Exploring Atmospheric Boundary Layer Depth Variability in Frontal Environments Over an Arid Region

Details about atmospheric boundary layer (ABL) dynamics under advection over arid regions remain unexplored. Most numerical weather prediction (NWP) models strictly rely on ABL parametrization schemes under steady-state assumptions while observation-based research also considers horizontally homogeneous atmospheric conditions for estimating ABL depth (zi) growth rates. However, how different frontal systems modify ABL thermodynamic features, including zi, remains sparse in the literature. This work investigates how synoptic events impact daytime zi variability in different seasons and provides new insights on front-relative zi variability over two sites located in an arid region. Radiosonde-derived thermodynamic profiles obtained during more than 40 synoptic events in 2020 from two sites (Amarillo and Midland, Texas) have been used. Individual soundings are divided into a three-day period: prefrontal, frontal, and postfrontal. The ABL regimes and associated soundings are further classified into four categories: (1) Type-I with elevated mixed layer (EML) only, (2) Type-II with dryline only, (3) Type-III with both EML and dryline, and (4) Type-IV without dryline or EML. Results suggest that zi decreases substantially during frontal passages and is shallower in the cold sector than the warm sector. We also find that the zi variability in the postfrontal airmass is more uniform throughout the year compared to the zi in the prefrontal airmass indicating complexities associated with airmass advection. Regression analyses comparing frontal strength and observed Δzi (i.e., frontal contrasts in zi estimated via zi in warm sector minus zi in cold sector) do not yield any correlations, which suggests that advection from frontal passages has considerable influence in governing zi variability unlike in the conditions when zi is mainly dependent on surface forcings. By explaining how airmass exchange associated with frontal environments impacts overall ABL dynamics, new parametrizations for ABL modelling can be developed with an emphasis on zi advection.


Introduction
The atmospheric boundary layer (ABL) is the part of the troposphere that is directly influenced by surface forcing. Knowledge of ABL thermodynamics and turbulence are important for understanding convection initiation, cloud formations, waves, eddies, and localized wind shear (Stull 1988). However, like any other layers of the atmosphere, the ABL thermodynamics are prone to changes pertaining to airmass advection. These advective processes in the atmosphere are considered equally important as vertical fluxes and turbulence (Stull 1988;Lenschow 1973). Numerical models of ABL thermodynamics under advective processes suffer from two limitations: (1) the "real" vertical profiles of thermodynamic parameters (i.e., observations) are influenced by advection while models find it difficult to simulate the impact of advection on ABL depth (z i ) and (2) the parametrizations that diagnose z i are not fully accurate due to the fact that they are based on steady-state assumptions. Lenschow (1973) and Stull (1988) stated that in addition to horizontal the advection of momentum, moisture, heat, and pollutants, advection of z i needs to be considered in the investigation of ABL properties under advection on different temporal (diurnal, interdiurnal, synoptic, etc.) and spatial scales (mesoscale and synoptic scale in this context). How the z i changes with time ∂z i ∂t mainly depends on three factors: (1) changes in z i due to horizontal advection by the mean wind (u j ) along horizontal changes of z i e.g., −u j entrainment, and (3) subsidence processes (Stull 1988) as outlined in Eq. 1 for onedimensional advective flows, where w e and w l refer to the entrainment velocity and subsidence velocity, respectively. One should note, in essence, entrainment term implicitly includes encroachment since entrainment defines the mixing process at z i while encroachment describes the thermodynamic growth of the ABL (Stull 1988). Thus, understanding how z i changes under the impact of advection is important because neglecting these changes can result in forecasting errors in z i tendencies (i.e., z i growth rate). In synoptically active environments, these errors in ABL parametrizations increase since an interaction of two different air masses leads to significant inhomogeneities in both the horizontal and vertical ABL structures (Pal et al. 2021). When spatial inhomogeneity in the ABL persists during the afternoon hours, model simulations using several ABL parametrizations (e.g., mixed-layer model, eddy diffusivity or K-closure) yield different values of z i compared to observations (Lac et al. 2013;Anurose and Subrahamanyam 2015). To quantify the contributions of the advection of heat and moisture by using numerical simulations and observations, Pietersen et al. (2015) found that by only taking surface and entrainment fluxes into account the value of z i is overestimated by 70%. Additionally, most of the observation-based studies of z i variability assumed horizontally homogeneous conditions (i.e., ∂z i ∂ x j = 0), ignoring horizontal advections (i.e., from frontal systems, or mesoscale circulations) altogether (Seidel et al. 2012;Mehta et al. 2017;Bianco et al. 2021). Thus, oftentimes, the interpretation of the observations also suffers from the omission of advection leading to errors and an incomplete understanding on the impact of advection on measured z i variability (i.e., tendency term, ∂z i ∂t , in Eq. 1). In the past literature, four key advective processes were reported that directly or indirectly influence ABL features and spatial z i variability across: (1) urban-rural interface, (2) land-sea interface (i.e., in coastal areas), (3) mountains and adjacent plains, and (4) frontal boundaries. The first three advective processes (i.e., 1-3 in the list) are mainly related to different types of geographical locations and related to fixed features in the landscape that lead to inhomogeneities in the ABL. In contrast, the advection due to frontal passages (i.e., fourth in the list) is primarily driven by airmass exchange across a large region, thus, inhomogeneities in the atmosphere. In essence, these advective processes are not fundamentally different from each other, as they create airmass inhomogeneities (e.g., Davis et al. 2021;Walley et al. 2022). However, these processes utilize different types of advective fluxes and the impact of different types of advections differ on the spatial scale. In particular, the first three advective features are fixed in space, while a frontal passage is a dynamical feature. Table 1 summarizes the similarities and differences among the four advective processes. For instance, at the urban-rural interface, the advection of urban boundary layer airmass was found to be dominant over rural regions for 30-40 km downwind (e.g., Angevine et al. 2003;Zhang et al. 2011;Barlow 2014) while the onshore flow often dominates more than 100 km inland in coastal areas (e.g., Liu et al. 2001;Pal and Lee 2019a).  Pal and Lee (2019a, b) Mountain and Adjacent Plains 4-6 h 300-500 km Stagnant θ , q, U, W Arritt et al. (1992), Stensrud (1993), Pal and Lee (2019b) Frontal Boundaries 1-3 days 500-1000 km Moving T , θ , q, U, V, Q, and Γ Bond and Fleagle (1988), Shafer and Steenburgh (2008), Sinclair et al. (2010), Boutle et al. (2010), Jenkner et al. (2010), Payer et al. (2011), Pal et al. (2020a) Additionally, midlatitude cyclones modify the atmosphere, and thus the ABL, on a larger scale (Bond and Fleagle 1988;Sinclair et al. 2010;Boutle et al. 2010). Advection in the context of frontal passages modifying the ABL features not only contribute to the airmass exchange associated with advective flux but also impact the land-atmosphere feedback processes (LAFPs) via extensive cloudiness, enhanced precipitation, and an increase in soil moisture and heat fluxes.
In a frontal environment over the south-west US, an elevated mixed layer (EML) advected off the higher elevations of the Mexican Plateau is often transported over the adjacent plains (i.e., the Southern Great Plains) via westerly or south-westerly upper-level flows. These EMLs have three distinct types: (1) clearly separated EML with an underlying ABL; (2) EML and ABL completely merged; and (3) an interim regime of 1 and 2 with EML merging with ABL (see Sect. 2.2.2 for additional details). The horizontal advection of EML formed over terrains due to diurnal surface heating influences convection initiation in the adjacent plains (e.g., Lanicci & Warner 1991). In a frontal environment, often these EMLs play an important role in building up low-level instability, as the mid-level winds push steep lapse rates from the high terrain atop the moist Gulf of Mexico air yielding conditional instability. The extension of EMLs off the mountains dominates more than 100-200 km downstream (e.g., Arritt et al. 1992;Stensrud 1993;Pal and Lee 2019b). Thus, an exploration of ABL depths in a frontal environment remains incomplete without the consideration of an EML for a region where they frequently appear. Therefore, in this study, we explored front-relative z i variability in different EML regimes. Additionally, Hoch and Markowski (2005) found that a moisture boundary often occurs before the cold front passages at the interface of west/southwesterly (drier airmass) and southerly/south-easterly (humid airmass) flows in the south-west US region yielding the occurrence of drylines. Other studies also reported climatologies of front-relative changes in stability, heat flux, and associated thermal advection (Boutle et al. 2010;Sinclair 2013).
A large number of studies about z i climatology exist in the literature documenting dynamics of z i on different time scales (diurnal, seasonal, annual, and interannual) over different sites across the world (Bianco et al. 2011;Guo et al. 2011;Seidel et al. 2012;Chan and Wood 2013;Lee and Pal 2017;Mehta et al. 2017). However, no studies exist that report z i variability around frontal passages or investigate front-relative z i features in the presence or absence of EMLs or drylines. Thus, our knowledge about z i variability during the course of synoptic-scale weather systems remain underexplored.
We hypothesize that horizontal advection associated with the frontal passages impact z i variability over land, since fronts extensively modify the ABL thermodynamics by advecting different airmasses on a larger region (warm-humid-southerly flows and cold-dry-northerly during prefrontal and postfrontal conditions, respectively; Sinclair et al. 2010;Pal et al. 2020a;Clark et al. 2022). Additionally, precipitation associated with the frontal passages change LAFPs via increasing the soil moisture and hence help reduce z i . Relatively less attention was paid to z i changes via weather, in particular, over arid regions (Hua et al. 2016).
Within this work, we aim to explore three research questions: (1) how advection impacts z i variability during the course of frontal passages through the year over an arid region (i.e., south-west US); (2) how the presence of EMLs, dryline passages, and vertical wind shear impacts the ABL thermodynamic structures during each of the three frontal phases; and (3) how changes in z i during the course of a respective cold front passage may be explained by the strength of the aforementioned front? Additionally, since the presence of vertical wind shear is not uncommon during frontal passages, this study gives an opportunity to explore the ABL depth changes as a function of vertical wind shear, though it remains complicated to disentangle the impact of frontal passages and vertical wind shear on z i variability.

Datasets and Methods
Here, we provide a comprehensive overview on the datasets and methodologies applied to obtain front-relative z i variability, in particular, focusing on (1) a brief presentation of the experimental region and a detailed overview of datasets used (e.g., radiosonde profiles, surface meteorological measurements); (2) the rationale behind the selection of the variables required to answer the research questions; and (3) an outline explaining the connections among the variables (dependent and independent) to determine how different types of fronts influence the changes in z i during a frontal passage at the surface (i.e., pre-cold-frontal region through frontal to post-cold-frontal region) using a flowchart at the end of Sect. 2.2.3.

Experimental Region and Datasets
The south-west US, in particular, the West Texas region, lies at a complex interface of cold semi-arid (BSk), hot semi-arid (BSh), and humid subtropical (Cfa) climates (Beck et al. 2018, Fig. 1). The two sites located in the experimental area (i.e., Amarillo (35.2331°N, 101.7092°W, and1094 m MSL) and Midland (31.9425°N, 102.1892°W, and 873 m MSL)), in the Texas Panhandle region, encounter extreme seasonal variability in temperature (seasonal temperature ranges of 28°C and 27°C for Amarillo and Midland, respectively). Midland is partly drier than Amarillo in terms of annual precipitation (NWS Amarillo 2020; NWS Midland 2020). Both Amarillo and Midland are located on flat terrain. Amarillo is located in the grasslands of Northern Texas and surrounded by dense prairies. Midland is located approximately 387 km south of Amarillo (Fig. 1a) in the Permian Basin of West Texas and surrounded by oil and natural gas fields.
The experimental region is also characterized by frequently occurring mesoscale boundaries distinguishing maritime, tropical airmasses from continental, dry airmasses from arid Fig. 1 Overall synoptic set-up of the continental US at 0000 UTC on 28 March 2020 (frontal day of one of the selected cases for this study illustrating a typical frontal regime with the passage of a cold front and associated dryline) (a) using the surface map analysis obtained from WPC (The locations of the two IGRA sites (Amarillo (red dot) and Midland (green dot) in West Texas are also marked: Source of the surface chart: NOAA/NWS/WPC (2020). Radiosonde profiles of mixing ratio (g kg −1 ) (b), potential temperature (K) (c) from Amarillo on 17 February 2020 at 0000 UTC with z i indicated regions in northern Mexico, eastern New Mexico, and western Texas. Both sites are often affected by synoptically active weather conditions, including dryline passages and advection of EMLs from the higher terrains (the Rocky Mountains and the Mexican Plateau) to the west (e.g., Hoch and Markowski 2005). Thus, this experimental region provides an excellent testbed to obtain empirical evidence on the impact of frontal passages on ABL depth variability under different meteorological conditions, including the presence or absence of EMLs and drylines. Additionally, in previous studies (e.g., Seidel et al. 2012;Lee and Pal 2017;Clark et al. 2022), very deep z i were observed over the region. However, no distinction was made on the role of EMLs on ABL thermodynamic features including z i . Furthermore, Stensrud (1993) illustrated the impact of EMLs to limit the mixing in the ABL and thus lead to shallower z i , but their study did not have a closer look at different types of EML evolution (e.g., EML merging with the underlying ABL, EML remaining separated from ABL).
To address the aforementioned research questions, we used three different data sources: (1) radiosonde measurements obtained from two sites, Amarillo and Midland, to determine z i (see Sect. 2.2.1 for details); (2) surface analysis maps (3-h interval) obtained from the Weather Prediction Center (WPC) to determine the frontal passage cases and to classify the z i regimes with respect to frontal boundaries (Sect. 2.2.2); and (3) measurements from near-surface meteorological stations located in the West Texas region to determine frontal strengths (Sect. 2.2.3).
Radiosonde profiles were obtained from the Integrated Global Radiosonde Archive (IGRA, Durre and Yin 2008) for both Amarillo and Midland (Fig. 1). These profiles were used to determine z i . The vertical resolution of the soundings was less than 100 m at the surface layer and was 100-200 m (depending on the ascent rates) in the ABL. In general, the radiosonde derived z i measurements suffer from two major issues: vertical resolution in the measurements and errors due to sampling by the sensors themselves. The profiles of state variables obtained from the soundings are often limited by the vertical resolution and the representativeness of (horizontal) point measurements, which can impact the observed vertical structure of the atmospheric thermodynamics (Wang et al. 2009;Seidel et al. 2012;Chan and Wood 2013). Recently, Lee and Pal (2020) performed some detailed analyses on the impact of differently resolved thermodynamic parameters on z i retrieval. They found that the radiosonde-based method results in errors (1) in the radiosonde measurements themselves based on manufacturer-reported uncertainties and (2) errors caused by the environment (e.g., radiative effects on the thermodynamic measurements).
To characterize surface meteorological conditions and relate them back to the observed z i measurements during the selected cases, we used daily precipitation (i.e., 24-h accumulation) measurements (NWS Amarillo and Midland 2020) and high-resolution (5-min) measurements of temperature and dew point obtained at Amarillo and Midland via the Automated Surface Observing System (ASOS) network (Iowa State University 2020a, b).

Retrieval of Boundary-Layer Depth
In this work, we are mainly interested in exploring daytime z i changes during frontal passages rather than nocturnal z i variability. In order to determine the top of the ABL, a gradient-based approach was used to determine the height of the strongest vertical gradients of potential temperature (i.e., ∂θ ∂z ) and mixing ratio (i.e., ∂q ∂z ) (Hennemuth and Lammert 2006;Pal et al. 2010;Seidel et al. 2010). In Fig. 1b, c the ABL top height is marked as the location where the mixing ratio started sharply decreasing and potential temperature started increasing with height.
We analyzed only the 0000 UTC soundings. Since the experimental region is located in the central time zone of the US, 0000 UTC during March-November corresponds to 7 h past local noon while for the rest of the year 0000 UTC corresponds to 6 h past local noon. Thus, in the winter season, the 0000 UTC sounding takes place around local sunset, while in the summer season it takes place at the end of the afternoon. During the detection of the ABL top height, we scanned upward in each sounding and filtered the stable portion of the sounding (i.e., ∂θ ∂z > 0). We then determined the value of z i as the height at which the strongest potential temperature inversion occurs (e.g., Vogelezang and Holtslag 1996;Seidel et al. 2010;2012). Doing so allowed us to estimate the depth of quasi-stationary afternoon ABL. For this method, it is assumed that the daytime ABL top becomes the top of the residual layer after sunset (Stull 1988), which was previously used a number of studies (e.g., Seidel et al. 2010;2012;Lee and De Wekker 2016;Lee and Pal 2017).

Surface Analyses and Selection and Classification of Frontal Cases
The surface synoptic chart analyses obtained from WPC were subjectively used to determine the cold front passages at the surface (henceforth, referred to as frontal passages only) at the two sites between 1 January and 31 December 2020 (see Fig. 1a for an example). We also analyzed the ASOS datasets to confirm those frontal passages via locating the time of sharp temperature and dewpoint drops. As illustrated in Fig. 1, using the surface synoptic chart, the selection was based on the premise that the cold front moved entirely through the respective radiosonde site in a 3-day sequential period such that (1) the radiosonde site was generally located in the prefrontal sector (i.e., ahead of the frontal boundary in the warm sector of the cold front, often referred to as the pre-cold-frontal region) on Day 1, which we refer to as the sounding on the prefrontal day; (2) approximately at or near the frontal boundary on Day 2 when the cold front passage occurred over the site, which we refer to as the sounding on the frontal day; and (3) the day after when the cold front passed the radiosonde site on Day 3, which we refer to as the sounding on the postfrontal day (i.e., the site was behind the frontal boundary within the cold sector regime, often referred to as post-cold-frontal region).
For z i measurements obtained on the day of the frontal passage (frontal regime, Fig. 2b), some were sampled in the warm sector, like in Fig. 2a, while others were sampled in the cold sector. This idea helps explain the inconsistent variability for the z i measurements on the day of the frontal passage. We note the sequential soundings, sampling the prefrontal, frontal, and postfrontal conditions (i.e., Day 1, 2, and 3) of a cold front passage and the relevant impact of the ABL depth variability, provided a complete picture on how the three days are related to the position of the front on the map. It was almost impossible that a frontal passage at the surface (determined from ASOS stations) took place exactly at the time of radiosonde launch. Since ASOS measurements were continuous (i.e., 5-min temporal resolution) and daily radiosonde measurements were used for determination of z i , one must consider that this remains one of the limitations of the method.
For a systematic evaluation of the impact of frontal passages on z i variability, we selected at least two frontal passage cases in each month of 2020. We considered two cases (i.e., 6 soundings or 6 days) per month, which helped us to obtain at least two frontal cases in all the months of each season. Also, such selection helped us find seasonal dependence of the frontal signatures on the z i variability (if any) and present an unbiased statistical representation of the results. But the synoptic conditions in July and August did not allow us to find two cases in those months. In general, during July and August, there exists a lack of frontal passages Schematics illustrating selection of the three types of front-relative z i samplings (i.e., in prefrontal condition, often referred to as pre-cold-frontal region, a; frontal condition b; and postfrontal conditions, often referred to as post-cold-frontal region, c using the radiosonde measurements at a site (here Amarillo or Midland) indicating how the three days (hence, three radio soundings) are related to the position of the front on the map. An idealized schematic d illustrating z i variability for (I) cases with only EML (left), (II) cases with only dryline (middle), and (III) cases with both EML and dryline (right). Both ABL and EML have an adiabatic profile. The horizontal displacement between the two columns in each panel is a spatial displacement. With synoptic systems moving eastward with our analyses evincing the pre-versus postfrontal z i regimes, one should interpret the temporal development of ABL features by looking at each panel from right to left as marked by the horizontal purple arrows at the bottom of each panel. Light blue, green boxes, and white region above mark ABL, EML, and FA (free atmosphere), respectively. Brown lines with half circles denote the passage of dryline from west to east over the sites. Both dry and moist sectors are marked. Dotted curve indicates the z i (Davis et al. 1997). In particular, we noted that a strong area of high pressure over the region generally dominated for the most part of summer 2020. In general, for both sites, the months of April and May yielded more frequent frontal and dryline passages than any other times of the year. Consequently, we selected some additional cases, which helped provide a holistic view on the impact both dryline and cold fronts have on the ABL depth and thermodynamic variability.
Based on the aforementioned studies and our knowledge about the region's climate, we hypothesized the z i evolution over the region is influenced not only by classical synoptic weather systems and land-surface forcing, but also by EML and dryline. After exploring the WPC charts, we identified 21 and 24 frontal passage cases over Amarillo and Midland, respectively. We then subdivided those frontal passages into a number of 'types' of frontal passages based on two criteria: presence of EML and passage of a dryline. The selection of the frontal cases and associated dryline passages were determined via analyzing the WPC surface chart analysis while the determination of the presence of an EML was made using the radiosonde-derived θ profiles (Stensrud 1993). Using θ profiles, we sought for two adiabatic potential temperature regions in the vertical profile; the first one being the ABL while the second one is the EML. As discussed before, each frontal passage case is comprised of soundings during prefrontal, frontal, and postfrontal regimes. One should note that the first and second case within a month was denoted as C1 and C2, respectively (see , Tables 3, 4).
Consequently, based on the analyses of individual soundings, we categorized the frontal passage cases into 4 groups: (1) cases with only EML (Type I), (2) cases with only dryline (Type II), (3) cases with both EML and dryline (Type III), and (4) cases where neither of the features (i.e., drylines and EML) were observed (Type IV). We illustrated the classification via a conceptual framework (Fig. 2d). For instance, we categorize a case as Type I (i.e., with only EML) when the boundary-layer structure is modified from prefrontal to frontal day, due to the development of an EML, but without a horizontal frontal passage (here cold front). It is not the frontal passage at the surface that causes the EML in these cases, rather it is the EML coming from the higher terrain west of Amarillo and Midland (the Rocky Mountains and the Mexican Plateau). This framework illustrates how the structural differences among an EML case, a dryline case, and a case with both features impact z i during cold front passages. All the cases were segregated using the above criteria and Table 2 provides an overview of all the cases with frequency for four different categories (Types I, II, III and IV).
Based on this framework, we hypothesize that an EML in a frontal environment (Type I) results in a shallower z i . However, if the capping inversion associated with the ABL top is weak, the EML would eventually merge with the ABL over the site the following day and result in a deeper z i . In terms of z i during the dryline passage (Type II), we hypothesize z i would increase once the dryline moves east of the respective site due to greater mixing behind the dryline (Fig. 2d) (Hoch and Markowski 2005). For Type III, we hypothesize that the stronger the EML and thus capping inversion, the shallower the z i in the moist sector of the dryline. Regarding the differences between Types II and III, we note that in the pre dryline sector, one would generally observe an EML due to westerly winds aloft advecting the ABL from the higher terrain over the moist ABL. However, a weak EML could have developed and merged with the underlying ABL quickly and was not properly observed at the time of the radiosonde measurements (in this case, an interval of 24 h in between two radiosonde profiles). Finally, if neither an EML or dryline is present in the frontal environment (Type IV), we hypothesize that there will be a deeper z i present ahead of the cold front, with a shallower z i observed behind the cold front due to cold air advection and subsidence.
We also analyzed the relationship between z i and wind shear at the top of the ABL. According to Pino et al. (2003) and Conzemius and Fedorovich (2006), shear in the entrainment zone under homogeneous conditions can result in the ABL growing faster and thus result in a greater depth compared to a ABL with no shear. The presence of shear at the entrainment zone helps to enhance the entrainment fluxes thus leading to increased ABL growth. However, this principle has not been studied within a frontal environment. To accomplish this, the wind shear at the ABL top was obtained by calculating the change in wind speed around that respective altitude across a depth of 1 km for each sounding. We segmented the shear values for each case based on the three frontal regimes (prefrontal, frontal, and postfrontal) to produce an analysis showing the shear values observed for the three-day period of each case. We did not analyze wind shear based on the four aforementioned front-relative categories above to prevent further reduction in the sample size for each category. We also grouped z i with their predetermined frontal regime into associated shear ranges, and developed analyses of the mean, standard deviation, and ranges of these z i samples on two different shear ranges (e.g., 2.5-7.5 m s −1 km −1 and 7.5-12.5 m s −1 km −1 ) for the three frontal sectors (prefrontal, frontal, and postfrontal).

Thermodynamic Characteristics and Frontal Strength
In addition to z i variability, the impact of frontal passages was also analyzed through changes in mixing ratio and potential temperature in the ABL and FT (free troposphere). This was accomplished through analyzing the mean, standard deviation and range of mixing ratio and potential temperature in the ABL and FT for each frontal passage case over both sites as illustrated in idealized vertical profiles of θ (potential temperature) and q (mixing ratio) for both prefrontal (warm sector marked in red) and postfrontal (cold sector marked in blue) sectors where z i for both profiles are also marked (Fig. 3). The purpose of these analyses was first to investigate the front-relative changes in both ABL and FT moisture and potential temperatures individually and then identify how ABL-to-FT changes in both parameters varied during the frontal passages. To estimate the mean ABL temperature and moisture, we averaged the q and θ observations across 400 m thickness keeping the altitude of z i /2 at centre. We selected a number of samples (i.e., 400 m thickness) to reveal the variability within the ABL and FT, if any. Otherwise, one sample or mean value chosen may not be representative of ABL and FT. For estimating the mean FT temperature and moisture, we averaged the q and θ observations sampled across the altitude of 2z i . First, for each sounding, we determined mean θ and q for both ABL and FT regions (i.e., ABL-θ , FT-θ , ABL-q, and FT-q). Then, we found Fig. 3 Idealized vertical profiles of potential temperature (θ , left panel) and mixing ratio (q, right panel) for both prefrontal (i.e., warm sector) and postfrontal (i.e., cold sector) with z i marked using black arrows for both profiles. Red and blue lines mark θ for prefrontal and postfrontal conditions, respectively in the left panel while green and brown lines mark q for prefrontal and postfrontal conditions, respectively, in the right panel. The methods for estimating ABL-θ and ABL-q and relevant ABL-to-FT contrasts in both θ and q are also shown which helps fulfill the objective of connecting all variables derived from the sounding data the temporal differences (i.e., prefrontal to postfrontal) in the magnitudes of vertical contrasts in θ (i.e., ABL-θ minus FT-θ ). We repeated the same analyses for vertical contrasts in q (i.e., ABL-q minus FT-q). Finally, we determined ABL-to-FT contrasts in both parameters (q and θ ) for the three frontal sectors (i.e., prefrontal, frontal, and postfrontal). These analyses were performed to investigate the changes in the thermodynamic parameters during the course of an individual case and then for all the cases.
Additionally, near-surface temperature and dewpoint measurements (high resolution ASOS measurements) were used to determine frontal strength of each case using two approaches. Within the first method, we analyzed the changes in the temperature and moisture from the time of the frontal passage (i.e., actual hour of frontal passage) to 24-h after the time of the frontal passage while for the other method, we analyzed the change in the temperature and moisture over a six-hour period during the frontal passage (one hour before to five hours after the frontal passage) (Alpert 1947). The six-hour method helps to show short-term temperature and moisture advection caused by the front itself, while the 24-h method shows both the temperature and moisture advection caused by the front as well as removing diurnal cycle impact on these two parameters. For instance, + 24 h from the time of frontal passage is actually day + 1 relative to the day of frontal passage.
Based on the previous studies focusing on LAFP related to the impact of soil moisture changes on z i (Findell and Eltahir 2003;Ek and Holtslag 2004;Smith et al. 2021), we hypothesized that for our cases an increase in precipitation resulted in an increase in soil moisture yielding smaller amounts of sensible heat fluxes and shallower z i . Due to lack of comprehensive measurements of soil moisture, heat fluxes and precipitation amounts at both sites, it was not possible to determine the relative importance of LAFP via soil moisture change versus the impact of frontal passages on the z i variability over the sites. Additionally, a similar impact of soil moisture changes on z i were found in both mesoscale environment (Desai et al. 2006) and anomalously high annual precipitation event (Pal et al. 2020b).
An overview of the overall methodology to determine the front-relative changes in z i and ABL thermodynamic features during frontal passages over the two sites is shown in Fig. 4. The flowchart explains how the datasets were used to achieve the research goals and connect the dots between the dependent and independent variables through four major analyses: (1) how the classification of frontal types is used to determine how different frontal types influence the changes in z i from prefrontal through frontal to postfrontal conditions; (2) how different shear environments impact the front-relative z i changes (see Sect. 2.2.2); (3) exploiting the dependence of ABL-to-FT q and θ contrasts on frontal passages via comparing the findings during prefrontal versus postfrontal conditions; and (4) regression analyses between the Fig. 4 A flowchart showing an overall methodology to explore the front-relative z i variability and changes in the vertical structures of ABL features (e.g., ABL-to-FT q contrasts, ABL-FT shear) using IGRA radiosonde profiles obtained at two upper-air sounding sites (Amarillo and Midland), surface analysis maps, and nearsurface meteorological measurements at ASOS sites. The green and blue text in the lowermost rows indicate the dependent and independent variables considered for exploring the frontal modification of ABL features from prefrontal through frontal to postfrontal conditions frontal strengths and magnitude and changes in z i due to frontal passages for all the cases to determine if there was any correlation between temperature change and z i change caused by the cold front.

Overall Boundary-Layer-Depth Variability
Here, we first provide a comprehensive overview on the overall z i variability observed over both sites for all the selected cases (prefrontal, frontal, and postfrontal) during 2020. Figure 5 shows the observed z i (in m above ground level, AGL) at each frontal stage for 21 frontal cases observed for Amarillo and 24 frontal cases observed for Midland. For most frontal cases at both sites, the deeper z i was generally observed during the prefrontal stage and the shallower z i was generally observed during the postfrontal stage, with some exceptions (e.g., 24-26 May 2020, 14-16 October 2020 and 24-26 November 2020 in Amarillo and 12-14 April 2020, 22-24 June 2020, and 27-29 September 2020 in Midland) (Fig. 5). A one-toone intercomparison between the prefrontal versus postfrontal z i also confirms the decrease in z i due to the frontal passages over both sites (see Fig. 5c, d for Amarillo and Midland, respectively). In particular, over both sites, prefrontal z i were found to be very deep during spring (~4000 m a.g.l.) and late summer months (~3000 m a.g.l.). These results suggest that at both sites, a frontal passage usually resulted in a decrease in z i due to an incoming airmass with different thermodynamic characteristics. Additionally, subsidence often present behind the frontal boundaries might have produced shallower postfrontal z i based on the z i tendency equation (Eq. 1).
The z i variability on the day of frontal passage yielded significant case-to-case variability throughout the year and did not evince any noticeable seasonal pattern in them (Fig. 5). A number of 0000 UTC soundings were released during the prefrontal and postfrontal stages of the case, with very few soundings released when the surface front was exactly over the respective radiosonde site due to the relative timing of the radiosonde launches to the frontal passage. One should note that since our methodology includes the investigation of z i variability during the entire sequence of frontal passage (i.e., prefrontal, frontal, and postfrontal) for multiple cases, we investigated the z i variability over both sites for all three regimes. Future investigation using lidar or similar ground-based remote sensing measurements of continuous z i variability would allow additional insights on z i changes during the frontal passages in addition to the z i variability across frontal boundary in pre and postfrontal time-domain (e.g., Behrendt et al. 2005;Davis et al. 2018). Figure 5a, b show the variability in z i for different cases over Amarillo and Midland, respectively. Since we emphasized the front-relative changes in z i , the number of samples to ascertain the seasonal variability in z i (if any) remained limited for both pre-and postfrontal z i regimes. The results presented suggest that the seasonal amplitude for postfrontal z i regimes (~1500 m) was smaller than for the prefrontal z i regimes (~3000 m change) indicating that cold air advection behind a frontal boundary mostly minimizes z i variability, which illustrate that the air mass properties have a larger impact on z i growth for the postfrontal air mass or that this air mass is less variable through the year. Additionally, frontal precipitation would also allow more soil moisture which will further reduce the z i . Thus, a combination of increased soil moisture and a colder air mass helps reduce z i for the postfrontal regimes via soil moisture impact on sensible heat fluxes (i.e., higher soil moisture yielding lower sensible heat). However, further research is needed to confirm the relationship between airmass types and z i variability.
Also, the increase in soil moisture due to precipitations associated with frontal passages could be another potential factor in reducing z i for the postfrontal regimes via soil moisture impact on sensible heat fluxes and relevant LAFP (Blad and Rosenberg 1974;Todd et al. 2000). For instance, when comparing z i in each case with days where precipitation was observed, for more than 50% cases, shallower z i (< 1000 m) were observed on days with precipitation. Similar impact of soil moisture during prefrontal ABL sampling cannot be ignored as well. For instance, during the 19-21 March 2020 case in Amarillo, 3.8 mm of precipitation (NWS Amarillo 2020) was observed on the prefrontal day (0000 UTC 19 March 2020) resulting in a shallower z i of 1004 m. During the 27-29 March 2020 case in Amarillo, no precipitation was observed on the prefrontal day (0000 UTC 27 March 2020), leading to a deeper z i of 2129 m (Fig. 5a) (see Appendix, Table 3). Similarly, during the 19-21 March 2020 case in Midland, 33 mm of precipitation (NWS Midland 2020) was observed on the prefrontal day (0000 UTC 19 March 2020) resulting in a shallower z i of 595 m. During the 27-29 March 2020 case in Midland, no precipitation was observed on the prefrontal day (0000 UTC 27 March 2020), leading to a deeper z i of 2366 m (Fig. 5b) (see Appendix Table  4).
The LAFP and relevant precipitation and soil moisture relationship is not straightforward without the measurements of the all the components of the energy balance equation (Stull 1988). There exists some uncertainty in the assessments on the role of soil moisture mentioned above in modulating heat fluxes versus cloudiness affecting the energy balance. We note that additional future work needs to be performed using measurements at other sites (e.g., the Southern Great Plains Site in the US, SIRTA in Paris, Smith et al. 2021;Pal and Haeffelin 2016) where multi-instrument measurements of both LAFP and z i are available to quantify the relative impact of soil moisture changes on z i variability during frontal events.

Impact of Elevated Mixed Layer and Dryline on Boundary-Layer Depths
The values of z i observed at each of the 21 and 24 frontal cases for Amarillo and Midland, respectively, were categorized into four groups: cases with EML and dryline, only EML, only dryline, and with neither dryline nor EML ( Table 2). The aim of this segregation is to show the variability in z i (mean and spread) among the four categories. The z i variability for both Amarillo and Midland for all four types for both prefrontal and postfrontal regimes is shown in Fig. 6. The number of samples for each case are also marked. We note the presence of a dryline in a postfrontal airmass (i.e., Day 3 here) is not observed, thus appeared as null cases for Type II (only dryline) and Type III (both EML and dryline). In general, the results reveal, the days associated with the deeper z i (> 3000 m) were those with only a dryline present in the region (Type II in Fig. 6). We note a higher spread in z i for Type II in prefrontal regimes which mainly occurred due to the location of the sites relative to the position of the drylines (i.e., either behind or ahead of the dryline). In particular, once the site is behind the dryline, there is no longer a capping inversion caused by the low-level moisture ahead of the dryline (Fig. 2), thus increasing the entrainment of air from the FT and mixing depth of the ABL. While comparing pre-versus postfrontal z i variability, we found z i medians of 1004, 3484, 1896, and 1001 m a.g.l. in the prefrontal regime versus 884 and 934 m a.g.l. in the postfrontal regime for Amarillo while for Midland the median in the prefrontal z i samples were found to be 716, 2171, 1137, and 1653 m a.g.l. for the prefrontal sector versus 945 m and 1287 m a.g.l. for the postfrontal sector confirming the z i frontal contrasts, in particular, for two categories (Type I and IV, see Fig. 6).
Histogram analyses for all the cases are also shown in the Appendix (see Fig. 15) illustrating the frequency of days for particular z i ranges for all four frontal passage categories. Results also reveal that a higher number of cases with shallower ABLs were observed for the cases when only an EML was observed (Fig. 6a, b). When EMLs are advected from the higher terrain west of Midland and Amarillo, the lower part of the layer contains a stout inversion thus limiting the mixing and depth of the ABL below it (Stensrud 1993).
Additionally, based on the thermodynamic profiles containing an EML obtained over both sites (as shown on Table 2), we found a distinct impact of three different types of EML scenarios on z i variability (Fig. 7). For instance, results reveal EML regimes with different strengths: (1) clearly separated EML and ABL (8 June 2020 for Amarillo; 22 June 2020 for Midland; see For moderate interaction, the ABL and EML were in the process of merging with each other with a weaker inversion at the lower part of the EML (Fig. 7c, d). Also, days with moderate z i (between 1500 and 3000 m) usually contained an EML and a dryline (Type III) in the region as reported in Figs. 6 and 15. Thus, in a nutshell, the z i for a particular day  Table 2 in Appendix for the classifications front-relative z i patterns) in prefrontal (warm colors in the boxes) versus postfrontal (cold color in the boxes) conditions over Amarillo (a) and Midland (b). Medians are marked and also number of samples for each category are also shown Fig. 7 A multipanel view (columns are the two sites and the rows are different days with variable EML regimes) of radiosonde profiles of potential temperature (i.e., θ in K) obtained over Amarillo (a, c, and e) and Midland (b, d, and f) on three days (dates are marked) with z i indicated illustrating the varying EML strengths observed over the two sites. Each row depicts different EML strengths from well-defined EML (a and b) to EML merging with ABL (c and d) to completed merged EML and ABL (e and f) based on the potential temperature profile from the aforementioned days. The x-axis scales for different cases were kept variable since they were from different seasons greatly depends on the presence, location, vertical depth, and strength of an EML over the respective site and whether the site is ahead or behind the dryline boundary in the region. These two features finally help determine how deep the z i is in the late afternoon hours.

Impact of Shear on Boundary-Layer Depths during Frontal Passages
So far results presented provided some important details on the z i features relative to frontal boundaries (Sect. 3.2.1) related to the advection term in Eq. (1), while the analysis in this section is related to the entrainment term in Eq. (1). However, we observed that the frontal passages are often accompanied by temporary changes in vertical wind shear and found it important to investigate if the shear caused by a frontal passage could play a role in the z i tendency during the course of a frontal passage. In general, in addition to the buoyancy, mechanical turbulence governed by shear around z i in the entrainment zone also impacts z i growth rates (Pino et al. 2003).
However, it remained unclear how shear-dominated turbulence caused by the frontal passage structure and associated changes in z i occur over the course of a frontal passage during different seasons over land. To accomplish this, we calculated the wind shear across the top of the ABL (Fig. 8) for each sounding within all the frontal cases of the study using a methodology described within Sect. 2.2.3. In general, lower (higher) shear values were observed on the day before (during and after) the frontal passage, especially for Amarillo (Fig. 8). This could be due to the vertical wind structure of the fronts providing more shear for frontal and postfrontal wind profiles. Fig. 8 A chronological overview on the observed wind shear (in m s −1 km −1 ) across the top of the boundary layer at each stage (prefrontal (red square), frontal (green circle), and postfrontal (blue triangle)) for all frontal cases in both Amarillo (a) and Midland (b) during the year 2020. C1, C2, and C3 represent Case 1, 2, and 3, respectively for different months indicated. The wind shear magnitude was calculated across a depth of 1 km around z i To illustrate the relationship between the observed wind shear for each case across the top of the ABL to the observed z i and relate the z i tendency during different frontal regimes for various shear ranges, z i for the prefrontal, frontal, and postfrontal stages of all cases were grouped with their associated shear ranges (see Appendix, Table 5). We decided to neglect very low shear values (< 2.5 m s −1 km −1 ) for this analysis at both sites (Fig. 9). Additionally, we performed analyses of the mean, standard deviation, and ranges of z i samples on two different shear ranges (e.g., 2.5-7.5 m s −1 km −1 and 7.5-12.5 m s −1 km −1 ) for the three frontal sectors (prefrontal, frontal, and postfrontal) (Fig. 9). We did not perform similar analyses for the 12.5-17.5 m s −1 km −1 and greater than 17.5 m s −1 km −1 due to a limited number of samples. Overall, this analysis would help bring together the combined effect of both the entrainment term and the advection term −u j ∂z i ∂ x j on the change in z i (Eq. 1) over the time when the frontal passage moves over the respective site. It is important to note since z i varies greatly throughout the year due to seasonal effects and different thermodynamic conditions, a regression analysis comparing z i with shear values would not provide a holistic result.

Fig. 9
Box and whisker plots depicting the ranges in z i during the prefrontal, frontal, and postfrontal stage for shear ranges of 2.5-7.5 m s −1 km −1 (a, c) and 7.5-12.5 m s −1 km −1 (b, d) for both Amarillo (a, b) and Midland (c, d) Based on these analyses ( Fig. 9 and Table 5), we found that as shear increases the average z i becomes deeper within all three frontal regimes. For both sites, the increase in average z i from lower shear range (i.e., 2.5-7.5 m s −1 km −1 ) to higher shear range (i.e., 7.5-12.5 m s −1 km −1 ) is more pronounced for the prefrontal sector compared to the other two sectors. This is in line with the schematic we presented in Fig. 2 showing that cold air advection caused by the frontal passage reduces the z i variability in the frontal and postfrontal sector even when grouping them with their respective shear ranges. Additionally, since there is a more uniform z i in the postfrontal regimes for all shear ranges, the change in z i from the prefrontal to the postfrontal sector ends up being greater for higher shear ranges than with lower shear ranges. While comparing the z i variability under high sheared environment (i.e., 7.5-12.5 m s −1 km −1 ) at the two sites, results reveal deeper mean z i over Amarillo (Fig. 9b) compared to Midland (Fig. 9d) for both prefrontal and postfrontal regimes.
One should note that for the cases selected, we had larger number of samples for Midland than for the cases in Amarillo for different shear ranges. To reiterate, due to sampling differences, we did not perform further analyses and classifications on different shear ranges versus the scenarios of the presence or absence of drylines and EML. For instance, for one case we found a very deep z i (5030 m a.g.l.), and it was also associated with the presence of a dryline. Meanwhile, Midland had a larger range in a frontal z i compared to Amarillo for both shear ranges. It should also be noted that over Amarillo, for both shear ranges, we found that deeper z i were associated with prefrontal samples with shallower z i for frontal and postfrontal samples. However, this tendency was not clear for the observations at Midland.
To conclude, lower shear generally results in shallower z i in the prefrontal sector while higher shear generally results in deeper z i . However, higher shear generally has less of an impact, in terms of deeper z i , in both the frontal and postfrontal sector. It should be noted though that horizontal wind shear mainly affects z i growth rates while radiosonde provides a "snapshot" of the ABL yielding the integrated effect of ABL development. Thus, further detailed investigation on the impact of shear on z i growth rates certainly warrants further research using continuous measurements of z i (e.g., using lidar, ceilometer, sodar, etc.).

Boundary Layer to Free Tropospheric Differences in Potential Temperature and Moisture
So far, we have discussed the changes in the value of z i due to frontal passages at the two sites.
Here, we aim to accomplish the goal of explaining how the vertical thermodynamic structures change during the course of an individual frontal passage which help characterize the frontal passage as well. Indeed, ABL-to-FT differences in moisture are inherently dependent on frontal environment and thus, z i changes via the intricate processes involving z i development, inversion strength, entrainment mixing and finally the ABL-to-FT differences (Stull 1988). The purpose of these analyses (Fig. 10) was to determine the overall changes in the mean, standard deviation and range of the moisture and potential temperature values in both ABL and FA from the prefrontal through frontal to the postfrontal stage for one individual cold front event. In other words, how is the vertical moisture and temperature profile being altered during the course of a synoptic frontal passage and what impact does this have on the ABL development and overall characteristics. A number of studies investigated the impact of frontal passages on the near-surface meteorological features (Shafer and Steenburgh 2008;Sinclair 2013) while we extended those types of analyses for the entire ABL and FA. For individual frontal cases, the vertical structure of the ABL moisture profile was found to be more uniform in the cold sector, while in contrast, the vertical variability in ABL potential temperature was found to be more uniform in the warm sector. An example is provided in Fig. 10. For this frontal case (17-19 February 2020), the ABL moisture increases from the prefrontal stage to the frontal stage, before decreasing in the postfrontal stage as typically observed the ABL during frontal passages (Pal et al. 2020b). Meanwhile, the FT moisture remains constant, with a slight increase during the frontal stage most likely due to the frontal lifting of moisture laden ABL airmass to the FT. As a result, a frontal passage helps decrease the variability in the overall vertical moisture profile (Fig. 10a). Meanwhile, the ABL potential temperature decreases with respect to time and the FT potential temperature remains constant during the course of the frontal passage. However, since the potential temperature always increases with height above z i , the frontal passage results in increasing the vertical variability in potential temperature from the prefrontal to postfrontal stage (Fig. 10b).
Next, we performed a systematic analysis of the ABL-to-FT differences for both moisture (Fig. 11) and potential temperature (Fig. 12) for all the cases. For the ABL-to-FT differences in moisture, substantial variability among the cases (smaller decrease in moisture during the winter to larger decrease during the summer) from the ABL-to-FT is observed (Fig. 11a, b for Amarillo and Midland, respectively). Additionally, an intercomparison between ABL-to-FT moisture differences for prefrontal and postfrontal regimes also confirms an overall decrease in ABL-to-FT moisture contrasts due to the frontal passages over both sites (Fig. 11c, d for Amarillo and Midland, respectively).
The vertical atmospheric profile is drier in both the prefrontal and postfrontal stages during the cooler months, versus during the summer months, resulting in a lower magnitude decrease in moisture from the ABL-to-FT. As a result, during the cooler months, frontal passages cause the moisture in the vertical profile to go from relatively dry in the prefrontal sector to extremely dry in the postfrontal sector. In contrast, during summer months, low-level moisture increases via the typical southerly/south-easterly flow from the Gulf of Mexico due to the presence of broad H-pressure system over the region, which leads to higher ABL-to-FT moisture contrast.
When examining the postfrontal ABL-to-FT mixing ratio contrasts throughout the year, mixing ratio has a much greater decrease with height during the summer months than during the winter months which could be attributed to the fact that frontal passages and associated frontal strengths are weaker in summer than the other seasons (e.g., fall and winter). When comparing the two sites, Midland is observed to have a slightly higher decrease in moisture content especially during the summer months (Fig. 11b). This could be due to the location of Midland with the more humid surface air coming from the Gulf of Mexico to the east while the westerly winds aloft bring in the drier continental air from the higher terrain west of Midland. Also, since Midland is further south than Amarillo: frontal passages and advection of drier continental air into the ABL do not extend far south in order to create a more uniform ABL-to-FT moisture profile.
For the ABL-to-FT differences in θ , the increase in θ with height is usually greater in the postfrontal profiles versus the prefrontal profile at both sites with a few exceptions (Fig. 12a,  b). The intercomparison between ABL-to-FT θ differences shown in Fig. 12c, d for prefrontal versus postfrontal regimes also confirms a substantial increase in ABL-to-FT θ contrasts due to the frontal passages over both sites. This shows that the postfrontal vertical profiles are generally more stable than the prefrontal vertical profiles due to the cold air advection behind the front. However, future work will help to better understand the high variability in the ABL-to-FT differences in potential temperature for frontal regimes at both sites.
While analyzing the summer cases at both sites, we did not find any substantial differences between the prefrontal and postfrontal profiles in terms of potential temperature increase with height when compared to those in the late fall to early spring cases (Fig. 12). Thus, these Fig. 10 Box-and-whisker plots depicting mixing ratio (g kg −1 ) variability (a) and potential temperature (K) (b) in the ABL and FA at Amarillo for each stage (prefrontal, frontal, and postfrontal) during the time period of 17-19 February 2020 illustrating the way the ABL values and FT values, each in their own way, impact the contrast in moisture and temperature over the ABL top. The orange line in the box represents the mean value around the altitude of z i /2 for the ABL and around the altitude of 2z i for the FT. The box ranges for both the ABL and FT represent the 25th to 75th percentile values observed around the altitude of z i /2 and 2z i , respectfully. This whisker ranges for both the ABL and FT represent the minimum and maximum values around the altitude of z i /2 and 2z i , respectfully

Fig. 11
Differences in average mixing ratio (g kg −1 ) from the ABL-to-FT at each stage (prefrontal, frontal, and postfrontal) for all frontal cases in both Amarillo (a) and Midland (b) during the year 2020. C1 represents Case 1 of respective month. Intercomparisons between ABL-to-FT q contrasts obtained during prefrontal and postfrontal regimes for observations obtained over Amarillo (c) and Midland (d). The grey dotted line in panels c and d marks the 1:1 line for comparison confirming an overall decrease in ABL-to-FT q contrasts due to the frontal passages over both sites. The shaded triangles in yellow in both panels c and d help highlight the region below the 1:1 line suggesting larger ABL-to-FT contrasts in q in the prefrontal sector than in the postfrontal sector results suggest that in contrast to winter, frontal passages during the summer have trivial impact in terms of affecting the stability of the vertical atmospheric profile at both respective sites. This occurs because during the summer months in the Northern Hemisphere, there is more uniform surface heating when going higher in latitude compared to during the winter months, resulting in a lower temperature gradient with increasing latitude. With a weaker temperature gradient across the front there is thus weaker warm air advection ahead of the front and cold air advection behind the front, thus resulting in weaker cold fronts. During the winter, the temperature gradient with increasing latitude is stronger, thus leading to stronger warm air advection ahead of the front and cold air advection behind the front. As a result, wintertime cold fronts are much stronger in terms of moisture and potential temperature changes across the front (Lackmann 2015).  Fig. 11 but for differences in average potential temperature (K) from ABL-to-FT and associated intercomparisons (c, d for Amarillo and Midland, respectively) confirming an overall increase in ABL-to-FT θ contrasts due to the frontal passages over both sites. The shaded triangles in yellow in both panels c and d help highlight the region above the 1:1 line suggesting higher ABL-to-FT contrasts in θ in the postfrontal sector than in the prefrontal sector

Front-relative Variability in Surface Meteorological Parameters
Finally, we aim to analyze the near-surface meteorological characteristics to investigate the front-relative changes in surface features yielding frontal strengths. While analyzing the frontal strengths for all the cases, we found that the cases with the sharpest change in temperature and moisture during the frontal passage were observed during the fall through early spring period of the year (Fig. 13). The summer months had the least change in temperature and moisture. This is because summer cold fronts are much weaker in intensity compared to winter and spring cold fronts if they can travel far enough south (Lagerquist et al. 2020). For most of the cases presented for both Amarillo and Midland, we observed a decrease in moisture behind the frontal passage, which is expected (Fig. 13b, d, f, and h). However, a few frontal cases at both sites had an increase in moisture content behind the front (e.g., 17-19 February 2020 for Amarillo, 11-13 December 2020 for Midland). This could be due to the north-east wind direction behind the front (which helps advect low-level moisture and causes upslope flow) as well as some of these cases observing precipitation as explained earlier (see Appendix Tables 3, 4).
When comparing the z i front-relative variability at the two sites, we found that temperature decrease at Amarillo was slightly stronger (~3-5°C) compared to Midland in the late winter to early spring months (Fig. 13a, c, e, and g). This occurs most likely due to the fact that Amarillo is further north and thus more susceptible to colder airmasses advecting in from the north. Meanwhile, Midland had a greater variation in surface moisture drop throughout the year, especially in the 6-h change (Fig. 13f, h). This could be due to Midland's location relative to the Gulf of Mexico as mentioned before.

Fig. 13
Six-hour and 24-hour surface temperature (°C) and moisture (g kg −1 ) change for Amarillo, TX (a-d) and Midland (e-h) for all cases in 2020. C1 represents Case 1 of respective month To summarize, there are several takeaways from the analyses of frontal strengths. For instance, 6-h temperature change is greater than the 24-h temperature change at both sites for some cases because the 6-h temperature change is highly dependent on the diurnal temperature change. For example, if the front moves through the site during the morning hours, the temperature drop would be much less than if the front moves through the site during the evening hours. For moisture change, the variability is greater in the 24-h method for Amarillo because it takes a longer time for moisture content to change due to Amarillo being further away from the Gulf of Mexico than Midland.

Dependence of Boundary-Layer Depths on Frontal Strengths
Here, we examine the relationship between front-relative z i variability and frontal strengths for all the cases. For both sites, the temperature change for both 6 and 24 h after a frontal passage was compared with z i change during the course of a respective frontal passage (Fig. 14). Results on the regression analyses revealed that temperature change (drop) due to a frontal passage was not correlated with changes in z i during the time of the frontal passage. There was also high variability in the z i observed on the day of the frontal passage when associated with a 24-h temperature drop between 5 and 15°C (Fig. 14b, d) and a 6-h temperature drop between 0 and 10°C (Fig. 14a, c). These regression analyses reveal changes in surface fluxes do not solely cause the changes in z i in a synoptic frontal environment.
Our findings are in contrast with the earlier studies on this topic (e.g., Seidel et al. 2012) where they compared the seasonal surface temperature changes with mean z i . Seidel et al. (2012) averaged out the frontal passages throughout the year in their analyses and ignored the role that advection plays in z i variability. In a frontal environment, the advection of a cooler airmass behind the frontal boundary is the main driver causing the changes in z i during the frontal passage rather than the surface temperature change solely due to the surface heat fluxes. These results clearly reveal the dominant impact of midlatitude cyclones on ABL features including z i changes during the course of cold front passage.

Summary and Outlook
Within this work, we analyzed the z i variability across cold front passages at two sites (Amarillo and Midland) in West Texas based on one year of radiosonde measurements. The effect of frontal passages was determined based on a sequence of three 0000 UTC soundings and several parameters and ABL features were analyzed including z i , change in contrast in potential temperature and humidity between the ABL and FT. Finally, z i variability was investigated for all the cases and associated frontal strength, top-of-ABL shear and near-surface meteorological conditions (dry lines, rainfall) and upper-air conditions (EMLs, secondary inversions). Results reported a clear contrast in z i confirming the fact that ABL undergoes substantial changes over the course of a frontal passage. To the best of the authors' knowledge, this is first-of-a-kind study documenting systematic observations to determine frontal contrasts in ABL depths over an arid region spanning over a one year period. Thus, this work serves as empirical evidence on the ABL depths variability on synoptic timescale.
Our analyses show how diverse synoptic events affected the daytime z i variability throughout the year over the two sites. In particular, a one-to-one comparison between prefrontal versus postfrontal z i yielded a significant reduction in z i in the postfrontal regime. A possible reason for this decrease in z i is that a strong frontal inversion tops the ABL during the frontal and postfrontal stage. This inversion helps form a cap for ABL mixing, thus limiting the z i in these stages. Additionally, the moisture content in the ABL decreases with time resulting in a more uniform moisture profile from the ABL to the FT at the postfrontal stage as shown through the box and whisker plots. In contrast, the vertical variability of potential temperature within the ABL was found to be more uniform in the warm sector than in the cold sector which could be mainly attributed to a more unstable vertical temperature profile in the warm sector compared to the cold sector. The analyses presented provide an excellent basis to observe and understand how the z i and ABL and FT thermodynamic properties evolved over the course of a particular frontal passage and among the frontal passage cases in different seasons throughout the year.
We also categorized the individual soundings into four categories: cases with only an EML, cases with only a dryline, cases with both an EML and dryline, and cases with neither EML nor dryline. Each of these categories had certain characteristics in terms of z i . For instance, we found the days with only a dryline had the deeper z i , while days where only an EML was observed had the shallower z i confirming the hypotheses outlined in Sect. 2.2.2. It was also found that the prefrontal ABL remained under three different regimes when z i and EML were completely separated, merged and between the two scenarios depending on the strength of the ABL inversion itself. However, a comprehensive detail on the impact of cold front on the day of frontal passage remained inconclusive here because it was not possible to obtain cases when the time of the frontal passage and the radiosonde launches (i.e., 0000 UTC) were identical. Nevertheless, this work is a starting point for investigating the impact of mid-latitude cyclones on z i variability over land and could be extended in future via using both ground-based and airborne lidar observations in a frontal environment (Pal et al. 2021).
For the experimental region, we also found that summer frontal cases were weaker, while winter to early spring cases were stronger in terms of temperature and moisture drops behind the front. For Amarillo, we found slightly stronger temperature decrease in late winter/early spring. Meanwhile, Midland had a greater variation in moisture content throughout the year. However, when comparing frontal strength to the change in z i over the period, there was not a strong correlation confirming the fact that the surface temperature changes do not properly convey changes in z i . Rather the advection of a cooler airmass is the main driving factor behind z i changes during the course of a frontal passage.
Although the work presented here does provide a better picture of how frontal passages impact the z i over time, gaps still remain in the overall evolution of z i changes in the frontal environment. For instance, the radiosonde measurements are only taken every 12 h and provide only a "snapshot" view of the thermodynamic conditions of the ABL and FT. This is where vertical lidar measurements, or any other continuous profiler measurements with range resolved information of atmospheric thermodynamic properties and aerosol stratifications, will be helpful in terms of providing a better depiction and evolution of the z i changes and depicting differences in turbulence and entrainment zone features in the frontal environment. Additionally, although this work outsets the research work required to better understand the ABL dynamical processes at the interface of both timescales, namely, diurnal, and synoptic time scales, it was not possible to untangle the z i variability on those timescales potentially due to lack of additional measurements, including surface radiation, heat fluxes, soil moisture, entrainment zone processes. Pietersen et al. (2015) estimated the contributions of the advection of heat, moisture, and subsidence on the ABL development and illustrated the importance of considering advection and subsidence although their study did not consider the frontal environment. Thus, a better understanding on the impact of all the factors (surface fluxes, entrainment, shear, advection, and subsidence, especially in the postfrontal airmass) during frontal passages would be an excellent addition to the boundary layer meteorology community. Nevertheless, our work was the first effort of demonstrating a method to investigate the impact of frontal passages on ABL depth variability over land, in particular, over an arid region using available regular observations, we decided to keep the investigation at the interim timescale (i.e., between case studies and climatological studies). However, further studies on this aspect would be important for a broader understanding and improved statistical strength on the impact of frontal passages on ABL depths over longer time period and over multiple sites over land.  According to precipitation climatology, Amarillo and Midland receive annual precipitation of 517 mm and 370 mm, respectively (NWS Amarillo 2020; NWS Midland 2020). For of the study period (i.e., in 2020), Amarillo and Midland received annual precipitation of 319 mm and 199 mm, respectively (NWS Amarillo 2020; NWS Midland 2020); thus, yielding a lower amount of precipitation than the climatological averages at both sites. In terms of annual average temperature in 2020, Midland was found to be warmer (19.17°C) than Amarillo (15.28°C) (NWS Amarillo 2020; NWS Midland 2020). The purpose of these climate statistics is to determine if the precipitation amounts, and temperature have a potential impact on z i differences observed at each respective site.
The following tables show the observed precipitation during the 21 frontal time periods analyzed in Amarillo and 24 frontal time periods in Midland. Data from these tables were compared with their associated z i in Sect. 3.1 to determine any trends between the two parameters (Tables 3, 4).