We focus on the way temporal distributions of key components of the water cycle are influenced by typically uncertain parameters embedded in a Land Surface Model. We rest on a joint analysis of multiple global sensitivity metrics to provide a comprehensive assessment of the ranking of the relative importance of uncertain factors of various origins on the hydrological system response. The latter is rendered in terms of the temporal dynamics of transpiration, evaporation, and groundwater recharge. The NIHM (Normally Integrated Hydrological Model) modular Land Surface model is applied to simulate realistic field conditions (in terms of, e.g., climate, vegetation, and soil type) associated with two watersheds in the Vosges region (France) across a one-year period. These watersheds are characterized by similar climatic conditions while being associated with differing soil types and vegetation. Uncertain model parameters we consider comprise monthly values of albedo and leaf area index, vegetation-related parameters, as well as parameters related to the soil types associated with the litter layer and root zone. Four diverse sensitivity indices are used to quantify impacts of uncertain model parameters on the whole probability distribution or given statistical moments of the density function of model outputs. Our results document that the strength of the relative importance of model parameters depends on the statistical moment considered. Evaporation is directly influenced by the energy flow through the canopy and by the parameters associated with the top litter layer. As one could expect, transpiration appears as mainly influenced by the vegetation characteristics and by albedo that influences the incoming radiation. Groundwater recharge is influenced only by a very limited number of model parameters. It mainly depends on soil-related parameters and is unexpectedly not sensible to any of the vegetation parameters considered, except the root layer thickness and the intercept.