Satellite data from SEVIRI is used, which provides 12 spectral channels covering the visible, the near infrared, and the infrared spectrum. The channels used here have a nadir resolution of 3 km × 3 km, which decreases towards the poles and is about 4 km × 6 km over our region of interest (central Europe). In this study we use the 5 min temporal resolution data from the Rapid Scanning Service (RSS). The SEVIRI radiances in the different channels are used as input for the Nowcasting Satellite Application Facility (NWC SAF) algorithm which provides a cloud mask, cloud top height (CTH), and cloud classification. To obtain the cloud mask, different multispectral tests using SEVIRI channels are applied in order to discriminate cloudy from cloud-free pixels. The cloud top height for low, liquid clouds is obtained by using a best fit between measured brightness temperatures in the 10.8 µm channel and simulated values using the RTTOV radiative transfer model applied to atmospheric profiles from the ECMWF (European Centre for Medium-Range Weather Forecasts) numerical weather prediction (NWP) model.

The NWC SAF cloud mask is used in order to derive cloud phase, cloud optical depth, and effective radius with the KNMI (Royal Netherlands Meteorological Institute) cloud physical properties (CPP) algorithm , developed in the context of the satellite application facility on climate monitoring CM SAF, . Using a channel in the visible spectrum (0.6 µm) together with an absorbing channel in the near infrared (1.6 µm) , the CPP algorithm retrieves τ as well as re representative for the uppermost cloud part. As this method relies on solar reflectance channels, it is applied only during daytime.

Also data from MODIS is used within this study. MODIS is an imaging spectrometer onboard the satellites Terra (descending node) and Aqua (ascending node) which probe the Earth's atmosphere from a polar orbit that results in one daytime overpass per satellite per day over the region of interest. MODIS measures in 36 bands in the visible, near-infrared, and infrared spectrum, with some bands having a spatial resolution of up to 250 m. The cloud physical properties are retrieved in a similar manner as for SEVIRI, but at 1 km spatial resolution using the channels 0.6 µm (band 1, over land) and 2.1 µm (band 7, over land and sea). In addition, re retrievals are available using the channels at 1.6 µm (band 6) and 3.7 µm (band 20) together with band 1. Note that band 6 on the Aqua satellite suffers from a stripe-problem . In this study MODIS collection 6 is used for the retrieved τ and re.

The ground-based remote sensing instruments of the Leipzig Aerosol and Cloud Remote Observations System (LACROS) comprise a 35-GHz MIRA-35 cloud radar, a HATPRO (Humidity And Temperature Profiler) microwave radiometer, and a CHM15X ceilometer, which are used also for field campaigns. All instruments are operated in a vertically pointing mode. The raw measurements are processed with the Cloudnet algorithm package . The output data is available at a unified temporal resolution of 30 s and a vertical grid of 30 m. Cloudnet uses further information such as temperature and pressure profiles from a NWP model (here: COSMO-DE). In this study we use the attenuation-corrected radar reflectivity Z from the cloud radar, QL obtained from the microwave radiometer, as well as the cloud base and top height retrieved from ceilometer and cloud radar, respectively. The vertical Doppler velocity from the cloud radar is also utilized. Furthermore Cloudnet provides a target classification applying a series of tests to discriminate cloud phase, drizzle or rain, and aerosols or insects.

For this study, we use a 2-year period covering 2012 and 2013. We focus on ideal cases to gain a better understanding of the microphysical processes within the cloud. In order to avoid uncertainties caused by inhomogeneous cloud scenes, such as multi-layer clouds, we consider single-layer cloud systems which are entirely liquid and non-drizzling as ideal.

Cloud profiles as observed from the ground are filtered according to the following conditions.

There is no occurrence of drizzle/rain in Cloudnet's target classification (and no drizzle/rain in the two nearest neighbour profiles allowed.)

The comparison of optical and microphysical properties between ground-based and MODIS and SEVIRI is only applicable under daytime conditions. Thereby, we have to consider the different spatial and temporal resolution, as well as the different viewing zenith angle on the cloudy scene. For SEVIRI a parallax shift occurs at higher latitudes. The satellite viewing zenith angle for Leipzig is 58.8∘. Within this study the average cloud top height is between 1 and 3 km (see Table ). This would result in a horizontal displacement of max. 5 km. did find a significant difference only for inhomogeneous clouds considering parallax correction. Also taking into account the spatial resolution of SEVIRI over central Europe of 4 km × 6 km, we decided to neglect the parallax correction for our study, instead we consider surrounding pixels. For SEVIRI a field of 3 × 3 pixels (case studies), and 5 × 5 pixels (longer-term statistics) centred on the ground site is used and spatially averaged.

We will furthermore present four hand-selected cases to highlight specific problems more closely. For the four case days, we calculate the spatial inhomogeneity parameter following , using the 3 × 3 SEVIRI pixel field, which can be interpreted also in terms of temporal inhomogeneity (χ) if advection of clouds over a fixed location is considered: χ=exp⁡(ln⁡τ‾)τ‾.

A short overview of the case characteristics is given in Table . The cloud boundaries are shown along with the Z profile in Fig. . The synoptic conditions for the cases are as follows. A high pressure system dominates the synoptic weather pattern on 21 October 2011 (Fig. a). The temperature at the 850 hPa pressure level over Leipzig is around 5 ∘C. Therefore the stratocumulus cloud layer that is observed between 10:30 and 13:00 Z consists entirely of water droplets. Its geometrical depth increases in the beginning of the observation period. The weather pattern on 21 April 2013 (Fig. b) is quite similar with the high pressure influence being stronger. The temperatures at the 850 hPa pressure level are slightly positive. During the whole observation period at Krauthausen a closed cloud deck is visible. The ground-obtained cloud top height shows only small variability, while the ceilometer-derived cloud base is more inhomogeneous during the beginning of the observation period. A thin overlying cirrus cloud deck can be observed around 10:00 Z and between 11:00–12:00 Z. An upper-level ridge covers central Europe on 1 June 2012 (Fig. c), but the area around Leipzig is also influenced by a surface low. Temperatures at 850 hPa lie around 10 ∘C. The stratocumulus cloud deck with the cloud tops slightly below 2000 m between 12:00 and 14:00 Z is broken. The weather pattern for the 27 September 2012 (Fig. d) shows Leipzig directly in front of a well pronounced trough. Temperatures at 850 hPa lie again around 10 ∘C and the cloud types vary between stratocumulus and shallow cumulus. The cloud base height increases throughout the day.

The ground-based fad is calculated using QL from the microwave radiometer, H as the difference of cloud top height from the cloud radar and cloud base height from the ceilometer, and Γad(Tcbh,pcbh) using NWP data in Eq. ().

suggests a range of typical values of [0.3, 0.9]. We omitted adiabatic factors with fad>1.0 since those are most likely affected by the measurement uncertainties, since the occurrence of “superadiabatic” cloud profiles in nature is physically implausible. Such artefacts especially arise due to uncertainties in QL and H for thin clouds. In contrast to the original Cloudnet code, our calculation of fad allows for values greater than 1.0. Within Cloudnet “superadiabatic” profiles are avoided by increasing the cloud top height if the integrated adiabatic qL is smaller than QL measured by the microwave radiometer.

An example time series for one case (21 April 2013) is shown in Fig.  (see the Supplement for more cases). For this case we find values of fad between 0.2 and 0.6 before 09:00 UTC. Measurements of Z (Fig. b) reveal that the cloud base is more inhomogeneous during this time period than later on. After 09:00 UTC, fad varies between 0.5 and 1.0.

From Fig. a we find a mean of fad=0.63 and the interquartile range (IQR) as [0.46, 0.81] for the entire data set covering 2012 and 2013. This corresponds well with the typical value of 0.6 given by . Overall, there is a large spread of values covering the full physical meaningful range from 0 to 1 (mean values for individual cases as presented in Fig.  are listed in Table ). fad not only changes from case to case, but also varies with time for individual days, reflecting the natural variability of entrainment processes. The variability of fad is larger for the inhomogeneous cases than for the homogeneous ones (Table ), but the range of values is similar. This shows that independent from temporal cloud homogeneity the majority of clouds seems to be sub-adiabatic. Therefore considering a constant fad like in previous studies (Table ) could affect retrievals of cloud properties.

When looking for proxies for fad, we find a tendency that geometrically thicker clouds are less adiabatic (Fig. b). Already found a decrease in fad with height. It also supports the findings of , who observed the tendency that thicker clouds are less adiabatic in the Southeast Pacific. Mainly the thin clouds (H<400 m) result in fad>1, as also found by , and therefore the investigation of such thin clouds remains challenging.

used observations of two cases with temporally homogeneous stratocumulus clouds over Leipzig, Germany, and found that in case of updrafts in clouds, the qL profile tends to be more adiabatic. To investigate if such a behaviour also occurs for our cases we apply the cloud radar Doppler velocity at the cloud base. The average vertical velocity at cloud base for all samples in 2012 and 2013 is found to be -0.1 m s-1 with the majority of points (93 %) in the range [-1, 1] m s-1. Considering the vertical velocity as function of fad (Fig. c) we find a large spread, which makes it difficult to detect a distinct influence of updraft speed on cloud adiabaticity. However, the notch around the median in the box–whisker plot does not overlap for updraft and downdraft regimes. According to the median can be judged to differ significantly on the 95 % confidence interval if there is no overlay in the notches. We further calculate the median fad for updraft and downdraft regimes for the four selected cases, and find for three out of four cases that clouds are slightly more adiabatic in the updraft regime (Table ). This behaviour is expected from adiabaticity and also supported by the findings of . They report that this effect is strongest at the cloud base and blurs when the data points are averaged over the whole cloud profile.

From ground-based observations we can show that fad is highly variable even for one location. Therefore we can also expect strong variability for cloud regimes over different regions observed by satellite (e.g. maritime vs. continental). To obtain ACI key quantities from passive satellite observations, fad is required over a larger domain. The German weather service (DWD) operates a ceilometer network which can be used to obtain the cloud base height (CBH). The question remains if QL and CTH from SEVIRI are accurate enough to allow for an estimate of the adiabatic factor using Eq. (). To address this question, we contrast QL and CTH obtained from SEVIRI with LACROS.

We investigate liquid clouds in a 2-year period covering 2012 and 2013. Since the estimate of fad from passive satellite observations is expected to be applied over a larger domain, it should be independent from ground-based information. Therefore the sampling is now done in terms of satellite observed quantities. An area of 5 × 5 pixels (total of 25 pixels) centred at the location of LACROS is considered for each available SEVIRI observation. For this pixel field we obtain average, standard deviation of CTH and the liquid cloud fraction. The liquid fraction is determined by the cloud type classification for each pixel from CPP. We require 90 % of the pixel field (23 out of 25 pixels) to be classified as pure liquid clouds. As additional constraint, the standard deviation of CTH for the 25 pixels has to be smaller than 400 m. For LACROS we use the observation averaged using a window of 10 min around the SEVIRI observation time. No requirements regarding the cloud phase are made for LACROS.

We first look at the CTH, which can be compared at daytime and night-time. The ground-based instruments give the actual geometrical CTH while from passive satellites a radiative CTH is obtained. Ignoring this physical difference we can see that the SEVIRI CTH is positively biased (Fig. a). reports a very similar overestimation (320 m) with a large standard deviation of 1030 m for low, opaque clouds. Considering the central pixel of the field does not change the result significantly, showing that the cloud fields are rather homogeneous and should therefore be suitable for such a comparison. The observed bias is not explained by the limited vertical step size of 200 m in the SEVIRI CTH product. A likely explanation of this bias is found in the representation of inversions. Splitting the sample by model inversions did not provide significantly better results, but the actual inversions might not be well represented by the model. Such a case can be seen for 27 October 2011. There, the CTH is roughly 1000 m lower than for the other three cases presented here, but the retrieved satellite CTH lies at 2000 m. Considering the closest radiosounding of Lindenberg (Germany), we find two inversion layers on top of each other between 900 and 3000 m, which results in ambiguities in finding the correct cloud height. Differences may also result from semitransparent cirrus cloud layers (21 April 2013), or broken cloud conditions (1 June and 27 September 2012).

For the comparison of QL we impose the condition that the values are between 20 and 400 g m-2. The comparison can only be applied during daytime. Both requirements reduce the number of samples by 56 % compared to the CTH sample. The difference of QL has a distribution with a distinct peak close to zero (Fig. c). There is a small negative bias of -21 g m-2, which is within the uncertainty range of the ground-based measurements, not even considering the uncertainty of the satellite-based estimate. Similar to the CTH comparison we see that the distribution of the central pixel is not significantly different from the field average, although the spread is larger. The distribution and the standard deviation are consistent with the observations in the validation study of for the Cloudnet stations of Chilbolton and Palaiseau. Similar to their study we see a slight negative skewness, which stems from larger QL values seen from the ground-based microwave radiometer. also reported that accuracy is reduced for higher QL values. Further possible explanations for differences in QL observed from ground and SEVIRI can be found in remaining cloud inhomogeneities and sampling differences. Generally, unfavourable viewing angles that occur especially in winter conditions can lead to large uncertainties in the satellite retrieval. In our sample the majority of the cases occur in summer months (April to September, 80 %). Looking at specific case days, we find the mean difference of QL for two homogeneous cases between SEVIRI and the ground-based microwave radiometer in reasonable agreement (8 g m-2 (10 %) for 21 April 2013, 25 g m-2 (32 %) for 27 October 2011), while there are larger differences for two inhomogeneous cases (50 g m-2 (87 %) for 1 June 2012 and 33 g m-2 (80 %) for 27 September 2012).

A similar study by found a standard deviation of 369 m between satellite-based adiabatic CBH and ceilometer CBH. They applied CTH and QL from AVHRR (Advanced Very High Resolution Radiometer) and assumed adiabatic clouds to compare the spatially and temporally averaged satellite product. The same comparison between SEVIRI and radiosonde observations resulted in a standard deviation of ±290 m . They suggest that this method can be applied for convective clouds in their early growth stage, which are located near the condensation level. Their sample is focused on relatively thin water clouds (∼ 250 m), which are more likely close to adiabaticity according to our Fig. b. As we will discuss in the following the adiabatic factor for such thin clouds is very sensitive to errors in H, so that an instantaneous retrieval of fad is not feasible.

To investigate the uncertainties that influence the calculation of fad, we consider an adiabatic cloud (fad=1) with QL=100 g m-2 and H=324 m and Γad=1.9 × 10-3 g m-4. The QL retrieval uncertainty (microwave radiometer instrument error + retrieval error) is approximately 25 g m-2 and the vertical resolution of the ceilometer and the cloud radar results in at least ±60 m uncertainty of H. Accounting for the maximum uncertainty (QL=125 g m-2, and Hobsground=264 m) or (QL=75 g m-2 and Hobsground=384 m), the resulting fad would be 1.89 or 0.54, respectively. This shows that with the current uncertainty limits of the ground-based observations fad is still prone to large uncertainties especially for geometrically thin clouds.

If we consider the root mean square differences (RMSD) of the comparison of ground and satellite-based values with ΔQL=67 g m-2 and ΔCTH = 1174 m, we can clearly see that especially the observed bias in CTH can result in large uncertainties of an instantaneous estimate of fad especially for thin clouds. For the adiabatic cloud considered above, this RMSDs result in a relative uncertainty for the adiabatic factor of 727 %, neglecting uncertainties at the CBH. Even considering a cloud that is twice as thick, the relative uncertainty is still 362 %. This shows that subsampling the SEVIRI observations to homogeneous, liquid clouds does still show differences when compared to a ground-based reference that are too large to estimate fad with sufficient reliability, mainly due to uncertainties in the CTH product. With this approach using QL and H we cannot determine the adiabaticity of clouds with a reasonable accuracy. Therefore we will have a look at the microphysical quantities.

Contrasting SEVIRI H (Eq. , using fad from ground-based observations) with the LACROS H, we are able to investigate the same quantity obtained with two independent physical retrieval approaches.

The correlation coefficient is 0.89 for 21 April 2013, 0.70 for 27 October 2011, 0.38 for 1 June 2012, and 0.45 for 27 September 2012 and increases by 10, 39, 118, and 71 % for 30 min temporal averaging, respectively (see Table ). The improvement of correlation is not surprising when comparing averaged data, e.g.. However, a longer averaging period removes the original variability of the data. The correlation for temporally averaged data is within the range of values that were obtained by , and . found correlations of 0.71 between SEVIRI and Cloudnet for a homogeneous stratocumulus cloud layer. found correlations of 0.62 between in situ and MODIS retrieved H, and could show a better agreement of H when fad is explicitly calculated and considered. found correlations of 0.54 (0.7 for H<400 m with cloud fraction > 90 %) comparing radiosonde-derived H to respective MODIS observations. In their study reported that satellite values were higher compared to the ground-based ones. The reason for this can potentially be explained by a bias of MODIS-retrieved re but also in the choice of fad in the retrieval of H.

The intercomparison of SEVIRI with LACROS retrieved τ results in differences of 2.3 (8 %) for 21 April 2013, 3.6 (21 %) for 27 October 2011, 9.3 (76 %) for 1 June 2012 and 8.0 (61 %) for 27 September 2012. The higher resolution of the ground-based observations leads to larger variability also for the homogeneous cases. The median conditions result in a good fit to the satellite (τ, QL)-pairs (Fig. ) for the homogeneous case on 21 April 2013. For this case the satellite pairs are also within the ground-based temporal IQR. The situation is similar even for the inhomogeneous case on 1 June 2012. The situation turns out to be more complicated when looking at the inhomogeneous case on 27 September 2012. Overall satellite τ and QL show lower values, which result likely due to broken-cloud effects in the SEVIRI retrieval. For broken clouds within the SEVIRI pixel the satellite receives a combined signal from the clouds but also from the surface. Such moving, broken cloud fields result in a smoother temporal pattern from the satellite perspective. From the time–height Z cross section on 27 September 2012 between 11:00 and 15:00 UTC a larger number of cloud gaps can be seen, which could explain why the subpixel surface contamination plays a larger role than on 1 June 2012. The Cloudnet observations on 27 September 2012 show rapid changes of QL with peaks around 400 g m-2 and cloud free periods. The observed larger deviations of SEVIRI found on 27 October 2011 are likely due to low values (< 5 µm) of effective radius in the KNMI–CPP retrieval. These are likely a result of the unfavourable viewing conditions with a large solar zenith angle (> 60∘) under relative azimuth angles close to 180∘ around noon for this case, for which pointed out the low precision of the retrieval. These values are filtered out following , but the remaining points might also be affected by the same issue.

To highlight the importance of considering the actual fad for the retrieval process, we calculated τ (Eq. ) from the ground-based observations following the radar–radiometer approach with fad=1 and with the ground-obtained fad. Afterwards we compare it to the satellite-retrieved values. Applying fad=1 the mean difference in optical depth is increased from 2.3 to 8.5 on 21 April 2013, and is also higher for the other cases (see Table ).

The distribution of differences between SEVIRI and ground-based τ for the 2012 and 2013 sample of low-level, homogeneous, liquid clouds is presented in Fig. b. As for QL there is a distinct peak around zero with negligible bias, but a considerable standard deviation of 16. This shows that on average the agreement between satellite and ground-based τ is reasonable, considering the number of uncertainties in the retrieval as well as uncertainties due to parallax, collocation, and spatial resolution. Those uncertainties will be discussed in more detail in the following sections.

The radar–radiometer retrieval depends upon the observations of QL, H, and Z(z). Also the choice of the mixing model is able to change the retrieved quantities, but comes to the conclusion that this effect is small. Nd depends further on k6, which only depends on the width of the DSD (see Eq.  in Appendix A).

We take two typical cloud profiles from our observations. For those cloud profiles we evaluate the sensitivity of the retrieved Nd to the uncertainties of the input parameters based on . In Table  we list the sensitivities to each input parameter when the other parameters are kept constant.

For Z(z) we follow and assume an uncertainty range of ±2 dBZ, which would represent a calibration bias constant with height. Drizzle does have a strong influence on Z, e.g.. Errors of 30–60 % have to be anticipated for qL profile retrievals. Those retrieval approaches are based on very similar principles as the radar–radiometer retrieval method . In our study we filtered out drizzling profiles as well as possible. For the four case days re observed from satellites near cloud top lies clearly below the value of 14 µm which was suggested by as the threshold for drizzle/rain forming clouds. The maximum of Z(z) in each profile also did not exceed -20 dBZ, which is commonly taken as a drizzle threshold . We cannot totally rule out the possibility that few larger droplets were present, to which Z is very sensitive. For the uncertainty of H, we assume ±60 m. For QL we assume a typical uncertainty of ±25 g m-2 given microwave radiometer observations. The width of the DSD for continental clouds exhibits a large spread of values in literature as can be seen in . If we consider the maximum range of observations, the effective variance ν of the gamma size distribution could take values between 0.043 up to 0.2 (k2=0.87 and k2=0.48, respectively). For the standard retrieval we assume ν=0.1 (k2=0.72).

Nd is most sensitive to the assumption about the width of the DSD, especially to changes in the range of smaller values of the effective variance. This can be understood as Nd∝k6 and k6 is a monotonically decreasing function of the effective variance. For higher values of ν the other uncertainty contributions are equally or even more important. Since the real DSD is usually unknown, it is difficult to estimate the actual uncertainty when assuming ν=0.1. From our cases we find that the uncertainty in QL might be more important than the uncertainty in radar reflectivity. Both can result in more than 50 % relative uncertainty for the retrieval of Nd.

As can be seen from Eq. (), the optical depth τ is sensitive to the same input parameters as Nd, but also depends on fad. Therein the combined uncertainty of QL and H is reflected. From Table  we find that τ is most sensitive to uncertainties in QL, especially for observed low values of QL. In contrast to Nd, it is not as sensitive to the assumption about the width of the DSD. While for Nd the uncertainty in the low-range of ν is above 100 %, it is below 20 % for τ. Since the natural variability of DSDs is large and difficult to constrain without in situ observations, τ turns out to be a more stable quantity for contrasting to other observation, as already suggested by .

In Fig.  we present the uncertainty of τ as a function of QL, based on the median observations from the ground-based time series. We use a representative average of Nd over the whole time period and investigate the effect of its temporal variability on the retrieved τ.

Recognizing the difficulty in retrieving Nd from the 3rd and 6th moments, used a climatological mean value for Nd in order to retrieve re. They reported an average Nd of 212±107 cm-3 at the Southern Great Plains site for continental clouds, which is similar to the median value found for our example cases in Fig. . We see that assuming a 50 % uncertainty for both, Nd and τ, results in an increasing uncertainty of τ with QL, with the uncertainty due to ΔNd being slightly larger, although Δfad cannot be neglected.