Soil pH macronutrients. In addition to macronutrients, plants also need has an influential affect on plant nutrient trace nutrients and both macro and trace nutrient availability is availability by controlling the chemical forms of the controlled by soil pH. Understanding of spatial variability of soil properties is important in site-specific management. The special nutrient. Knowledge about spatial variation of soil variability of soil property is often measured using various properties is considered a key variable when interpolation methods resulting in map generation.
Selecting a implementing "good farming rules" towards proper spatial interpolation method is crucial in surface analysis, since different methods of interpolation can lead to different sustainable rural development . The sustainable surface results. Ordinary Kriging OK , Inverse Distance soil properties for efficient crop production depend Weighting IDW , and Radial Basis Functions RBF are three heavily on the structural properties and the well-known spatial interpolation techniques commonly used for characterising the spatial variability and interpolating between concentration of the soil solution.
Spatial variability sampled points and generating the prediction maps. The variety of soil properties is somewhat inherent in nature of available interpolation methods has led to questions about because of variations in soil parent materials and which is most appropriate in different contexts and has stimulated several comparative studies. Knowledge of soil spatial In this work, three common interpolation methods are used to variability and the relationships among soil study the spatial distributions of soil pH in a vineyard. Geostatistics can dataset that could be represented over a map of the entire study be used for studying and predicting the spatial area.
The performance of conventional statistics showed that soil structure of georeferenced variables and generating pH had a moderate variation in this study area. According to I. Samples close to each other considerable attention due to the three main have similar properties than those far away from potential benefits of increasing input efficiency, each other.
Classical statistics are not capable of improving the economic margins of crop analyzing the spatial dependency of the variables production and reducing environmental risks. Among statistical methods, geo-statistical kriging-based techniques have been often used for spatial analysis . IDW and its modifications are the most applied deterministic interpolation method .
The variety of available interpolation methods has led to questions about which is most appropriate in different contexts and has stimulated several Fig.go site
Kriging: a method of interpolation for geographical information systems. : Rothamsted Research
The accuracy and efficiency of the data; 3 Both deterministic and geostatistical generated maps are examined and the most fitting interpolation methods was used to estimate soil pH technique for the soil properties in the study area is values at unsampled points and generate their also identified. The methods investigated in this II. Deterministic interpolation techniques create A. Study area and data sampling surfaces from measured points, based on either the The data were collected from the Kumeu extent of similarity IDW or the degree of vineyard located in Kumeu region in Auckland, smoothing RBF.
Geostatistical interpolation New Zealand in May Figure 1. Fifty four techniques OK use the statistical properties of the soil samples were collected as part of an ongoing observed points.
Geostatistical techniques quantify research project in the Geoinformatics Research the spatial autocorrelation among measured points Centre . The size of the study area was and account for the spatial configuration of the approximately x m. Soil samples were sample points around the prediction location .
Soil pH was measured three times on the used in this study: field using Field Scout pH Meter data logger. The assumption is that sampled points closer to the unsampled point are more similar to it than those further away in their values . The weight and have more influence on the performance of interpolation techniques, in terms of estimation, and the resultant spatial the accuracy of predictions, was based on the interpolation is local .
The importance of geostatistics in pyschical geographyFiziki coğrafyada jeoistatistiğin önemi
The G measure gives an indication of tension, completely regularised spline, multi- how effective a prediction might be. The exact interpolators predict Geostatistical parameters such as range, nugget values are identical with those measured at the and nugget ratio values were calculated for pH. Sill same point and the generated surface requires is the lag distance between measurements at which passing through each measured points. The one value of dataset does not weight its predicted values can vary above the maximum neighbouring values.
Range is the distance at which or below the minimum of the measured values the variogram reaches the sill value , .
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The estimated values of the methods are Theoretically, the semivariogram value at zero based on a mathematical function that separation distance i. However, minimises total curvature of the surface, at an infinitely small separation distance, the generating quite smooth surfaces. The spatial estimate at an unsampled point based on the dependency of soil properties was graded based on weighted average of observed neighbouring the nugget variance effect. The properties was points within a given area. The III. Coefficient Variation CV is the ArcGIS 10 was used to examine the spatial most discriminating factor for describing variability coloration between measured sample points through of soil properties than the other parameters such as semivariograms functions.
Experimental anisotropy SD, mean, median, etc. In this study, soil pH semivariogram were examined to model the spatial had CV of 7.
According to the grading of CV for model that passes through the points in the soil property variations provided by Warrick , semivariogram. Model selection for Darling normality test on soil pH values for both semivariograms was done by comparing the depths. The calculated P-Value for soil pH at both deviation of estimates from the measured data and depths was greater than 0.
A graphical summary dataset.
The values of mean error ME , root mean of descriptive statistic is presented in Figure 3. However trend was too weak in depth A identified Table 2. The best model was selected whereas for depth B both North-South and East- based on four criteria: the standardized mean West trend lines exhibited a clear curve.
The direct approach is to use a joint simulation of the dependent variables, but it requires the inference and modeling of direct and cross covariance matrices that are computational costly to determine . An alternative mode is first to decorrelate the input variables using Principal Component Analysis-PCA   and, after apply the geostatistical simulation procedure. So, the M interdependent input variables, denoted by , , are transformed in M independent variables, denoted by , as follows:.
To recover the interdependent variables applies the inverse transform function, as follows:. The indicator geostatistical approach for continuous variables, for example for the variables, allows to estimate a set of values at non sampled location, that represent a discretized approximation of the conditional cumulative distribution function ccdf  .
Initially the variables are transformed into indicator variables, considering cutoffs values, cutoffs. These transformations are defined by the relation:. So, for each cutoff value indicator fields are generated, with 0 and 1 values, of the indicator variable.
Next, empirical indicator semivariograms are determined for each one of the indicator fields to estimated their spatial correlation structures:. The indicator fields associated with their respective cutoff values and theoretical semivariograms are used by Indicator Kriging IK and Conditional Sequential Indicator Simulation SIS procedures for estimating probabilities values at non-sampled location Thus, this set of estimated probabilities, at non sampled location, is used to create a discretized approximation of the ccdf   and it represents the uncertainty model of the variable.
A stochastic simulation is a process of drawing equally likely realizations of values that are obtained from the probability distribution of a Random Variable RV. Consider the M independent factors Y M u. For example, to the Y 2 u independent variable, , where ; is the l-th simulated value at ; and the set represent the l-th random field generated by simulation of the Y 2 u.
In that case, the SIS procedures makes use of the ccdf, conditioned to the n nearest of RV Y 2 u and also to the pre-simulated values, inside the neighborhood, to get values. Then simulates a value of the from the univariate ccdf of , , conditioned to the n nearest sample data Y 2 u ;. The conditioning data is updated to ;. At this time was produced a random field of the Y 2 u ;.
Stop when you reach the desired number of simulations. Figure 1. Initially, the input variables Z 1 u and Z 2 u are decorrelated via PCA transformation in order to get two uncorrelated sample sets named Y 1 u and Y 2 u variables. The result is a set of the realizations equally likely, and. From theses realizations, prediction and uncertainty maps can be generated. These maps are intermediate results that help the analyst to better understand the spatial distribution of the variables involved in the SLR model and their respective uncertainties.