This work uses the commercially available elastic backscatter lidar Leosphere ALS 450. This lidar emits linearly polarized laser pulses with an energy of 16 mJ at a wavelength of 355 nm and a repetition rate of 20 Hz. The full-angle field of view of the receiver telescope and the laser beam divergence are 1.5 and 0.3 mrad, respectively.

The Nd:YAG laser of the ALS 450 is powered by a flash lamp. The flash lamp has a lifetime corresponding to 5×107 shots or 694 h or a month of continuous operation. In order to save flash lamp lifetime, the ALS 450 operated at Zürich and on the Jungfraujoch was coupled to a Vaisala Ceilometer CL31, which is a simple, low-maintenance elastic backscatter lidar (with a pulse energy about 3 orders of magnitude lower than the ALS 450). We use the ceilometer to detect thick clouds at low altitudes. Once thick clouds are present at an altitude lower than 1 km above the station, the lidar is automatically switched off (this is the case at roughly 30–40 % of the time), and it is automatically switched back on once the low-level clouds are gone. In Jülich, where no ceilometer was available, the ALS 450 was operated manually and switched off and on after visual inspection.

The range-corrected signal r2P(r) detected by the ALS 450 can be described with the lidar equation : r2P(r)=C×O(r)βm(r)+βp(r)exp⁡(-2∫r0rαm(r′)+αp(r′)dr′), where βm and βp describe the backscatter from molecules and particles and αm and αp specify molecular and particulate extinctions, i.e., light attenuation by scattering and absorption, and take changes of scatterer density with altitude into account. Instrumental properties are described by the constant C. O(r) is the overlap function which describes the overlap between the laser footprint and the telescope field of view. For the ALS 450 the complete overlap is achieved at a distance of 450 m from the lidar. As we analyze cirrus clouds that occurred entirely at greater heights above the lidar, we do not need to consider the overlap function.

The Leosphere ALS 450 measures the co- and cross-polarized components of the return signal. In order to solve Eq. () it is required to obtain the total signal from these two components. We calculate the total signal based on both channels as described by .

From the detected co- and cross-polarized signal components the depolarization ratio can be obtained . We assume an ideal lidar system, which means that there is no cross-talk between the co-polarized and the cross-polarized channels. has examined this for the lidar used in Jülich. He found that, for the parallel detector, every 2000th detected photon is actual perpendicular polarized and for the perpendicular detector about every 570 detected photon is parallel polarized. While this justifies our assumption of an ideal system for the Jülich lidar, we found considerable cross-talk in the Swiss lidar, depending on certain maintenance conditions. However, cross-talk influences in particular the perpendicular channel, which we use mainly for cloud detection but not for optical depth retrieval. Light that is scattered back by non-spherical particles changes its polarization state, whereas spherical particles do not change the state of polarization of the returned light. Therefore, the depolarization ratio provides information about the sphericity of the detected particles . The cross-polarized signal from aspherical ice particles in thin cirrus often provides the better contrast than the parallel signal, a property we will use in our cloud retrieval algorithm. The lidar is pointed to 5∘ off-zenith to avoid the effect of specular reflections of horizontally oriented ice crystal plates on the measured backscatter signal and depolarization ratio .

For our cloud detection scheme elaborated in Sect. , we use the backscatter ratio (BSR) defined as BSR=βp+βmβm. To solve the lidar equation (Eq. ) with four unknowns (βm, βp, αm, and αp) and only one measurement r2P(r), we need to make use of best current knowledge. The molecular quantities βm and αm are calculated from analysis data of the numerical weather prediction model (NWP) COSMO-2. We use pressure (p) and temperature (T) from COSMO-2 to calculate the molecular density of air and determine βm and αm using Rayleigh theory .

For the solution of Eq. () we use a lidar retrieval as described in . To ensure stable solutions, we use a far-end boundary condition . Further, we need to define the extinction-to-backscatter ratio (hereafter referred to as lidar ratio). We derive ϵ=0.234, the anisotropy of the molecules present in the atmosphere, from Eq. (6) in and Table 1 in for our lidar wavelength of 355 nm. The lidar ratio of the molecular part is evaluated as Lm=8π3×180+40ϵ180+7ϵ≈8.7, where σR, given by Eq. (6) of , is divided by the expression for σπC, provided in Eq. (4) of , as the receiver optical bandpass spectral width of 0.3 nm (< 24 cm-1 at 28 170 cm-1) suppresses the rotational Raman wing spectral contribution . Note that our ϵ is called RA by . The particulate lidar ratio is defined as Lp=αpβp. Several studies have been performed to measure the particulate lidar ratio of cirrus clouds e.g.,. It can be obtained directly from Raman lidars that allow for an independent measurement of particle extinction and backscatter coefficients as well as from high-spectral-resolution lidar (HSRL) measurements e.g., . In our retrieval we determine the lidar ratio such that BSR = 1 above and below the cirrus cloud (e.g., ).

The lidar equation (Eq. ) assumes single scattering of the emitted light in the direction 180∘ to the emitted direction only. In reality, this is not strictly the case. As seen in Fig. 1 in , cloud particles produce strong forward scattering. This causes some of the scattered photons to remain within the field of view of the lidar, where they can be scattered back to the lidar receiver during a subsequent scattering process. These additional backscattered photons cause an underestimation of the particle extinction. The strength of multiple scattering depends mainly on the laser divergence, the telescope field of view, and the effective radius of the scattering particles . In order to provide extinction values that are comparable to other lidar systems and cloud conditions, the measured apparent, multiple-scattering, affected extinction coefficient αpobs needs to be corrected with the correction factor γ to obtain single-scattering related values αpsingle, such that αpsingle=αpobsγ. We use the multiple-scattering model by as described by and to derive γ. The effective radius of the cirrus particles is taken from a climatology provided by . For particles much larger than the detection wavelength, as is the case for ice crystals observed with lidar, about 50 % of the scattering occurs into the forward direction. In this study we find an average value for γ of 0.56 for Jungfraujoch and 0.52 (0.54) for Zürich (Jülich).

The lidar retrieval poses several uncertainties. Using NWP data to calculate the molecular properties results in a maximal error of 2 %. However, there are uncertainties pertained to the data themselves. The lidar detector counts photons, and we calculate the counting error by means of poisson statistics. The assumed lidar ratio is also an error source. Here, we use lidar ratios that deviate ±5 sr from the determined lidar ratios to assess for the uncertainty caused by determining a lidar ratio. To assess the total maximum uncertainty, we combine the individual contributions to provide an upper bound of the uncertainty. We calculate the largest possible error, which usually is larger than the error calculated by a Gaussian error (square root of the sum of the squares of the individual contributions). estimated the error in the multiple-scattering correction on the order of 10 %. The signal-to-noise ratio (SNR) is determined by the variation within the 5 min average profiles. As the Leosphere lidar does not allow to retrieve the photon counts directly from the data, we calculate the SNR from the original lidar profiles as SNR=N⋅meanr2P(r)SDr2P(r), where meanr2P(r) is the mean range-corrected signal and SDr2P(r) is the standard deviation of the originally retrieved lidar profiles over N=600 shots (following a suggestion by P. Royer, Leosphere, personal communication, 11 August 2014).

For an efficient evaluation of this extensive data set, the automated data evaluation algorithm FLICA was developed. The algorithm is based on a classical lidar retrieval e.g., combined with a cloud detection scheme. FLICA analyzes profiles over 5 min (i.e., averages over 5 min × 60 s mins-1 × 20 shots s-1 = 6000 shots). This time range was chosen to be short enough to ensure that all clouds could be detected by the algorithm while also long enough to provide profiles smooth enough for the lidar retrieval to function. The 5 min profiles of the lidar measurements are further smoothed using a moving average boxcar filter in the vertical coordinate over 150 m and 5 profiles in time to reduce the noise level and hence simplify the automatic evaluation by FLICA.

The output of the cloud detection scheme has been visually inspected for individual days and was found not to show any apparent artifacts. There is a trade-off between detecting cloud structures small enough and avoiding misclassifying noise as a cloud, especially for daytime measurements. The combination of the criteria below represents a rather conservative approach, which might result in missing some particularly small/thin clouds. The conservative approach ensures that no noise is misclassified as a cirrus cloud. An example of the resulting cloud detection can be seen in Fig. .

The FLICA algorithm contains the following steps. i.

Cloud top detection. The cloud top is needed as an upper boundary for the subsequent lidar retrieval. Our cloud top detection averages individual lidar profiles so that the resolution of one pixel is 5 min in time and 30 m in altitude. Areas of 3×3 pixels are examined, with the pixel to be checked for cloudiness in the center. At least eight of the nine examined pixels have to have a volume depolarization larger than 0.007(0.006) for day(night)-time measurements. At least eight of nine pixels also have to have larger co- and cross-polarized raw signals than empirical thresholds.

Here we present the retrieved lidar cirrus climatology. First, a description of the different measurement sites shown in Fig.  is provided. Subsequently, we present the climatology of the cirrus cloud properties. The section ends with a comparison of our data with previous midlatitude climatology studies.

Following Sect.  we present the climatological evaluation of more than 13 000 h of lidar measurements within the period 2010–2014 from the three midlatitude measurement sites. The main information on the measurement statistics for the three sites is compiled in Table . More measurements are available from Jungfraujoch and Zürich than from Jülich. For Jungfraujoch, most of the data were retrieved in the spring, whereas during the summer only very limited data are available. In Zürich, in contrast, a large number of the measurements took place during the summer, while the other seasons show similar coverage. The Jülich lidar was running predominantly during spring and summer, while the autumn and winter data are sparse. The amount of data has to be considered when judging seasonal variability. The retrieved cirrus properties listed in Table  indicate a temporal cirrus cloud coverage between 9 and 15 % for all stations, agreeing well with the CALIPSO measurements discussed by and being slightly smaller than the 18–19 % measured during the ECLIPS campaign by .

The seasonal dependence of the observed cirrus coverage is displayed in Fig. . The most striking feature is the difference between the wintertime measurements in Zürich and Jungfraujoch, showing a cirrus coverage of around 12 %, while in Jülich this is about 33 %. This is in qualitative agreement with geographical maps of high cloud amount (cloud pressure smaller than 440 hPa) for January observed by the TIROS-N Operational Vertical Sounder (TOVS) averaged over 8 years, 1987–1995 (http://ara.abct.lmd.polytechnique.fr/index.php?page=clouds). For January, these data suggest decreasing amounts of high clouds when the air passes from the North Sea towards the Alps. Also, a time series of 40 years of measurements of turbidity in Jülich confirms the high cloud coverage during wintertime (A. Knaps, personal communication, Forschungszentrum Jülich, 2014). However, there are large uncertainties in this part of our climatology, as the number of hours of measurements with the Leosphere ALS 450 available for the Jülich winter is small (Table ), the specific winter might have had a particularly high cirrus cloud coverage, and the applied manual operation of the lidar might add bias. Another remarkable feature is the autumn maximum in cirrus coverage observed above Jungfraujoch. This feature is also in qualitative agreement with the seasonal cycle suggested by the TOVS data set; interannual variability might again be important but cannot be derived from our measurements.

The first property of interest is the distribution of the optical depths of the detected cirrus clouds, which we classify according to (cf. Table ): clouds with an optical depth τ<0.03 are not visible to the naked eye and hence termed subvisible. Cirrus clouds with an optical depth τ in the range 0.03≤τ<0.3 are termed thin, while clouds with τ≥0.3 are referred to as opaque. The upper limit of detection for our lidars is τ≈3; as for larger optical depths, the light is almost fully extinguished within the cloud. Under these conditions no molecular signal from above the cloud can be detected , as would be required for an inversion. Therefore, we are not able to specify the optical thickness of the thickest cirrus clouds. classified clouds with tops above 440 hPa (≈ 6500 m) and optical depths larger than 3.6 as cirrostratus. These cirrus clouds may have a negative cloud radiative effect but cannot be considered here because of the detection limits of our lidar instrument.

Figure b shows the optical depth of the retrieved cirrus clouds for different seasons. The grey dashed lines indicate the categories defined by . The optical depth averaged over the whole data sets for each measurement site is displayed in Fig. a. These τ values agree well with the ECLIPS campaign , where most detected cirrus clouds had optical depths smaller than 0.1. A Wilcoxon Rank sum test reveals that the optical depth distributions of the different sites are significantly different from each other. The occurrence frequency of subvisible cirrus clouds is larger for Jungfraujoch than for the other two sites. Two reasons may be responsible for the observed differences. First, Jungfraujoch is located in the central Alps, where orography-driven lifting of air masses leads frequently to mountain-wave (lenticularis) cirrus. These clouds are thicker than large-scale cirrus clouds but thinner than the cirrus formed as outflow of anvils or in warm conveyor belts. The second reason is the enhanced detectability of optically thin clouds at Jungfraujoch as a result of improved SNR (see Eq. ). The alpine site is located at an altitude of 3500 m a.s.l., 3000 m above Zürich and 3400 m above Jülich. According to Eq.  the received signal depends on the inverse of the squared range between lidar and target. In addition, the Jungfraujoch is frequently above the boundary layer. Therefore, measurements from Jungfraujoch avoid strong beam extinction due to boundary layer aerosols.

Figure  provides vertical profiles of the cloud-mean SNR of the three stations, where the noise is obtained from Eq. (). From the profiles it can be seen that the SNR of Jungfraujoch extends to greater heights by about 3 km. This suggests that the increased detection rate of thin and subvisible cirrus clouds is a result of the increased SNR. Furthermore, the SNR at Jungfraujoch increases at heights above 13 km a.s.l. This suggests that the morphology of the clouds at these heights differs from the morphology of the highest clouds observed at Jülich and Zürich. The backscattering efficiency appears to be enhanced in these clouds, possibly because a large amount of small crystals formed in the observed cirrus clouds, when many ice crystals nucleated in the high supersaturations in rapid uplifts as they occur in lee waves above mountainous terrain .

The number of detected subvisible cirrus as function of optical depth and cloud top altitude is depicted in Fig. . As expected, Jungfraujoch displays a larger fraction of subvisible cirrus as well as higher cirrus cloud tops. Therefore, we have evidence for both a.

the advantage of location of the higher Jungfraujoch as evidenced by the ability to measure thinner subvisible clouds (by about a factor 5) and

To quantify the net radiative effect, CRFNET, for the cirrus clouds observed here we use the radiation model of , which is a simplified model based on the more sophisticated Fu–Liou radiative model . The accuracy of is better than 20 % in comparison with the Fu–Liou model. The cloud radiative forcing due to shortwave radiation, CRFSW, is dependent on the surface albedo, the solar zenith angle, as well as the cirrus cloud optical depth τ (see Eq. 13 of , for details). The longwave cloud radiative forcing, CRFLW, is mainly determined by the temperature difference between the Earth's surface and the cirrus cloud top temperature and by the cloud optical depth τ (see Eq. 6 of , for details). The CRFLW further correlates well with the brightness temperature of the atmosphere, which is related to the outgoing longwave radiation at top of atmosphere . This correlation has not been considered in the model of . CRFNET is calculated as a superposition of these two effects (i.e., CRFNET = CRFSW + CRFLW). The following parameters are needed as input for the calculation of the radiative effect:

solar constant S

We compare our computational results to satellite data, which have been averaged zonally at 50∘ N or globally and combined with a radiative transfer model . The results of this comparison are listed in Table  together with maximum possible uncertainty ranges (see last paragraph of Sect. ). The “overcast values” (i.e., taking only cloudy values into account) consider the radiative effect under conditions with cirrus clouds, while the “all-sky values” also include conditions without cirrus by considering the cirrus occurrence frequency.

While the cirrus cloud coverage at 50∘ N from the satellite-based climatology International Satellite Cloud Climatology Project (ISCCP) is similar to our observations, the ISCCP category of cirrus clouds show 1.5–3 times larger CRFLW and 1 order of magnitude larger CRFSW. The difference in the CRFSW can only be explained in terms of a much larger optical depth τ of the clouds observed by the satellites. The CRFSW is mostly linearly dependent on the optical depth τ, whereas the CRFLW depends linear on the temperature difference between ground and cloud as well as τ see. Clouds with an increased optical depth are mostly found at lower altitudes, where the air is more humid. Thus the temperature difference is smaller, which results in a smaller increase of the CRFLW compared to the CRFSW. Thus, warmer clouds with increased optical depth have larger negative CRFNET. This explains the difference between the CRFSW and CRFLW in , where more clouds with larger optical depth are included.

The reason for these (at first sight surprising) differences is the different definitions of “cirrus”. First, FLICA detects only clouds with lower cloud edge colder than -38 ∘C, which is typically above 7–8 km. instead used a pressure threshold of 440 hPa to separate clouds, which corresponds to an altitude of 6.3 km (standard atmosphere). The clouds in the range 6.3–7.5 km are missing in our study. Cirrostratus clouds with τ<3.6 occur particularly in this altitude range. Second, although our criteria allow for thick clouds up to τ=3.6 at altitudes clearly above lower edge, they cut clouds once their lower edge gets warmer than -38 ∘C, which is more likely for thicker clouds (see rounded edge in the red boxes in Fig. 6). Third, while we count vertically distinct cirrus layers as separate clouds, the geostationary ISCCP weather satellites add the signal of vertically staggered layers, which increases τ. Furthermore, it should be noted that satellite data reveal discrepancies amongst themselves (ISCCP, MISR, MODIS) with differences of 20–30 % in coverage of cirrus with τ<3.6 . Finally, the distribution of thicker cirrus with τ>0.3 is zonally inhomogeneous, with clouds preferentially occurring at the continental east coasts.

In our study, we want to address only cirrus clouds and not mixed-phase clouds. Therefore, we have chosen a conservative limit towards lower, thicker clouds. Also, a temperature-based selection criterion is a better for separating different cloud types than a pressure-based criterion because temperature is the main microphysical parameter for cloud formation. As ISCCP is based on the analysis of weather satellite images, clouds still must have optical depths τ≥0.2 in order to be reliably detected by such satellites . Large uncertainties can also be traced to different approaches to partly cloudy pixels, which are 30 km × 30 km for ISCCP and are treated as homogeneous, i.e., either cloud free or filled with a thinned homogeneous cloud .

The overcast and all-sky CRFNET are significantly higher in Jülich than at Jungfraujoch, which is also clearly reflected in overcast and all-sky optical depths found in the ISCCP data . This may be related to the frequent low-pressure systems and fronts rolling in from the northwest across the North Sea. The related cirrus clouds weaken with distance from the coast.

The effect of the optically thicker clouds above Jülich compared to the Jungfraujoch is also evident in Fig. . The magenta lines indicate positive (i.e., warming) cirrus cloud radiative forcing (in W m-2) as a function of altitude and optical depth calculated by the model of with mean temperature profiles from COSMO-2 (Jungfraujoch and Zürich) and COSMO-7 (Jülich) during the time period of our measurements. The blue isolines indicate negative (i.e., cooling) cirrus radiative forcing. A zero net effect, CRFNET=0, is indicated by a cyan line. The occurrence frequency of the cirrus clouds measured at the different sites is color-coded. The occurrence frequency is categorized by 40 logarithmically spaced bins in optical depth between 10-4 and 10 and 500 m bins in cloud top altitude. From Fig.  we clearly see that the cirrus clouds observed in this study have all a positive (warming) CRFNET. It is important to note that with the FLICA algorithm we do not find cirrostratus or cumulonimbus outflow clouds, i.e., no clouds with τ>3.6. Of course, such clouds do exist also above our measurement sites. However, such clouds always have lower edges warmer than -38 ∘C and thus are not considered.

The pattern of cirrus cloud occurrence is quite similar above Jungfraujoch and Zürich, although the Jungfraujoch cirrus clouds show a slightly broader distribution in optical depths. Most cirrus layers are present at 11 km a.s.l. with optical depths between 0.01(0.04) and 0.2(0.4) above Jungfraujoch (in Zürich). Cirrus clouds above Jülich are frequent at altitudes between 8 and 12 km a.s.l. with optical depths ranging from 0.02 to 0.7. This wider distribution of high occurrence frequencies in altitude is likely related to the high frequency of frontal systems crossing Jülich. The lower CRFNET above Jungfraujoch is visible in the shift towards thinner clouds at Jungfraujoch as compared to the other two measurement sites. Due to the lower SNR over Zürich and Jülich at cirrus altitude, these two sites underestimate the amount of subvisible cirrus clouds as compared to Jungfraujoch.

Besides , other studies indicate also a general net warming effect of cirrus clouds in the midlatitudes. investigated the overall cloud radiative forcing based on a 24-year data set from the ISCCP. For cases with frequent occurrence of high clouds, a positive net cloud radiative forcing (warming) was obtained, whereas it was negative (cooling) for cases with frequent occurrence of low-level clouds. This confirms our results in which cirrus clouds create a positive net radiative forcing. A case study of found a cirrus cloud radiative forcing of 13.2 W m-2 at the Fukue observatory (32∘ N, Japan) by a combination of MODIS satellite and ground-based observations. This value is similar to what we found for Zürich and Jülich and obviously larger than the respective value reported by . Another study of found a radiative forcing of cirrus of 36.5 W m-2 over China using also CALIOP and MODIS satellite data. The authors ascribe the high value to cirrus observations above the Tibetan plateau where very thick cirrus clouds with a mean optical depth of 1 are observed frequently. For the other parts of China lower values of 20 W m-2 are found. The radiative forcing of the lateral boundary of cirrus clouds observed with CALIOP is investigated by . The radiative effect of observed cirrus cloud edges is discussed. In the transition region of large cirrus, defined as their optically thin rim (τ<0.3), which is often missed by satellite passive optical sensors such as MODIS, the CRFLW found to be still substantial (∼ 10 W m-2). This value is similar to our mean overcast radiative forcing of Zürich and Jülich and also demonstrates the sensitivity of cirrus cloud inhomogeneity on cloud forcing as found by . However, all these studies investigate single cases or different regions compared to our study. There is no study which investigates the cirrus radiative forcing over Europe.

In a study of , cirrus cloud observations over 2 years from the CALIPSO satellite lidar CALIOP are compared to four ground-based lidar stations (two sites in the USA and two in France) for their consistency of macrophysical and optical properties. They found larger discrepancies in the frequency distributions of cloud base, top, and thickness. They point out that the significant part of the deviations can be attributed to different sampling (seasonal, irregular sampling of ground-based stations, opaque low-level clouds). However, they found that for high cirrus clouds the optical depth distribution τ>0.1 from ground stations and CALIOP is consistent within 10 % using the same retrieval method. This shows that our optical depth distribution of all three stations is most likely not or only less affected by sampling issues of ground-based lidar compared to satellite measurements.

Subvisible cirrus clouds generally are not considered in numerical weather prediction models as their optical depths are considered to be too small. The overcast CRFNET, divided into the categories defined by , is shown in Fig. . We see that the subvisible cirrus clouds indeed have an effect on the CRFNET. On average they contribute about 4 % of the total CRFNET of cirrus clouds at Jungfraujoch and in Zürich and 3 % in Jülich. The maximal effect of 6 % is reached in Zürich during spring. As seen in Fig. , the thin and opaque cirrus clouds are the main contributors to CRFNET of cirrus clouds above each of the three stations, both by roughly equal shares (with a small dominance of opaque clouds).

Jungfraujoch displays the lowest CRFNET values throughout the whole year. This pattern is also seen in the optical depths shown in Fig. a. Generally, thinner clouds are detected above Jungfraujoch than at the other two sites. This influences the CRFNET: as more subvisible cirrus are observed at Jungfraujoch (cf. Table ) and their contribution to CRFNET is smaller than the contribution by thin and opaque cirrus, this leads to a smaller CRFNET on Jungfraujoch. Summing up the percentages listed in Table , Jungfraujoch shows a fraction of 57 % thin and opaque cirrus while Zürich and Jülich show occurrence frequencies of 65 and 68 % thin and opaque clouds, respectively. These different sums result in the CRFs listed in Table 3 (taking note of the fact that the thresholds for the cirrus cloud categories () are on a logarithmic scale).