Peak-fitting and integration imprecision in the Aerodyne aerosol mass spectrometer: effects of mass accuracy on location-constrained fits

The errors inherent in the fitting and integration of the pseudo-Gaussian ion peaks in Aerodyne high-resolution aerosol mass spectrometers (HR-AMSs) have not been previously addressed as a source of imprecision for these or similar instruments. This manuscript evaluates the significance of this imprecision and proposes a method for their estimation in routine data analysis. In the first part of this work, it is shown that peak-integration errors are expected to scale linearly with peak height for the constrained-peak-shape fits performed in the HR-AMS. An empirical analysis is undertaken to investigate the most complex source of peak-integration imprecision: the imprecision in fitted peak height, σ[subscript h]. It is shown that the major contributors to σ[subscript h] are the imprecision and bias inherent in the m/z calibration, both of which may arise due to statistical and physical non-idealities of the instrument. A quantitative estimation of these m/z-calibration imprecisions and biases show that they may vary from ion to ion, even for ions of similar m/z. In the second part of this work, the empirical analysis is used to constrain a Monte Carlo approach for the estimation of σ[subscript h] and thus the peak-integration imprecision. The estimated σ[subscript h] for selected well-separated peaks (for which m/z-calibration imprecision and bias could be quantitatively estimated) scaled linearly with peak height as expected (i.e. as n[superscript 1]). In combination with the imprecision in peak-width quantification (which may be easily and directly estimated during quantification), peak-fitting imprecisions therefore dominate counting imprecisions (which scale as n[superscript 0.5]) at high signals. The previous HR-AMS uncertainty model therefore underestimates the overall fitting imprecision even for well-resolved peaks. We illustrate the importance of this conclusion by performing positive matrix factorization on a synthetic HR-AMS data set both with and without its inclusion. In the third part of this work, the Monte Carlo approach is extended to the case of an arbitrary number of overlapping peaks. Here, a modification to the empirically constrained approach was needed, because the ion-specific m/z-calibration bias and imprecision can generally only be estimated for well-resolved peaks. The modification is to simply overestimate the m/z-calibration imprecision in all cases. This overestimation results in only a slight overestimate of σ[subscript h], while significantly reducing the sensitivity of σ[subscript h] to the unknown, ion-specific m/z-calibration biases. Thus, with only the measured data and an approximate estimate of the order of magnitude of m/z-calibration biases as input, conservative and unbiased estimates of peak-integration imprecisions may be obtained for each peak in any ensemble of overlapping peaks