Abstract Remote sensing, as a powerful tool for monitoring atmospheric phenomena, has been playing an increasingly important role in inverse modeling. Remote sensing instruments measure quantities that often combine several state variables as one. This creates very strong correlations between the state variables that share the same observation variable. This may cause numerical problems resulting in a low convergence rate or inaccurate estimates in gradient-based variational assimilation if improper error statistics are used. In this paper, two criteria or scoring rules are proposed to quantify the numerical robustness of assimilating a specific set of remote sensing observations and to quantify the reliability of the estimates of the parameters. The criteria are derived by analyzing how the correlations are created via shared observation data and how they may influence the process of variational data assimilation. Experimental tests are conducted and show a good level of agreement with theory. The results illustrate the capability of the criteria to indicate the reliability of the assimilation process. Both criteria can be used with observing system simulation experiments (OSSEs) and in combination with other verification scores.