To study the peculiarities of anomalous consolidation processes in saturated porous (soil) media in the conditions of salt transfer, we present a new mathematical model developed on the base of the fractional-fractal approach that allows considering temporal non-locality of transfer processes in media of fractal structure. For the case of the finite thickness domain with permeable boundaries, a finite-difference technique for numerical solution of the corresponding one-dimensional non-linear boundary value problem is developed. The paper also presents a fractional-fractal model of a filtration-consolidation process in clay soils of fractal structure saturated with salt solutions. An analytical solution is found for the corresponding one-dimensional boundary value problem in the domain of finite thickness with permeable upper and impermeable lower boundaries.

The paper presents the results of computational experiments for evaluating the impact of different evapotranspiration assessment methods usage on the accuracy of soil moisture dynamics simulation for the conditions of sprinkling irrigation. We consider a differential one-dimensional model of moisture transport stated in terms of water head which uses as an initial data the estimates of evapotranspiration according to the methods of Ivanov, Shtoiko, Penman-Monteith and SEBAL. The differential moisture transport model was discretized using the finite-difference scheme. Its unknown parameters values were found by solving an inverse problem using the metaheuristic particle swarm optimization algorithm. We perform water head modeling accuracy assessment using different methods of evapotranspiration evaluation along with their linear combination. The Ivanov’s method was found to be the most accurate in the conditions of soybean growing in the south of Ukraine under sprinkling irrigation while linear combination of four considered methods gives an additional increase of accuracy by 6.5%.