Location: The study site lies between latitude 25°39'29"N and longitude 88°35'44"E of Birol upazila, Dinajpur district in Bangladesh during July 2009.
Geology of terrace soils: Terrace soils/Barind Tracts (BT) are in the Pleistocene physiographic unit which occupies a nearly level to gently undulating landscape. Soil is mostly made up of older alluvium which differs from the surrounding floodplain. It comprises of three major sub-units: level, high and north - eastern BT. BT is floored by Pleistocene sediments which is compact and sticky known as the Madhupur Clay (MC). This semi-consolidated substratum is variably weathered, brown or yellowish brown in colour, deeply oxidised and assumed to be of fluvial origin and deposited towards the end of the last glacial period. Major part of this tract is poorly drained, mottled silty top soils merged with MC at shallower depth. The BT is fragmented, being made up separate uplifted fault blocks in the north eastern part of the country. It covers a total area of approximately 7,770 km² (Brammer, 2002 and 1996; Ibrahim and Baset, 1973). The soil is imperfectly to poorly drained developed in shallowly weathered MC in level areas of the BT. The top soil is silty and light grey, generally brightly oxidised with yellowish brown mottles along cracks and root channels, and bears low level of organic matter. The soil of studied area belongs to ‘ Amnura’ soil series and subgroup-Aeric Haplaquept and order-Inceptisols in the USDA Soil Taxonomy. The cultivated layer is puddle and reduced in the monsoon season and under irrigated rice in the dry season. The soil becomes white and powdery when dry. The reaction is medium or strongly acidic when dry but the surface layer becomes neutral in reduced condition. The subsoil has a mixed yellowish brown and grey, red mottled, silty loam or silty clay loam texture which is commonly friable and porous. The soil shows a pronounced increase in mottles and clay content with depth. The substratum is strongly structured and compacted heavy plastic clay. The soil bears low natural fertility and has low moisture holding capacity. The low structural stability of the top soil and presence of a ploughpan which is beneficial for transplanted paddy but providing severe limitations for dry land crops (Brammer, 2002 and 1996 ; Ibrahim and Baset, 1973).
Electromagnetic induction (EMI) survey: Soil conductivity sensor used in this research was EM38, which is a non-invasive proximal soil sensor. The ECa survey was conducted on the July 25, 2009 and point measurements were taken in grid spacing of 17 by 10 m from a wet field. The calibration was done according to t he steps described in the EM38 operating manual. ECa data in mS m-1 were recorded on a laptop computer. The EM38 was operated in both measurement modes, i.e., horizontal orientation (ECa-H) and vertical orientation (ECa-V). All the measurements were duly geo-referenced with a highly sensitive GPS manufactured by Navilock. ECa data are expressed at 25°C (Sheets and Hendrix, 2005 ), during the ECa measurements soil temperature was recorded at 20 cm depth using a soil thermometer. As the temperature of the soil was stable at 25.3°C, no temperature correction of ECa data was required .
Soil sampling design: The field was sampled according to a grid sampling design at 104 locations on a 17 by 10 m grid basis from a representative area of 2.02 ha. Composite soil samples were collected from a radius of 1 m. Soil samples were taken at three depth increments (0-30 cm, 30-60 cm and 60-90 cm) through augering from the marked geo-referenced locations the week following the ECa survey. The samples were analyzed by Central laboratory, Soil Resource Development Institute, Bangladesh.
Soil physical and chemical analysis: Texture was deter mined by Hydrometer method described by Day, 1965. The following USDA size fractions were determined: Sand (>50 μm), Silt (2 - 50 μm) and Clay (<2 μm). The pH was determined by a glass-electrode pH meter in the soil suspension having a soil: water ratio of 1:2.5, after 30 minutes of shaking. Dry combustion method was used for determination of organic matter. Total nitrogen content of soils was determined by the Kjeldahl digestion method. The available P content was determined by the B ray and Kurtz (1945) method. Cation exchange capacity (CEC) was calculated by the methods described by Hendershot and Duquette, 1986 . For determination of Potassium (K+), Calcium (Ca2+) and Magnesium (Mg2+) , ammonium acetate (NH4OAc) extract method was used, and the amounts of K determined by flame emission, and Ca2+ and Mg2+ determined by atomic absorption spectroscopy (AAS) (Knudsen et. al., 1982). Base saturation was calculated as, % Base saturation = [(Ca2+ + Mg2+ + K+)/CEC]*100.
Geostatistical analysis: The data analyses were conducted in three stages: i) Distribution was analyzed by classical statistics (mean, median, maximum, minimum, variance, standard deviation, skewness, kurtosis and coefficient of variation, frequency from histograms and scatter plots). Skewness is considered as the most common form of departure from normality. The exploratory statistical analyses were performed by PASW 18.0 (Predictive Analytics SoftWare) Statistics, ii) to find out the spatial structure of the selected soil properties, variography was used, variograms were calculated and modelled with VARIOWIN 2.2 software (Pannatier, 1996) and iii) kriged maps of spatial distribution of selected soil properties were constructed using SURFER Version 9.2 software (Golden Software, Inc.). Ordinary kriging method was used throughout.
Spatial variation through variography: Geostatistics view soil properties as continuous variables and models these as realizations of a random function or a random process ( Webster, 200 1). To characterize a random function assumptions are limited to the intrinsic hypothesis.
Spatial prediction through Kriging: Kriging is a geostatistical tool for the prediction of the value of a variable at an unsampled location on the basis of sample observations made in its neighbourhood. It is a weighted linear estimator where the weights are derived using the variogram ensuring an unbiased estimation with a minimum estimation error (Webster and Oliver, 1990). Kriging provides a Best Linear Unbiased Estimator (BLUE) (Burrough and McDonnel, 1998). A variety of Kriging algorithms are available, such as ordinary and simple Kriging use the target (primary) variable to make predictions. On the other hand, techniques such as co-kriging use the joint spatial variation of the target variables and densely measured ancillary variables, such as ECa, to improve the prediction accuracy. In this dissertation, ordinary Kriging was used as a common methodology for the prediction of soil variables. The probabilistic interpolators aim to give optimal representation of the stochastic part of the regionalized variable, the local interpolator is extended to a more geostatistical form giving general Kriging equation.
Ordinary Kriging (OK): Ordinary Kriging is the most common type of Kriging used in geostatistics and it serves to estimate a value at a point of a region for which a variogram is known using data in the neighbourhood of the estimation location. However it assumes the mean of the observations to be unknown but locally stationary.