The STRATfinder and CABAM algorithms are applied to automatically detect MLH at Payerne and Palaiseau (Section 2.5
). Analyses of the algorithms’ performance consider the MLH detection success when applied to the two ALC types (Section 3.1
), in comparison to independent thermodynamic ABL indicators (Section 3.2
), their ability to provide average diurnal and seasonal variations of ABL heights (Section 3.3
), and MLH agreement for individual time periods (Section 3.4
Common metrics are applied to quantify the agreement between STRATfinder and CABAM results: root mean square error (RMSE), mean bias error (MBE), mean absolute error (MAE), coefficient of determination (R2
), linear regression described by slope (a) and intercept (b), and hit rate (HR). The latter is defined as the percentage of discrepancies remaining below a set threshold. Statistics are calculated overall and split by time of day using four periods with distinct characteristics during the diurnal course of the ABL development: night-time (NT: sunset + 2 h until sunrise), morning (MO: sunrise until sunrise + 4 h), daytime (DT: sunrise + 4 h until sunset − 2 h), and evening (EV: sunset − 2 h until sunset + 2 h). Solar position at the two sites is estimated using the R package insol [38
3.1. Detection Rates and Quality Control
High data availability (attenuated backscatter at Payerne (Palaiseau) observed 98% (89–94%) of the time) allowed for MLH detection to be performed on large datasets. After all quality control flags are applied (Figure 2
), more MLH results are available from STRATfinder (82% at Payerne, 73% at Palaiseau) compared to CABAM (51% at Payerne, 56% at Palaiseau). Of these, MLH is detected by both algorithms simultaneously 44% (46%) of the time at Payerne (Palaiseau). Data availability by season and time of day at both sites are sufficient for analysis (37–54%; Table 2
In a few complex cases (2% at both sites), no layer was detected by STRATfinder. CABAM does not assume a continuous layer throughout the day so that layer heights may be interrupted when no significant gradient is present in the attenuated backscatter profile at a consistent height. These layer gaps and insufficient SNR explain the higher data fraction, with no MLH detected by the low-SNR ALC (12% at Payerne, 8% at Palaiseau). At Payerne, CABAM flags more periods with complex precipitation patterns (16%) compared to STRATfinder (2%), while the internal precipitation flag is more consistent between algorithms (7–9%) at Palaiseau. Further refinement of the respective modules implemented for detection of precipitation could help increase agreement of this quality flag between algorithms. Still, the internal precipitation flag is preferable to simply excluding time periods based on auxiliary precipitation measurements because such data may not always be available, and commonly used systems (such as tipping buckets) do not capture the complexity of precipitation affecting the attenuated backscatter profiles. During post-processing quality control (Section 2.3
), about the same amount of data (5–8%) are further excluded due to precipitation for results from the two algorithms.
Few periods are excluded due to unrealistic layer height variability below 300 m for both methods at both sites (1–2%). CABAM results are slightly more often discarded due to unrealistic temporal discontinuity (5% at both sites) compared to STRATfinder (3%). Additional 3–4% (~1%) of CABAM results are flagged for daytime underestimation (nocturnal overestimation).
3.2. Evaluation against Thermodynamic Boundary Layer Height
The Palaiseau MLH from STRATfinder and CABAM are evaluated using thermodynamic layer heights derived for the Paris region based on temperature profiles collected by AMDAR (Section 2.4
). The high density of reporting airplanes permitted the parcel method height (zPM
) and the height of first temperature inversion (zΔT
) to be detected 7% and 21% of the time, respectively. Given multi-layer clouds at the top of the ABL are often associated with high temporal variability in the observed temperature profile, days with multi-layer clouds (range of reported CBH between 5 h after sunrise and sunset > 1000 m) or rainfall (diagnosed from ALC) are excluded from analysis. Further, only days are selected when all three methods have data. With most zPM
available in spring and summer, simultaneous layer estimates with the ALC are available for about 2% of the total analysis period.
Overall comparison between the AMDAR layer height zPM
and CABAM and STRATfinder estimates (Table 3
; Figure 3
) indicate the two ALC-based methods have similar statistical agreement. Absolute deviations are slightly smaller for STRATfinder leading to lower MAE and RMSE values and slightly higher hit rates, i.e., overall 79% (75%) of the STRATfinder (CABAM) MLH are within 300 m of the parcel method estimates.
STRATfinder has a small negative bias to zPM
, consistent with other comparisons of thermodynamic layers heights and aerosol-derived MLH [32
]. CABAM overestimates occur (Figure 3
) at times when false layers are detected within the noise region above the ABL as a result of the low SNR signal recorded by the CL31. As the quality control procedure (Section 2.3
) is not able to capture all such instances, these over-estimations bring the MBE closer to zero for CABAM (Table 3
Assessed against AMDAR thermodynamic layer heights, the performance of CABAM at Palaiseau (Table 3
) is markedly better than reported for the long-term dataset from London, UK [17
]. Improvements of the CABAM MLH by application of the automatic quality control is unlikely responsible for the smaller errors reported here, given supervised layer detection was used in London to minimise false layer attribution. However, zPM
is a more appropriate MLH reference than the temperature inversion height used to evaluate the London MLH, with the latter often marking the top of the residual layer [17
]. As synoptic conditions and cloud dynamics modify ABL complexity and sublayer configurations, they may also influence the performance statistics at the two sites.
Comparison of STRATfinder MLH to AMDAR zPM
) indicates slightly poorer performance than previous evaluations of its predecessors to radiosonde ascents interpreted with the bulk Richardson method [40
]. Estimates at noon for one year at Payerne using pathfinderTURB had a similar MBE (~−50 m) but a RMSE of 162 m (R2
= 0.85) [22
]. STRAT+ MLH at Palaiseau during spring and summer (5 months) was found to be within ± 150 m of radiosonde layer estimates for 94% of the time (R2
= 0.968). The higher discrepancies between STRATfinder and the AMDAR layer estimates could be explained by a combination of different sources of uncertainty:
While previous evaluations against radiosondes were limited to midday conditions (noon ascents), the current AMDAR assessment spans the whole day, including nocturnal periods (Figure 4
The mode of data collection for the temperature profile contributes to the uncertainty. While the absolute measurement accuracy of AMDAR data is less than for radiosondes [41
], systematic temperature biases are not critical to the ABL layer height detection [34
]. However, the vertical resolution of the temperature profiles is usually higher for radiosondes compared to AMDAR. Further, horizontal displacement is greater for airplane flight paths (~10 km km−1
, ∆x ∆z−1
) than radiosondes (~1 km km−1
], which cause changes in both vertical mixing and ABL height when there are variations in orography and/or land-cover [42
]. Substantial spatial variations in ABL heights have been found in the Paris area during spring and summer [43
Uncertainty arises from thermodynamic retrieval of layer heights from AMDAR and radiosonde profiles. The parcel method and the bulk Richardson method can give different results (e.g., peak MLH at Payerne had MAE of 50–250 m [5
]). By selecting only days when these two methods are in “good” agreement (difference < 250 m), Poltera et al. [22
] likely removed more complex conditions that lead to a mismatch between aerosol-derived and radiosonde-based MLH estimates. Unfortunately, as the bulk Richardson method requires wind data that are very rarely reported in the AMDAR system, it is not applied here despite being considered better for estimating the convective boundary layer height [5
The auxiliary data used by STRAT+ to derive MLH may help reduce uncertainty in aerosol-based layer detection. Further, application to a high-power lidar [15
] rather than an ALC likely decreases false layer detection.
Still, the AMDAR dataset provides a beneficial reference for the evaluation the ALC methods as radiosonde ascents [44
] do not allow full diurnal evolution of the ABL heights to be assessed.
It is further evaluated how the average seasonal diurnal evolution of the ABL heights compares between the aerosol-based methods and the thermodynamic approach (Figure 4
). More simultaneous data are available in spring and summer (Table 3
) when unstable atmospheric conditions are more frequent. Here, the MLH is the median zPM
from sunrise + 3 h until sunset, the 10th
percentile of zΔT
for the night and early morning. The average ABLH is the 75th
percentile of the seasonal zΔT
MLH from both ALC-based methods have a similar diurnal pattern to the AMDAR derived diagnostics (Figure 4
a,b). While the AMDAR MLH has considerable uncertainty and temporal variability at night when layers are shallower, the median MLH agrees well during the early morning growth (2–3 h past sunrise). Overall, median AMDAR MLH is within the inter-quartile range of both ALC-derived MLH. In summer, STRATfinder daytime maxima are closer to the AMDAR results (Figure 4
b) as the low SNR of the CL31 means periods with deep ABL development are neither always captured accurately by CABAM nor filtered by the quality control (Section 2.3
The various physical processes related to turbulent mixing and entrainment may result in characteristic vertical profiles of wind, temperature, moisture, and aerosol [45
]. Detected layer boundaries differ slightly depending on the method and tracer(s) used. Previous studies found thermodynamic layer heights derived from Doppler wind lidar measurements tend to rise ahead of ALC-based MLH, often reaching greater daytime peak values [31
]. Layer heights derived from microwave radiometer profiles [5
] showed an earlier and faster boundary layer morning growths of results derived based on the bulk Richardson method compared to those from the parcel method. Here, AMDAR MLH starts growing at a similar time as the ALC-derived MLH estimates but then continues to rise at a higher rate to slightly greater heights. Hence, it appears that layer estimates that incorporate wind or turbulence observations tend to detect earlier and faster boundary layer growth compared to methods solely based on temperature and aerosol-based MLH further lag behind the latter.
Given the considerable uncertainty in the ABLH statistics (e.g., substantial temporal variability, Figure 4
c,d), only a qualitative first-order comparison of the seasonal average diurnal ABLH based on temperature inversions and ALC is conducted. All three methods indicate an ABLH at a reasonable height above the nocturnal MLH. However, the median diurnal ABLH from the ALC are systematically lower compared to the AMDAR ABLH reference, with a greater underestimation by CABAM (−405 m/−189 m on average in spring/summer) than by STRATfinder (−191 m/−84 m in spring/summer) for the time between sunset and sunrise + 3 h. After this, the AMDAR ABLH mostly falls in-between the CABAM and STRATfinder layer estimates. In autumn and winter (insufficient data for metrics), the temperature inversions are frequently closer to the ABLH results from CABAM.
According to classical ABL theory [45
], the mixed layer is expected to extend over the whole ABL following the morning growth period. However, not all methods show the MLH merging into the ABLH (Section 2
) during the day on average (Figure 4
). While this behaviour is nicely reproduced by ABLH from STRATfinder and AMDAR, CABAM ABLH is strongly overestimated, hence exceeding peak MLH by 512 m (610 m) in spring (summer). This is the first time ABLH is derived in addition to MLH from both AMDAR and ALC observations. Although considerable uncertainty remains for the ABLH derived from low-SNR ALC observations, both AMDAR and ALC analysis have the potential to capture the full ABL sublayer configuration including both the mixed layer and the residual layer. This illustrates the need and benefits of further algorithm development and improved quality control.
3.3. Average ABL Heights
The STRATfinder and CABAM ability to characterise the ABL heights at the two study sites is assessed. The two independent aerosol-based methods have very similar median diurnal cycle of MLH by season at both Payerne (Figure 5
a–d) and Palaiseau (Figure 5
e–h). MLH tends to decrease through the night, most evident in the CABAM Palaiseau results. As expected [28
], MLH starts to rise a few hours after sunrise, with peak values in the afternoon. Median MLH peaks at similar levels at these two sites (Figure 5
). The average growth is slightly steadier at Payerne. MLH decreases once there is reduced buoyant activity in the afternoon. In Palaiseau, in spring and summer, this may be hours before sunset, while the height remains rather constant in Payerne. In winter and autumn, at neither site do the two algorithms detect a decay in median MLH before sunset. However, in summer during the evening transition, differences between two ALC types are apparent with the CABAM MLH on average decreasing ahead of the STRATfinder results. These findings should be interpreted with care as the number of data points used to calculate average MLH is considerably lower around sunset (Figure 5
) due to changes in solar position over the course of a season. Furthermore, the time of MLH decay is particularly challenging to track using aerosol-based methods as the formation of gradients in attenuated backscatter is likely to depend on aerosol characteristics (e.g., size distributions).
Mostly, the two algorithms capture a very similar behaviour of the nocturnal MLH. However, STRATfinder has slightly larger values at both sites during winter. The very low variability of nocturnal STRATfinder MLH around sunrise in spring and summer at Payerne suggests the algorithm tends to follow the lowest detection limit (Section 2.1
) leading to a small average under-estimation compared to CABAM. During morning growth, CABAM MLH occasionally rises ahead of the STRATfinder results, which could be explained by aerosol gradients within or at the top of the residual layer being mistaken for the mixed layer height. This leads to a very small positive bias for CABAM during this time of day.
Overall, the seasonal average MLH from the two ALC have both mean and median differences mostly within ±100 m and very similar diurnal ABL behaviour.
When differentiating between clear and cloudy conditions (not shown), a similar agreement between the average MLH patterns from the two algorithms is found. At both sites, the two algorithms detect greater summer peak MLH on days with convective clouds compared to cloud-free conditions. The effect of a deeper MLH when clouds are forming at the top of the ABL during deep convection is consistent with earlier studies at Palaiseau [36
] and London [28
3.4. Direct Comparison of MLH from High-SNR and Low-SNR ALC
Comparison of individual 15 min MLH estimates from STRATfinder and CABAM (Table 4
, Figure 6
) confirms the general agreement of the two algorithms at both sites (Section 3.3
). Across all data, the linear regression slope is close to unity with a negligible intercept and small MBE. Substantial deviations between MLH from the two methods do occur occasionally (Figure S1
) leading to MAE ~200 m and RMSE ~350 m. Still, MLH from the two methods are within 300 m of each other for 77–80% of the time (Figure 6
). Given the slightly larger scatter at Payerne, there is marginally better statistical agreement between the methods at Palaiseau. From the summary statistics (Table 4
), the aerosol-based MLH determined using the two ALC algorithms are in similar agreement as when either is compared to the thermodynamic layer heights (Section 3.2
Positive and negative deviations between the STRATfinder and CABAM MLH occur during all periods of the day (Figure 6
). At night, the MAE remains below 200 m and the MBE indicates no clear bias between methods. As CABAM’s MLH morning growth is occasionally too rapid (Section 3.3
), a small negative bias of STRATfinder is detected for morning (MO) and daytime (DT) periods. When the MLH estimates are particularly similar (< 100 m), CABAM MLH is 6% (10%) more likely to be greater than the STRATfinder-derived layer estimate at Payerne (Palaiseau).
As the CABAM MLH starts to decrease earlier than the STRATfinder MLH (Section 3.3
), the MBE is positive and substantial around sunset. During the evening (EV), STRATfinder MLH is 15% (21%) more likely to exceed the corresponding CABAM result by more than 100 m than vice versa at Palaiseau (Payerne). Although a similar number of MLH results from the two algorithms are within 100 m of each other during all periods of the day (Figure 6
), the relative deviations are smaller during DT and EV when the absolute magnitude of MLH is greatest. Hence, more MLH values are close to the 1:1 line in the direct comparison (Figure S1
) during daytime and evening, leading to an improved linear regression slope and higher coefficient of determination compared to night-time (NT) and MO (Table 4
The relatively low linear regression slope and coefficient of determination during night and early morning (Table 4
) are partly explained by the increased likelihood of STRATfinder MLH being close to its minimum detection height. At night, CABAM frequently has MLH below 200 m at Payerne (Palaiseau) (28% (30%) of the times when both have values). STRATfinder can only detect layers below the minimum detection limit associated with the incomplete optical overlap (Section 2.5
) when low clouds or fog are present. As a result, the distributions of MLH at night clearly differ between the two ALC sensor types (Figure 7
). Instead of detecting layers below 200 m, STRATfinder assigns layers above 250 m (200 m) at Payerne (Palaiseau). 40% of the nocturnal MLH are between 250–300 m at Payerne as the CHM15k detection limit is higher than for the Palaiseau sensor (Section 2.5
). Both algorithms agree nocturnal MLH ≤ 300 m are similarly likely at the two sites (42% at Payerne; 44% at Palaiseau of times when both have data, which is 42% (Payerne) and 45% (Palaiseau) of the possible nocturnal periods).
CABAM nocturnal layer heights have a slightly wider distribution at Palaiseau, but MLH up to ~550 m occur more frequently with the STRATfinder method as its nocturnal search region is restricted by an upper boundary (Section 2.1
). Hence, the nocturnal distribution of STRATfinder MLH is sensitive to the user-specified search region. For example, using a search region of 1000 m (cf. 700 m used in the current analysis, Appendix A
) creates a positive nocturnal bias (cf. CABAM) at both sites. Note, as the maximum search region also depends on the tracked ABLH (Section 2.1
), it is possible for the MLH to exceed the nocturnal maximum specified by the user.