The observed backscattered signal detected by a lidar consists of the true atmospheric signal and the background signal . The true atmospheric signal consists of backscattered contributions from particles (βp) and molecular scattering (βmol), whilst the background signal includes contributions from both atmospheric background signal Patmosphere (such as solar radiation, moonlight, or artificial light) and instrumental background Pinstrument signal (dark signal). Although the instrument already determines and performs the background correction internally, residual background components may still remain in the measured signal, such as the dark signal observed during termination hood measurements (see Sect. 3.1.1). Therefore, we extend Eqs. (2) and (3) to account for the residual background signal (hereafter referred to as the background signal), Bres, that is not removed by the internal correction: 6∥β′=∥(P(r)-Bestimated)r2CLO(r)+∥Bres(r)r2CLO(r)=∥βcorrected′+∥Bres(r)r2CLO(r),7⟂β′=⟂(P(r)-Bestimated)r2CLO(r)+⟂Bres(r)r2CLO(r)=⟂βcorrected′+⟂Bres(r)r2CLO(r). To eliminate the range dependence from the background terms, we divide each expression by r2, yielding: 8∥β′r2=∥βcorrected′r2+∥Bres(r)CLO(r),9⟂β′r2=⟂βcorrected′r2+⟂Bres(r)CLO(r). For simplicity, we define the background terms as: 10Pres(r)≡Bres(r)CLO(r), where Pres(r) = Patmosphere(r)+Pinstrument(r).

To derive the βcorrected′, the background signals need to be quantified. Since the measured ∥β′ and ⟂β′ signals include contributions from background signal in their respective polarization channels, it is necessary to estimate the background signal separately for each polarization (∥Pres and ⟂Pres). To achieve this, a background identification methodology has been developed. It identifies regions within the dataset that are free of aerosols and hydrometeors, where the ∥β′r2 and ⟂β′r2 values are assumed to predominantly represent background signal.

The methodology proceeds as follows. First, the data is averaged over 5 min intervals. The ∥β′r2 and ⟂β′r2 profiles are then decomposed using the stationary wavelet transform (SWT) with the bior.1 wavelet, implemented via PyWavelets . Subsequently, the background signal variance is reduced by applying a hard-threshold shrinkage function to the approximation and detail coefficients from levels 1 through 7, using minimax thresholding . The profile is reconstructed via the inverse stationary wavelet transform. Finally, the background range gates are identified as regions with values below half of the previously computed minimax threshold. The mean and variance of the background are computed from the original, non-averaged data with the identified background range gates using 5 min time intervals and 2 km range-bin intervals.

An example of this methodology applied to data in Kenttärova on 28 March 2024 is illustrated in Fig. . During daylight hours, solar radiation significantly increases the variance (σ∥Pres2 and σ⟂Pres2) of the background signal, resulting in a daytime variance much higher than that observed at night, as shown in panels (g) and (h). Above the aerosol and cloud layers, both the mean (μ∥Pres and μ⟂Pres) and variance of the background signals in both polarizations remain relatively stable with range, or at least exhibit considerably smaller variations compared to the diurnal fluctuations.

By applying this methodology to the full dataset, we obtained the time series of Pres for all instruments in both polarizations. Comparing these background signals with other housekeeping parameters, such as laser power, enables us to evaluate the operational performance of each instrument. Moreover, since each background component is quantified independently, we can correct the signal and estimate its uncertainty in both polarizations ∥β′ and ⟂β′ and, consequently, in the derived linear depolarization ratio.

To ensure the CL61 produces a consistent and accurate backscatter signal, the ceilometer signal must be manually calibrated in addition to its internal calibration. This involves calibrating the backscatter signal from the CL61 using a reference target with known backscatter characteristics. Two commonly used calibration methods for deriving CL are based on different types of reference targets: atmospheric molecules (Rayleigh calibration) and liquid clouds (liquid cloud calibration).

The Rayleigh calibration , often referred to as the backward inversion approach, is the standard method to derive the particle backscatter coefficient (βp) for most research aerosol lidars due to their sensitivity to molecular signal . As illustrated in Fig. b, the attenuated backscatter coefficient profile from CL61 closely follows the attenuated molecular backscatter coefficient above the aerosol layer at 4 km. This indicates a significant contribution of molecular scattering to the total CL61 signal, especially in aerosol- and hydrometeor-free regions. Therefore, the Rayleigh calibration can be applied to the CL61, provided a sufficiently long averaging time (more than 2 h) is used.

The Rayleigh calibration method requires an assumed lidar ratio for aerosol particles (Sp). At sites equipped with a sun photometer, Sp can be constrained ; otherwise, a value of 50 sr was used. The first 50 m range has been discarded due to unreliable data (see Sect. 4.5), and it has been demonstrated that the resulting loss in optical depth for ignoring near range gates is negligible . After the βp profile is derived, the lidar constant CL can be determined from the lidar equation .

The liquid cloud calibration relies on the fact that the lidar ratio for liquid water clouds at the ceilometer wavelength is known. This method involves calculating the integrated attenuated backscatter coefficient for fully attenuated liquid water clouds, including the contribution from multiple scattering. The theoretical contribution from multiple scattering is computed for droplet diameters ranging from 8 to 20 µm, taking into account the CL61 beam divergence and receiver field of view. The integrated backscatter coefficient is then scaled to fit within the expected theoretical values. This scaling factor is the calibration factor C, which is the reciprocal of the lidar constant CL. The primary advantage of this approach over Rayleigh calibration is the substantially higher signal-to-noise ratio of the backscatter from water clouds compared to the molecular backscatter. As a result, it eliminates the need for long nighttime averaging periods required to obtain a reliable molecular signal.

A methodology was developed to identify suitable liquid cloud profiles. First, a representative liquid cloud profile containing a single liquid cloud layer and exhibiting complete signal attenuation approximately 200 m above the cloud base was selected as the reference profile. Each β′ profile in the dataset was then cross-correlated with this reference to quantify their similarity. For each time step, the height corresponding to the maximum cross-correlation value was identified as the most similar location and treated as a pseudo in-cloud height. Next, the ratio of total in-cloud β′, calculated over a 150 m layer centered at the pseudo in-cloud height, to the integrated β′ of the entire profile was computed. A profile was classified as containing a liquid cloud if this ratio exceeded 90 %, ensuring that the integrated β′ was not significantly influenced by strong aerosol loading or precipitation. Additionally, the cross-correlation value at the identified height was required to exceed 5 × 10⁻⁷. This threshold was selected to ensure that at least 1000 valid data points were available for each month.

To ensure robust data fitting, the cloud calibration is performed monthly using all suitable liquid cloud observations detected from the methodology. To validate the cloud calibration results, Rayleigh calibration was also computed occasionally when possible. Data from a co-located sun photometer was used to constrain the lidar ratio for Rayleigh calibration. If no sun photometer data is available, a lidar ratio of 50 sr is used.

The calibrated volume attenuated backscatter coefficient and its uncertainty can then be determined as follows, assuming the cloud calibration factor has an uncertainty of approximately 10 % : 20βv′=βcorrected′⋅C,21σβv′2=σβcorrected′2+0.01⋅βcorrected′2⋅C2.

For those instruments where termination hood measurements are not available: 22βv′=β′⋅C,23σβv′2=σPatmosphere2+0.01⋅β′2⋅C2=σ∥Patmosphere2+σ⟂Patmosphere2+0.01⋅β′2⋅C2.

The calibration is assumed to affect both polarization channels equally. Hence, δcorrected remains unchanged.

The particle backscatter coefficient profile (βp) is retrieved using the forward Klett solution after applying the previously derived cloud calibration factor and assuming that the instrument does not undergo significant degradation within a one-month period. Similar to the previous section, the first 50m range has been discarded. The cloud calibration factor is estimated to have an uncertainty of approximately 10 % . The forward inversion does not require extensive temporal averaging. When available, sun photometer observations are used to constrain the lidar ratio Sp; otherwise, a constant value of 50 sr is applied to all aerosol layers in the retrieval.

Let βp=f(βv′,C,Sp) represent the inversion function; then the uncertainty of βp is calculated as 24σβp2=∂f∂βv′σβv′2+∂f∂CσC2+∂f∂SσSp2.

The partial derivatives can be approximated using central differences: 25∂f∂βv′σβv′≈fβv′+σβv′,C,Sp-fβv′-σβv′,C,Sp2,26∂f∂CσC≈fβv′,Cmax⁡,Sp-fβv′,Cmin⁡,Sp2,27∂f∂SσSp≈fβv′,C,Sp,max⁡-fβv′,C,Sp,min⁡2 with Cmin⁡=0.9⋅C, Cmax⁡=1.1⋅C, Sp,min⁡=Sp-10, and Sp,min⁡=Sp+10

Following , the particle linear depolarization ratio (δp) is then obtained as 28δp=1+δmδvR-1+δvδm1+δmR-1+δv, where the backscatter ratio R is defined as 29R=βp+βmβm, and δv is the volume linear depolarization ratio, which is δcorrected in Eq. (17), or ⟂β′∥β′ for instruments lacking termination hood measurements.

The molecular depolarization ratio (δm) is estimated following , accounting for major atmospheric gases and the influence of water vapor. The input data for these calculations are taken from a numerical weather prediction model (ECMWF IFS forecast) provided via the ACTRIS Cloudnet data portal .

The uncertainty of δp can be determined using partial derivatives 30σδp2=∂δp∂δmσδm2+∂δp∂δvσδv2+∂δp∂RσR2.

Assuming σβm and σδm are negligible and approximating σR≈σβpβm, this reduces to 31σδp2≈∂δp∂δvσδv2+∂δp∂Rσβpβm2.

The partial derivatives are calculated as: 32∂δp∂δv=1+δm2R(R-1)1+δmR-1+δv2,33∂δp∂R=1+δm1+δvδm-δv1+δmR-1+δv2.

Figure  shows the time series of background noise (variance of the background signal), normalized by integration time assuming Poisson statistics (σ∥β′/r22×tintergration), alongside the laser power. Most instruments (except for Vehmasmäki) exhibit a gradual decline in laser power, accompanied by corresponding increases in background noise, likely due to weaker return signal. These changes often occur in discrete steps rather than as a continuous trend. Notably, fluctuations in background noise are consistently related to changes in laser power. Periods of restored laser power and decreased background noise align with documented hardware interventions, such as transmitter replacements at Vehmasmäki (December 2022; Fig. a) and Hyytiälä (February 2024; Fig. b).

At Hyytiälä and Kenttärova, laser power gradually decreases from 100 % to around 40 % over 2 years. In contrast, the CL61 at Vehmasmäki maintains a consistently high laser power, ranging between 90 % and 100 % throughout the same period, with only a slight decrease during the summer, likely to regulate the internal temperature to prevent overheating. Meanwhile, the CL61 at Lindenberg experienced a sharp decline in laser power, from 80 % to below 10 % within just 1 year of operation. We also found that changes in the firmware version do not appear to have any noticeable effect on background noise levels.

The relationship between background noise, normalized by integration time, and laser power across several instruments is illustrated in Fig. . Nighttime measurements (23:00 to 01:00 local time; LT), shown in blue, are unaffected by solar radiation, while all-day measurements are displayed in grey. It is important to note that the selected nighttime window is arbitrary and used solely for this analysis; for instance, locations such as Kenttärova experience no true nighttime during summer. The nighttime data clearly indicate that a decrease in laser power leads to an increase in background noise across all instruments. Daytime background noise is generally higher due to solar radiation, which varies with factors such as solar angle, cloud height, and surface albedo, making direct comparisons more complex. Nevertheless, the figure suggests that lower laser power also contributes to increased noise levels during daytime conditions.

An increase in background noise can significantly reduce an instrument's ability to detect weak aerosol signals. This effect is clearly illustrated in Fig. S3. On 7 March 2024, an elevated aerosol layer was observed above 3 km in Lindenberg, indicated by enhanced attenuated backscatter coefficient values compared to those at lower altitudes between 1 and 3 km (Fig. S3a, c). However, by 2 December 2024, a reduction in laser power led to a higher noise floor, which meant that if a similar aerosol layer were present, it would no longer be distinguishable from the background noise (Fig. S3b, c).

In this section, we examine how the instrumental background bias (μPinstrumentO(r)) and noise (σPinstrumentO(r)2) with the overlap correction reverted, vary with temperature and over time. The termination hood measurement was deployed multiple times at Vehmasmäki, Hyytiälä, and Kenttärova. Figure  presents the instrumental background profiles recorded during these termination hood measurement periods, which have been averaged and grouped according to the instruments' internal temperatures.

For the instruments located in Hyytiälä and Kenttärova, the μ∥PinstrumentO(r) profiles remain relatively stable around zero from the far range down to about 2 km, then increase sharply as the range decreases. On the other hand, in Vehmasmäki, it also remains near zero at far range, but μ∥PinstrumentO(r) begins to increase already at around 5 km and continues to rise toward shorter ranges. Meanwhile, the μ⟂PinstrumentO(r) profiles for all three instruments remain near zero from the far range to about 2 km, after which they increase rapidly with decreasing range.

Overall, the internal temperature T has a more pronounced effect on the μPinstrumentO(r) profiles below 1 km than at higher ranges. In particular, the μPinstrumentO(r) profiles in both polarizations deviate substantially from zero at below 200 m (see Fig. ) across all instruments. Notably, each instrument shows the same small peak in the instrumental background bias in both polarizations at approximately 150 m.

All instruments exhibit profiles of σPinstrumentO(r)2 in both polarizations that remain constant above 500 m, followed by a sharp increase below this range. These instrumental background noise profiles show a pronounced sensitivity to internal temperature (from 4 to 38 °C). Notably, very low temperatures are associated with elevated instrumental background noise across the entire measurement range. This can be explained by the effect of the internal heater. As the internal temperature falls below an instrument-specific threshold (15 °C for Hyytiälä and Kenttärova), the internal heater is turned on. This leads to an increase in σPinstrumentO(r)2, with the effect becoming more pronounced as the temperature decreases. When the internal temperature is high and the internal heater is off, internal temperature positively correlates with σPinstrumentO(r)2.

Similar to Figs. , , S4 and S5 show the same profiles obtained during the termination hood measurements, but include range correction and the instrument-provided overlap correction. These profiles of ∥β′ and ⟂β′ provide a direct quantification of the impact of instrumental background bias and noise on the measurements and their dependence on temperature. For all CL61 instruments, the instrumental biases, μ∥β′ and μ⟂β′, remain below the order of 10-7, while the noise terms, σ∥β′2 and σ⟂β′2, remain below the order of 10-11. These biases are even smaller below 5 km. Below a range of 1 km, μ∥β′ remains below 5 × 10⁻⁹ and μ⟂β′ below 3 × 10⁻⁹. These small biases are usually negligible comparing to the typical atmospheric signal.

However, at very clean sites such as Kenttärova, the instrumental bias in ⟂β′ can still affect the retrieved aerosol depolarization ratio, particularly under conditions of low depolarization. An example is shown in Fig. S6, which presents measurements from Kenttärova on 3 October 2023 under weakly depolarizing aerosol conditions. During this period, the ⟂β′ profile below 400 m is on the order of 10-9, while ∥β′ remains on the order of 10-6. As a result, the instrumental bias becomes relatively significant for ⟂β′, leading to a noticeable, although quantitatively small, reduction in δ (from 0.002 to 0.001 at 200 m) after the bias correction is applied. Furthermore, the previously mentioned peak at 150 m is clearly visible in this case and is effectively mitigated after the removal of the instrumental bias. Overall, the impact of the bias correction is expected to be most pronounced under clean atmospheric conditions, such as in this case in Finland, where the δ profile remains consistently low. The correction improves the overall shape of the profile, particularly around 150 m, by removing the artificial peak in ⟂β′ at that height (Fig. S6). However, the change remains small in absolute terms.

For all instruments, the signal near the surface exhibits much more rapid fluctuations than at higher range gates. Figure S7 displays example profiles of ∥β′, ⟂β′, and the instrument's internal temperature during a termination hood measurement at Kenttärova, revealing periodic variations in the signal below 50 m. To investigate this, the Fourier transforms of these signals were computed at each range gate over time and compared to that of the laser temperature recorded simultaneously. The results show that both the signals and the laser temperature exhibit a coincident spectral peak at approximately 0.0079 Hz (about 120 s), indicating a strong influence of laser temperature on the signals. Furthermore, additional distinct peaks in the signal spectra imply the presence of other instrument-related effects. Overall, these periodic variations appear sporadically across all instruments, with no consistent pattern indicating when they appear or disappear. Given the difficulty in developing a reliable correction method, we recommend excluding measurements below 50 m.

Figure  shows how the instrumental bias during the termination hood measurement at Vehmasmäki varies over time under consistent internal temperature conditions. Over a 6-month period, the calibration profiles at each temperature show only minor fluctuations. Therefore, we recommend performing termination hood checks at least once across the operating temperature range to determine the instrumental background bias and noise.

Figure  presents the time series of calibration factor from the cloud calibration and Rayleigh calibration methods for all the ceilometers. Detailed results of the cloud calibration factors derived from liquid cloud signals at each site are presented in Figs. S8–S11. Overall, the calibration factors obtained from the two methods agree well within their respective uncertainties, In Lindenberg, the calibration factor from the cloud calibration exhibits an approximate threefold decline over time, reflecting notable signal degradation. During this degradation period, Rayleigh calibration could not be performed because the elevated background-noise level (see Sect. 4.1) obscured the molecular return. In contrast, the other instruments show only short-term fluctuations without any clear long-term trend. Two periods with notable deviations in the calibration factor were also identified: June to October 2023 and November to December 2024 in Vehmasmäki. The issue in the CL61 at Vehmasmäki is due to the fogged window that attenuates the outgoing signal. This will be analyzed in more detail in the following section.

Across all instruments, the calibration factor generally stays within the range of 0.9 to 1.5 as long as laser power remains above 40 %, aside from occasional deviations due to specific instrument issues. In Vehmasmäki, as the laser power remains above 90 %, the calibration factor fluctuates around 1 within 10 % fluctuation. In Hyytiälä, the highest changes in calibration factor is observed when the instrument's laser power is below 80 % with the firmware 1.1.10 and then below 60 % with the firmware 1.2.7. However, the calibration factor remains relatively stable at 1.25 even when the laser power drops from 100 % to 40 % with the firmware 1.2.7. In Kenttärova, laser power percentages were not recorded before June 2023, but the observed increase in the calibration factor is likely linked to a decrease in laser power. After a new transmitter was installed, the calibration factor returned to around 1. In Lindenberg, a noticeable decline in the cloud calibration factor was observed as laser power dropped from 40 % to 10 %. It is still to be ascertained whether this trend also appears in instruments running the newer firmware version 1.2.7.

Figure S12 demonstrates the utility of cloud calibration for two cases; one with 80 % laser power on 3 March 2024 and another with just 10 % on 16 November 2024. This indicates that the method can still be used in situations with low laser power. Since the internal calibration value may not scale with low laser power values, regular cloud calibration is necessary to understand instrument performance and continue to provide profiles that can be used quantitatively, especially for laser power values below 40 %.

After recording the termination hood profiles at different temperatures and determining the calibration factor, the correction and forward Klett inversion can be applied, and the associated uncertainty can be estimated using the method described in Sect. 3.3. Example results of this procedure are illustrated in Figs.  and  showcasing a typical Finnish low aerosol load condition in Kenttärova. During this period, the calibration factor was close to 1. On this date (Fig. ), aerosol was present below 1000 m within the boundary layer close to the ground, while several layers of clouds extended from 2 up to 3.5 km. Figure  presents the β, δ and their associated uncertainties in the aerosol layer below 1000 m obtained from a measurement profile recorded at 13:01 UTC on the same day.

At below 1000 m range, the corrected βv′ differs only slightly from the original uncorrected β′, with the difference ranging from 1 × 10⁻⁹ to 2.5 × 10⁻⁹ sr⁻¹ m⁻¹ (Fig. a). This difference is expected to be relatively smaller within the clouds, where the signal is stronger and the instrumental bias decreases with increasing range. In contrast, the particle backscatter coefficient βp is substantially lower than βv′ by approximately 1.5 × 10⁻⁷ sr⁻¹ m⁻¹, indicating a significant contribution from molecular scattering. The σβv′2 and σβp2 profiles are relatively similar to each other, and they both increase exponentially with height (Fig. b).

Similarly, the original uncorrected (δ) and the corrected (δv) profiles differ only slightly, by the difference is about 0.001 to 0.005 (Fig. c) while δ itself being around 0.07. In contrast, the particle linear depolarization ratio δp is substantially higher, differing from the original δ by approximately 0.1 with δp at around 0.1 to 0.15. For example, during pollen seasons in Finland, δp has been observed at 0.23 for pine and 0.26 for birch at this wavelength . The variances (σδv2, σδp2) are comparable below 200 m, but at higher ranges, σδp2 becomes markedly larger.

Overall, the pronounced differences between βv′ and βp, as well as between δv and δp, highlight the importance of accounting for the molecular contribution when performing quantitative assessments of aerosol measurement with CL61 for low aerosol load conditions in Finland. While the difference between β′ and βv′ (and δ and δv) may be small, the termination hood remains important as it allows the estimation of measurement uncertainties. Averaging multiple profiles reduces the uncertainties, as illustrated in Fig. S13, which shows the profiles averaged over 10 min.

Figure  illustrates the time series of βv′, δv, βp, and δp profiles, along with their corresponding variances on the same day. Similar to Fig. , βv′ is higher than βp, while δv is lower than δp in this period. The profiles of σβv′2 and σβp2 vary with time during this period, exhibiting an exponential increase with range. On the other hand, the σδv2 and σδp2 profiles demonstrate a more pronounced dependence on the signal magnitude (Fig. d and h), with stronger atmospheric signals resulting in smaller uncertainties.

As previously noted, abrupt changes in the cloud calibration factor at Vehmasmäki were observed from June to October 2023 and again from November to December 2024. Similar deviations are present during the same periods, as seen in the window condition housekeeping variable (Fig. S14). These patterns indicate that an obstruction, likely on the instrument window, was attenuating both outgoing and incoming laser beams.

Figure  illustrates a specific example from 19 May 2023. On this date, a sudden drop in the attenuated backscatter signal below 2000 m occurred just before 06:00 UTC. At the same time, the window condition value sharply declined from around 100 % to 70 %. This coincided with the automatic deactivation of the window blower heater. Housekeeping data, including internal temperature and relative humidity, were used to estimate the internal dew point, which was then compared to the external air temperature. When the window blower heater was off, the window cooled to match the outside air temperature. Once the window temperature dropped below the internal dew point, condensation began to form on the inside surface of the window and attenuated the signal. This occurred despite the measured internal relative humidity remaining below 70 %. This is because the measurement does not represent the relative humidity at the window surface, where the temperature is closer to ambient temperature.

Since condensation affects the entire signal profile and the degree of attenuation depends on its severity, it is not possible to precisely quantify the signal loss or reconstruct the original profile. This issue could be mitigated by keeping both the window blower and heater always on. However, at the time of this writing, this is not possible (personal communication with Vaisala). Additionally, hardware modifications may be required to maintain a sufficiently low internal dew point and prevent fogging.