Aerosol profiling with the Jenoptik ceilometer CHM15kx

Since a few years, the number of active remote sensing systems has been rapidly increasing as national weather services started to build up networks of ceilometers. As ceilometers can be considered as “simple” backscatter lidars, it is obvious to investigate to which extent they can provide quantitative aerosol information. In this context, the calibration of the ceilometer is the most crucial point: whereas previous studies primarily have relied on the comparisons with co-incident sun photometer measurements and the Rayleigh calibration, we provide an absolute calibration of the ceilometer. The advantage of this approach is that backscatter profiles can be derived during daytime and nighttime, and even in cases when the signal-to-noise ratio of signals from the free troposphere is very low. Moreover, the retrieval can easily be automated. In this paper, we consider the Jenoptik CHM15kx-ceilometer. We discuss the methodology and the achievable accuracy and present a set of examples to highlight the wide range of applications, and the limitations. The achievable temporal resolution is of the order of a few minutes; the relative error of the particle backscatter coefficient is less than 10 %. It is emphasized that the accuracy of extinction coefficients and – as a consequence – of the aerosol optical depth is limited due to the unknown lidar ratio. This is, however, an inherent problem of any backscatter lidar and not a special feature of the ceilometer.


Introduction
There is broad evidence that lidar is an excellent tool for aerosol remote sensing.  pending on the complexity of the systems with respect to number of wavelengths and the implementation of polarimetric channels it is possible to derive a variety of properties to characterize aerosols. Backscatter lidars provide the derivation of geometrical properties (e.g. the detection of aerosol layers and their vertical extent), advanced systems (high spectral resolution lidars or Raman lidars with polarimetric measure-25 ments) provide the assessment of optical properties, namely extensive properties as 3396 the extinction coefficient as well as intensive properties as the lidar ratio or depolarization ratio. This has been demonstrated in several field campaigns when lidars were key instruments to characterize specific aerosol types, including INDOEX (e.g. Müller et al., 2000), ACE-2 (e.g. Flamant et al., 2000;Ansmann et al., 2001), ACE-Asia (e.g. Shimizu et al., 2004), or AMMA (e.g. Heese and Wiegner, 2008). A recent example are the two 5 SAMUM campaigns where Saharan dust was characterized near the source and at the beginning of its transport over the Atlantic ocean (e.g. Groß et al., 2011;Tesche et al., 2011). During the last decade lidar related aerosol studies were extended towards attempts to derive microphysical properties (e.g. Böckmann, 2001;Kolgotin and Müller, 2008;Gasteiger et al., 2011).
Most of the current lidar activities are research oriented. This is in particular true when very complex systems are operated, but also when lidar networks are considered. Though the European aerosol research lidar network EARLINET (Bösenberg et al., 2003) -established in 2000, currently comprising 27 systems, and probably the most mature network worldwide -provides measurements on a regular schedule it is 15 far from being a monitoring network. EARLINET is focused on improvements of the hardware, the elaboration of robust data evaluation schemes including a complete error analysis and a strict quality control. Following this approach it aims to ultimately establish a European aerosol climatology.
The benefit of these state-of-the-art lidar systems is undoubted, however, unat-20 tended and continuous operation of advanced lidar systems is still an exceptional case. As a consequence, the use of ceilometers as sort of secondary network is fostered. Ceilometers are simple one-wavelength backscatter lidars with low pulse energy and high pulse repetition frequencies. Recently, several weather services set up ceilometer networks, e.g. the German Weather Service (DWD) installed more than 50 systems in Introduction the assessment of the boundary layer height was investigated (e.g. Emeis et al., 2004;Wiegner et al., 2006;Münkel et al., 2007;Haeffelin et al., 2011). With the improvement of the ceilometers' hardware, it became clear that there might be a certain potential for aerosol remote sensing. To be of benefit for aerosol research, it is desired to derive the aerosol extinction coefficient α p as a function of height, or at 5 least the backscatter coefficient β p . It is obvious that the derivation of α p suffers from the inherent problem of any backscatter lidar: as the lidar ratio S p (defined as the ratio of the particle extinction and backscatter coefficients, α p /β p ) is unknown, the retrieval of α p is strongly influenced by the accuracy of the estimated lidar ratio. The accuracy of the retrieval of β p normally is less sensitive to erroneous estimates of S p , in particular 10 at wavelengths in the near infrared. The calibration of lidar signals by means of an aerosol-free atmospheric layer -the so called Rayleigh calibration -is not an issue for advanced lidar systems, but could raise serious problems in case of ceilometers. The reason is the low pulse energy of the laser resulting in a (very) low signal-to-noise ratio from layers in the free troposphere where aerosol-free conditions are expected. This is 15 in particular true for daytime measurements.
One approach to evaluate ceilometer measurements is based on the combination with co-located and coincident sun photometer measurements (e.g. Takamura et al., 1994;Sicard et al., 2006;Heese et al., 2010). This approach relies on the photometer derived aerosol optical depth, i.e. the integral of α p over the atmospheric column, as 20 a constraint for the inversion of the ceilometer signals. The underlying concept is to change the lidar ratio until there is agreement between the integral over α p and τ p . However, there are a number of problems associated with this approach: as sun photometer measurements are only available during daytime and under conditions of low cloudiness the range of application is limited. Unfortunately, during night time, when 25 the ceilometer is in principle better suited for aerosol remote sensing due to the missing background radiation, this methodology cannot be applied. The extrapolation of the optical depths from the previous or following day might be possible under stable conditions but will introduce additional uncertainties in any case. As the determination of aerosol optical depth at large solar zenith angles (sunset, sunrise) could be critical due to incorrect cloud clearing, the extrapolation to nighttime is further complicated. Another problem of the combined evaluation of ceilometer and sun photometer measurements is based on the region of incomplete overlap z ovl of the ceilometer (Stachlewska et al., 2010). The larger z ovl the more critical becomes the usage of τ p to estimate the lidar ra-5 tio for the ceilometer inversion. This problem is in so far quite serious, as under typical conditions most of the particles are concentrated in the lowermost atmospheric layers. If this layer is below z ovl and no reliable overlap correction is available, the adjustment of S p by comparing optical depths is not possible. For these reasons we follow an approach briefly outlined by Wiegner (2010). It is 10 based on the absolute calibration of the ceilometer and provides a more robust method to provide quantitative aerosol profiles. The methodology including a discussion of its accuracy is outlined in Sect. 2. In this paper we use data of a JenOptik ceilometer CHM15kx as explained in the following section. Next, the two-step calibration of the ceilometer is described in detail. To demonstrate the potential of the ceilometer with 15 respect to aerosol profiling, we provide a few example when the method is applied to measurements at Munich (Sect. 5). A brief summary concludes the paper.

Theoretical concept
The derivation of β p (or α p ) in case of backscatter lidars is provided by the Klett-or Fernald-algorithm (Klett, 1981;Fernald, 1984). A general description of the concept 20 can already be found in Fernald et al. (1972): in brief, α p is expressed in terms of the transmission T p and then inserted into the lidar equation. Then, a linear differential equation for T 2 p is obtained. The solution requires an estimate of the lidar ratio S p , whereas the lidar constant C L is normally substituted by a boundary value β p (z ref  be free of aerosols. Thus, the aerosol backscatter coefficient is set to β p (z ref ) = 0 and can be used to calibrate the signals. This solution can be expressed in an equivalent form that includes the lidar constant C L , i.e, C L is not replaced by a reference value. Then, β p can be derived from the lidar signal P (z) according to with The functions Z and N can be calculated starting from the range of complete overlap ("forward direction"). Though there is a minus sign in the denominator, solution (Eq. 1) does not become mathematically unstable due to the low optical depths in the near infrared (C L 2 Z d z). The backscatter and extinction coefficients of the air molecules, β m and α m , can readily be calculated from the air density known from radiosonde as-15 cents. Both variables are assumed to be known whenever lidar signals are evaluated.
It can be concluded that when the lidar constant is known (frequently referred to as absolute calibration) the derivation of the backscatter coefficient profiles only requires an estimate of the lidar ratio. Whereas the conventional method based on the Rayleigh calibration is only applicable for systems that provide sufficient signal-to-noise ratios in 20 the free troposphere, this alternative inversion is valid for any absolutely calibrated lidar or ceilometer with equal performance.

Ceilometer and data
In this paper we use data of the JenOptik ceilometer CHM15kx. The main specifications relevant for this study are briefly summarized. The system emits laser pulses at 1064 nm (Nd:YAG-laser, class M1) with a typical pulse energy of 8 µJ and a pulse repetition frequency of about 6500 Hz. The beam divergence is 0.33 mrad, the field of 5 view is 1.8 mrad. In contrast to the JenOptik ceilometer CHM15k, the optical axes of the laser and the telescope are tilted by 0.46 mrad. As a consequence, the height of complete overlap is very low with z ovl ≈ 150 m according to own measurements and information provided by S. Frey (personal communication, 2012). The backscattered photons are measured by an APD in photon counting mode.

15
The sensitivity of the ceilometer changes automatically with the background radiation: during daytime and in case of low, bright clouds in the line of sight the sensitivity is reduced. This is realized by reducing the high voltage supply of the APD. These modifications can be tracked from the data files: the difference between the actual and the breakdown voltage of the APD is stored in the NetCDF-files (parameter NN1, given in 20 0.1 V) henceforward referred to as ∆. The background signal is monitored by means of the "daylight correction factor" in the data file, here it is denoted as B for the sake of brevity. For our ceilometer ∆ ranges between 120 and 155. Whenever B exceeds 0.3, ∆ is increased by 5. In some cases, more than one of these changes is made with in a few minutes, resulting in an effective increase of ∆ of e.g. 10 or 15. Then, the system Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | cases ∆ is decreased by 5 as soon as B is lower than 0.001. From our investigations we found, that about 85 % of all changes of ∆ are not larger than ±10. The backscatter and extinction coefficients β m and α m , required to determine the optical properties of the particles (see Eq. 1), are calculated from pressure and temperature profiles of radiosonde ascents at Oberschleißheim, which is 10 km north of 5 the ceilometer site.

Calibration of the ceilometer
The assessment of the lidar constant C L in the case of the CHM15kx is complicated as the sensitivity of the detection unit changes under different meteorological conditions. Thus, the absolute calibration is carried out in two steps. One step provides the 10 absolute calibration for a certain ∆. This is done for 14 cases only because very strict requirements with respect to the independent data sets and the meteorological conditions must be fulfilled. Note, that we have almost 1000 days of ceilometer observations (June 2009 until January 2012). The second step concerns the determination of the relative change of the lidar constant as a function of ∆. This part is performed in al-15 most 250 cases because this procedure only relies on the ceilometer data alone, and the meteorological requirements are met much easier. The combination of both parts provides the absolute calibration of all ceilometer measurements.

Relative calibration
A typical example of one day of measurements with several changes of the sensitivity of 20 the system can be seen in Fig. 1 The relative change of C L as a function of ∆ is determined first. The decrease or increase of C L during the change of the high voltage difference from ∆ i to ∆ j (corresponding to times t i and t j , respectively) can directly be determined from the ratio of the corresponding signals. If the aerosol distribution is constant during this time, all 10 "atmospheric" terms (β = β m + β p , and the transmission) in the lidar equation  cancel out and a very simple relation for the conversion factor η x remains: The conversion factors η x are expressed in terms of the difference of ∆ at t j and t i , 15 that means η −5 stands for a decrease of ∆ by 5 (x = ∆(t j ) − ∆(t i ) = −5, e.g. from 155 to 150), whereas η 5 describes an increase of ∆ by 5. The factors η −5 and η 5 are determined when the aerosol distribution is stable in the mixing layer, in particular below height z that is used in Eq. (2). Typically, z is selected in a height below 1000 m where the aerosol backscatter is strong enough that the signal 20 is virtually unaffected by noise.
One example of the determination of the conversion factor η −5 is shown in Fig. 2 Fig. 1). To calculate η −5 we consider a temporal average over ten minutes before (P (t i ) z 2 ) and after (P (t j ) z 2 ) the change as indicated in the figure. Longer temporal averages neither seem to be necessary nor adequate as the signal slowly decreases due to a changing aerosol distribution. The accuracy of η −5 depends on the accuracy 5 of the averages of the involved range corrected signals and is estimated from a set of calculations with different temporal averages. In this case we find a relative error of η −5 of 3.5 %. This number is typical, note, that we consider only cases when the atmosphere is stable in time. Thus, it can be expected that the associated errors of the conversion factors are small.

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Following this procedure, conversion factors η −5 are determined for 111 cases. It is found that the conversion factor is virtually independent of ∆, in other words, a change of ∆ from 150 to 145 and a change from 145 to 140 have the same effect on the signal strength. As can be seen in Table 1 η −5 = 1.247 on average, with an error of 0.033. The error is calculated from the individual errors of each of the 111 cases. 15 We also consider cases, when the background radiation increases and consequently ∆ increases. Analog to the previous paragraph, we calculate η 5 for any ∆. From a total of 23 cases we find as an average η 5 = 0.830 with an error of 0.033. As an increase of ∆ and a subsequent decrease of the same magnitude (or vice versa) should result in an unchanged sensitivity of the detection unit, it can be expected that η x = (η −x ) −1 20 is valid. To make clear the good agreement between both values we have included the inverse of η 5 in Table 1.
As already mentioned also larger changes of ∆, as a rapid sequence of two or three steps, occur. From these cases we calculate η −10 = 1.540 (63 cases) and η −15 = 1.948 (30 cases). It is expected that a decrease of ∆ by 10 is equivalent to two subsequent 25 decreases by 5 each, i.e. η −10 = (η −5 ) 2 . For the same reasons, η −15 = (η −5 ) 3 should hold. Thus, we include the square root of η −10 and the cubic root of η −15 in Table 1 of η −5 . The corresponding conversion factors when ∆ increases by multiples of 5 are determined in the same way. From the good agreement of all cases when normalized to an ∆-decrease of 5 we define an "overall" conversion factor η according to The exponent n ranges from −3 ≤ n ≤ 3, as x ranges from −15 to 15 in steps of 5. From Table 1 we find η = 1.238 ± 0.037. From Eq. (3) it is clear that the knowledge of η is sufficient to account for any change of the sensitivity of the ceilometer: if C L (∆ i ) is 10 known, we get C L (∆ j ) according to Equation (4) shows

Absolute calibration
Measurements are considered suitable for the absolute calibration of the ceilometer 15 when two conditions are fulfilled. The first condition is, that the background radiation is low and Rayleigh calibration is possible for 60 to 120 min averages of the signals. Shorter time periods have been found to be unrealistic (Wiegner, 2010). The second condition is, that the aerosol optical depth is derived independently from AERONET measurements (Holben et al., 1998)  a typical α p = 0.05 km −1 at z = 150 m. If we assume a constant α p down to the ground, the optical depth of this "missing" layer is τ p,ovl = 0.0075. Even a very large relative error of 50 % of α p would result in an over-or underestimate of the optical depth of less than 0.004. Furthermore, we apply this method only when the time difference between the ceilometer measurement and the AERONET retrieval is below two to three hours, 5 and when there are no indications that the aerosol distribution has undergone changes during that time period. For these reasons we primarily choose cloud-free time periods close to sunset or sunrise. If the aerosol extinction coefficient profile α p is retrieved from the Klett algorithm, the lidar constant can directly be determined from the lidar equation For the assessment of the errors of C L we consider two main contributions: the error due to the uncertainty of τ p as derived from the Cimel radiometer, and the error of the Rayleigh calibration. The uncertainty of τ p based on a single measurement is typically 0.015 depending on the calibration and the maintenance of the radiometer. Taking into 15 account that we only select meteorological conditions when the aerosol stratification is stable, and that we average over one to two hours, the resulting error is certainly smaller. We estimate it from the variability of individual Cimel measurements during the calibration period; in all cases it is smaller than 0.006. Errors due to the different spatial sampling of the ceilometer (observing the vertical atmospheric column) and 20 the radiometer (observing a slant path in the direction of the sun) are impossible to be quantified and assumed to be negligible. With respect to the Klett-algorithm we assume that in the Rayleigh calibration range the scattering ratio R = 1 + β p /β m is not larger than 1.1. This uncertainty has a larger influence on the retrieved C L than the uncertainty of τ p . Due to these error sources we get a range of possible solutions of 25 C L . This range can be described by C L ± ∆C L , where C L is the mean of the maximum 3406 Introduction and minimum, and ∆C L is defined as half of the difference of the maximum and the minimum; ∆C L is considered as a systematic error. As a result of the strict requirements we get 14 cases suitable to calculate the lidar constant of the ceilometer. These cases include different values of ∆, the most frequent setting is ∆ = 140. According to the discussion in Sect. 4.1, the ratio of lidar constants 5 should fulfill Eq. (4). Therefore, they can serve as an independent check of the validity of the calibration factor η. Finally, it is obvious from Eq. (4) that it is sufficient for the absolute calibration to define a reference value of the lidar constant C * L for one specific An example of this procedure is given in Fig. 3. Shown is the range corrected sig- Klett inversion algorithm is applied to derive α p (z), assuming a height-independent lidar ratio. The lidar ratio follows from the condition, that the integrated aerosol extinction coefficient from the ceilometer data and the aerosol optical depth from the Cimel measurements (12 October 2010, 13:00-15:00 UTC) must agree. In this case we find S p = 48 ± 9 sr, and a lidar constant of C L =,17.68 ± 1.20 km 3 sr (with P being dimen-20 sionless). In Fig. 4 the lidar constants C * L as determined from the 14 cases with different ∆ are shown; case no. 9 refers to the example discussed above. The conversion from the individual ∆-value to ∆ ref is applied according to Eq. (4), and the involved errors are considered. The good agreement of the lidar constants confirms the η-value derived in 25 the previous section. The reference lidar constant is finally determined as the average over all cases and found to be C * L = 17.39 ± 0.67 km 3 sr (corresponding to 3.9 %).
It is worthwhile to briefly discuss the lidar ratios that are found from the calibration (Fig. 5) constants. They range from 24 sr to 63 sr with an average of 43 sr. The uncertainty ranges of S p are consistent to the uncertainty of the corresponding lidar constants (see Fig. 4). It seems that during summer and fall the lidar ratios are significantly lower compared to the other two seasons. It will be interesting whether an annual cycle can be confirmed by more and independent measurements. It should be stressed that Fig. 5 5 may not be misunderstood as a representative sample of a lidar ratio climatology over Munich, it is rather meant as a demonstration that no unrealistic lidar ratios are found when we calculate the lidar constant. With the limited data set currently available we use S p = 43 sr for all retrievals discussed later.

Special cases 10
When cumulus clouds develop at the top of the boundary layer and solar illumination is high, the background radiation could be quite strong. This situation is associated with a sudden rise of B and the exceedance of the threshold B = 0.5. From the point of aerosol remote sensing with a ceilometer these situations are less relevant -for the investigation of cloud-aerosol interactions one would rather rely on multi-wavelength 15 lidar observations. Nevertheless, very high background conditions can also happen when the derivation of β p -profiles makes more sense, e.g. when the top of the planetary boundary layer and the lower boundary of the clouds are well separated. An example is shown in Fig. 1 when one of these changes occurs at 13:30 UTC. A conversion factor of η 1 = 0.385 is found here. It is important to emphasize, that this 20 change does not affect the ∆ in the data files, only a special service code is set. As a consequence, it is not sufficient to consider ∆ as the only criterion to determine the lidar constant; moreover, before the measurements are evaluated it is required to check whether or not changes of the service code took place. The conversion factors should be determined individually for each change of the detector settings. This is 25 in particular true, when B exceeds 0.5 more than once during a day. Though this is a tedious work there are no fundamental problems associated to this procedure; one has only to be sure that the aerosol distribution is stable for a sufficient time period. For 3408 Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | our ceilometer we perform the determination of different conversion factors, however, it is not of general interest to publish these factors here. At 01:00 UTC these changes are reset and a new optimum ∆ is selected. Depending on the previous ∆ a significant change of the system's sensitivity might be associated with this. This is obviously the case on 22 April 2010 as can be seen in Fig. 1. As 5 a consequence, from 01:00 UTC the lidar constant can be determined as described in the previous section.

Application
The potential of the calibration procedure to derive optical properties of aerosols is demonstrated for 22 April 2010. The result of normalizing the signals according to 10 Eq. (4) at 06:57 UTC, 08:28 UTC, 18:24 UTC and 19:27 UTC, and η 1 at 13:30 UTC is shown in Fig. 6. As in Fig. 1, the range corrected signal is plotted. It is clearly visible, that all "steps" due to the changes of the sensitivity disappear. Thus, the "forward" Klett inversion using the lidar constant C * L (according to Eq. 1) can be used to determine aerosol backscatter profiles β p (z) at 1064 nm with a quite high temporal resolution. If 15 we concentrate on the aerosol mixing layer, averages over two minutes are sufficient to retrieve "smooth" signals as will be shown later in more detail.
For illustrating quantitative retrievals of aerosol properties a series of β p -profiles (Fig. 7) and the diurnal cycle of τ p (Fig. 8)  it is below 2 % in the boundary layer or even smaller if the optical depth is very low at 1064 nm. Thus, the accuracy of β p is primarily determined by the error of the lidar constant.
To compare two independent data sets, we consider the aerosol optical depth τ p . It can directly be derived from Cimel data and from integration of the α p -profiles from 5 the ceilometer. To make τ p comparable we extrapolate the optical depth from the wavelength of the Cimel measurements (1020 nm) to the ceilometer's wavelength (1064 nm) assuming a λ −1 -dependence of α p . Note, that the α p -profiles from the ceilometer data are integrated up to 4 km only. Above 4 km the retrieval is too noisy for the integration, however, we do not expect a significant underestimate of τ p as there are no indications 10 of aerosol layers in the upper troposphere. Below z ovl the constant value α p (z ovl ) is assumed for the extinction coefficient. The diurnal cycle of 22 April 2010 is shown in Fig. 8. Sunrise and sunset are at 04:12 UTC and 18:14 UTC, respectively. From Fig. 8 two main conclusion can be drawn: first, the agreement between the two τ p -retrievals is very good though this day is 15 not among the 14 cases used for the absolute calibration. Thus, the mean lidar ratio of 43 sr is obviously a good estimate in this case. However, it should be emphasized that the uncertainty of τ p derived from the ceilometer is large. In contrast to the β p -profiles the uncertainty of the lidar ratio has a significant influence on α p and consequently on τ p . Assuming again an uncertainty of S p of ±10 sr (corresponding to 23 % relative 20 error) and taking into account the uncertainty of C L (4 %), the relative error of τ p is calculated as 27 % if ∆ = 140. In cases with different instrument settings the additional error of the (successive) application of η has to be considered resulting in an overall uncertainty of up to 30 %. For illustration the calculated errors of τ p for 04:00 UTC and 16:00 UTC are included in Fig. 8. The second conclusion is that the slight decrease of 25 the aerosol optical depth during the daylight period as derived from Cimel measurements cannot be confirmed by the ceilometer measurements as the uncertainty is too large. The uncertainty is significantly reduced if the integrated backscatter (not shown here) is used as a measure of the overall temporal development. Then, the ceilometer AMTD Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | retrievals demonstrate that the trend is not constant over the full day. The peak shortly after 02:00 UTC and the large optical depth before 03:00 UTC is certainly due to hygroscopic aerosols in an environment of high relative humidity in 1.6 km (see Fig. 6). This example underlines that the extrapolation of optical depths from daytime to nighttime can be misleading; the assumption of a constant aerosol optical depth as well as the 5 assumption of a constant change can be wrong. It is worthwhile to compare vertically integrated aerosol optical depth (τ p , Fig. 8) and the vertical aerosol distribution (β p , Fig. 7). It can be seen that the aerosol distribution is changing throughout the day: as already mentioned a strong aerosol layer exists (maximum at 1.6 km) in the early morning. In the course of the day, the height dependence of β p changes significantly: at 06:00 UTC, different clearly separated layers are present, from 10:00 UTC till 18:00 UTC the distribution is approximately height-independent, whereas at 22:00 UTC a strong increase of β p from z = 200 m to z = 900 m is observed. The top of the mixing layer changes by approximately 300 m during the daylight period. The temporal variability of β p is different in each altitude and the magnitude of 15 the changes is up to 50 % and more; in particular close to the surface the variability is large. This is in clear contrast to the slow change of the aerosol optical depth during the same time period. This suggests (not unexpectedly) that no general relationship exists between τ p and β p at a certain height, e.g. at the surface. Ceilometer measurements can help to mitigate this problem: with the provision of β p in the lowermost troposphere 20 and the good temporal resolution, it is possible to link atmospheric and ground based measurements more reliable than can be done with integrated properties.
An essential point of the benefit of aerosol remote sensing is the achievable temporal resolution of the profiles. This can be assessed individually by calculating the signalto-noise ratio of any specific measurement (e.g. Wu et al., 2006). From our data we 25 conclude that for nighttime measurements averages over two minutes are fully sufficient to monitor the evolution of the boundary layer and the residual layer by means of β p -profiles. To illustrate the daytime-capability of the ceilometer measurements, three different temporal resolutions of β p -profiles are shown in Fig. 9 (dashed lines) illustrate the uncertainty range due to the unknown S p and the error of C L . As an example, we again consider 22 April 2010 and select the β p -profile at 12:00 UTC, when the atmosphere above the boundary layer is apparently aerosol-free as suggested from Fig. 6. Averages over 30 s (i.e. the resolution of the raw data), two minutes and twenty minutes are shown for comparison. The signal-to-noise ratios are are resolved. For instance, the evolution of the pronounced aerosol layer between 3 km and 4 km can be clearly monitored, as its backscatter coefficient is as large as β p in the boundary layer. Though the retrieved profiles become more noisy, the existence and the extent of this optically thick elevated layer can be documented even after sunrise (04:16 UTC). The errors of β p are the same as described before and thus are omitted 20 in the figure.
Finally, we want to present an example of a quantitative analysis of ceilometer data covering a full month. We calculate the aerosol optical depth at 1064 nm on a daily basis for March 2011, applying a constant lidar ratio of S p = 43 sr for all cases. In Fig. 11  (including the extrapolation as described above) up to an altitude of typically 4 km or 5 km. The main criterion for the choice of the upper level is that elevated aerosol layers -if present -are included; then it is possible to compare τ p derived from ceilometer measurements with independent data sets. From Fig. 11 a large variability of τ p , from day to day but also from night to the subsequent day or vice versa is obvious.

5
For March 2011 we find a monthly mean optical depth at 1064 nm of 0.068 and 0.056 for daytime and nighttime, respectively. Assuming anÅngström exponent between 1 and 1.5 leads to an optical depth at 532 nm of 0.12 < τ p < 0.18 which is a plausible value for Munich. However, the error of τ p is in the order of 25-30 % as discussed before; for illustration it is sufficient to include one typical example (5 March 2011). This 10 large uncertainty makes it impossible to resolve the difference between successive daytime and nighttime optical depths. Only if we assume that the lidar ratio does not change from day to night the difference can be determined. Then, it is 0.024 on average but it can be as large as 0.08. Only in 6 out of 15 cases the difference is below 20 %.

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The assessment of the performance of ceilometers for aerosol remote sensing is urgently needed in view of the rapidly increasing number of such "simple backscatter lidars". As a consequence of the low laser pulse energy, calibration of the signals is challenging. In this paper we elaborate a method for the absolute calibration of the JenOptik ceilometer CHM15kx. The advantage of this approach is obvious: whereas 20 the calibration relies only on measurements under favorable conditions resulting in a high accuracy, the retrieval of profiles of β p is possible under virtually any meteorological condition -daytime and nighttime -with a temporal resolution of a few minutes. This offers a wide range of applications: it is possible to monitor profiles of the particle backscatter coefficient, to study correlations between integral quantities (integrated Introduction a network of ceilometers is available, the horizontal distribution of aerosols can be assessed. A very important advantage of our approach is that it can easily be automated to evaluate large data sets, e.g. to establish an aerosol climatology. The main drawback of ceilometer data is the low signal-to-noise ratio in the free troposphere compared to more powerful lidar systems. As a conclusion, elevated aerosol layers cannot be re-5 solved if their optical depth is very low or if the optical depth of the boundary layer is very large. The low signal-to-noise ratio does not, however, prevent the inversion of β p in the mixing layer, because the data evaluation starts -in contrast to the standard Klett retrieval -close to the surface ("forward integration"). In this altitude range, typical signal-to-noise ratios in the order of 100 or more are found, even if averages of not 10 more than two minutes are considered. The accuracy of the aerosol retrieval depends on the accuracy of the lidar constant of the ceilometer. According to our study, the relative error of (reference) lidar constant C * L is as low as 4 %. Additional small errors must be considered in case of the JenOptik CHM15kx because of the changing APD-settings. In summary, we find that 15 the relative errors of β p profiles are less than 8 %. Large errors are introduced when an estimate of the lidar ratio is required, e.g. for the retrieval of extinction coefficients. This is, however, an inherent problem of any system -ceilometer or lidar -that is based on the backscatter lidar technology. Note, that the lidar ratio at 1064 nm cannot be determined from Raman lidars, so that one has to rely on model calculations, on (rare) 20 comparisons with co-located and coincident sun photometer measurements, or independent measurements e.g. high spectral resolution lidar). As a consequence, optical properties that are related to the extinction coefficient must be treated with care. The same is true, if surface values are extrapolated from integral values, e.g. from aerosol optical depth or integrated backscatter.

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In case of the CHM15kx the determination of the lidar constant is a tedious work as the sensitivity of the system changes with the solar background. However, due to the very low overlap, data from the CHM15kx can provide a limited but very useful set of aerosol information. For systems with a "constant" lidar constant (e.g. JenOptik Introduction   Fig. 11. Aerosol optical depth at 1064 nm as derived from the inversion of the ceilometer data of March 2011, separately for nighttime (red dots) and daytime (black squares). As an example we include the uncertainty range of the nighttime measurement of 5 March 2011.