GNSS integrity monitoring requires proper bounding to characterize all ranging error sources. Unlike classical approaches based on probabilistic assumptions, our alternative integrity approach depends on deterministic interval bounds as inputs. The intrinsically linear uncertainty propagation with intervals is adequate to describe remaining systematic uncertainty, the so-called imprecision. In this contribution, we make a proposal on how to derive the required intervals in order to quantify and bound the residual error for empirical troposphere models, based on the refined sensitivity analysis via interval arithmetic. This will contribute to a realistic uncertainty assessment of GNSS-based single point positioning.