Geostatistical Methods Research Articles

A Stepwise Cosimulation Framework for Modeling Critical Elements in Copper Porphyry Deposits

The increased attention given to batteries has given rise to apprehensions regarding their availability; they have thus been categorized as essential commodities. Cobalt (Co), copper (Cu), lithium (Li), nickel (Ni), and molybdenum (Mo) are frequently selected as the primary metallic elements in lithium-ion batteries. The principal aim of this study was to develop a computational algorithm that integrates geostatistical methods and machine learning techniques to assess the resources of critical battery elements within a copper porphyry deposit. By employing a hierarchical/stepwise cosimulation methodology, the algorithm detailed in this research paper successfully represents both soft and hard boundaries in the simulation results. The methodology is evaluated using several global and local statistical studies. The findings indicate that the proposed algorithm outperforms the conventional approach in estimating these five elements, specifically when utilizing a stepwise estimation strategy known as cascade modeling. The proposed algorithm is also validated against true values by using a jackknife method, and it is shown that the method is precise and unbiased in the prediction of critical battery elements.

DESARROLLO DE MÉTODOS BASADOS EN REDES NEURONALES EN LA ESTIMACIÓN DE RECURSOS MINERALES

Due to economic and physical limitations, our understanding of mineral resources in a specific area of interest is limited and fragmented. Traditionally, this problem has been solved using the Kriging geostatistical method, where the ore grade is estimated at unmeasured locations using known values of the grade at surrounding points. The advantage of this method lies in the calculation of weights through a spatial variability model known as a variogram. However, the method is imperfect, as it is based on the assumption of stationarity, aditivity, linearity and potential subjectivity in variographic modelling. This study proposes to approach the mineral resource estimation problem as a regression problem using neural networks, which are not subject to the restrictions of stationarity, aditivity, linearity and spatial modelling of geostatistics methods. Kriging and a radial basis function neural network and a multilayer perceptron have been compared using different validation metrics. The results show that a properly trained neural network model, with appropriate labelling of the mineral grade and its input characteristics, achieves similar results to the geostatistical approach, with a significant reduction in time, while avoiding all the aforementioned assumptions. However, neural networks do not consider the spatial correlation of ore grade or reproduce it at the locations where it was measured, characteristics that have marked distrust in its industrial implementation and that are discussed in this article, finally proposing an adjustment between both approaches at a minimum sacrifice of time and labor costs. Keywords Neural networks; machine learning; geostatistics.

Monitoring and estimation of mining and geometric indicators of the deposit

The article presents the results of mining and geometric modeling of indicators of mineral deposits. In order to estimate and monitor them, a wide range of geoinformation systems-based methods and techniques of geometrization is applied. The sequence and stages of mining and geometric estimation of deposits are described considering specific mining and geological conditions. The built models are used at Ukraine’s mining enterprises that develop solid minerals. Much attention is paid to processing initial mining and geological data, providing the basis for mining and geometric modeling. Geostatistical methods give high results when processing and assessing reliability of the input modeling data and processing and presenting modeling results. Different types of deposits require different approaches to geometrization. Deposits with high variability of indicators require accounting, data grouping and zoning. For this purpose, a heuristic algorithm is developed, which is an efficient independent method of modeling and enables considering the high level of heterogeneity of the spatial distribution of mining and geological indicators of the deposit. The results of the modeling can be used for deposit estimation and monitoring, reserves calculation, and mining operations planning.

Assessment and mapping of noise pollution in recreation spaces using geostatistic method after COVID-19 lockdown in Turkey

Increased use of recreational areas after the lifting of COVID-19 pandemic restrictions has led to increased noise levels. This study aims to determine the level of noise pollution experienced in recreational areas with the increasing domestic and international tourism activities after the lifting of pandemic lockdowns, to produce spatial distribution maps of noise pollution, and to develop strategic planning suggestions for reducing noise pollution in line with the results obtained. Antalya-Konyaaltı Beach Recreation Area, the most important international tourism destination of Turkey, is determined as the study area. To determine the existing noise pollution, 31 measurement points were marked at 100 m intervals within the study area. Noise measurements were taken during the daytime (07:00–19:00), evening (19:00–23:00), and nighttime (23:00–07:00) on weekdays (Monday, Wednesday, Friday) and weekends (Sunday) over 2 months in the summer when the lockdown was lifted. In addition, the sound level at each measurement point was recorded for 15 min, while the number of vehicles passing through the area during the same period was determined. The database created as a result of measurements and observations was analyzed using statistical and geostatistical methods. After the analysis of the data, it was found that the co-kriging-stable model showed superior performance in noise mapping. Additionally, it was revealed that there is a high correlation between traffic density and noise intensity, with the highest equivalent noise level (Leq) on weekdays and weekend evenings due to traffic and user density. In conclusion, regions exposed to intense noise pollution were identified and strategic planning recommendations were developed to prevent/reduce noise sources in these identified regions.

A multisensor approach coupled with multivariate statistics and geostatistics for assessing the status of land degradation: The case of soils contaminated in a former outdoor shooting range

Soil contamination in outdoor shooting ranges (OSRs) is a major threat for human health, particularly when, after the end of activities, the land is used for recreational areas or agricultural production. The status of land degradation of an OSR in southern Italy was assessed using a multisensor approach. It was based on: i) proximal sensors, including electromagnetic induction (EMI) for measuring soil electrical conductivity (ECa) and magnetic susceptibility (MSa), γ-ray spectrometry for K, eU and eTh analyses and ultrasonic penetrometry detecting cone index (CI) data representative of soil's strength, ii) field surveys on soil thickness (ST), and iii) laboratory analyses of potentially-toxic-elements (PTEs) by portable X-ray fluorescence spectrometry and polycyclic aromatic hydrocarbons (PAHs) by gas-chromatography. Spatial variability of measurements was modelled and mapped using geostatistical methods. The most densely measured covariate (i.e., the ECa of the topsoil) was used within kriging with external drift to improve the PTEs predictions. The PTEs maps were complemented by maps of spatial uncertainty. A robust multivariate principal component analysis (rPCA) was applied to proximal sensor and laboratory data and allowed to identify associations of PAHs, lead, CI with the topsoil ECa along the first component (PC1), highlighting the correlation between land anthropogenic effects and EMI measures; while the association between the ST (estimating the depth of underground travertine hard-layers) and the bottom soil ECa and MSa along the second component (PC2) evidenced the influence of soil stratigraphy on the EMI measures. This study demonstrates that the simultaneous use of different proximal sensors associated with laboratory analysis can allow to assess and model the spatial variability of the land degradation status of an OSR, including soil compaction, organic and inorganic contamination. The correlation between EMI data with the PTEs content highlights the potential of this technique in the field of soil contamination.

A Comparison of Markov and Mechanistic Models for Soil-Transmitted Helminth Prevalence Projections in the Context of Survey Design.

Globally, there are over 1 billion people infected with soil-transmitted helminths (STHs), mostly living in marginalized settings with inadequate sanitation in sub-Saharan Africa and Southeast Asia. The World Health Organization recommends an integrated approach to STH morbidity control through improved access to sanitation and hygiene education and the delivery of preventive chemotherapy (PC) to school-age children delivered through schools. Progress of STH control programs is currently estimated using a baseline (pre-PC) school-based prevalence survey and then monitored using periodical school-based prevalence surveys, known as Impact Assessment Surveys (IAS). We investigated whether integrating geostatistical methods with a Markov model or a mechanistic transmission model for projecting prevalence forward in time from baseline can improve IAS design strategies. To do this, we applied these 2 methods to prevalence data collected in Kenya, before evaluating and comparing their performance in accurately informing optimal survey design for a range of IAS sampling designs. We found that, although both approaches performed well, the mechanistic method more accurately projected prevalence over time and provided more accurate information for guiding survey design. Both methods performed less well in areas with persistent STH hotspots where prevalence did not decrease despite multiple rounds of PC. Our findings show that these methods can be useful tools for more efficient and accurate targeting of PC. The general framework built in this paper can also be used for projecting prevalence and informing survey design for other neglected tropical diseases.

Generalized Yang Chizhong filtering and interpolation method without stationarity assumption

The stationarity assumption of geostatistical methods is difficult to satisfy in practice. To overcome this limitation, this study proposed a geometric and statistical coupling strategy for modeling spatial dependence structures and developed a generalized Yang Chizhong filtering and interpolation (GYangCZ) method without the assumption of stationarity. In this work, we theoretically prove the effectiveness of Yang Chizhong filtering in fitting spatial dependence structures from a geometric perspective, and develop an orientation-constrained Yang Chizhong filtering to fit the local and discontinuous spatial dependence structures. To measure nonstationary spatial dependence structure, we define a local statistical indicator (i.e., fundamental variation function) by comparing the variance of the original data and the fitted geometric surfaces obtained under different filtering radii. The fundamental variation function is used as the kernel function to obtain the approximate best linear unbiased estimators at unobserved locations. We theoretically demonstrate that when only a linear drift exists in local areas, GYangCZ does not require the stationarity assumption. GYangCZ was used to estimate the gold grade of the Xiadian gold deposit in China. The results show that GYangCZ outperformed ordinary kriging, moving window kriging, and kriging convolution networks. GYangCZ is easy to implement with wide applications in geoscience.

Geo-visualizing the hotspots of smog-induced health effects in district Gujranwala, Pakistan: a community perspective.

This study aims to examine the health effects of smog on different age groups in Gujranwala and its associated health effects. To achieve this, primary data was gathered through a questionnaire survey focused on health issues faced by elderly individuals during the smog season. The results of the survey revealed that older adults in Gujranwala are particularly vulnerable to a range of health problems during this period, including coughing, throat infections, irritated eyes, runny noses, shortness of breath, chest pain while breathing, wheezing, asthma, heart problems, and respiratory issues. In order to analyze the spatial distribution of these health concerns, spatial and geo-statistical methods were employed utilizing ArcGIS 10.5. By integrating field data and secondary sources, hotspot and cold spot zones were identified. Employing the statistical model within ArcMap 10.5, hotspot analysis was performed to determine areas with elevated air quality index (AQI) values and associated health problems. The application of the inverse distance weighted approach, incorporating the Z value, facilitated a visual representation of areas with heightened and reduced AQI and health-related issues. The study's outcomes underscore the prevalence of health challenges among older adults during the winter months in Gujranwala, particularly linked to smog-induced throat infections, irritated eyes, and runny noses. The research identified zones with escalated AQI values, encompassing regions such as Gujranwala, Chandaqella, Alam Chowk, Khali Shahpur, Sialkot Bypass, and Pindi Bypass. It was established that industrial pollutants and vehicular emissions are the primary contributors to smog in the area. Given the detrimental consequences of pollution on individuals of all age groups, it is imperative to take action to mitigate its impact. This can be achieved through addressing pollution sources, implementing effective emission control measures, and fostering public awareness. By adopting proactive measures, the adverse health effects of pollution can be minimized, thereby fostering a healthier and safer environment for the entire population. This study offers valuable insights for policymakers and environmentalists to implement targeted interventions and improve air quality, ultimately safeguarding the health of local populations.

Linear Geostatistical Estimating Methods Compared Using Annual Average Daily Traffic Data from Low-Volume Roads in Minnesota

Geostatistical methods are utilized to analyze and predict values associated with spatial or spatiotemporal phenomena. These techniques incorporate both the spatial and, in some cases, temporal coordinates of the data. The mining industry prefers these methods for ore reserve estimation, and they have also gained popularity in other specialized fields. Notably, the transportation industry is gradually adopting them to estimate annual average daily traffic (AADT). Although researchers use various predictive techniques to estimate AADT, many of them are experiential or based on simple subjective assessments, especially for low-volume roadways. The shortcomings of these assessment techniques include high margins of error, non-integrated spatial and temporal variability in the datasets, and inadequate consideration of total coverage. Geostatistical techniques are superior predictive tools in many fields because their algorithms account for these limitations. Moreover, geostatistical methods can predict data at both sampled and unsampled locations with minimal available data. Therefore, the crucial question arises as to which method best estimates AADT. This paper focuses on investigating linear univariate geostatistical methods, namely empirical Bayesian Kriging (EBK), ordinary Kriging (OK), simple Kriging (SK), and universal Kriging (UK), along with proportional valuations, to estimate AADT on low-volume roadways and provides a recommendation based on the findings. The study utilizes AADT data from 1,486 and 2,731 locations on low-volume roads throughout Minnesota in 2009 and 2016, respectively. The results obtained from this investigation hold significant systematic and practical implications for estimating AADT on low-volume roads and can be adapted for high-volume roadways as well.

Spatial coal seam modeling and reserve estimation using geostatistical methodologies by GIS technique in a selected coalfield in Ermenek Basin, Turkey

The accurate and reliable calculation of tonnage and quality of coal is vital for the success of mining projects. The Ermenek coal basin is located in the Western Taurus Mountains in the southern part of Turkey, which covers an area of approximately 620 km2 and is a Neogene coal basin. This paper generates spatial modeling of Pamuklu-Tepebaşı coal seams in the Ermenek Basin and the prediction of coal reserve by using geostatistical methods with Ordinary Kriging (OK) based on the GIS technique. The data used in the study were obtained from 82 boreholes belonging to a private company that has actively produced coal in the Pamuklu-Tepebaşı coalfield. In this study, the OK method was applied to spatial coal seam modeling for comparison of the performance of 11 distinct models. Using the rational quadratic models better explained the spatial structure of the coal seam depth data. The nugget-sill ratio indicated high spatial dependency with 0.01 and 0.02 for coal seam upper-lower surfaces, respectively. The kriged coal depth maps for upper and lower coal seam surfaces have been created using ArcGIS 10.2 software. As a result of these analyses, it was calculated that there is a coal reserve of 3.734.017 m3 using the determined surfaces with OK in the study area. Furthermore, developed spatial distribution maps in the study area could be helpful to plan further exploration activities.

Unlocking the potential of soil potassium: Geostatistical approaches for understanding spatial variations in Northwestern Himalayas

This study delves into the heterogeneity of total soil potassium (TSK) in the Northwestern Himalayas (NWH) region by employing standard and geostatistical methods on surface soils (0–20 cm) randomly collected from various land use systems. This research aims to unveil the spatial dynamics of TSK in the challenging context of the NWH region, by unravelling connections between TSK levels, land use practices, and soil properties. The findings of this study are instrumental for sustainable agriculture and ecological resilience in the region. The results of this work reveal that soil TSK levels in different land use types were significantly different in the order: horticulture (13.76 g/kg) > agricultural (11.25 g/kg) > forest (7.38 g/kg) > fallow (4.72 g/kg), which is clearly associated with different K application rates. The stepwise multiple regression analysis provides a significant correlation between TSK levels and soil organic matter, clay, and other fine-grained particles. Spatially, the nugget ratios of TSK exhibit an apparent decrease correlated to land use types, in the order: agriculture > horticulture > forest > mixed. Among the Gaussian, exponential, linear, and spherical geostatistical models considered, the linear model yields the best fit. The isotropy models of TSK optimization vary based on land use type. The role of land use types is very important for modelling and predicting the TSK status at the scientific and industrial scale, ensuring the relevance and applicability of such insights for global scientific audiences and policymakers. This work provides a novel contribution to soil science, with direct implications for sustainable land management practices in fragile agroecological regions beyond geographical boundaries.

EVALUATION OF DIFFERENT INTERPOLATION METHODS VIA ArcGIS, APPLIED TO SATELLITE DATA OF SEA SURFACE TEMPERATURE SST, CASE OF THE ALBORAN SEA

In various fields such as Oceanography, interpolation methods are pivotal in generating continuous surface data from discrete point data. This research endeavors to conduct a comprehensive comparison and evaluation of deterministic interpolation techniques, including Radial Basis Function (RBF), Inverse Distance Weighting (IDW), and geostatistical methods like Kriging Universal (KU) and Kriging Ordinary (KO), in the context of mapping sea surface temperature (SST) within the Alboran Sea. Among these methods, the KO interpolation method emerges as particularly promising, boasting a Root Mean Square Error (RMSE) of 0.035 and an impressive coefficient of determination (R²) approaching unity (0.999). Furthermore, the cross-validation results reveal that the KO method not only provides the most accurate estimates but exhibits minimal bias, as evidenced by a mean error close to zero. These findings not only contribute to the field of SST mapping but also have broader implications for the interpolation of other climate parameters.

Improving permeability prediction via Machine Learning in a heterogeneous carbonate reservoir: application to Middle Miocene Nullipore, Ras Fanar field, Gulf of Suez, Egypt

Predicting and interpolating the permeability between wells to obtain the 3D distribution is a challenging mission in reservoir simulation. The high degree of heterogeneity and diagenesis in the Nullipore carbonate reservoir provide a significant obstacle to accurate prediction. Moreover, intricate relationships between core and well logging data exist in the reservoir. This study presents a novel approach based on Machine Learning (ML) to overcome such difficulties and build a robust permeability predictive model. The main objective of this study is to develop an ML-based permeability prediction approach to predict permeability logs and populate the predicted logs to obtain the 3D permeability distribution of the reservoir. The methodology involves grouping the reservoir cored intervals into flow units (FUs), each of which has distinct petrophysical characteristics. The probability density function is used to investigate the relationships between the well logs and FUs to select high-weighted input features for reliable model prediction. Five ML algorithms, including Linear Regression (LR), Polynomial Regression (PR), Support Vector Regression (SVR), Decision Trees (DeT), and Random Forests (RF), have been implemented to integrate the core permeability with the influential well logs to predict permeability. The dataset is randomly split into training and testing sets to evaluate the performance of the developed models. The models’ hyperparameters were tuned to improve the model’s prediction performance. To predict permeability logs, two key wells containing the whole reservoir FUs are used to train the most accurate ML model, and other wells to test the performance. Results indicate that the RF model outperforms all other ML models and offers the most accurate results, where the adjusted coefficient of determination (R2adj) between the predicted permeability and core permeability is 0.87 for the training set and 0.82 for the testing set, mean absolute error and mean squared error (MSE) are 0.32 and 0.19, respectively, for both sets. It was observed that the RF model exhibits high prediction performance when it is trained on wells containing the whole reservoir FUs. This approach aids in detecting patterns between the well logs and permeability along the profile of wells and capturing the wide permeability distribution of the reservoir. Ultimately, the predicted permeability logs were populated via the Gaussian Random Function Simulation geostatistical method to build a 3D permeability distribution for the reservoir. The study outcomes will aid users of ML to make informed choices on the appropriate ML algorithms to use in carbonate reservoir characterization for more accurate permeability predictions and better decision-making with limited available data.

Using geostatistical methods in soil magnetometry: a review

Using geostatistical methods in soil magnetometry: a review

Spatial distribution, sources, and human health risk assessment of elevated nitrate levels in groundwater of an agriculture-dominant coastal area in Hainan Island, China

In order to comprehend the groundwater nitrate contamination in Hainan Island, which is recognized as China's sole “tropical agricultural production base,” the distribution characteristics of nitrate in different aquifers and land-use types were elucidated through hydrochemical and geostatistical analysis methods. Principal component analysis (PCA), hierarchical cluster analysis (HCA), and absolute principal component score-multiple linear regression (APCS-MLR) were employed for qualitative and quantitative analysis of the nitrate source. The results showed that NO3−-high (>88.57 mg/L) groundwater accounted for about 10 % of the total distribution area of the western coastal area in Hainan Island. Moreover, the proportions of NO3−-high groundwater in pore water and fissure water were 10 % and 7 %, respectively. The order of groundwater nitrate concentration in different land-use types was as follows: bare land, cultivated land, construction land, grassland, and woodland. The main sources of elevated nitrate concentrations in pore water were animal feces and nitrogen/potassium fertilizers, accounting for 45.4 % of the overall contribution. These substances infiltrated through the vadose zone, leaching out and mobilizing selenium within this zone, ultimately leading to the characteristic enrichment patterns observed in pore water, including nitrate, arsenic, potassium, and selenium. Furthermore, the occurrence of high nitrate in fissure water was mainly attributed to the leaching of cultured manure, septic tank leakage, and infiltration of domestic sewage, accounting for a contribution rate of 32.9 %. Simultaneously, under oxidizing conditions, selenium became activated and entered groundwater through water flow, thereby exhibiting common enrichment characteristics with nitrate and potassium in fissure water. In addition, the assessment of human health risks revealed that 16 % and 40 % of groundwater samples posed unacceptable non-carcinogenic risks to adults and children respectively, with a higher risk for local children. The study recommends the reasonable application of chemical fertilizers, as well as the strengthening of sewage treatment capacity and standardized disposal of manure and feces, to reduce nitrate contamination of groundwater at source and ensure the safety of drinking water.

Geometric anisotropic Semi-variogram analysis of ozone levels in Daerah Istimewa Yogyakarta, Indonesia

Identification of areas with high O3 levels that pose a risk to public health is necessary. Ordinary co-kriging is a geostatistical method that determines the value of primary variables at specific locations using weighted values of secondary parameters. A Semi-variogram is required to demonstrate the spatial correlation between the observations measured using this method. This study aims to determine the best Semi-variogram model and produce a map of the predicted O3 level interpolation results using the ordinary co-kriging method with a geometric anisotropic Semi-variogram. Data from the first quarter of 2018’s air quality monitoring in Daerah Istimewa Yogyakarta (DIY) were used to interpolate O3 levels, with 72 points for CO levels and 53 points for O3 levels. The results showed that the Semi-variogram model with the lowest mean error (ME) value is a gaussian model that differs from the spherical model by only 0.003. The Gaussian model has the lowest root mean squared error (RMSE), but it is only 0.002 different from the spherical model. However, by comparing the mean squared deviation ratio (MSDR) values of the three models, the spherical model’s MSDR value is the lowest. A comprehensive analysis showed that the spherical geometric anisotropic Semi-variogram model performed superior, resulting in the smallest minimum mean error (ME), root mean square error (RMSE) and minimum squared deviation ratio (MSDR) values. These findings highlight the potential of this approach to accurately map the spatial distribution of O3 and support evidence-based decision-making related to public health.

Advanced Machine Learning application for Permeability Prediction for (M) Formation in an Iraqi Oil Field

Permeability estimation is a vital step in reservoir engineering due to its effect on reservoir's characterization, planning for perforations, and economic efficiency of the reservoirs. The core and well-logging data are the main sources of permeability measuring and calculating respectively. There are multiple methods to predict permeability such as classic, empirical, and geostatistical methods. In this research, two statistical approaches have been applied and compared for permeability prediction: Multiple Linear Regression and Random Forest, given the (M) reservoir interval in the (BH) Oil Field in the northern part of Iraq. The dataset was separated into two subsets: Training and Testing in order to cross-validate the accuracy and the performance of the algorithms. The random forest algorithm was the most accurate method leading to lowest Root Mean Square Prediction Error (RMSPE) and highest Adjusted R-Square than multiple linear regression algorithm for both training and testing subset respectively. Thus, random Forest algorithm is more trustable in permeability prediction in non-cored intervals and its distribution in the geological model.

Assessments of Gravity Data Gridding Using Various Interpolation Approaches for High-Resolution Geoid Computations

This article investigates the role of different approaches and interpolation methods in gridding terrestrial gravity anomalies. In this regard, first of all, simple and complete Bouguer anomalies are considered in gravity data gridding. In the comparison results of gridding these two Bouguer anomaly datasets, the effect of the high-frequency contribution of topographic gravitation (by means of the terrain correction) is clarified. After that, the role of the used interpolation algorithm on the resulting grid of mean gravity anomalies and hence on the geoid modeling accuracy is inspected. For this purpose, four different interpolation methods including geostatistical Kriging, nearest neighbor, inverse distance to a power (IDP), and artificial neural networks (ANNs) are applied. Here, the IDP and nearest neighbor methods represent simple-structured algorithms among the interpolation methods tested in this study. The ANN method, on the other hand, is preferred as a complex, optimization-based soft computing method that has been applied in recent years. In addition, the geostatistical Kriging method is one of the conventional methods that is mostly applied for gridding gravity data in geodesy and geophysics. The calculated gravity anomalies in grids are employed in high-resolution geoid model computations using the least squares modifications of Stokes formula with additive corrections (LSMSA) technique. The investigations are carried out using the test datasets of Auvergne, France that are provided by the International Service for the Geoid for scientific research. It is concluded that the interpolation algorithms affect the gravity gridding results and hence the geoid model determination. The ANN method does not provide superior results compared to the conventional algorithms in gravity gridding. The geoid model with 4.1 cm accuracy is computed in the test area.

Greenery in times of crisis: Accessibility, residents' travel preferences and the impact of travel time

Urban green spaces (UGSs) played a pivotal role in easing the effects of COVID-19 pandemic restrictions. It is, therefore, relevant to identify factors influencing why people choose specific UGSs. This paper aims to investigate the preferences of residents of Kraków (Poland) regarding the selection of UGSs in times of crisis. Distance or travel time from home are among the key factors affecting the choice of UGSs. The paper verifies whether such other factor considerations as age, type of housing, and physical activity influence travel preferences to UGSs. We analyse residents' preferences regarding travelling to UGSs by integrating survey research with statistical and geostatistical methods, which is the innovative value of the research. The Computer Assisted Web Interview (CAWI) survey yielded 1353 returned questionnaires, which provided input data when combined with geostatistical analyses of network distance (routing). With nonparametric statistical methods, we could identify preferences of Kraków residents regarding travelling to UGSs during times of crisis. The primary results show that travel time was not always a factor when selecting UGSs. In times of crisis, the respondents were willing to cover larger distances to UGSs, namely up to 51 minutes on foot and 16 minutes by bicycle. We also demonstrated that there is a relationship between age and UGS travel time and a link between type of housing and UGS travel time. The results are inconclusive regarding the importance of distance to UGSs for people who are physically active. Note that accessibility recommendations for travel time often presented in the literature did not apply to Kraków in times of crisis.

Research Progress on Spatiotemporal Interpolation Methods for Meteorological Elements

With the development of mathematical statistics, people have developed the spatiotemporal interpolation methods based on the spatial interpolation method or the temporal interpolation method. These methods fully consider the comprehensive effects of time series changes and spatial distribution to better handle complicated and changeable meteorological element data. This article systematically reviews the current research progress of spatiotemporal interpolation methods for spatiotemporal sampling data of meteorological origin. Spatiotemporal interpolation methods of meteorological elements are classified into three categories: spatiotemporal geostatistical interpolation methods, spatiotemporal deterministic interpolation methods, and spatiotemporal mixed interpolation methods. This article summarizes the theoretical concept and practical application of the spatiotemporal interpolation methods of meteorological elements, analyzes the advantages and disadvantages of using spatiotemporal interpolation methods for estimating or forecasting meteorological elements, combined through some measures and their application to explain the accuracy of the spatiotemporal interpolation methods; and discusses the problems and challenges of spatiotemporal interpolation. Finally, the future research focus of spatiotemporal interpolation methods is proposed. This article provides a valuable method reference for estimating or predicting meteorological elements such as precipitation in unsampled points.