#### 3.1. Measurement Bias from Environmental Fluctuations

The response of an ABCD operating outdoors with a High Efficiency Particulate Air (HEPA) filter on its inlet for a two-week period is shown in

Figure 4. The output voltages (

Figure 4a) are clearly dependent on ambient conditions, oscillating in sync with the diurnal trends in temperature and relative humidity (

Figure 4c). These output voltage oscillations are likely the result of the optical electronics’ temperature sensitivity. The LEDs are rated to dim 0.3% for every 1 °C temperature rise [

44], which is approximately what is observed (0.1 V reduction relative to a 1.5 V baseline with a 20 °C temperature increase), suggesting that the temperature sensitivity of the LEDs plays a major role. Photodiode sensitivity (the voltage output per watt of incident light intensity) decreases by 0.01% for every 1 °C temperature rise [

45], and likely also contributes to the diurnal voltage oscillations. It should be noted that the ABCD measures the temperature of the air flowing through the optical cell, but it is assumed that the electronics nearby are at a similar temperature. Expected variations in the optical thickness of the fibrous filters due to sorption and desorption of water vapor from the sampled air are opposite to the observed voltage oscillations, suggesting that RH sensitivity is smaller than the temperature dependence of the optical electronics.

Although the sample and reference output voltage oscillations track one another closely, the rates of voltage change over time are not identical. Consequently, reported BC concentrations are not zero, as would be expected for a sensor sampling particle-free air. Rather, BC concentrations exhibit a diurnal trend typically in the ± 0.3 μg m

^{−3} range (

Figure 4b, black), with a mean absolute error (MAE) on the order of 0.1 μg m

^{−3} and a two-week average BC concentration of −0.003 μg m

^{−3}. BC concentrations computed using only the output from the photodiode monitoring the sample filter are much larger, in the ± 2 μg m

^{−3} range (

Figure 4b, gray), which illustrates that computing BC concentrations using both the reference and sample signals significantly reduces, but does not completely eliminate, the sensor’s sensitivity to environmental conditions. If ambient BC concentrations are much larger than ±0.3 μg m

^{−3}, then further compensation may not be necessary. However, in many locations, ambient BC concentrations are comparable to 0.3 μg m

^{−3} and, thus, temperature compensation is employed to further reduce the environmental sensitivity.

#### 3.2. Temperature Compensation

The temperature response of each ABCD optical cell was determined by operating each instrument outdoors with a HEPA filter on the inlet for at least 24 h. In all cases, sample and reference photodiode voltage outputs display a highly linear dependence on the recorded cell temperature. In order to quantify this temperature dependence, the relative change (

RC) in each photodiode’s output voltage is calculated as:

where

V(

t) is the photodiode voltage (V) at time

t, and

V(0) is the first voltage logged during the particle-free sampling event. In

Figure 5,

RC is plotted as a function of sensor temperature for three ABCD optical cells, and linear regression factors (slope, intercept, and R

^{2}) are shown. The temperature sensitivities of an optical cell’s sample and reference channels (i.e., the slopes of the linear regressions, m

_{smpl} and m

_{ref}) are often not equal. Therefore, the ratio of these slopes (m

_{smpl}/m

_{ref}, hereafter referred to as “slope ratio”) is often either greater than or less than unity. For example, ABCD 1 has a slope ratio of 0.57, indicating that the sample voltage output is less temperature sensitive than the reference. Consequently, as the temperature fluctuates over time, the sample and reference voltage outputs do not change at an equal rate. The result is non-zero BC measurements, as the effect of changing temperature on the sample voltage output is not exactly compensated by the effect of changing temperature on the reference voltage output. For example, the optical cell referenced in

Figure 4 has a slope ratio of 0.89, and the reference voltage output significantly reduces, but does not completely eliminate, the environmental influence on reported BC concentrations.

In Equation (2), the linear regression equations for each photodiode output are set equal to Equation (1), except that the voltage change is now evaluated relative to the temperature-compensated voltage:

where

V_{comp}(

t) is the temperature-compensated voltage output (

V),

T(

t) is the sample flow temperature (°C), and

m (°C

^{−1}) and

b are the slope and intercept of the linear regression, respectively. Rearranging Equation (2) yields an equation that allows the photodiode voltage,

V(

t), to be compensated using real-time temperature measurements:

BC concentrations calculated using the temperature-compensated sample and reference voltage outputs from Equation (3) are generally significantly less sensitive to temperature fluctuations.

We observed considerable variability in the temperature sensitivity of optical cells (e.g., as illustrated in

Figure 5), likely because of variations in the LEDs, photodiodes, and related circuitry. Consequently, we evaluated the temperature sensitivity and determined the linear regression coefficients in Equation (3) uniquely for each individual ABCD optical cell. The slope and intercept for both photodiode outputs are stored on SD cards assigned to each optical cell. The SD card is inserted into the ABCD’s AUX board, and the respective linear regression coefficients are uploaded to the MCU to compensate BC measurements in real time as a function of measured temperature.

In

Figure 6, temperature-compensated (TComp) responses are shown in addition to the uncompensated (Raw) responses for the ABCD shown in

Figure 4. Throughout the trial, temperature-compensated voltage outputs steadily maintain their initial values (

Figure 6a) and temperature-compensated BC concentrations (

Figure 6b) exhibit a diurnal trend typically in the ±0.1 μg m

^{−3} range (compared to ±0.3 μg m

^{−3} when uncompensated) with an MAE of 0.02 μg m

^{−3} (compared to 0.1 μg m

^{−3} when uncompensated).

To further illustrate the implementation of the temperature compensation method, both uncompensated and temperature-compensated BC concentrations are shown in

Figure 7 for five ABCDs with HEPA-filtered inlets. The slope ratios for these cells range from 0.57 to 1.47 and uncompensated BC concentrations ranged between ±2 μg m

^{−3}. As shown in

Figure 7a, uncompensated diurnal BC oscillations and corresponding MAE values are largest for ABCD optical cells whose slope ratios are farthest from unity (cells 1 and 5) and smallest for the cell with a slope ratio of 1.00 (cell 3). Furthermore, as a consequence of the temperature dependence illustrated in

Figure 5, BC oscillations for optical cells with slope ratios less than unity (cells 1 and 2) are opposite those for optical cells with slope ratio greater than unity (cells 4 and 5).

As shown in

Figure 7b, all temperature-compensated BC concentrations are very close to the true zero, with MAE values on the order of 0.02 μg m

^{−3} irrespective of the optical cell’s slope ratio. BC concentrations and MAE for cell 3 whose slope ratio is ~1 are essentially unaltered by the procedure, as expected.

Figure 8 summarizes the zero response of all 150 ABCD optical cells manufactured in this study. MAEs of uncompensated and temperature-compensated BC concentrations are plotted against the absolute deviation of each cell’s slope ratio from unity (|m

_{smpl}/m

_{ref} − 1|). The figure illustrates that uncompensated MAE generally increases proportionally with increasing absolute slope ratio deviation from unity. In contrast, temperature compensation works to significantly improve performance: all ABCD optical cells report BC concentrations near zero such that, across the fleet of 150 cells, the temperature-compensated MAE averages 0.016 ± 0.001 μg m

^{−3} (mean ± 90% confidence interval).

#### 3.3. Field Validation

Following acquisition of temperature compensation parameters for all optical cells, ABCDs were operated outdoors atop the Bay Area Air Quality Management District’s near-roadway monitoring station (see

Figure A1).

Figure 9 shows time series of uncompensated and temperature-compensated BC concentrations for five ABCDs with optical cell slope ratios ranging from 0.66 to 1.69. BC concentrations reported by the aethalometer (Magee Scientific, Model AE33) housed inside the monitoring station are also shown for comparison.

Uncompensated BC concentrations deviate more notably from the AE33 reference for ABCD optical cells with slope ratios that are significantly offset from unity (

Figure 9a). Uncompensated BC concentrations include erroneous negative values over substantial portions of the sampling period. For ABCD optical cells with slope ratios of 0.66 and 1.69, the corresponding mean absolute percent error (MAPE) in BC concentration relative to the AE33 (~70%) is about three times larger than the MAPE for the ABCD optical cell with a slope ratio of 1.02 (23%). Furthermore, optical cells with slope ratios less than unity tend to overestimate BC concentrations when the temperature increases (and vice-versa). Temperature compensation reduces measurement bias (

Figure 9b). The five ABCDs have temperature-compensated MAPEs ranging from 22% to 31%, and negative BC measurements are nearly eliminated.

Figure 10 shows the precision and accuracy of these ABCDs during the field evaluation period. The precision of each ABCD is evaluated relative to mean BC concentrations from the fleet of five ABCDs, while accuracy is evaluated relative to the AE33. Sensor precision (compare

Figure 10a,b) and accuracy (compare

Figure 10c,d) are much improved through the temperature compensation method. Temperature-compensated data are less scattered and have lower MAPEs. For example, uncompensated BC concentrations from optical cells with slope ratios farthest from unity have MAPEs of ~70% relative to both the ABCD fleet average and the AE33 reference. In contrast, most temperature-compensated ABCDs have a precision error of ~8% and accuracy error of ~25%. However, temperature-compensated hourly data from ABCD 5, whose optical cell slope ratio is 1.69, still contain a few negative BC measurements that significantly increase both the precision and accuracy error. This suggests that the method presented does not fully compensate the temperature dependence of optical cells with slope ratios that deviate excessively from unity. On the other hand, the precision and accuracy of ABCD 3, whose optical cell slope ratio is 1.02, are essentially unaltered by temperature compensation, as expected.

The field performance of 105 ABCD optical cells is plotted in

Figure 11 as a function of the slope ratios’ absolute deviation from unity (|m

_{smpl}/m

_{ref} − 1|). The precision and accuracy of uncompensated BC concentrations diminish as the slope ratio increasingly deviates from unity, but temperature compensation generally improves measurement performance throughout. Similarly to the ABCDs featured in

Figure 10, the temperature-compensated fleet-average precision and accuracy MAPEs of the 105 ABCD optical cells are 9.2 ± 0.8% and 24.6 ± 0.9%, respectively (mean ± 90% confidence interval).

Uncompensated and temperature-compensated ABCD BC concentrations are ~15% lower than those reported by the AE33 (see linear regressions in

Figure 10c,d), and even after temperature compensation, the MAPEs of most ABCDs are above 20% relative to the AE33 (

Figure 11b). This bias may be related to the value chosen to convert ABCD optical absorption to BC mass concentration (i.e., the mass attenuation coefficient in Equation (A2)) or the so-called “loading artifact”. The loading artifact causes underestimation of BC concentrations with increased loading of the sample filter [

41,

42,

43]. Whereas the AE33 periodically changes its filter and incorporates a software algorithm to correct for the loading artifact [

46], the ABCDs in this study are operated using only a single set of filters for each trial, and the data presented here have not been adjusted for a loading artifact.