The PESHMELBA model simulates water and pesticide transfers at the catchment scale. Its objective is to help the process of decision-making in the common management of long-term water quality. Performing the global sensitivity analysis (GSA) of this type of model is necessary to trace the output variability to the input parameters. The goal of the present work is to perform a GSA, while considering the spatio-temporal nature and the high dimensionality of the model. The output considered is the surface moisture simulated over a two-month period on a catchment of assorted mesh elements (plots). The GSA is performed on the dynamical outputs, rewritten through their functional principal components. Sobol' indices are then estimated through polynomial chaos expansion on each principal component. The analysis differs between the two types of behavior observed in the surface moisture outputs. The hydrodynamic properties of the surface soil have a dominant influence on the average surface moisture. Nonetheless, the parameters describing deeper soil layers influence the output dynamics of those plots where the surface moisture is saturated. We obtain Sobol' indices with high precision while using a limited number of model estimations and considering the model's spatio-temporal nature. The physical interpretation of the GSA confirms and augments our knowledge on the model.