Temperature and relative humidity are measured using a Met One (Met One Instrument, Grants Pass, OR) model 083E sensor located inside an aspirated radiation shield. Wind speed and direction are measured with a Met One model 010C lightweight three-cup anemometer, and a Met One model 020C lightweight airfoil vane. The temperature and relative humidity sensors are positioned in a meteorological tower 4 m above the ground. The anemometer and vane are located at the top of the 10 m meteorological tower. All sensors are calibrated annually. The ultraviolet radiation, over the wavelength range from 320 to 400 nm (UV-A), is measured with a Solar Light UVA model 501 radiometer that outputs its data in mW cm-2. The UV-A measurements used in this paper are not made at the “supersite”, but are an average from six stations across the city (see Fig. 1): Merced (MER), Montecillo (MON), Pedregal (PED), San Agustin, (SAG), Santa Fe (SFE) and Tlalnepantla (TLA).

Ozone is measured by ultraviolet photometry (Teledyne API model 400E, San Diego CA). The NOx, defined operationally, is measured by chemiluminescence following conversion in a heated molybdenum NO2-to-NO converter (Teledyne-API model 200E, San Diego, CA). The CO is measured by a gas filter correlation, non-dispersive infrared analyzer (Teledyne API model 300E, San Diego, CA). The gas analyzers are tested every 2 weeks with a known standard and calibrated quarterly.

PM2.5 is measured with a TEOM 1400A ambient particulate monitor 8500C FDMS (Thermo Scientific, Franklin, MA), with a BGI VSCC PM2.5 cyclone inlet for size selection. PM2.5 hourly concentrations are reported at local temperature and pressure conditions. The TEOM is operated at a temperature of 35 ∘C in order to measure dry particle mass.

The eBC, Bscat and Babs are derived from the PAX, a sensor that evolved from the Photoacoustic Soot Spectrometer (PASS) developed at the University of Nevada (e.g., Arnott et al., 2005, 2006; Moosmüller et al., 2009) and commercialized by Droplet Measurement Technologies (Chan et al., 2011; Holder et al., 2014; Liu et al., 2014; Nakayama et al., 2015). The PAX performs simultaneous measurements of aerosol scattering and absorption coefficients using a single diode laser modulated at approximately 1500 Hz. The 375, 405, 532 and 870 nm single wavelength versions of the instrument have identical measurement cells and differ only in a few optical components. The PAX whose measurements are reported in the current study uses the 870 nm laser.

Figure 2 shows a diagram of the PAX measurement cells. The nominal 1 LPM sample flow first passes a solenoid pinch valve (not shown) that allows for periodic filter sampling to determine the instrument background signals. The lengths of sample tubing between the filter line and sample line are the same to provide the same acoustic properties along both channels. The sample flow passes into an acoustically insulated enclosure containing the sample cells, where it is then split, making opposing 90 degree turns into the scattering and absorption measurement regions. The sample is exhausted through two ports at the ends of the absorption cells before being filtered and pumped out of the instrument. The flows are controlled using critical orifices and do not affect the calculated absorption and scattering coefficients, which depend only on the properties of the sampled particles and geometry of the measurement region. Sample flow does affect the residence time of particles in the measurement cells, which is approximately 7 s.

The absorption cell includes a 0.635 cm diameter tube 10.8 cm long, called the resonator. A small microphone located at the top of the resonator detects the pressure perturbations induced by the heating of the light-absorbing particles. The microphone signal is passed through a fast Fourier transform circuit that gives the peak power at the resonator frequency, which is calculated based on the resonator geometry, air pressure, temperature and dew point temperature measured in the cell. The microphone raw pressure signal (pmic) is converted to the raw light absorption coefficient using the equation babs,raw=pmicAπ2fPLγ-1Qcos⁡ϕraw, where A is the resonator cross section, f is the calculated resonator frequency, PL is the laser power, γ is the ratio of isobaric and isochoric specific heat for air, Q is the calculated resonator quality factor (also calculated from measured cell pressure, temperature and dew point temperature) and ϕraw is the phase raw absorption signal relative to the phase of the laser power signal plus the phase correction. The phase correction accounts for the difference between the speed of light and sound that translates to a phase shift in the acoustic pressure measured by the microphone relative to the modulated laser power incident on the absorbing material. See Arnott et al. (2005) for more details on applying phase corrections to photoacoustic measurements of light absorption coefficients.

The raw absorption and scattering signals must be corrected for background absorption and scattering signal in the cell to give the desired light absorption and scattering coefficients due to the sampled aerosol particles. Background absorption arises from absorbing gases (not important for the 870 nm version of the PAX but relevant for shorter wavelength versions), absorption by the cell and particles deposited to the cell surfaces (especially the cell windows) and acoustic and electrical noise that contributes to signal at the resonator frequency. The background scattering is not sensitive to acoustical noise, but is affected by electrical noise and light scattering from the cell surfaces and particles deposited to the cell surfaces and windows. The background signals are measured simultaneously at a user-specified interval, typically once every 10 min, by passing the sample air through a filter before it enters the measurement cell. The background measurement period occurs after a 20 s flush with particle-free air to mix sampled particles out of the measurement cells and lasts 30 s, followed by another 20 s flush before regular measurements resume. Background absorption and scattering values are saved in the data record and automatically subtracted from the measured raw signals to give the absorption and scattering coefficients in real time. Typically the background drift is small (< 3 Mm-1) compared to the observed scattering and absorption coefficients, especially in more polluted environments like Mexico City. Background drift occurs due to small changes in the sampling environment, such as temperature and relative humidity. Over longer periods of time, backgrounds are affected by contamination on the cell windows and minor changes in the optical alignment. Cleaning and re-alignment of the system can be necessary when the magnitude of the background drift becomes comparable to changes in the scattering and absorption values on the timescales of the filtered background measurements. Post-processing of background values to apply a linearly interpolated correction (using background measurements before and after a sample point) provides a better correction for background drift compared to the standard background correction performed in real time by the instrument.

The PAX absorption and scattering sensitivity depends on the sampling conditions and laser power in the cell. The laser power in turn depends on the quality of the alignment and level of contamination on the cell windows. The scattering sensitivity is mainly limited by the small measurement volume and variability in the particle sample stream. The absorption sensitivity is mainly limited by electrical and acoustical noise that cannot be distinguished from the true particle signal. While noise in the sampling environment can reach the acoustic cell through vibrations in the case, a bigger factor is acoustical noise transmitted through the sampling line directly into the resonator. Helmholtz notch filters can be inserted into the sampling line to filter noise at the measurement frequency in environments with high acoustic noise and relatively low aerosol loadings. In Mexico City, however, these were not necessary because the PAX was installed in a temperature- and noise-controlled environment with minimal acoustic noise.

Figure 3 shows the corrected absorption coefficients and Allan variance plot for the absorption signal measured during overnight sampling of filtered air with an 870 nm PAX. The instrument performed a background measurement approximately every 10 min, which corrected for the instrument drift on timescales longer than 10 min, so the variance is only shown up to a 5 min averaging interval. At the highest temporal resolution of 1 s, the variance was 0.14 Mm-1, equivalent to about 0.03 µg m-3 black carbon using the factory-applied mass-specific absorption cross section (MAC) of 4.74 m2 g-1. This is the value at 870 nm, derived using the λ-1 correction to the 7.5 m2 g-1 recommended by Bond and Bergstrom (2006). The three-sigma sensitivity for 1 s averaging was 1.1 Mm-1 (0.23 µg m-3 BC). The values are a “best case” scenario where the environmental conditions were very stable (running overnight in an empty laboratory) and because the particle filter also acted to block acoustical noise from the sampling environment from reaching the cell. We have observed 1 s variance in PAX absorption signals ranging from ∼ 1–5 Mm-1 depending on the sample environment.

The PAX uses a wide-angle (6–174∘) integrating reciprocal nephelometer to measure the light-scattering coefficient. The scattering detector consists of a Teflon diffuser placed in front of a photodiode (Fig. 2). The scattering measurement responds to all particle types regardless of chemical makeup, mixing state, or morphology.

The PAX is calibrated through a two-step process by first introducing high concentrations of purely light-scattering particles followed by high concentrations of partially absorbing particles to the measurement cells (Arnott et al., 2000; Nakayama et al., 2015). The concentrations must be high enough to allow direct measurement of the extinction coefficient (bext) from the reduction in laser power measured at the laser power monitor (Fig. 2) using Beer's law: bext=-1llnII0 106[Mm-1], where I is the average laser power measured when the high concentration of particles is being sampled, I0 is the average laser power immediately before and after the high concentrations are introduced to the cell and l is the path length of the laser beam through the entire optical cavity (scattering region and absorption region) between the two windows, which for the PAX is 0.354 m.

Ignoring truncation in the nephelometer cell, an error that is of order 6 % (Nakayama et al., 2015), the measured extinction coefficient equals the measured scattering coefficient for purely scattering particles (e.g, nebulized, dry ammonium sulfate). The relationship between the measured extinction and scattering coefficients are fit using a linear regression giving a calibration factor for the scattering measurement. Introducing calibration particles that have non-zero absorption means the measured extinction equals the now-calibrated scattering coefficient plus the absorption coefficient. Subtracting the measured scattering coefficient from the extinction coefficient determined from Beer's law gives the absorption coefficient, which can be regressed against the measured absorption coefficient to obtain a second calibration factor for the absorption cell. One major uncertainty introduced by this method of calibration is it assumes the measured particles have similar scattering-phase functions so the truncation error in the scattering cell cancels.

The PAX measures the light-scattering and absorption coefficients, Bscat and Babs, directly using the in-line nephelometer and photoacoustic technique, respectively. The single scattering albedo (SSA), defined as the ratio of Bscat to the sum of Bscat and Babs (extinction coefficient) is also derived and recorded, along with the eBC that is derived from the Babs as described previously.

The PAX was operated with a PM2.5 cyclone particle separator on the inlet in order to remove larger particles and the particle stream was also dried using a diffusion drier in order to minimize measurement effects at high relative humidity (e.g., Lewis et al., 2009; Murphy, 2009) and also to provide the scattering coefficients of dry particles only. The PAX was connected to the cyclone by 3/8” conductive tubing. Transmission losses are insignificant at the flow rate of 1 Lpm, based on calculations made using the Aerocalc program developed by Baron and Willeke (2001).

The uncertainty in the measured Bscat is ca. ±10 % due to the accuracy with which the instrument can be calibrated, the truncation error and aerodynamic losses in the inlet system that brings the ambient air into the sample cavity. The uncertainty in the measured Babs is ca. ±20 %. This uncertainty stems primarily from the accuracy of the calibration but the losses in the inlet system also contribute to the overall accuracy. Given the range of possible MAC values that depend on the composition and size distribution of the black carbon (Bond and Bergstrom, 2006), the uncertainty in the MAC is of order 50 % and hence the derived eBC from Babs is approximately 55–60 %. In addition, Bond et al. (2006) show that BC coated by non-light-absorbing material can cause a lensing effect that leads to enhanced absorption, perhaps as much as a factor of 1.5; hence, the derived eBC mass concentrations may be as much as 50 % higher than the actual concentration of BC due to this coating effect.

The average, median, daily average maxima and the quantiles values at 5, 25, 75 and 95 % were calculated for CO, NOx and O3 and are shown in Fig. 5a–c by season, workdays and Sundays. The box and whisker plots show median (horizontal line within the box), 25 % quantile (bottom of box), 75 % quantile (top of box), 5 % quantile (bottom whisker) and 95 % quantile (top whisker). In addition the average of the daily maxima are shown with the red filled circles. The same information for eBC, PM2.5, Bscat and SSA is shown in Fig. 6a–d, respectively. The values used to generate these graphs are tabulated in Table 1.

Table 2 summarizes the average and standard deviations about the average maximum daily values tabulated by season, workdays and Sundays. A Student's t test was applied to the differences and the significance was evaluated at a confidence level of P < 0.10, i.e., that there is less than a 10 % probability that the observed differences are due to chance. For each season and each measured parameter, the significance of the differences between the workday and Sunday values was tested using the hypothesis that the average values were from the same population. This hypothesis was rejected when the value of T>|1.7|, the critical value for P < 0.10 with the pooled degrees of freedom of the two samples in each comparison. In the Table, underlined numbers i had Sunday values significantly smaller than for the workdays, i.e., the null hypothesis that they were from the same population was rejected. Likewise, the numbers in bold were the cases when the Sunday values exceeded the workday values.

Using the same approach the difference in the average maximum values between each of the three seasons was tested (last three columns in Table 1). The underlined numbers indicate a significant decrease in a parameter value from one season to the next and the numbers in bold highlight significant increases. The value in parentheses in each of these cells is the computed value of the t statistic.

Median concentrations of CO and NOx (Fig. 5a and b, respectively) do not significantly change with season, whereas there is a clear increase in O3 (Fig. 5c) during the WDS compared to either the RS or CDS. The maximum concentrations for all three of the gas species increase significantly (Table 2) in the dry seasons (cold and warm) compared to the RS. This increase is seen for workdays as well as Sundays. A significant increase from the CDS to the WDS is only observed in the O3 concentrations, due to the larger actinic flux late in the spring. Of note is that the maximum CO concentrations on Sundays actually decrease between the CDS and WDS (numbers in underlined italics in Table 2).

A “weekend effect” is observed for CO, NOx and O3. The maximum CO and NOx concentrations decrease between workdays and Sundays by more than 30 % during all three seasons (Table 2). As discussed by Stephens et al. (2008) the lack of a decrease in the O3 concentrations on Sundays is a “weekend effect” because with the decrease in VOCs (CO is a surrogate for VOCs), the O3 was expected to decrease as well. As detailed by Stephens et al. (2008) for Mexico City in particular, there are several possible mechanisms responsible for this behavior; however, the one that was discussed as most plausible is related to the inhibition of O3 by NOx under VOC-limited conditions. The production of O3 is positively correlated with VOC emissions and negatively correlated with NOx. Since the CO (VOC) and NOx are both decreasing, there is a balancing effect on O3 production, i.e., less production from VOC reactions but less inhibition from NOx

Figure 6a and b display the same grouping of comparisons as Fig. 5 but for the mass concentrations of PM2.5 and eBC. The median PM2.5 concentrations increase between RS and CDS and between CDS and WDS. In contrast, the median concentration of eBC does not show a seasonal trend. When evaluating the seasonal trends of the maximum concentrations, both the PM2.5 and eBC have much larger values in the dry seasons than during the rainy season; however, unlike the PM2.5 that also shows a significant increase between the CDS and WDS, the eBC actually decreases slightly between these two seasons, but not significantly (Table 2). There is a clear “weekend effect” that is seen in the maximum concentrations drawn in Fig. 6, and highlighted in Table 2. The concentrations decrease from workdays to Sundays over all seasons; however, unlike the eBC whose decreases are statistically significant over all seasons, the PM2.5 decreases are only significant during the RS and CDS.

The seasonal impacts on the optical properties of the aerosol particles are illustrated in Fig. 6c and d that show Bscat, and SSA, respectively. The figures suggest that the differences between seasons of Bscat and SSA are small; however, as seen in Table 2, there are statistically quantifiable differences, although for Bscat, only the increase from RS to WDS is significant. The SSA values are much more sensitive to season, even though the median values do not appear that different. The SSA decreases from the RS to CDS but increases from the CDS to WDS. A decrease in the SSA can be a result of decreases in Bscat or from increases in Babs, since SSA is directly proportional to Bscat and inversely proportional to Babs; however, since Bscat is seen to be relatively insensitive to seasonal changes, the changes with SSA are primarily a result of the seasonal sensitivity of Babs, i.e., changes in the eBC. It should be noted that other aerosols like certain organics, as well as dust, will also absorb light, but at shorter wavelengths than the 870 nm used by the PAX. Hence, the majority of the absorption measured in this study is by BC.

Figure 7a–c show the differences in the average daily UV-A radiation (Fig. 7a), temperature (Fig. 7b) and relative humidity (RH, Fig. 7c). The UV radiation is averaged over the daylight hours from 10:00 to 16:00 local standard time (LST), whereas the temperature and RH are hourly averages. In Fig. 7b and c the red, green and blue curves differentiate the trends by season: WDS, RS and CDS, respectively. There is on average 30 % more UV radiation in the CDS and WDS than during the RS. The WDS temperature (Fig. 7b) is generally about 5∘ warmer than either the RS or CDS, except in the early mornings just before sunrise when the RS and WDS are the same. The WDS is always much drier throughout the day (Fig. 7c) than during the other seasons while the humidity during the rainy season is 30–50 % higher than the dry seasons. As will be further discussed below, the seasonal radiation, temperature and humidity difference are principal factors that underlie the associated seasonal differences in gas and particle properties.

An examination of the average hourly properties of the pollutants, differentiated by season and by workday/Sunday, provides a different perspective than the comparison of just the daily quantiles and maxima that are shown in Figs. 5 and 6. All of the pollutants have daily cycles that are linked to the traffic patterns, photochemical processes and boundary layer depth (vertical mixing with clean air). Figure 7a–c illustrate these cycles for CO, NOx and O3, respectively. The solid and dashed lines separate the measurements into the workdays (Monday–Saturday) and Sunday. The red, green and blue curves represent the seasons as described for Fig. 7b and c.

The average hourly CO and NOx (Fig. 8a, b) have very similar patterns over all three seasons. The maximum concentrations are reached between 07:00 and 08:00 LST during the RS and WDS and between 08:00 and 09:00 in the CDS, respectively. A secondary, broader maximum is seen near midnight, formed after the concentration begins increasing after the minimum at 16:00. As was illustrated in Fig. 5a, b, the maximum CO and NOx values during the RS are ca. 40 % lower than the dry seasons; however, when comparing the rRS with the WDS, this difference appears to be dominant only from about 04:00 to 11:00 LST. Outside of this time period the concentrations are nearly the same. Likewise, after 13:00 LST there is no longer a significant difference in the CO and NOx concentrations in the RS and CDS. This is a result of the manner in which the vertical mixing progresses and the boundary layer depth increases during the three seasons. The shift in the time of the peaks between the CD and other seasons is due to the shift in Mexico from daylight savings time (DST) the first Sunday in November to standard time then back to DST the first Sunday in April; however, the measurement time base does not shift with changes in DST.

In the RS, as discussed previously, the boundary layer growth is accelerated by the vertical motions as convective clouds develop, resulting in much larger updrafts that reach higher in the troposphere than during the dry season. This leads to more rapid dilution of the primary emissions. At the same time, the clouds reduce the solar radiation, hence limiting photolysis and the photochemical reactions that produce O3 (Fig. 8c). In the dry seasons there is also vertical mixing but not as intense as during the rainy season, and it is only due to dry turbulent eddies within the boundary layer that slowly erode the inversion at the top by mixing with the free tropospheric air. There is less O3 during the CDS because the solar zenith angle is larger with subsequent decreased photochemical activity.

The minimum in concentrations at 16:00 LST, and steady increase thereafter, is due to the maximum boundary layer depth in late afternoon (Stull, 1988; Pérez-Vidal and Raga, 1998), followed by its gradual collapse as the solar insolation diminishes and the dilution decreases, while the daytime primary emissions remain more or less constant. There is actually an increase in emissions from traffic during the evening rush hour in Mexico City that contributes to the increase in CO and NOx at night (Edgerton et al., 1999; Schifter et al., 2003)

A “weekend effect” (only Sunday) is also evident during all seasons whereby the maximum concentrations on Sundays are 50–70 % lower than on workdays (See Table 2) regardless of the time of day. Given that the meteorology on Sundays is not expected to differ from workdays, i.e., the boundary layer depth and solar radiation should not be dependent on the day of the week, this decrease over all seasons must be due to decreased, work-related traffic on Sundays.

The hourly average O3 (Fig. 8c) reaches the maximum concentrations between 13:00 and 14:00 LST during the rainy season and between 14:00 and 15:00 LST during the dry periods. Differences in the O3 concentrations between the rainy and cold-dry seasons are only obvious between the hours of approximately 14:00 and 20:00 LST and between 10:00 and midnight LST, when comparing the RS and WDS. The differences in O3 are primarily being driven by the photochemical production of O3. As summarized in Table 1, the CDS maximum O3 is 13 % larger than the RS, whereas the maximum during the warm-dry season is 47 % larger. The impact of available solar radiation on the production of O3 from the precursor gases (NOx and VOCs) can be better understood by comparing measurements of the UV-A that are shown in Fig. 7a. The summer months of June–August are a period with minimum solar zenith angle; yet, as this figure shows, the daily averaged UV-A in the RS is about 20 % less than the CDS and 30 % less than the WDS. Hence, a major fraction of the difference between RS and WDS O3 can be explained by the decreased actinic flux in the RS with the remaining difference due to the increased vertical mixing produced by the cloud formation.

Figure 9a and b display the hourly trends in PM2.5 and eBC where it is seen that there are large differences, not only in the hourly concentrations that vary with season, but the hours during which these PM2.5 mass concentrations peak. These peak hours change with season, although the eBC to a lesser extent. The differences between the rainy and dry season PM2.5 maximum average mass concentrations are 36 and 56 %, respectively, when compared to the CDS and WDS (Table 2). For the eBC, these differences are 38 and 48 %. Whereas the PM2.5 concentrations during the CDS and WDS are always larger than those in the RS, regardless of the time of day, the eBC concentrations in the dry seasons only exceed those during the rainy season from approximately midnight until 12:00 LST. After this time the concentrations are the same on average. This is a reflection of the same atmospheric process that was discussed for CO and NOx, i.e., the difference in vertical mixing between the rainy and dry seasons. There is much greater dilution of the eBC during the rainy season, since clouds are responsible for the vertical mixing.

The daily cycles in PM2.5 have seasonal patterns that are much more distinctive than either the gases (Fig. 8a–c) or the eBC. There is a slight shift in the hour of maximum concentrations for the eBC, between 06:00 and 07:00 for the RS and WDS, and between 07:00 and 08:00 for the CDS. This shift is only a result of the change from daylight savings time (DST) in November and April, so that in the CDS the major commuter traffic begins an hour later relative to the clock used on the RAMA data that doesn't change to DST. The PM2.5 reaches maximum concentrations between 07:00 and 08:00, 09:00 and 10:00 and 10:00 and 11:00, respectively, for the WDS, CS and RS. The large shift in the peaks of the daily cycles is the result of both the atmospheric dynamics, i.e., boundary layer growth, and the chemical processes behind the formation and growth of the particles that make up the PM2.5.

There is a very distinctive “weekend effect” displayed in the eBC and PM2.5 concentrations. As summarized in Table 2, the maximum eBC concentrations decrease by more than 50 % from workdays to Sundays during all seasons. As can be observed in Fig. 9b, the difference is distinct over all hours of the day but is the most predominant between around 05:00 to 18:00. One of the major differences in primary emissions of BC between workdays and Sundays is that the use of large, diesel-burning trucks and machinery is much less on Sundays. Although vehicular traffic in general is much less on Sundays, since combustion of diesel fuel is the major contributor of BC emissions in the city, the large decrease in BC is linked more to the decrease in diesel combustion than gasoline. To support this assertion, looking only at the dry season to remove any effects of precipitation, the average eBC to CO ratio on workdays was 3.6 µg m-3 of eBC to 1.0 ppm of CO. This compared to the Sunday ratio that is 2.1 µg m-3 of eBC to 1.0 ppm of CO; hence, the eBC decreases by a much larger percentage than the CO.

The hourly trends in the optical properties of the aerosol particles, Bscat and SSA, are shown in Fig. 10a and b, respectively. The maximum Bscat falls between 09:00 and 10:00 LST during the WDS and between 10:00 and 11:00 LST in the RS and CDS. Unlike the particle mass concentrations of PM2.5 and eBC, there are no distinct differences from season to season in the maximum values. The differences are instead seen in the morning hours before reaching the maximum then again in the afternoon. During both of these periods the dry season values are about 30 % larger than the rainy period. In the same way that the trends in PM2.5 are a balance between the processes that drive particle growth and the dynamic processes that dilute the number concentration, likewise the trends in the scattering are driven by complex interactions. The intensity of light scattering and the PM2.5 mass concentrations are strongly correlated because both are proportional to particle concentration and size. The Bscat and PM2.5 values peak at the same time periods during the three seasons (Figs. 9a and 10a).

The SSA reaches its minimum value in the morning between 06:00 and 07:00 LST in the WDS and RS and between 07:00 and 08:00 LST in the CDS. As mentioned previously, the SSA appears to be much more sensitive to changes in eBC, i.e., light absorption, than in Bscat. Since the minimum in the SSA corresponds to the maximum in the eBC this further reinforces the sensitivity of SSA to changes in the eBC concentration in this environment. The changes with season of the SSA do not mirror those of eBC. Whereas the maximum eBC in the dry seasons was significantly larger than the rainy season (Table 2), the trends in the SSA are more complicated with the RS and WDS values being nearly equal until they separate after midday at 13:00 LST, with the RS SSA decreasing while the WDS maintains an almost constant value. These trends can be best understood by comparing the trends in PM2.5, the parameter that is correlated with Bscat, and eBC and observing that while the eBC decreases rapidly after its morning maximum during all seasons, the PM2.5 is decreasing much more slowly, due to photochemical reactions leading to the growth of pre-existing particles (Baumgardner et al., 2004) and to the secondary production of particles (e.g., de Gouw et al., 2009; Herndon et al., 2008). This illustrates that whereas the minimum in SSA observed during the morning is being driven by the presence of particles with eBC, the afternoon SSA is being driven mainly by changes in non-absorbing particles represented by Bscat.

In addition to deducing the potential relationships between co-pollutants by comparing the hourly trends in Figs. 8, 9 and 10, these links can be further investigated by calculating the cross correlations to highlight the temporal shifts that may change with season and might offer additional evidence of how photochemical and thermodynamic processes drive the daily trends in gas concentrations and particle properties.

Figures 11–13 are correlations between pairs of pollutants, as a function of the lag time that is varied from -10 to +10 h, in 10 min increments. The vertical black dashed line is drawn at the zero lag time and the horizontal black dashed line is drawn at the crossover point from positive to negative correlation. The colors of the lines denote the season using the same coding as previous figures. Figure 11a illustrates the relationship between CO and NOx and indicates that these two pollutants are highly correlated (R=0.9) with no lag time, i.e., they are being produced at the same time and likely by the same sources. The correlation between O3 and NOx (Fig. 11b), shows that their highest correlations are at lag times of -8, -7.5 and -7 h, for the WDS, CDS and RS, respectively. The maximum correlation at negative lag indicates that O3 is linked to the NOx that was formed approximately 8 h earlier, an expected correlation. These lag times are just another way of quantifying the time differences between the peaks in NOx and O3 that were seen in Fig. 8b and c. The 1 h difference between the CDS and WDS is caused by the change in DST as was explained earlier for the daily trends.

There is additional information contained in these cross correlations by evaluating the time from maximum to zero correlation. The time at which the correlation coefficient crosses the zero point is a measure of a characteristic timescale, referred to as the integral timescale, that is related to the rate at which atmospheric processes produce, dilute or remove the pollutants. This integral timescale indicates how quickly two pollutants are being de-correlated by dilution and mixing with other atmospheric components. For example, there is a single, season-independent integral timescale for the CO and NOx correlation, 4–5 h, whereas for the O3 and NOx there are three timescales: 5, 4.5 and 4 h, respectively, for the CDS, WDS and RS.

The eBC and CO concentrations are highly correlated (R>0.8) with no lag as seen in Fig. 12a, indicating that their sources are located in the same region. The high correlation between CO and BC mass (derived by an alternative method) in Mexico City was already reported by Baumgardner et al. (2000, 2002). The integral timescales are 6, 7 and 8.5 h during the WDS, RS and CDS, respectively.

The cross-correlation between the eBC and PM2.5 (Fig. 12b) presents a more complicated picture that is related to the complex relationship between the black carbon that is produced by primary emissions and particle mass that is a mixture of primary and secondary processes. Looking at the average maximum values in Table 2, we see that eBC is approximately 20 % of the mass of PM2.5. Hence, the good correlation at zero lag for all seasons represents the fraction of the PM2.5 that is made up of BC. The trends in the correlation coefficients rapidly diverge as the lag time increases. This reflects the secondary processes that either produce new particles or lead to the increase in mass of existing particles. These secondary processes can be aqueous, photochemical or a combination of both, so the rate at which particles grow will depend on the temperature, relative humidity, pH and UV radiation flux. Since BC is a primary particle onto which organics, sulfates or nitrates can condense, a correlation between BC and PM2.5 will remain. As the BC particle evolves and takes on a coating or mixture of other substances, when it is measured by the PAX it will continue to absorb energy and be identified as eBC, i.e., there is still a “memory” of the original particles that are being emitted even over very long lag times. As Fig. 12b illustrates, the integral timescales exceed 10 h during all seasons. The much larger integral timescale of the rainy season is most likely due to the higher humidity during this period that promotes aqueous-phase reactions and particle growth. During the dry seasons, the secondary processes are only related to photochemical reactions. These interpretations are purely speculative without corroboration using a chemical growth model, which is beyond the scope of this current study.

The correlations between the particle optical properties (Bscat and SSA) and the eBC and PM2.5 are displayed in Fig. 13a, b. The relationship between Bscat and PM2.5 that was discussed previously is highlighted in Fig. 13a, showing a correlation coefficient > 0.8 at zero lag time. The very long integral timescale is a result of the same complex processes that led to the greater than 10 h timescales for the eBC and PM2.5 (Fig. 12b). Figure 13b underscores the earlier discussion about the sensitivity of the SSA to eBC. The negative correlation is due to the inverse relationship between SSA and eBC. The correlations are higher in the dry months than in the rainy season because of the additional contribution to light scattering by the particles that are formed under conditions of high humidity in the RS. The separation in the integral timescales is also linked to the relative rate by which the Bscat increases as secondary processes promote particle growth in the different seasons.