Non-sampled Locations Research Articles

Mapping of Soil Micronutrients in Kashmir Agricultural Landscape Using Ordinary Kriging and Indicator Approach

Soil nutrient maps based on intensive soil sampling are useful to adopt site-specific management practices. Geostatistical methods have been widely used to determine the spatial correlation and the range of spatial dependence at different sampling scales. If spatial dependence is detected, the modeled semivariograms can then be used to map the interested variable by kriging, an interpolation method that produces unbiased estimates with minimal estimation variance. The objectives of this paper were to examine and map the spatial distribution of the soil micronutrients Cu, Zn, Fe and Mn on an agricultural area in Kupwara, J&K, under temperate climatic conditions. The ordinary kriging was first used to determine the values for the non-sampled locations, and then the indicator approach was used to transform the micronutrient content values into binary values having the mean values of each nutrient as the threshold content. All four elements analyzed showed spatial dependence using the indicator semivariograms. The strength of spatial dependence was assessed using the values of nugget effect and range from the semivariogram, the fitted range values decreased in the order Zn > Cu > Mn > Fe. The spatial dependence of the combination of two or more of the studied micronutrients was also examined using indicator semivariograms. In opposition to spatial analysis of individual microelements, indicator semivariograms obtained for the binary coding of the variables showed a great nugget effect value or a low proportion of sill. The maps for each nutrient obtained using indicator kriging showed some similarity in the spatial distribution, suggesting the delimitation of uniform management areas.

Mapping malaria risk among children in Côte d'Ivoire using Bayesian geo-statistical models.

BackgroundIn Côte d’Ivoire, an estimated 767,000 disability-adjusted life years are due to malaria, placing the country at position number 14 with regard to the global burden of malaria. Risk maps are important to guide control interventions, and hence, the aim of this study was to predict the geographical distribution of malaria infection risk in children aged <16 years in Côte d’Ivoire at high spatial resolution.MethodsUsing different data sources, a systematic review was carried out to compile and geo-reference survey data on Plasmodium spp. infection prevalence in Côte d’Ivoire, focusing on children aged <16 years. The period from 1988 to 2007 was covered. A suite of Bayesian geo-statistical logistic regression models was fitted to analyse malaria risk. Non-spatial models with and without exchangeable random effect parameters were compared to stationary and non-stationary spatial models. Non-stationarity was modelled assuming that the underlying spatial process is a mixture of separate stationary processes in each ecological zone. The best fitting model based on the deviance information criterion was used to predict Plasmodium spp. infection risk for entire Côte d’Ivoire, including uncertainty.ResultsOverall, 235 data points at 170 unique survey locations with malaria prevalence data for individuals aged <16 years were extracted. Most data points (n = 182, 77.4%) were collected between 2000 and 2007. A Bayesian non-stationary regression model showed the best fit with annualized rainfall and maximum land surface temperature identified as significant environmental covariates. This model was used to predict malaria infection risk at non-sampled locations. High-risk areas were mainly found in the north-central and western area, while relatively low-risk areas were located in the north at the country border, in the north-east, in the south-east around Abidjan, and in the central-west between two high prevalence areas.ConclusionThe malaria risk map at high spatial resolution gives an important overview of the geographical distribution of the disease in Côte d’Ivoire. It is a useful tool for the national malaria control programme and can be utilized for spatial targeting of control interventions and rational resource allocation.

A fuzzy interval analysis approach to kriging with ill-known variogram and data

Geostatistics is a branch of statistics dealing with spatial phenomena. Kriging consists in estimating or predicting a spatial phenomenon at non-sampled locations from an estimated random function. It is assumed that, under some well-chosen simplifying hypotheses of stationarity, the probabilistic model, i.e. the random function describing spatial variability dependencies, can be completely assessed from the dataset. However, in the usual kriging approach, the choice of the random function is mostly made at a glance by the experts (i.e. geostatisticians), via the selection of a variogram from a thorough descriptive analysis of the dataset. Although information necessary to properly select a unique random function model seems to be partially lacking, geostatistics, in general, and the kriging methodology, in particular, does not account for the incompleteness of the information that seems to pervade the procedure. The paper proposes an approach to handle epistemic uncertainty appearing in the kriging methodology. On the one hand, the collected data may be tainted with errors that can be modelled by intervals or fuzzy intervals. On the other hand, the choice of parameter values for the theoretical variogram, an essential step, contains some degrees of freedom that are seldom acknowledged. In this paper, we propose to account for epistemic uncertainty pervading the variogram parameters, and possibly the dataset, and lay bare its impact on the kriging results, improving on previous attempts by Bardossy and colleagues in the late 1980s.

Using landscape characteristics to define an adjusted distance metric for improving kriging interpolations

Interpolation of point measurements using geostatistical techniques such as kriging can be used to estimate values at non-sampled locations in space. Traditional geostatistics are based on the spatial autocorrelation concept that nearby things are more related than distant things. In this study, additional information was used to modify the traditional Euclidean concept of distance into an adjusted distance metric that incorporates similarity in terms of quantifiable landscape characteristics such as topography or land use. This new approach was tested by interpolating soil moisture content, pH and carbon-to-nitrogen (C:N) ratio measured in both the mineral and the organic soil layers at a field site in central Sweden. Semivariograms were created using both the traditional distance metrics and the proposed adjusted distance metrics to carry out ordinary kriging (OK) interpolations between sampling points. In addition, kriging with external drift (KED) was used to interpolate soil properties to evaluate the ability of the adjusted distance metric to incorporate secondary data into interpolations. The new adjusted distance metric typically lowered the nugget associated with the semivariogram, thereby better representing small-scale variability in the measured data compared to semivariograms based on the traditional distance metric. The pattern of the resulting kriging interpolations using KED and OK based on the adjusted distance metric were similar because they represented secondary data and, thus, enhanced small-scale variability compared to traditional distance OK. This created interpolations that agreed better with what is expected for the real-world spatial variation of the measured properties. Based on cross-validation error, OK interpolations using the adjusted distance metric better fit observed data than either OK interpolations using traditional distance or KED.

Mapping of soil micronutrients in an european atlantic agricultural landscape using ordinary kriging and indicator approach

Nutrient maps based on intensive soil sampling are useful to develop site-specific management practices. Geostatistical methods have been widely used to determine the spatial correlation and the range of spatial dependence at different sampling scales. If spatial dependence is detected, the modelled semivariograms can then be used to map the interested variable by kriging, an interpolation method that produces unbiased estimates with minimal estimation variance. The objectives of this paper were to examine and to map the spatial distribution of the micronutrients Cu, Zn, Fe and Mn on an agricultural area in Galicia, Spain, under European Atlantic climatic conditions. The ordinary kriging was first used to determine the values for the non-sampled locations, then the indicator approach was used to transform the micronutrient content values into binary values having the mean values of each nutrient as the threshold content. All four elements analyzed showed spatial dependence using the indicator semivariograms. The strength of spatial dependence was assessed using the values of nugget effect and range from the semivariogram, the fitted range values decreased in the order Mn &gt;Fe &gt;Zn &gt;Cu. The spatial dependence of the combination of two or more of the studied micronutrients was also examined using indicator semivariograms. In opposition to spatial analysis of individual microelements, indicator semivariograms obtained for the binary coding of the variables showed a great nugget effect value or a low proportion of sill. The maps for each nutrient obtained using indicator kriging showed some similarity in the spatial distribution, suggesting the delimitation of uniform management areas.

Spatial risk profiling of Plasmodium falciparum parasitaemia in a high endemicity area in Côte d'Ivoire

BackgroundThe objective of this study was to identify demographic, environmental and socioeconomic risk factors and spatial patterns of Plasmodium falciparum parasitaemia in a high endemicity area of Africa, and to specify how this information can facilitate improved malaria control at the district level.MethodsA questionnaire was administered to about 4,000 schoolchildren in 55 schools in western Côte d'Ivoire to determine children's socioeconomic status and their habit of sleeping under bed nets. Environmental data were obtained from satellite images, digitized ground maps and a second questionnaire addressed to school directors. Finger prick blood samples were collected and P. falciparum parasitaemia determined under a microscope using standardized, quality-controlled methods. Bayesian variogram models were utilized for spatial risk modelling and mapping of P. falciparum parasitaemia at non-sampled locations, assuming stationary and non-stationary underlying spatial dependence.ResultsTwo-thirds of the schoolchildren were infected with P. falciparum and the mean parasitaemia among infected children was 959 parasites/μl of blood. Age, socioeconomic status, not sleeping under a bed net, coverage rate with bed nets and environmental factors (e.g., normalized difference vegetation index, rainfall, land surface temperature and living in close proximity to standing water) were significantly associated with the risk of P. falciparum parasitaemia. After accounting for spatial correlation, age, bed net coverage, rainfall during the main malaria transmission season and distance to rivers remained significant covariates.ConclusionIt is argued that a massive increase in bed net coverage, particularly in villages in close proximity to rivers, in concert with other control measures, is necessary to bring malaria endemicity down to intermediate or low levels.

Invasive snails and an emerging infectious disease: results from the first national survey on Angiostrongylus cantonensis in China.

BackgroundEosinophilic meningitis (angiostrongyliasis) caused by Angiostrongylus cantonensis is emerging in mainland China. However, the distribution of A. cantonensis and its intermediate host snails, and the role of two invasive snail species in the emergence of angiostrongyliasis, are not well understood.Methodology/Principal FindingsA national survey pertaining to A. cantonensis was carried out using a grid sampling approach (spatial resolution: 40×40 km). One village per grid cell was randomly selected from a 5% random sample of grid cells located in areas where the presence of the intermediate host snail Pomacea canaliculata had been predicted based on a degree-day model. Potential intermediate hosts of A. cantonensis were collected in the field, restaurants, markets and snail farms, and examined for infection. The infection prevalence among intermediate host snails was estimated, and the prevalence of A. cantonensis within P. canaliculata was displayed on a map, and predicted for non-sampled locations. It was confirmed that P. canaliculata and Achatina fulica were the predominant intermediate hosts of A. cantonensis in China, and these snails were found to be well established in 11 and six provinces, respectively. Infected snails of either species were found in seven provinces, closely matching the endemic area of A. cantonensis. Infected snails were also found in markets and restaurants. Two clusters of A. cantonensis–infected P. canaliculata were predicted in Fujian and Guangxi provinces.Conclusions/SignificanceThe first national survey in China revealed a wide distribution of A. cantonensis and two invasive snail species, indicating that a considerable number of people are at risk of angiostrongyliasis. Health education, rigorous food inspection and surveillance are all needed to prevent recurrent angiostrongyliasis outbreaks.

A Forensic Look at Groundwater Arsenic Contamination in Bangladesh

A comprehensive forensic analysis of AS contamination in Bangladesh was undertaken using geographic information system (GIS), univariate, and bivariate statistics. The assessment provided the background needed for fine-tuning emerging/evolving methods of spatial mapping based on nonlinear deterministic dynamics and multivariate factorial analyses. Data were derived from a nationwide AS survey completed in 1999 by the British Geological Survey (BGS) in collaboration with the Department of Public Health Engineering (DPHE) of Bangladesh. It was found that the standard deviation of arsenic concentration is highest along the river flood plains of the major rivers. The distribution of arsenic concentration was found to be symmetric in regions of very high mean concentration, while the regions of low and moderate contamination reveal a highly skewed distribution, suggesting the need for data transformation at these points prior to spatial interpolation. The mean value of Ca and Mg concentrations showed a strong spatial similarity in the southwest region of Bangladesh. This spatial similarity was also reflected in terms of skewness of the data. It was inferred that the mapping of AS concentrations at nonsampled locations on the basis of multivariate factorial or regression models may not require the dual presence of both Ca and Mg parameters; hence, one of them is redundant. Both the skewness and kurtosis of the distribution of Si concentration appeared very similar and highly heterogeneous in space, suggesting that Si data require careful transformation prior to modeling only in the smaller scale but not for country-wide/regional purposes. The age of wells was found to be nonlinearly correlated in the southeast region. The correlation of AS with Fe appeared strongest in the southwest region, indicating that the oxidation–reduction hypothesis may be more appropriate as a release mechanism in the southwest region. In another regard, the sulphate concentration was found to be more correlated to AS in the northwest Pleistocene region of Bangladesh, suggesting that the pyrite oxidation hypothesis may be appropriate. Overall, our forensic analysis using GIS revealed useful findings for data transformation and selection of parameters towards spatial mapping based on multivariate factorial and nonlinear deterministic models in the resource-poor settings of developing countries.

Unbiased Resource Evaluations with Kriging and Stochastic Models of Heterogeneous Rock Properties

This paper revisits the computation of product combinations for quantification of resources (e.g., pore volume for hydrocarbon reservoir formations). The explanations have been simplified by considering the exhaustive numerical model for properties that are multiplied first and then added or averaged for evaluation. The analysis starts without any probabilistic considerations. Abbreviated (up-scaled) computations in the sum of multiplications are proposed by substituting the individual values by averages for each rock property in the coarser cell resolution model. A result found is that averaged properties can be utilized for estimation at non-sampled locations, instead of individual values; however, covariances and cumulants must also be included in the abbreviated computations. The smoothing effect of kriging is found to be irrelevant if the kriging variance is also included in the up-scaled abbreviated pore volume computations. Thus, the equivalence between computation of resource volumes from kriging estimates and conditional stochastic simulations is established, with the condition that numerical estimation must incorporate the complete covariance and cumulant information as well. An example shows pore volume prediction from a kriging model matches the unbiased result from stochastic simulations.

Geostatistical and multi‐elemental analysis of soils to interpret land‐use history in the Hebrides, Scotland

Abstract In the absence of documentary evidence about settlement form and agricultural practice in northwest Scotland before the mid‐18th century, a geoarchaeological approach to reconstructing medieval land use and settlement form is presented here. This study applies multielemental analysis to soils previously collected from a settlement site in the Hebrides and highlights the importance of a detailed knowledge of the local soil environment and the cultural context. Geostatistical methods were used to analyze the spatial variability and distribution of a range of soil properties typically associated with geoarchaeological investigations. Semivariograms were produced to determine the spatial dependence of soil properties, and ordinary kriging was undertaken to produce prediction maps of the spatial distribution of these soil properties and enable interpolation over nonsampled locations in an attempt to more fully elucidate former land‐use activity and settlement patterns. The importance of identifying the spatial covariance of elements and the need for several lines of physical and chemical evidence is highlighted. For many townships in the Hebrides, whose precise location and layout prior to extensive land reorganization in the late 18th–early 19th century is not recoverable through plans, multi‐elemental analysis of soils can offer a valuable prospective and diagnostic tool. © 2007 Wiley Periodicals, Inc.

Multi-lag cluster designs for estimating the semivariogram for sediments affected by effluent discharges offshore in San Diego

Maps are useful tools for understanding, managing, and protecting the marine environment, yet few useful and statistically defensible maps of environmental quality and aquatic resources have been developed in near-coastal regions. Current environmental management efforts, such as ocean monitoring by sewage dischargers, routinely sample areas of potential impact using sparse sampling grids. Heterogeneous oceanic conditions often make extrapolation from these grids to non-sampled locations questionable. Although rarely applied in coastal monitoring, kriging offers a more rigorous statistical approach to mapping and allows confidence intervals to be calculated for predictions. Its usefulness relies on accurate models of the spatial variability through estimating the semivariogram. Many optimal designs for estimating the semivariogram have been proposed, but these designs are often difficult to implement in practice. In this paper, we present simple design strategies for augmenting existing monitoring designs with the goal of estimating the semivariogram. In particular, we investigate a multi-lag cluster design strategy, where clusters of sites, spaced at various lag distances, are placed around fixed stations on an existing sampling grid. We find that these multi-lag cluster designs provide improved accuracy in estimating the parameters of the semivariogram. Based on simulation study findings, we apply a multi-lag cluster enhancement to the monitoring grid for the City of San Diego’s Point Loma Wastewater Treatment Plant as part of a special study to map chemical contaminants in sediments around its sewage outfall.

Geostatistically based management of arsenic contaminated ground water in shallow wells of Bangladesh

This paper investigates the effectiveness of geostatistical approaches, specifically ordinary kriging, for regional management of arsenic contaminated shallow ground water in Bangladesh. The arsenic database for reference comprised the nation-wide survey (of 3534 drinking wells) completed in 1999 by the British Geological Survey (BGS) in collaboration with the Department of Public Health Engineering (DPHE) of Bangladesh. A Monte Carlo (MC) framework was devised for selection of randomly-sampled networks of wells from this reference database. Each randomly sampled network was assumed an equi-probable exploratory field campaign designed commensurably with the requirements of rapidity and cost-effectiveness in a rural setting. In general, the kriging method was found to underestimate the arsenic concentration at non-sampled locations. This underestimation exceeded the safe limits at the Holocene region of Southcentral Bangladesh. The probability of successful prediction of safe wells for this region was found to be 72% (WHO safe limit – 10 ppb) and 78% (Bangladesh safe limit – 50 ppb). For the Pleistocene Northwestern region of Bangladesh, the safe well prediction probability was in the ranges of 90%–97%. The relatively more contaminated Holocene region in Southcentral Bangladesh, on other hand, was found more amenable to accurate geostatistical prediction of unsafe wells. Findings from this study exemplify that, while mainstream geostatistical approaches (e.g., ordinary kriging) may not provide the most accurate prediction of mean arsenic concentration at non-sampled locations, they can delineate an approximate strategy for management of arsenic contaminated shallow ground water if applied carefully. The kriging methodology is applied to a test case in Bangladesh; the approach, however, is general and is expected to have application in rural settings for other developing countries where arsenic contamination of ground water is also widespread (e.g., parts of India, Vietnam, Taiwan and Mexico).

Bayesian spatial analysis and disease mapping: tools to enhance planning and implementation of a schistosomiasis control programme in Tanzania

To predict the spatial distributions of Schistosoma haematobium and S. mansoni infections to assist planning the implementation of mass distribution of praziquantel as part of an on-going national control programme in Tanzania. Bayesian geostatistical models were developed using parasitological data from 143 schools. In the S. haematobium models, although land surface temperature and rainfall were significant predictors of prevalence, they became non-significant when spatial correlation was taken into account. In the S. mansoni models, distance to water bodies and annual minimum temperature were significant predictors, even when adjusting for spatial correlation. Spatial correlation occurred over greater distances for S. haematobium than for S. mansoni. Uncertainties in predictions were examined to identify areas requiring further data collection before programme implementation. Bayesian geostatistical analysis is a powerful and statistically robust tool for identifying high prevalence areas in a heterogeneous and imperfectly known environment.

Spatial risk prediction and mapping of Schistosoma mansoni infections among schoolchildren living in western Côte d'Ivoire

The objectives of this study were (1) to examine risk factors for Schistosoma mansoni infection among schoolchildren living in western Côte d'Ivoire, and (2) to carry forward spatial risk prediction and mapping at non-sampled locations. First, demographic and socio-economic data were obtained from 3818 children, aged 6-16 years, from 55 schools. Second, a single stool sample was examined from each child by the Kato-Katz technique to assess infection status of S. mansoni and its intensity. Third, remotely sensed environmental data were derived from satellite imagery and digitized ground maps. With these databases a comprehensive geographical information system was established. Bayesian variogram models were applied for spatial risk modelling and prediction. The infection prevalence of S. mansoni was 38.9%, ranging from 0% to 89.3% among schools. Results showed that age, sex, the richest wealth quintile, elevation and rainfall explained the geographical variation of the school prevalences of S. mansoni infection. The goodness of fit of different spatial models revealed that age, sex and socio-economic status had a stronger influence on infection prevalence than environmental covariates. The generated risk map can be used by decision-makers for the design and implementation of schistosomiasis control in this setting. If successfully validated elsewhere, this approach can guide control programmes quite generally.

Interpolation and mapping of probabilities for geochemical variables exhibiting spatial intermittency

In monitoring a minor geochemical element in groundwater or soils, a background population of values below the instrumental detection limit is frequently present. When those values are found in the monitoring process, they are assigned to the detection limit which, in some cases, generates a probability mass in the probability density function of the variable at that value (the minimum value that can be detected). Such background values could distort both the estimation of the variable at nonsampled locations and the inference of the spatial structure of variability of the variable. Two important problems are the delineation of areas where the variable is above the detection limit and the estimation of the magnitude of the variables inside those areas. The importance of these issues in geochemical prospecting or in environmental sciences, in general related with contamination and environmental monitoring, is obvious. In this paper the authors describe the two-step procedure of indicator kriging and ordinary kriging and compare it with empirical maximum likelihood kriging. The first approach consists of using a binary indicator variable for estimating the probability of a location being above the detection limit, plus ordinary kriging conditional to the location being above the detection limit. An estimation variance, however, is not available for that estimator. Empirical maximum likelihood kriging, which was designed to deal with skew distributions, can also deal with an atom at the origin of the distribution. The method uses a Bayesian approach to kriging and gives intermittency in the form of a probability map, its estimates providing a realistic assessment of their estimation variance. The pros and cons of each method are discussed and illustrated using a large dataset of As concentration in groundwater. The results of the two methods are compared by cross-validation.

Interpolation of temperature and non-urban ozone exposure at high spatial resolution over the western United States

CR Climate Research Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsSpecials CR 18:163-179 (2001) - doi:10.3354/cr018163 Interpolation of temperature and non-urban ozone exposure at high spatial resolution over the western United States E. Henry Lee*, William E. Hogsett US Environmental Protection Agency, Western Ecology Division, 200 SW 35th Street, Corvallis, Oregon 97333, USA *E-mail: lee.ehenry@epamail.epa.gov ABSTRACT: In order to assess the impact of natural and anthropogenic stresses on forest ecosystems, it is necessary to interpolate air temperature and tropospheric ozone (O3) exposure values at high spatial resolution over complex terrain. The proposed interpolation approach was selected because of its ability to (1) account for the effect of elevation on temperature and their effects on tropospheric ozone, (2) use auxiliary data at higher spatial resolution than the variables of interest to improve the precision and accuracy of the prediction surfaces, (3) handle large amounts of data, and (4) provide not only a prediction at nonsampled locations but also a prediction standard deviation. The approach used auxiliary digital elevation model (DEM) data at 1 km resolution to improve the precision and resolution of the predictions for temperature and O3 exposure in the western United States. Initially, the study area was stratified into O3 regions based on seasonality and variability of monthly SUM06 values at 111 stations for the period 1990-1992 using rotated principal component analysis. Monthly mean daily maximum air temperatures were spatially interpolated using loess nonparametric regression and kriging of the loess residuals and interpolated to 2 km grid points of a DEM and to the ambient air quality monitoring points. Monthly O3 exposures were spatially interpolated using loess fits to relate O3 levels to elevation, predicted temperature, and the geographic coordinates and interpolated to 2 km grid points of a DEM. The elevation-based spatial interpolation procedure produced accurate and precise temperature and O3 exposure surfaces which had desirable statistical properties and were logically consistent with local topographical features and atmospheric conditions known to influence O3 formation and transport. The leave-one-out cross-validation mean absolute error was 0.93°C for the monthly mean daily maximum temperature and 1.93 ppm-h for the monthly SUM06 index for June 1990 for the western United States, comparable to published results for other regions at smaller spatial scales with less complex terrain. KEY WORDS: Spatial interpolation · Ozone · Temperature · Regionalization · Principal components analysis · Kriging · Loess regression · Western United States Full text in pdf format NextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in CR Vol. 18, No. 3. Online publication date: November 02, 2001 Print ISSN: 0936-577X; Online ISSN: 1616-1572 Copyright © 2001 Inter-Research.