On the distribution of scaling hydraulic parameters in a spatially anisotropic banana field

When modeling soil hydraulic properties at field scale it is desirable to approximate the variability in a given area by means of some scaling transformations which relate spatially variable local hydraulic properties to global reference characteristics. Seventy soil cores were sampled within a drip irrigated banana plantation greenhouse on a 14×5 array of 2.5 m×5 m rectangles at 15 cm depth, to represent the field scale variability of flow related properties. Saturated hydraulic conductivity and water retention characteristics were measured in these 70 soil cores. van Genuchten water retention curves (WRC) with optimized m (m≠1−1/n) were fitted to the WR data and a general Mualem-van Genuchten model was used to predict hydraulic conductivity functions for each soil core. A scaling law, of the form νi=αiνi*, was fitted to soil hydraulic data, such that the original hydraulic parameters νi were scaled down to a reference curve with parameters νi*. An analytical expression, in terms of Beta functions, for the average suction value, hc, necessary to apply the above scaling method, was obtained. A robust optimization procedure with fast convergence to the global minimum is used to find the optimum hc, such that dispersion is minimized in the scaled data set. Via the Box-Cox transformation P(τ)=(αiτ−1)/τ, Box-Cox normality plots showed that scaling factors for the suction (αh) and hydraulic conductivity (αk) were approximately log-normally distributed (i.e. τ=0), as it would be expected for such dynamic properties involving flow. By contrast static soil related properties as αθ were found closely Gaussian, although a power τ=3/4 was best for approaching normality. Application of four different normality tests (Anderson-Darling, Shapiro-Wilk, Kolmogorov-Smirnov and χ2 goodness-of-fit tests) rendered some contradictory results among them, thus suggesting that this widely extended practice is not recommended for providing a suitable probability density function for the scaling parameters, αi. Some indications for the origin of these disagreements, in terms of population size and test constraints, are pointed out. Visual inspection of normal probability plots can also lead to erroneous results. The scaling parameters αθ and αK show a sinusoidal spatial variation coincident with the underlying alignment of banana plants on the field. Such anisotropic distribution is explained in terms of porosity variations due to processes promoting soil degradation as surface desiccation and soil compaction, induced by tillage and localized irrigation of banana plants, and it is quantified by means of cross-correlograms.