Sampling the soil in long-term forest plots: The implications of spatial variation

Long-term monitoring of forest soils as part of a pan-European network to detect environmental change depends on an accurate determination of the mean of the soil properties at each monitoring event. Forest soil is known to be very variable spatially, however. A study was undertaken to explore and quantify this variability at three forest monitoring plots in Britain. Detailed soil sampling was carried out, and the data from the chemical analyses were analysed by classical statistics and geostatistics. An analysis of variance showed that there were no consistent effects from the sample sites in relation to the position of the trees. The variogram analysis showed that there was spatial dependence at each site for several variables and some varied in an apparently periodic way. An optimal sampling analysis based on the multivariate variogram for each site suggested that a bulked sample from 36 cores would reduce error to an acceptable level. Future sampling should be designed so that it neither targets nor avoids trees and disturbed ground. This can be achieved best by using a stratified random sampling design.

Estimating the spatial scale of herbicide and soil interactions by nested sampling, hierarchical analysis of variance and residual maximum likelihood

An unbalanced nested sampling design was used to investigate the spatial scale of soil and herbicide interactions at the field scale. A hierarchical analysis of variance based on residual maximum likelihood (REML) was used to analyse the data and provide a first estimate of the variogram. Soil samples were taken at 108 locations at a range of separating distances in a 9 ha field to explore small and medium scale spatial variation. Soil organic matter content, pH, particle size distribution, microbial biomass and the degradation and sorption of the herbicide, isoproturon, were determined for each soil sample. A large proportion of the spatial variation in isoproturon degradation and sorption occurred at sampling intervals less than 60 m, however, the sampling design did not resolve the variation present at scales greater than this. A sampling interval of 20-25 m should ensure that the main spatial structures are identified for isoproturon degradation rate and sorption without too great a loss of information in this field.

A geostatistical analysis of soil, vegetation, and image data characterizing land surface variation

The elucidation of spatial variation in the landscape can indicate potential wildlife habitats or breeding sites for vectors, such as ticks or mosquitoes, which cause a range of diseases. Information from remotely sensed data could aid the delineation of vegetation distribution on the ground in areas where local knowledge is limited. The data from digital images are often difficult to interpret because of pixel-to-pixel variation, that is, noise, and complex variation at more than one spatial scale. Landsat Thematic Mapper Plus (ETM+) and Satellite Pour l'Observation de La Terre (SPOT) image data were analyzed for an area close to Douna in Mali, West Africa. The variograms of the normalized difference vegetation index (NDVI) from both types of image data were nested. The parameters of the nested variogram function from the Landsat ETM+ data were used to design the sampling for a ground survey of soil and vegetation data. Variograms of the soil and vegetation data showed that their variation was anisotropic and their scales of variation were similar to those of NDVI from the SPOT data. The short- and long-range components of variation in the SPOT data were filtered out separately by factorial kriging. The map of the short-range component appears to represent the patterns of vegetation and associated shallow slopes and drainage channels of the tiger bush system. The map of the long-range component also appeared to relate to broader patterns in the tiger bush and to gentle undulations in the topography. The results suggest that the types of image data analyzed in this study could be used to identify areas with more moisture in semiarid regions that could support wildlife and also be potential vector breeding sites.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

Multiscale geostatistical analysis of AVHRR, SPOT-VGT, and MODIS global NDVI products

Global NDVI data are routinely derived from the AVHRR, SPOT-VGT, and MODIS/Terra earth observation records for a range of applications from terrestrial vegetation monitoring to climate change modeling. This has led to a substantial interest in the harmonization of multisensor records. Most evaluations of the internal consistency and continuity of global multisensor NDVI products have focused on time-series harmonization in the spectral domain, often neglecting the spatial domain. We fill this void by applying variogram modeling (a) to evaluate the differences in spatial variability between 8-km AVHRR, 1-km SPOT-VGT, and 1-km, 500-m, and 250-m MODIS NDVI products over eight EOS (Earth Observing System) validation sites, and (b) to characterize the decay of spatial variability as a function of pixel size (i.e. data regularization) for spatially aggregated Landsat ETM+ NDVI products and a real multisensor dataset. First, we demonstrate that the conjunctive analysis of two variogram properties – the sill and the mean length scale metric – provides a robust assessment of the differences in spatial variability between multiscale NDVI products that are due to spatial (nominal pixel size, point spread function, and view angle) and non-spatial (sensor calibration, cloud clearing, atmospheric corrections, and length of multi-day compositing period) factors. Next, we show that as the nominal pixel size increases, the decay of spatial information content follows a logarithmic relationship with stronger fit value for the spatially aggregated NDVI products (R2 = 0.9321) than for the native-resolution AVHRR, SPOT-VGT, and MODIS NDVI products (R2 = 0.5064). This relationship serves as a reference for evaluation of the differences in spatial variability and length scales in multiscale datasets at native or aggregated spatial resolutions. The outcomes of this study suggest that multisensor NDVI records cannot be integrated into a long-term data record without proper consideration of all factors affecting their spatial consistency. Hence, we propose an approach for selecting the spatial resolution, at which differences in spatial variability between NDVI products from multiple sensors are minimized. This approach provides practical guidance for the harmonization of long-term multisensor datasets.

SRTM resample with short distance-low nugget kriging

The shuttle radar topography mission (SRTM), was flow on the space shuttle Endeavour in February 2000, with the objective of acquiring a digital elevation model of all land between 60 degrees north latitude and 56 degrees south latitude, using interferometric synthetic aperture radar (InSAR) techniques. The SRTM data are distributed at horizontal resolution of 1 arc-second (similar to 30m) for areas within the USA and at 3 arc-second (similar to 90m) resolution for the rest of the world. A resolution of 90m can be considered suitable for the small or medium-scale analysis, but it is too coarse for more detailed purposes. One alternative is to interpolate the SRTM data at a finer resolution; it will not increase the level of detail of the original digital elevation model (DEM), but it will lead to a surface where there is the coherence of angular properties (i.e. slope, aspect) between neighbouring pixels, which is an important characteristic when dealing with terrain analysis. This work intents to show how the proper adjustment of variogram and kriging parameters, namely the nugget effect and the maximum distance within which values are used in interpolation, can be set to achieve quality results on resampling SRTM data from 3"" to 1"". We present for a test area in western USA, which includes different adjustment schemes (changes in nugget effect value and in the interpolation radius) and comparisons with the original 1"" model of the area, with the national elevation dataset (NED) DEMs, and with other interpolation methods (splines and inverse distance weighted (IDW)). The basic concepts for using kriging to resample terrain data are: (i) working only with the immediate neighbourhood of the predicted point, due to the high spatial correlation of the topographic surface and omnidirectional behaviour of variogram in short distances; (ii) adding a very small random variation to the coordinates of the points prior to interpolation, to avoid punctual artifacts generated by predicted points with the same location than original data points and; (iii) using a small value of nugget effect, to avoid smoothing that can obliterate terrain features. Drainages derived from the surfaces interpolated by kriging and by splines have a good agreement with streams derived from the 1"" NED, with correct identification of watersheds, even though a few differences occur in the positions of some rivers in flat areas. Although the 1"" surfaces resampled by kriging and splines are very similar, we consider the results produced by kriging as superior, since the spline-interpolated surface still presented some noise and linear artifacts, which were removed by kriging.

Spatial variability of soil CO2 emission in a sugarcane area characterized by secondary information

Soil CO2 emission (FCO2) is governed by the inherent properties of the soil, such as bulk density (BD). Mapping of FCO2 allows the evaluation and identification of areas with different accumulation potential of carbon. However, FCO2 mapping over larger areas is not feasible due to the period required for evaluation. This study aimed to assess the quality of FCO2 spatial estimates using values of BD as secondary information. FCO2 and BD were evaluated on a regular sampling grid of 60 m × 60 m comprising 141 points, which was established on a sugarcane area. Four scenarios were defined according to the proportion of the number of sampling points of FCO2 to those of BD. For these scenarios, 67 (F67), 87 (F87), 107 (F107) and 127 (F127) FCO2 sampling points were used in addition to 127 BD sampling points used as supplementary information. The use of additional information from the BD provided an increase in the accuracy of the estimates only in the F107, F67 and F87 scenarios, respectively. The F87 scenario, with the approximate ratio between the FCO2 and BD of 1.00:1.50, presented the best relative improvement in the quality of estimates, thereby indicating that the BD should be sampled at a density 1.5 time greater than that applied for the FCO2. This procedure avoided problems related to the high temporal variability associated with FCO2, which enabled the mapping of this variable to be elaborated in large areas.

Métodos estatísticos recursivos aplicados ao problema de estimação de vazão de gás em plantas de Plunger-lift

This work has as main objective to find mathematical models based on linear parametric estimation techniques applied to the problem of calculating the grow of gas in oil wells. In particular we focus on achieving grow models applied to the case of wells that produce by plunger-lift technique on oil rigs, in which case, there are high peaks in the grow values that hinder their direct measurement by instruments. For this, we have developed estimators based on recursive least squares and make an analysis of statistical measures such as autocorrelation, cross-correlation, variogram and the cumulative periodogram, which are calculated recursively as data are obtained in real time from the plant in operation; the values obtained for these measures tell us how accurate the used model is and how it can be changed to better fit the measured values. The models have been tested in a pilot plant which emulates the process gas production in oil wells

Geochemical characterization of heavy metal contaminated area using multivariate factorial kriging

This paper describes a geostatistical method, known as factorial kriging analysis, which is well suited for analyzing multivariate spatial information. The method involves multivariate variogram modeling, principal component analysis, and cokriging. It uses several separate correlation structures, each corresponding to a specific spatial scale, and yields a set of regionalized factors summarizing the main features of the data for each spatial scale. This method is applied to an area of high manganese-ore mining activity in Amapa State, North Brazil. Two scales of spatial variation (0.33 and 2.0 km) are identified and interpreted. The results indicate that, for the short-range structure, manganese, arsenic, iron, and cadmium are associated with human activities due to the mining work, while for the long-range structure, the high aluminum, selenium, copper, and lead concentrations, seem to be related to the natural environment. At each scale, the correlation structure is analyzed, and regionalized factors are estimated by cokriging and then mapped.

Simulação geoestatística na caracterização espacial de óxidos de ferro em diferentes pedoformas

Os minerais da fração argila, goethita e hematita, são óxidos de ferro (Fe) indicadores pedoambientais com grande influência nos atributos físicos e químicos do solo. O conhecimento dos padrões espaciais desses óxidos auxilia a compreensão das interrelações de causa e efeito com os atributos do solo. Nesse sentido, a qualidade das estimativas espaciais produzidas pode alterar os resultados obtidos e, por consequência, as interpretações dos padrões espaciais obtidos. O presente estudo teve o objetivo de avaliar o desempenho dos métodos geoestatísticos de estimativas (KO) e simulações sequenciais gaussianas (SSG) na caracterização espacial de teores de óxidos de Fe, goethita (Gt) e hematita (Hm), em uma pedoforma côncava e outra convexa. Foram coletadas 121 amostras de solos em cada pedoforma de um Argissolo em pontos com espaçamentos regulares de 10 m. Os teores de óxidos de Fe foram obtidos por meio de difração de raios-X. Os dados foram submetidos a análises geoestatísticas por meio da modelagem do variograma e posterior interpolação por KO e SSG. A KO não refletiu a verdadeira variabilidade dos óxidos de Fe, hematita e goethita, demonstrando ser inapropriada para a caracterização espacial dos teores dos óxidos de Fe. Assim, o uso da SSG é preferível à krigagem quando a manutenção dos altos e baixos valores nas estimativas espaciais é necessária. O desempenho dos métodos geoestatísticos foi influenciado pelas pedoformas. Os mapas E-type devem ser recomendados em vez de mapas de KO para os óxidos de Fe, por serem ricos em detalhes e práticos na definição de zonas homogêneas para o manejo localizado em frente de KO, sobretudo em pedoforma côncava.

Dental caries and the nutritional status of preschool children: a spatial analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Consideracoes sobre a aplicacao da geoestatistica a dados geoquimicos.

Deals with some common problems in structural analysis when calculating the experimental semi-variogram and fitting a semi-variogram model. Geochemical data were used and the following cases were studied: regular versus irregular sampling grade, presence of 'outliers' values, skew distributions due to a high variability of the data and estimation using a kriging procedure. -from English summary

Calculo de reserva de uma jazida de carvao por metodologia geoestatistica

A coal deposit was studied at Sapopema (PR) in the upper part of the Tubarao Group. The eliptical deposit is made up by a single layer of 1.2 m mean thickness and lies at a depth of 380 to 700 m. The semi-variogram, using the spherical model, revealed a range of 1.5 km and no nugget effect. Area kriging estimation for a grid of 0.5 × 0.5 km showed a value of 50.121.750 ton, very close to the real reserve one. -from English summary

Estudo do nivel piezometrico por analise geoestatistica

160 groundwater bores in the Ribeirao Preto region were used to study the behaviour of the piezometric surface of the Botucatu Formation aquifer by geostatistical methodology. The semi-variogram showed the following results: nugget = 50 m2; sill = 450 m2 and range = 4.5 km. The piezometric surface, obtained by punctual kriging in a 100 x 100 knot grid, revealed two lowered zones: one in a southwest to north-northeastern trend, indicating the groundwater flow north toward the Rio Pardo; and the other in the central part due to the high concentration of holes in the urban region of Ribeirao Preto city. -from English summary

Análise espacial de nutrientes e produção de alface cultivada em ambiente protegido

The objective of this work was to study spatial variability of some chemical soil attributes and lettuce production (total shoot fresh matter mass - MF; commercial shoot fresh matter mass - MFC; commercial shoot dry matter mass - MCS; and head commercial diameter - DCC) offering subsidies to the protected environment mapping in nutrients management areas in lettuce culture aiming for a higher productivity with application of fertilizers. The experiment was conducted in a protective environment (greenhouse) with lettuce irrigated by drip irrigation and sampling grid with 152 points. The special dependence analysis, determined by the variogram, was obtained with the aid of the GS+ Program. Considering the need for crop nutrients through the map obtained for element P (phosphorus) it was possible to establish two distinct areas for the application of this element in plantation fertilization. Through the lettuce yield maps obtained with MFC and DCC attributes was difficult to establish distinct areas for its management with data observed in only one crop cycle. Krigagem has proved useful for mapping the attributes studied.