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In this paper, we quantify the impact of different formulations of model discrepancy propagation in coupled multidisciplinary systems. Standard Gaussian process formulations of model discrepancy leave room for interpretation when incorporated into coupled system analyses. The objective of this work is to analyze resulting coupling variable distributions under different assumptions regarding these model discrepancy interpretations. The goal is to identify efficient, implementation independent, methods and rationale for the rigorous propagation of uncertainty in coupled systems. We demonstrate our methodology on an aerostructural wing analysis problem.