Variogram Model Research Articles

The coupling coordination between tourism urbanization and ecosystem services value and its obstacle factors in ecologically fragile areas: a case study of the Wuling Mountain area of Hunan Province, China.

The interrelationship between tourism urbanization (TU) and the ecological environment is extremely complex. Some studies have analyzed the interaction between them but ignored the ecosystem services. Therefore, exploring the coupling coordination relationship between TU and ecosystem services value (ESV) is significant. In this research, we established a coupling coordination degree (CCD) model between TU and ESV and used exploratory spatial data analysis (ESDA), spatial variogram model, and obstacle degree model to evaluate the evolution characteristics of CCD and its obstacle factors in the Wuling Mountain area of Hunan Province (WMAHP). The results are as follows: (1) the comprehensive TU level shows an upward trend, and TU levels in the west are generally higher than in the east. The total ESV shows a fluctuating upward trend, and the average ESV is relatively low in the west and southeast. (2) The comprehensive CCD shows an increasing trend, and the coupling coordination relationship has changed from uncoordinated to coordinated in most counties. Spatially, the global spatial autocorrelation and spatial variation degree of CCD are insignificant. Wulingyuan and Yongding are uplift areas, and a subsidence area is in the southeast. It is worth noting that the problem of TU lag generally exists. (3) For the whole area, TU and economy are always the primary obstacle factors in the system and category layer, respectively, but the obstacle degree of the population has gradually increased. At the county level, TU restricts the CCD improvement in most counties, and the proportion of counties where the economy is the primary obstacle in the criterion layer exceeds 60%. Policymakers need to formulate targeted promotion strategies based on the coupling coordination and relative development level between TU and ESV for different counties. This paper provides valuable references for achieving coordinated development between TU and ESV in ecologically fragile areas worldwide.

A deep CNN-LSTM model for predicting interface depth from gravity data over thrust and fold belts of North East India

Geological interface depth modeling from the gravity field data is crucial for the exploration of oil and gas, mapping of sediment-basement interfaces and many other geological modeling studies. Two-dimensional radially averaged power spectrum analyses yield ensemble mean depth from the gravity anomaly which lacks information away from the focus of the depth point modeled. This paper aims to introduce adeep learning techniquecombining a convolutional neural networkand long short-term memory network (CNN-LSTM) with variogram modeling to model interface depths using geospatial coordinates, Bouguer gravity anomaly and altitude variations data over the thrust and fold belts of North-East India. Prior to actual data analysis, the method is tested on a synthetic model. After the optimal network selection with the ‘Relu’ transfer function and ‘Adam’ optimization, the robustness of the CNN-LSTM model is examined and the test results show that the model is robust up to the data assorted with moderate level (∼20%) of correlated noise. The CNN-LSTM model detects important geological structures, subsurface faults, and thrust zones namely, Kohima Synclinorium, Naga and Disang thrust, and Eastern boundary thrust. Comparative results suggest that the CNN-LSTM is skillful based on the mean-squared error (MSE) between the observation and the prediction (MSECNN-LSTM ∼ 0.014) relative to the other machine learning models (Adaptive-Neuro-Fuzzy-Inference System (MSEANFIS ∼ 0.020), Random Forest with Extra Tree(MSERF ∼ 0.075), Support Vector Regression (MSESVR ∼ 0.025), Bayesian Neural Network(MSEBNN ∼ 0.116), Convolutional Neural Network(MSECNN ∼ 0.022), Long Short-Term Memory Network(MSELSTM ∼ 0.023), and Gaussian Process(MSEGP ∼ 0.095)) used in the study. We, therefore, conclude that the proposed approach is robust enough to model the various geological interface depths precisely with appropriate input data of geospatial coordinates, Bouguer gravity anomaly and altitude variation. The approach used here has potential and could be explored further in other complex geological provinces around the world.

The structure of beta-diversity explains why the relevance of phytoindication increases under the influence of park reconstruction

Urbanization causes the highest local extinction rates and often leads to the loss of the vast majority of native species. Plant communities are sensitive to urban expansion and are therefore indicators of human land use. A city park, part of which has undergone reconstruction, was studied. The study found that the changes in ecological conditions caused by the reconstruction of a city park can be detected using phytoindication. The informativeness of phytoindication scales was shown to increase under conditions of anthropogenic load. The phytoindication scales are a reliable source of information for assessing the state of the vegetation cover of park plantations. The ecological regimes were assessed based on descriptions of the vegetation cover using Didukh's phytoindication scales. The phytoindication approach allows one to identify changes in ecological regimes that occur as a result of park reconstruction and to separate them from ecological regimes of natural origin. The study showed that the reconstruction of the park significantly affects the conditions of the park and the diversity of vegetation. The ratio of useful phytoindicative information compared to information noise in the structure of beta-diversity of the park's plantations increases significantly as a result of the park's reconstruction. The reconstruction of the park has led to changes in the spatial organization of the vegetation cover. The results obtained indicate a decrease in soil moisture as a result of the park's reconstruction. The park’s reconstruction leads to a significant change in the light regime of the park’s plantings, which leads to changes in the park’s vegetation and soils. Reducing the density of plantations as a result of their pruning during the reconstruction process also decreases the amount of fallen leaves that form leaf litter. A significant increase in the variability of the moisture regime under the influence of the park reconstruction was found. The phytoindication revealed a decrease in the acidity of the soil solution as a result of the reconstruction. The changes in soil acidity are accompanied by an increase in phytoindication estimates of carbonate content in the soil. The observed increase in carbonate content estimates may be an artifact when representatives of another ecological group also have related ecological properties that can be misinterpreted as indicators of certain regimes. The phytoindication also revealed trends in the variability of microclimatic conditions in the park as a result of reconstruction. The reconstruction of the park leads not only to a change in the modal levels of ecological regimes, but also to the formation of specific patterns of their spatial distribution. The heterogenization of the ecological space under the influence of reconstruction has been established. This heterogenization is evident in the fact that areas with homogeneous vegetation cover are decreasing. The accuracy of the description of the spatial process was found to have decreased after the park reconstruction procedures. Smooth spatial structures of the park’s vegetation cover without reconstruction are changing into rough spatial structures of the park after reconstruction. The park’s reconstruction obviously disrupts the course of long-term processes that structure the vegetation cover, which leads to temporal and spatial desynchronization of the dynamics of ecological processes. The spatial variation of variables that indicate soil processes can best be described. In contrast, the phytoindication scales that indicate climatic factors are much less spatially structured. The best variogram model to describe the spatial process is also changing under the influence of reconstruction. The significant consequences of the park reconstruction are time variability and spatial heterogeneity of ecological processes.

Inversion géostatistique par itérations de la tomographie de résistivité électrique

AbstractElectrical resistivity tomography (ERT) is a geophysical method used to create an image of the subsurface due to its sensitivity to porosity, water saturation, and pore fluid salinity. This geophysical method has been widely applied in the investigation of mineral and groundwater resources, as well as in archaeological, environmental, and engineering studies. The prediction of subsurface properties, such as electrical conductivity, from measured ERT data requires solving a challenging geophysical inversion problem. This work proposes an iterative geostatistical resistivity inversion method using stochastic sequential simulation and co-simulation as stochastic model perturbation and update techniques. Electrical resistivity models are generated conditioned to a target histogram, often retrieved from available resistivity borehole data, and assuming a spatial continuity pattern described by a variogram model. From the electrical resistivity models, a finite-volume approximation of Poisson’s equation is used to compute synthetic ERT data. The misfit between predicted and observed data drives the convergence of an iterative procedure and conditions the co-simulation of new models in the subsequent iterations. This methodology is applied to a two-dimensional synthetic case, and a set of two-dimensional profiles obtained from an ERT survey carried out in southern Portugal. In both application examples, the final models predict ERT data that match the observed ones while reproducing borehole data and imposed variogram models. The results obtained in both data sets are compared against a commercial deterministic ERT inversion methodology, showing the ability of the proposed method to model small-scale variability and assess spatial uncertainty.

Geostatistical analysis of groundwater levels in a mining area with three active mines

AbstractMining activities can significantly impact groundwater reservoirs in their vicinity. Different approaches have been employed, with varying success, to investigate the spatial variability of groundwater levels in mining areas. Typical problems include the small sample size, the non-Gaussian distribution of the data, and the clustering of sample locations near the mines. These conditions complicate the estimation of spatial dependence. Under sparse and irregular sampling conditions, stochastic methods, which can provide estimates of prediction uncertainty, are preferable to deterministic ones. This research focuses on the comparison of two stochastic methods, stochastic local interactions (SLI) and universal Kriging (UK), using water level data from 72 locations around three mines in Northern Greece. UK is a well-known, variogram-based geostatistical method, while SLI is a computationally efficient kernel-based method that can cope with large spatial datasets. The non-Gaussian distribution of the data is handled by means of a flexible, data-driven Gaussian anamorphosis method that uses kernel functions. The spatial prediction performance of both methods is assessed based on cross-validation. UK performs better than SLI, due to the fact that the former incorporates a linear trend function. On the other hand, a comparison of the two methods using data from a single mine that contains only 28 measurement locations shows that SLI performs slightly better than UK. The prediction uncertainties for both methods are also estimated and compared. The results suggest that SLI can provide better estimates than classical geostatistical methods for small sample sizes that do not allow reliable estimation of the variogram model.

A Smartphone-Enabled Imaging Device for Chromotropic Acid-Based Measurement of Nitrate in Soil Samples.

In this study, a novel chromotropic acid-based color development method was proposed for quick estimation of soil nitrate (NO3-). The method utilized a 3D printed device integrated with the rear-end camera of a smartphone and a stand-alone application called SMART NP. By analyzing the mean Value (V) component of the sample's image, the SMART NP provides instant predictions of soil NO3- levels. The limit of detection was calculated as 0.1 mg L-1 with a sensitivity of 0.26 mg L-1. The device showed a % bias of 0.9% and a precision of 1.95%, indicating its reliability. Additionally, the device-predicted soil NO3- data, combined with kriging interpolation, showcased spatial variability in soil NO3- levels at the regional level. The study employed a Gaussian model of variogram for kriging, and the high Nugget/Sill ratio indicated low spatial autocorrelation, emphasizing the impact of management factors on the spatial distribution of soil NO3- content in the study area. Overall, the imaging device, along with geostatistical interpolation, provided a comprehensive solution for the rapid assessment of spatial variability in soil NO3-content.

Integration of rock physics, geostatistics, and Bayesian algorithm to estimate porosity in tight oil reservoirs

The conglomerate reservoirs in the Triassic Baikouquan Formation have been identified as the major target for hydrocarbon exploitation in the Mahu Sag, Junggar Basin, Western China. Nevertheless, conglomerate reservoirs typically have lower porosity than sandstone reservoirs. Therefore, determining sweet spots is critical in reservoir modeling and further hydrocarbon exploitation. To investigate favorable areas and better predict the porosity of the Baikouquan tight oil reservoir, integrated methods were employed, including casting thin sections, scanning electron microscopy (SEM), wireline logs, rock physics template (RPT) modeling, geostatistical simulation, and Bayesian updating. The results showed that pore types consist of microfractures, intercrystal micropores, residual intergranular pores, and dissolution pores. Four rock types (RT) were identified via the built RPT, wherein velocity and porosity had a nonlinear relationship. Afterward, porosity simulation was performed and compared using sequential gaussian simulation (SGS), SGS with collocated cokriging (SGSC), and SGS with Bayesian updating (SGSB). Prior to the simulation, all the data were preprocessed to follow a Gaussian (normal) distribution. The range and azimuth of different RT in variogram modeling were then determined using data from horizontal wells. Consequently, it was revealed that the probability distribution frequency (PDF) of SGS with Bayesian updating was very similar to the hard data, whereas the PDF associated with SGS and SGSC may be biased. Particularly the PDF was too narrow for high values. The cumulative distribution function (CDF) of SGSB also showed a similar trend to the CDF of the input data. The ensemble-averaged (E-type) maps and quantiles maps revealed that SGSB had an advantage over collocated cokriging because it could capture the non-linear relationships between impedance and porosity. This study indicates that Bayesian updating is a reliable technique for incorporating secondary data in the calculation of reservoir properties.

Merging machine learning and geostatistical approaches for spatial modeling of geoenergy resources

Geostatistics is the most commonly used probabilistic approach for modeling earth systems, including quality parameters of various geoenergy resources. In geostatistics, estimates, either on a point or block support, are generated as a spatially-weighted average of surrounding samples. The optimal weights are determined through the stationary variogram model which accounts for the spatial structure of the samples. Recently, efficient modeling workflows using various machine learning algorithms (MLAs) have been expanded to the spatial context for modeling geological heterogeneity. The flexible use of MLAs as a spatial estimation tool stems mainly from the fact that unlike kriging, they do not require any variogram, nor do they depend strongly on a prior stationarity assumption (i.e., second order stationarity). This study evaluates the performance of two MLAs (ensemble super learner and elliptical radial basis neural network), ordinary kriging, and hybrid spatial modeling approaches using ordinary intrinsic collocated cokriging. The aforementioned modeling techniques are compared for estimating resources for four coal variables (wash yield, ash yield, calorific value and thickness) as an example. The results suggest that MLAs, when implemented alone, do not outperform ordinary kriging, but the estimation accuracy of the final model, measured by the root mean squared error tends to subtly improve (1.7% for wash yield, 6.98% for ash yield, 4.94% for calorific value and 0.36% for seam thickness) when MLAs and geostatistical algorithms are merged through the hybrid spatial modeling approaches.

Addressing Geological Challenges in Mineral Resource Estimation: A Comparative Study of Deep Learning and Traditional Techniques

Spatial prediction of orebody characteristics can often be challenging given the commonly complex geological structure of mineral deposits. For example, a high nugget effect can strongly impact variogram modelling. Geological complexity can be caused by the presence of structural geological discontinuities combined with numerous lithotypes, which may lead to underperformance of grade estimation with traditional kriging. Deep learning algorithms can be a practical alternative in addressing these issues since, in the neural network, calculation of experimental variograms is not necessary and nonlinearity can be captured globally by learning the underlying interrelationships present in the dataset. Five different methods are used to estimate an unsampled 2D dataset. The methods include the machine learning techniques Support Vector Regression (SVR) and Multi-Layer Perceptron (MLP) neural network; the conventional geostatistical methods Simple Kriging (SK) and Nearest Neighbourhood (NN); and a deep learning technique, Convolutional Neural Network (CNN). A comparison of geologic features such as discontinuities, faults, and domain boundaries present in the results from the different methods shows that the CNN technique leads in terms of capturing the inherent geological characteristics of given data and possesses high potential to outperform other techniques for various datasets. The CNN model learns from training images and captures important features of each training image based on thousands of calculations and analyses and has good ability to define the borders of domains and to construct its discontinuities.

Assessment of the Spatial Variability and Uncertainty of Shreddable Pruning Biomass in an Olive Grove Based on Canopy Volume and Tree Projected Area

Olive pruning residues are a by-product that can be applied to soil or used for energy production in a circular economy model. Its benefits depend on the amount of pruning, which varies greatly within farms. This study aimed to investigate the spatial variability of shreddable olive pruning in a traditional olive grove in Córdoba (Spain) with an area of 15 ha and trees distanced 12.5 m from each other. To model the spatial variability of shreddable olive pruning, geostatistical methods of stochastic simulation were applied to three correlated variables measured on sampled trees: the crown projected area (n = 928 trees), the crown volume (n = 167) and the amount of shreddable pruning (n = 59). Pearson’s correlation between pairs of variables varied from 0.71 to 0.76. The amount of pruning showed great variability, ranging from 7.6 to 76 kg tree−1, with a mean value of 37 kg tree−1. Using exponential and spherical variogram models, the spatial continuity of the variables under study was established. Shreddable dry pruning weight values showed spatial autocorrelation up to 180 m. The spatial uncertainty of the estimation was obtained using sequential simulation algorithms. Stochastic simulation algorithms provided 150 possible images of the amount of shreddable pruning on the farm, using tree projected area and crown volume as secondary information. The interquartile range and 90% prediction interval were used as indicators of the uncertainty around the mean value. Uncertainty validation was performed using accuracy plots and the associated G-statistic. Results indicate with high confidence (i.e., low uncertainty) that shreddable dry pruning weight in the mid-western area of the farm will be much lower than the rest of the farm. In the same way, results show with high confidence that dry pruning weight will be much higher in a small area in the middle east of the farm. The values of the G-statistic ranged between 0.89 and 0.90 in the tests performed. The joint use of crown volume and projected areas is valuable in estimating the spatial variability of the amount of pruning. The study shows that the use of prediction intervals enables the evaluation of farm areas and informed management decisions with a low level of risk. The methodology proposed in this work can be extrapolated to other 3D crops without requiring modifications. On a larger scale, it can be useful for predicting optimal locations for biomass plants, areas with high potential as carbon sinks or areas requiring special soil protection measures.

A power-law exponential model for variograms with quick transition and known range: Construction and application to geostatistical time series

The variogram is an important element in geostatistical studies that has been used as a tool to investigate the variability and continuity of the study phenomenon. The classical Matheron estimator for calculating the experimental variogram is used in this paper. A new variogram model is proposed, the power-law exponential model and a comparative study of three-time series datasets with the characteristic of being periodic is performed: rainfalls, particulate matter PM10, and Ozone series. Three other models were considered for comparison: spherical, exponential, and quadratic–exponential. The numerical fit and analysis are carried out using the least-squares method provided by the R statistics software, and testing the solutions by the coefficient of determination R2 and the RMSE measure. Our results provided a good adaptation of the proposed model to the different datasets, satisfying the equality of variances, and also showing a robust fit when adding noise. Moreover, our model presented several advantages over the others, regarding the mentioned characteristics. This suggests that the power-law exponential model is a variant that adds new attributes to the set of existing variogram models.

Determining sampling spacing according to volume of investigation in geophysical surveys, application of air dose rate mapping

SUMMARY Geophysical measurements are a sort of averaging a physical property over a volume of investigation (VOI). Within the VOI, the spatial elements closer to the detector contribute more to the measured value compared to farther elements. In this study, a VOI-oriented algorithm is proposed which establishes a relation between the localization probability, the sampling spacing and the size of the exploration target. Hence, the probability of localizing a target could be calculated as a function of sampling spacing when the target dimension is known. The novelty of this work is the use of VOI in the sampling optimization, which is important for geophysical survey design in environmental sampling and mineral exploration. Although the published sampling optimization methods are often variogram-oriented, the one presented here is based on the spatial variability of the measured property. Finally, coupling the VOI-oriented algorithm with a variogram model could be recommended in order to consider both the measurement mechanism and the spatial variability in the sampling design.

Combination of geostatistics and self-organizing maps for the spatial analysis of groundwater level variations in complex hydrogeological systems

Successful modelling of the groundwater level variations in hydrogeological systems in complex formations considerably depends on spatial and temporal data availability and knowledge of the boundary conditions. Geostatistics plays an important role in model-related data analysis and preparation, but has specific limitations when the aquifer system is inhomogeneous. This study combines geostatistics with machine learning approaches to solve problems in complex aquifer systems. Herein, the emphasis is given to cases where the available dataset is large and randomly distributed in the different aquifer types of the hydrogeological system. Self-Organizing Maps can be applied to identify locally similar input data, to substitute the usually uncertain correlation length of the variogram model that estimates the correlated neighborhood, and then by means of Transgaussian Kriging to estimate the bias corrected spatial distribution of groundwater level. The proposed methodology was tested on a large dataset of groundwater level data in a complex hydrogeological area. The obtained results have shown a significant improvement compared to the ones obtained by classical geostatistical approaches.

An approach based on Machine Learning Algorithms, Geostatistical Technique, and GIS analysis to estimate phosphate ore grade at the Abu Tartur Mine, Western Desert, Egypt

Purpose. This paper aims to estimate phosphate ore grade in the Abu Tartur area, Western Desert, Egypt, using four Machine Learning Algorithms (MLA), Geostatistical Techniques (variogram and kriging models), and GIS-analysis. Methods. Four machine-learning techniques include Optimizable Decision Tree (ODT), Optimizable Support Vector Machine (OSVM), Optimizable Gaussian Process Regression (OGPR), Artificial Neural Network (ANN) are applied in this paper. The constructed variogram and kriging models, as well as GIS-analysis, provide a clear understanding of all the elements distributed in the Abu Tartur phosphate ore and are very useful at the planning and mining stages. Findings. Phosphate content has been estimated with high accuracy based on the results of four machine-learning techniques. The most efficient technique for estimating phosphate content is optimizable (OGPR), which gives correlation coefficients (R) of 0.933 and 0.927 with Mean Absolute Errors (MAE) of 0.983 and 0.933 for the training and validation data, respectively. In addition, geostatistical and GIS methods have shown that percentage of P2O5, thickness, and Fe% are suitable for phosphate mining processes, except for small pockets that require little attention at the mining stage. Originality. This research attempts to develop a quick estimation of phosphate ore grade and to provide a clear understanding about the distribution of different constituents within the ore body using different techniques. Practical implications. Grade estimation is commonly reduced to a function approximation. Artificial intelligence (AI) techniques, and in particular the chosen type of AI techniques, can provide, a valid methodology for estimating grade, and the proposed models can be applied to any other data in the range used in this research.

Spatial variability of the granulometric composition within arable field on soddy-podzolic soil

T e spatial variability of the content of granulometric fraction d>0,25 mm in the arable layer of soddy-podzolic cultivated soil on an area of 18 hectares was studied. T e soil formed in the loess-like loam, underlain by moraine deposits. Samples were taken from the upper (0-10 cm) and lower parts of the arable layer (10-20 cm) following a random-stratif ed sampling scheme. T e total number of samples was 350 cores. T e average fraction content was about 22%, the coef cient of variation was 39-41%, the distributions were approximated by a logarithmically normal distribution. T e Spearman correlation coef cient between values at dif erent depths equaled to 0,87. T e spatial distribution cartograms were constructed by the ordinary kriging method using a spherical variogram model. It is shown that preliminary censoring of high sample values (quantile 0,95) gives better results when constructing a cartogram than removing a linear spatial trend and logarithm of the original data. Spatial structures with reduced and increased values were found on the site, the average linear sizes of which was about 100 m. Presumably, they were associated with the heterogeneity of soil-forming material.

Analysis on the Characteristics and Geological Significance of Variation Function in Mineral Geological Modeling

Variation function is a basic tool used in geostatistics. Modern geostatistics using variation function as a tool for the result of the qualitative geology to quantitative geology development. Variation function has not only been widely used in the calculation of modern geological and mineral resources reserves, but also extended to the description of environmental pollution and the spatial migration of elementions. Variogram is a set of deterministic and statistical theoretical tools for understanding and simulating spatial variables. Taking the variogram as a tool which is in the most commonly used in modern geostatistics, the variogram model can be divided into three categories according to the value of the base station or not, the first is the base-station value, which is divided into spherical model, exponential model, Gauss model and pure nugget effect model; The second is the base-free model, which is divided into linear model, power function model, logarithmic function model and cubic model, and the third is hole effect model. Based on the modern geostatistics is most commonly used for variational function tool, analyses the spatial structure change and the variational function of geological body composition variables between the mathematical characteristics, types and its related geological significance, combined with solid mineral, oil and gas resources in the field of practical application examples of analysis of the variation function application problems of stability, etc, and gives his own understanding. It is considered that variation function is a meaningful tool for geological quantitative analysis and visual display of composition in the modeling of mineral geological features when the data amount meets certain sufficient conditions and the research object is applied.

Updating Local Anisotropies with Template Matching During Geostatistical Seismic Inversion

Iterative geostatistical seismic inversion methods are widely used to predict petro-elastic rock properties from seismic reflection data. When the model perturbation technique uses two-point geostatistics, these methods struggle to reproduce complex and nonstationary geological environments such as faults, folds and highly variable depositional systems. These limitations are often due to the use of a global variogram model to express the expected spatial continuity pattern of the property of interest. In complex geological environments a global variogram model might be unable to detect local heterogeneities and rapid variations of lithology, and result in nonrealistic geological models. Local heterogeneities might be predicted from the data using seismic attribute analysis, which can be imposed during geostatistical seismic inversion as local anisotropy models. In these approaches, the information about the local spatial continuity patterns is fixed and will guide and condition the entire inversion procedure, which can lead to errors and uncertainty in areas where this approach is not appropriate due to high local uncertainty of geological features, given the poor signal-to-noise ratio of the data or the presence of important geological features below the seismic resolution. This work proposes an iterative geostatistical seismic inversion method which iteratively updates the local spatial continuity models based on the trace-by-trace misfit between observed and predicted seismic data. The update of the local spatial continuity models aims at surpassing the limitations of the seismic inversion methods that use a fixed a priori variogram model. The method is successfully illustrated in a challenging two-dimensional synthetic data set and in a real case application. The results demonstrate the benefit of updating iteratively the imposed local spatial continuity patterns based on the data misfit. The inverted models are capable of better predicting the location of faults and reproducing the continuity of sinuous channels.

Spatial Interpolations of Annual Rainfall in Ethiopia Using Simple and Universal Kriging Techniques

The study of spatial distribution of precipitation is an important aspect of water-related research like, hydrological modeling, disaster prediction and watershed management. But, spatial interpolations of annual average rainfall in Ethiopia using Simple and Universal Kriging type through different models has not yet investigated. This study was focused on to select the best fit semivarogram model for annual rainfall interpolation and to map the spatial distribution of rainfall of Ethiopia. In this study, long term mean annual rainfall which was collected from 931 meteorological stations were interpolated using different mathematical variogram models of Kriging to select the best fit variogram model useful to predict continuous surface values of annual average rainfall in Ethiopia. Spherical model was found to be the best fitted variogram model and most accurate model for interpolation using both Simple and Universal Kriging with the value of ME (0.005), RMSE (1.21) and MSDR (121.32) and ME (0.001), RMSE (0.88) and MSDR (144.11), respectively. Since the kriging results of spherical model indicate good model efficacy for this study, it may be useful to map spatial pattern of annual rainfall in Basin level in Ethiopia.

Spatiotemporal Landscape Pattern Analyses Enhanced by an Integrated Index: A Study of the Changbai Mountain National Nature Reserve

The analysis of spatiotemporal changes of landscape patterns is of great significance for forest protection. However, the selection of landscape metrics is often subjective, and existing composite landscape metrics rarely consider the effects of spatial correlation. A more objective approach to formulating composite landscape metrics involves proper weighting that incorporates spatial structure information into integrating individual conventional metrics selected for building a composite metric. This paper proposes an integrated spatial landscape index (ISLI) based on variogram modeling and entropy weighting. It was tested through a case study, which sought to analyze spatiotemporal changes in the landscape pattern in the Changbai Mountains over 30 years based on six global land-cover products with a fine classification system at 30 m resolution (GLC_FCS30). The test results confirm: (1) spatial structure information is useful for weighting conventional landscape pattern metrics when constructing ISLI as validated by correlation analysis between the incorporated conventional metrics and their variogram ranges. In terms of the range parameters of different land cover types, broadleaf forest and needleleaf forest have much larger range values than those of other land cover types; (2) DIVISION and PLAND, two of the conventional landscape metrics considered for constructing ISLI, were assigned the greatest weights in computing ISLI for this study; and (3) ISLI values can be used to determine the dominant landscape types. For the study area, ISLI values of broadleaf forests remained the largest until 2020, indicating that forest landscape characteristics were the most prominent during that period. After 2020, the dominance of needleleaf forest gradually increased, with its ISLI value reaching a maximum of 0.91 in 2025. Therefore, the proposed ISLI not only functions as an extension and complement to conventional landscape metrics but also provides more comprehensive information concerning landscape pattern dynamics.

SciKit-GStat Uncertainty: A software extension to cope with uncertain geostatistical estimates

This study is focused on an extension of a well established geostatistical software to enable one to effectively and interactively cope with uncertainty in geostatistical applications. The extension includes a rich component library, pre-built interfaces and an online application. We discuss the concept of replacing the empirical variogram with its uncertainty bound. This enables one to acknowledge uncertainties characterizing the underlying geostatistical datasets and typical methodological approaches. This allows for a probabilistic description of the variogram and its parameters at the same time. Our approach enables (1) multiple interpretations of a sample and (2) a multi-model context for geostatistical applications. We focus the sample application on propagating observation uncertainties into manual variogram parametrization and analyze its effects. Using two different datasets, we show how insights on uncertainty can be used to reject variogram models, thus constraining the space of formally equally probable models to tackle the issue of parameter equifinality.