The VI's Hg atomic fluorescence signal processing method parses the Tekran^® analyzer's serial data output (RAWDUMP format; see Sect. S1 in the Supplement) using text delimiters associated with each component (Figs. S1 and S2 in the Supplement).

At the start of an analysis, the VI computes the overall mean baseline standard deviation, σbl, for all samples in the data file to be analyzed. The baseline standard deviation for each sample is first calculated as the 10-point (1 s) running mean of the baseline measurements made from 1 s after the start of the AF signal recording interval to 2 s prior to the approximate start of the Au trap desorption cycle (i.e., the value of the “BL time” parameter in Table S1 in the Supplement). The value of σbl is then calculated from the values for all individual samples.

For each sample analysis cycle, the VI carries out the following operations:

The “raw data” string (Fig. S1) is converted to an array of 10 Hz AF signal values.

At the end of an analysis, an output data file is created, which contains, among other parameters, the baseline-slope-corrected Hg TD peak height (step 10) for each sample in the data file that was processed.

Hereafter I refer to three different configurations of the VI: VIm,m when the peak start and end times are both identified manually, VIm,a when only the peak start time is identified manually, and VIa,a when the peak start and end times are both identified automatically. I abbreviate the Tekran^® peak integration method as “the Tekran^® method”.

The VIm,a and VIa,a methods are “initialized” by fitting Eq. (1) to the Hg thermal desorption peaks recorded for a pair of calibration gas analysis cycles (i.e., one A SPAN and one B SPAN; example fits are shown in Fig. 1 and in Fig. S4; see Sect. S1 for further details on cycle-type flags). S(t)=A×eb×t+Soffset Here, S(t) is the time-dependent 10 Hz Hg fluorescence signal along the tail of the Hg TD peak, A is the peak amplitude (which is approximately equal to the peak height, H), b is the decay constant, Soffset is the baseline offset (i.e., the difference between lim[S(t)]t→∞ and zero), and t is expressed in units of deciseconds (ds). The fit includes 150 S(t) values, starting with the peak maximum, Smax⁡ (Figs. 1 and S4). The values of Soffset and A are constrained to the baseline minimum, Smin⁡, and Smax⁡-Soffset, respectively. (For the data shown in Fig. 1, the values of Soffset and A are approximately equal to 70 and 170 mV, respectively.)

The two decay constants (one for each Au trap) are the key parameters derived from the initialization procedure (see Sect. 2.3). I estimate the uncertainty in each b value from the linear sum of two terms: (1) the relative difference between unity and the slope of a linear regression fit to a plot of the calculated versus measured Hg TD peak decays (Figs. 1b and S4b) and (2) the 95 % confidence interval in the slope of the fit. For the data shown in Fig. 1, the uncertainty in b is estimated to be 9 %.

During initialization, peak start times, tstart, are also calculated for the pair of calibration gas analysis cycles. For this purpose, the VI defines tstart as the first 10 Hz Hg fluorescence signal value in a series of seven consecutively increasing signal values. If the operator chooses (via a control on the VI's front panel) to automatically define the Hg TD peak start times, the values of tstart calculated during initialization are assigned (paired by Au trap identity) to all samples in the data file to be processed.

It is necessary to define each Hg thermal desorption peak's end time, tend, within the interval during which the Tekran^® analyzer's Hg atomic fluorescence signal is recorded (38.9 s in Figs. 1a and S4a). Therefore, for each sample the VI defines tend as the time at which S(t) decays to a value equal to, or less than, a fraction, f, of the amplitude, ASPAN (derived as in Sect. 2.2), determined from a calibration gas analysis cycle on the same Au trap: Stend≤f×ASPAN+Soffset. Substituting the right-hand side of Eq. (2) for S(t) in Eq. (1) and solving for t(=tend) yields an analytical expression for the upper-bound value of tend: tend=ln⁡f×ASPANAi×b-1≅ln⁡f×ASPANHi×b-1. Here, Ai and Hi are the TD peak amplitude and the initial peak height (from step 6 in Sect. 2.1), respectively, of the sample for which the baseline-slope-corrected peak height is to be quantified. The partial equality in Eq. (3) reflects the facts that ASPAN/Ai≅HSPAN/Hi and ASPAN≅HSPAN. The Au-trap-dependent value of the decay constant, b, is derived as in Sect. 2.2.

The value of f is chosen such that tend is ≥ 0 at the smallest expected value of Hi, which the VI approximates as σbl (Sect. 2.1). The upper-bound value of f is estimated separately for each Au trap by solving Eq. (3) for f, with tend=0 and Hi=σbl: f=σblASPAN. The Au-trap-dependent f values are then averaged prior to application in Eq. (3). I estimate the uncertainty in f to be twice the standard deviation in the mean for the two Au traps. Uncertainty in the value of Hi is estimated to be equal to twice the baseline standard deviation calculated in step 9 of Sect. 2.1. Uncertainty in the automatically derived value of tend, δtend, is estimated by propagating uncertainties in b, f, and Hi through Eq. (3) (see below).

It is necessary to further constrain tend such that for large TD peaks (e.g., those recorded for SPAN samples) the automatically determined value of tend is at least 10 ds before the upper-bound time, tn, of the interval during which the instrument's Hg AF signal is recorded. The VI therefore defines tend as the smaller of the results of Eq. (3) and tn-10, where n represents the number of AF signal values recorded (n=389 in Figs. 1a and S4a). A minimum value of 10 ds is also prescribed for tend such that for very small TD peaks the automatically determined peak end does not occur at or before the peak max time (e.g., when f≥Hi/ASPAN in Eq. 3). (See Sect. S3 for further details.)

I evaluate the performances of the VIm,a and VIa,a methods by applying both methods to laboratory data collected with two Tekran^® analyzers (one model 2537A and one model 2537B). One dataset is processed for each analyzer. The test dataset collected with the 2537A instrument is shown in Fig. 2. (The test dataset for the 2537B instrument is shown in Fig. S3.)

I consider the manual definition of the Hg thermal desorption peaks (the VIm,m method) to be the benchmark for signal processing accuracy, and I assess the accuracies of the VIm,a and VIa,a methods by comparing Hg sample loadings derived from both methods with loadings derived from the VIm,m method. A similar comparison is used to evaluate the accuracy of the Tekran^® method. The performances of all methods are further evaluated and compared based on the Hg limits of detection (LODs) they achieve.

For Hg loadings derived from the Tekran^® method, HgTekran, I define absolute bias as HgTekran-Hgbenchmark, where Hgbenchmark represents loadings derived from the VIm,m method. I define relative bias as 100×(HgTekran-Hgbenchmark)/Hgbenchmark. As illustrated in Fig. 3 (and Fig. S5), Hg loadings derived using the Tekran^® method tend to be biased low, with the relative bias becoming more negative with decreasing loading. I present in Table 1 relative bias values from Fig. 3b at several discrete Hg sample loadings (analogous results for the 2537B dataset are presented in Table S2). The corresponding Hg concentrations (ng m-3) under typical operating conditions for the Tekran^® analyzer (5 L sample volumes) are also shown. My results are consistent with those of Swartzendruber et al. (2009) and Slemr et al. (2016) but also demonstrate that the Tekran^® method can produce significant low biases (≥ 5 %; see Tables 1 and S2) at tropospheric background GEM and THg concentrations (∼ 1 to 2 ng m-3; sample loadings of 5–10 pg under typical Tekran^® operating conditions).

To further characterize the performance of the Tekran^® method, Fig. 4 compares Hg atomic fluorescence baselines calculated by the Tekran^® method and by my VI-based peak height determination methods for samples with Hg loadings of approximately 0.5, 1, 2, and 4 times the estimated ∼ 0.8 pg LOD achieved with the Tekran^® method (see below). (See Sect. S6 for details on how I reproduced the baselines calculated by the Tekran^® method.) Figure 4 illustrates the tendency of the Tekran^® method to truncate the Hg thermal desorption peaks. The peaks tend to become more severely truncated as they become smaller, and as a result, the relative biases in the corresponding Hg loadings tend to become more negative as the loadings decrease, as shown in Figs. 3b and S5b (see also Fig. 2 in Slemr et al., 2016).

It is possible that the bias introduced by the Tekran^® method can be made smaller by calibrating at loadings more similar to the loadings in the samples of interest. The measurements in Figs. 3a and S5a are calibrated with SPAN loadings > 10 times higher (see Figs. 2 and S3, respectively). Calibrating the measurements in Fig. S5a using the external SPANs (Fig. S3; loadings > 5 times higher) yields the linear regression equation (as in Fig. S5a) y=0.96(1)x-0.09(5) pg. The slope of the latter equation is closer to unity (though not significantly) than that of the equation derived from Fig. S5a.

Table 2 presents Hg LODs for the Hg fluorescence signal processing methods and datasets I tested. The nominal Hg limit of detection of the Tekran^® analyzer is 0.5 pg (see Sect. S7 for further details). However, some Hg thermal desorption peaks in the 2537A dataset are undetected by the Tekran^® method for Hg loadings ≤ 0.8 pg (Figs. 2 and 3a). My results suggest that the actual Hg LOD achieved with the Tekran^® method is ∼ 60 % higher than the nominal value. By comparison, the LOD achieved with the VIm,m method (estimated as twice the standard deviation of blank samples, n=62) is 0.10 pg.

For the 2537B dataset, all Hg thermal desorption peaks are detected by the Tekran^® method for Hg loadings > 0.2 pg (Figs. S3 and S5), suggesting the LOD is ∼ 60 % lower than the nominal value. The lower Hg LOD achieved with the Tekran^® method when applied to the 2537B dataset is attributable to the hardware modifications that were made to the 2537B instrument to increase its signal-to-noise ratio (Sect. 2). The 0.085 pg LOD achieved with the VIm,m method is 56 % lower than the Tekran^®-based LOD (Table 2).

By comparison with the Tekran^® method, the VIa,a method usually identifies the Hg thermal desorption peak baseline with good accuracy, even at Hg loadings near to or below the LOD achieved with the Tekran^® method (Fig. 4). As a result, most Hg loadings derived from the VIa,a method are quite accurate (Figs. 2 and 5; Table 1). For samples with Hg loadings below the estimated 0.8 pg LOD of the Tekran^® method, the mean absolute and relative unsigned biases in the loadings derived from the VIa,a method are 0.028 ± 0.005 pg and 15 ± 3 %, respectively (n=78). The biases are very small and much smaller in magnitude than those for the Tekran^® method (estimated at -0.80 pg and -100 %). Based on the equations of the linear regressions shown in Figs. 3a and 5a (Hg loadings ≤ 10 pg), the VIa,a method achieves ≥ 94 % reduction in absolute unsigned bias in calculated Hg loadings when compared with the Tekran^® method.

The Hg LOD achieved with the VIa,a method is 0.12 pg (estimated as twice the standard deviation of blank values; n=62). That value is 20 % higher than the LOD achieved with the VIm,m method but 85 % lower than the LOD achieved with the Tekran^® method (Table 2). Similarly, the width of the residual distribution in Fig. 5c is 78 % narrower than that in Fig. 3c, which reflects the improved analytical precision achieved with the VIa,a method in comparison with the Tekran^® method.

Evaluation of the VIa,a method as in Fig. 5 for the 2537B dataset (Fig. S6, Table S2) yields the linear regression equation y=1.015(2)x-0.017(8) pg (r2=0.9998, n=132). For samples with Hg loadings below 0.8 pg, the observed mean absolute and relative unsigned biases in the loadings derived from the VIa,a method are 0.031 ± 0.007 pg and 33 ± 9 %, respectively (n=41). The VIa,a method yields a larger relative bias when applied to the 2537B dataset than when applied to the 2537A dataset. However, absolute unsigned biases are equivalent (at the 95 % confidence interval) for the two datasets. Based on the equations of the linear regressions shown in Figs. S5a and S6a, the VIa,a method achieves ≥ 82 % reduction in absolute unsigned bias in calculated Hg loadings when compared with the Tekran^® method. The Hg LOD is 0.14 pg (Table 2), which is 59 % higher than the value achieved with the VIm,m method but 31 % lower than the value achieved with the Tekran^® method. The VIa,a method appears to yield a comparable improvement in analytical precision over the Tekran^® method when applied to the 2537A and 2537B datasets (the width of the residual distribution in Fig. S6c is 72 % narrower than that in Fig. S5c).

The VIa,a method poorly identifies the start of the Hg thermal desorption peak for some blank samples with the lowest Hg loadings. As a result, the Hg TD peak height and the calculated Hg loading tend to be underestimated for those samples (Figs. 2 and S3).

I developed the VIm,a method as a compromise between the Hg TD peak definition accuracy achieved with the VIm,m method and the data processing speed achieved with the VIa,a method. (Peak height determination for a single sample requires from < 1 s with the VIa,a method to several seconds for the VIm,m method; the data processing time for the VIm,a method is approximately half that for the VIm,m method.) Comparison of the VIm,a and VIa,a results in Fig. 2 (and Fig. S3) shows that defining tstart manually instead of automatically yields more accurate measurements for samples with the lowest Hg loadings.

Evaluation of the VIm,a method as in Fig. 5 yields the linear regression equation y=1.001(1)x+0.004(3) pg (r2=0.99998, n=152). Comparison between the latter equation and that of the regression in Fig. 5a suggests that biases in Hg loadings derived from the VIa,a and VIm,a methods are not significantly different over the range of loadings in the 2537A dataset (see also Table 1). However, biases in Hg loadings derived from the VIm,a method are lower at low loadings than those determined for the VIa,a method (Sect. 3.2): for samples with Hg loadings below 0.8 pg, the mean absolute and relative unsigned biases in the loadings derived from the VIm,a method are 0.012 ± 0.003 pg and 6 ± 1 %, respectively (n=78). The estimated 0.10 pg Hg LOD achieved with the VIm,a method is equivalent to that achieved with the VIm,m method (Table 2).

The VIm,a method performs consistently better for the 2537B dataset than does the VIa,a method. The equation of the linear regression (as in Fig. 5a) is y=1.005(1)x+0.009(5) pg (r2=0.99994, n=132). For samples with Hg loadings below 0.8 pg, the observed mean absolute and relative unsigned biases in the loadings derived from the VIm,a method are 0.010 ± 0.003 pg and 6 ± 2 %, respectively (n=41). The estimated LOD achieved with the VIm,a method is 0.10 pg and falls between the LODs achieved with the VIm,m and VIa,a methods (Table 2).

To test the sensitivity to initialization parameters of Hg loadings derived from the VIa,a and VIm,a methods, I recalculated those loadings after making a series of modifications to the method initialization parameters. After each modification I recalculated the parameters of the Hg regression (e.g., Fig. 5a). The modifications tested for the 2537A dataset (described further in Tables S3 and S4) include shifts in tend by ±δtend (as defined in Sect. 2.3), shifts in tstart to the values determined (as described in Sect. 2.2) for the second pair of SPAN samples in Fig. 2 (applicable only to the VIa,a method), and initialization of the VI using the second pair of SPAN samples. (Details on the sensitivity tests applied to the 2537B dataset are described in Tables S5 and S6.)

The above modifications result in insignificant changes (at the 95 % confidence interval) to the bias parameters derived (as in Fig. 5a) for the VIa,a method and the 2537 dataset (Table S3). Two sensitivity tests applied to the VIa,a method and the 2537B dataset result in significant changes (at the 95 % confidence interval) to the calculated bias parameters (Table S5). Results obtained with the VIa,a method therefore appear to be sensitive to initialization parameters in some cases, although signal processing uncertainties remain quite low and well below those estimated for the Tekran^® method (Table 2). It is possible that a large shift in tstart for SPAN samples over the course of an analysis would increase the sensitivity of the VIa,a method to initialization parameters. Results obtained with the VIm,a method are insensitive (at the 95 % confidence interval) to initialization parameters (Tables S4 and S6).

I estimate signal processing uncertainties in the Hg thermal desorption peak heights derived from the VIm,m method to be equal to twice the mean baseline standard deviation (σbl, Sect. 2.1), corresponding with a Hg loading of 0.053 pg for the dataset in Fig. 2 (0.030 pg for the dataset in Fig. S3). I estimate signal processing uncertainties in the Hg loadings derived from the Tekran^®, VIa,a, and VIm,a methods as the sum of the biases in those methods (derived as in Fig. 3) and the resulting increase (relative to the VIm,m method) in the Hg limit of detection (Table 2). For the VIa,a and VIm,a methods, I estimate a conservative threshold uncertainty value of ±2σbl.

Signal processing uncertainty attributable to my VIa,a method, as applied to the 2537A dataset, is estimated to be within ±[0.2 % + 0.053 pg]. (The first term in the latter expression represents the slope of the regression in Fig. 5a; the second term represents 2σbl, which in this case is larger than the sum of the 0.000 ± 0.006 pg intercept of the fit in Fig. 5a and the 0.02 pg difference in Hg LODs achieved with the VIa,a and VIm,m methods). Estimated signal processing uncertainty attributable to the VIm,a method is also within ±[0.2 % + 0.053 pg]. By comparison, signal processing uncertainty attributable to the Tekran^® method is within ±[1 % + 1.2 pg]. The above uncertainty results, together with estimated Hg LODs and analogous results for the 2537B dataset, are summarized in Table 2. For both test datasets, signal processing uncertainties estimated for my VI-based methods are significantly lower than those for the Tekran^® method. Signal processing uncertainty ranks as follows for the VI-based methods: VIm,m< VIm,a ≤ VIa,a.