Ceilometers are basic near-infrared lidar systems. They emit eye-safe laser pulses with a high frequency. The pulses are then scattered back to the instrument by cloud droplets, aerosols and gas-phase constituents. From the run-time, the distance to the scattering target is estimated. The intensity of the scattered signal can be used to determine the optical properties of the scattering target. The measured power P at the ceilometer receiver as a function of range r and time t can be described by the following equation : 1P(r,t)=1r2CL(t)O(r,t)β(r,t)e-2∫0rσ(r′,t)dr′+B(t)

Here CL represents a calibration factor (also known as lidar-constant), which contains device-specific parameters. The signal is also dependent on the overlap function O(r,t), the extinction coefficient σ, the backscatter coefficient β and a solar background signal B(t). It is common to define the range corrected signal (RCS) as: 2RCS=(P(r,t)-B(t))r2 Each ceilometer generates manufacturer-dependent raw data that were brought to unified L1 data by the E-Profile algorithm Raw2L1 .

JOYCE is equipped with two ceilometers (Table 1) representing the two main types of ceilometers, namely monoaxial (CT25k) and biaxial (CHM15k) setups. Monoaxial systems use a single light path for emitting and receiving the laser pulses and a semi-transparent mirror to split the beam. In contrast, biaxial ceilometers use two separate light paths. The downside of this approach is a range with incomplete overlap, which affects measurements of the CHM15k in the lowest about 350 m . This problem is significantly reduced for the Vaisala CT25k, which covers the lowest range gate but has a significantly lower pulse energy. Based on an internal overlap correction, measurements are usable starting at 0 m . However, hardware and software related artefacts were reported for measurements below 70 m for a comparable ceilometer (Vaisala CL31) . The Lufft CHM15k uses an avalanche photon detector (APD) in photon-counting mode, which allows higher SNR at high altitudes, compared to photocurrent method instruments like the Vaisala CT25k . It should also be noted that the CT25k and the CHM15k by now have been operational since 16 years and 12 years, respectively, which may have lowered their sensitivity. More advanced, modern ceilometers can produce data of higher quality. However, the intention of this work is to utilize the existing long-term dataset, which requires a characterization of the available instruments. The comparison with the in situ tower measurements will be confined to the CT25k data because of the overlap issue of the CHM15k at 120 m.

To evaluate the ceilometer aerosol-retrieval, a comparison setup was created as shown in Fig.  using the meteorological tower with an OPS for in situ measurements of aerosols installed at 120 m above ground. At this altitude, a representative measurement can be made undisturbed by any small-scale influence from the ground or nearby buildings.

The instrument consists of an inlet connected to the OPS in a water-tight box allowing for an omnidirectional aerosol sampling and rain protection . A photograph of the setup is shown in Fig. a. The airflow through the inlet of about 15 standard liter per minute (slm) was driven by a pump and controlled by a mass flow controller (MFC). Inside the laminar airflow about 1 slm of air was taken by the OPS instrument. The airflow of the MFC was regulated in a way that an isokinetic sampling by the OPS from the main airflow was obtained (assuming laminar flow conditions). The air was not dried actively. A schematic of the sampling and OPS setup is illustrated in Fig. b. Specifications of the OPS can be found in Table .

The instrument works on the principle of light scattering as illustrated in Fig. . The inlet air flow (1 L min⁻¹) is focused by a sheath air stream and goes through a light trap where a continuous laser beam (660 nm) passes the particle stream. Scattered light from a range of scattering angles is focused on a photodetector by a mirror. Light scattered by single aerosol particels is registered and assigned to a particle size dependent on the scattered light intensity.

The system allows the measurement of aerosol mass and number concentrations, sorted in 16 user-defined size channels, based on their scattering intensity. According to the manufacturer, data are processed as follows. For each channel, the number concentration Cn in a bin is determined. Based on the number concentration, a mass concentration Cm can be estimated: 3Cm=CnρπDpv36 ρ is the particle density (typically in the range 1.2 to 2.5 g cm⁻³; ) taken as 1.5 g cm⁻³ and Dpv is an effective particle diameter, which is calculated from the bin upper boundary (DU) and bin lower boundary (DL): 4Dpv=DL141+DUDL21+DUDL13 Size bins were selected based on a predefined protocol (TSI Default) as summarised in Table  in the appendix to cover the full size range the instrument provides (0.3–10 µm). Moreover, a temporal resolution of 5 min and a sample time of 1 min were selected for the measurements.

The Cloudnet target classification is utilized to characterize the atmospheric boundary layer regarding the presence of aerosols, insects, clouds and precipitation. Cloudnet was founded to combine ground based cloud remote sensing instruments to a network and to generate synergistic products . The minimum instrumentation consists of a Doppler cloud radar, a ceilometer and a dual-frequency microwave radiometer. Today, Cloudnet is integrated into the center for cloud remote sensing (CCRES) within ACTRIS . Currently there are 29 contributing sites registered . The Cloudnet target classification combines radar reflectivity, ceilometer backscatter, model parameters, microwave radiometer LWP measurements and rain gauge measurements into a single classification product. For each height layer, the bit values can be set for presence of small liquid droplets, presence of falling hydrometeors, wet-bulb temperature below 0 °C, presence of melting ice particles, presence of aerosols and presence of insects. At JOYCE, the Cloudnet target classification, which utilises the Lufft CHM15k ceilometer, is available on a grid of 36 m vertical resolution and 30 s temporal resolution. In the following, it will be used to filter out conditions where remote aerosol detection by the ceilometers may be adversely affected by liquid clouds, ice clouds or precipitation.

To use the RCS of a ceilometer for aerosol measurements, a calibration of the signal is necessary. The goal of this calibration is to determine the lidar constant CL to convert the RCS (Eq. ) into an attenuated backscatter coefficient βatt. 5βatt=RCSCL The commonly used Rayleigh calibration could not be applied to the Vaisala CT25k ceilometer due to the low signal-to-noise ratio (SNR) in high altitudes for this instrument. In recent years, an additional method was established. The liquid cloud calibration uses the attenuation of the ceilometer signal in liquid clouds. The lidar ratio S, defined as the ratio of the extinction-to-backscatter coefficient is assumed to be constant inside liquid clouds with a value of S≈18 sr . For cases where the ceilometer signal is fully attenuated by a liquid cloud, the total path integrated attenuated backscatter B can be described as a function of the observed attenuated backscatter coefficient βatt, the height above ground z, the range corrected signal RCS, the multiple-scattering correction η, the lidar ratio and a calibration coefficient C : 6B=∫0∞βattdz=∫0∞CRCSdz=12ηS In the algorithm, the calibration coefficient C is varied until Bη = 0.0266 m⁻¹. This value represents liquid cloud droplets with S = 18.8 sr . Only profiles with a negligible aerosol backscatter contribution (< 5 %) below the cloud are considered. The optimised calibration coefficient C is the reciprocal of the lidar constant CL. This method does not require high SNR values in high tropospheric regions and so it can be applied also to avalanche photon detectors in photocurrent detection mode like the Vaisala CT25k.

The JOYCE CT25k already performs an internal calibration, which was verified by the liquid cloud calibration , based on the program code of E-Profile . A lidar constant of CL=0.97±0.06 was determined in the years 2023 and 2024, confirming the internal calibration of the instrument. The manufacturer does not disclose the nature of the internal calibration.

To derive extinction profiles from the ceilometer attenuated backscatter signal the Klett-Fernald-Sasano method is mostly used where a backward inversion approach is applied to solve the lidar equation. The calculations start in the high, aerosol-free part of the atmosphere (Rayleigh-atmosphere) and iteratively derive the extinction coefficients.

To use the Klett-Fernald-Sasano approach, a high SNR in high layers is necessary. This requirement can not be fulfilled when using a Vaisala CT25k ceilometer. For this reason, a forward method was used . For each layer zi, starting at the ground with initial conditions based on the βatt, the aerosol transmittance Ta, the molecular transmittance Tm, the aerosol backscatter coefficient βa and the molecular backscatter coefficient βm are calculated in an iterative process (k = 1, 2, 3 …). The values of Tm(zi) and βm(zi) were calculated from the station altitude based on an algorithm-specific Rayleigh atmosphere. Here τa represents the aerosol optical depth and σa the aerosol extinction coefficient. 7τa(zi,k)=τa(zi-1)+σa(zi,k-1)⋅Δzi8Ta2(zi,k)=e-2τa(zi,k)9βa(zi,k)=βatt(zi)Tm2(zi)⋅Ta2(zi,k)-βm(zi) At every iteration step k, the extinction coefficient σa is calculated with the lidar ratio Sa: 10σa(zi,k)=Sa⋅βa(zi,k)

The iterative process is stopped if either 30 iteration steps are reached or if the relative change of the extinction coefficient σa is smaller than 0.01 %. Then the current value of σa, τa and βa are set and the process starts for the next layer. This method was implemented in the Python-library A-Profiles . For this study, we used this forward inversion algorithm for the Vaisala CT25k ceilometer.

The lidar ratio Sa=σa/βa is unknown for ceilometer measurements. Therefore, it was estimated based on a multi-year mean value of Sa=(47±13) sr for a wavelength of 1020 nm from the AERONET (AErosol RObotic NETwork; ) inversion product of a CIMEL sun photometer installed next to the ceilometers. The uncertainty of Sa is a major contributor to the overall uncertainty of retrieving σa from a ceilometer with this method.

Aerosol mass concentration Cm can be calculated from the aerosol extinction coefficient σa by an extinction to mass coefficient (EMC): 11Cm=σaEMC The EMC is dependent on the aerosol type, size distribution and the ceilometer wavelength. The EMC can either be predicted theoretically by Mie simulations or determined based on in situ Cm and ceilometer-derived σa. A discussion of the experimental EMC values found in this study compared to literature values can be found in Sect. .

A dataset of ceilometer-derived attenuated backscatter coefficients in 120 m and of in situ aerosol mass concentrations in the same height was acquired for the period 1 February to 20 June 2023. There was a 10 d interruption from 22 February to 3 March because of a blocked exhaust filter and a 7 d interruption from 4 to 12 April caused by an outage in ceilometer measurements. The dataset was screened to avoid contamination by hydrometeors in the ceilometer signal, based on the Cloudnet target classification (Sect. ). To further refine this selection, data were discarded when the relative humidity (RH) measured at 120 m exceeded 95 % and cloud radar reflectivity at the lowest possible measurement height (255 m) was above -20 dBZ at 35 GHz.

Figure  provides an overview of the dataset, including additional measurements from the meteorological tower. The mean aerosol mass concentration during the observation period was Cm = 11.5 µg m⁻³. The mean temperature and relative humidity were θ = (12 ± 7) °C and RH = (76 ± 19) %, respectively. The wind speed at 120 m above ground on average was (6 ± 3) m s⁻¹. For the measurement period, no coherent wind direction measurement in 120 m was available. For this reason, the wind direction at the meteorological tower 50 m above ground is shown in Fig. . The predominant wind direction at 50 m was west-southwest.

To illustrate typical diurnal changes in aerosol concentration, 14 February 2023 was selected as an example. This day was dominated by a high-pressure ridge over Central Europe. The ridge went along with a surface high-pressure system. This situation creates stable conditions with no clouds or precipitation over the day.

As shown in Fig. a, the Cloudnet target classification confirmed no clouds or precipitation in the boundary layer while aerosols were present for the whole day. These conditions make that day ideal for comparing the ceilometer aerosol retrieval with the in situ observation. In the time range from 00:00 to about 09:00 UTC low aerosol mass concentrations of Cm < 5 µg m⁻³ are visible in the tower observations (Fig. e). This goes along with low ceilometer backscatter coefficients of βatt<40×10-5 sr⁻¹ km⁻¹ (Fig. c). The vertical extent of the aerosol layer below 250 m is visible in the ceilometer backscatter profiles (Fig. b). With the development of the mixing layer after 09:00 UTC, the aerosol mass concentration increased up to Cm = 30 µg m⁻³. This trend is also visible in the ceilometer-derived aerosol extinction coefficients (Fig. d) and in the ceilometer backscatter coefficients, which increased up to βatt = 100×10-5 sr⁻¹ km⁻¹ (Fig. c).

This example demonstrates qualitativly that ceilometer backscatter coefficients can reproduce the overall change in aerosol concentration. Steplike levels of ceilometer backscatter coefficients can be explained by the low signal resolution of the Vaisala CT25k (Sect. ).

In the next step, we now statistically relate measured attenuated backscatter coefficients βatt to in situ measured aerosol mass concentrations Cm.

For the following analyses, a combined dataset based on OPS-measurement, ceilometer, and Cloudnet data was generated. All data were mapped on the 5 min time grid of the OPS-measurements based on a nearest neighbour approach, resulting in a total of 5443 data points after applying the filtering criteria (Sect. ). Figure  indicates a linear correlation between ceilometer attenuated backscatter coefficient βatt and in situ aerosol mass concentration Cm with a Pearson correlation coefficient R = 0.73. This result is in reasonable agreement with a previous study by who obtained a correlation coefficient of R = 0.84 between ground-level PM₁₀ aerosol mass concentration and the attenuated backscatter coefficient of a co-located CT25k in an urban environment.

To derive an empirical relationship between attenuated backscatter coefficients and total aerosol mass concentrations, a least squares linear regression was derived resulting in the following expression for a ceilometer-derived aerosol mass concentration Cmβ: 12Cmβµgm-3=0.18⋅βatt10-5sr-1km-1 Neglecting the small contribution of molecular backscatter that is discussed in Sect. , the line was forced through the origin. The corresponding regression line is shown in Fig. . Its slope is again in reasonable agreement with the result by who derived a value of 0.20 × 10⁵ µg m⁻³ sr km and a small offset of -1.6 µg m⁻³.

To estimate the uncertainty of deriving aerosol mass concentration from βatt, a mean absolute percentage error (MAPE) was calculated considering all N data points: 13ΔCmβ=1N∑i=1NCm,iβ-Cm,iCm,i×100%=31% The corresponding RMSE is 4.7 µg m⁻³. As is evident from Fig.  the scatter is significant and can be explained by instrumental uncertainties, varying aerosol optical properties, aerosol composition, particle size, and particle shape. The color-coding based on the diameter Dmode of the OPS size bin with the maximum aerosol mass concentration implies a dependence of the relationship on the particle size distribution that is addressed in Sect. .

This analysis demonstrates that ceilometer βatt measurements are, in principle, suitable for obtaining information on aerosol mass concentration. However, the statistical relation obtained here is valid only for the site- and instrument-specific set-up. Additionally, they represent only measurements during defined environmental conditions, as described above, from a five-month dataset.

In this section we now analyse the relation of the in situ measured aerosol mass concentrations to the aerosol extinction coefficients, derived from βatt. Any influence of molecular backscatter that is included in βatt should be eliminated in the retrieval of aerosol extinction coefficients. Ceilometer-derived σa were calculated from the ceilometer attenuated backscatter coefficient βatt by the forward inversion method described in Sect.  . Figure  shows the obtained σa as a function of the corresponding βatt revealing a compact linear relationship with a correlation coefficient close to unity. A linear regression results in: 14σakm-1=-0.008+47.6⋅βattsr-1km-1 The slope of 47.6 sr closely resembles the a priori lidar ratio of Sa=47 sr that was applied (Sect. ) with a y-intercept of (-0.008 ± 0.002) km⁻¹. This intercept corresponds to the influence of molecular backscatter that is included in βatt and should be eliminated in the retrieval of σa. The intercept value can be converted to a pure air backscattering coefficient of about (1.7 ± 0.4) × 10⁻⁴ sr⁻¹km⁻¹. Taking the theoretical Rayleigh scattering lidar ratio of 8π/3 sr, an extinction coefficient of (1.4 ± 0.4) × 10⁻³ km⁻¹ at 120 m was obtained. This estimate is in reasonable agreement with a value of (1.50±0.04) × 10⁻³ km⁻¹ for 906 nm derived from the literature for the measurement conditions . In contrast, a comparison of the vertically integrated σa with AERONET aerosol-optical-depths (AOD) shows a significant underestimation. This can be explained by the low SNR of the CT25k at higher altitudes leading to an underestimation of the derived σa. The comparison is provided in Sect.  of the Appendix.

Because of the strong correlation between βatt and σa, a plot of Cm as a function of σa exhibits virtually the same scatter as Cm as a function of βatt (Fig. ) with a similar Pearson correlation coefficient of R = 0.73. The corresponding plot is shown in Fig. .

A linear regression through the origin between Cm and σa results in an empirical relation for an extinction-derived aerosol mass concentration Cmσ: 15Cmσµgm-3=460⋅σakm-1 Consistently, no improvement in the relative uncertainty of deriving aerosol mass concentration from σa was achieved, i.e. ΔCmσ = 39 % (RSME = 5.7 µg m⁻³), compared to ΔCmβ = 31 %. However, knowledge of the true lidar ratio for each measurement is expected to reduce ΔCmσ, making σa a better proxy for the aerosol mass concentration. This hypothesis is discussed in the next section.

Equation () corresponds to EMC = (2.2 ± 0.9) m² g⁻¹, which is high compared to literature values from ceilometer networks like ALICEnet: EMC = (0.9–1.2) m² g⁻¹ and UK Met Office: EMC = (0.7–1.3) m² g⁻¹ . Part of this difference can be explained by the smaller wavelength of the Vaisala CT25k (906 nm) compared to the Lufft CHM15k (1064 nm) for which the literature values apply. Typical Angström exponents of 1.2 ± 0.5 would result in ratios σa,1064/σa,906=0.83±0.06 shifting the EMC closer to the literature values, i.e. EMC = (1.8 ± 0.7) m² g⁻¹ for a wavelength of 1064 nm. A recent study reported 911 nm extinction-to-volume coefficients of 0.448 Mm µm³ cm⁻³ for continental aerosols , confirming a lower EMC of 1.5 m² g⁻¹ based on a common density of 1.5 g cm⁻³.

In this section, we now attempt to explain the discrepancies in the derived EMC to previous literature studies. For this, we simulated βa and σa based on Mie-theory and the measured OPS size distributions. Following an approach by , particle extinction efficiencies Qext for the ceilometer wavelength of λ = 906 nm were calculated for 1000 spherical aerosol particles with diameters linearly distributed between 0.3 and 10 µm. Refractive indices were varied between m = 1.3-0i (water) and m = 1.7-0i (dolomite), covering a typical range of naturally occurring particle properties . For each size bin of the OPS (Table ), the mean of Qext was calculated and converted to the aerosol extinction cross section by multiplication with the geometrical cross section πDpv2/4. The total aerosol extinction coefficients σaMie for each OPS measurement were then calculated based on the measured aerosol number size distribution. Mean size bin lidar ratios were determined accordingly from the phase functions of the spherical particles. Combined with the extinction coefficients, aerosol backscatter coefficients were obtained for the size bins and finally the βaMie of the measured size distributions. The different ranges of βaMie for the different refractive indices are shown in Fig. . Lidar ratios SaMie=σaMie/βaMie for the size distributions can be defined as well.

The results of the calculations are summarized in Table . Slopes and correlation coefficients of regression lines for different particle refractive indices are listed for Cm as a function of σaMie and βaMie, σaMie as a function of σa, as well as the lidar ratios SaMie for the 5443 size distributions. With one exception, correlation coefficients range above 0.82.

As an example, Fig.  shows the dependence of measured Cm as a function of σaMie for a refractive index of 1.5, revealing a comparable scatter and color-coding pattern as in Figs.  and . A plot of calculated and ceilometer-derived extinction coefficients against each other is shown for this example in Fig.  and confirms that the Dmode dependence no longer affects the relationship, which is reflected in a greater correlation coefficient of R = 0.92 compared to R = 0.73 in Figs.  and , and R = 0.84 in Fig. . This result can be explained by different particle size dependencies of the aerosol particle mass (∝D3) and scattering cross section (∝D2) which adversely affect the correlations of aerosol mass concentrations and extinction coefficients for the investigated collection of variable size distributions. However, despite the strong correlation in Fig. , the σaMie and σa differ by a factor of about 0.5. Comparable results were obtained for other refractive indices which produce ratios between σaMie and σa in a reasonably narrow range of 0.49 ± 0.17 (Table ).

In contrast, the Cm to βaMie relationships and the SaMie exhibt a much greater dependence on refractive index, compared to the Cm to σaMie relationships (Table ) because of strongly increasing backscattering efficiencies with increasing refractive index. In addition, as already shown by , for spherical particles in the size range 1–10 µm strong variations and distinct maxima in the phase function in backscattering direction exist, i.e. minima in the lidar ratios. On the other hand, demonstrated that these minima do not occur for non-spherical particles which can explain the overall smaller SaMie compared to the AERONET based value of 47 sr used in the retrieval (Sect. ). Note that lidar ratios in a range 40–50 sr are applied in the aforementioned ceilometer networks in agreement with the value used in this work. However, a column-mean lidar ratio might not be representative of the boundary layer. Nevertheless, the theoretical calculations summarized in Table  confirm that the slopes of the empirical linear relationships between Cm and σa are robust with regard to variations of refractive indices in the particle phase. This is relevant because a natural aerosol will be composed of particles with different refractive indices and the composition can vary with time. Moreover, the resulting EMC = 1/r3 (Table ) of (1.3 ± 0.4) m² g⁻¹ are in the range of the literature values.

The Mie-theory calculations of the previous section rely on accurately determined size distributions from the OPS measurements. The uncertainties of these measurements are challenging to estimate and are not provided by the manufacturer. But major systematic errors are unlikely relying on careful characterisations by the manufacturer. However, the size range that is covered by the OPS is limited to 0.3–10 µm. The influence of particles greater than 10 µm is uncertain. They are probably correctly discarded because of scattered light signals that are too high. On the other hand, such particles will contribute to the scattered light received by the ceilometer. Similarly, particles smaller than 0.3 µm are not registered because they produce too small signals, but their contribution to the backscatter may still be significant. In addition, particles may be lost in the upstream inlet system before they can enter the OPS. These limitations have in common that they decrease the registered number and mass concentrations of particles that are nonetheless present and potentially relevant for the ceilometer measurements. Without a full characterisation of the size distribution beyond the size range of the OPS, a quantification of the missed aerosol mass concentration and the corresponding simulated aerosol extinction is not meaningful.

To illustrate the problem, Fig.  depicts the full measurement period's mean aerosol size distribution of this work showing the typical increase of number concentrations towards smaller particle diameters which can be expected to continue to diameters below 0.3 µm and greater than 10 µm. On the right hand axis, the cumulative, relative contributions of the size bins to the measured total aerosol mass concentration Cm and the simulated aerosol extinction coefficient σaMie for a refractive index of 1.5 are shown on a linear scale for comparison. The extinction coefficient increase towards the greatest Dpv is already levelling out. The contribution of particles greater than 10 µm is therefore assumed to be limited. On the other hand, the contributions of the size bin with the smallest Dpv are already on the order of 10 % for both aerosol mass concentration and aerosol extinction coefficient. It is therefore plausible that particles with diameters < 0.3 µm have contributed substantially to the ceilometer backscatter and the retrieved extinction coefficients. This could qualitatively explain why the EMC obtained in this work is greater than those in literature and those derived from Mie theory. For the latter the size range limitations seem to be less significant because of compensating effects, i.e. by missing aerosol mass concentration and missing aerosol extinction. Figure  also illustrates the apparent Dmode dependence of the σa vs. Cm relationships in Figs. 6 and 7. An elevated contribution of particels with Dpv < 1 µm would increase the σaMie more strongly than Cm while for particles with Dpv > 2 µm the opposite is the case: the Cm increase would exceed that of σaMie.

An approach to quantify the contribution of particles < 0.3 µm based on AERONET showed an underestimation of the total volume concentration by this limitation of approximately 20 % as shown in Fig.  of the Appendix. However, it should be noted that AERONET refers to column data, whereas the OPS refers to a measurement altitude of 120 m. For this reason, the 20 % are considered as an upper limit, assuming a higher fraction of large particles in the boundary layer.

An additional factor is the possibility of unintentional drying of the aerosol in the OPS. The sample stream was not actively dried to preserve the ambient size distribution. Hygroscopic growth within the sampling line is not likely because the temperature inside the box is slightly higher than outside, caused by the waste heat of the instruments. Accordingly, a drop in RH is expected, which could lead to a size-decrease of a fraction of particles prior to detection. It is expected that at higher relative humidities the effect is more pronounced because growth factors typically increase non-linearly with humidity . To identify a potential bias, the regression analysis for the relation between σa and Cm (Eq. ) was reevaluated as a function of the upper limit in ambient relative humidity. The results are presented in Sect.  in the appendix showing an increase in the slope with decreasing humidity limits. Though within the estimated uncertainties, these data indicate a clear trend consistent with a drying effect by a temperature increase in the OPS. This trend is levelling out towards the lowest limit of 50 % RH. Accordingly, EMC values decrease to values in better agreement with literature.