Ordinary Point Kriging Research Articles

ON THE USE OF FREELY DISTRIBUTED GLOBAL DIGITAL ELEVATION MODELS OF THE HIGH SPATIAL RESOLUTION FOR CALCULATIONS OF WATER EROSION OF SOIL

Problem Statement and Purpose. In the last two decades, when digital elevation models (DEMs) of global coverage and high spatial resolution have appeared in free access, the problem of assessing not only the planned or vertical accuracy of these DEMs but also the assessment of their applicability for mathematical modeling of hydrological or geomorphological processes has become relevant. The aim of this article is to evaluate the possibility of using freely distributed global digital elevation models of high spatial resolution for calculations of soil erosion losses, including their spatial distribution within a slope or a small catchment area.Data & Methods. The article evaluated the global DEMs SRTM with spatial resolution of 3 angular seconds and 1 angular second, ASTER GDEM (ASTER30) and AW3D30 with spatial resolution of 1 angular second. Estimation of the DEMs was performed for a test site with an area of about 340 km2, located in the north of Odessa region on the southern spurs of the Podolsk Upland. A digital elevation model based on the dig­itization of a large-scale topographic map and subsequent spatial interpolation of the results by the method of ordinary point Kriging was used as a reference. Calculations of soil erosion losses were performed using a spatially distributed GIS-implemented physical-statistical model of erosion-accumulation, developed at the Department of Physical Geography and Nature Management of ONU named after I. I. Mechnikov.Results. All evaluated digital elevation models in general well reflect the basic fea­tures of a relief of a test site. The average absolute heights of the estimated digital el­evation models differ from the average height of the local reference DEM by no more than 0.5 %. However, the minimum and maximum heights, average surface slopes, length of current lines, slope exposure and, especially, their spatial distributions ob­tained using evaluated global DEMs, to some extent differ from those obtained using a cartographic digital elevation model. In addition to the technical features of the survey, this is influenced by the presence within the test site of trees, buildings, struc­tures (ASTER30 and AW3D30), as well as the representation of heights in integers (SRTM90, SRTM30 and ASTER30). For ASTER30, it is also important the existance of post-processing errors ("artifacts") that have not been eliminated.The inadequacy of a quantitative assessment of the main factors of the erosion process, which are the slopes and exposure of slopes, as well as the lengths of water flow lines, inevitably affect the accuracy of calculating both the average values of soil erosional losses and, especially, their spatial distribution. This inadequacy manifested itself to the greatest extent in the digital elevation model ASTER GDEM. Based on the study for calcu­lations and mapping of soil erosion losses using spatially distributed mathematical models, we recommend digital elevation models AW3D30 and SRTM90, which pro­vided good compliance of the results of calculations of both average values of soil erosion losses and spatial distribution of them to the corresponding characteristics obtained using cartographical digital elevation model.

Comparison of interpolated soil nutrients maps obtained with application of various approaches of ordinary kriging

To create maps of the available forms of nutrients in arable land for implementation of systems of mineral fertilizers differential application, various approaches of interpolation by the ordinary kriging method were used. Maps of the availability were built according to the agrochemical analysis of mixed samples compiled from elementary plots of 5 ha. In the first case, the result of the agrochemical analysis was tied to the centroids of the elementary plots, and the interpolation was carried out using point ordinary kriging. In the second case, the indicator value was attached to blocks corresponding to the area of elementary sites. In this case, the interpolated cards were obtained using block kriging. It was shown that the application of various approaches to interpolation gives similar maps of spatial distribution. At the same time, maps obtained by ordinary point kriging are characterized by a more accurate forecast compared to maps obtained using block kriging. Therefore, the construction of interpolated maps of the availability of arable lands with nutrients based on the results of agrochemical analysis of mixed samples with data binding to the centroids of the sampling cells and compiling the combined samples is more preferable.

Prediction of Spread Shear Strength of Rock with Ordinary Point Kriging Method using GStat-R

Prediction of Spread Shear Strength of Rock with Ordinary Point Kriging Method using GStat-R

METODE ORDINARY POINT KRIGING UNTUK MEMPREDIKSI INFLASI DI KABUPATEN/KOTA YANG TIDAK TERSAMPEL

Inflasi sebagai indikator makro ekonomi memiliki peran penting bagi pemerintah dalam perencanaan dan evaluasi pembangunan. Penghitungan inflasi yang dilakukan oleh BPS masih terbatas di beberapa kabupaten/kota sampel SHK. Penelitian ini mengusulkan metode Ordinary Point Kriging untuk memprediksi nilai inflasi di beberapa kabupaten/kota tidak tersampel di pulau Jawa berdasarkan nilai inflasi di kabupaten/kota sampel yang ada di sekitarnya. Hasil penelitian ini menunjukkan bahwa dengan metode Ordinary Point Kriging dan model semivariogram Gaussian diperoleh prediksi nilai inflasi di beberapa kabupaten/kota kontrol dengan nilai MAPE sebesar 12,56 persen. Sementara itu, hasil penerapan metode kriging pada kabupaten/kota yang tidak tersampel cenderung menunjukkan kemiripan nilai inflasi dengan lokasi sampel yang berdekatan.

Rain gauge network design using coupled geostatistical and multivariate techniques

A methodology for the design of a rain gauge network is developed in this study. To the best of the authors’ knowledge, this is the first time a combination of geostatistical tools and factor analysis, along with a clustering technique, has been used to prioritize rain gauge stations in terms of information content over the study area. The whole study area is divided into homogeneous subregions and a conventional variance-based approach is implemented in each subregion to rank rain gauge stations. For this purpose, factor analysis coupled with ordinary block kriging is used to identify the number of homogeneous subregions, and then, ordinary point kriging is used to assign rain gauge stations to each subregion. The developed scheme is quite time-efficient as it is not sensitive to initial guesses on cluster centers, there is no need to specify the number of clusters in advance and, above all, it is highly relevant to the overall objective stipulated in rain gauge network design. The proposed methodology is implemented on real data set in the south west of Iran. The results show that the proposed approach compares well with existing paradigms in rain gauge network design and only six rain gauge stations are required to provide the necessary information. In particular, the measure of network accuracy lies somewhere in between the so called time consuming and more simplified approaches used in rain gauge network design.

On the soil information content of visible–near infrared reflectance spectra

We describe the information content of soil visible–near infrared (vis–NIR) reflectance spectra and map their spatial distribution across Australia. The spectra of 4030 surface soil samples from across the country were measured with a vis–NIR spectrometer in the range 350 to 2500 nm. The spectra were compressed by a principal component analysis (PCA) and the resulting scores were mapped by ordinary point kriging. The largely dominant and common feature in the maps was the difference between the more expansive, older and more weathered landscapes in the centre and west of Australia and the generally younger, more complex landscapes in the east. A surface soil class map derived from the clustering of the principal components was similar to an existing soil classification map. We show that vis–NIR reflectance spectra (i) provide a rapid and efficient integrative measure of the composition of the soil, (ii) can replace the use of traditional soil properties to describe the soil and make pedological interpretations of its spatial distribution and (iii) can be used to classify soil objectively.

Effects of microsite variation on growth and adaptive traits in a beech provenance trial

ABSTRACT: The effects of the within-trial spatial variation of environmental factors on phenotypic traits were studied in the Slovak plot of the international beech provenance trial coordinated by BFH Grosshansdorf with 32 provenances, established under a randomized complete block design with three adjacent blocks. Five indicators of soil properties (soil moisture, bulk density and pH) and microclimate (average daily temperature and temperature amplitude) were assessed at 96 points distributed over a 10 × 10 m grid and their values for the positions of individual trees were estimated by ordinary point kriging. The evaluation of phenotypic variation (height, diameter, Julian days of spring flushing and autumn leaf discoloration, vegetation period length, late frost damage) using a common two-way analysis of variance showed a significant provenance × block interaction effect indicating the heterogeneity of blocks. Analysis of covariance using single-tree kriging estimates of environmental variables as covariates showed that in addition to provenance, all phenotypic traits were significantly affected by microsite, especially by temperature fluctuation. Employing methods incorporating the spatial component in the evaluation of tree breeding field experiments is advocated.

Optimizing interpolation of shoot density data from aPosidonia oceanicaseagrass bed

AbstractA case study on the optimization ofPosidonia oceanicadensity interpolation, using a data set from a large meadow at Porto Conte Bay (NW Sardinia, Italy), is presented. Ordinary point kriging, cokriging and a weighted average based on inverse square distance were used to interpolate density data measured in 36 sampling stations. The results obtained from different methods were then compared by means of a leave‐one‐out cross‐validation procedure. The scale at which interpolation was carried out was defined on the basis of the Hausdorff dimension of the variogram. Optimizing spatial scale and data points search strategy allowed obtaining more accurate density estimates independently of the interpolation method.

Influence of Spatial Structure on Accuracy of Interpolation Methods

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

Estimates of soil movement in a study area in Gonghe Basin, north-east of Qinghai-Tibet Plateau

Accurate data on soil erosion rates by wind and patterns of soil movement are essential for guiding control planning in Gonghe Basin, north-east of Qinghai-Tibet Plateau. This study was conducted to estimate soil erosion rates and assess patterns of soil movement by wind erosion in a 600 ha area during a 37-year period using the 137Cs tracer technique. Two hundred and fifty-five soil samples were collected from 125 137Cs sampling points on a modified grid pattern and analysed for 137Cs activity. Using ordinary point kriging, soil movement rates were interpolated at 7350 points in the sample grid. The kriged mean net soil movement rates were −3·496, −5·026 and 1·77 kg m −2 year −1 on uncultivated grassland, cultivated grassland (farmland) and semi-shifting sand land, respectively. Soil movement by wind erosion in semi-arid steppe area is closely related to land use and soil landscape.

How good is your weed map? A comparison of spatial interpolators

Recent interest in describing the spatial distribution of weeds and studying their association with site properties has increased the use of interpolation to estimate weed seedling density from spatially referenced data. In addition, farmers and consultants adopting elements of site-specific farming practices are using interpolation methods for mapping weed densities as well as soil properties. This study was conducted to compare the performance of four interpolation methods, namely inverse-distance weighting (IDW), ordinary point kriging (OPK), minimum surface curvature (MC), and multiquadric radial basis function (MUL), with respect to their ability to map weed-seedling densities. These methods were evaluated on data from four weed species, velvetleaf, hemp dogbane, common sunflower, and foxtail species, of contrasting biology and infestation levels in corn and soybean production fields in Nebraska. Mean absolute difference (MAD) and root mean square (RMS) between the observed point sample data and the estimated weed seedling density surfaces were used to evaluate the performance of the interpolation methods. Four neighborhood search types were compared within each interpolation method, and Search3 (12 to 16 neighboring locations) generated an interpolated surface with the smallest MAD and RMS indicating the highest precision. IDW with a power coefficient of p = 4 gave the smallest MAD and RMS, as did a test with an elliptical search and no anisotropy. The level of precision of all four interpolation methods was very poor for weed species with low infestation levels (> 75% of field weed-free; MAD ranged from 100 to 187% of the observed mean density), whereas precision was improved for weed species with high infestation levels (< 25% of field weed-free; MAD ranged from 45 to 85%). No single interpolator appears to be more precise than another. Implications of this study indicate that grid sample spacing and quadrat size are more important than the specific interpolation method chosen.

The influence of sampling scheme and interpolation method on the power to detect spatial effects of forest birds in Ontario (Canada)

Spatial ecology is becoming an increasingly important component of resource management, and the general monitoring of how human activities affect the distribution and abundance of wildlife. Yet most work on the reliability of sampling strategies is based on a non-spatial analysis of variance paradigm, and little work has been done assessing the power of alternative spatial methods for creating reliable maps of animal abundance. Such a map forms a critical response variable for multiple scale studies relating landscape structure to biotic function. The power to reconstruct patterns of distribution and abundance is influenced by sample placement strategy and density, the nature of spatial auto-correlation among points, and by the technique used to extrapolate points into an animal abundance map. Faced with uncertainty concerning the influence of these factors, we chose to first synthesize a model reference system of known properties and then evaluate the relative performance of alternative sampling and mapping procedures using it. We used published habitat associations of tree nesting boreal neo-tropical birds, a classified habitat map from the Manitou Lakes area of northwestern Ontario, and point count means and variances determined from field studies in boreal Canada to create 4 simulated models of avian abundance to function as reference maps. Four point sampling strategies were evaluated by 4 spatial mapping methods. We found mixed-cluster sampling to be an effective point sampling strategy, particularly when high habitat fragmentation was avoided by restricting samples to habitat patches >10 ha in size. We also found that of the 4 mapping methods, only stratified ordinary point kriging (OPK) was able to generate maps that reproduced an embedded landscape-scale spatial effect that reduced nesting bird abundance in areas of higher forest age-class fragmentation. Global OPK was effective only for detecting broader, regional-scale differences.

Evaluating Soil Movement Using Cesium‐137 and the Revised Universal Soil Loss Equation

AbstractMore complete information is needed on the rates and patterns of soil movement in Palouse watersheds to better guide conservation planning. Water erosion has historically been predicted from rates using the Universal Soil Loss Equation (USLE) or the Revised USLE (RUSLE). These equations, however, do not account for deposition or tillage erosion. This study was conducted to assess patterns of soil movement in an open Palouse watershed during a 27‐yr period using the 137Cs tracer technique and to statistically compare transect‐ and point‐based RUSLE soil loss rates with 137Cs‐based soil loss rates measured at 74 137Cs sampling points located on 89 landscape profiles. One hundred fifty‐eight soil samples were collected from a modified grid pattern and analyzed for 137Cs activity. Soil movement rates were interpolated at 8025 points in the sample grid using ordinary point kriging. Hillslopes were classified into geometric and geomorphic components. The kriged mean net soil movement rate for the 27‐yr period was −3.3 kg m−2 yr−1. Doubly convex landscape positions have experienced the most severe erosion, apparently due to tillage erosion. The measured 137Cs and transect‐based RUSLE median soil loss rates were both significantly higher than the point‐based RUSLE median; however, no significant difference existed between the transect‐based RUSLE and measured 137Cs median soil loss rates (α = 0.05). Meaningful comparisons between 137Cs and RUSLE soil loss rates can only be made if a tillage movement rate, history of crop management, and the accuracy of RUSLE relationships and operating files are known.

Developing and Validating a Model for Predicting Gypsy Moth (Lepidoptera: Lymantriidae) Defoliation in Connecticut

A logistic regression model was developed that predicts the probability of forest defoliation by the gypsy moth, Lymantria dispar L., in Connecticut. Data used to develop the model were obtained from sketch maps of defoliation in Connecticut from 1982 to 1994, interpolations (using ordinary point kriging) of fixed area egg mass counts from permanent plots in Connecticut from 1986 to 1994, digital soil maps, and digital elevation models. Subjective comparisons of predicted and actual defoliation maps over years used to fit model parameters were similar. The model was validated with data from years not used in developing the model (1975 to 1985 and 1995). When defoliation was averaged over all locales for validation years, average predicted defoliation tracked actual average defoliation, although the association between them was not significant. Correlations between predicted and actual defoliation, when pairs being compared were at the same locations, were below 0.2 for years in which 2% of the state was defoliated, correlations ranged up to 0.9. The model developed here should be useful in providing probabilities of defoliation that can be used in population suppression programs.

The performance of spatial interpolation methods and choropleth maps to estimate properties at points: A soil survey case study

A study was designed to compare the performance of six spatial interpolation methods to estimate soil properties at unvisited points. These methods were global mean, moving average, nearest neighbour, inverse squared distance, Laplacian smoothing splines and ordinary point kriging. These methods were also applied in combination with a choropleth map (soil map) by stratifying the area. The soil properties estimated were thickness of A1 horizon, maximum areic mass of phosphate adsorbed by soil, mean highest water table and mean lowest water table. The performance of the methods was measured by estimating the spatial means of the squared and absolute error (quality criteria not conditional on the sample of test points) by a stratified simple random sample of test points. The mean squared error was very large in proportion to the spatial variation over the total area for all methods and properties. Differences between methods were small. In general, no statistically significant stratification or weighting effects were found. The effect of weighting plus stratification was usually not significant either. Overall, weighting with inverse squared distance was as satisfactory as weighting by ordinary point kriging. However, the latter was superior near data points. Also, when combined with soil map stratification, kriging was more reliable in the sense that it estimated all properties well. Estimates obtained using the means of six soil map units were better, although not significantly, than those obtained from unstratified kriging and as good as kriging within three map units.

Kriging of Eocene Sand Channels From Depth-Averaged I Overburden pH, Jewett Lignite Surface Mine, East-Central Texas

Ordinary point kriging was used to map twenty-six vertically-averaged soil and oxidized overburden acidity values for a future mine block at the Jewett lignite mine, east-central Texas. The pH data were collected as part of a geochemical overburden characterization study to be used in post-mining reclamation decision-making. The authors used kriging, and its estimation standard error, to test the completeness of their data set and to indicate areas of need for additional closely spaced sampling. Because pH can be readily measured in the field, they chose it as the parameter of interest in the kriging. In general pH increased with depth; however, a more exciting result was that the trend and geometry of a major paleo-channel could be mapped from pH values because of the relatively higher acidity of the sand in the channel. Kriged maps were compared with manually-contoured and inverse-distance weighting interpolated maps, and found to be more easily interpretable. The kriging performed better because it allows of anisotropies in the data to be naturally included in the interpolation. Prior to the kriging, the data were studied to validate the assumptions involved in the modeling. The data are clean, well-behaved and statistically homogeneous, and the interpolation was successfulmore » even with sparse data. The knowledge of the location and morphology of the paleochannels is essential for the engineering aspects of the mining, and is useful in reclamation decision-making.« less