Standardized Ordinary Cokriging Research Articles

Early stage variable rate nitrogen fertilization of silage maize driven by multi-temporal clustering of archive satellite data

Nitrogen fertilization of silage maize in Central Italy is typically carried out with two applications at early stages of crop development: 2nd (V2) and 6th (V6) leaf respectively. In such conditions, the crop has not yet fully covered the soil and proximal or remote sensing of the canopy is hindered by the strong soil background signal. There is thus great interest in rapid and inexpensive approaches to N fertilization prescription. Therefore, an indirect method for inferring information on yield potential and soil variability, through a field-based clustering of multi-temporal satellite data, has been developed using archive Landsat images to identify temporally constant patterns. This method is potentially useful for the creation of prescription maps. The usefulness of the method was evaluated during an N fertilisation field trial in Maccarese (Central Italy), in 2016. At the V2 stage, both uniform and variable rate applications were performed and compared. A pseudo-cross variogram and a standardized ordinary co-kriging methodology was used to highlight spatially variable significant differences among the treatments.

Integration of different-quality data in short-term mining planning

AbstractDecisions, from mineral exploration to mining operations, are based on grade block models obtained from samples. This study evaluates the impact of using imprecise data in short-term planning. The exhaustive Walker Lake dataset is used and is considered as the source for obtaining the true grades. Initially, samples are obtained from the exhaustive dataset at regularly spaced grids of 20 × 20 m and 5 × 5 m. A relative error (imprecision) of ±25% and a 10% bias are added to the data spaced at 5 × 5 m (short-term geological data) in different scenarios. To combine these different types of data, two methodologies are investigated: cokriging and ordinary kriging. Both types of data are used to estimate blocks with the two methodologies. The grade tonnage curves and swath plots are used to compare the results against the true block grade distribution. In addition, the block misclassification is evaluated. The results show that standardized ordinary cokriging is a better methodology for imprecise and biased data and produces estimates closer to the true grade block distribution, reducing block misclassification.

Optimal Rainfall Estimation by Considering Elevation in the Han River Basin, South Korea

AbstractMore than 70% of South Korea has mountainous terrain, which leads to significant spatiotemporal variability of rainfall. The country is exposed to the risk of flash floods owing to orographic rainfall. Rainfall observations are important in mountainous regions because flood control measures depend strongly on rainfall data. In particular, radar rainfall data are useful in these regions because of the limitations of rain gauges. However, radar rainfall data include errors despite the development of improved estimation techniques for their calculation. Further, the radar does not provide accurate data during heavy rainfall in mountainous areas. This study presents a radar rainfall adjustment method that considers the elevation in mountainous regions. Gauge rainfall and radar rainfall field data are modified by using standardized ordinary cokriging considering the elevation, and the conditional merging technique is used for combining the two types of data. For evaluating the proposed technique, the Han River basin was selected; a high correlation between rainfall and elevation can be seen in this basin. Further, the proposed technique was compared with the mean field bias and original conditional merging techniques. Comparison with kriged rainfall showed that the proposed method has a lesser tendency to oversmooth the rainfall distribution when compared with the other methods, and the optimal mean areal rainfall is very similar to the value obtained using gauges. It reveals that the proposed method can be applied to an area with significantly varying elevation, such as the Han River basin, to obtain radar rainfall data of high accuracy.

Enhancing the value of field experimentation through whole-of-block designs

Precision agriculture (PA) offers opportunities for the development of new approaches to on-farm experimentation to assist farmers with site-specific management decisions. Traditional agricultural experiments are usually implemented in fields with the least possible soil heterogeneity under the assumption that responses to inputs and inherent variation of the soil are additive components of yield variation. However, because the soil in typical fields is not homogeneous, PA has much to offer. Farmers faced with variable conditions need to optimize their management to the variation over space and time on their farm, a problem that is not solved by conventional approaches to experimentation. New designs for on-farm experiments were developed in the 1990s for cereal production in which the whole field was used for the experiment rather than small plots. We explore the extension of this type of experiment to a vineyard in the Clare Valley of South Australia aiming to evaluate options to increase grape yield and vine vigour. Manually sampled indices of vine performance measured on georeferenced ‘target’ grapevines were analysed geostatistically. The major advantage of such an approach is that the spatial variation in response to experimental treatments can be examined. Linear models of coregionalization, pseudo cross-variograms and standardized ordinary cokriging are used to map treatment responses over the experimental area and also the differences between them. The results indicate that both treatment responses and the significance of differences between them are spatially variable. Thus, we conclude that whole-of-block on-farm trials are useful in vineyards.

Restoration of clouded pixels in multispectral remotely sensed imagery with cokriging

The presence of clouds and their shadows in remotely sensed images limits their potential uses for extracting information. The commonly used methods for replacing clouded pixels by land cover reflection estimates usually yield poor results if the images being combined exhibit radical differences in target radiance due, for example, to large date separation and high temporal variability. This study focuses on introducing geostatistical techniques for interpolating the DN values of clouded pixels in multispectral remotely sensed images using traditional ordinary cokriging and standardized ordinary cokriging. Two case studies were conducted in this study. The first case study shows that the methods work well for the small clouds in a heterogeneous landscape even when the images being combined show high temporal variability. Although the basic spatial structure in large size clouds can be captured, image interpolation‐related artefacts such as smoothing effects are visually apparent in a heterogeneous landscape. The second case study indicates that the cokriging methods work better in homogenous regions such as the dominantly agricultural areas in United States Midwest. Various statistics including both global statistics and local statistics are employed to confirm the reliability of the methods.

Standardized vs. customary ordinary cokriging: Some comments on the article “The geostatistical analysis of experiments at the landscape-scale” by T.F.A. Bishop and R.M. Lark

In this comment on a recent article by Bishop and Lark, I show that standardized ordinary cokriging (Goovaerts, 1997, p. 232) is an inferior variant of customary cokriging. The authors' recommendation of standardized cokriging for the analysis of data, collected in landscape-scale field experiments, is therefore not justified. I further discuss the connection between customary ordinary cokriging and ordinary cokriging with a single unbiasedness constraint (Goovaerts, 1997, pp. 228–229). I argue that the latter method is not adequate for analysing experimental data because it excludes a priori that the treatments may have nonzero fixed effects that are constant across the study area. In contrast to Bishop and Lark, I recommend to use customary cokriging for the analysis of experimental data, gathered by landscape-scale experimentation.

Gaps‐fill of SLC‐off Landsat ETM+ satellite image using a geostatistical approach

Using appropriate techniques to fill the data gaps in SLC‐off ETM+ imagery may enable more scientific use of the data. The local linear histogram‐matching technique chosen by USGS has limitations if the scenes being combined exhibit high temporal variability and radical differences in target radiance due, for example, to the presence of clouds. This study proposes using an alternative interpolation method, the kriging geostatistical technique, for filling the data gaps. The case study shows that the ordinary kriging techniques may provide a powerful tool for interpolating the missing pixels in the SLC‐off ETM+ imagery. While the standardized ordinary cokriging has been shown to be particularly useful when samples of the variable to be predicted are sparse and samples of a second, related variable are plentiful, the case study demonstrates that it provides little improvement in interpolating the data gap in the SLC‐off imagery.

Extending Multivariate Space-Time Geostatistics for Environmental Data Analysis

Environmental studies require multivariate data such as chemical concentrations with space-time coordinates. There are two general conditions related to such data: the existence of correlations among the coregionalized variables and the differences in numbers of data which occur because of insufficient data caused by measurement error or bad weather conditions. This study proposes geostatistical techniques for space-time multivariate modeling that take into consideration these correlations and data absences. These techniques consist of suitable modeling of semivariograms and cross-semivariograms for quantifying correlation structures among multivariables and of extending standardized ordinary cokriging. The tensor product cubic smoothing surface method is used for space-time semivariogram modeling. These methods are applied to the chemical component data of the Ariake Sea, a typical closed sea in southwest Japan. In order to clarify environmental changes in the Ariake Sea, the concentration data of four nutritive salts (NO2–N, NO3–N, NH4–N, and PO4–P) at 38 stations over 25 years are used as environmental indicators. For each of the kinds of data, there are spaces and times for which there is no data available. The effectiveness of the modeling of space-time semivariograms and the high estimation capability of the extended cokriging are demonstrated by cross-validation. Compared with ordinary kriging for a single variable, multivariate space-time standardized ordinary cokriging can provide a more detailed concentration map of nutritive salts and while elucidating their temporal changes over sparsely spaced data areas. In the space-time models by ordinary kriging, on the other hand, smooth trends are obvious.

Identifying potential management zones in a layered soil using several sources of ancillary information

AbstractVariation in soil texture has a profound effect on soil management, especially in texturally complex soils such as the polder soils of Belgium. The conventional point sampling approach requires high sampling intensity to take into account such spatial variation. In this study we investigated the use of two ancillary variables for the detailed mapping of soil texture and subsequent delineation of potential management zones for site‐specific management. In an 11.5 ha arable field in the polder area, the apparent electrical conductivity (ECa) was measured with an EM38DD electromagnetic induction instrument. The geometric mean values of the ECameasured in both vertical and horizontal orientations strongly correlated with the more heterogeneous subsoil clay content (r = 0.83), but the correlation was weaker with the homogenous topsoil clay content (r = 0.40). The gravimetric water content at wilting point (θg(−1.5 MPa)) correlated very well (r = 0.96) with the topsoil clay content. Thus maps of topsoil and subsoil clay contents were obtained from 63 clay analyses supplemented with 117θg(−1.5 MPa)and 4048ECameasurements, respectively, using standardized ordinary cokriging. Three potential management zones were identified based on the spatial variation of both top and subsoil clay contents. The influence of subsoil textural variation on crop behaviour was illustrated by an aerial image, confirming the reliability of the results from the small number of primary samples.

The geostatistical analysis of experiments at the landscape-scale

In conventional field experiments inherent variability is managed by design. In all cases the inherent variation is treated as additive random variables (a residual and any block and/or covariate effects). This assumption is generally reasonable in most field experiments where our basic units are plots within a relatively small and uniform region of a field. It is less plausible when we wish to conduct experiments across heterogeneous landscapes, with inherent variation of the soil over a wide range of many variables. In this paper we present a geostatistical approach to the design and analysis of landscape-scale experiments. We no longer regard the treatment response as a fixed effect, but rather as a random variable. Therefore, at any target site we can estimate the response to different treatments and treatment contrasts. This could be done by ordinary kriging, or by cokriging after we model the treatment responses as coregionalized variables. The advantage of cokriging is that contrasts and their confidence limits may be estimated optimally, and are coherent with estimates of the responses (i.e. the difference between two optimal estimated responses is the optimal estimate of the contrast between them). Since only one treatment response can be observed at a particular location we use the pseudo cross-semivariogram [Papritz, A., Kunsch, H.R., Webster, R., 1993. On the pseudo cross-variogram. Mathematical Geology 25, 1015–1026] to model the cross-covariances of the responses. We compared ordinary kriging and three variants of cokriging; standardized ordinary cokriging, ordinary cokriging and the method of Papritz and Fluhler [Papritz, A., Fluhler, H., 1994. Temporal change of spatially autocorrelated soil properties: optimal estimation by cokriging. Geoderma 62, 29–43]. Standardized ordinary cokriging was found to be the best predictor of the treatment contrast and responses under different levels of spatial auto-correlation and structural correlation, and different experimental designs. The results showed that the plots of different treatments should be placed as close together as possible to give the best predictions of treatment contrasts. A field-scale nitrogen-response experiment was used to illustrate the proposed methods.

Improved Prediction and Mapping of Soil Copper by Kriging with Auxiliary Data for Cation-Exchange Capacity

Measurements of Cu or other trace elements in soils are rarely available in sufficient abundance to permit accurate mapping of large areas. In contrast, information is more widely available for major soil characteristics, such as cation-exchange capacity (CEC). Using data for soils of northern North Dakota, we compared four geostatistical methods as predictors of soil Cu: ordinary kriging (OK), ordinary kriging combined with regression (OKR), ordinary cokriging (OCK), and standardized ordinary cokriging (SCK). Ordinary kriging utilized data for soil Cu only, whereas the other three methods made use of CEC, which served as a secondary variable to improve the prediction and mapping of soil Cu. Quantitative predictions of soil Cu were tested by partitioning 619 sites of Cu into a training set of 310 sites, which was used to build models, and a testing set of 309 sites, which was reserved to test predictions derived from the training set. All three of the methods utilizing CEC data improved predictions substantially in comparison to OK. A larger data set containing data for soil Cu, CEC, or both was compiled from several comparable sources to prepare maps of Cu in soils of the 18 counties of northern North Dakota. These maps, based on data for 1002 sites within northern North Dakota, were quite similar for the three kriging methods which used data for both Cu and CEC, but different from the map derived from OK. Thus, the differences among the maps for soil Cu were consistent with our conclusion that the prediction of soil Cu was substantially improved by the use of CEC as an auxiliary variable.

Improved Prediction and Mapping of Soil Copper by Kriging with Auxiliary Data for Cation-Exchange Capacity

Measurements of Cu or other trace elements in soils are rarely available in sufficient abundance to permit accurate mapping of large areas. In contrast, information is more widely available for major soil characteristics, such as cation-exchange capacity (CEC). Using data for soils of northern North Dakota, we compared four geostatistical methods as predictors of soil Cu: ordinary kriging (OK), ordinary kriging combined with regression (OKR), ordinary cokriging (OCK), and standardized ordinary cokriging (SCK). Ordinary kriging utilized data for soil Cu only, whereas the other three methods made use of CEC, which served as a secondary variable to improve the prediction and mapping of soil Cu. Quantitative predictions of soil Cu were tested by partitioning 619 sites of Cu into a training set of 310 sites, which was used to build models, and a testing set of 309 sites, which was reserved to test predictions derived from the training set. All three of the methods utilizing CEC data improved predictions substantially in comparison to OK. A larger data set containing data for soil Cu, CEC, or both was compiled from several comparable sources to prepare maps of Cu in soils of the 18 counties of northern North Dakota. These maps, based on data for 1002 sites within northern North Dakota, were quite similar for the three kriging methods which used data for both Cu and CEC, but different from the map derived from OK. Thus, the differences among the maps for soil Cu were consistent with our conclusion that the prediction of soil Cu was substantially improved by the use of CEC as an auxiliary variable.

INTEGRATED INTERPOLATION METHODS FOR GEOPHYSICAL DATA: APPLICATIONS TO MINERAL EXPLORATION

Geophysical data are used routinely in mineral exploration to delineate the geology of an area.Because geophysical attributes are sparsely sampled, interpolation methods are used to gridthe individual sets of data. Whereas traditional techniques interpolate constituent attributes ofinterest independently, frequently resulting in simplistic geological models, alternativetechniques interpolate by integrating secondary data sets collected in the explored area. Traditionaltechniques include minimum curvature and ordinary kriging. Alternative integrated interpolationtechniques include standardized ordinary cokriging, collocated cokriging, and kriging withexternal drift. Application of these techniques to a specific exploration area in interpolatinggravity measurements (primary data) using weakly correlated aeromagnetics (secondary data)suggests that when gravity is well sampled, all techniques generate similar results. However,when gravity is undersampled, the secondary data can contribute substantially to identifyinggeophysical anomalies. Considering the high cost of geophysical data collection, this observationcan make geophysical data collection more efficient and cost effective. The case studyshows how, in the absence of a strong correlation, cokriging varieties tend to produce mapssimilar to those generated by traditional techniques. Kriging with external drift is shown togenerate a gravity map reproducing all gravity anomalies. The technique produces excellentresults when features identified in the secondary data need to be reflected in the map of theprimary data.