Universal Kriging Interpolation Research Articles

Spatial Distribution of Soil Heavy Metal Concentrations in Road-Neighboring Areas Using UAV-Based Hyperspectral Remote Sensing and GIS Technology

Monitoring and restoring soil quality in areas neighboring roads affected by traffic activities require a thorough investigation of heavy metal concentrations. This study examines the spatial heterogeneity of copper (Cu) and chromium (Cr) concentrations in a 0.113 km² area adjacent to Jin-Long Avenue in Wuhan, China, using Unmanned Aerial Vehicle (UAV)-based hyperspectral remote sensing technology. Through this UAV-based remote sensing technology, we innovatively achieve a small-scale and fine-grained analysis of soil heavy metal pollution related with traffic activities, which represents a major contribution of this research study. In our approach, we generated 4375 spectral variates by transforming the original spectrum. To enhance result accuracy, we applied the Boruta algorithm and correlation analysis to select optimal spectral variates. We developed the retrieval model using the Gradient Boosting Decision Tree (GBDT) regression method, selected from a set of four regression methods using the LOOCV method. The resulting model yielded R-square values of 0.325 and 0.351 for Cu and Cr, respectively, providing valuable insights into the heavy metal concentrations. Based on the retrieved heavy metal concentrations from bare soil pixels (17,420 points), we analyzed the relationship between heavy metal concentrations and the perpendicular distance from the road. Additionally, we employed the universal kriging interpolation method to map heavy metal concentrations across the entire area. Our findings reveal that the concentration of heavy metals in this area exceeds background values and decreases as the distance from the road increases. This research significantly contributes to the understanding of spatial distribution characteristics and pollution caused by heavy metal concentrations resulting from traffic activities.

Методика выделения водосборов Cанкт-Петербурга для определения поступления общего азота и фосфора в Невскую губу и восточную часть Финского залива

The Neva Bay and eastern part of the Finnish Gulf are affected by toxic contamination and eutrophication due to superfluous anthropogenic income of total nitrogen and phosphorus. Monitoring of the total nitrogen and phosphorus content within Saint Petersburg is carried out only in the Neva River and its spill-streams. Therefore, it is necessary to evaluate modules of the total nitrogen and phosphorus outflow from watersheds of the watercourses without monitoring river stations. For this reason, it is necessary to definite boundaries of the watersheds. The paper presents proprietary technology for the watershed boundary definition within Saint Petersburg and its outskirts. The methodology is based on usage of the digital terrain model, which was created as result of topographic maps digitalization. Usage of the most popular global digital terrain models such as SRTM, ASTER GDEM makes difficulties under the conditions of big cities. The models were developed on the basis of remote sensing of the Earth’s surface. Therefore, the values have distortions due to the signal reflection from roofs, structures, trees, scrubs, and so on. Thus, the global models include noisy data. The distortions can lead to mistakes at definition of watershed boundary. Topographic maps digitalization allows elaborating of digital terrain models without distortions of altitude values. We have made the new digital terrain model of Saint Petersburg and the outskirts by means of Saint Petersburg and Leningrad Region topographic map digitalization. The map was published in 2001. Its scale is equal to 1:200 000. The feature point layer of the altitudes in the Baltic system was created on the base of the map. The digital terrain model was created in ArcGIS by universal kriging interpolation. Dimension of the model cell side is equal to 100 meters. Definition of the watersheds boundaries was carried out by means of the ArcGIS tool Watershed. In addition, we use for the definition some tools of QGIS and SAGA.

MULTIVARIATE STATISTICAL METHODS IN DETERMINING THE SPATIAL DISTRIBUTION OF CHEMICAL ELEMENTS IN SOILS (KUMANOVO REGION, NORTH MACEDONIA)

The results of the distribution of various chemical elements in soil samples from the region of Kumanovo, North Macedonia, are presented. In order to determine the occurrence of chemical elements, soil samples were collected from a total of 51 locations. At each location, soil samples were collected from two layers, topsoil (0–5 cm) and subsoil (20–30 cm), in an area of 5×5 km2. The soil samples were analyzed for 5 elements using two instru-mental methods: inductively coupled plasma – atomic emission spectrometry (ICP-AES) for 17 macroelements (Al, B, Ba, Ca, Cr, Cu, Fe, K, Li, Mg, Mn, Na, Ni, P, Pb, V, and Zn) and inductively coupled plasma – mass spectrometry (ICP-MS) for 38 trace elements (Ag, As, Be, Bi, Br, Cd, Ce, Co, Cs, Dy, Er, Eu, Ga, Gd, Ge, Hf, Ho, In, La, Lu, Mo, Nb, Nd, Pr, Rb, Sb, Sc, Sm, Sn, Sr, Ta, Tb, Ti, Tm, W, Y, Yb, and Zr). Factor analysis was applied to analyze the factors affecting the linear combination variables grouped under the same factor. Spatial distribution maps for each factor as well as distribution maps for the analyzed elements were obtained by universal kriging interpolation. It was found that the distribution of most elements follows the lithology of the studied area, except for some elements (As, Pb, and Zn) whose higher contents were found in some specific parts of sub-areas, which is due to the current and past mining activities in the region.

The Performance of Several Current Interpolation Methods for Variability of cations in Groundwater in Esfarayen Plain, Iran: A Case Study

Acquiring information about groundwater quality is essential in developing management strategies. In this article, spatio-temporal variations of cations in groundwater in Esfarayen plain were investigated using data monitored in 134 groundwater wells, active in 1988, and 47 wells, active in 2019. To evaluate groundwater quality, interpolation methods have been used to interpolate existing limited spatial data. The performance of 8 current interpolation methods on the data for the two selected years (1988 and 2019) was compared. Finding the optimum interpolation method for the considered groundwater quality parameters is essential. Cross-validation and three indexes of R2, mean absolute error (MAE), and root mean square error (RMSE) were used to compare the performance of the methods. By identifying universal kriging (UK) and global polynomial interpolation (GPI) methods as the optimum methods and using those for the selected years (1988 and 2019), spatial variation of the concentration of cations in groundwater across the plain has been presented. In 1988, the maximum concentration of the cations occurred in the southwest of the plain (about 80 mg/L), and the minimum concentration of the cations was observed in the northwest of the plain (approximately 8 mg/L). Similarly, in 2019, the highest concentration of the cations was found in the southwest of the plain (almost 64 mg/L), and its lowest concentration was observed in the northeast of the plain (roughly 13 mg/L). Moreover, temporal variations of the concentration of cations in groundwater from 1988 to 2019 have also been presented. The concentration of the cations increased by approximately 23 mg/L in the northwest and decreased to about 37 mg/L in the southwest of the study area from 1988 through 2019. According to the results, changes in the quality of groundwater are a complex problem and it is necessary to adopt proper strategies to reduce its adverse effects.

Assessment of natural and anthropogenic factors on the distribution of chemical elements in soil from the Skopje region, North Macedonia

The main objective of this study is to present the distribution of different chemical elements in soil samples from the Skopje region, North Macedonia. To determine the level of presence of chemical elements, soil samples are collected from a total of 60 locations. From each location, from an area of 5 × 5 km2 samples of soil are collected: topsoil (0–5 cm) and subsoil (20–30 cm). The soil samples were analyzed for 69 elements by using two instrumental methods: inductively coupled plasma-atomic emission spectrometry (ICP-AES) for macro-elements and inductively coupled plasma-mass spectrometry (ICP-MS) for trace elements. A factor analysis was applied to analyze the factors affecting the linear combination variables grouped at the same factor. Spatial distribution maps of each factor as well as distribution maps for the analyzed elements were prepared by universal kriging interpolation. It was found that the distribution of most elements follows the lithology of the examined area, except for some elements (Cd, Cu, Fe, Hg, Mn, Pb, and Zn) whose higher contents are found in the area of the city of Skopje as a result of urban and industrial activities (traffic, metal processing, fossil fuel combustion for heating).

Geochemical Anomaly Characteristics of Cd in Soils around Abandoned Lime Mines: Evidence from Multiple Technical Methods

Lime mines are a potential source of pollution, and the surrounding soil environment is generally at threat, especially in abandoned lime mines. This paper focuses on the study area in eastern Anhui, attempting to analyze whether Cd enrichment is related to abandoned mines. On the basis of geological investigation, this study systematically used XRD, XRF, GTS and universal Kriging interpolation to determine the distribution law of Cd in the study area, and evaluated the potential ecological risk of Cd. The results showed that the main mineral types of soil samples of red clastic rock soil parent material (RdcPm) and soil samples of carbonate soil parent material (CPm) were not completely the same. Correlation analysis showed that CaO, MgO and Cd were positively correlated with the CPm. Human activities led to the accumulation of Cd in the study area. High Cd was mainly concentrated in the northwest of the study area, which was correlated with abandoned mines and soil parent materials. The study area was dominated by slight potential risks, although some areas had medium potential risks and high potential risks. All potential high risks were in the CPm field. This study provides a scientific basis for the comprehensive utilization and development planning of soil in the study area.

Infilling the missing values of groundwater level using time and space series: case of Nantong City, east coast of China

Dynamic monitoring data of the groundwater level form an important basis to understand the current state of groundwater development and utilization, which is required to plan its sustainable exploitation. The dynamic data of groundwater level are typical space-time series data with the characteristics of nonlinear strong space-time correlation. However, because of the influences of human or natural factors, long-term monitoring data of the groundwater level are often incomplete to varying degrees. Consequently, the efficiency and accuracy of traditional data in-filling methods for the missing groundwater level data are low. Additionally, restoration methods based on spatio-temporal geostatistics and machine learning are not sufficiently comprehensive to consider spatio-temporal correlations, which results in low restoration accuracy. Therefore, this study was based on an analysis of the characteristics and the missing status of the groundwater level dynamic monitoring data of the pore confined aquifer III of Nantong City, east coast of China. Both the universal Kriging (UK) interpolation method and the support vector regression (SVR) method were used for spatial missing correction and temporal missing correction, respectively. A separable spatial-temporal missing correction coupling model of groundwater level monitoring data was constructed and named UK-SVR. The reliabilities and accuracies of UK-SVR, UK, SVR, and K-nearest neighbor were evaluated by a cross-validation algorithm. The results showed that UK-SVR achieved higher accuracy than other single data-infilling models.

Spatial variation of gully development in the loess plateau of China based on the morphological perspective

Gullies characterized by frequent material exchange have profoundly affected the loess landforms evolution in the Loess Plateau of China. Accompanying gully development, various types of gullies have shaped the distinctive loess landforms. Thus, the spatial variations of gully morphology map the regional differences of gully development and loess landforms. Based on 6 key test areas with 5 m resolution DEM and 156 evenly distributed test areas with 25 m resolution DEM, a comprehensive gully-shape index system of topographic feature points, lines, and surfaces was constructed to describe spatial differences of the gully development. After comparing gully-shape indexes in the key test areas, an obvious correlation existed between these indexes and loess landform types. The gully development degree was low in Shenmu and Chunhua, high in Suide, Yanchuan, and Ganquan, while Yijun lay in-between. Using the method of Universal Kriging interpolation, a series of spatial interpolation maps of the gully-shape indexes were obtained, which revealed gully development degree in the whole Loess Plateau. Overall, The active areas of gully development were basically distributed along loess hilly ridges, loess hills, loess ridges, and in a few medium mountain areas, while the inactive areas were basically distributed in the thin loess coverage areas, including plains, river terraces, aeolian dunes, and a few loess platforms. Finally, the gully development regionalization was realized, which contained 6 subzones. These results provided significant references for loess landform research and soil erosion management in the Loess Plateau.

Correcting GPM IMERG precipitation data over the Tianshan Mountains in China

Point-scale gauge observations have inherent limitations, making it difficult to study the spatial and temporal distributions of precipitation in alpine regions due to gauge undercatch and complex terrains. The Global Precipitation Measurement (GPM) mission provides new-generation satellite precipitation products that are promising alternative data sources in mountainous areas. However, quality evaluations and bias corrections should be conducted prior to the application of satellite data. In this study, an unprecedentedly dense ground station network composed of more than 1000 automatic weather stations (AWSs) over the Tianshan Mountains in China are used for bias correction of the Integrated Multisatellite Retrievals for GPM (IMERG) product. First, universal kriging interpolation is used to downscale IMERG from 0.1° to 500 m to ensure a fair comparison with the gauge observations. Then, the downscaled IMERG precipitation data over this region are corrected by two methods, i.e., stepwise regression (STEP) and geographically weighted regression (GWR). Both methods are established on various terrain factors and vegetation indexes that have strong relations with precipitation. The results show that (1) GWR outperform the conventional STEP method as well as the original IMERG; (2) the original IMERG performs best over the plain region (less than 1000 m), while the best correction effect was found in middle and low-elevation region (1000–1500 m); and (3) the performance of the GWR model is largely dependent on the number of available training stations in mountainous areas. Overall, the methods and results presented in this study provide insight into the correction of satellite precipitation data in mountainous areas with scarce ground observations.

Using the random forest algorithm to integrate hydroacoustic data with satellite images to improve the mapping of shallow nearshore benthic features in a marine protected area in Jamaica

Hydroacoustic and optical remote sensing have been commonly used to map shallow nearshore benthic features. However, the number, type, scale, and accuracy of the mapping products that can be obtained from the two sensors differ; as such, there can be limited agreement between their mapping products. These differences can be further accentuated if the hydroacoustic data are interpolated to produce a map. Interpolation introduces spatial uncertainty and reduces map accuracy. Consequently, maps generated from the two sensors may provide dissimilar spatial and temporal representations of the same benthic features. We therefore compared the performance of a random forest regression (RFr) and a universal kriging (UK) interpolation method and a post-classification enhancement that can be used to increase the accuracy and complementarity of benthic habitat maps derived from hydroacoustic data. First, we used single beam echosounder (SBES) survey bathymetry data from the Bluefields Bay marine protected area (MPA) in western Jamaica (13.82 km2 in size), to create a bathymetric surface model (BSM), from which rugosity and bathymetric position index (BPI) maps were generated. Next, the RFr was used to create submerged aquatic vegetation (SAV) percentage cover maps from the SBES SAV cover data by predicting cover at un-sampled locations. Predictors included auxiliary data such as depth, BPI, survey points coordinates and radiometrically corrected, deglinted and water column corrected image reflectance index values from each of the following: WorldView-2, Geoeye-1 and Landsat 8. Additionally, a SAV map was created using the UK. The most accurate SAV cover thresholds were identified and were used to create binary maps from the RFr and UK maps. A rugosity derived coral reef map was then added to the binary maps. The resulting benthic habitat maps had comparable accuracies and class coverage to benthic maps classified from GeoEye-1 and WorldView-2 images using pixel and object-based classifiers. However, map accuracies were calculated using a suboptimal number of reference points (<50) for two of the benthic map classes (SAV absent and coral reef). This was not considered to be problematic as the addition of the coral reef class to the binary maps resulted in a significant decrease in uncertainty (standard error and confidence interval width of the overall accuracy) and a significant increase in the user’s accuracy of the SAV absent map class. Also, the difference in uncertainty and accuracy between the map classes did not change. The methods used in this study can therefore be used to increase the accuracy (and to decrease the uncertainty) and the complementarity of maps derived from hydroacoustic data.

Classifying Urban Climate Zones (UCZs) Based on Spatial Statistical Analyses

The objective of this study is the classification of urban climate zones (UCZs) based on spatial statistical approaches to provide key information for the establishment of thermal environments to improve urban planning. To achieve this, using data from 246 automatic weather stations (AWSs), air temperature maps in the summer of the study area were prepared applying universal kriging interpolation analysis. In addition, 22 preliminary variables to classify UCZs were prepared by a 100 m × 100 m grid. Next, six influential urban spatial variables to classify UCZs were finalized using spatial regression analysis between air temperature and preliminary variables. Finally, the UCZs of the study area were delineated by applying K-mean clustering analysis, and each spatial characteristic of the UCZs was identified. The results found that the accuracy of the air temperature of the study area ranged from ±0.184 °C to ±0.824 °C with a mean 0.501 root mean square predict error (RMSPE). Elevation, normalized difference vegetation index (NDVI), commercial area, average height of buildings, terrain roughness class, building height to road width (H/W) ratio, distance from subway stations, and distance from water spaces were identified as finalized variables to classify UCZs. Finally, a total of 8 types of UCZs were identified and each zone showed a different urban spatial pattern and air temperature range. Based on the spatial statistical analysis results, this study delineated clearer UCZs boundaries by applying influential urban spatial elements that resulted from previous classification studies of UCZs mainly based on pre-determined spatial variables. The methods presented in this study can be effectively applied to other cities to establish urban heat island counter measures that have similar weather observation conditions.

Position of Fingerprint Location based on Improved Universal Kriging Interpolation Method

Position of Fingerprint Location based on Improved Universal Kriging Interpolation Method

Rainfall and potential evapotranspiration patterns and their effects on climatic water balance in the Western Lithoral Hydrological Zone of Nigeria

This study examined the climatic water balance and aridity in the Western Lithoral hydrological zone of Nigeria. Monthly climatic data from 1976-2015 collected from six Nigeria Metrological Agency (NIMET) stations located in Ikeja, Ibadan, Akure, Abeokuta, Osogbo and Ilorin were used. The climatic variables are rainfall amount, temperature, sunshine hour, relative humidity and wind speed. The FAO Penman-Monteith method was adopted in estimating the potential evapotranspiration (PET). Water balance was determined from PET and rainfall amount. The spatial and temporal pattern of rainfall amount and PET were evaluated using universal kriging interpolation method, Mann-Kendall and regression trend analysis. The results of the Mann-Kendall and regression trend analysis revealed a statistically significant (Z= 2.74, P= 0.005) upward trend in rainfall amount between 1976 and 2015. Similarly, a statistically significant (Z= 4.40, p= 0.001) increasing trend was observed in PET during the same period. Six months of water surplus (May-October) and six months of water deficit (November-April) were identified. Overall, 27 years of water deficit was discovered over the 40 years period. Water balance pattern revealed the highest annual mean water surplus (324.51 mm) in the hinterland of Idanre, Akure, and Owo rather than the coastal city of Ikeja which can be attributed to orographic effect in the hinterland. The study area with a mean Aridity index (AI) of 0.94 can still be regarded as humid environment, although the spatial variability of AI indicates that the northern part is tending towards a dry sub-humid condition (AI= 0.76). This study recommends conservation of water surplus in the wet months for the augmentation of deficit in the dry months; this will not only boost agricultural production, but also alleviate water supply problem in the study area. Keywords. Aridity index, potential evapotranspiration, water balance.

A Method of Simulating Regional Groundwater level Distribution Based on Digital Elevation Model

It is very important to use the measured data to obtain the regional groundwater level distribution in groundwater flow modeling, which can provide the initial flow field or boundary condition for modeling, and can be used as the verification basis for the simulation results. Traditional methods are usually interpolated using existing water level data, and the accuracy of the results is greatly influenced by the number of boreholes and the rationality of distribution, so it is not applicable in ungauged region of northwest China. Actually, the flow of groundwater in most areas is affected by the topography at the regional scale, and the terrain and groundwater flow path are correlated. In this paper, a method based on digital elevation model to simulate the regional groundwater level distribution is presented. The selection of the trend surface equation and parameter calibration are the key points and difficulties, because low order polynomial may lead the trend surface equation cannot fit the measured data well, and high order polynomial maybe lead the instability of the solution to the equation. Therefore, this paper established the high order polynomial as the initial trend surface equation, then the correlation between each parameter in the trend surface equation and the elevation of the measured groundwater level was analyzed, and the parameters with obvious correlation with the elevation of groundwater level compose the trend surface equation, and then using the measured data realized the optimal estimation of the average trend level of groundwater, to ensure the best trend surface equation, finally, according to Lanczos singular value decomposition theory, the trend surface equation solution were obtained, and an unbiased and optimal estimation of the residual using the method of universal kriging interpolation was presented. This method was applied in a certain area of northwest China, and the error of the calculation results was much less than that of the kriging interpolation method, which was more consistent with the measured values and could be used to extrapolate. This method has a good prospect in the simulation of groundwater flow field in ungauged region of northwest China.

Threshold contour production of rainfall intensity that induces landslides in susceptible regions of northern Turkey

This study is aimed at developing rainfall intensity contour lines to illustrate upper and lower rainfall intensity limits that trigger landslides. The first phase began by developing precipitation empirical thresholds as follows: (i) the relationship between intensity (I) and accumulative rainfall (E) and date (I-date and E-date, respectively); (ii) the antecedent rainfall up to 3, 5, 10, 15, and 30 days prior to landslide occurrence; (iii) the relationship between the I and the duration (D); and (iv) the relationship between the cumulative rainfall event and the D (ID and ED, respectively). The data recorded by two rain gauges (Rize and Rize–Pazar) in the province of Rize in Northwest Turkey were used to analyze 24 previous landslide events during the period 1985 to 2006. The second phase began by developing surface interpolation maps after deriving threshold and assumption of normality, thereby producing contours of the rainfall intensity data of the rain gauges. All thresholds were verified by no-rainfall events, and the ID threshold successfully distinguished 97 and 95% (in Rize and Rize–Pazar, respectively) of false alarm days with the highest accuracy among the thresholds (antecedent rainfall days, I-date, and E-date thresholds). Thus, a descriptive analysis was conducted using the rainfall data of selected rain gauges to test the normality of rainfall between the selected rain gauges in the study area. The linear correlation coefficient was found at 0.75, and other tests verified the normality with optimistic results. A universal or collaborative kriging interpolation (UK) in a geographic information systems’ environment was used to estimate the spatial distribution of rainfall intensity because rainfall is controlled robustly by topography and other factors. This distribution corresponds to the landslide day event and hole-effect mathematical models that are used to forecast un-sampled values in the study area. Topographic elevation, slope, and normalized difference vegetation index (NDVI) maps were integrated into the landslide day events by using rainfall intensity. The UK map was validated by a cross-validation procedure using root-mean-square error. The highest interpolated surface map accuracy was reached without using an external drift (using rainfall intensity values only) and when using an NDVI as the external drift. The optimal model was selected by comparing the measured and predicted values at approximately 78% accuracy. Ultimately, the rainfall intensity contour lines were used to illustrate the upper and lower rainfall intensity limits that trigger landslides. This study used well-documented spatio-temporal data of landslide events and introduced a primary threshold that can be validated for any future event.

OpenCL Implementation of a Parallel Universal Kriging Algorithm for Massive Spatial Data Interpolation on Heterogeneous Systems

In some digital Earth engineering applications, spatial interpolation algorithms are required to process and analyze large amounts of data. Due to its powerful computing capacity, heterogeneous computing has been used in many applications for data processing in various fields. In this study, we explore the design and implementation of a parallel universal kriging spatial interpolation algorithm using the OpenCL programming model on heterogeneous computing platforms for massive Geo-spatial data processing. This study focuses primarily on transforming the hotspots in serial algorithms, i.e., the universal kriging interpolation function, into the corresponding kernel function in OpenCL. We also employ parallelization and optimization techniques in our implementation to improve the code performance. Finally, based on the results of experiments performed on two different high performance heterogeneous platforms, i.e., an NVIDIA graphics processing unit system and an Intel Xeon Phi system (MIC), we show that the parallel universal kriging algorithm can achieve the highest speedup of up to 40× with a single computing device and the highest speedup of up to 80× with multiple devices.

Geostatistical interpolation model selection based on ArcGIS and spatio-temporal variability analysis of groundwater level in piedmont plains, northwest China

Based on the geo-statistical theory and ArcGIS geo-statistical module, datas of 30 groundwater level observation wells were used to estimate the decline of groundwater level in Beijing piedmont. Seven different interpolation methods (inverse distance weighted interpolation, global polynomial interpolation, local polynomial interpolation, tension spline interpolation, ordinary Kriging interpolation, simple Kriging interpolation and universal Kriging interpolation) were used for interpolating groundwater level between 2001 and 2013. Cross-validation, absolute error and coefficient of determination (R2) was applied to evaluate the accuracy of different methods. The result shows that simple Kriging method gave the best fit. The analysis of spatial and temporal variability suggest that the nugget effects from 2001 to 2013 were increasing, which means the spatial correlation weakened gradually under the influence of human activities. The spatial variability in the middle areas of the alluvial–proluvial fan is relatively higher than area in top and bottom. Since the changes of the land use, groundwater level also has a temporal variation, the average decline rate of groundwater level between 2007 and 2013 increases compared with 2001–2006. Urban development and population growth cause over-exploitation of residential and industrial areas. The decline rate of the groundwater level in residential, industrial and river areas is relatively high, while the decreasing of farmland area and development of water-saving irrigation reduce the quantity of water using by agriculture and decline rate of groundwater level in agricultural area is not significant.

Comparison of Ordinary and Universal Kriging interpolation techniques on a depth variable (a case of linear spatial trend), case study of the Šandrovac Field

Universal Kriging has not until now been used for mapping of geological data in Croatia. However, it is one of the most frequently used methods of Kriging, probably the most adequate in cases when the input data is marked by a common trend. That exact feature is often an attribute of deep geological data, and thereby that of structural maps. Mapped surfaces in a row of examples have a structural trend towards one cardinal direction, or a sequence of geological structures, like anticlinorium, is a part of a structural unit of a higher order such as regional monocline. An example is given of geographical trend recognition in e-log Z’ surface spread in Šandrovac Field as well as successful mapping of that marker depth variable by using Universal Kriging.

Dose rate estimates and spatial interpolation maps of outdoor gamma dose rate with geostatistical methods; A case study from Artvin, Turkey

In this study, compliance of geostatistical estimation methods is compared to ensure investigation and imaging natural Fon radiation using the minimum number of data. Artvin province, which has a quite hilly terrain and wide variety of soil and located in the north–east of Turkey, is selected as the study area. Outdoor gamma dose rate (OGDR), which is an important determinant of environmental radioactivity level, is measured in 204 stations. Spatial structure of OGDR is determined by anisotropic, isotropic and residual variograms. Ordinary kriging (OK) and universal kriging (UK) interpolation estimations were calculated with the help of model parameters obtained from these variograms. In OK, although calculations are made based on positions of points where samples are taken, in the UK technique, general soil groups and altitude values directly affecting OGDR are included in the calculations. When two methods are evaluated based on their performances, it has been determined that UK model (r = 0.88, p < 0.001) gives quite better results than OK model (r = 0.64, p < 0.001). In addition, as a result of the maps created at the end of the study, it was illustrated that local changes are better reflected by UK method compared to OK method and its error variance is found to be lower.

Large-scale spatial variation in feather corticosterone in invasive house sparrows (Passer domesticus) in Mexico is related to climate.

Ecologists frequently use physiological tools to understand how organisms cope with their surroundings but rarely at macroecological scales. This study describes spatial variation in corticosterone (CORT) levels in feathers of invasive house sparrows (Passer domesticus) across their range in Mexico and evaluates CORT–climate relationships with a focus on temperature and precipitation. Samples were collected from 49 sites across Mexico. Feather CORT (CORTf) was measured using methanol-based extraction and radioimmunoassay. Relationships between CORTf and spatial and climate variables were examined using simple linear regressions. Ordination was used on climate data, CORTf was plotted against the resulting axes, and univariate regression trees were used to identify important predictors of CORTf. Universal kriging interpolation was used to illustrate spatial variation in CORTf across Mexico. Correlations with ordination axes showed that high CORTf was associated with low precipitation during the rainy season and low dry season temperatures. Specifically, CORTf was negatively related to May precipitation and January and July minimum temperatures, and positively related to April deuterium excess and June minimum temperatures. CORTf was higher in second-year birds compared to after-hatch years and after-second years. House sparrows had higher CORTf levels in the hot, dry, north-central region of Mexico, and CORTf was negatively related to temperature and precipitation. House sparrows molt primarily from August–September but climate conditions throughout the year were important predictors of CORTf, suggesting that conditions outside of molt can carry over to influence energetics during feather growth. These data suggest that dry conditions are challenging for house sparrows in Mexico, supporting previous work showing that precipitation is an important predictor of broad-scale CORT variation. This work highlights the utility of CORTf for evaluating the influence of physiology on current avian range limits; furthermore, these data may allow us to predict future changes in species distributions.