This paper presents an efficient method to perform uncertainty and sensitivity analyses in a cesium adsorption model upstream chained with a pore water composition model. As the number of uncertain input parameters is about twenty for each of the two models, a dimension reduction technique is implemented to build a polynomial approximation of the cesium distribution coefficient in a reduced subspace. Two approaches are tested depending on the water composition and adsorption models are treated as a single block or two separate blocks. In view of assessing the robustness of the approaches, three initial cesium concentrations are considered to explore different regimes of the adsorption model. The interpretation of the linear transformations projecting the original inputs to the reduced coordinates is broadly consistent with the geochemical features of the model. Validation results show that the relative error levels of the surrogate models are around a few percent for both approaches with only one thousand realizations of the chained model. Global sensitivity analysis highlights that the variance of the cesium distribution coefficient is overwhelmingly governed by the adsorption model. Still, this conclusion is nuanced when considering the whole cumulative distribution function for which the interaction effects between the two models account for a fifth.