= Chromatographic baseline-area uncertainty
<Chromatographic baseline-area uncertainty> quantifies uncertainty in the integrated baseline subtracted when assigning a chromatographic <extracted-ion chromatogram peak area>. For an <extracted-ion chromatogram baseline> $b(t)$ over fixed limits $t_1,t_2$, let $B=\int_{t_1}^{t_2}b(t)\,dt$. The baseline's uncertainty is shared across time whenever fitted parameters or other common inputs are shared.
For sampled times with integration weights $w_i$ and baseline estimates $b_i$,
$$
B\approx\sum_iw_ib_i,\qquad
u_B^2\approx\sum_i\sum_jw_iw_j\operatorname{Cov}(b_i,b_j).
$$
The weights include the actual sampling intervals and chosen integration rule. This is correlated-input <uncertainty propagation>, not an assumption that each drawn baseline point is independently uncertain.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[§5.2, covariance law for a function of correlated inputs.]{ref}
An original constant-baseline example uses 100 equal intervals of $0.1\,\mathrm{min}$ and one common fitted baseline with <standard uncertainty>0.2 signal units. Its integrated uncertainty is $10(0.2)=2$ signal-unit minutes. Treating those 100 appearances of the same fitted quantity as independent would instead give $\sqrt{100}(0.1)(0.2)=0.2$, underestimating uncertainty tenfold. More sampling points do not average away a shared offset.
For total recorded area $P$ and assigned peak area $Q=P-B$,
$$
u_Q^2\approx u_P^2+u_B^2-2\operatorname{Cov}(P,B).
$$
With stipulated $u_P=0.5$, $u_B=0.4$ and <correlation coefficient>0.6, the result is $u_Q=\sqrt{0.17}\approx0.412$ area units, compared with 0.640 under independence. The appropriate covariance depends on how the trace and its baseline were estimated; it cannot be selected to obtain a preferred uncertainty.
Changing integration limits or choosing a different baseline form can create additional effects beyond parameter uncertainty within one fixed model. Inspect neighboring peaks and baseline regions, and record the fitted model and boundary choices. A precisely computed <extracted-ion chromatogram peak area> can still depend on an unsuitable baseline model.
Back to article page
