Atmospheric boundary layer characteristics from Ceilometer measurements part 2: application to London’s urban boundary layer

Long-term measurements of mixed layer height (Z ML ) are possible with advances in detecting Z ML based on Automatic Lidars and Ceilometers (ALC) observations. Six years of ALC measurements in central London are analysed using the CABAM (“Characterising the Atmospheric Boundary layer (ABL) based on ALC Measurements”) algorithm which provides Z ML and an ABL classification by cloud cover and type. The boundary-layer dynamics are shown to respond to day-length, cloud cover and cloud type. Seasonal median daily maxima range from 707 m (strati-form clouds) to 1704 m (days with convective boundary-layer clouds following a clear night). A common approach to ABL classification and clear definition of key Z ML -indicators can facilitate inter-city comparison. A simple parametrisation based on empirical coefficients derived from the London measurements is proposed to gen-eralise the description of diurnal and seasonal variations in Z ML , including cloud conditions. This has the potential to aid improved understanding of the complex relations between surface air quality and boundary-layer dynamics.

Interpretation of pollutant concentrations observed near the surface requires insights into atmospheric boundary-layer (ABL) dynamics (e.g. Curci et al., 2015;Tang et al., 2016), given that the height (Z ML ) of the mixed layer (ML) determines the volume within which aerosols, greenhouse gases and moisture emitted at the surface are diluted. On days with little cloud cover and calm winds, air pollution levels can correlate negatively with Z ML , as shown e.g. for particulate matter (PM: Münkel et al., 2007;Schäfer et al., 2012;Tang et al., 2016), volatile organic compounds (VOCs: Wagner and Kuttler, 2014), and NO x (Wagner and Schäfer, 2017). These "text-book" days often have a shallow nocturnal layer that grows into a convective mixed-layer which comprises the whole depth of the ABL in the afternoon. Through entrainment, clear air from the free atmosphere or potentially aerosol-laden air from residual layers may be brought into the ML and contribute to ground-level conditions. For example, aerosols present in the residual layer for several days above Milan undergo extended chemical reactions so that secondary aerosols eventually mixed down may account for 40% of surface PM 2.5 (Curci et al., 2015). Z ML is often used for evaluation of air quality models and atmospheric dispersion models (Davies et al., 2007), as key boundary conditions for footprint models estimating the source area of observed turbulent fluxes (Kljun et al., 2015), for the improvement of the inversion of surface PM concentrations from satellite-derived aerosol optical depth (Boyouk et al., 2010), and, as it responds to surface energy exchange processes, it is critical for modelling climate conditions in urban settings (Onomura et al., 2015).
While ML growth is linked to solar radiation, sensible heat flux (e.g. Pal and Haeffelin, 2015) and friction velocity (Batchvarova and Gryning, 1991), local circulation patterns induced by orography or land-sea contrasts generate very complex layering of the near-surface atmosphere (e.g. Boselli et al., 2009). Similarly, cities can cause the ML to grow higher than over their moist rural surroundings (e.g. Barlow et al., 2015). However, high PM concentrations (e.g. measured in Chinese cities) may cause the ABL to become more stable (Petäjä et al., 2016), restricting ML growth which again increases near-surface PM levels. Given the diversity of urban areas across the world (e.g. geographic location, size, population density, building morphology, orography and surrounding land cover) a wide range of boundary-layer characteristics need to be quantified. While modelling studies help explore the relative importance of enhanced roughness, anthropogenic heat, the urban heat island effect , orography, local circulation patterns, and synoptic conditions, observations to verify results remain scarce.
Automatic lidars and ceilometers (ALC) are very suitable for operation in urban areas (e.g. Wiegner et al., 2006;Pandolfi et al., 2013;Curci et al., 2015) due to their compact design with eye-safe lasers, low cost, few maintenance requirements, high range resolution (∼10 m), and their lack of noise pollution. ALC studies have examined local, synoptic-and large-scale circulation patterns such as sea-breezes, mountain-breezes, or monsoon winds which are widely recognised to affect diurnal and seasonal patterns of the boundary layer over cities (e.g. Beijing, Tang et al., 2016;Marseille, Lemonsu et al., 2006;Vancouver, van der Kamp and McKendry, 2010). Based on 3 years of lidar observations in Naples, Boselli et al. (2009) demonstrate the complex structure of the ABL when influenced by a combination of land-sea contrast and orographic effects.
Long-term studies (≥1 year) at (sub-) urban locations are increasingly available (Table 1) allowing for seasonal variations in the diurnal evolution of the urban boundary layer to be evaluated. While instrument set-up, Z ML -detection method and the derived statistics (e.g. how average growth rate is defined; seasonal or monthly statistics) may differ, patterns of Z ML do start to emerge (Table 1). Average daily maximum Z ML usually is lowest in winter, while highest values may be reached in summer (commonly in Europe, Houston), spring (Beijing), or autumn (Shanghai, Hong Kong), depending on the seasonal variations of synoptic conditions in the study area. Coastal sites tend to have significantly lower maximum values compared to continental settings (e.g. Leipzig, Paris). For Barcelona, marine suppression of ML growth is stronger in summer, so Z ML tends to be higher during colder months (Sicard et al., 2006).
Average statistics and day-to-day variability of maximum Z ML change with season (e.g. standard deviation in summer is greater than in winter in Paris: Pal and Haeffelin, 2015). However, the range of diurnal maxima across seasons decreases with reduced seasonality in incoming short-wave radiation towards the Equator (e.g. Shanghai, Hong Kong). Long-term studies show Z ML statistics may vary inter-annually (e.g. Stachlewska et al., 2012;Yang et al., 2013;Zhang et al., 2013;Pal and Haeffelin, 2015).
As atmospheric pollution is a major concern in London (e.g. Visser et al., 2015), several campaigns have studied boundary-layer dynamics in this city based on Doppler lidar and ceilometer measurements (as part of e.g. REPARTEE: Barlow et al., 2011;ACTUAL: Barlow et al., 2015;Halios and Barlow, 2018;ClearfLo: Bohnenstengel et al., 2015). However, no long-term analysis covering all months and several years has yet been performed. The findings of Barlow et al. (2011), comparing cloud-free and overcast case-studies, highlight the impact of boundary-layer clouds on ABL dynamics. Detailed analysis of Z ML statistics is required to assess the implications of cloud cover and cloud type.
The objective of this work is to determine general ABL characteristics in the dense urban setting of central London using the CABAM ("Characterising the Atmospheric Boundary layer based on ALC measurements": Kotthaus and Grimmond, 2018) algorithm applied to six years of ALC measurements. Following the introduction of the study area and methods used (section 2), the general characteristics of London's urban boundary layer are derived from CABAM results (section 3). The results are analysed with respect to how cloud    type, cloud cover and solar angle modify seasonal and diurnal patterns. A simple but general Z ML -parameterisation scheme is presented summarising the London results to facilitate future inter-city comparisons.

Study area and data
London, United Kingdom, with an area of 1,572 km 2 and population of 8.8m in 2016 (ONS, 2017), clearly affects atmospheric conditions via the urban energy balance and emissions of pollutants (e.g. Kotthaus and Grimmond, 2014a;2014b;Ward et al., 2015;Björkegren and Grimmond, 2017).
For evaluation purposes, additional data are used. Cloud amount and cloud base height (CBH) of the lowest cloud layer are extracted from hourly SYNOP reports (Met Office, 2012) for 2017 and processed according to Kotthaus and Grimmond (2018). All data recording and analysis use UTC. Time stamps denote time ending of an averaging period. Data analysis is done in R (R Core Team, 2017).

Characterisation of the atmospheric boundary layer
The CABAM algorithm (Kotthaus and Grimmond, 2018) is used to automatically track the mixed layer height and to classify the ABL into different classes based on cloud cover and cloud type. This algorithm is solely based on ALC measurements (i.e. attenuated backscatter profiles and CBH). The details of the methods are open and results perform well against independent reference observations (Kotthaus and Grimmond, 2018). The mixed layer height was evaluated against temperature inversion heights from Aircraft Meteorological Data Relay (AMDAR: Met Office, 2008) observations and the CABAM classification was compared against SYNOP reports. The latter performs especially well during daytime (Kotthaus and Grimmond, 2018). Ripple effects and near-range artefacts  lead to erroneous layers being associated with Z ML at times. Hence, supervised Z ML results (Kotthaus and Grimmond, 2018) are used here for analysis.
To classify ABL cloud conditions, cloud cover and cloud type are determined from the ALC measurements. This allows the methodology to be independent from auxiliary observations which may be unavailable for a study area (e.g. cloud type is unavailable for central London). The classification uses CBH reported by the ALC with the continuous 24 hr from sunset to sunset as a base period. The day centred on sunrise is hereafter indicated as day SR (subscript "SR" for sunrise). This definition ensures the nocturnal period is treated as a continuous entity. For each night and following day, the ABL class is determined: Clear -predominantly clear sky, Cu -dominated by convective clouds, St -dominated by stratiform clouds, "Z ML < Cu" -mixed layer height remains below CBH of convective ABL clouds, and "Z ML < St" -mixed layer height remains below CBH of stratiform ABL clouds.

General description of the ABL diurnal pattern
Several indicators are commonly used to describe the diurnal evolution of the mixed layer height: nocturnal minimum, daily maximum, morning transition (MT) growth rate, growth duration, and timing of the evening transition (ET) when turbulence breaks down. Long-term or automated studies require clear definitions of these metrics. MT onset may be defined as sunrise, the time when the surface sensible heat flux changes sign (e.g. Pal and Haeffelin, 2015), or the time of "significant" increase in growth rate, while its end is often assigned to the time when 90% of the diurnal maximum value is reached (e.g. Pal and Haeffelin, 2015).
The ET is more difficult to identify using aerosols as tracers, given that changes in atmospheric conditions are not as distinct as in the morning. Uncertainty of ALC-derived Z ML is pronounced as aerosols may remain dispersed within the ABL even if turbulent mixing is reduced. This leads to the emerging residual layer often associated with Z ML (Haeffelin et al., 2012;Peng et al., 2017). Atmospheric stability (e.g. measured via lapse rates or eddy covariance) can help identify transitions of the nocturnal (often stable) layer into the convective daytime boundary layer during MT and back to the nocturnal stratification during ET (e.g. Pal and Haeffelin, 2015).
Given that the objective of the current work is to only require ALC observations, general indicators are defined using these and significant solar positions (Table 2).

Classification
ABL conditions in central London for the study period (2011-2016) are classified based on ALC observations using the CABAM algorithm (Kotthaus and Grimmond, 2018). Of the total possible SR-centred 24 hr periods (number of General indicators used to describe the diurnal evolution of the mixed layer height Z ML in this study. Significant solar positions are marked by sunrise (SR), solar noon (SN), sunset (SS), and midnight (MN); MT and ET are the morning and evening transition, respectively. Thresholds for the definition of MT are chosen in accordance with median diurnal patterns of MT growth rate ( Figure S2, Supporting Information).  day SR = 2192), 5% could not be classified because of insufficient data and 8% are classified as rainy (i.e. complex rain patterns with a duration of >4 hr impede the successful tracing of Z ML ). Another 12% experience >2 hr of precipitation with no major impact on Z ML -detection so they are merged with their respective cloud class for the analysis presented. The frequency distribution of ABL classes (Table 3) shows convective clouds clearly dominate London's boundary layer during daytime (Cu: 60%, Z ML < Cu: 5%), with 12% considered cloud free, and 22% are dominated by stratiform clouds at the top of the mixed layer. During night, all categories apart from Z ML < St show a similar frequency between 20 and 31%, with clear nights being most likely. It should be noted that the conditions for a night to be classified as Clear are more relaxed than during daytime, i.e. some of the Clear nights may have a cloud layer above the ML. The mixed layer is "cloud-topped" if Z ML is located near the reported CBH. The CABAM classification scheme performs better during daytime when compared to SYNOP reports (Kotthaus and Grimmond, 2018).
While both Clear (79%) and St (54%) nights are most likely to follow a night of the same class, the Cu category is less persistent with similar chances for a Cu day to be detected after a night classified as Clear (28%), Cu (28%) or Z ML < Cu (24%). Days with the mixed layer remaining below CBH most often follow a clear or Z ML < CBH night.
Classes with similar diurnal and seasonal evolution (not shown) are combined to increase the number of samples for statistical analysis (sections 3.2, 3.3), i.e. for days with Cu, the nocturnal classes of Z ML < Cu and Clear are merged, all classes with Z ML < CBH during day are combined, and the   two nocturnal cloud classes are combined for both the daytime Cu and St class, respectively. This leaves five major ABL classes to be analysed: Clear -predominantly clear, Cu -dominated by convective clouds, St -dominated by stratiform clouds, ClearCu -predominantly clear night followed by a day with convective clouds, and "Z ML < CBH" -mixed layer height remains below CBH of ABL clouds during daytime.
The frequency of these major ABL classes by season (Figure 1) reveals more periods are excluded due to rainfall in the summer compared to colder seasons as cloud patterns are more complex and inhibit successful Z ML detection. The likelihood for St is 4.5 times greater in winter than summer, while the seasonal variability for the Cu class is much smaller. Clear nights in summer are ∼2.5 times more likely to be followed by a day with convective clouds (ClearCu) than in winter. Completely clear days are most frequent in spring, while the generally rare Z ML < CBH class is least frequent in autumn. These results are similar to those obtained from SYNOP reports for the Greater London area (Kotthaus and Grimmond, 2018) which indicate St is 3.7 times more frequent in winter than summer and which confirm low seasonality of Cu. From SYNOPS, both the Clear and ClearCu classes are most likely in spring.

Seasonal-diurnal patterns
Median diurnal patterns of Z ML are calculated by season and major ABL class (section 3.1) for the 24 hr periods centred at sunrise (day SR ). Data availability (Figure 2, line plots) for each 15 min interval is shown as a percentage of the total number of days (no. of day SR ) within the category (i.e. for a class occurring with the same frequency in all seasons, the maximum possible availability is 25%). Excluding the "rain" class (section 2.2), data availability ( Figure 2f) peaks between 22.3% (summer) and 24.8% (winter) and is rather consistent throughout the day for all classes (apart from near sunset with the seasonal changes in solar angle). Z ML of all classes and seasons ( Figure 2) generally have the expected diurnal evolution with a minimum around sunrise and peak values in the afternoon. Overall, seasonal variations are distinct and diurnal patterns clearly depend on ABL class. Under Clear conditions (Figure 2a), nocturnal Z ML varies with season with lowest values in winter and autumn (25 th percentile ∼130 m agl) and highest in summer. In all seasons, growth starts several hours after sunrise. Daytime evolution is very similar in spring and autumn, with values levelling off after solar noon only slightly lower than in summer (1200-1400 m agl), while the maximum of the median cycle is only 719 m in winter.
When convective clouds are present on the day following a clear night (Figure 2b), higher afternoon Z ML occur in most seasons compared to clear days (Figure 2a). Only in autumn does growth level off shortly after solar noon in the cloudy case ( Figure 2b). As growth continues under clear conditions ( Figure 2a), the maximum values reached are similar. Afternoon Z ML does not differ much between spring and summer for ClearCu conditions. Before sunrise, spring, summer and autumn all have the same seasonal relation as found for the Clear ABL class. However, in winter the detected mixed layer starts to grow earlier so that median values around sunrise are highest in the cold season. This is explained by CBH of convective clouds near sunrise being higher in winter ( Figure  S1, Supporting Information) and a higher fraction (28% compared to 17% in summer) of Z ML in the 4 hr around SR being associated with clouds.
Under Cu conditions (Figure 2c), the median nocturnal Z ML in winter differs from those observed in the other seasons, again due to seasonality in CBH ( Figure S1, Supporting Information). While Z ML exhibits a slight decrease in the time from sunset to sunrise for the other seasons, nocturnal decay is less pronounced in winter with rather stable median values in the time before SR. Overall, nocturnal values are higher for Cu ( Figure 2c) compared to Clear nights (Figure 2a,b) leading to reduced growth rates in the cloudy class. It appears that CBH and associated Z ML are slightly lower on days with convective clouds following a cloudy night (Figure 2c) compared to ClearCu (Figure 2b) conditions.
As expected, the amplitude of the diurnal cycle is least when stratiform clouds (Figure 2d) occur, with minimal seasonal differences. As the "Z ML < CBH" class is rare in all seasons (Figure 2 Across all classes (Figure 2f), Z ML is highest in summer throughout day and night compared to spring and autumn. In winter, Z ML decreases less through the long nights so that median values of Z ML at sunrise are higher than in all other seasons. The low growth rates and short day-length still result in winter afternoon Z ML being the lowest. This analysis of seasonal diurnal patterns (Figure 2) demonstrates the importance of boundary-layer clouds to the interpretation of Z ML in areas such as the United Kingdom, where both convective and stratiform clouds often affect ABL dynamics.

Generalised ABL characteristics
To quantify ABL characteristics in central London, several indicators related to diurnal Z ML -evolution (section 2.3, Table 2) are calculated for each day SR by season and ABL class ( Figure 3). As expected from the analysis of median diurnal patterns (section 3.2), many indicators show distinct seasonal variations. Nocturnal Z ML tends to decrease slightly (Figure 3s), especially under clear-sky conditions in spring and summer with median Δz night = 33 m/hr. Winter nights and those associated with stratiform clouds show less height variation. When considering all ABL classes, the time of minimum Z ML (Figure 3k) varies through the night. The overall median t min is at 0.72 × H night . Minima occur slightly later in the warmer seasons compared to winter and autumn, and slightly earlier for clear nights compared to cloudy cases, e.g. median t min in summer is 0.75 × H night for Clear and 0.98 × H night for St. Minimum Z ML observed in central London (Figure 3o) strongly depends on the ABL class. Median z min ranges between 134 m agl (Clear) and 303 m agl (Cu). Seasonal differences within the same class are smaller than inter-class variations, e.g. for the Clear class median z min is between 128 m agl (DJF and SON) and 181 m agl (JJA). These heights are a little lower than reported for Vienna and Paris (Table 1). Beyond location, land use and synoptic conditions, the lower values reported for London may be due to a reduced bias to higher layers being detected with the current approach, given values as low as 50 m are detectable (Kotthaus and Grimmond, 2018).  (Kotthaus and Grimmond, 2018) using ALC measurements (2011. Results are grouped by major ABL class (Clear, ClearCu, Cu, St, Z ML < CBH, and All combined; section 3.1) and season. See section 2.3 and Table 2 for symbol definitions. To account for impact of changes in daylight hours (H day ), (a) t1 MT , (b) t2 MT , (m) t max , (p) z max , and (q) Δz MT are displayed also (c,d,n,t,u) normalised by day-length; (f) t1 ET , (g) t2 ET , and (k) t min are (h,i,l) divided by night-length (H night = 24 − H day ). Temporal indicators are given in time relative to sunrise (SR) or sunset (SS), respectively While long-term eddy covariance (Wood et al., 2010) and scintillometry (Crawford et al., 2016) observations in central London suggest a likelihood of 20-40% for the nocturnal mixed layer to remain < 200 m, CABAM detects Z ML < 200 m for 13% (between SS + 1 hr and SR). For another 5% of this time, no Z ML is found but at least one higher layer (representing e.g. the residual layer) is identified suggesting the algorithm considers the possibility that Z ML might be located below the detection limit of 50 m or measurement noise prevents successful tracking of Z ML at heights below 100 m. While this indicates general consistency between CABAM-derived Z ML and tower-based observations, direct comparison should be performed to assess conditions that might cause disagreement between the approaches. z max clearly varies with both ABL class and season (Figure 3p). The latter effect is partly explained by the prolonged growth duration (Figure 3e) in spring and summer, as the maximum is reached much later in the day (Figure 3m) with median t max converging around 0.74 × H day (Figure 3n). Consistently, statistics of z max become more similar (∼105 m/hr) when normalised by H day (Figure 3t), especially for the Clear class. However, for cloudy daytime conditions additional factors must play a role as the seasonal variation is reversed after normalisation (cf. Figure 3p,t). With all classes combined, z max in summer (winter) is 1516 m agl (921 m agl). Lowest median z max is detected during winter St conditions (707 m agl) and highest during summer ClearCu (1704 m agl). For the class Z ML < CBH, median normalised z max (82 m/hr) is lower compared to Clear conditions (100 m/hr). This London z max is similar to that observed in Leipzig and Vienna, but slightly lower than in Paris and Houston (Table 1).
Start and end of the MT define the period of most significant increase in Z ML . While MT starts on average ∼2 hr after sunrise (Figure 3a,c), the end of MT is clearly a function of day-length (Figure 3b,d). The inter-quartile range (IQR) is highest for the St class due to the increased uncertainty in detecting ABL indicators associated with the shallow diurnal amplitude (Figure 2d). On average, MT spans from 0.17 × H day to 0.62 × H day and lasts (Figure 3e) 3.5 hr (6.75 hr) in winter (summer). Baars et al. (2008) note that very short MT duration is often linked to extremely high growth rates.
The MT dilution height Δz MT (Figure 3q) here represents the increment of Z ML during MT ( Table 2) and ∼80% of the daily amplitude (z max − z min ). When normalised by H day (Figure 3u), Δz MT is very consistent within ABL classes, with median values ranging from 42 m/hr (St) to 62 m/hr (ClearCu). The MT growth rate (Figure 3v) is not normally distributed (mean > median), which is consistent with statistics reported elsewhere (e.g. Pal and Haeffelin, 2015). Median growth rate for the Clear class is identical with the overall average of 174 m/hr, which is only slightly stronger than for Cu (169 m/hr). Growth rate is strongest (weakest) for the ABL class ClearCu (St) with 212 m/hr (92 m/hr) and in-between for Z ML < CBH (134 m/hr). This is consistent with findings for Paris (Pal et al., 2013) where enhanced growth rates were also found on days when cumulus clouds form at the top of the mixed layer during daytime, compared to completely clear-sky conditions. However, growth rates in London are generally slightly weaker than in Paris (Pal and Haeffelin, 2015).
For London, seasonal variations in growth rate are negligible compared to inter-class differences (Figure 3v). Other urban studies (Table 1) suggest MT growth to be stronger in spring (e.g. Magurele (Romania): Sokół et al., 2014) or summer (e.g. Paris: Pal and Haeffelin, 2015) when energy fluxes of radiation and sensible heat flux peak.
Compared to the MT statistics, greater overall variability (IQR) is found in the temporal indicators of ET (Figure 3f,g). Seasonal variations are of similar magnitude for beginning (t1 ET ) and end (t2 ET ) of this transition, so that the overall duration Δt ET (Figure 3j) consistently varies around the median value of 2.5 hr.
Overall median statistics are consistent with other European studies. However, care should be taken when directly comparing Z ML indicators reported for different cities, given the variety of methods used. Not only do the studies differ in terms of instrumentation and Z ML -detection algorithm (Table 1); also, a range of definitions are applied to determine the significant indicators. Most notably, MT onset (here t1 MT ) is identified based on a range of criteria, including sunrise, time of increasing growth rate, time of Z ML reaching a certain increment compared to z min , and time of cross-over of the surface sensible heat flux from negative to positive values. The definition of this point clearly affects derived statistics of growth rate and MT duration. Given that reports on ET indicators are still rare, no common definition for its indicators is available yet.
The statistical analysis (Figure 3) suggests that for central London, a substantial proportion of seasonal variability in indicators that describe the diurnal pattern of Z ML is related to variations in daylight hours; while the behaviour of MT and ET mostly depends on solar position, minimum and maximum Z ML as well as MT growth rate are clearly also a function of ABL class.

ABL parameterisation
General Z ML characteristics of London's urban boundary layer are extracted based on the statistical analysis (section 3.3) of long-term observations by season and ABL class and used to compile a simple, first-order parameterisation of the Z ML diurnal cycle solely based on ABL class and day-length. While temporal indicators are expressed relative to day-length, heights are estimated as a function of three ABL-class dependent parameters, namely z min , MT growth rate (GR MT ), and nocturnal decay rate (DR noc ; Table 4). Representative GR MT and DR noc estimates are the overall median values by class, while the 75 th percentile of z min is found most appropriate.
Using examples for the winter and summer solstice, results from this empirical model are determined for the range of possible daylight hours at the study site (Figure 4a,b), exemplary for all ABL classes combined (All), St and ClearCu. Comparison to observed median diurnal patterns for the three months around the solstice dates shows the first-order parameterisation is capable of reproducing seasonal dependence and general behaviour for the major ABL classes. As expected, morning and evening transition periods are the most challenging times to describe. Further studies are required to gain a better understanding of these transition times.
To qualitatively assess the ability of the proposed parameterisation to describe the ABL structure, an independent year (2017) is analysed. The ABL classes (Clear, ClearCu, Cu, and St) determined from SYNOP observations (Kotthaus and Grimmond, 2018) are used with the empirical model (Table 4) to obtain the diurnal evolution of Z ML . These results are compared to median supervised Z ML observations (Figure 4c-f) for those days.
Using only the commonly available SYNOP observations, the parameterisation results show generally good agreement with the average ABL patterns observed for the different categories (Figure 4c-f). Some uncertainty is introduced considering Greater London SYNOP reports might not fully represent the central urban study area (Kotthaus and Grimmond, 2018). The simple model is not designed to resolve day-to-day variability of the ABL structure within a category for comparable sun-angles. However, interannual variations (e.g. Pal and Haeffelin, 2015) might explain some of the discrepancies such as the tendency for underestimation of Z ML during Cu days (Figure 4e) or the premature rise during mornings with St cloud cover (Figure 4f). Future studies covering a range of time periods and additional study areas will be conducted to further evaluate the general applicability of this simple model.

SUMMARY AND DISCUSSION
The CABAM (Characterising the Atmospheric Boundary layer (ABL) based on automatic lidar and ceilometer (ALC) Measurements) algorithm (Kotthaus and Grimmond, 2018) is used with ALC data to automatically track the mixed layer height Z ML and to classify ABL characteristics with respect to cloud cover and cloud type. Classes distinguish nights and days affected by clear sky (Clear), convective clouds (Cu), stratiform clouds (St), or Z ML remaining below cloud base height (CBH) of boundary-layer clouds. CABAM is applied to characterise ABL conditions for central London, United Kingdom, for a multi-year period (2011-2016) based on observations of a Vaisala CL31 ceilometer. Excluding days when complex rain patterns prevent tracking of Z ML , five major ABL classes occur: (a) Clear, (b) Cu, (c) St, (d) clear night followed by day with convective clouds (ClearCu), and (e) days with Z ML < CBH. While convective clouds generally dominate, the relative frequency of the major ABL classes varies with season. Cu always makes up ∼30%, while the likelihood for St is 4.5 times greater in winter than summer. Clear nights are ∼2.5 times more likely to be followed by a day with convective clouds (ClearCu) in summer than winter. Completely clear days are most frequent in spring. The rare "Z ML < CBH" class is least likely in autumn. These findings are generally in agreement with SYNOP reports again omitting days with complex rain patterns.
From this dataset, median statistics for critical points in the diurnal evolution of the mixed layer (minimum, morning transition, maximum, evening transition) are determined. Two aspects clearly shape the diurnal evolution of Z ML over London: (a) day-length and (b) ABL category related to cloud cover and cloud type. With all data combined, the median daytime maximum is clearly lower in winter (921 m agl) than in summer (1516 m agl). A dependence on ABL class is detected. The median morning transition growth rate ranges from 92 m/hr (St) to 212 m/hr (ClearCu), with an overall average of 174 m/hr. These differences by ABL class clearly translate into the overall statistics of Z ML by season due to the seasonal variations in cloud characteristics. In general, these indicators are similar to values reported for other European cities.
Where clouds of various types frequently affect the ABL, such as in the United Kingdom, general mixed layer height characteristics may vary distinctly depending on the frequency of cloud types present in the sample analysed. While observational ABL studies often apply a cloud cover filter, cloud type is usually neglected. The findings presented here clearly demonstrate the importance of cloud cover, cloud type and cloud base height for the sound interpretation of mixed layer height measurements, as suggested in previous studies (e.g. Schween et al., 2014;Pal and Haeffelin, 2015). Especially stratiform clouds should be interpreted separately, as the ALC-derived mixed layer height likely coincides with the CBH rather than the actual mixed layer height due to strong attenuation of the lidar signal in such clouds.
To facilitate inter-city comparison in future studies, a simple, first-order parameterisation is proposed to describe seasonal and diurnal variations of Z ML based on only ABL class and daylight hours. Three class-dependent parameters (minimum Z ML , morning transition growth rate, and nocturnal decay rate) are required to determine the general evolution of Z ML as a function of solar geometry (i.e. time of day, day in year) only. Comparison between this simple model and median diurnal patterns for the examples of summer and winter solstice shows overall patterns are well-described. Further, the model enables first-order prediction of Z ML diurnal evolution if information on cloud type is available (e.g. from SYNOP reports). The parameterisation is considered to provide valuable insights for studies addressing the dependence of air quality on mixed layer height dynamics under different cloud conditions. Due to limitations of the methods used, many observational studies of mixed layer height development focus on daytime conditions or do not report nocturnal statistics. Omitting the nocturnal boundary layer might increase the uncertainty in estimating the onset time of the morning transition (if determined based on Z ML ) and complicates the interpretation of Z ML in the afternoon and evening transition when turbulent mixing decays.
While most studies focus on the morning growth period, this is one of the first studies to also address the evening transition. At this central London site a new aerosol layer usually starts forming near the surface after sunset which helps detect the end of the evening transition. Application of the CABAM algorithm on ALC observations with complete overlap at low ranges (such as the CL31) at a rural, low-polluted site could identify if the formation of the nocturnal layer is also detectable where aerosol emission at the surface is less significant compared to the dense city centre. Results presented here for central London show the timing of the evening transition is less clearly defined than in the morning. A common definition of indicators to characterise the evening transition is critical.
While number of daylight hours, a first-order proxy for incoming short-wave radiation, explains much of the seasonal variability, other physical drivers such as anthropogenic heat emissions, sensible heat flux and atmospheric stability likely play a role (e.g. Pal and Haeffelin, 2015). Links between these processes and ABL dynamics will be evaluated in future studies using turbulent heat flux measurements and weather station observations available at different heights in central London (e.g. Kotthaus and Grimmond, 2014a;Crawford et al., 2016). Definition of the critical points within the diurnal cycle of the mixed layer could be refined with interpretation of these physical drivers. The results from this study will be valuable for examining the relation between mixed layer height and atmospheric pollution concentrations in central London.