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Producing probability maps to assess risk of exceeding critical threshold value of soil EC using geostatistical approach Case Study: Soil EC measurements were taken in units of decisiemens per meter (dS/m) to study which part of soil land area are contaminated based on the threshold value 250 dS/m. The study soil site was sampled on a 15 X 15 m grid spacing in the eastwards direction and more than 20 meters to 40 meters in the northwards direction at regular interval with total number of 197 observations. Sample EC configuration is provided as shown in the graph 1 below. A geostatistical analyst package part of ESRI ArcGIS software is used produce the graph. Although EC has no direct effect on crop growth or yield but EC could be related to other soil properties such as water holding capacity, topsoil depth, soil nutrients levels, salinity, and subsoil characteristics. From graph 1 it can be roughly seen that the pattern of the soil EC tends to increase in south-east and south-west directions.  Graph 1 The histogram is also produced to check the stationary assumptions of the geostatistical theory and can be seen below in graph 2. It shows that EC data are not normal distribution and contain some outliers and shows mixture of two populations.  Graph 2 A probability plot is also shown to conclude that data violate stationary assumptions probability plot shows that there are some outliers above 95%.  Graph 3 The indicator variogram values are estimated at least in two directions to detect any anisotropy in the data. Checking and detecting anisotropy is important process as it has larger or shorter spatial correlation (range) in some directions, and can be useful in selecting neighbouring data to improve the performance of indicator kriging estimates (interpolation techniques). Anisotropy can be seen in the graph 4 and 5 below where spatial correlation of the variogram model (one with range 370m and other with range of 200m) changes with directions. A spherical variogram model was fitted to experimental variogram values and 3 main parameters of spherical model called nugget effect, sill and range were estimated to provide overall spatial variation of EC. In graph 4 the nugget effect is very small compared to total spatial variation of the EC.  Graph 4 The nugget effect accounted for about one-fourth of the total spatial variance of the EC data in the south-west direction. This model includes a structure with range of 200m compared to the first variogram model with spatial structure range of 370m. The first variogram model shows better spatial continuity than second variogram model. The second variogram model shows some existence of trend after 90 meters.  Graph 5 Indicator kriging has been chosen appropriate interpolation techniques in this case study as data do not follow symmetric distribution and mean and variance as defined in the equation (1.1) and (1.3) over the region is not constant. In this situation, kriging indicator is a robust method to deal with skewed distribution and outliers and resulted improved spatial estimate at unknown locations where no measurement were taken. An important contribution of geostatistics is the assessment of uncertainty about unsample values. Geostatistical interpolation is controlled by above indicator variogram model and the sampling configuration (regular, irregular, trangle cells) of the EC data. Therefore, it is also possible to optimize sampling strategy through variogram modeling after one forth of sample information is collected that has resulted in minimizing interpolation error. The sample below threshold values were assigned to zero and samples above the threshold values were assigned to 1. The probability output values are also between 0 and 1. The output prediction can be interpreted as the probability of the variables belonging to class of 1 which are above the threshold value by producing soil map of probability of exceeding critical values such as regulatory threshold for soil quality. The probability of values higher than threshold value is mapped as shown in the graph 6. For decision making point of view, in fact, it is often to assess risk of soil zones rather than computing single spatial estimate at unknown location with associated indicator kriging variance. The soil with high probability values in the south-west direction has been identified and separate zone of high risk area and some remedial treatment should be recommended to provide some economic yields of agriculture crops and is shown in the graph 6. The formers would be advised to apply fertilizer in this area as the output probability prediction are high compared to critical threshold value (critical value). The delimiting zones have been identified in the south-west direction which require some remedial treatment action if they want to produce some economic yields of agriculture crops.  Graph 6 |