Our analysis focuses on data from the TRACER campaign, organized by the U.S. Department of Energy, from October 2021 through September 2022. The primary measurements were made in the Greater Houston Area, Texas. Throughout the campaign, the ARM Mobile Facility (AMF-1) operated continuously at La Porte, Texas shown in Fig. 1 (Jensen et al., 2025). Additional aerosol and meteorological data were collected by deploying Texas A&M University's Rapid Onsite Atmospheric Measurement Van (ROAM-V) alongside radiosonde launches at multiple locations spanning coastal and inland environments (Fig. 1) on selected days when isolated convection was expected (Rapp et al., 2024; Thompson et al., 2025a, b; Lei et al., 2025). As shown in Fig. 1, the coastal site is in Galveston, Texas, while the inland sites include locations in Hempstead and Hockley, Texas.

In this work, we employ a method to integrate micropulse lidar and ground-based aerosol measurements to retrieve aerosol vertical distributions corrected for aerosol hygroscopic growth (Chen et al., 2025). Interested readers are referred to Chen et al. (2025) for methodological details. In brief, the procedure first applies an inversion to lidar measurements of attenuated backscatter to obtain an hourly time-averaged cloud-free aerosol backscatter coefficient profile. Next, we use the aerosol hygroscopicity parameter κ, along with Mie scattering theory, to account for aerosol hygroscopic growth at increased humidity measured by the radiosonde, allowing us to convert the retrieved ambient backscatter coefficient to its dry equivalent. The aerosol hygroscopicity parameter κ used for AMF-1 retrieval was estimated from Aerosol Chemical Speciation Monitor (ACSM) aerosol composition measurements collected during the TRACER campaign, with κ values provided by Maria A. Zawadowicz (personal communication, 2025), and are shown in Fig. S1 in the Supplement. The κ values used for TAMU retrieval were estimated from CCN concentration and aerosol size distribution (Chen et al., 2025). This step is crucial because lidar measures optical signals affected by aerosol hygroscopic growth. As aerosols take up water, they grow in size, scatter more light, and increase the lidar backscatter signal without increasing aerosol concentration. Correcting for the aerosol hygroscopic growth effect prevents overestimation of aerosol concentration at altitudes with higher relative humidity. Finally, we calculate the surface aerosol number concentration by integrating the measured aerosol number size distribution and scale this concentration vertically by the ratio of the dry backscatter at each altitude to that near the surface. No standard temperature and pressure (STP) normalization is applied, and all aerosol number concentrations are reported per unit ambient air volume at each altitude. This scaling assumes that the surface aerosol number size distribution is representative aloft. Houston aircraft measurements show that aerosol concentrations and size distributions differ among urban and industrial plumes (Brock et al., 2003; Lance et al., 2009). Such vertical variability cannot be resolved by the single wavelength lidar and remains a source of uncertainty in the retrieved aerosol concentration profiles.

Following Chen et al. (2025), uncertainty in the retrieved aerosol concentration profile was estimated by repeating lidar retrieval and humidity correction with different aerosol lidar ratios, calibration scattering ratios, κ values, and aerosol refractive indices. A geometric standard deviation of 1.5 was used to define the κ sensitivity range by multiplying and dividing the central κ value by 1.5. Temporal variability in the surface aerosol concentration was included using the relative standard error of the mean (SEM) calculated from the condensation particle counter measurements during each retrieval period. This relative SEM was applied to the surface aerosol concentration and propagated into the profile uncertainty. The range of resulting profiles was taken as the uncertainty. This range reflects only the retrieval parameters and surface-concentration variability considered here and should not be interpreted as a complete confidence interval or as indicating high confidence in the retrieved aerosol concentration profile.

Figure 2 shows a typical micropulse lidar measurement and aerosol profile retrieval result at the AMF1 site on 4 August 2022 from 17:00 to 18:00 UTC. The retrieved aerosol profile (Fig. 2c) exhibits an approximately exponential decrease from the surface through the lowest 1 km, then remains relatively uniform up to ∼ 2 km before sharply transitioning to a clean background concentration aloft.

From the retrieved aerosol profiles, we typically observe high near-surface concentrations, with a steep decrease immediately above the surface, a more gradual decline aloft, and then a sharp transition to low background concentrations in the free troposphere. To capture this behavior, we developed a fitting function (Eq. 1) to parameterize the aerosol vertical profile data when no long range transported aerosol is present at upper altitudes, and aerosols primarily originate from near surface sources. 1X(r)=X0-Xf1+f⋅1+fe-rγ1+rrmrmk+Xf where:

r: vertical range from the lidar (km)

Equation (1) provides a parameterization for aerosol concentration that decreases from the higher concentrations fixed near the surface to the cleaner air aloft through a single S-shaped transition. It allows for flexible control over the key observable features of the profile as shown in Fig. 3. To arrive at this equation, we define the transition zone as the altitude range over which aerosol concentration drops most rapidly from a well-mixed lower layer to the cleaner background aloft. The transition zone height, rm, represents the midpoint of the transition zone and is obtained by fitting Eq. (1) to measured aerosol vertical distributions. Although rm can coincide with the top of the planetary boundary layer, we use it here strictly as a metric of aerosol profile rather than as a direct boundary layer height estimate. In Eq. (1), X0 controls the aerosol concentration at the surface, Xf represents the cleaner background concentration aloft, and k constrains how rapidly the aerosol concentration changes within the transition zone. The variables γ and f affect how aerosol concentration decreases with height below the transition zone. The parameters rm and k are later compared with boundary layer height and potential temperature gradients to examine how boundary layer structure relates to aerosol vertical distribution.

In this study, γ is fixed at 0.3 to improve fit stability and reduce parameter trade-offs. Because γ and f both affect the profile curvature below the transition zone, allowing both parameters to vary can produce similar fits from different parameter combinations. Fixing γ reduces this trade-off, thereby providing more stable estimates of f and other parameters. To determine a fixed value to use for γ, Eq. (1) was first fitted with γ allowed to vary for all 313 aerosol profiles collected at AMF-1 during the six-month analysis period. The median fitted γ was 0.334, so we selected 0.3 as a representative fixed value near the center of the fitted distribution (Fig. S9a in the Supplement). Fitting Eq. (1) to the same profiles with γ fixed at 0.3 retained high goodness of fit, with a median R2 of 0.980 (Fig. S9b in the Supplement).

While Eq. (1) models the monotonic, surface-anchored profiles typical of cases dominated by local emissions, it cannot represent distinct elevated aerosol layers that are separated from the boundary layer, such as those produced by long-range transport or secondary particle formation aloft. In this study, the parameters of Eq. (1) are constrained by near-surface aerosol measurements together with lidar-derived aerosol profiles. To represent elevated layers observed in the lidar profiles, one or more Gaussian peak terms can be added to Eq. (1). Each Gaussian is centered at the altitude of an observed elevated layer and providing a simple parametric description of that feature. To avoid overfitting, we use as few Gaussian terms as necessary. Elevated layers were identified by visual inspection of the lidar-derived aerosol concentration profiles and were counted only when a distinct local maximum above the surface-connected profile was separated from the lower aerosol layer by a relative local minimum. Specifically for this study, we allow at most two Gaussian terms when elevated layers are apparent. The fitting function with N elevated aerosol layers is given by: 2Xaug(r)=X0-Xf1+f⋅1+fe-rγ1+rrmrmk+∑j=1NAjexp-12r-rc,jσj2+Xf

Equation (2) adds N Gaussian terms to Eq. (1), each representing an elevated aerosol layer centered at altitude rc,j with amplitude Aj and width σj. The value of N was selected as the minimum number of Gaussian terms needed to represent visually distinct elevated layers, with N=0, 1, or 2 corresponding to no elevated layer, one elevated layer, or two elevated layers, respectively. An example profile derived from Eq. (2) with a single Gaussian term is illustrated in Fig. 3f.

Boundary-layer height may contribute to aerosol profile shape and therefore may covary with the fitted parameters in Eq. (1). To compare the aerosol profiles with BLH, we use two BLH products from the Houston observational dataset from Lamer et al. (2024).

The first estimate, referred to as BLH-RiB, is derived from the bulk Richardson number (RiB), which combines virtual potential-temperature stratification and horizontal wind to characterize their influences on turbulent mixing (Stull, 2012). BLH-RiB is assigned to the lowest altitude at which RiB reaches 0.5 (Lamer et al., 2024).

The second estimate, referred to as BLH-LL, follows the potential-temperature approach adapted by Lamer et al. (2024) from Liu and Liang (2010). Each profile is first categorized as convective, stable, or neutral residual according to its near-surface potential-temperature structure. The boundary-layer top is then diagnosed using features appropriate to the identified regime. For convective and neutral-residual profiles, the method uses the increase in potential temperature from near the surface with its vertical gradient. For stable profiles, BLH-LL represents the top of the shallow stable layer, identified from the minimum potential-temperature gradient (Lamer et al., 2024; Liu and Liang, 2010).

The first case on 18–19 May 2022 showcases the evolution of the aerosol vertical profile within a well-mixed boundary layer capped by a strong temperature inversion. The largest normalized relative backscatter (NRB) is found close to the surface, forming a distinct boundary where it transitions to lower NRB around 1 km, above which elevated aerosol layers between 3 and 6 km are also visible (Fig. 4a). Figure 4b more clearly reveals elevated aerosol layers through the depolarization ratio. The aerosol layer below 1 km exhibits a smaller NRB and larger depolarization ratio during the daytime, which mirrors the evolution of surface relative humidity, as shown in Fig. S2 in the Supplement, where the relative humidity decreases from 100 % at nighttime to 50 % in the early afternoon. The larger relative backscatter and smaller depolarization ratios observed near the surface at night are due to greater humidity, causing aerosols to take up water and become larger and more spherical. In Fig. 4b, one elevated aerosol layer can be identified between 1 and 2.5 km, separated from the aerosol layer below 1 km. Relative humidity drops sharply around 1 km (Fig. 5), and aerosol aloft are therefore more likely dry and less spherical, which increases the depolarization ratio. HYSPLIT back trajectories (Fig. S5 in the Supplement) indicate that the low-level and 1–2.5 km layers were transported from over the Gulf of Mexico during the preceding 12–24 h. The pronounced relative humidity dependence of the depolarization ratio in these layers, together with the HYSPLIT results, is consistent with contributions from hygroscopic aerosol, such as sea salt aerosol or water soluble organic aerosol. Elevated aerosol layers between 3 and 6.6 km show large depolarization ratios, with the 5 km layer traced by 24 h HYSPLIT back trajectories to long range free tropospheric transport.

Aerosol, potential temperature, and RH profiles, as well as BLH estimates at different times of the day on 18–19 May 2022 are shown in Fig. 5. The four aerosol profiles throughout the day are similar. For all four profiles, aerosol concentrations are approximately 1500 to 2000 cm-3 near the surface and decrease sharply to less than 500 cm-3 above 1 km altitude. Equation (2) is used to fit to the aerosol vertical profiles (with fit parameters listed in Table S1 in the Supplement). All four potential temperature profiles in Fig. 5 show a strong inversion near 1 km, and BLH-RiB remains near this level throughout the day, closely matching the fitted transition zone height rm. The alignment of the sharp decrease in aerosol concentration with the potential-temperature inversion is consistent with the stable layer limiting vertical mixing and maintaining the observed aerosol stratification. The RH profile also exhibits features that align with the aerosol distributions. Below 1 km, RH reaches around 90 % or higher except in the early afternoon (68.6 % at 17:00–18:00 UTC; Fig. 5b), and it drops sharply near 1 km at the primary aerosol-layer top. This pattern is consistent with boundary-layer turbulent transport shaping both moisture and aerosol distributions. Note that the influence of RH and hygroscopic growth on the aerosol lidar signal has already been accounted for in the retrieval of the aerosol vertical profile (Chen et al., 2025).

As described in Sect. 2.4, BLH-RiB and BLH-LL are based on different measurements and criteria. BLH-RiB is defined using a bulk Richardson-number threshold calculated from virtual potential-temperature and wind profiles, whereas BLH-LL is determined from regime-specific features of the potential-temperature profile alone. While BLH-RiB remains near the ∼ 1 km inversion described above, BLH-LL is much lower, 140 m in the early morning (10:59–11:59 UTC; Fig. 5a) and 320 m around midnight (05:00–06:00 UTC; Fig. 5d), consistent with a shallow nocturnal stable boundary layer near the surface. The two BLH estimates agree more closely in the early afternoon (17:00–18:00 UTC; Fig. 5b) and early evening (23:00–00:00 UTC; Fig. 5c). This separation between the shallow nocturnal BLH and the higher inversion is consistent with the formation of a residual layer. Aerosols that accumulate within the deeper daytime boundary layer often remain suspended above the much shallower nocturnal layer, forming a residual layer at night.

The aerosol vertical profile in this case study is strongly governed by boundary layer processes, with well-mixed near surface layers during the day and residual layering at night. The aerosol profile exhibits sharp stratification near inversion layers, and elevated aerosol layers persist aloft, decoupled from surface influences. The vertical distributions thus highlight the importance of diurnal boundary layer evolution in shaping aerosol structure.

The second case, recorded on 21–22 July 2022, demonstrates the evolution of the aerosol vertical structure during the development and collapse of the daytime boundary layer. Figure 6 shows the 24 h NRB and depolarization ratio measurements from the micropulse lidar, capturing the vertical structure of aerosols and clouds throughout the diurnal cycle. Figure S3 in the Supplement shows the corresponding surface meteorological measurements. As seen in Fig. 6a, shallow cumulus clouds developed during the local morning and extended to just below 2 km by early afternoon (18:00 UTC), marking the growth of the daytime boundary layer, whose top is often associated with boundary layer cumulus cloud top (Stull, 2012). Around 18:00 UTC, surface winds shifted from southwesterly to easterly, accompanied by a sudden increase in RH (Fig. S3), marking a change in near-surface air-mass influence. By late afternoon, around 22:00 UTC, banded and optically thick cirrus moved over the site (shown in Fig. S6 in the Supplement). This coincided with reduced vertical mixing and an early collapse of the mixed layer, as indicated by a decrease in BLH from Fig. 7b to c. An elevated aerosol layer between approximately 2.5 and 4 km is visible in Fig. 6b, which shows larger depolarization ratios in the 0–2 and 2.5–4 km ranges, separated by a layer of smaller depolarization ratio in between. The elevated aerosol layer becomes more distinct in the evening hours and persists into the night. A similar elevated layer between around 2.5 and 4 km is also faintly visible in the backscatter signal of Fig. 6a. The separation between the low-level aerosol layer and the elevated layer indicate possible stratification and limited vertical mixing between these layers during the observation period. HYSPLIT back trajectories (Fig. S7 in the Supplement) show the ∼ 3 km layer arrived from the east along the Gulf Coast, unlike the low-level air mass, indicating the elevated layer is decoupled from the boundary layer and likely has a distinct source, potentially from long-range transport.

Figure 7 presents aerosol vertical profiles, potential temperature, relative humidity, and BLHs at four different times. Surface aerosol concentrations remain consistently large throughout the 24 h period, ranging approximately from 1700 to 2500 cm-3. Equations (1) and (2) are used to curve fit the aerosol vertical profiles, as illustrated in dashed black lines in Fig. 7. The profiles follow an S-shaped decrease in concentration, with the transition zone height rm diagnosed from the fitted curve. One dominant aerosol layer is observed in early morning (11:00–12:00 UTC; Fig. 7a) and early afternoon (17:00–18:00 UTC; Fig. 7b) shown in Fig. 7a and b. In the early morning (11:00–12:00 UTC; Fig. 7a), rm is near 1 km, indicating the nighttime residual aerosol layer. By early afternoon (17:00–18:00 UTC; Fig. 7b), rm rises to just below 2 km as the mixed layer deepens, as indicated by BLH-RiB and BLH-LL, which closely agree and coincide with rm. The potential temperature structure is consistent with this evolution. In Fig. 7a, a modest temperature inversion near 1 km aligns with the sharp drop in aerosol concentration, suggesting limited vertical mixing. In Fig. 7b, the height of the inversion increases, with the inversion occurring just below 2 km, consistent with the deeper mixed layer. Above these heights, aerosol concentrations remain small, with minor aerosol features aloft. As seen in Fig. 7c, in the early evening (22:59–23:59 UTC), both BLH-RiB and BLH-LL dropped to around 0.9 km and coincide with a temperature inversion, consistent with early boundary-layer collapse. However, rm remained elevated at around 2 km, suggesting a decoupling between the BLH and rm as the boundary layer collapsed. At midnight (04:59–05:59 UTC; Fig. 7d), the rm remained around 1 km, while BLH-RiB (0.7 km) and BLH-LL (0.2 km) both fell below rm. The sharpness of the transition zone is also weaker at midnight (04:59–05:59 UTC; Fig. 7d), with the lowest curve fitted k on this day (Table S2 in the Supplement). The diurnal aerosol vertical profile evolution shows that aerosol vertical structure is coupled to the boundary layer during its growth but not its collapse. This phenomenon is typical for the nighttime boundary layer, when the residual layer remains aloft as a new nocturnal boundary layer forms (Bourgeois et al., 2018). Together, the elevated rm after BLH collapse and the weaker nighttime transition indicate that abrupt boundary layer collapse before sunset can decouple the aerosol layer from the surface before the nocturnal boundary layer is fully established. In addition, the disagreement between BLH-RiB and BLH-LL in Fig. 7a and d reflects the different sensitivities of the two BLH diagnostics under stable nighttime conditions.

In addition to the low-level aerosol structure discussed above, elevated aerosol layers between 2.5 and 4 km can be seen in early evening (22:59–23:59 UTC; Fig. 7c) and at midnight (04:59–05:59 UTC; Fig. 7d). These layers remain separated from the lower aerosol layer by a region of lower aerosol concentration, indicating limited merging between the elevated and lower layers during this period. These layers also coincide with a high-RH layer aloft and are bounded by upper-level inversions, consistent with stratification helping maintain vertical separation. While these profiles suggest distinct layers, they cannot entirely rule out some degree of downward mixing; furthermore, the co-location with RH and inversions does not establish causality or rule out a shared driver.

The third case, on 8–9 August 2022, showcases the evolution of the aerosol vertical profile under the influence of a sea breeze circulation. On this day, the ROAM-V sampled at multiple TAMU sites: it began measurements in Galveston in the morning and later relocated inland to Hempstead, while AMF-1 operated continuously at La Porte. To visualize the progression of the sea-breeze front relative to the active ROAM-V location and AMF-1, Fig. 8 presents GOES-16 Geocolor imagery (Miller et al., 2020). The sea breeze front was identified based on the characteristic inland advancing cumulus cloud bands visible in the satellite imagery (Planchon et al., 2006; Sharma et al., 2024). The sea breeze front marks a sharp boundary that separates cooler, moister maritime air along the coast from the continental air farther inland. According to Fig. 8, by about 17:00 UTC, the sea breeze front had already passed the TAMU Galveston site but was only just beginning to move across the AMF-1 site at La Porte. By 21:00 UTC, the sea breeze front had moved past the coastal sites at Galveston and La Porte but had not yet reached the inland TAMU Hempstead site.

As seen in Fig. 9, no notable elevated aerosol layers are observed on this day. The NRB field shows some variability near 1 km throughout the day, but the depolarization ratio does not show a distinct separation at this altitude. This suggests that the aerosol structure is more continuous than in the previous cases. Together with the weaker inversion shown in Fig. 10, this pattern is consistent with weaker stratification and more effective vertical mixing within the lower atmosphere.

Aerosol concentration, potential temperature, and RH profiles, as well as BLHs at selected times at the AMF-1 site are shown in Fig. 10. Corresponding profiles measured at the TAMU Galveston and Hempstead sites are also included (marked in Fig. 10). The TAMU profiles use longer averaging windows because the lidar measurements required longer temporal averaging to obtain enough cloud-free profiles for the retrieval. For both ARM and TAMU Galveston sites, the potential temperature profiles have a distinctly different vertical structure compared to the previous two cases, featuring a much weaker inversion at around 0.8 km and less inhibition to vertical mixing. The aerosol profiles also appear less structured, with a smoother vertical gradient and no clear separation between layers as seen in the previous two cases. Since measurements from multiple sites are available on this day, we can investigate how the sea breeze circulation shapes aerosol vertical distributions across the urban coastal area. This analysis compares the observed aerosol vertical profiles, the transition zone height rm derived from Eq. (1) curve fit, and the BLHs obtained from radiosonde measurements across the maritime and continental side of the sea breeze front.

At the AMF-1 site, the near-surface aerosol concentration increases from approximately 4400 cm-3 in the early morning (10:58–11:58 UTC; Fig. 10a), to 7200 cm-3 around noon (17:00–18:00 UTC; Fig. 10b), accompanied by higher concentration aloft. During this period, the BLH increased from below 0.2 km to approximately 1 km. Although boundary layer development may enhance mixing and dilution, local emissions or transport of aerosol rich air may have contributed to the observed increase. Shortly after, concentrations begin to decrease throughout the late afternoon and evening, reaching a minimum of around 2900 cm-3 in the late afternoon (21:30–22:30 UTC, Fig. 10d). The decline in concentration coincides with the arrival of maritime air south of the sea breeze front, replacing the earlier continental air mass. Easterly to southeasterly surface winds at AMF-1 (Fig. S4a in the Supplement) during this period are consistent with the increasing maritime influence. Aerosol concentrations aloft follow a similar trend, with larger concentrations around noon (17:00–18:00 UTC; Fig. 10b) that gradually decline into the evening. The fitted transition zone height rm at the AMF-1 site is around 1.2 km throughout the day. Both BLH-RiB and BLH-LL agreed well, increasing from < 0.2 km in early morning (10:58–11:58 UTC; Fig. 10a) to about 1 km in early afternoon before gradually decreasing toward midnight (05:04–06:04 UTC on 9 August; Fig. 10e) . The BLH remained shallow, peaking near 1 km after the sea breeze passage. The weak mixed-layer growth may explain the limited change in rm. The sea breeze and the HYSPLIT back trajectories (Fig. S8 in the Supplement) indicate that the aerosol sampled at AMF1 were primarily of maritime origin.

At the TAMU Galveston site, from late morning to early afternoon (16:14–18:47 UTC; Fig. 10f), the aerosol vertical distributions resemble that observed at the AMF1 site in the afternoon (18:30–19:30 UTC; Fig. 10c), and the fitted transition zone height rm at Galveston closely matches the rm at the AMF1 site around noon (17:00–18:00 UTC; Fig. 10b) at around 1 km (see Tables S3 and S4 in the Supplement). This similarity reflects the influx of maritime air behind the sea breeze front, which carries relatively cleaner marine air and establishes a boundary layer structure comparable at both locations once the sea breeze front has passed. HYSPLIT trajectories indicate Galveston air also arriving from the southeast over the Gulf, explaining its close resemblance to AMF-1 once the sea breeze has passed (Fig. S8 in the Supplement). At the TAMU Hempstead site in the late afternoon (21:09–22:55 UTC; Fig. 10g), aerosol concentrations throughout the profile were greater than at the coastal sites, and the fitted transition height rm was about 1.94 km. The fitted rm at the Hempstead site is also closer to the BLH, which is at around 2.5 km. The greater aerosol concentration and deeper transition region height are characteristic of the continental air mass that persists inland, rich in urban and biogenic emissions and less influenced by marine dilution. In addition, HYSPLIT trajectories for Hempstead remain near the surface until close to arrival of the sea breeze front (Fig. S8 in the Supplement), supporting the interpretation that the site was influenced by a local or continental air mass, which helps explain the larger aerosol concentration and higher rm observed there.

The comparison between the aerosol vertical distributions at different sites and times of the day reveals that the aerosol vertical distributions can have strong spatial heterogeneity, especially when there is a sea breeze circulation. During TRACER, near-surface aerosol properties differed systematically between polluted-marine and continental airmasses (Thompson et al., 2025a). This case study shows that, in a coastal urban environment like the Greater Houston area, the aerosol vertical distributions can be affected by sea breeze circulation and air mass transitions.

The AMF-1 deployment in the Greater Houston area offers a large dataset to study which environmental predictors are associated with and can potentially be used to predict the shape of aerosol vertical profiles. Six months of data from March 2022 to September 2022 were curve fitted using Eqs. (1) or (2). Profiles that were first fitted with Eq. (1) with R2 < 0.98 and were visually classified as containing an elevated aerosol layer were then refit using Eq. (2) with one or two Gaussian terms. A profile was visually classified as having an elevated layer when it showed a distinct local maximum in aerosol concentration above the low-level aerosol layer and was separated from it by a relative local minimum. After model selection, only profiles with final fit quality R2 > 0.98 were retained for the statistical analysis to ensure that the fitted parameters represented well-resolved profile structure. Overall, 157 of 313 profiles met this strict quality criterion. 34 out of 157 selected profiles are classified as containing elevated aerosol layers and are fitted with Eq. (2). The frequency distributions of fitted parameters are presented in the supporting information in Fig. S10 in the Supplement. As shown qualitatively in the case studies, we observe that BLH and rm may have a positive correlation during the daytime. Comparing the case studies, a more abrupt transition from the low-level aerosol-rich layer to the air aloft, quantified by a larger k, is associated with stronger potential-temperature inversions. As we observed, the aerosol profiles on 18–19 May 2022 exhibit both a tighter transition zone and a steeper transition (larger k) than the profiles on 8–9 August 2022. Motivated by these patterns, we compare BLH and stability with the curve-fitted transition height rm and the shape parameter k. For reference, we also provide the corresponding BLH–rm and stability–k scatter plots obtained when Eq. (1) is applied to all profiles (i.e., without elevated-layer refitting) in the Supplement (Figs. S11 and S12).

In Fig. 11, we compare the thermodynamically determined BLH from radiosonde data with the curve fitted transition zone height rm to examine how the BLH covaries with structure of the aerosol vertical profiles using available data from March to September 2022 measured at the AMF-1 site. Comparison between the curve fitted transition height rm and BLH shows that rm tends to be systematically higher, as most data points lie above the 1:1 reference line. This overestimation may reflect the fact that aerosol layers often extend above the diagnosed boundary layer, particularly when the boundary layer is not well mixed. As shown in Fig. 11, BLH values are greater during the daytime and can reduce the discrepancy between rm and BLH. In contrast, during nighttime or under stable stratification conditions, the diagnosed BLH becomes much shallower, while elevated aerosol layers may persist. In these cases, the Liu and Liang (2010) method appears more effective at capturing shallow stable boundary layers than the Richardson number method, potentially providing a closer match to the aerosol-defined transition height during daytime.

We performed linear regression analysis using daytime data only, comparing the fitted aerosol transition height rm with BLH derived from both the Richardson number and Liu and Liang methods. We find a weak but statistically significant positive correlation between the curve fitted transition height rm and the BLH. The relationship is stronger when using the BLH-LL (R2 = 0.11, p = 0.0021) than when using the BLH-RiB (R2 = 0.07, p = 0.0158). The positive correlation indicates that higher BLHs are generally associated with deeper aerosol transition heights, suggesting that BLH plays a contributing role in shaping the aerosol vertical structure. However, the relatively low R2 shows that the BLH only explains a small fraction of the variability in rm. Therefore, the regression is used here to summarize the observed correlation between BLH and rm and to assess the explanatory power of BLH. Based on the results, the regression should not be used as a standalone predictor of aerosol transition height.

The limited explanatory power of BLH likely reflects several contributing factors. First, the aerosol vertical profile is shaped not only by the instantaneous thermodynamic structure, but also by the boundary layer's recent evolution. As seen in the case study of 21 July 2022, during boundary layer growth, surface emitted aerosols become mixed throughout a deepening layer. As BLH decays, previously mixed aerosols can remain aloft even as the boundary layer becomes shallow, causing a mismatch between BLH and rm. Second, aerosol layers from long range transport can reside over the local boundary layer and later subside and merge with near surface aerosol layer. Even with additional Gaussian peaks, the fitting routine may not always cleanly separate the transported signal from locally emitted aerosols. And finally, uncertainties in both BLH diagnostics and the aerosol curve fitting, particularly under weak stratification or merged layers, can mask the link between BLH and rm.

In conclusion, although BLH exhibits a weak but statistically significant positive correlation with the fitted transition height rm, BLH explains only a small fraction of the variability in rm. This result indicates that BLH alone cannot reliably determine the depth of the near-surface aerosol layer or the overall structure of the aerosol vertical profile.

We then examine whether the local vertical gradient in potential temperature (i.e., the static stability) can help explain variations in k. Since atmospheric stability influences vertical mixing and stratification, a stronger gradient in potential temperature is expected to be associated with a steeper vertical aerosol gradient, k, at the transition zone, rm. The local maximum vertical gradient of potential temperature (dθ/dz) was calculated within ± 100 m of the fitted transition height rm, using smoothed radiosonde profiles to reduce high frequency noise. The smoothing was performed with a Gaussian kernel with a full width at half maximum of 100 m, consistent with common boundary layer profiling practice of applying vertical averaging at a scale of tens of meters (Bhimireddy and Kristovich, 2024). The comparison between static stability and k is shown as a scatterplot in Fig. 12.

A statistically significant (p ≪ 0.01) and limited positive correlation (R2 = 0.20) is found between the potential temperature gradient at rm and the curve-fitted transition sharpness parameter k. Sensitivity tests using different Gaussian smoothing scales and search-window widths show that the positive relationship remains, although the slope and R2 vary with the operational definition of the local stability metric (Fig. S13 in the Supplement). This result shows that the local atmospheric stability near rm appears to contribute to the shape of the aerosol profile but does not fully define it. A possible physical explanation is that stronger stability can suppress vertical exchange across the aerosol transition zone, allowing a sharper aerosol concentration gradient to persist. In contrast, weaker stability may permit more gradual mixing between the lower aerosol rich layer and cleaner air aloft, resulting in a more gradual transition zone and smaller k values. Because the correlation is limited, we interpret dθ/dz near rm as a partial constraint on aerosol stratification rather than as the only control on k. Additional variability may arise from transported aerosol mixing with the lower layer, residual uncertainty in the hygroscopic-growth correction, and the history of boundary-layer growth, collapse, and residual-layer formation.

Using the significant but weak empirical relationships established above, we next demonstrate aerosol vertical-profile prediction using these variables in place of vertical lidar measurements, as shown in Fig. 13. Because BLH-LL showed a slightly stronger empirical relationship with rm than BLH-RiB in the daytime AMF-1 analysis (Fig. 11), the BLH-LL is used in the following analysis. The transition height rm is estimated using the linear regression relationship with the Liu and Liang (2010) based BLH, expressed as rm = 0.27 × BLH + 1.25 km. The sharpness of the transition zone k is then estimated as k = 0.609 × (dθdz)max⁡,rm±100m + 2.022. γ is set as 0.3, consistent with the previous curve fitting. Since a predictive relationship was not found for f, fixed values of f=1 and f=2 are selected for testing, guided by the distribution shown in Fig. S10, where the mode of f is centered around 1.1. The aerosol concentration measured on the surface is used for X0. Xf is set to 150 cm-3, as a representative background value close to the overall median obtained from the quality-controlled AMF-1 profile fits. The prediction equation then becomes: 3X(r)=X0-1501+f×1+fe-r0.31+r0.27×BLH+1.250.27×BLH+1.250.609×dθdzmax⁡,rm±100m+2.022+150

The TAMU coastal and inland site's aerosol vertical profiles for 8 August and 18 September were chosen for the demonstration. The TAMU site was not included in the derivation of the empirical relationships from the AMF-1 dataset, allowing the demonstration to test how the AMF-1-derived relationships perform when applied to profiles from other sites. Although the predictive relationships for rm and k are only weak to moderate, the demonstration is useful for showing both what profile features can be approximated from these variables and where the approach breaks down, particularly in situations where direct vertical measurements are unavailable.

To quantify the profile-level uncertainty in this demonstration, we calculated the normalized RMSE between the predicted and lidar-retrieved aerosol concentration profiles for each case (Table S5 in the Supplement). The 8 August cases show lower errors when f=2 is used, with normalized RMSE values of 41.7 % at Galveston and 19.5 % at Hempstead, compared with 72.3 % and 56.7 % when f=1 is used. In contrast, the 18 September cases retain larger errors even when f=2 is used, with normalized RMSE values of 59.5 % at Galveston and 48.0 % at Hockley. This result indicates that the accuracy of the predicted profile depends strongly on reliable estimation of rm, consistent with the weak BLH–rm relationship shown in Fig. 11. This indicates that BLH alone is not a strong predictor of rm. Uncertainty in the estimated rm also affects the altitude range used to determine the temperature gradient and therefore the estimated k. These linked uncertainties may affect both the location and sharpness of the transition in the predicted aerosol profile. Thus, an accurate rm is crucial for an accurate estimate of k. Additionally, the factor f has a strong influence on the shape of the aerosol profile and thus requires further investigation.

Our analysis uses a single retrieved aerosol number concentration profile based on the assumption that the surface aerosol is representative aloft, although particles of different sizes and composition may have different vertical distributions. Tethered balloon measurements during TRACER showed variability in aerosol sizes and composition with height, although they were not co-located with our lidar observations (Mei et al., 2026). Differences in physicochemical properties do affect the conversion from lidar backscatter to number concentration and, consequently, affect the fitted profile shape and its relationship with BLH and atmospheric stability. However, the available measurements for this study do not allow us to determine how accounting for these vertical variations would change our result.