine reinforced concrete structures involves numerous uncertainties related to environmental exposure zone. The exposure zone is strongly correlated with surface chloride content, which exhibits significant spatiotemporal variability. In this study, the scale of fluctuation of the chloride content in different exposure zones was estimated to explore the effect of the exposure zone on the spatial variability of the marine chloride environment. Based on the detection data of surface chloride content over a time span of 18 years at Zhapu Port, we present a modified spatiotemporal Kriging interpolation method that extends interpolation from 2D plane to 3D space by replacing surface distance with the Euclidean distance. The chloride environmental spatiotemporal distance field model was constructed using the particle swarm optimization algorithm. The results show that the prediction of surface chloride content is physically more realistic when modified spatiotemporal Kriging is used with the spatiotemporal distance amplified by 2–3 times. Additionally, a method to optimise the location of the detection point is proposed, which can improve the cost–benefit ratio of surface chloride content detection on reinforced concrete structures by 37.5%.

Spatiotemporal Kriging for Days without Rainfall in a Region of Northeastern Brazil

Climate change has had several negative effects, including more severe storms, warmer oceans, high temperatures and, in particular, increased drought, directly affecting the water availability in a region. The Northeast Region of Brazil (NEB) is known to have scarce rainfall, especially in the northeastern semiarid region. Droughts and high temperatures in the NEB negatively affect water resources in the region, resulting in a gradual decrease in the storage volume in the reservoirs and contributing to unprecedented water scarcity. The objective of this research was to investigate the spatiotemporal behavior of the number of days without rain (DWR) in a region of northeastern Brazil, making use of the spatiotemporal geostatistical methodology. Cross-validation resulted in an R2 of 71%, indicating a good performance of spatiotemporal kriging for predicting DWRs. The results indicate a spatial dependence for a radius of up to 39 km and that the DWR observations in a certain location influence its estimates in the next 2.8 years. The projection maps from 2021 to 2030 identified a growing trend in the DWRs. With the results presented in our study, it is expected that they can be used by government agencies for the adoption of public policies aiming to minimize the possible damage caused by long periods of drought.

Spatiotemporal dynamic interpolation simulation and prediction method of fine particulate matter based on multi-source pollution model

Taking the air pollution monitoring data of 34 air monitoring stations in Beijing from February 8 to February 9, 2020, as an example. A spatiotemporal dynamic interpolation model of PM2.5 based on a multi-source pollution model was established. Based on the hourly spatiotemporal data of the day, the dispersion and attenuation of non-point source pollution in Beijing were interpolated. An improved hybrid genetic algorithm was used to solve the parameters of the air pollution model. The spatiotemporal Kriging model was used to predict the PM2.5 concentration diffusion on an hourly scale. The data of this area were analyzed quantitatively and qualitatively. The prediction data based on the spatiotemporal data before the current time was verified by the actual monitoring data. The results show that the model and method constructed in this paper could simulate and predict PM2.5 concentration on an hourly scale well, which could provide a good reference for the analysis, simulation, and prediction of air pollution.

Spatiotemporal prediction and optimization of environmental suitability in citrus-producing areas

The increasing need for citrus has driven the rapid expansion of citrus planting areas. However, not all areas are suitable for growing citrus. It is necessary to understand the future changing trend of environmental suitability in citrus-producing areas. Here, based on the soil nutrient data of citrus cultivation from 2006 to 2018, the spatiotemporal kriging method was used to predict the spatiotemporal distribution of soil nutrients in Zigui County, Hubei Province. Then, geographical and meteorological conditions were combined to evaluate the suitability for citrus cultivation at temporal and spatial levels, and the results were verified by the yield and quality data of citrus. The results showed that from 2018 to 2027, the overall suitability of the citrus-producing area displayed a gradually rising trend, with the “suitable” producing area increasing from 4.5% to 20.16%. The validation results indicated that the mean relative errors of spatiotemporal predictors were less than 30% except for the effective iron. Correlation analysis revealed that the proportion of “moderately suitable” and “suitable” orchards had significant positive correlations with annual yield. The low suitability of Maoping town was mainly attributed to its soil acidification and available P content, and that of Shazhenxi town was ascribed to its low soil contents of available P and N. The optimal fertilization scheme was constructed by an artificial neural network to optimize the fertilization status of some citrus producing areas. This study has created a dynamic assessment of the environmental suitability of citrus production areas to support improvements in citrus production.

A stabilized spatiotemporal kriging method for disease mapping and application to male oral cancer and female breast cancer in Taiwan

Mapping spacetime disease rates can provide a more in-depth understanding of their distribution and trends. Traditional spatiotemporal kriging methods can break the constraints of geopolitical boundaries and time intervals. Still, disease rates in densely and sparsely populated areas are stabilized to the same degree, resulting in a map that is oversmoothed in some places but undersmoothed in others. The stabilized spatiotemporal kriging method proposed in this study overcomes this problem by allowing for nonconstant variances over space and time. A spatiotemporal map of the standardized incidence ratio for oral cancer in men in Taiwan between 1997 and 2017 reveals that the high-risk areas for oral cancer are in the midwestern and southeastern regions of Taiwan, spreading toward the center and north, with persistent cold spots in the northern and southwestern urban regions. However, the corresponding map for breast cancer in women in Taiwan reveals that the high-risk areas for breast cancer are concentrated in densely populated urban regions in the west. Spatiotemporal maps facilitate our understanding of disease risk dynamics. We recommend using the proposed stabilized spatiotemporal kriging method for mapping disease rates across space and time.