1 Introduction

Understanding the Atmospheric Boundary Layer (ABL), its temporal evolution and height, is crucial for forecasting air quality, particularly in urban zones (Toledo et al. 2017; de Arruda Moreira et al. 2019; Vivone et al. 2021). The ABL height (ABLH) determines the available volume in which anthropogenically emitted pollutants can accumulate (Compton et al. 2013; de Arruda Moreira et al. 2018; Dang et al. 2019; Zhang et al. 2020; Vivone et al. 2021). However, there is no single, reliable, and widely accepted technique for retrieving ABLH (Seibert et al. 2000; Herrera-Mejía 2019; Hennemuth and Lammert 2006). Some methods are based on the thermal structure of the ABL (Seibert et al. 2000; Wang and Wang 2016), while others consider the height up to which aerosols disperse vertically (Emeis and Schäfer 2006; García-Dalmau et al. 2022) and others the height at which there is a notable decay in turbulence fluxes (Barlow et al. 2011; Huang et al. 2017; Manninen et al. 2018). The comparison between different ABLH retrievals is crucial for a better understanding of the ABL processes as well as for improving ABL parametrizations in numerical models. Moreover, ABLs over topographically complex terrain usually present a complex vertical structure, which we are encouraged to better elucidate, given that urbanization has expanded in mountainous regions. It is estimated that roughly 30% of the world’s mountain population presently lives in cities, and this percentage reaches 50% in developing countries (Giovannini et al. 2020). The present research aims to compare different ABLH retrievals and better characterizing the ABL over Mexico City, which constitutes a topographically complex terrain and one of the most populated urban areas in the world.

In the traditional framework presented by Stull (1988), the ABL is considered as a well-defined structure that evolves with the diurnal cycle. The diurnal component of the ABL is known as the mixed layer (ML) which is characterized by convectively driven turbulence and is bounded by a capping stable layer. This stable layer is often classified as a temperature inversion, where the vertical temperature gradient becomes positive, \(\partial T/ \partial z >0\). The ML is usually characterized as having higher pollutant concentration, while the free troposphere remains relatively free of high pollutant concentrations. Given that a thermally stable layer typically caps the ABL, its height has been frequently estimated via the thermal profile measured by radiosondes (Hennemuth and Lammert 2006; Basha and Ratnam 2009; Seidel et al. 2010; Guo et al. 2016; Wang and Wang 2016; Zhang et al. 2018). However, ABL temporal evolution and variability during its daily evolution requires high temporal resolution observations for continuous monitoring, which is, given the cost, not viable with radiosondes (de Arruda Moreira et al. 2018). Remote sensing techniques that provide high temporal resolution by utilizing the interaction of electromagnetic radiation with the aerosols in the ABL, are crucial for elucidating the diurnal evolution of ABL.

Over flat terrain, the ABL has been widely investigated (Steyn et al. 1999; Stull 1988; Martucci et al. 2007; Compton et al. 2013; Luo et al. 2014; Schween et al. 2014; Barlow 2014; Dang et al. 2019). In non-complex terrain with strong surface heating and without larger-scale dynamical forcing, turbulent convective motions essentially determine the height of the boundary layer, often referred to as the convective boundary layer height (CBLH). The mixing mechanisms that disperse aerosols vertically are mainly determined by convective turbulent eddies, which result in a general coincidence between methods that retrieve ABLH via aerosol dispersion or via measures of turbulence. Nevertheless, the height up to which mixing is effective in ABLs over complex terrain has been shown to significantly differ from ABLs in the traditional (flat terrain) framework (Serafin et al. 2018; Giovannini et al. 2020).

The circulation over topographically complex terrain usually includes advection, thermally driven winds, and mountain waves and their breaking, all which strongly affect diurnal ABL variability and diversify the mixing mechanisms (Doyle and Durran 2007; Zardi and Whiteman 2013; Adler and Kalthoff 2014; Lehner and Rotach 2018; Giovannini et al. 2020). Given this diversity of mixing processes, previous authors have argued that one height corresponds to the CBL top, while a more elevated one corresponds to the aerosol layer (AL) top (De Wekker and Kossmann 2015; Serafin et al. 2018). This height could also be argued to relate to the MLH (de Haij et al. 2006). Furthermore, it is not solely the dispersion of aerosols and other pollutants that is affected by mountains, but also the vertical thermal structure that frequently shows multiple stable layers over topographically complex terrain (De Wekker and Kossmann 2015; Lehner and Rotach 2018; Burgos-Cuevas et al. 2021).

Mexico City, one of the world’s most populated urban areas, experiences a heavy daily load of automobile and industrial emissions, which strongly degrade air quality (Molina et al. 2007; Chavez-Baeza and Sheinbaum-Pardo 2014; Peralta et al. 2019). Moreover, the topographically complex terrain, in which this city is located, results in an complex interaction between synoptic and local circulations forced by the mountainous terrain (Doran et al. 1998; Jáuregui 1988; Whiteman et al. 2000; Jazcilevich et al. 2003; Doran 2007; Foy et al. 2005, 2008; Molina et al. 2007; Pozo et al. 2019; Díaz-Esteban et al. 2022). This complex circulation can stifle ventilation and the dispersion of pollutants (Jazcilevich et al. 2003; Doran 2007; Foy et al. 2006; Díaz-Esteban et al. 2022; García-Franco 2020; Burgos-Cuevas et al. 2021). The characterization of the ABL and its diurnal evolution in this urbanized zone are crucial for assessing the vertical dispersion of pollutants.

In the last decade, the implementation of newer observational platforms has given rise to observational research with enough temporal resolution to elucidate the variability of the mixing layer height and its diurnal evolution. For example, García-Franco et al. (2018) estimated the diurnal and seasonal cycles of ABLH using ceilometer backscattering data. A Doppler lidar acquired by the Red Universitaria de Observatorios Atmosféricos (The University Network of Atmospheric Observatories) (RUOA) within the Instituto de Ciencias Atmosféricas y Cambio Climático (Institute for Atmospheric Sciences and Climate Change) (ICAyCC) was located at the same site as the ceilometer utilized by García-Franco et al. (2018) near the southern end of the Valley of Mexico. To date, no studies of Mexico City ABLH based on turbulence thresholding from Doppler lidar retrievals have been carried out. As such, this study is novel in its approach to estimating ABLH as well as offering the first direct comparison with ceilometer backscatter data and radiosonde retrievals (0600 and 1800 LT (local time = UTC– 6 h)) over Mexico City. The differentiation between these two ABLHs obtained by both remote sensors elucidates the complexity of the ABL over Mexico City in the present research, accomplishing our most important objective of better characterizing this ABL. Additionally, the different ABLH retrievals are compared in terms of monthly means. In this manner, we are able to not only differentiate between the ABLH retrievals depending on the method and mixing mechanisms, but also to analyse the seasonal variation of these mechanisms.

2 Study Site and Data

In the present study, the height at which diurnal convection is reached in the ABL is retrieved using the Leosphere Wind Cube 100 Doppler lidar. Additionally, we compare this retrieval with the height up to which aerosols disperse, which is measured via a VaisalaCL31 ceilometer data. This height is estimated by identifying a coherent decrease in backscatter using a wavelet transform algorithm described in García-Franco et al. (2018). Finally, both ABL heights, obtained by remote sensor’s data, are compared with thermally stable layers identified in the thermal profiles of twice-daily radiosonde data. These radiosondes are launched by the Servicio Meteorológico Nacional (Mexican Meteorological Service) (SMN) at the Tacubaya Observatory. All the analyses are performed for one year from November 2018 to October 2019, and the locations of all the instruments are shown in Fig. 1.

Fig. 1
figure 1

Mexico City and surrounding elevated terrain. The map was created with SRTM30 DEM database (Shuttle Radar Topography Mission (SRTM) 30-m digital elevation model) and with the Shuttle Radar Topography Mission Global 1 arc second dataset. The gray contours denote the elevation contours every 1000 ms. The black solid lines represent the state division within the metropolitan area, while the purple-shaded polygons correspond to the urban extent and the blue polygons are the water bodies nearby. The green dot represents the ceilometer and Doppler lidar location, and the blue dot represents the radiosonde site \(\approx \) 10  km to the north. The mountainous regions are shown in a colourbar scale that corresponds to meters above sea level

Figure 1 also reveals the complex orography that surrounds Mexico City. In the south-western section of the Valley, there is the “Sierra Ajusco-Chichinautzin” that reaches around 1000 m above the valley floor, which on average is 2240 m above sea level, whereas the highest peak of the Ajusco is at 4118 m above sea level. Along the central, western edge of the valley, the “Sierra de las Cruces” trend north–south about 1000 m above the valley floor and the “Sierra Guadalupe” is located in the north of the urban area. There is a valley in the eastern section of the Valley of Mexico, separated from Mexico City by smaller hills (\(\approx \) 200 m above the valley floor). However, upslope on the eastern side, two prominent volcanoes, “ Volcan Popocatepetl” and “Volcan Iztaccihuatl,” which is part of “Sierra Nevada,” rise reaching up to 5.6 km above sea level. The valley opens in the north-eastern direction close to “Monte Tlaloc.” The atmospheric circulation over the Valley of Mexico experiences two basic regimes: anticyclonic weather dominates with mostly clear skies from November to April and a more unstable, deep convective regime from May to October (Jáuregui 1988; Foy et al. 2006). During the rainy season, horizontal advection and vertical mixing (associated with deep convection) enhances ABL ventilation. In contrast, during the dry season, thermal inversions contribute to a more stable ABL, which frequently results in poor air quality and has strongly motivated previous research, as well as our present study, on the ABL (Bossert 1997; Jazcilevich et al. 2003; Foy et al. 2006; Burgos-Cuevas et al. 2021).

3 Methodology

The present research not only has the goal of characterizing the ABL over Mexico City, but also is strongly motivated by the detailed inter-comparison between various approaches to deriving ABL heights. Here, we provide details on our approach using these two remote sensing techniques as well as our analysis based on radiosonde data. The characteristics of the remote sensors and their data acquisition is explained in the following subsections, as well as the data analysis that we performed.

3.1 Thresholding Method for Doppler Lidar Data

The Wind Cube 100 Doppler lidar retrieves 3-dimensional velocity components with a vertical resolution of 50 m. This lidar has a maximum power of 5 mW, emitting pulses of 1543 nm (infrared) wavelength. The present study utilizes Wind Reconstructed data files that provide 3-dimensional velocity retrievals and CNR (Carrier-to-Noise Ratio), which is related to elastic backscatter and thus depends on aerosol concentration. These files correspond to Doppler beam swinging (DBS) scans twice an hour (starting at 00:25 and 00:55 min). However, the Wind-Cube 100 also performed Range Height Indicator (RHI) and Plan Position Indicator (PPI) scans every hour. Each of the DBS files contains 148 sub-scans, i.e. 148 profiles of the measured quantities, which have a temporal resolution of 5 s. Finally, the analysis of the retrieved velocities in these files every half an hour provides us with the same temporal segments that previous authors have utilized in order to capture most of the scales of turbulence (Huang et al. 2017).

In order to ensure the quality of the data that was later employed to estimate ABL heights, different filters were performed directly on the Wind-Cube 100 raw data. Firstly, we followed previous authors recommendations and discarded data for which CNR \(< -\) 20 dB (Pearson et al. 2009; de Arruda Moreira et al. 2018; Boquet et al. 2016; Gryning and Floors 2019). Secondly, we ensured that in every half-an-hour file there were enough sub-scans performed to estimate a robust variance of the vertical velocity. In order to do this, we took into consideration that the usual number of sub-scans in each file is 148. Then, we discarded data files where less than half the sub-scans were performed. Then, with these already filtered files we applied an algorithm for which variances of the vertical velocity are estimated. This routine utilises only velocity retrievals from the vertical line-of-sight (i.e. elevation angle = 90\(^{\circ }\)) and also disregarded near-surface data given that close-to-surface velocities are very noisy and, more importantly, could not reasonably represent a realistic ABLH value. Therefore, we ignored data that corresponded to ABL heights below 100 m. Finally, given that it is the vertical velocity (w) that we use to retrieve ABLH, another criterion was imposed directly on w. As recommended by Huang et al. (2017), velocities that exceed 2.5 standard deviations from the mean value were disregarded. Additionally, very high vertical velocities that could reflect other mechanisms (such as falling rain droplets) were disregarded by adding an additional filter that does not take into account vertical velocities higher than 2.5 m\(^2\) s\(^{-2}.\) The vertical profile of \(\sigma _w ^2\) is calculated utilising the sub-scans in each of the half-an-hour files. Once these data are processed, daily files are obtained and averages of the variance of the vertical velocity (\(\sigma _w ^2\)) are estimated every half an hour over the diurnal cycle. These data are then monthly averaged, and the monthly mean diurnal cycle values of \(\sigma _w ^2\) are obtained. However, in order to assure reliability on the monthly averaged heights, this mean values are only computed for each time and height if there is a variance value from at least 14 days in each month.

The implementation of Doppler lidar data for investigating ABL have been shown to provide reliable results that include not only height retrievals, but also the identification of turbulence sources (Huang et al. 2017; Barlow et al. 2011; Manninen et al. 2018). The Wind Cube 100, with which data we estimate CBLH, automatically retrieves a diurnal ABLH via a thresholding. Nevertheless, the retrieved heights and thresholds are found to be strongly site dependent (Barlow 2014) and this site variability as well as the comparison with other remote-sensing estimated heights constitutes an open question that is being investigated in different locations around the world (Pearson et al. 2009; Schween et al. 2014; Huang et al. 2017; Krishnamurthy et al. 2021a, b). At a low turbulent intensity site, \(\sigma _\textrm{thld} ^2 = 0.04\) m\(^2\) s\(^{-2}\) was proposed by Tucker et al. (2009). In contrast, for a tropical rainforest, \(\sigma _\textrm{thld} ^2 = 0.3\) m\(^2\) s\(^{-2}\) was proposed by Pearson et al. (2010). Given that we are estimating ABLH in a urban environment, we employed the threshold proposed by Barlow et al. (2011) and Huang et al. (2017) over London and Beijing, respectively, which is \(\sigma _\textrm{thld} ^2 = 0.1\) m\(^2\) s\(^{-2}\). Additionally, we estimate ABLH with \(\sigma _\textrm{thld} ^2 = 0.2\) m\(^2\) s\(^{-2}\), which is the standard value utilized by the Wind Cube 100. In this manner, we not only fit possibly appropriate thresholds, but also provide a threshold sensitivity-test ourselves. Moreover, the automatically generated ABLH retrieved from the Wind Cube 100 is performed once an hour, while the files employed here to estimate ABLH, are available every 30 min. Hence, we improve temporal resolution, providing for more robust statistical analysis.

3.2 Ceilometer Mixed Layer Height

Our comparison technique for ABLH is based on data derived from a Vaisala CL31 (Münkel et al. 2007) ceilometer operating at the same location as the Doppler lidar. The estimation of the mixed layer height derived from the ceilometer backscatter data is described in detail in García-Franco et al. (2018). In brief, the methodology consists of applying a time-height filter to the raw ceilometer backscatter signal to smooth out noise with an output frequency of 10 min. A covariant wavelet transform methodology (Brooks 2003; Grabon et al. 2010) was used to obtain the ABLH from the smoothed backscattering matrix producing an estimate of the mixed layer height with a 10-min resolution. The MLH retrievals from November 2018 to October 2019 are compared with the \(\sigma _\textrm{thld} ^2\) thresholding ABLH retrievals from Doppler lidar data. The MLH are estimated only for clear-sky conditions due to the effect of clouds and rain over the backscatter profile, using the cloud-filter described in García-Franco et al. (2018). Note that a multi-layer structure of aerosols, as well as the presence of cloud and rain, can cause increases in the backscatter measured by the ceilometer above the boundary layer (Grabon et al. 2010; Haeffelin et al. 2012; García-Franco et al. 2018; García-Franco 2020).

The MLH retrievals from the ceilometer have 10-min temporal resolution, whereas the thresholding-estimated one from the Doppler lidar is estimated every 30 min. The difference between this temporal resolution is a result of the different scans that are performed by the Doppler lidar and not by the ceilometer and because of the fact that only zenith scans from the lidar are utilized. However, both suffice to elucidate the diurnal cycle.

3.3 Identification of Thermally Stable Layers

Radiosondes from the (SMN) were obtained from the University of Wyoming radiosonde database and analyzed. These radiosonde data provide thermal profiles that can present multiple stable layers over Mexico City (Burgos-Cuevas et al. 2021), i.e. layers in which potential temperature (\(\theta \)) increases with height (Whiteman et al. 2000). These statically stable layers can stifle the dispersion of pollutants (Nodzu et al. 2006). If not only \(\theta \), but also the actual temperature increases with height, \(\partial T/ \partial z >0\), then the stable layer corresponds to a thermal inversion. In our analysis, these layers are identified when \(\Delta T/ \Delta z > -\,0.01\) K  km\(^{-1}\). Because of the lack of reliable measurements very close to the surface and the fact that we want to disregard surface inversions (given that they cannot correspond to ABLH), the algorithm is performed only above 250 m. Additionally, we only search for stable layers up to 3000 m (a.g.l), where realistic candidates of thermally stable layers (corresponding to the ABLH) are found (Doran et al. 1998; García-Franco et al. 2018). Furthermore, our algorithm contemplates that more than one stable layer might be present in the ABL and is capable of identifying two of them. In the case of multiple stable layer profiles, we first assure that these layers are separated from each other. This is done by identifying non-stable layers between one stable layer and the following stable layer. Then, we retrieve their corresponding heights. In order to later associate them with the two remote-sensing retrievals, we identify a lower and an upper thermally stable layer. If only one stable layer is found, we consider it to be a lower one if it is less than 1500 m a.g.l. and we consider it to be a higher one if it is above 1500 m. above ground level (a.g.l.). Figure 2 shows the ABLHs for a sample 0600 LT sounding derived from the vertical profiles of temperature, \(\theta \) and \(\theta _v\). Finally, these corresponding sounding heights at which both stable layers are found, are averaged at each time (0600 h and 1800 h LT) over a given month. This is done in order to compare them with the Doppler lidar and ceilometer retrievals, which are also monthly averaged but provide higher temporal resolution.

Fig. 2
figure 2

Sample sounding (10/07/2018 0600 LT) of vertical profiles of a temperature, b \(\theta \) and c \(\theta _v\). A lower stable layer is identified in the three profiles and indicated with a blue triangle. An elevated stable layer is identified with a red triangle

4 Results and Discussion

4.1 Diurnal Evolution of \(\sigma _w ^2\)

In this subsection, we present twice-hourly values of the variance of the vertical velocity, \(\sigma _w ^2\), averaged over each month. Given that \(\sigma _w ^2\) is a proxy for vertical turbulent transport (Barlow et al. 2011; Huang et al. 2017), a clear signal in the diurnal cycle is apparent in Fig. 3. The diurnal evolution of the ABL is only visible during daytime hours when utilizing this methodology; because of this, we did not make ABLH estimations for times before 0700 h LT or after 1900 h LT. This is due to the fact that nocturnal conditions are usually free of convective turbulence as it has been shown by previous authors (Manninen et al. 2018). White gaps are visible in all the monthly means, specially at higher elevations. These gaps represent lack of enough information to provide the monthly mean at that time and height; if there were not at least 14 days for which we could estimate this average, the monthly mean variance was disregarded. The lack of information at higher elevations makes sense because the lidar beam can be attenuated by perturbations such as clouds.

Fig. 3
figure 3

Twice-an-hour values of \(\sigma _w^2\) in the ABL are monthly averaged and shown. The diurnal cycle is clearly followed by \(\sigma _w^2\), which reaches its highest values during April and May. The black bar in the lower part shows the mean nocturnal times (between sunset and sunrise) for each month. The white gaps correspond to a lack of enough data to provide a monthly mean

During April and May, when insolation is greatest due to limited cloud cover and high solar elevation angle, the magnitude of \(\sigma _w^2\) is greatest during early afternoon hours. During the months of October to January, the magnitude of \(\sigma _w^2\) in the afternoon hours is much weaker given solar insolation is decreased and surface temperatures are reduced. Though solar insolation is potentially greatest for June through September, these months represent the rainy season for the Valley of Mexico. During these summer months, given the increase in humidity, deep convective activity and precipitation, cloud cover diminishes incoming insolation. Likewise, surface temperatures can also be lower as the surface heat flux budget increases the latent heat flux contribution at the expense of surface sensible heat flux, hence decreasing turbulent convective fluxes. Additionally, these rainy months present a wider spread of high \(\sigma _w^2\) along daytime hours, starting at about 1000 LT. Nevertheless, the velocity retrievals during these months can be influenced by the presence of rain which can significantly affect the Doppler Lidar measurements as shown in Sect. 4.3. The monthly diurnal cycle behaviour is in general coincident with the higher MLH found by García-Franco et al. (2018) for March and April, whereas they found lower MLHs during September–December.

4.2 Distinguishing Boundary Layer Height Retrievals

ABLH monthly composites retrieved from the different methods are plotted conjointly for the purpose of comparison to gain insight into diurnal cycle of the boundary layer in Mexico City and its complexity. For interpreting ABLH estimations via these observational methods, the definition of ABL utilized is critical. Defining the ABL as a stably stratified layer based on thermal profiles, relies on the fact that temperature stratification is the essential factor for controlling turbulent mixing and the subsequent spread of aerosols and other tracers. This thermal stability is compared with both remote sensing techniques in the present subsection.

The three methodologies utilized to estimate ABL height are presented in Fig. 4; physically realistic heights are shown. Doppler lidar and ceilometer have high enough temporal resolution to elucidate ABL diurnal evolution, while radiosondes provide the thermally stable layers and their heights twice a day, at 0600 and 1800 LT. Given that in a previous study we found that multiple thermally stable layers are frequently present in the ABL over Mexico City (Burgos-Cuevas et al. 2021), a lower and an elevated stable layer are identified in those soundings as it is described in Sect. 3.3 and their heights are averaged over each month, as Fig. 4 shows.

The MLHs estimated from ceilometer backscatter (García-Franco et al. 2018) are continuously reported by the RUOA computed every 10 min. The monthly averaged MLHs for November 2018 to October 2019 show that the MLH starts growing at around 0800 LT, shortly after sunrise. However, it is when the insolation becomes higher, at about 1000 LT that the growth of this MLH becomes faster and it reaches its highest elevation near 1600 LT. Likewise, ABLHs retrieved from the threshold method that utilizes the vertical velocities from the Doppler lidar, grow slightly during the day as solar insolation enhances the convective processes. The diurnal cycle of the heights estimated from the Doppler lidar is not as clearly elucidated as for the ceilometer-retrieved ones, but noteworthy growth rates of the ABLHs are observed for daytime hours especially for the most sunny months, such as April and May. However, the comparison of these retrievals shows that the heights obtained via thresholding are always lower than those heights obtained from the ceilometer backscatter. The diurnal maximum height from these thresholding-estimated ABLHs does not reach higher than 1500 m, and only during May do the heights get closer to the ceilometer-retrieved height, reaching 2000 m at 1400 LT (with \(\sigma _\textrm{thld}^2 = 0.1 \)m\(^2 \)s\(^{-2}\)). Nevertheless, during the remaining months, the thresholding-obtained heights are close to 1000 m lower than the heights retrieved from the ceilometer backscatter during daytime hours. Although the lack of coincidence between both techniques may appear unusual, this behaviour can be crucial in terms of elucidating the complexity of a boundary layer when the aerosol layer does not coincide with the instantaneous and purely convective boundary layer.

Fig. 4
figure 4

al Monthly averaged diurnal cycles for the retrieved heights obtained from the Doppler lidar data with \(\sigma _\textrm{thld}^2 = 0.2\) m\(^2\) s\(^{-2}\) (blue line) and \(\sigma _\textrm{thld}^2 = 0.1\) m\(^2\) s\(^{-2}\) (green line), and the ceilometer backscatter (red line). The shaded areas correspond to the variance around the mean values. Additionally, thermally stable layers obtained by analysing radiosonde profiles at 0600 and 1800 LT are shown for a lower layer (blue triangle) and an upper one (red triangle); the black lines around these triangles correspond to the standard deviation of the radiosonde-obtained heights. Finally, the gray line corresponds to the percentage of available data for computing the thresholding-obtained heights and its corresponding axis is on the right side of each plot

As previous authors have shown, aerosol distribution in the ABL represents the history of mixing processes, whereas the vertical velocity represents concurrent vertical mixing, presumably mainly due to convection (Träumner 2013; Schween et al. 2014). Additionally, a schematic diagram by De Wekker and Kossmann (2015) (Fig. 11 in their article) shows that, due to mountain venting exerted by the complex terrain, convection is not the only mixing mechanism that produces mixing in these complex boundary layers and, therefore, aerosols may disperse vertically above the convective boundary layer. The present research also suggests that aerosols might be transported to higher levels by other mechanisms different from convective movements; these other mixing processes could include thermally driven winds associated with the topography. Additionally, this height reached by aerosols seems to be similar to the upper stable layer identified with radiosonde measurements (red triangle) at 1800 LT in Fig. 4, whereas the lower thermally stable height (blue triangle) is similar to the heights retrieved via thresholding. In particular, the daytime height where the thermally stable layer is found is roughly coincident with the threshold-obtained height corresponding to \(\sigma _\textrm{thld}^2 = 0.1\) m\(^2\) s\(^{-2}\) for most of the months. On the other hand, at 0600 LT the elevated thermally stable layer is not coincident with the ceilometer-obtained ABLH and may correspond to the residual layer, which is not estimated in the present study. This residual layer develops during nighttime, and although the sunrise and sunset times change over the year, this variation is usually small as it can be seen in Fig. 3.

4.3 Case Studies: Differences Between Cloudy and Clear-Sky Days

In the present research, the estimated ABL heights are mainly analysed through monthly averages of the diurnal cycle which, in general terms, elucidates the physically realistic behaviour of the diurnal cycle. Nevertheless, different atmospheric conditions can significantly affect the measurements of these remote sensing techniques (Löhnert et al. 2008; García-Dalmau et al. 2022; Duncan Jr et al. 2022). In order to investigate the variability between days with different conditions, a case study is also presented. In particular, both the wind lidar and the ceilometer measurements are affected by the presence of clouds and precipitation. In Fig. 5, the variance of the vertical velocity and the backscatter plots are presented for an essentially clear sky and a mainly cloudy and rainy day.

The cloud detection algorithm implemented in García-Franco et al. (2018) was used to separate clear-sky and cloudy-rainy conditions for the ceilometer. This algorithm uses the composite mean variance of the ceilometer backscatter using all the profiles to establish a threshold to detect cloud or rain in a vertical profile. If at any height, the backscatter is higher than the threshold, then that 10-min window is classified as cloudy. One example of a generally clear sky day was February 7, 2019, as it only has 4.9% of the 10-min periods with clouds detected by the ceilometer. In contrast, June 24, 2019, was chosen to illustrate a cloudy day because it has 68% of the 10-min periods with clouds detected. Additionally, on this cloudy day, the backscatter in the lower right panel of Fig. 5 shows a strong backscatter signal throughout the day, which reveals the presence of clouds and precipitation.

Fig. 5
figure 5

The two upper panels correspond to a clear-sky day (February 7, 2019) and the two lower panels to a cloudy day (June 24, 2019). In the left side, the diurnal evolution of the variance of the vertical velocity is shown, whereas the right side shows the backscatter from the ceilometer. In the plots at the left, the estimated heights with the thresholding method are presented with black circles filled in green for \(\sigma _\textrm{thld} ^2 = 0.1\) m\(^{2}\) s\(^{-2}\) and in blue for \(\sigma _\textrm{thld} ^2 = 0.2\) m\(^{2}\) s\(^{-2}\). In the ceilometer-obtained plots, the ABL heights estimated from the backscatter are shown as magenta dots when the cloud filter was not applied and as red dots when this filter was applied. However, in clear sky conditions, these two estimated heights are roughly coincident

In Fig. 5 we show that, for the clear sky case, the diurnal cycle is replicated better and more smoothly, followed by high variance values of the vertical velocity than during the cloudy (and partially rainy) day. In fact, for the cloudy and rainy day, the available data for computing the variance of the vertical velocity from the lidar measurements are highly diminished. Because of the strong attenuation that the Doppler lidar suffers during cloudy-rainy conditions, there are only data available at lower elevations during daytime hours, hardly reaching 700 m. The ABLHs estimated from this criteria are also very low and are affected by the weather conditions. For the MLH estimated from the backscatter, we only see magenta dots in the clear sky case that corresponds to the not cloud-filtered data because the red filtered dots are covered by the non-filtered ones. MLH estimations are mainly available in the early morning slightly elucidating the beginning of the diurnal cycle, and very few estimations are present over the more developed daytime ABL. However, daytime MLH values reach more than 2000 m from the backscatter data. In the cloudy case, it is shown that filtered and non-filtered MLH estimations do not match each other due to the strong presence of clouds and precipitation. The early morning evolution of MLHs is also elucidated for this day, and more elevated heights (between 1500 and 2500 m) are estimated for later daytime hours. These case studies elucidate the fact that both ceilometer and Doppler lidar are strongly affected by clouds and rain. However, the daytime ABL heights estimated from the backscatter criteria are more elevated than the ones from the thresholding Doppler lidar technique, for both clear-sky and cloudy cases.

4.4 ABLH Retrievals and Radiation at 1800 LT

In addition to comparing different ABLH retrievals during the diurnal cycle, the present research also examines the monthly evolution of all these estimated heights for the entire year of study. Figure 6 compares the ABLH estimated heights obtained by both remote sensing techniques and by radiosonde at 1800 LT. This radiosonde is the only one available at daytime hours and because of that, we chose to perform such a figure at that time, despite the fact that at 1800 LT there is not high convective turbulence. Additionally, we plotted the monthly mean radiation at that time in order to qualitatively elucidate its relation with the retrieved ABL heights. These radiation measurements were taken from a radiometer Hukseflux SR20-T1, located in the same station as the ceilometer and Doppler lidar (green point in Fig. 1).

Fig. 6
figure 6

ABL monthly averaged heights estimated via thresholding (blue and green lines), from the ceilometer backscatter (red line) and thermally stable layers obtained from radiosonde data (orange and cyan lines). Additionally, the monthly averaged radiation is plotted as gray bars. All the above data correspond to 1800 LT

Figure 6 shows monthly means of the retrieved heights during the year of study. It can be seen that the upper thermally stable layer (orange line) has roughly the same magnitude as the mixing layer height derived from ceilometer backscatter (red line). On the other hand, the lower thermally stable layer estimated from radiosonde profiles (cyan line) has a similar magnitude to that obtained via thresholding from Doppler lidar measurements with \(\sigma _\textrm{thld}^2 = 0.1\) m\(^2\) s\(^{-2}\) (green line). The backscatter-retrieved heights reach their highest values during February, April, May and June, whereas radiation is shown to reach higher values over late winter and early spring moths of February, March and April, when more sunny days occur. Radiation monthly mean values are shown to decrease during summer given that more cloudy and rainy conditions develop in that season. The heights obtained via thresholding do not illustrate a strong tendency in the annual cycle at 1800 LT. This relates to the fact that, as shown in Fig. 4, at 1800 LT the CBLH’s are much shallower than the maximum diurnal height, which in turn is related to the lack of strong convective movements at 1800 LT. Therefore, Fig. 6 does not show any clear relation between threshold-obtained ABL heights and solar radiation at 1800 LT.

5 Conclusions

The present research describes and compares different techniques for estimating the ABL height over Mexico City. Firstly, the vertical turbulent transport in the daytime boundary layer is shown to realistically grow and decrease during the diurnal cycle. Monthly averaged \(\sigma _w ^2\)s are shown, as well as two case studies that correspond to a cloudy-rainy and a clear-sky days. This \(\sigma _w ^2\) has been shown to be a crucial estimate for convectively driven turbulence in the ABL of other locations (Huang et al. 2017; Barlow et al. 2011; Schween et al. 2014; Tucker et al. 2009). However, to the best of our knowledge, it had not been investigated in Mexico City before. ABL heights are estimated here via thresholding from November 2018 to October 2019, and mean monthly heights are performed. Given that the value of the threshold is site dependent, we considered two different thresholds and compare them. In addition, based on the comparison with the thermally stable layers (obtained from radiosonde data) we argue that, when determining ABLH over Mexico City with Doppler lidar data, \(\sigma _\textrm{thld}^2 = 0.1\) m\(^2\) s\(^{-2}\) is preferable. Furthermore, this value agrees with the one proposed in previous studies over other urban areas (Barlow et al. 2011; Huang et al. 2017). A physically realistic diurnal evolution of these estimated heights is roughly shown for every month. Although clouds and precipitation stifle the remote sensing measurements, the majority of the estimated ABL heights are still physically realistic. Additionally, these retrieved heights are compared with heights estimated from ceilometer backscatter, as in García-Franco et al. (2018).

The comparison of the daytime ABL heights obtained by the different methodologies shows that at \(\approx \) 1600 LT the maximum diurnal value is reached by both remote sensing techniques for almost every month. However the ceilometer-retrieved height reaches up to 3000 m, whereas the heights obtained via thresholding hardly reach more than 2000 m. This difference between both methods has been found by previous authors in other locations and has been attributed to the fact that thresholding-estimated heights reveal the current mixing, whereas heights retrieved via backscatter show a history of mixing (Träumner et al. 2011; Schween et al. 2014). Additionally, it seems likely that this difference between heights may be related to a variety of mixing mechanisms, due to the complex topography around Mexico City. This argument is supported by the fact that diurnal ABL over mountainous terrains develops mixing mechanisms that are not only due to convection, but also influenced by mountain venting (De Wekker and Kossmann 2015; Serafin et al. 2018; Herrera-Mejía 2019). In addition, we show that multiple thermally stable layers are recognized from radiosonde profiles at 0600 and 1800 LT. This multilayer behaviour has also been shown previously over Mexico City (Burgos-Cuevas et al. 2021). However, as noted in this study, the estimated ABL height depends intrinsically on the very definition of the ABL itself. Over this topographically complex terrain, it appears that the aerosol layer height is not coincident with the convective boundary layer height. Therefore, this present study constitutes a revealing example of this difference previously pointed out. Future research that includes the analysis of a dense network of surface meteorological networks covering in some respect the complex terrain and considering also the horizontal components of the wind is necessary to further elucidate the complexity of the mixing mechanisms over Mexico City.

The present study illustrates the advantage of retrieving ABLH via different techniques. On the one hand, the backscatter-obtained heights show the elevation up to which aerosols (and therefore other pollutants) can disperse vertically. This height is crucial in terms of air quality, and it has been shown to be related to trace-gas concentrations (García-Franco et al. 2018) and aerosol content (García-Franco 2020). Although backscatter-derived ABLH is generally not able to distinguish between daytime mixed layer and the residual layer, it does determine the vertical pollutant dispersion and, therefore, it is likely to be the most important one in terms of air quality. On the other hand, the Doppler lidar-obtained height corresponds to the dynamic elevation up to which convective motions are important, and, therefore, may be the most useful for model parametrization. This is crucial in order to investigate the dynamics of the ABL and the improvement of air quality forecasting, which, in turn, is essential to predict contamination episodes and, ultimately, contribute to their prevention.