Introducing a mathematical model for calculation of subsurface drains spacing using fractional - order derivatives

One of the limitations of Boussinesq equation is that its parameters (e.g., hydraulic conductivity) are scale-dependent. In this work, a fractional Boussinesq equation was obtained by assuming power-law changes of flux in a control volume and using a fractional Taylor series. Unlike Boussinesq equation, the parameters of fractional Boussinesq equation are constant and scale-invariant. The linear form of fractional Boussinesq equation was solved by using spectral representation method and an analytical mathematical model was derived to calculate subsurface drains spacing. The optimal values of parameters of mathematical model developed in this study and Glover-Dumm's model were estimated from inverse modeling. In the inverse methodology, water table data between two subsurface drains and the optimisation method of Bees algorithm was used. The accuracy of obtained model was investigated using water table data between the two subsurface drains and was compared to Glover-Dumm's model. The results indicated that the mathematical derived in this study predicts the water table profile between two subsurface drains more exactly than Glover-Dumm's model.