Relation between ice and liquid water mass in mixed-phase cloud layers measured with Cloudnet

An analysis of the Cloudnet dataset collected at Leipzig, Germany, with special focus on mixed-phase layered clouds is presented. We derive liquid and ice water content together with vertical motions of ice particles falling through cloud base. The ice mass flux is calculated by combining measurements of ice water content and particle fall velocity. The efficiency of heterogeneous ice formation and its impact on cloud lifetime is estimated for different cloud-top temperatures by relating 5 the ice mass flux and the liquid water content at cloud top. Cloud radar measurements of polarization and fall velocity yield, that ice crystals formed in cloud layers with a geometrical thickness of less than 350m are mostly pristine when they fall out of the cloud. It is also found that current and future spaceborne cloud radars might miss a large portion of that primary ice formation, especially for cloud layers with top temperatures warmer than −15◦C. 10


Introduction
Understanding the process of heterogeneous ice formation is currently one of the major topics in weather and climate research (Cantrell and Heymsfield, 2005;Hoose et al., 2008).Heterogeneous ice formation drives the generation of rain (Mülmenstädt et al., 2015), impacts cloud stability (Morrison et al., 2005) and atmospheric radiative transfer (Sun and Shine, 1994).It is therefore a crucial (2007).Basically, liquid water droplets are detected by a threshold in lidar signal followed by a characteristic decrease of the latter above liquid cloud base.Ice particles are in general defined to be 110 present if the radar-observed vertical velocity of the targets indicates falling particles and the dewpoint temperature within a range gate is below 0 • C. If, in addition, the analysis of the lidar signal of the considered pixel meets the criteria for the presence of liquid droplets, the pixel is categorized as mixed-phase.The height of the melting layer is derived either from the meteorological data (dewpoint temperature is 0 • C) or from an LDR measurement above −15 dB.Thus, the decision between 115 liquid-only, mixed-phase or ice-only cloud layers is made primarily based on the modeled temperature and changes in the vertical-velocity profile.However, there is no way to unambiguously decide between drizzle and/or falling ice crystals.
For this work, an automated algorithm has been developed that runs on this basic target-classification product of Cloudnet.Single 30-s profiles are analyzed to search for liquid water.If liquid water is 120 found, the base and top height of the liquid layer is stored and the height-range below this liquid water bin is searched for ice.If ice is found below, also the height of transition between liquid and ice is stored.This procedure is done for all profiles of the dataset.Afterwards neighboring cloud profiles are merged if they lie within 300 s of temporal and 350 m of vertical distance.A set of connected profiles constitutes a cloud for which we assume that the driving microphysics are similar 125 throughout the whole cloud layer.For the statistical analysis, a cloud must pass certain quality criteria: A coherent cloud structure must be found for more than 20 minutes, no seeding of particles from higher-level clouds must be present and at least 85% of the cloud's occurrence time a liquid After cloud identification, the cloud-classification scheme from Bühl et al. (2013) is used to dis-140 criminate between liquid and mixed-phase cloud layers (see Fig. 2).This classification method reduces the dependence on model temperature by taking into account information from all cloud profiles to make a decision between the microphysical states "liquid" or "mixed-phase".Depolarization measurements from lidar and radar are used to directly identify ice crystals falling from a cloud layer.Mixed-phase clouds close to 0 • C also often show a melting layer, which is the most 145 unambiguous sign of the presence of ice particles (Di Girolamo et al., 2012).High LDR values are also produced by the needle-like ice crystals prevailing for clouds with a CTT between −8 and −2 • C (Fukuta and Takahashi, 1999).Such clear LDR signal make the decision between ice and liquid water fortunately very easy close to the 0 • C level, where model temperature in most cases is not accurate enough and the increase in particle fall speed due to melting is not significant.For 150 low signal-to-noise ratios (SNR) of −10...0 dB and no detection of a melting layer, the depolarized signal is usually too weak to be detected by the cross-polarized channel of the MIRA-35 cloud radar.
In this case, measurements of volume linear depolarization ratio from a collocated PollyXT lidar is used (Engelmann et al., 2015), if available.In Fig. 3  A quantitative retrieval of ice mass is done by Cloudnet via the method of Hogan et al. (2006).
IWC values are obtained for each range bin with a simple empirical function depending on Z and 165 the ambient temperature.The uncertainty of the method is estimated by Hogan et al. (2006) to be (+50/ − 30)% below a temperature of −10 • C and (+100/ − 50)% above.Uncertainties in the measurements of Z add to these errors.Hence, for the quantitative understanding of ice formation in the Atmos.Chem. Phys. Discuss., doi:10.5194/acp-2016-25, 2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 27 January 2016 c Author(s) 2016.CC-BY 3.0 License.

LWP(t)
Height for analysis of ice particle properties (e.g., IWC CB ) LWC(t,h)   within the plots.Please note that the ice detection threshold is not only depending on the radar signal threshold, but also on temperature.For spaceborne systems Z thr is nearly constant for the complete troposphere.The measurement distance of about 400−800 km leads to a range-induced signal varia-190 tion of maximum 5% between 0 and 12 km height.For ground-based systems, however, the detection threshold varies dramatically for different heights.This phenomenon is depicted in Fig. 7d, where

Sensitivity of measurements on geometrical cloud thickness
195 Fukuta and Takahashi (1999) provide comprehensive laboratory measurements of the growth of ice crystals.They found different distinct features in the resulting shape of ice crystals for different growth times and calculated corresponding residence times within a cloud layer, taking into account increasing fall speed with increasing particle size.For a residence time of 20 minutes within a mixedphase cloud layer, particles could still be considered pristine.Also Yano and Phillips (2010) found 200 that within this time, secondary processes like riming do not influence heterogeneous ice formation significantly.According to Fukuta and Takahashi (1999), a residence time of 20 minutes corresponds to a geometrical thickness of a mixed-phase cloud top layer of 350 m.Hence, for the present study only clouds with a geometrical thickness of below 350 m were selected to avoid altering of the ice crystals by riming, splintering or aggregation processes.

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The necessity to select thin clouds in order to analyze pristine ice crystals is demonstrated in Fig. 8, where, in contrast to Fig. 7c, cloud layers up to a geometrical thickness of 600 m are taken into account.For this cloud height, the residence time of the ice crystals within the mixed-phase cloud layer is about 30 min.Accordingly, the detected ice mass becomes considerably larger, especially in the temperature range between −8 and 0 • C where the efficiency of ice multiplication processes 210 (Hallett and Mossop, 1974) is known to be largest.On the other hand, it is visible from Fig. 8  properties that are only related to primary ice production.

Fall velocity and radar depolarization of pristine ice crystals
In contrast to the extensive properties Z CB and IWC CB , the measurements of the cloud radar can also be used to derive the intensive properties of the ice crystals (e.g., v and LDR).The latter are  Fukuta and Takahashi (1999) also found several distinct features in the distribution of ice particle size, shape and mass with temperature.Some of these features can be seen within the measurements of LDR and v CB :

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-An enhanced growth of ice crystal mass around −14 • C was found by Fukuta and Takahashi (1999).The effect can also be seen in Figs.-The high values of LDR measured at a CTT of −5 • C correspond to a needle-or column-like 245 particle shape (see Figs. 9a and 9c).In the temperature range around −14 • C LDR values can be found to be around −28 dB, corresponding to plate-like crystal shapes.Please note that these features are also displayed in Fig. 3.In Reinking et al. (1997) the LDR values values of −15 to −20 dB are computed for these ice crystals shapes.
-Hints on the presence of these isometric ice crystals are found in the increase of fall velocity in Figure 11b shows that T l is typically larger than one day for all observed cloud cases.It is also an important finding that shallow mixed-phase cloud layers with δ h < 350 m mainly 315 produce pristine ice.This means that the flux of ice crystals measured at cloud base is directly connected to the rate of ice nucleation within the mixed-phase layer.The direct measurement of the complete process of ice nucleation seems therefore feasible with remote sensing.However, in future, more advanced particle typing methods such as presented in Myagkov et al. (2015a, b) should be applied to further characterize shape and size of the particles on an operational basis.

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The relative impact of the loss of ice water on a mixed-phase cloud layer can be measured.However, it has to be noted again, that the cloud lifetime parameter presented here might not directly be connected to the absolute lifetime of a cloud.Even the definition of a cloud lifetime is difficult, because particles are mixed between cloud parcels and the apparent motion of clouds can be independent from horizontal wind speed.However, the cloud lifetime parameter presented here can be  (2008) showed that the cloud layers under study here actually are able to recreate liquid water via re-330 curring upward air motion, these clouds seem to be extremely stable with respect to water depletion due to ice formation.The lifetime parameter is a considerable step forward compared to Bühl et al. (2013), where the mass ratio of ice and liquid water in mixed-phase layered clouds was estimated with a ratio of IWP and LWP on manually selected clouds.The ratio of IWC CB and LWP, combined The presented algorithm to classify mixed-phase clouds in Cloudnet datasets is universal.It is not only applicable on Cloudnet datasets, but in general on all datasets that separate an atmospheric column into liquid, ice and mixed-phase.The evaluation of mixed-phase clouds predicted by weather models seems therefore possible if suitable data output is given.The established relation between

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LWP and IWC CB could also be used as a parameterization to derive the mass of ice from the LWP alone in numerical models.
The LACROS cloud radar has a depolarization decoupling of −33 dB, which stands out from all radars currently operated within the framework of Cloudnet.Only this technical prerequisite makes high-quality measurements of LDR possible.Also the detection threshold of −47 dBZ at a range of 345 5000 m is outstanding.Satellite missions equipped with cloud radars like Cloudsat (Stephens et al., 2002) and EarthCare (Illingworth et al., 2014) have detection thresholds within the troposphere of −27 dBZ and −33 dBZ respectively.Hence, these satellites will miss probably more than 90% of the ice-signals below mid-latitudinal cloud layers with a CTT above −10 • C (see Fig. 7a).
or mixed-phase cloud top must be detected.The properties of the detected clouds, e.g., cloud-top height (CTH), geometrical cloud thickness δ h , standard-deviation of cloud-top height σ CTH , cloud-130 top temperature (CTT), radar reflectivity factor (Z), ice-water content (IWC), liquid-water content (LWC), LDR, lidar attenuated backscatter coefficient (β) and lidar volume linear depolarization ratio are stored for further analysis.See Fig. 1 for an overview where the different properties are derived Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-25,2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 27 January 2016 c Author(s) 2016.CC-BY 3.0 License.for one cloud case.The picture also shows, that some measurement values are taken only from a height-level 60 m below the mixed-phase cloud base.At this point, cloud droplets should be absent 135 and ice particles should still be largely unaltered by evaporation or aggregation processes.Hence their size and shape should only be related to processes having taken place within the mixed-phase cloud top layer.In the context of this work, all measurement values derived in this way are marked with the index "CB" (for "cloud base").
three example cases with different CTT from different dates are shown together.Cloud radar measurements of Z, LDR and v are shown together 155 with the attenuated backscatter coefficient from the lidar.The CTT of the three cases are chosen in such a way that distinct differences in LDR measurements are visible between the cases.As an example for cloud detection/selection, all clouds with δ h < 350 m and σ CTH < 150 m detected on 2 October 2012 at Leipzig are marked in Fig. 4. The CTT statistics of all selected and classified cloud layers with these selection criteria (δ h < 350 m and σ CTH < 150 m) are shown in Figs.5a and 5b.It 160 is visible that no mixed-phase clouds are detected below −40 • C. 4 Quantitative description of heterogeneous ice formation in cloud layers over Leipzig 4.1 Ice-mass retrieval and detection thresholds

Figure 1 .Figure 2 .Figure 3 .
Figure 1.Schematic representation of the different measurement and averaging schemes in a mixed-phase cloud layer.On top the predominantly liquid water top is detected by lidar.The ice precipitation below is mainly detected by the cloud radar.IWC and LWC are provided by Cloudnet and are a function of height (h) and time (t).IWP and LWP are the column integrated values of LWC and IWC over the liquid cloud top and the ice precipitation, respectively.IWCCB represents the mean of all IWC values measured about 60 m below current cloud base height (CBH).

Figure 4 .Figure 5 .
Figure 4. Example of automated detection of mixed-phase cloud layers on the basis of the Cloudnet target classification scheme for 2 October 2012.Blue squares mark liquid-only layers and red squares mark mixedphase layers.The colors are only for a very basic visualization of the layer detection.The decision between mixed-phase and liquid clouds in the following analysis is more complex and described in the text.

Figure
Figure 7a depicts all measurements of Z CB sorted by CTT.In Fig. 7b the values of Z CB are shown

Figure 6 .
Figure 6.The 90% percentile of cloud-radar SNR is shown for each cloud case together with mean detected LDR.

Figure 7 .
Figure 7. (a) All values of ZCB column-normalized, (b) ZCB averaged for each cloud case together with averaged LDR values, (c) IWCCB averaged for each cloud case, (d) values of ZCB depicted depending on CTH instead of CTT.Thresholds for Z and IWC are illustrated within the graphs.

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connected to size, shape and orientation of the ice particles.Values of LDR and v CB averaged for each cloud case are shown in Figs.9c and 9d.One has to keep in mind that LDR is dependent both on particle shape and particle orientation, so this information is not unambiguous(Reinking et al.,   10    Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-25,2016   Manuscript under review for journal Atmos.Chem.Phys.Published: 27 January 2016 c Author(s) 2016.CC-BY 3.0 License.

Figure 8 .
Figure 8. IWCCB for an extended dataset with cloud layers included that are up to 600 m thick (instead of 350 m in Fig. 7c).
7a and Fig. 7b as a strong increase of Z CB at this 11 Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-25,2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 27 January 2016 c Author(s) 2016.CC-BY 3.0 License.temperature.The cloud radar is sensitive to the square of the particle mass and reacts therefore very sensitive on changes of this quantity.

250Figure 9 .Figure 10 .
Fig. 9d.Measured fall velocities peak at around −10 and −22 • C, while minima of LDR can be found at −12 and −22 • C.This connection also points towards more isometric ice crystals around these temperatures.

Figure 11 .
Figure 11.(a) The ice mass flux at cloud base.(b) The estimated lifetime index tl = LWP/F of each cloud.

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used to study the impact of ice on predominantly liquid cloud layers occurring at different temperature levels.Measurements of ice mass flux and the cloud lifetime parameter T l indicate a minimum cloud layer lifetime of 3 hours around −25 • C. At temperatures above −15 • C the relative impact of ice formation has already shrunk by 2 orders of magnitude.Given the fact that Korolev and Field Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-25,2016   Manuscript under review for journal Atmos.Chem.Phys.Published: 27 January 2016 c Author(s) 2016.CC-BY 3.0 License.with the particle fall velocity gives a much more direct measure of the actual impact of the ice on 335 the liquid water within a mixed-phase layer.