Strength Of Spatial Correlation Research Articles

A generic random field approach for stratification uncertainty quantification

Geological uncertainty is a crucial factor in the reliability design of geotechnical structures, necessitating advanced probabilistic approaches for robust subsurface stratification and uncertainty quantification. However, the spatial existence of geological formations at a specific location is indeed a nominal categorical variable. Unlike the spatial variability of soil properties that has been widely addressed using random field theory or geostatistics, quantifying the spatial correlations of formation existence poses unique challenges. In this study, a generic framework for geological uncertainty quantification is proposed. The spatial existence of each formation is modeled with individual latent random fields, such that the spatial correlation strength of formation existence can be defined in a consistent manner as that in geotechnical random fields. Moreover, an effective distance metric is introduced to accommodate spatial correlations within a distorted random field, allowing for the incorporation of stratigraphic dip naturally. The latent random fields are subsequently input into the generalized linear mixed model (GLMM) to derive the probabilistic distribution of formation existence in the form of discrete random fields. The simulation framework is further formulated as a Bayesian inference problem to incorporate existing information from borehole records of a site. The proposed formulation offers great flexibility and versatility in simulating various complex stratigraphic configurations, which is demonstrated through a hypothetical case study with an inter-layer and a real case study in Perth, West Australia. This study advances rigorous quantification of stratification uncertainty, facilitating more reliable geotechnical design and risk assessment in complex geological environments.

Analysing the influence of surface greening on soil conservation in China using satellite remote sensing

Global surface greening is very important to slow down regional warming, promote ecological balance and sustainable development, and China has made a significant contribution to this in the past 30 years, and effectively alleviated environmental problems such as land degradation, water shortage and air pollution by rapidly increasing vegetation coverage. Previous studies have shown that vegetation plays a positive role in alleviating soil erosion, but there is no quantitative description of runoff erosion and sediment transport under vegetation evolution with long time series and high resolution in China area. In this study, we use the RUSLE model and multi-source satellite remote sensing data to simulate overland soil erosion in China from 1990 to 2020 and analyze both the temporal and spatial variation of vegetation avoided erosion (VAE) and its correlation with multiple driving factors, such as Gross Primary Production (GPP). The results show that: 1)The distribution has increased by 12.89 % from 1990 to 2020, which is significant, and indicates that greening of the surface has significantly prevented soil and water loss;2)The spatial correlation strength of VAE-GPP in China is roughly in line with the division of the Hu Huanyong line (Hu-line), which is the result of the combined effect of vegetation distribution and human activities;3)The efficiency of VAE was significantly improved, especially the forest, accounting for about 76.50 % of the total, which was twice the sum of the other types. The research conclusion is of great significance to soil erosion prevention and control, soil ecological improvement, vegetation dynamic planning and regional sustainable development.

Strength of spatial correlation between gray matter connectivity and patterns of proto-oncogene and neural network construction gene expression is associated with diffuse glioma survival.

Like other forms of neuropathology, gliomas appear to spread along neural pathways. Accordingly, our group and others have previously shown that brain network connectivity is highly predictive of glioma survival. In this study, we aimed to examine the molecular mechanisms of this relationship via imaging transcriptomics. We retrospectively obtained presurgical, T1-weighted MRI datasets from 669 adult patients, newly diagnosed with diffuse glioma. We measured brain connectivity using gray matter networks and coregistered these data with a transcriptomic brain atlas to determine the spatial co-localization between brain connectivity and expression patterns for 14 proto-oncogenes and 3 neural network construction genes. We found that all 17 genes were significantly co-localized with brain connectivity (p < 0.03, corrected). The strength of co-localization was highly predictive of overall survival in a cross-validated Cox Proportional Hazards model (mean area under the curve, AUC = 0.68 +/- 0.01) and significantly (p < 0.001) more so for a random forest survival model (mean AUC = 0.97 +/- 0.06). Bayesian network analysis demonstrated direct and indirect causal relationships among gene-brain co-localizations and survival. Gene ontology analysis showed that metabolic processes were overexpressed when spatial co-localization between brain connectivity and gene transcription was highest (p < 0.001). Drug-gene interaction analysis identified 84 potential candidate therapies based on our findings. Our findings provide novel insights regarding how gene-brain connectivity interactions may affect glioma survival.

A conditional GAN-based approach to build 3D facies models sequentially upwards

This paper presents an alternative way of simulating 3D facies models using conditional generative adversarial networks (GANs) by reconstructing the 3D volume upward with customised thickness from generated 2D slices. To mimic natural fluvial reservoirs, GANs need to learn the complicated facies’ lateral and vertical sequences, connectivity patterns and spatial correlation, e.g. the distribution of channel deposits and lateral accretion packages, including channel lags and point bars in a meandering fluvial system. 3D GAN modelling remains challenging, despite some success in 3D, due to the increased data and GAN model complexity caused by the 3D training data. For example, a 3D facies model with a larger number of voxels introduces more complex geobody shapes and requires 3D convolutions that increases the computational burden compared to 2D convolutions.Our proposed conditional GAN-based framework predicts 2D upper layers slice by slice to build 3D facies models, mimicking the sedimentary process in a purely aggrading system, which is less computationally costly than generating the facies models used as training data and generating facies models directly in 3D from a GAN. Each upper layer is predicted conditionally to a lower layer that contains the facies distributions in all layers below the target using several unique training enhancements. All those methods help prevent the simulated 3D models from gradually losing realism and the preset sedimentary settings vertically while inferring the plausible evolution of the channel system. The results demonstrate that the trained conditional generator, a SPADE generator, can work as a simulator to produce unconditional 3D meandering fluvial facies models by inputting a user-defined spatial correlation strength between layers and the number of layers needed (thickness in metres) without post-processing or retraining. This framework’s performance was evaluated using a connectivity metric towards the range of avulsion scenarios that represent a range of depositional uncertainty.

Uniform Nonparametric Inference for Spatially Dependent Panel Data

This article proposes a uniform functional inference method for nonparametric regressions in a panel-data setting that features general unknown forms of spatio-temporal dependence. The method requires a long time span, but does not impose any restriction on the size of the cross section or the strength of spatial correlation. The uniform inference is justified via a new growing-dimensional Gaussian coupling theory for spatio-temporally dependent panels. We apply the method in two empirical settings. One concerns the nonparametric relationship between asset price volatility and trading volume as depicted by the mixture of distribution hypothesis. The other pertains to testing the rationality of survey-based forecasts, in which we document nonparametric evidence for information rigidity among professional forecasters, offering new support for sticky-information and noisy-information models in macroeconomics.

The Spitzer Extragalactic Representative Volume Survey and DeepDrill extension: clustering of near-infrared galaxies

ABSTRACT We have measured the angular autocorrelation function of near-infrared galaxies in SERVS + DeepDrill, the Spitzer Extragalactic Representative Volume Survey and its follow-up survey of the Deep Drilling Fields, in three large fields totalling over 20 deg2 on the sky, observed in two bands centred on 3.6 and 4.5 μm. We performed this analysis on the full sample as well as on sources selected by [3.6]–[4.5] colour in order to probe clustering for different redshift regimes. We estimated the spatial correlation strength as well, using the redshift distribution from S-COSMOS with the same source selection. The strongest clustering was found for our bluest subsample, with 〈z〉 ∼ 0.7, which has the narrowest redshift distribution of all our subsamples. We compare these estimates to previous results from the literature, but also to estimates derived from mock samples, selected in the same way as the observational data, using deep light-cones generated from the SHARK semi-analytical model of galaxy formation. For all simulated (sub)samples, we find a slightly steeper slope than for the corresponding observed ones, but the spatial clustering length is comparable in most cases.

Spatiotemporal heterogeneity and influencing factors on urbanization and eco-environment coupling mechanism in China.

High-quality urbanization is the core for realizing human well-beings, for which reason investigating how the relationship evolves between urbanization and eco-environment is of crucial importance. Differing from the rationale of revealing spatial spillover effects using traditional tests, we consider spatial network characteristics to enrich the notion of local coupling and telecoupling from a relational perspective. First, we adopt coupling coordination degree model (CCDM) and decoupling model (DM) to calculate the urbanization and eco-environment coupling coordination degree (UECCD) and the decoupling index (DI) in 30 provinces and municipalities of China from 2008 to 2017. Second, we use gravity model to construct urbanization and eco-environment coupling coordination network (UECCN), in which provinces are nodes and spatial connection relationships of UECCD are edges between nodes. Third, we introduce social network analysis (SNA) to reveal spatial network characteristics of UECCN without using local spatiotemporal heterogeneity. Finally, we employ spatial econometric model to reveal factors that influence urbanization and eco-environment coupling effect. The major findings and conclusions of this study are summarized as follows. (1) The main subclasses of UECCD and DI are basically uncoordinated patterns with eco-environment lagging and weak decoupling, respectively. (2) Only two spatial agglomeration types of UECCD exist, the high-high (H-H) clustering in Shanghai and the low-low (L-L) clustering in western China, whereas no significant spatial agglomeration effect is observed among most provinces. (3) The distribution characteristics of UECCN are sparse in western China and dense in eastern China, and the spatial correlation strength of UECCN improves. (4) Technological innovation plays a critical role in promoting UECCD, while the total population, per capita disposable income, coupling network structure, and environmental regulations exert significant impact on UECCD. Collectively, we propose to prioritize governance provinces with low UECCD in western China as well as adequately utilize the positive externalities of key node provinces in eastern China. Equally importantly, we suggest that it is also critical to fully exert a driving force of technological innovation on improving the UECCD by promoting renewable energy utilization.

Suppressing reactivity in a degenerate Fermi molecular gas via the statistical potential

We present a simple theoretical model used for describing the suppressing reactivity of an ultracold Fermi molecular gas in a degenerate regime via the statistical potential. The statistical potential originates from the symmetry properties of the wave function of identical particles, and is derived by using the density matrix. We use our theoretical model to well reproduce recent experimental results of a potassium-rubidium molecule gas in the deep quantum degenerate regime reported by De Marco et al. [Science 363, 853 (2019)]. The suppression of the chemical reaction rate observed in the experiment is quantitatively reproduced by using the $p$-wave scattering volume as an adjusting parameter. The strength of spatial correlation can be intuitively captured by the statistical potential.

Complex Network Construction and Pattern Recognition of China’s Provincial Low-Carbon Economic Development with Long Time Series: Based on the Detailed Spatial Relationship

Low-carbon economic development has become the orientation of high-quality economic construction in the era of climate change. Because it involves multi-dimensional elements and is driven by the concept of regional integration and common development, the development pattern among China’s provinces should show the characteristics of complex networked spatial correlation. However, most of the existing research are for is based on attribute data and combined with traditional spatial econometric models, which cannot describe the complex networked spatial correlation. Concurrently, the network construction is mainly based on undirected-unweighted sparseness, which makes it difficult to truly restore the asymmetric detailed spatial relationship, making the related research about development pattern recognition and its evolution based on the detailed spatial relationship relatively lacking. Therefore, based on the perspective of relational data, this study constructs a multi-dimensional gravity model by using the comprehensive quality of China’s provincial low-carbon economic development, measured by the multi-dimensional evaluation index system and dynamic weight method, and the comprehensive distance based on geography, society, economy, and adjacency. And then the spatial correlation strength among China’s provincial low-carbon economic development is determined, and constructs a directed-weighted complex network. Then, it further explores the inter-provincial detailed spatial relationship of low-carbon economy development from the three dimensions of overall, individual and group, to recognize the development patterns and evolution rules of low-carbon economic development in different provinces, and clarify the development orientation. The results show that, during the study period, the spatial correlation of China’s provincial low-carbon economic development has become increasingly close, showing a complex networked correlation structure with multi-linearity, asymmetry, and geographical proximity as a whole. The division of general structure is consistent with China’s regional economic development strategy. The unbalanced development of China’s provincial low-carbon economy is the result of multi-center drive in the eastern and central regions, and the distance from the network center in the western regions. In general, China’s provincial low-carbon economic development patterns can be roughly divided into spillover, main bridge, auxiliary bridge, and benefit type. In the future, we should make full use of the power source role of spillover provinces, and the bridge support role of bridge provinces to drive the development of benefit provinces. Among them, Chongqing, Shaanxi, Hebei and Sichuan are expected to become new regional growth poles. The research on the inter-provincial spatial correlation effect and development pattern recognition of low-carbon economic development is expected to provide guidance for the sustainable development of low-carbon economy in China.

Transregional spatial correlation revealed by deep learning and implications for material characterisation and reconstruction

Computational microstructure characterisation and reconstruction of materials with a cementitious nature are essential for understanding their behaviour and predicting properties in the macro scale. Modelling cementitious materials with a representative spatial scale with precise characterisation has troubled researchers for decades. Although numerous physical descriptors have been applied for the characterisation of cementitious materials, only a few of them describe high-order information within the microstructure such as spatial arrangements. In this work, we demonstrated the capturing of the spatial correlation in cementitious material using deep convolutional neural networks at multiple scales based on imaging data with nanoscale resolution. Our results revealed the presence of a spatial correlation in the cementitious system and give the first indication of its distribution among the diverse features of the microstructure. We also propose functions of the discovered correlation for representative scale determination of cement materials and suggest the implications for the reconstruction of the cement microstructure based on its spatial correlation. • Transregional spatial correlation in material microstructure detected by deep learning • Fractality of spatial correlation from both scale and distance aspect • Spatial correlation distribution among various microstructure features • Prototype of spatial correlation strength function • Implications for microstructure characterisation and reconstruction

Revisiting spatial correlation in crash injury severity: a Bayesian generalized ordered probit model with Leroux conditional autoregressive prior

To account for the spatial correlation of crashes that are in close proximity, this study proposes a Bayesian spatial generalized ordered probit (SGOP) model with Leroux conditional autoregressive (CAR) prior for crash severity analysis. Proposed model can accommodate the ordinal nature of injury severity and relax the assumption of monotonic effects of explanatory factors. Additionally, strength of spatial correlation is considered. Results indicate that the proposed SGOP model with Leroux CAR prior outperforms the conventional ordered probit model and SGOP model with intrinsic CAR. There is moderate spatial correlation for the crashes. Results indicate that factors including vehicle type, horizontal curvature, vertical grade, precipitation, visibility, traffic composition, day of the week, crash type, and response time of emergency medical service all affect the crash injury severity. Findings of this study can indicate the effective engineering countermeasures that can mitigate the risk of more severe crashes on the freeways.

A guideline to select an estimation model of daily global solar radiation between geostatistical interpolation and stochastic simulation approaches

This study compares geostatistical interpolation and stochastic simulation approaches for the estimation of daily global solar radiation (GSR) on a horizontal surface in order to fill in missing values and to extend short record length of a meteorological station. A guideline to select an approach is suggested based on this comparison. Three geostatistical interpolation models are developed using the nearest neighbor (NN), inverse distance weighted (IDW), and ordinary kriging (OK) schemes. Three stochastic simulation models are also developed using the artificial neural network (ANN) method with daily temperature (ANN(T)), relative humidity (ANN(H)), and both (ANN(TH)) variables as predictors. The six models are compared at 13 meteorological stations located across southern Quebec, Canada. The three geostatistical interpolation models yield better performances at stations located in a high density area of GSR measuring stations compared to the three stochastic simulation models. The guideline suggests an optimal approach by comparing a threshold distance, estimated according to a performance criteria of a stochastic simulation model, to the distance between a target and its nearest neighboring station. Additionally, the spatial correlation strength of daily GSRs and the at-site correlation strength between daily GSRs and the predictor variables should be considered.

ID 305 – Effect of levodopa on resting state functional connectivity in Parkinson’s disease: A partial least squares correlation study

Objective We performed partial least squares correlation (PLSC) analysis to study functional connectivity in resting-state networks (RSN) in PD patients. Methods We acquired rs-fMRI data in PD patients (18 non-demented and non-depressed males) in the ON and OFF medication conditions and rs-fMRI data in healthy controls (15 males). We chose 2 coordinates for motor seeds and 6 coordinates for non-motor seeds. We extracted the BOLD signals and computed their correlations. These correlations were analyzed by PLSC. Results The PLSC analysis revealed significant impact of the disease on the connectivity strength of spatial correlation maps seeded by R caudate ( p = 0.047), anterior cingulate cortex ( p = 0.006), right middle temporal gyrus/middle occipital gyrus ( p = 0.045), and R orofacial SM1 ( p = 0.025). The connectivity in PD patients within all studied networks decreased in most of the brain regions as compared to HC. Conclusions We observed impact of the disease (PD vs. HC status). Connectivity in PD was decreased as compared with HC and was detected in a number of large-scale brain networks including the motor, insular, ventral visual, and the default mode networks. Key message PLSC is able to detect differences in RSN between PD patients and HC.

Impact of Parkinson's disease and levodopa on resting state functional connectivity related to speech prosody control

BackgroundImpaired speech prosody is common in Parkinson's disease (PD). We assessed the impact of PD and levodopa on MRI resting-state functional connectivity (rs-FC) underlying speech prosody control. MethodsWe studied 19 PD patients in the OFF and ON dopaminergic conditions and 15 age-matched healthy controls using functional MRI and seed partial least squares correlation (PLSC) analysis. In the PD group, we also correlated levodopa-induced rs-FC changes with the results of acoustic analysis. ResultsThe PLCS analysis revealed a significant impact of PD but not of medication on the rs-FC strength of spatial correlation maps seeded by the anterior cingulate (p = 0.006), the right orofacial primary sensorimotor cortex (OF_SM1; p = 0.025) and the right caudate head (CN; p = 0.047). In the PD group, levodopa-induced changes in the CN and OF_SM1 connectivity strengths were related to changes in speech prosody. ConclusionsWe demonstrated an impact of PD but not of levodopa on rs-FC within the brain networks related to speech prosody control. When only the PD patients were taken into account, the association between treatment-induced changes in speech prosody and changes in rs-FC within the associative striato-prefrontal and motor speech networks was found.

Model-Based Sampling Design for Multivariate Geostatistics

The quality of inferences made from geostatistical data is affected significantly by the spatial locations, or design, of the sites that are sampled. A large body of published work exists on sampling design for univariate geostatistics, but not for multivariate geostatistics. This article considers multivariate spatial sampling design based on criteria targeted at classical co-kriging (prediction with known covariance parameters), estimation of covariance (including cross-covariance) parameters, and empirical co-kriging (prediction with estimated covariance parameters). Through a combination of analytical results and examples, we investigate the characteristics of optimal designs with respect to each criterion, addressing in particular the design’s degree of collocation. We also consider the robustness of the optimal design to the strength of spatial correlation and cross-correlation; the effects of smoothness and/or separability of the sampled process on the optimal design; the relationship between optimal designs for the multivariate problems considered here and univariate problems considered previously; and the efficiency of optimal collocated designs. One key finding is that optimal collocated designs are highly efficient in many cases. Supplementary materials are available online.

MIMO Diversity in the Presence of Double Scattering

The potential benefits of multiple-antenna systems may be limited by two types of channel degradations-rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multiple-input multiple-output (MIMO) systems, with an emphasis on orthogonal space-time block codes (OSTBC), in terms of the symbol error probability (SEP), the effective fading figure (EFF), and the capacity at low signal-to-noise ratio (SNR). In particular, we consider a general family of MIMO channels known as double-scattering channels-i.e., Rayleigh product MIMO channels-which encompasses a variety of propagation environments from independent and identically distributed (i.i.d.) Rayleigh to degenerate keyhole or pinhole cases by embracing both rank-deficient and spatial correlation effects. It is shown that a MIMO system with transmit and receive antennas achieves the diversity of order in a double-scattering channel with effective scatterers. We also quantify the combined effect of the spatial correlation and the lack of scattering richness on the EFF and the low-SNR capacity in terms of the correlation figures of transmit, receive, and scatterer correlation matrices. We further show the monotonicity properties of these performance measures with respect to the strength of spatial correlation, characterized by the eigenvalue majorization relations of the correlation matrices.

Stereoscopic PIV measurements of swirling flow entering a catalyst substrate

This experimental study investigates the stagnation region of a swirling flow entering an automotive catalyst substrate. A methodology is established using stereoscopic particle image velocimetry (PIV) to determine three-component velocity distributions up to 0.2 mm from the catalyst entrance face. In adverse conditions of strong out-of-plane velocity, PIV operating parameters are adjusted for maximum spatial correlation strength. The measurement distance to the catalyst is sufficiently small to observe radial flow spreading. A scaling analysis of the stagnation flow region provides a model for the flow uniformization as a function of the catalyst pressure drop.

Using Information about Spatial Variability to Improve Estimates of Total Soil Carbon

Changes in soil C as a result of changes in management are relatively slow, and several years of experimentation are needed before differences in management practices can be detected using traditional statistical procedures such as randomized complete block design (RCBD). Using spatial analyses (SA) that take into account spatial variability between plots has a potential for faster and more efficient detection of soil C differences. We hypothesize that for variables with strong spatial continuity, such as total soil C, accurate spatial variability assessment can be obtained even in relatively small experiments. Thus, SA can significantly improve the statistical efficiency of even these experiments. The objective of this study is to test this hypothesis by comparing performances of RCBD analysis and SA for simulated small‐sized experiments where soil C is the response variable. Total soil C data collected from 11 field sites at the Long‐Term Ecological Research (LTER) experiment in Michigan were used as an input for simulated experiments. Performance of SA depended on the strength of spatial correlation in soil C and was found to be related to topographical diversity of the experimental sites. In the sites with more diverse topography and stronger spatial correlation of soil C the SA produced lower standard errors for treatment means than those of the RCBD analysis (8 out of 11 sites). In two sites with the flattest topography and weak spatial correlation, SA did not have advantages over RCBD.

On the value of 3D seismic amplitude data to reduce uncertainty in the forecast of reservoir production

Three-dimensional (3D) seismic data are commonly used to identify the size and shape of putative flow barriers in hydrocarbon reservoirs. It is less clear to what extent determining the spatial distribution of engineering properties (e.g., porosity, permeability, pressures, and fluid saturations) can improve predictions (i.e., improve accuracy and reduce uncertainty) of hydrocarbon recovery, given the multiple non-linear and often noisy transformations required to make a prediction. Determining the worth of seismic data in predicting dynamic fluid production is one of the goals of this paper. We have approached the problem of assessing uncertainty in production forecasts by constructing a synthetic reservoir model that exhibits much of the geometrical and petrophysical complexity encountered in clastic hydrocarbon reservoirs. This benchmark model was constructed using space-dependent, statistical relationships between petrophysical variables and seismic parameters. We numerically simulated a waterflood in the model to reproduce time-varying reservoir conditions. Subsequently, a rock physics/fluid substitution model that accounts for compaction and pressure was used to calculate elastic parameters. Pre-stack and post-stack 3D seismic amplitude data (i.e., time-domain amplitude variations of elastic responses) were simulated using local one-dimensional approximations. The seismic data were also contaminated with additive noise to replicate actual data acquisition and processing errors. We then attempted to estimate the original distribution of petrophysical properties and to forecast oil production based on limited and inaccurate spatial knowledge of the reservoir acquired from wells and 3D seismic amplitude data. We compared the multiple realizations of the various predictions against predictions with a reference model. The use of seismic amplitude data to construct static reservoir models affected production performance variables in different ways. For example, seismic amplitude data did not uniformly improve the variability of the predictions of water breakthrough time; other quantities, such as cumulative recovery after the onset of production, did exhibit an uncertainty reduction as did a global measure of recovery. We evaluate how different degrees of spatial correlation strength between seismic and petrophysical parameters may ultimately affect the ensuing uncertainty in production forecasts. Most of the predictions exhibited a bias in that there was a significant deviation between the medians of the realizations and that the value from the reference case. This bias was evidently caused by noise in the various transforms (some of which we introduced deliberately) coupled with nonlinearity. The key nonlinearities seem to be in the numerical simulation itself, specifically in the transformation from porosity to permeability, in the relative permeability relationships, and in the conservation equations themselves.

Influence of Spatial Structure on Accuracy of Interpolation Methods

Effectiveness of precision agriculture depends on accurate and efficient mapping of soil properties. Among the factors that most affect soil property mapping are the number of soil samples, the distance between sampling locations, and the choice of interpolation procedures. The objective of this study is to evaluate the effect of data variability and the strength of spatial correlation in the data on the performance of (i) grid soil sampling of different sampling density and (ii) two interpolation procedures, ordinary point kriging and optimal inverse distance weighting (IDW). Soil properties with coefficients of variation (CV) ranging from 12 to 67% were sampled in a 20‐ha field using a regular grid with a 30‐m distance between grid points. Data sets with different spatial structures were simulated based on the soil sample data using a simulated annealing procedure. The strength of simulated spatial structures ranged from weak with nugget to sill (N/S) ratio of 0.6 to strong (N/S ratio of 0.1). The results indicated that regardless of CV values, soil properties with a strong spatial structure were mapped more accurately than those that had weak spatial structure. Kriging with known variogram parameters performed significantly better than the IDW for most of the studied cases (P &lt; 0.01). However, when variogram parameters were determined from sample variograms, kriging was as accurate as the IDW only for sufficiently large data sets, but was less precise when a reliable sample variogram could not be obtained from the data.