Search

O_LIComparing traits across species has been a hallmark of biological research for centuries. While inter-specific comparisons can be highly informative, phylogenetic inertia can bias estimates if not properly accounted for in comparative analyses. In response, researchers typically treat phylogenetic inertia as a form of autocorrelation that can be detected, modelled, and corrected for. Despite the range of methods available for quantifying the strength of phylogenetic autocorrelation, no tools exist for visualising these autocorrelation structures. C_LIO_LIHere we derive variogram methods suitable for phylogenic data, and show how they can be used to straightforwardly visualise phylogenetic autocorrelation. We then demonstrate their utility for three empirical examples: sexual size dimorphism (SSD) in the Musteloidea, maximum per capita rate of population growth, r, in the Carnivora, and brain size in the Artiodactyla. C_LIO_LIWhen modelling musteloid SSD, the empirical variogram showed a tendency for the variance in SSD to stabilise over time, a characteristic feature of Ornstein-Uhlenbeck (OU) evolution. In agreement with this visual assessment, model selection identified the OU model as the best fit to the data. In contrast, the infinitely diffusive Brownian Motion (BM) model did not capture the asymptotic behaviour of the variogram and was less supported than the OU model. Phylogenetic variograms proved equally useful in understanding why an OU model was selected when modelling r in the Carnivora, and why BM was the selected evolutionary model for brain size in the Artiodactyla. C_LIO_LIBecause the variograms of the various evolutionary processes each have different theoretical profiles, comparing fitted semi-variance functions against empirical semi-variograms can serve as a useful diagnostic tool, allowing researchers to understand why any given evolutionary model might be selected over another, which features are well captured by the model, and which are not. This allows for fitted models to be compared against the empirical variogram, facilitating model identification prior to subsequent analyses. We therefore recommend that any phylogenetic analysis begin with a non-parametric estimate of the autocorrelation structure of the data that can be visualized. The methods developed in this work are openly available in the new R package ctpm. C_LI

BACKGROUND The gram pod borer, Helicoverpa armigera (Lepidoptera: Noctuidae) is an economically important pest of pigeonpea crop in India. Fixed plot surveys for H. armigera larvae were carried out at 28 pigeonpea fields located in the Southern Plateau and Hills agro-climatic zone of India for three crop seasons (nine sampling weeks per season). The spatiotemporal dynamics of H. armigera larvae in the experimental area (=Hanamkonda) was analysed using geostatistics tools, namely a variogram and Voronoi diagram, and H. armigera larval distribution patterns were further characterized and mapped. RESULTS A significant difference in H. armigera larval incidence was noticed between sampling weeks, with greater larval incidence observed between 26 November and 2 December. Pod formation phenophase (Meteorological Standard Week 44) of pigeonpea favoured the initial H. armigera larval incidence. Variogram analysis revealed moderate to strong larval aggregation (spatial dependence) of H. armigera in all nine sampling weeks. Based on the range value of the variogram, the average aggregation distance of H. armigera larvae in pigeonpea was estimated to be 2425.48 m. Voronoi diagrams illustrated the spatial heterogeneity of H. armigera larva between sampling weeks, which can be linked to availability of food sources. CONCLUSION This study witnessed intrapopulation variability in H. armigera larvae associated with geographical space and temporal patterns. Based on our findings, a sampling distance of 2425.48 m may be used in larger pigeonpea fields (experimental area) to reduce scouting fatigue. The interpolated maps generated in this study may be of value in developing effective H. armigera larva monitoring and management tools in pigeonpea crop.

BACKGROUND Understanding the spatio‐temporal dynamics of prey and predator distributions can provide valuable insights into pest management strategies and conservation of natural enemies in agro‐ecosystems. The alfalfa weevil, Hypera postica (Gyllenhal), is an economically important pest of alfalfa throughout the western United States. Coccinellids and nabids are among the most important natural enemies of this species, contributing to the biological control of H. postica in alfalfa fields. The spatio‐temporal dynamics of H. postica and these two predator groups were investigated using 81 (= 9 × 9 grid) sample points in each of five alfalfa fields in north‐central Montana. The data were analyzed using variogram and spatial analysis by distance indices (SADIE). RESULTS Variogram analysis revealed the spatial dependence (aggregation) of H. postica in 17 of 19 sampling times for larvae, and three of 12 sampling times for adults. Using SADIE, statistically significant aggregation distribution was evident in four of 19 sampling times for larvae, and five of 12 sampling times for adults of H. postica. Combined variogram and SADIE showed strong evidence of spatial aggregation of H. postica larval population (~95%) while a moderate level of aggregation in the adult population (~67%) of the sampling times analyzed. The average aggregation distances based on the range value of the variogram were 22.3 m and 14.7 m for larvae and adults, respectively. Based on variogram results, populations of natural enemies, coccinellids and Nabis spp. were found spatially aggregated in 57.9% and 5.6% of the sampling times, respectively. SADIE further supported the variogram results as coccinellid populations (52.6% of sampling times) were highly aggregated in contrast with the Nabis spp. populations (5.6% of sampling times) in alfalfa fields. There was no evidence of significant spatial synchrony between H. postica and its predators, coccinellids and Nabis spp. CONCLUSION Our study was able to determine the spatial and temporal distribution of H. postica and its two natural enemies (coccinellids and nabids) in irrigated alfalfa fields. The possible implications of these findings for integrated pest management (IPM) of alfalfa weevil populations are discussed., This study determined the spatial and temporal distribution of Hypera postica and the population of its two natural enemies (coccinellids and nabids) in irrigated alfalfa fields.

It is commonly accepted that an estimated soil variogram can be transferred to another similar area for deriving the tolerable spacing of a sampling grid or, more generally, the sample size, given a requirement on the quality of the soil property map of the recipient area. The quality of the derived tolerable grid spacing depends on how similar the population variograms of the donor area and recipient area are. In practice we are uncertain about the variograms of both areas due to sampling errors. Ideally, the uncertainty about the variogram of the donor area is accounted for in deriving the tolerable grid spacing. To assess the transferability, we should also account for uncertainty in the estimated variogram of the recipient area. In this study the transferability of variograms of soil pH, P, Mg and K is analysed for three grassland fields in Ireland, which are similar in soil-forming factors. One field served as donor area, the other two as recipient area. For all three fields and for each soil property, 500 variograms were sampled from the posterior distribution of the variogram parameters. Results showed that the estimated variogram parameters of the recipient fields differed largely from those of the transferred variograms. The ranges of estimated mean kriging variance values for the various grid spacings, as obtained with the two sets of variograms (one set of the donor field, one set of the recipient field), did not overlap. Even after scaling the transferred variogram with an estimate of the variance of the recipient field, the transferred variogram was of no use for determining the tolerable grid spacing. The difference in the variograms can possibly be explained by the difference in historical land use. Highlights: Transferability of variograms to derive tolerable grid spacing for mapping grassland fields is assessed Transferability should be based on the uncertainty distributions of the tolerable grid spacings Due to difference in historical land use, local and transferred variograms differed largely Transferability of a variogram is very poor, even after scaling the transferred variogram.

Soil scientists are accustomed to geostatistical methods and tools such as semivariograms and kriging for analysis of observational data. Such methods assume and exploit that observations are spatially correlated. Conversely, analysis of variance (ANOVA) of designed experiments assumes that observations from different experimental units are independent, an assumption that is justified based on randomization. It may be beneficial, however, to perform an ANOVA assuming a geostatistical covariance model. Also, it is increasingly common to have multiple observations per experimental unit. Simple ANOVA assuming independence of observations is not appropriate for such data. Instead, a linear mixed model accounting for correlation among observations made on the same plot is required for proper analysis. The purpose of this paper is to demonstrate the benefits of integrating geostatistical covariance structures and ANOVA procedures into a linear mixed modelling framework. Two examples from designed experiments are considered in detail, making a link between terminologies and jargon used in geostatistical analysis on the one hand and linear mixed modelling on the other hand. We provide code in R and SAS for both examples in two supporting companion documents. HIGHLIGHTS: Analysis of variance and geostatistical analysis can be joined in a mixed model. Randomization justifies the independence assumption in analysis of variance. Geostatistical models imply a correlation of errors and can improve efficiency. Lacking randomization, spatial correlation can be accounted for in a mixed model.

In this study, we evaluate uncertainties propagated through different climate data sets in seasonal and annual hydrological simulations over 10 subarctic watersheds of northern Manitoba, Canada, using the variable infiltration capacity (VIC) model. Further, we perform a comprehensive sensitivity and uncertainty analysis of the VIC model using a robust and state‐of‐the‐art approach. The VIC model simulations utilize the recently developed variogram analysis of response surfaces (VARS) technique that requires in this application more than 6,000 model simulations for a 30‐year (1981–2010) study period. The method seeks parameter sensitivity, identifies influential parameters, and showcases streamflow sensitivity to parameter uncertainty at seasonal and annual timescales. Results suggest that the Ensemble VIC simulations match observed streamflow closest, whereas global reanalysis products yield high flows (0.5–3.0 mm day⁻¹) against observations and an overestimation (10–60%) in seasonal and annual water balance terms. VIC parameters exhibit seasonal importance in VARS, and the choice of input data and performance metrics substantially affect sensitivity analysis. Uncertainty propagation due to input forcing selection in each water balance term (i.e., total runoff, soil moisture, and evapotranspiration) is examined separately to show both time and space dimensionality in available forcing data at seasonal and annual timescales. Reliable input forcing, the most influential model parameters, and the uncertainty envelope in streamflow prediction are presented for the VIC model. These results, along with some specific recommendations, are expected to assist the broader VIC modelling community and other users of VARS and land surface schemes, to enhance their modelling applications.

We estimate model parameters of Lévy‐driven causal continuous‐time autoregressive moving average random fields by fitting the empirical variogram to the theoretical counterpart using a weighted least squares (WLS) approach. Subsequent to deriving asymptotic results for the variogram estimator, we show strong consistency and asymptotic normality of the parameter estimator. Furthermore, we conduct a simulation study to assess the quality of the WLS estimator for finite samples. For the simulation, we utilize numerical approximation schemes based on truncation and discretization of stochastic integrals and we analyze the associated simulation errors in detail. Finally, we apply our results to real data of the cosmic microwave background.

A localized rainfall kinetic energy (E) equation and an erosivity map were developed, and the suitability of the universal soil loss equation (USLE) for assessing the soil erosion of a non‐US region was investigated. After accurately measuring and gathering data regarding raindrop size using disdrometers in four northern Taiwan locations, this study investigated the drop size distribution under different conditions by categorizing the rainfall patterns to develop regression equations for estimating the unit volume‐specific kinetic energy (KEₘₘ) and the unit time‐specific kinetic energy (KEₜᵢₘₑ) of northern Taiwan. Climate zoning, which is not considered in currently used designs, was then implemented along with two‐stage cluster analysis to construct a rainfall erosivity (R) distribution map using the kriging model. The binary polynomial regression function of KEₜᵢₘₑ, which had the highest correlation (R² = 0.98), was suggested to estimate E in northern Taiwan. It was found that the pattern and intensity (I) of rainfall will slightly affect E. The climatic influence on the root mean square of the semivariogram was significant, which suggests that climate zoning can help estimate the rainfall erosivity (R). The outcomes were extended to estimate R in areas without rainfall stations.

It is well known that snow plays an important role in land surface energy balance; however, modelling the subgrid variability of snow is still a challenge in large‐scale hydrological and land surface models. High‐resolution snow depth data and statistical methods can reveal some characteristics of the subgrid variability of snow depth, which can be useful in developing models for representing such subgrid variability. In this study, snow depth was measured by airborne Lidar at 0.5‐m resolution over two mountainous areas in south‐western Wyoming, Snowy Range and Laramie Range. To characterize subgrid snow depth spatial distribution, measured snow depth data of these two areas were meshed into 284 grids of 1‐km × 1‐km. Also, nine representative grids of 1‐km × 1‐km were selected for detailed analyses on the geostatistical structure and probability density function of snow depth. It was verified that land cover is one of the important factors controlling spatial variability of snow depth at the 1‐km scale. Probability density functions of snow depth tend to be Gaussian distributions in the forest areas. However, they are eventually skewed as non‐Gaussian distribution, largely due to the no‐snow areas effect, mainly caused by snow redistribution and snow melt. Our findings show the characteristics of subgrid variability of snow depth and clarify the potential factors that need to be considered in modelling subgrid variability of snow depth.

The assessment of long‐term trends in environmental extremes is a challenging and important subject in the current discussion on global climate change. We propose a new approach for evaluating temporal trends and spatial homogeneity in extremes accounting also for spatial dependence. Based on exceedances over a space–time threshold, we provide estimators for a so‐called scedasis function and the extreme value parameters. Two novel test statistics based on the scedasis function provide a way to assess space–time inhomogeneities. Finally, we propose a procedure to achieve stationarity in space and time and evaluate residual extremal dependence over space through a variogram analysis that includes anisotropy. The methods are applied to daily accumulated precipitation data observed at 64 weather stations in North‐Western Germany. The time period from 1931 to 2014 is considered, separately for northern hemispheric winter (November – March) and summer (May – September). The results reveal a clear seasonal differentiation on extremal behavior with the highest precipitation records and generally heavier tails during summer. Spatial inhomogeneities in the frequency of precipitation extremes are related to topography and are particularly significant during winter. During this season, we further observe significant deviations from time‐stationarity at a few stations, related to a period of a high frequency of extremes around 1992. Spatial anisotropy in the extremal dependence structure is stronger during winter than during summer and reveals an increased dependence in the east–west direction.

Kriging is a means of spatial prediction that can be used for soil properties. It is a form of weighted local averaging. It is optimal in the sense that it provides estimates of values at unrecorded places without bias and with minimum and known variance. Isarithmic maps made by kriging are alternatives to conventional soil maps where properties can be measured at close spacings. Kriging depends on first computing an accurate semi‐variogram, which measures the nature of spatial dependence for the property. Estimates of semi‐variance are then used to determine the weights applied to the data when computing the averages, and are presented in the kriging equations. The method is applied to three sets of data from detailed soil surveys in Central Wales and Norfolk. Sodium content at Plas Gogerddan was shown to vary isotropically with a linear semi‐variogram. Ordinary punctual kriging produced a map with intricate isarithms and fairly large estimation variance, attributed to a large nugget effect. Stoniness on the same land varied anisotropically with a linear semi‐variogram, and again the estimation error of punctual kriging was fairly large. At Hole Farm, Norfolk, the thickness of cover loam varied isotropically, but with a spherical semi‐variogram. Its parameters were estimated and used to krige point values and produce a map showing substantial short‐range variation.

This work proposes a new method to treat spatial and spectral information interactively. The method extracts spatial features, ie, variogram, gray-level co-occurrence matrix (GLCM), histograms of oriented gradients (HOG), and local binary pattern (LBP) features, from each wavelength image of hypercube and principal component analysis (PCA) is applied on this spatial feature matrix to identify wavelength-dependent variation in spatial patterns. Resultant image is obtained by projecting the score values to the original data. Three datasets, including a synthetic hyperspectral image (Dataset 1), a set of real hyperspectral images of salmon fillets (Dataset 2), and remote-sensing images (Dataset 3), were utilized to evaluate the performance of the proposed method. Results from Dataset 1 showed that the spatial-spectral methods had the potential of reducing baseline offset noise. Dataset 2 revealed that spatial-spectral methods can alleviate noisy pixels with strong signal and reduce shadow effects. In addition, substantial improvements were obtained in case of classification between white stripe and red muscle pixels by using the HOG-based approach with correct classification rate (CCR) of 0.97 compared with the models directly built from raw and standard normal variate (SNV) preprocessed spectra (CCR = 0.94). Samson image of Dataset 3 suggested the flexibility and effectiveness of the proposed method by improving CCR of 0.96 using conventional PCA on SNV pretreated spectra to 0.98 using GLCM-based approach on SNV preprocessed spectra. Overall, experimental results demonstrated that the spatial-spectral methods can improve the results found by using the spectral information alone because of the spatial information provided. European Commission - Seventh Framework Programme (FP7) University College Dublin

A spatial characterization was undertaken to demonstrate the presence of hexavalent chromium (Cr (VI)) in surface waters (maximum depth of 0.5 m) in the Cienaga de las Quintas mangrove swamp, located in the city of Cartagena de Indias, Colombia. This characterization was geostatistical in nature, an approach that is little used in such studies, although it offers two‐dimensional profiles of the concentration of relevant contaminants (hexavalent chromium in this case) with concentrations between 3 and 9.2 μg/L. Sampling was carried out systematically on a square grid with a cell size of one ha (100 m × 100 m). To corroborate the relationship between the sample positions and concentrations, the Euclidean distance matrices of each variable were calculated previous step for conducting the Mantel test, which indicated a positive correlation between the distance and concentration of hexavalent chromium (R = 0,1674: p value = 0.1275). The Moran Index was also calculated for Cr (VI). The experimental semivariogram (γ)was also calculated and fit to the exponential theoretical model, with a correlation coefficient of 99.4%. Using this analytical model of variance, predictions of Cr (VI) concentrations were made for unsampled locations, using the Kriging method with a new mesh side of only 10 m. This approach indicated the new mesh points exhibiting the higher concentrations coincided with locations in the swamp that receiving sewage effluents from the Bazurto public grocery market and the Chinatown neighbourhood. The Cr (VI) contamination was of anthropogenic origin because its concentration displays a gradient from the zone of human activities to the Cartagena de Indias bay.

Obtaining accurate soil depth information is critical to improving how we assess the health and manage of soil resources that contribute to sustainable management of agricultural lands. While there are many techniques to assess soil characteristics, using ground penetrating radar (GPR) to determine soil depth has received little attention. This study aimed to determine the suitability of GPR for obtaining accurate soil depth information over a 10 km intervals grid system in a generally flat grasslands ecosystem in the Sichuan Province of China. Geographic information system (GIS) and geostatistical techniques were used to map the spatial distribution of soil depth across the field site. Images created from GPR were filtered using DC removal and automatic gain control, and log‐transformation was used to transform the raw data in order to conform a normal distribution. The soil depth data were spatially interpolated across the field site using the geostatistical techniques of (semi‐) variogram and ordinary kriging (OK), then ground‐truthed and validated via comparison with traditional methods and previously collected data. A total of 39 random data points (ruler‐measured and GPR data) were selected to evaluate the accuracy of the GPR, and results showed that the difference were within 3 cm of the actual soil depth in 93% of all samples, and within 5 cm in all samples (R² = 0.914). Results confirmed that this GPR reflection technique has the potential to precisely and quickly measure soil depth over large areas and under variable topography, contributing to the body of technical information that can help inform soil management policy for sustainable agriculture. The spatial distribution map of soil depth produced with the aid of OK demonstrated the accuracy and non‐destructive features of GPR, which is able to provide a more detailed map of soil depth than methods used in previous grassland soil depth studies.

In this paper, we set out general principles and develop geostatistical methods for the analysis of data from spatio-temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify parsimonious geostatistical models for prevalence mapping. A general variogram-based Monte Carlo procedure is proposed to check the validity of the modelling assumptions. We describe and contrast likelihood-based and Bayesian methods of inference, showing how to account for parameter uncertainty under each of the two paradigms. We also describe extensions of the standard model for disease prevalence that can be used when stationarity of the spatio-temporal covariance function is not supported by the data. We discuss how to define predictive targets and argue that exceedance probabilities provide one of the most effective ways to convey uncertainty in prevalence estimates. We describe statistical software for the visualisation of spatio-temporal predictive summaries of prevalence through interactive animations. Finally, we illustrate an application to historical malaria prevalence data from 1 334 surveys conducted in Senegal between 1905 and 2014.

Complex hydrological models are being increasingly used nowadays for many purposes such as studying the impact of climate and land-use change on water resources. However, building a high-fidelity model, particularly at large scales, remains a challenging task, due to complexities in model functioning and behavior and uncertainties in model structure, parameterization, and data. Global Sensitivity Analysis (GSA), which characterizes how the variation in the model response is attributed to variations in its input factors (e.g., parameters, forcing data), provides an opportunity to enhance the development and application of these complex models. In this paper, we advocate using GSA as an integral part of the modelling process by discussing its capabilities as a tool for diagnosing model structure and detecting potential defects, identifying influential factors, characterizing uncertainty, and selecting calibration parameters. Accordingly, we conduct a comprehensive GSA of a complex land surface-hydrology model, Modelisation Environmentale–Surface et Hydrologie (MESH), which combines the Canadian Land Surface Scheme (CLASS) with a hydrological routing component, WATROUTE. Various GSA experiments are carried out using a new technique, called Variogram Analysis of Response Surfaces (VARS), for alternative hydroclimatic conditions in Canada using multiple criteria, various model configurations, and a full set of model parameters. Results from this study reveal that, in addition to different hydroclimatic conditions and SA criteria, model configurations can also have a major impact on the assessment of sensitivity. GSA can identify aspects of the model internal functioning that are counter-intuitive, and thus, help the modeler to diagnose possible model deficiencies and make recommendations for improving development and application of the model. As a specific outcome of this work, a list of the most influential parameters for the MESH model is developed. This list, along with some specific recommendations, is expected to assist the wide community of MESH and CLASS users, to enhance their modelling applications.

The high heterogeneity of petroleum reservoirs, represented by their spatially varying rock properties (porosity and permeability), greatly dictates the quantity of recoverable oil. In this work, the estimation of the spatial permeability distribution, which is crucial for predicting the future performance of a reservoir, is carried out through a history matching technique based on constrained ensemble Kalman filtering (EnKF). The main contribution in this work is the novel implementation of hard and soft constraints in the recursive EnKF estimation methodology for petroleum reservoirs. Hard data is obtained from the actual values of the reservoir parameters at discrete locations obtained by core sampling and well logging, while the soft data considered is obtained from correlograms, which characterize the spatial correlation of the rock properties in a reservoir. In each time update, the parameter estimates obtained from the unconstrained EnKF are modified by one of two novel algorithms. In the first, the correlation matrix obtained after the unconstrained EnKF update is transformed to honour the true correlation structure from the correlogram by applying a projection-based method. The second algorithm involves the use of a technique for soft constrained covariance localization. We observe that the soft data constrained localization method results in the best estimates of the permeability and also reduces the computational time significantly. We quantify the improvement in estimation performance of each of the constrained methods over unconstrained estimation. The method, while developed for estimation in petroleum reservoirs, is also generally applicable to systems with spatial heterogeneity and underlying spatial correlations. This article is protected by copyright. All rights reserved

Hydrologic model development and calibration have continued in most cases to focus only on accurately reproducing streamflows. However, complex models, for example, the so-called physically based models, possess large degrees of freedom that, if not constrained properly, may lead to poor model performance when used for prediction. We argue that constraining a model to represent streamflow, which is an integrated resultant of many factors across the watershed, is necessary but by no means sufficient to develop a high-fidelity model. To address this problem, we develop a framework to utilize the Gravity Recovery and Climate Experiment's (GRACE) total water storage anomaly data as a supplement to streamflows for model calibration, in a multiobjective setting. The VARS method (Variogram Analysis of Response Surfaces) for global sensitivity analysis is used to understand the model behaviour with respect to streamflow and GRACE data, and the BORG multiobjective optimization method is applied for model calibration. Two subbasins of the Saskatchewan River Basin in Western Canada are used as a case study. Results show that the developed framework is superior to the conventional approach of calibration only to streamflows, even when multiple streamflow-based error functions are simultaneously minimized. It is shown that a range of (possibly false) system trajectories in state variable space can lead to similar (acceptable) model responses. This observation has significant implications for land-surface and hydrologic model development and, if not addressed properly, may undermine the credibility of the model in prediction. The framework effectively constrains the model behaviour (by constraining posterior parameter space) and results in more credible representation of hydrology across the watershed.

Kriging is an interpolation method commonly applied in empirical modeling for approximating functional relationships between impact factors and system response. The interpolation is based on a statistical analysis of given data and can optionally include a priori defined trend functions. However, Kriging can so far only be used with trend functions that are linear with respect to the parameters. In this contribution, we present an extension of the Kriging approach for handling trend functions that are nonlinear in their parameters. Our approach is based on Taylor linearization combined with an iterative parameter estimation procedure whose solution is practically computed via a root finding problem. We demonstrate our novel approach with measurement data from the application field of biocatalysis.

In this article, we assume the spatio‐temporal process to be intrinsically stationary in time and stationary in space. Our objective here is to present an alternative way, based on frequency domain methods, for modelling the data. We consider the discrete Fourier transforms (DFTs) defined for the (intrinsic) time‐series data observed at several locations as our data. We use the well‐known property that DFTs are asymptotically uncorrelated and distributed as complex Gaussian in deriving many results. Our objective here is to emphasize the usefulness of the DFTs in the analysis of spatio‐temporal data. Under the assumption of intrinsic stationarity, we consider the estimation of frequency variogram (FV) and discuss its asymptotic sampling properties. We show that FV introduced earlier is a frequency decomposition of space–time variogram. The DFTs can be computed very fast using fast Fourier transform algorithms. Assuming that the DFTs of the incremental process satisfy a Laplacian model, an analytic expression for the space–time spectral density and an expression for the FV in terms of the spectral density function for the intrinsic stationary process are derived. The estimation of the parameters of the spectral density is also considered. A statistical test for spatial independence of spatio‐temporal data is proposed.

The spatial structure of the vertical component of the electric field emitted by base stations in the Brussels region (Belgium) is measured, and studied using the variogram. A relationship between the variogram shape and base station antenna density in each measurement area is found; the variogram range and sill level are shown to depend on cellular base stations’ antenna density, following exponential laws. Bioelectromagnetics. © 2016 Wiley Periodicals, Inc.

We discuss a numerical algorithm for calculating a large class of analytically intractable theoretical variogram functions that arise in studies of random fields on regular lattices. Examples of these random fields include conditional and intrinsic autoregressions, fractional Laplacian differenced random fields, and regular block averages of continuum random fields. Typically, the variogram functions for these random fields appear in the form of multi-dimensional integrals, often with singularities at the origin, and the algorithm laid out to evaluate these integrals invoke certain quadrature rules and regression formulas based on the asymptotic expansions of these integrals. This is so that singularities at the origin can be accounted for in a straightforward manner. This numerical algorithm opens new avenues to advancing geostatistical data analysis, solving kriging and estimation problems and exploring properties for various lattice-based random fields. The usefulness of this numerical method is illustrated by fitting certain theoretical variogram functions to ocean color and the Walker Lake data. Copyright © 2016 John Wiley & Sons, Ltd.

Low-cost approaches for measuring soil organic C (SOC) stocks are essential for verifying farm management effects on C sequestration in agroecosystems. This study compared sampling and data analysis optimization approaches for estimating SOC stocks of a complex agroecosystem. Soil samples were collected from a 232-ha area of a working dairy farm with multiple land uses, crop rotations, topographic features, and manure application rates. The SOC stocks were estimated by (i) simple mean, (ii) ordinary kriging, (iii) regression kriging, and (iv) using the USDA Soil Survey Geographic (SSURGO) database. Relationships among sampling schemes, estimation approaches, auxiliary information, and SOC stocks were explored. Slope, elevation, soil type, and land use types displayed a high degree of variation at the study site, yet relationships with SOC stocks were weak or nonsignificant. Systematic sampling provided the best coverage of both geographic and attribute space, allowing reliable variogram estimates and RMSEs that increased little with reduced sample number. Random and stratified random sampling approaches resulted in reduced accuracy. Ordinary kriging had lower RMSEs than either regression kriging or the simple mean, and total SOC stocks estimates fluctuated less when sample sizes were reduced. Using SSURGO overestimated total SOC stocks by up to 5.1% compared with the other approaches, suggesting that this approach may be worthy of evaluation for circumstances with a low budget and low confidence level requirements. Systematic sampling and ordinary kriging can provide an optimal strategy for estimating SOC stocks in agroecosystems with complex topography and land uses.

Non-stochastic simulation models, such as finite element or computational fluid dynamics, often support real experiments in industrial research. It has become a common practice to provide a meta-model as computer experiments can be highly complex and time-consuming, and the design space is often broad. The meta-model is an approximation of the computer experiments response adapted both globally and locally on the design space, in order to capture local minima/maxima. The Kriging model, first proposed in Geostatistics, is doubtlessly the most popular meta-model because of its recognized ability to provide high- quality predictions. The underlying correlation structure can be evaluated either by estimating the parameters of correlation or by means of a variogram. In this paper, the performance of the Kriging model is compared with an Artificial Neural Network meta-model in order to determine which model guarantees higher accuracy in predicting the result of four-dimensional com- putational fluid dynamics experiments for low pressure turbines where energy loss values are provided

Soil surface roughness not only delays overland flow generation but also strongly affects the spatial distribution and concentration of overland flow. Previous studies generally aimed at predicting the delay in overland flow generation by means of a single parameter characterizing soil roughness. However, little work has been done to find a link between soil roughness and overland flow dynamics. This is made difficult because soil roughness and hence overland flow characteristics evolve differently depending on whether diffuse or concentrated erosion dominates. The present study examined whether the concept of connectivity can be used to link roughness characteristics to overland flow dynamics. For this purpose, soil roughness of three 30-m2 tilled plots exposed to natural rainfall was monitored for two years. Soil micro-topography was characterized by means of photogrammetry on a monthly basis. Soil roughness was characterized by the variogram, the surface stream network was characterized by network-based indices and overland flow connectivity was characterized by Relative Surface Connection function (RSCf) functional connectivity indicator. Overland flow hydrographs were generated by means of a physically-based overland flow model based on 1-cm resolution digital elevation models. The development of eroded flow paths at the soil surface not only reduced the delay in overland flow generation but also resulted in a higher continuity of high flow velocity paths, an increase in erosive energy and a higher rate of increase of the overland flow hydrograph. Overland flow dynamics were found to be highly correlated to the RSCf characteristic points. By providing information regarding overland flow dynamics, the RSCf may thus serve as a quantitative link between soil roughness and overland flow generation in order to improve the overland flow hydrograph prediction.

For obtaining maps of good precision by the spatial inference method, the distribution of sampling sites in geographical and feature space is very important. For a regional variable with trends, the predicting error comes from trend estimation, variogram estimation and spatial interpolation. Based on the cLHS (conditioned Latin hypercube Sampling) method, a sampling method called scLHS (spatial cLHS) considering all these three aspects with the help of ancillary data is proposed in this article. Its advantage lies in simultaneously improving trend estimation, variogram estimation and spatial interpolation. MODIS data and simulated data were used as sampling fields to draw sample sets using scLHS, cLHS, cLHS with x and y coordinates as covariates, simple random and spatial even sampling methods, and the distribution and prediction errors of sample sets from different methods were evaluated. The results showed that scLHS performed well in balancing spreading in geographic and feature space, and can generate points pairs with small distances, and the sample sets drawn by scLHS produced smaller mapping error, especially when there were trends in the target variable.

Visualizing and quantifying spatial patterns of co-occurrence (i.e., of two or more species, or of species and underlying environmental variables) can suggest hypotheses about processes that structure species assemblages and their relevant spatial scales. Statistical models of spatial co-occurrence generally assume that underlying spatial processes are isotropic and stationary, but many ecologically realistic spatial processes are anisotropic and non-stationary. Here, we introduce codispersion analysis to ecologists and use it to detect and quantify anisotropic and nonstationary patterns and their relevant spatial scales in bivariate co-occurrence data. Simulated data illustrated that codispersion analysis can accurately characterize complex spatial patterns. Analysis of co-occurrence of common tree species growing in a 35-ha plot revealed both positive and negative codispersion between different species; positive codispersion values reflected positive correlation in species abundance (aggregation), whereas negative codispersion values reflected negative correlation in species abundance (segregation). Comparisons of observed patterns with those simulated using two different null models showed that the codispersion of most species pairs differed significantly from random expectation. We conclude that codispersion analysis can be a useful exploratory tool to guide ecologists interested in modeling spatial processes.

This study is proposing a classification for the Holdridge's life zones associated with the surface climatic variables over Turkey. Holdridge's scheme is aiming to group meteorological and climatic quantities at the regional scale according to some pre-defined rules. On the other hand, without rules or pre-defined restrictions, the process of combination of similar stations in groups is recognized as clustering. A spectral clustering method was suggested for identifying the characteristics of the local climate over the country. To increase the proxy value of the estimated life zones, the missing values in the data sets of temperature and precipitation series were filled by fitting appropriate theoretical variogram. A programme coded in Fortran 95 was developed for determining the life zones. The probabilistic features of the life zones were estimated by using empirical cumulative frequencies. In addition, a new spectral clustering method based on Sampson correlation ratio was developed for clustering high-dimensional data. From these results, four major categorical life zones were obtained, namely montane, lower montane, cool temperate and warm temperate. Additionally, 14 types of the Holdridge's vegetation classes were estimated, the frequent zones are cool temperate steppe and warm temperate dry forest; some moist forests are seen particularly in the eastern Black Sea region, the rainiest region of the country. The suggested spectral clustering method is capable of capturing the principal life zones. The tendency of life zones shifting towards the climate conditions of lower latitudes indicates that the long-term meteorological normals changed; this is exactly the point of climate change. A better understanding of life zones of Holdridge hopefully can contribute to sustainability plans of the policy makers.

A novel clustering method for bivariate functional data is proposed to group streams based on their water–air temperature relationship. A distance measure is developed for bivariate curves by using a time-varying coefficient model and a weighting scheme. This distance is also adjusted by spatial correlation of streams via the variogram. Therefore, the proposed distance not only measures the difference among the streams with respect to their water–air temperature relationship but also accounts for spatial correlation among the streams. The proposed clustering method is applied to 62 streams in Southeast US that have paired air–water temperature measured over a ten-month period. The results show that streams in the same cluster reflect common characteristics such as solar radiation, percent forest and elevation. Copyright © 2015 John Wiley & Sons, Ltd.

Soil health deterioration due to intensive agricultural activity is a worldwide problem. To better understand this process, there is a prime need to map soil health over wide areas. This paper aims to quantify soil health in a spatially explicit manner over a large area using soil health indicators. The methodology includes sampling design, autocorrelation analysis and Kriging interpolation. The following variables were measured from vertisol clayey soils: aggregate stability (AS); available water capacity (AWC); surface and subsurface penetration resistance (PR15 and PR45 respectively); root health (RH); organic matter (OM); pH; electrical conductivity (EC); cation-exchange capacity (CEC); exchangeable K; nitrification potential (Np); and P. Stratified random sampling was found to be a more efficient method than random sampling for representing a large area with a limited number of sampling locations. The variogram envelope method was found to be more conservative in determining the significance of autocorrelation than the classical Moran’s I approach. Phosphorus, CEC, PR15, EC, and K exhibited strong autocorrelation in space; other variables showed no autocorrelation. Land management factors were found to control the spatial variability of most soil variables. Kriging with an external drift (KED) was found to be the most useful approach for spatial prediction of soil health. A positive correlation was found between the interpolated soil health index and NDVI (Normalized Difference Vegetation Index). These results suggest that soil health maps can be used to explore how cultivation activities limit crop yields at the catchment scale, and to determine whether these activities create distinctive soil characteristics.

Quantification of the character and spatial distribution of porosity in carbonate aquifers is important as input into computer models used in the calculation of intrinsic permeability and for next-generation, high-resolution groundwater flow simulations. Digital, optical, borehole-wall image data from three closely spaced boreholes in the karst-carbonate Biscayne aquifer in southeastern Florida are used in geostatistical experiments to assess the capabilities of various methods to create realistic two-dimensional models of vuggy megaporosity and matrix-porosity distribution in the limestone that composes the aquifer. When the borehole image data alone were used as the model training image, multiple-point geostatistics failed to detect the known spatial autocorrelation of vuggy megaporosity and matrix porosity among the three boreholes, which were only 10 m apart. Variogram analysis and subsequent Gaussian simulation produced results that showed a realistic conceptualization of horizontal continuity of strata dominated by vuggy megaporosity and matrix porosity among the three boreholes.

Networks of rain-gauges provide an accurate but highly localized measure of rainfall, with limited coverage and resolution, whereas radars provide rain-rate and accumulation estimates over wide areas at high spatial and temporal resolution but low accuracy. When quantifying rainfall accumulations for applications such as flood forecasting, combining the two sets of data can be beneficial for producing a high-resolution merged product with a lower error than the gauge-only or the radar-only product. In this study, three kriging methods (kriging with external drift (KED), kriging with radar-based error correction (KRE) and ordinary kriging (OK)) as well as a multiquadric (MQ) scheme have been used to merge radar and gauge data. The results were cross-validated with true rainfall readings at the surface for a number of different meteorological events covering England and Wales. Overall, all the merging schemes trialled produced a merged product that was superior to the individual radar or gauge data. The KED was the best performing method across all rainfall thresholds and meteorological conditions, with the use of a parametric variogram best suited to short (15 min) accumulation periods and a non-parametric variogram preferable for hourly accumulations. The study also shows that the merged product deteriorates when the gauge-network density is reduced; exceptions to this are made in situations where spatially isolated rainfall is observed by the radar and where the gauges that are found least likely to represent the rainfall are carefully removed prior to merging. The latter process was found to improve the quality of the merged product, regardless of the meteorological conditions, providing a viable method for producing a KED-based merging scheme that is applicable to all meteorological conditions.

Summary Soil scientists often use prediction models to obtain values at unsampled locations. The spatial variation in the soil is best captured by using the empirical best linear unbiased predictor (EBLUP) based on a restricted maximum likelihood (REML) approach that efficiently exploits available data on both mean trends and correlation structures. We proposed a practical two-step implementation of the REML approach for model-based kriging, exemplified by predicting soil organic carbon (SOC) concentrations in mineral soils in Estonia from the large-scale digital soil map information and a previously established prediction model. The prediction model was a linear mixed model with soil type, physical clay content (particle size

Fishery-dependent catch per unit effort (CPUE) comprises critical input for many stock assessments. Construction of CPUE indices usually employs some method of data standardization. However, conventional methods based on linear models do not effectively deal with the fact that samples are collected with a selection bias or with the problem of filling spatial gaps. Geostatistical interpolation methods can ameliorate some of the biases caused by both of these problems while remaining complementary to traditional linear model-based CPUE standardization. In this paper we present geostatistical estimates of sea scallop Placopecten magellanicus CPUE from tows recorded by onboard observers during an opening of Georges Bank Closed Area II in 1999. By selecting tows for which there was little prior effort (on the basis of accumulated effort measured by vessel monitoring systems), we obtained tows that reflected initial abundance as closely as possible. These tows were used to obtain a variogram which was u...

Summary There is growing recognition that linking patterns to their underlying processes in interconnected and dynamic ecological systems requires data sampled at multiple spatial and temporal scales. However, spatially explicit and temporally resolved data sets can be difficult to analyze using classical statistical methods because the data are typically autocorrelated and thus violate the assumption of independence. Here, we describe the synchrony package for the R programming environment, which provides modern parametric and nonparametric methods for (i) quantifying temporal and spatial patterns of auto- and cross-correlated variability in univariate, bivariate, and multivariate data sets, and (ii) assessing their statistical significance via Monte Carlo randomizations. We illustrate how the methods included in the package can be used to investigate the causes of spatial and temporal variability in ecological systems through a series of examples, and discuss the assumptions and caveats of each statistical procedure in order to provide a practical guide for their application in the real world.

16 pages; International audience; This paper concerns the second order marginals of biphased random media. We give discriminating necessary conditions for a bivariate function to be such a valid marginal, and illustrate our study with two practical applications: (1) the spherical variograms are valid indicator variograms if and only if they are multiplied by a sufficiently small constant, which upper bound is estimated, and (2) not every covariance/indicator variogram can be obtained with a Gaussian level set. The theoretical results backing this study are contained in a companion paper.

A frequency domain methodology is proposed for estimating parameters of covariance functions of stationary spatio-temporal processes. Finite Fourier transforms of the processes are defined at each location. Based on the joint distribution of these complex valued random variables, an approximate likelihood function is constructed. The sampling properties of the estimators are investigated. It is observed that the expectation of these transforms can be considered to be a frequency domain analogue of the classical variogram. We call this measure frequency variogram. The method is applied to simulated data and also to Pacific wind speed data considered earlier by Cressie and Huang (1999). The proposed method does not depend on the distributional assumptions about the process.

Measurement surveys using passive diffusion tubes are regularly car-ried out to elaborate atmospheric concentration maps over various areas. Sampling schemes must be designed to characterize both contaminant concentrations (of benzene or nitrogen dioxide for example) and their re-lations to environmental variables so as to obtain pollution maps as precise as possible. Here, a spatial statistical methodology to design benzene air concentration measurement surveys on the urban scale is exposed. In a first step, an a priori modeling is conducted that is based on the analysis of data coming from previous campaigns on two different agglomerations. More precisely, we retain a modeling with an external drift which consists of a drift plus a spatially correlated residual. The statistical analysis per-formed on available data leads to choose the most relevant auxiliary vari-ables and to determine an a priori variogram model for the residual. An a priori distribution is also defined for the variogram parameters, whose values appear to vary from a campaign to another. In a second step, we optimize the positioning of the measuring devices on a third agglomera-tion according to a Bayesian criterion. Practically, we aim at finding the design that minimizes the mean over the urban domain of the universal kriging variance, whose parameters are based on the a priori modeling, while accounting for the prior distribution over the variogram parameters. Two global optimization algorithms are compared: simulated annealing and a particle filter based algorithm.

We integrate systems of measurement and modeling to improve estimation of uncertainties in above-ground biomass AGB derived from remote sensing. The outcome provides a unified starting point for the climate-change carbon community to assess uncertainty and sensitivity data and methodologies, and ultimately supports decision-making about which missions and instruments to develop for a desired cost/benefit ratio. Initial results include fusion of remote-sensing techniques e.g., radar and lidar, uncertainties associated with measurement and modeling, and the impact of potential uncertainty correlations across aggregated unit areas. Biomass uncertainty estimates are presented at the single-hectare level for the forestlands of California. Using a forest biomass map of California, we calculate changes in variance e.g., 2 orders of magnitude as a function of uncertainty correlation assumptions, with correlations extending to spatial scales up to 100 km. Using a variogram formalism to derive the correlation shape and magnitude, we show that the estimated variance for California above-ground biomass is between 1% and 2% 1 standard deviation for our current best estimate of the correlation range at 5-10 km-i.e., we bound the standard deviation by a factor of 2. This contrasts with 0.025% 1 standard deviation if one does not include the correlation term.

Validation of ground-based microwave remote sensing measurements with point measurements of soil moisture remains an important task. The number of point measurements needed to characterize the mean soil moisture of an area on the order of tens of square meters, and the manner in which these observations should be made remain unknown. We conducted a field experiment in central Iowa to characterize the spatial process of soil moisture and sampling strategies for estimating the mean soil moisture of an area that represents the footprint of a ground-based microwave radiometer. We determined the spatial dependence of the moisture content of bare soil at this scale, which allows the determination of the mean soil moisture from point measurements. This spatial dependence can be described by an exponential variogram model. The parameters of this model vary according to mean moisture conditions. The accuracy of the estimate of mean soil moisture depends on the number of point measurements, what sampling technique is used, and mean moisture conditions. When we use spatial dependence, we increase the accuracy and precision of our estimates of the mean. Lattice and stratified sampling schemes require fewer measurements than random sampling when a higher level of accuracy in the estimate of mean soil moisture is desired. Practically, if measurements of soil moisture are made in random locations and spatial dependence is not used, we found that approximately 20 measurements within a 7 by 9 m footprint would estimate the mean to within close to 0.01 m 3 m −3 of the true value for the entire range of soil moisture conditions that we observed.

Summary The commonly used variogram function is incapable of modelling complex spatial patterns associated with repetitive, connected or curvilinear features, because it is a two-point statistic. Because this was strongly limiting to petroleum- and hydrogeologists, they developed multiple-point geostatistics (MPG), an approach that replaces the variogram by a training image (TI). However, soil scientists also face complex spatial patterns and MPG might be of use to them as well. Therefore, this paper aims to introduce MPG to soil science and demonstrate its potential with a case study of polygonal subsoil patterns caused by Weichselian periglacial frost cracks in Belgium. A high-resolution proximal soil sensing survey provided a reference image from which a continuous (655 sensor data) and a categorical (100 point observations) dataset were extracted. As a continuous TI, we used the geophysical data of another part of the field, and as categorical TI we used a classified photograph of an ice-wedge network in Alaska. The resulting MPG maps reconstructed the polygonal patterns very well and corresponded closely to the reference image. Consequently, we identify MPG as a promising technique to map complex soil patterns and suggest that it should be added to the pedometrician's toolbox.