Quantification of temporal variability of vertical soil moisture movement through an unsaturated zone

•An unsaturated zone is treated as a nonlinear soil moisture reservoir.•The effective infiltration is considered as the single random input in time.•The recharge to the aquifer is considered as the single random output in time.•The infiltration-soil moisture process is described by a nonlinear functional series.•The temporal variability of soil moisture movement is assessed.