The 2 case-study days selected have clear-sky conditions, ensuring dry-convective ABL conditions and facilitating the use of aerosol as a tracer for the mixed layer. Case one in spring, 18 April 2022 (“April case”), had scattered clouds in some locations in the afternoon. A colder airmass approached the Berlin region from the Baltic Sea from the northeast during the afternoon and evening (Fig. 1a), resulting in a northeasterly-dominated flow over the city. Case two, 4 August 2022 (“August case”), occurred near the climax of an intense western-central European heat wave (Copernicus Observer, 2022). On 4 August, eastern Germany was located in a region of persistent warm southerly flow (Fig. 1b) contributing to 2 m air temperatures that reached up to 37 °C in Berlin (Fenner et al., 2024, Appendix A1).

We use the UK Met Office UM (version 13.0; Davies et al., 2005; Wood et al., 2014) one-way nested within the 10 km Global UM (Global Atmosphere v8.0 and Global Land v9.0 science configurations, updated from Walters et al., 2019). Three nested domains (Fig. 2a) are used with grid-spacings of 1.5 km, 333 m (referred to as 300 m model), and 100 m with 70, 70, and 140 vertical levels, respectively (Table 1). In the 70 vertical level grid-set, there are 16 levels in the lowest kilometre above the model surface (ams) with the first level at 5 m ams. In the 140-level configuration the first level is at 2 m ams, with 37 levels in the lowest kilometre. In the 300 m domain, the vertical spacing below 200 m is less than ∼ 60 m increasing to ∼ 120 m at 1 km, whereas in the 100 m domain it is ∼ 20 and ∼ 40 m respectively (Fig. S1 in the Supplement). The three nested domains are centred over the central point of Berlin derived from urban form data in Fenner et al. (2024). The 300 m domain contains all urbisphere-Berlin observation sites, whilst the 100 m domain (Fig. 2b) extends 30 km from the city centre.

The simulations use the Regional Atmosphere and Land science configuration version 3.1 (RAL 3.1; Bush et al., 2025) which encompasses the physics schemes in the model such as radiation, and microphysics. The turbulence scheme used is “scale-aware” (Boutle et al., 2014) which practically means a conventional 1-D non-local turbulence scheme (Lock et al., 2000) is used when the ABL is shallow and the length scales for turbulence are small compared to the grid length (i.e. not resolved well). When the ABL is deeper, and turbulence has a larger length scale (i.e. more likely resolved by a hm-scale model) a local 3-D Smagorinsky (1963) scheme has more weighting. Thus, weighting depends on the ABL depth and horizontal grid-spacing. This implies that as grid-spacing decreases, the turbulence in the model increasingly comes more from the 3-D Smagorinsky scheme and less from the conventional parameterised scheme. This is important when considering the difference between the 100 and 300 m simulations in the representation of turbulence in the ABL, as we might expect the 100 m model to begin using the 3-D scheme earlier in the day compared to the 300 m model.

The JULES (Joint UK Land Environment Simulator v7.0; Best et al., 2011; Clark et al., 2011; Walters et al., 2019) land-surface model with the MORUSES option is used for built land-cover fractions (Porson et al., 2010a, b; Bohnenstengel et al., 2011) split between roof and street canyon tiles. Land-cover fractions are derived from European Space Agency (ESA) Climate Change Initiative (CCI) version 1 data (ESA, 2017). Anthropogenic heat flux varies monthly based on a UK-based mean value and built land-cover fraction in each grid cell (Hertwig et al., 2020).

Within the UM a single-species aerosol scheme is included which is described in Clark et al. (2008). Aerosol species are grouped into a single-species, referred to as “MURK”. The scheme defines the concentration of aerosol as a prognostic quantity that is advected via a semi-Lagrangian tracer advection scheme and mixed consistent with other scalar quantities in the model (e.g. water vapour). Aerosol sinks are accounted for via precipitation and non-emissions sources are treated via a conversion factor. Surface emissions are provided by the European Monitoring and Evaluation Programme (EMEP/CEIP, 2023) at 0.1° resolution. A sinusoidal diurnal variation is applied to the surface emissions with the peak occurring at midday. In the model, emissions are vertically distributed near the surface depending on type of source. Most sources are from area emissions and are evenly distributed in model levels between the model surface and a height of 150 m. For large point sources, emissions are spread evenly over model levels within a minimum and maximum plume height for the source. When the plume height is unknown, the minimum is set to 150 m and the maximum to 365 m.

For the 2 case study days the UM is run for 36 h, from 12:00 UTC (local time is UTC+2) on the day prior to each study day. The first 12 h are treated as spin-up. This is found to be important for the MURK aerosol as it needs to be transported from the surface emissions across the domains.

For evaluation of the model output to observational data at specific sites, we use the nearest UM grid cell to the observation site. All times referred to in this paper are UTC.

Hall et al. (2024) previously noted biases in the downscaling of soil moisture and soil moisture stress from the Global UM resulting in sharp gradients and a wet bias in urban areas. As this bias appears amplified during the heatwave/drought conditions of 4 August, we replaced the urban soil moisture state with the surrounding rural area average state (see Sect. S2 in the Supplement).

Between autumn 2021 and autumn 2022 the urbisphere-Berlin campaign deployed 25 ALC sensors (Table S1 in the Supplement), including 11 within Berlin's city limits and 14 within the surrounding rural area but within 90 km of Berlin's centre (Fig. 2b). The three ALC models used are Lufft CHM15k (13), Vaisala CL31 (7), and Vaisala CL61 (5), with not all operational at all times (Fenner et al., 2024, SM2). As some ALCs were deployed on roofs of tall buildings, all MLH measurements are adjusted to metres above ground level (m a.g.l.). On the case-study days (Sect. 2.1) the number of operating ALCs were 24 (18 April 2022) and 21 (4 August 2022). To facilitate intra-urban and urban-rural analyses, Fenner et al. (2024) define three spatial extents/rings – inner (A, radius 6 km) and outer (B, 18 km) city, and rural (C, 90 km). The 100 m model domain covers all of urbisphere-Berlin inner (A) and outer (B) city rings, but not the entire rural (C) ring (Fig. 2b). The terrain surrounding Berlin is generally flat with low hills (∼ 90 m) to the northeast and southwest. Vegetation in the rural (ring C) areas are dominated by either croplands or needle leaf forests.

The ALC-observed attenuated backscatter profiles were analysed with sensor-specific algorithms to derive the observed MLH (hereafter ZO). CABAM (Kotthaus and Grimmond, 2018a), which was designed for a low signal-to-noise ratio (SNR) ALC, was used for the Vaisala CL31s, whereas STRATfinder (Kotthaus et al., 2020, 2023b), designed for high-SNR ALC, was used for the Vaisala CL61s and Lufft CHM15k devices. Kotthaus et al. (2020) compared these two ALC algorithms systematically and found very good agreement in MLH in diverse ABL conditions. However, the largest discrepancies between the two can occur in early morning and evening when detecting shallow and weak layers that may be more sensitive to the difference in SNR and optical overlap. The data processing in STRATfinder yield a constant vertical spacing of 30 m up to ∼ 15 km height. For CABAM the vertical spacing is maintained for the original CL31 range gates which is 10 m up to ∼ 7.5 km height. The ZO data are aggregated to 15 min means. Fenner et al. (2024) provides details about sensor location and data processing chains.

During stable or nocturnal stratification periods the ABL can be shallow (< 200 m). The Lufft CHM15k optical overlap is incomplete at these heights, making data unavailable in the early morning and after sunset for these devices, whereas the CL31 and CL61 sensors reach sufficient optical overlap at lower heights and with suitable overlap correction built in (Kotthaus et al., 2020), hence data availability is better for these periods. At sunset, with developing nocturnal stratification, weak aerosol backscatter gradients make confidence in deriving ZO low.

First, we evaluate ZM determined using the MMLH algorithm (Sect. 3) with ZO derived from ALC observations in Berlin and its surroundings (Sect. 2.3). Initially, we focus on an inner-city site (WEDD; Fig. 2b, star) north of the city centre where a Vaisala CL61 ALC was deployed.

The time series on both days show consistent agreement between ZO and ZM in the morning and when the mixed layer begins to grow, especially for the August case (Fig. 4b, d). In the morning of the August case, a residual layer is present in both the model (Fig. 4b, d) and the ALC observations (Fig. S5) which appears to cause ZM to be too high during the growth period in the 300 m domain (Fig. 4b). After sunset (tSS), both the MMLH and STRATfinder algorithms begin looking for the top of a nocturnal stable layer which is well captured by MMLH on both case days. At around 21:30 in the August case a relatively short but sharp increase in MLH is seen in both ZM and ZO.

Comparing the two model configurations, there is an improved ability in the 100 m model (Fig. 4c, d) in distinguishing the mixed layer from a residual layer during the Growth period, compared to the 300 m (Fig. 4a, b). This is possibly the result of increased vertical resolution, which allows for sharper vertical gradients in aerosol, and/or increased horizontal resolution leading to a better representation of turbulence.

For comparison, Fig. 4 also shows a thermodynamic ABL height metric (“BLD diagnostic”, grey, Fig. 4) that is available as diagnostic output from the model. During unstable conditions (e.g. afternoon) the BLD diagnostic uses a parcel method which is defined as the height to which an air parcel can rise dry adiabatically from the surface via convection up to its intersection with the environmental temperature profile (Holzworth, 1964). In stable conditions it is the first height above the model surface where the gradient Richardson number is supercritical (> 0.25). In the late afternoon and evening, a marked discrepancy is evident between BLD and both ZO and ZM, especially for the August case. This is consistent with expectations from thermodynamic and aerosol-based observations (Collaud Coen et al., 2014; Kotthaus and Grimmond, 2018a). However, it is notable that this is demonstrated in the hm-model simulations themselves, and the ALC observations support this. Possible explanation for this is seen in the continued strong vertical velocities (cf. April case Fig. S7a, c) in the late afternoon above BLD (Fig. S7b, d), which imply that additional vertical mixing is possible above a weak thermal inversion (Fig. S6b, d). Additionally, Lean et al. (2022) identified wave features above the mixed layer which may be contributing to what is seen in Fig. S7b, d.

Next, we evaluate MMLH at each ALC location (Fig. 5), with ALC sites outside the 100 m domain (Table S1 in the Supplement) using 300 m model MMLH values. On both days there is a tendency for ZM to overestimate MLH in the Afternoon compared to ZO (green, Fig. 5), especially at the highest MLHs in the August case. However, in both the Morning and Evening periods on 18 April ZM has a negative bias (red and blue, Fig. 5a, c).

Despite the large difference in maximum MLH between the two cases, MMLH has consistent behaviour both in terms of the separation of periods and in comparison to the ALCs. During the Morning and Evening periods of the August case (Fig. 5d) there is consistent agreement when MLHs are below ∼ 200 m. In the April case (Fig. 5c) an underestimation of MLHs < 200 m occurs, which is related to weak aerosol gradients causing ZM to be diagnosed close to the model surface (not shown). Given the difference in maximum MLH between April and August, the normalized mean absolute error (nMAE, Appendix A1) is used to quantify the deviation of the model from the ALCs in each ring. On both days nMAE becomes larger with distance from the city centre (rings A to C, urban to rural areas) (Fig. 5a, b). The overall mean absolute differences between ZO and ZM (18 April (170 m); 4 August (289 m)) are an order of magnitude higher than that found in an intercomparison of CL61 ALCs (Looschelders et al., 2025), suggesting differences between ZO and ZM can largely be attributed to model error.

To assess the performance of MMLH as a function of time we use hit rate thresholds of 10 % (HR₁₀) and 50 % (HR₅₀) (Appendix A2) in Fig. 6. Performance is generally better in the afternoon (12:00–18:00) on both days with HR > 80 %, even for the more stringent HR₁₀ threshold, in the 100 m domain. Outside of the afternoon, there is a maxima in HR in the morning in both cases: at around 06:00 (HR₅₀ ∼ 80 %) on 18 April and between 06:00 and 09:00 (HR₅₀ = 100 %) on 4 August. This may relate to strengthening aerosol gradients before the mixed layer begins to rapidly grow. When HR is normalised by the hit window (Fig. S8; Appendix A2) the performance during this morning period stands out. Additionally, there is increasing hit rate into the evening (after SS) on both days which could be related to a strengthening of the nocturnal stable layer as the evening progresses. Interestingly, the HR for the 300 and 100 m domains are similar for the April case (Fig. 6a, c) whereas for the August case the 100 m domain has higher HRs compared to the 300 (Fig. 6b, d).

Note that there are generally more ALC sites with data in the April case compared to the August case (black line, Fig. 6). As noted in Sect. 2.3, there is a drop in ALC data availability at tSS in both cases that is associated with weaker backscatter gradients making MLH diagnosis challenging.

In addition to the MMLH performance relative to the individual ALCs, we can also exploit the full 2-D spatial fields of ZM to investigate the spatial characteristics of the mixed layer at both regional and neighbourhood scales, in conjunction with the network of 25 ALC sites.

First, we consider the April case at four times (03:00, 09:00, 15:00, and 21:00 UTC [05:00, 11:00, 17:00, 23:00 local time]) for both the 300 m (Fig. 7a–d) and 100 m (Fig. 7e–h) domains. The model bias error is shown at each ALC site. Table 2 also provides a summary comparing various metrics between ZM and ZO, separating stations by spatial groups of rings A, B, and C, and whether stations were upwind or downwind of the city centre (excluding city sites).

Although at 03:00 (Fig. 7a,e, before SR) the mixed layer is generally characterised by nocturnal stable conditions, the influence of the urban surfaces is evident in the MLH, especially in the 100 m domain (Fig. 7e). The mean flow on this day is from the northwest, and higher MLHs occur roughly downwind of the urbanized land surfaces in the model. In Table 2 between 03:00 and 05:00 there is a marked difference going from A to C rings in ZM with a higher MLH in ring A compared to C by as much as ∼ 100 m (100 m domain). In the morning, the model appears to show an urban bulge in MLH. However, this does not seem to extend outside the city. In contrast, ALC sites (ZO) show very little variability spatially in the morning.

At 09:00 the mixed layer is actively growing with increasing sensible heat fluxes, however this growth is not uniform and ZM is lower downwind of the city in the 100 m domain (Fig. 7f). Compared to ZO there is a general overestimation by ZM, however, this is reduced in the 100 m domain. This could be the result of a faster growth rate in the model on the 300 m domain compared to the 100 m (Table 2).

In late afternoon (15:00, Fig. 7c, g) ZM is more uniform across the region, however, the ALC observations indicate a possible urban plume with higher MLH in the downwind areas (cf. ZM). In the afternoon (13:00–15:00, Table 2) the ZO downwind MLH is higher by ∼ 300 m compared to upwind, with the model also showing this difference. In the 100 m domain (Fig. 7g) ZM is too shallow downwind of the city, whereas upwind it is too deep (cf. ZO). Ignoring wind direction, ZM in the 300 m domain for rural sites (Fig. 7c) is too deep (cf. ZO) at this time (Table 2, ring C).

At night (21:00, Fig. 7d, h) a downwind effect of the city is apparent in ZM, consistent with Fenner et al. (2024). Over urban surfaces downwind of the city centre the MLH is deeper compared to non-urban land surfaces around the city. The observations indicate the 300 m domain ZM is generally underestimated, especially downwind of the city (Fig. 7h, Table 2). That is, an urban plume is observed by the ALCs and is deeper than in the model at this time. Similar statistical significance between rings in ZM is indicated during evening and morning (Table 2). However, for ZO this only occurs in the evening. Thus, while the model tends to show an urban influence on MLH in both morning and evening, the observations only support this in the evening.

Second, for the August heatwave case, at 03:00 the spatial variability in rings A to C is similar to the April case with a higher MLH over urban areas in ZM in both domains (Fig. 8e, Table 3). By 09:00 the mixed layer is growing rapidly in most rural areas. However, near and over the city the growth is delayed (Fig. 8b, f), suggesting the soil moisture is still too large (Sect. 2.2), resulting in too much energy going to the latent heat flux (Fenner et al., 2024). The growth rates (Table 3) indicate steeper growth in ring C in ZO and ZM (100 m) possibly indicating that the mixed layer is indeed slow to grow in the urban areas. At 15:00, ZM is generally too high in the 300 m domain (Fig. 8c), but in the 100 m domain this model deviation from the ALCs is improved (Fig. 8g; Table 3).

With the mean flow generally from the south on this day, any urban plume would be expected to the north of the city. At 21:00 ZM (Fig. 8d, h) is deeper north and east of the inner-city (ring A) area and to a lesser degree following the urban land cover in the outer city urban extent (ring B). The ZO data suggest a shallower MLH over the city compared to ZM (Fig. 8h). For Downwind sites both ZO and ZM (300 m) are deeper than upwind (Table 3), indicating an urban influence on the mixed layer downwind of the city. However, with fewer sensors available in the plume direction (cf. April case) it is harder to clearly evaluate this. At the one sensor site north of ring A (Fig. 8h) ZM is ∼ 500 m too low, while for all surrounding sites there is little difference or ZM is too high. Between 20:00 and 22:00 (Table 3) there are significant differences found between upwind and downwind for ZM (300 m).

To evaluate the representation of an urban plume in the model for the April case, we analyse cross sections along the mean flow through the Berlin centre (Fig. 9a) and perpendicular to the mean flow (Fig. 9b) at 12:00. At this time, the MURK aerosol is being mixed into the ABL with convective updrafts characterised by high aerosol concentrations (possibly linked to the peak in the emissions, Sect. 2.2), but there is little variability in MLH along or cross wind, suggesting strong thermal forcing in the entire region. There is consistent agreement between ZM and ZO at this time with ZM within ∼ 100 m at most sites (Fig. 9a, b).

By 21:00, an urban plume has developed in the ZM along-wind cross section (Fig. 10a). Beginning near the start of urban surfaces at 20 km upwind of the city centre, ZM begins to deepen until about 15 km downwind where it abruptly falls, and this is roughly aligned with the edge of the city and the beginning of non-built land cover (Fig. 10a). At this time, a relatively cold mesoscale airmass was advecting through the Berlin region, bringing a cooler mixed layer upwind which interacts with the warmer air over the urban surface (Fig. 10a). At this time, Berlin was experiencing a canopy-layer urban heat island intensity of up to 8 K (Fenner et al., 2024, their Fig. 7). This warmer urban air is advected downwind of the city overtop a cooler shallow stable layer and MMLH identifies this nocturnal surface layer as the mixed layer, as this is where the sharpest aerosol gradient exists. The ALCs indicate an urban plume with similar horizontal scale and higher ZO downwind. However, the urban-rural difference in MLH is larger in the model (Fig. 10a). ZM is lower than ZO generally in Fig. 10, with a low bias across most sites (e.g. Fig. 5c). We speculate this could be related to weaker aerosol gradients (cf. August case) in the evening, or a cold bias noted when comparing to ERA5 (not shown). Along the cross-wind direction (Fig. 10b) there is a deeper MLH over the city but with symmetry along the cross section as might be expected.

For the August case at 12:00, convection and overturning are apparent, especially in the cross-wind cross section (Fig. 11b). An exceptionally deep mixed layer (∼ 3 km) occurs in the model, in agreement with ZO in both directions. As noted previously, at 09:00 the mixed-layer growth is delayed over the city (Fig. 8f). This is not unexpected, as the larger thermal mass of the city results in initially larger storage heat fluxes and delayed turbulent sensible heat fluxes, consequently slowing mixed layer growth over the city, which is supported by surface sensible heat flux measurements in the region (Fenner et al., 2024, their Fig. 8b). Given the low soil moisture in the surrounding rural area during this heat wave case, we also expect more rapid increases in rural turbulent sensible heat fluxes. Evidence of this urban delay is still apparent at 12:00 in both cross sections, with a higher ZM in rural areas (Fig. 11a, b).

A southwesterly flow at 21:00 (Fig. 12c) creates an urban plume downwind of the city centre with higher ZM consistent with the ALC measurements. However, there are large differences between some ALC observations which are < 10 km apart (e.g. ∼ 500 m MAVI and HELL; Fig. 12a), and this large spatial variability adds some uncertainty for evaluating ZM. Upwind of the city on the along-wind cross-section, ZM is ∼ 100 m whereas 10 km downwind of the city it is nearly 800 m. Farther downwind of the city, as in the April case, ZM variability is linked to a shallow layer beneath the downwind plume of aerosol and warmer city air. Northwest of the city in the cross-wind cross section (Fig. 12b), a shallow stable layer over rural areas outside the city is evident, whereas the southeast transect shows a deeper nocturnal layer with MLHs ∼ 300 m higher.

In summary, on both case days an evening/nighttime urban plume is noted up to 15 km downwind of the city centre. In comparison with Chicago (Cosgrove and Berkelhammer, 2019) and Washington DC (Zhang et al., 2011) the plume effect seen here is somewhat smaller in spatial extent however our measure of the plume is based on MLH characteristics rather than near surface air temperature.