1. Introduction
The limited understanding of dynamical and microphysical processes in deep convective clouds and their observable signatures poses a significant challenge for weather and climate research. One particular aspect concerns the application of our current knowledge of convective growth to the detection and short-term prediction of developing deep moist convection based on observational networks within the context of nowcasting (Wilson et al. 1998). Current observational systems approach their limits for rapidly developing deep convective clouds with temporal scales of tens of minutes and spatial scales on the order of 1 km or even less. To supplement radar measurements, cloud observations based on geostationary satellites have been proposed as important predictors of early detection of convective initiation (CI; Roberts and Rutledge 2003; Mecikalski and Bedka 2006; Zinner et al. 2008; Mecikalski et al. 2010a,b; Siewert et al. 2010; Sieglaff et al. 2011; Merk and Zinner 2013; Sieglaff et al. 2014). Several of the above-mentioned studies have shown that detailed knowledge about the growth phase of developing storms can be utilized to increase the predictive skill of nowcasting applications. Temporal changes in satellite-observed thermal radiation can indicate the rapid speed of cloud-top cooling (CTC) and therefore vertical ascent of cloud tops. For example, satellite-based CTC rates have been calculated by Roberts and Rutledge (2003) to quantify the growth of convective clouds induced by boundary layer convergence in the United States. It has been found that satellite-derived cloud growth rates potentially provide precursor information up to 30 min before radar-derived storm initiation. In addition, Mecikalski and Bedka (2006), Mecikalski et al. (2008), and Walker et al. (2012) have combined multispectral estimates of cloud depth, growth, and glaciation to assess the potential of convective storm development. Based on their CI scheme, average nowcast lead times of 30 min for early detection of convective events were achieved. An additional important parameter that is related to cloud growth and is readily detectable from geostationary satellites is the anvil area expansion rate. For instance, Machado et al. (1998) and Machado and Laurent (2004) have shown that the initial areal expansion of convectively forced anvils is proportional to the life times of mesoscale convective systems over the Amazon region. They have also demonstrated that, on average, the maximum area expansion occurs close to the time of maximum precipitation intensity. There is a long record of investigations connecting satellite-based cloud-top features with storm severity [e.g., Adler and Fenn (1979a,b), Reynolds (1980), and Heymsfield et al. (1983), among many others]. In essence, very cold cloud-top temperatures in the convective cores and several cloud-top morphological features as well as enhanced growth rates in terms of CTC and anvil expansion rate have been identified as discriminating factors for storm severity.
In the current study, we investigate convective cloud-top characteristics of growing storms over central Europe using geostationary satellite observations. We aim to provide relationships between cloud depth, growth, and glaciation properties and characterize the timing of formation of radar-derived moderate to heavy precipitation with regard to satellite-based growth and glaciation measures. We further discuss the relevance of our analysis within the context of satellite-based CI nowcasting. Our current approach is an extension of an earlier study (Senf et al. 2015) that was concerned with the characterization of initiation and growth of a few selected severe storms over central Europe. We are now able to confirm the significance of earlier results about the interrelationship between CTC and anvil macro- and microphysical changes. Furthermore, we supplement the investigation of cloud dynamical characteristics by a joint analysis of multispectral glaciation rate estimates and their relationship to radar-derived precipitation formation. The paper is structured as follows: In section 2, we introduce the satellite and radar data. Storm tracking and the collection of along-track characteristics are explained in section 3. In section 4, we present the results of our study, which is concerned with the temporal behavior of indicators of cloud depth, growth, glaciation, and anvil and precipitation formation as well as interrelationships between the different variables. We finally give a summary and draw conclusions from our study in section 5.
2. Data
a. Satellite data
We analyze data from the Spinning Enhanced Visible and Infrared Imager (SEVIRI), which is an optical imaging radiometer aboard the geostationary Meteosat Second Generation (MSG) satellites operated by the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT; Schmetz et al. 2002). So-called rapid-scan observations with a repeat cycle of 5 min have been chosen for the summer half-year periods, that is, from April to September, between 2012 and 2014. The operational rapid-scanning satellite, which was Meteosat-8 until 9 April 2013 and was followed by Meteotsat-9, is located at 
(left) Overview of the domain of interest, which is marked by a red box, and (right) a collection of satellite-based storm tracks for all investigated cases. The tracks are plotted by red lines, and red circles with white edges highlight the track starting position. The black circle and line marks the case shown in Fig. 2.
Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0293.1
SEVIRI is a multispectral instrument with 12 channels in the visible and infrared [see Schmetz et al. (2002) for further detail]. We use the high-resolution visible (HRV) channel, which has a threefold higher resolution than the narrow-band channels, and the window channel at 
b. Satellite products
A set of cloud products, including cloud mask, cloud type, and cloud-top height (CTH), has been generated using EUMETSAT’s Satellite Application Facility on support to Nowcasting and Very Short-Range Forecasting (NWCSAF) software package for the set of selected cases. The masking of the along-track fields is performed on the basis of the NWCSAF cloud mask and type product (Derrien and Le Gléau 2005). We examine the discrimination between cloudy and clear-sky pixels, but allow for cloud contaminated or partially cloudy pixels. Furthermore, semitransparent cirrus is identified based on the cloud type classification and is excluded from further analysis. The retrieval of properties of growing cumulus underneath cirrus clouds is challenging, and an in-depth discussion of this topic can be found in Mecikalski et al. (2013b). NWCSAF cloud-top height, which is calculated using temperature profiles obtained from ECMWF forecasts, and cloud-top ascent rates from corresponding height time trends are derived for investigation of convective development.
We use the Royal Netherlands Meteorological Institute [Koninklijk Nederlands Meteorologisch Instituut (KNMI)] cloud physical properties (CPP) retrieval (see Roebeling et al. 2006; Meirink et al. 2010) to derive the cloud-top thermodynamic phase, cloud optical thickness, and the cloud-top effective particle radius 
The cloud-top effective radius and visible optical thickness can exhibit large variations and uncertainties (Marshak et al. 2006; Wolters et al. 2010). Product uncertainties are caused by deviations from the retrieval assumptions, which include homogeneous cloud-top properties and thereby, for example, neglect 3D radiative effects. The complex morphology of convective cloud clusters leads to illuminated cloud sides, shaded cloud regions behind convective towers and, furthermore, partly cloud-filled pixels at cloud edges. A high degree of subpixel variability thus decreases the accuracy of cloud products. The high-resolution information contained in the HRV reflectances can be extracted to downscale information in SEVIRI’s low-resolution channels (see, e.g., Deneke and Roebeling 2010; Mecikalski et al. 2013a) or to construct high-resolution cloud products (Bley and Deneke 2013). However, these promising approaches have not been applied in the current study and are left for future investigations. We hence emphasize that the retrieved cloud microphysical properties should be interpreted carefully. The reader should keep in mind that the products always refer to a hypothetical microphysical state of an idealized, horizontally homogeneous prototype cloud with similar radiative signatures to the observation, and does not necessarily match the actual convective cloud properties because of violations of the retrieval assumptions.
c. Precipitation radar data
The radar reflectivity factor Z is used as a simple proxy of precipitation intensity in this study. The value of Z is obtained from the German Radolan RX composite, in which radar data from a Germany-wide network of 16 C-band Doppler radar stations are merged into one homogenized and regularly gridded product (see, e.g., Wapler et al. 2015). The RX composite only uses data from precipitation scans that are performed at the lowest elevation following the apparent horizon. No attenuation correction is applied. The data are available every 5 min, and the scan is finished in less than 1 min after the nominal scan time. The spatial resolution is 1 km in both grid directions. Depending on the surrounding landscape and the distance between the radar antenna and the scattering target, the signal can be reflected up to 2 to 3 km above ground level. However, because of the merging strategy in regions of overlapping radars, accurate scan height information is not always available. No further quality assessments or corrections have been applied to the radar data in this study.
3. Method
a. Satellite-based tracking and calculation of along-track properties
The satellite-based tracks of storm cells are constructed in a semiautomated fashion, which is described in detail in appendix A. In essence, convective anvils are tracked automatically forward in time relying on the overlap of cells in successive satellite images, whereas growing cumulus clouds are manually tracked backward in time during the early development stage. A set of more than 100 satellite-based tracks has been chosen for the analysis that were randomly sampled from the summer half-year periods between 2012 and 2014 to limit the effort for manual tracking. These tracks and their initial starting location are shown in Fig. 1.
Along-track properties and 5-min time rates are calculated for several satellite-based proxies of cloud depth, growth, and glaciation. Uncertainties of along-track properties that are mainly caused by limitations in the spatial resolution of the satellite sensor are estimated from a 3 × 3 region centered around the track. One particular time rate that has special importance for our study is the negative time trend of 
The time of maximum CTC (
b. Anvil and precipitation area calculations
The methodology of anvil detection and characterization closely follows the method applied by Senf et al. (2015). The anvil area is determined by 4-connectivity clustering, which assigns the connected area of the 
Precipitation data are also collected along satellite-based tracks. After parallax correction, a combination of automatic clustering and manual selection was applied to derive radar objects that are causally related to the satellite-derived cloud information (see appendix A for details). Each radar object is composed of a set of Z values above 35 dBZ that are not necessarily connected. This reflectivity threshold agrees with the typical threshold used for the definition of CI [see, e.g., Roberts and Rutledge (2003) and Mecikalski and Bedka (2006), among many others]. Using a standard Z–R relationship, it corresponds to a rainfall rate of 6 mm h−1. Please note that it is a common situation, at least for our set of cases, that developing convective cells observable at the resolution of the satellite observations are associated with multiple precipitation cores resolved by the radar composite.
In a further analysis step, two different thresholds at 46 and 55 dBZ are applied separately to each radar object. Cell area, diameter, and expansion rate are calculated for the parts of the Z field above the respective threshold. For simplicity, we only calculate diameters and radius rates of equal-area circles even for very complex-shaped precipitation clusters, and do not consider shape or other morphological properties in the analysis. The threshold of 46 dBZ is used in the German Weather Service nowcasting tool Konvektionsentwicklung in Radarprodukten (convection evolution in radar products) (KONRAD) [see, e.g., Wapler and James (2015) and references therein]. It is typically related to heavy rain of 35 mm h−1 or more. The largest threshold of 55 dBZ is considered as first indicator for hail, and is used for issuing hail warnings at the German Weather Service. In a last step, the precipitation cell properties have also been synchronized to 
Figure 2 shows a representative example of a developing convective cell characterized by the combined use of satellite and radar data. Prior to the deep convective development, a convective cloud field is noticeable from the HRV reflectances. Precipitation develops around 30 min before the maximum CTC. The later anvil development is evident in the 10.8-μm BTs.
Sequential convective development of a convective storm that initiated at 51.666°N, 10.920°E and 0945 UTC 27 Jul 2014. The numbers in the upper-left boxes indicate the nominal scan time relative to the CTC maximum in minutes. The HRV reflectance 
Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0293.1
4. Results
a. Cloud depth and growth indicators
Figure 3 shows indicators of cloud-top height and vertical extent for the set of developing convective storms synchronized to the relative time 
Temporal behavior of (a) 
Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0293.1
The CTC rates (Fig. 3a) and cloud-top vertical ascent rates (Fig. 3b) show a characteristic peak around the time of maximum CTC. This is essentially due to the synchronization strategy and therefore not unexpected, but is, however, an encouraging confirmation of this strategy. The maximum CTC rates, which are calculated as negative 5-min time trends of 
We also analyzed the temporal evolution of optical thickness and the BT difference 
b. Cloud-top microphysics and glaciation
In the following, we present an overview of the temporal evolution of several satellite-derived cloud-top products and radiance combinations that will be used to characterize the cloud-top microphysical state and the phase partitioning between liquid and frozen hydrometeors. A binary decision about the condensate phase is essentially inappropriate for the mixed-phase region of developing convective clouds, and cloud phase determination is highly uncertain. We therefore also consider radiance combinations that contain information about the phase partitioning within one pixel, which are approximately related to the ratio of total hydrometeor cross sections. The challenge, however, is that these kind of radiance combinations are also very sensitive to the size and habit of the considered hydrometeors (see, e.g., Baum et al. 2000). Furthermore, the depth of the considered cloud-top layer varies for different sensor wavelengths depending on the penetration depth of radiation (Platnick 2000).
Figure 4a shows the time series of cloud phase fraction, which is defined as the fraction of pixels classified as ice within the 3 × 3 region around the satellite-based track. The average phase fraction starts around 0.5 at 
As in Fig. 3, but for (a) cloud phase, (b) NDSI, (c) 
Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0293.1
In addition, Fig. 4b gives the difference in solar reflectances 
The 5-min time trends of cloud phase fraction and the previously discussed radiance combination are also depicted in Fig. 4. The rates connected to solar reflectances (cloud phase rate in Fig. 4a, NDSI rate in Fig. 4b, and 
c. Anvil formation
Deep convective clouds develop cirrus anvils as a result of a converging vertical mass flux close to the tropopause, or equivalently another equilibrium level. By mass conservation, air has to diverge horizontally. The spreading anvil is easily detected in satellite observations and its expansion rate contains information about the strength of convective updrafts as well as compensating downdrafts within the cloud interior (see derivations in appendix B).
Figure 5 shows the properties of our case set related to anvil size and expansion. Figure 5a displays the median anvil diameter, which increases from around 10 km at time of maximum CTC up to 30 and 45 km at 30 and 60 min, respectively. The behavior of the anvil diameter before and in the vicinity of 
As in Fig. 3, but for (a) anvil diameter and (b) anvil area rate. Time of maximum CTC and maturation time have been marked with green and red intervals, respectively. The anvil is defined as connected area with 
Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0293.1
We further provide estimates of median anvil behavior in case of a hypothetical, time-constant vertical mass flux in the different panels of Fig. 5. In a stationary setting, the anvil area A is supposed to increase linearly in time, that is, 
d. Precipitation formation
The temporal evolution of radar-derived precipitation objects is analyzed here. First, the fraction of the precipitation cells relative to the number of cases with valid satellite and radar data is shown in Fig. 6a. Around 80% of the precipitation objects already exist at 
As in Fig. 3, but for the characteristics of radar-derived precipitation objects. (a) The fraction of precipitation objects conditioned on different maximum Z intensities relative to the total number of tracks points with valid radar data. Further shown are (b) cell maximum radar reflectivity 
Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0293.1
In addition, Fig. 6 presents the evolution of maximum precipitation cell reflectivity 
Furthermore, Figs. 6c and 6d show the time rate of the radii (
e. Weak versus strong growth
This subsection contrasts the temporal evolution of convective cloud and precipitation characteristics for two disjunct subsets of our set of storm cases corresponding to weak versus strong growth. The median of the maximum CTC rate with a value of 17 K per 15 min for all cases is chosen as discriminator to separate the subsets, with cases having a maximum CTC rate smaller than the median assigned to a “weak growth” subset, and a maximum CTC rate larger than the median to the “strong growth” subset. Figure 7a shows that the 
Temporal evolution of (a) 
Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0293.1
f. Synthesis
Figure 8 presents a schematic view of the convective growth phase, combined with satellite-derived glaciation and growth rate as well as changes in precipitation intensity and core size. Two glaciation indicators, based on the CPP phase fraction rate and 
(top) Schematic view on stages in the convective growth phase. Typical values of cloud-top ascent and anvil expansion velocities are indicated. (bottom) Combination of the case-to-case median of cloud phase rate (green) and 
Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0293.1
The average temporal evolution of convective growth, glaciation, and anvil properties reported so far is relatively robust and can also be reproduced when the time interval between the available satellite observations is increased from 5 to 15 min. Therefore, we have artificially decreased the temporal sampling frequency of the satellite-based properties to 15 min similar to the operational Meteosat prime service. Satellite-based time rates have been recalculated from 15-min differences, and synchronization of the storm tracks has been carried out based on the maximum CTC rates available at 15-min intervals. Thus, the alignment of along-track radar data is also affected, which has been kept at 5-min time resolution. With this setup, the temporal evolution of storm characteristics discussed previously was reproduced with similar behavior and magnitudes. As expected, a reduced accuracy and much higher uncertainty is found, however, which highlights the importance of a high temporal sampling frequency for nowcasting applications.
g. Cross correlations
Finally, we focus on the investigation of the interrelationships between different convective storm characteristics. For instance, the CTC rate and anvil edge velocity are expected to be linked by mass conservation. However, intrinsic differences between the initial motion of the cloud-top edge and the subsequent intensification of the cloud-internal mass flux might partly obscure any connection. Figure 9a displays the cross correlation between the maximum CTC rate derived at 
(left) Cross correlation between two variables: the first one selected at fixed relative time and the second one sequentially evaluated at different times 
Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0293.1
The connection between cloud microphysical properties and growth characteristics is illustrated in Figs. 9c and 9d. The cross correlation between 
As a third cross-correlation example, Figs. 9e and 9f present the connection between satellite-based glaciation measures and the subsequent precipitation intensity. As a glaciation indicator, the 
We conclude the section with a discussion of interrelationships between storm properties at the beginning of the mature phase. A sketch is shown in Fig. 10, where we have analyzed the instantaneous cross correlations between combinations of satellite-based and radar-derived storm characteristics. Each arrow in Fig. 10 represents a scatterplot evaluated at a certain time, which is indicated above the arrow. At this time, the highest statistical significance is found for the observed cross correlation between two connected variables. The thickness of the arrow and the number below the arrow indicate the magnitude of this cross correlation. Either 
Sketch of connections between convective cloud and precipitation characteristics within the mature phase. Solid lines mark simultaneous cross correlations between storm properties at fixed relative times, which are indicated above the lines. The linear correlation value is given below the connection lines. Similar to Fig. 9, only the time and the corresponding correlation at minimum p value is indicated. Note however, that the cross-correlation values can have a broad time range in which significant values are obtained.
Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0293.1
5. Conclusions
We have investigated the growth phase of developing convective storms and their transition to maturity. The study is based on a synergistic combination of cloud-top signatures from geostationary satellite and precipitation intensity estimates from a ground-based radar network. The major goals of the study are 1) to show the satellite-derived characteristics of growing cloud tops and illuminate interrelationships between cloud depth, growth, and glaciation properties depending on the stage within the growth phase, 2) to investigate the timing of the onset and subsequent change to moderate and heavy intensity of the radar-derived precipitation with respect to satellite-based growth and glaciation processes, and 3) to show and discuss implications for satellite-based nowcasting of convective initiation (CI), when a generalization seems to be reasonable.
For the characterization of convective development from satellite, we have used solar reflectances, infrared BTs, and cloud products from the SEVIRI instrument on board the geostationary Meteosat satellites. Dynamical growth properties have been studied based on cloud-top cooling (CTC) rates and anvil expansion speeds. Cloud-top glaciation has been estimated based on several multispectral measures: cloud phase fraction, solar reflectances at 1.6 and 3.9 μm, and a combination of brightness temperatures at 8.7, 10.8, and 12 μm. A gridded composite of radar reflectivities has been obtained from surface precipitation scans of the German radar network.
One major advantage of the two observational systems for the characterization of convective growth is their high scan frequency of 5 min, which allows us to calculate Lagrangian changes of cloud and precipitation properties at high temporal resolution. More than 100 satellite-based convective storm tracks have been determined and analyzed for the years 2012–14 and the region of central Europe. For most of the investigated cases, we find that the CTC rate shows a pronounced maximum during the growth phase. The time of the maximum CTC has been utilized to synchronize the satellite-derived and radar-based storm properties. The main findings of the analysis of these properties are summarized as follows:
- The satellite-derived growth duration, determined by the half-maximum width of the CTC rate, lasts around half an hour, at least for the spatial resolution of Meteosat SEVIRI. A good correlation between CTC and anvil edge velocity exists, suggesting that a synergistic use of the satellite-based growth properties might be beneficial for nowcasting applications.
- Anvil properties, computed from connected areas of 10.8-μm brightness temperatures less than 240 K, deviate significantly from properties expected for constant vertical mass flux. Ignoring anvil thinning by particle sublimation, we infer that the in-cloud mass flux is highly nonstationary and seems to increase by a factor of 1.5 on average within 45 min after the maximum in CTC, which is likely caused by an increase of the updraft core size.
- Satellite-based glaciation rate estimates reach a maximum 15 min prior to the maximum in CTC, indicating that release of latent heat of freezing prior to the maximum is important to invigorate convective updrafts.
- We find a weak connection between maximum CTC magnitude during the growth phase and ice-particle size in the mature phase. Slightly smaller particles are retrieved for larger cloud-top ascent velocities. We interpret this as an observable indication that ice particles may form later and may have less time to grow in stronger convective updrafts.
- Furthermore, higher maximum precipitation intensities and larger precipitation cores are found for mature convective clouds with higher cloud tops, larger anvil sizes and expansion rates, and smaller ice crystals in the cloud-top region.
- By investigating the onset of precipitation in relation to CTC signatures, we find that the probability is large that significant precipitation already exists at an early stage of satellite-derived convective growth. Satellite-based techniques for early CI detection therefore have to target the early updraft intensification period 30 min prior to the maximum in CTC. Moreover, information from solar channels should be used whenever possible to obtain an increased accuracy for inferring cloud-top glaciation from satellite observations.
Our study has aimed at identifying common features in the convective growth, without taking into account the impact of the environment on convective strength and organization. We expect, however, that some part of the uncertainty in our inferred relationships can be reduced by meaningful inclusion of environmental properties like convective instability, moisture supply, and flow characteristics, which is planned for future analyses. Moreover, we hope to attribute modifications of convective growth and glaciation processes to changes in aerosol load, a challenge to clarify a potentially important anthropogenic influence on convection and climate (Rosenfeld et al. 2008a). We further aim to incorporate observations from lightning networks in future research to increase our understanding of the relationships between multispectral cloud-top signatures from satellite and the accompanying hazards of thunderstorms.
We also like to stress that a further quantification and validation of Meteosat-based CI capabilities for the central European domain is needed. Concerning operational nowcasting in general, we see our study as a guide on which future conceptual models of the life cycle of convection can be built that combine temporal changes in satellite- and radar-based proxies of convective activity. Challenges for the application in operational environments are related to the quality of the automated detection of convective clouds, the tracking methods, and the discrimination of strong convective growth and other measures of storm severity from signatures that might arise from algorithm artifacts. However, not all these important issues have been treated in our current study and are left for future efforts.
Acknowledgments
The work has been partially conducted within the OASE project of the Hans Ertel Center for Weather Research, coordinated by the German Weather Service and funded under Grant T1-A9-EZ-2011b, as well as within the HD(CP)2 project funded by the BMBF under Grant 01LK1507C. We thank three anonymous reviewers, whose comments helped to improve the manuscript. We acknowledge EUMETSAT for providing SEVIRI data and DWD for providing the Radolan RX composites. Special thanks are given also to the members of the EUMETSAT convection working group for stimulating discussions.
APPENDIX A
Details on Tracking Methodology
a. Construction of satellite-based tracks and along-track properties
The satellite-based tracks are constructed in two steps. In the first step, automatic detection and tracking of convective anvils is performed. For detection, the observed 
In a second step, the automatically obtained tracks have been randomly shuffled. Thereafter, we started to sequentially extend the tracks manually into the early stages of the convective growth phase, with emphasis on spatial coherence in the 
For calculation of along-track properties and rates, small cutouts (typically 51 × 51 pixels) of satellite data and products are first obtained centered on the track positions and stacked in time. Second, masking of the 3D data cube with the cloud mask and type conditions as described in section 2, as well as solar illumination conditions for solar channels and cloud microphysical and optical properties, is applied. All the following analysis steps exclude invalid pixels from the calculations. In a third step, the masked data are smoothed with a Gaussian kernel of two pixels, one pixel, and 5-min width in the respective space and time dimensions. The filtering was chosen to enhance our ability to extract convective growth properties on temporal scales of 10 min or larger. We are aware that current studies show the improved capabilities of so-called superrapid scans with update cycles between 1 and 2.5 min to characterize the rapid parts of cumulus development (Mecikalski et al. 2016).
For derivation of along-track properties and to obtain quantitative estimates of uncertainty, we apply the method developed in Senf et al. (2015). We assume that the actual cell track can be misplaced by one pixel because of ambiguities in subsequent images and subpixel shifts. A 3 × 3 core region centered around the track location is selected from the masked and filtered satellite data stack. Thereafter, a random-track set is generated by randomly choosing new track positions out of the respective 3 × 3 region. The bootstrapping procedure is repeated 100 times. The median and interquartile range is calculated from the random-track set of each time step. In addition, we derive temporal rates from the random-track set using 5-min centered differences. Please note that the calculated time rates have been rescaled by a factor of 3 to allow for easy comparison with existing literature, which usually presents rates in units per 15 min.
For the object-based anvil properties, smoothing of the time series with a Gaussian kernel of width 15 min is applied. This is especially important to reduce noise in the outward-pointing anvil edge velocity. For an uncertainty estimate, a running average is applied to the time series, and a running standard deviation with the same kernel width is computed.
b. Derivation of radar-based objects
First, the tracks have been parallax corrected using the NWCSAF cloud-top-height product and standard routines. Next, along-track Z cutouts centered around the parallax-corrected track (121 × 121 grid boxes) are gathered and stacked in time and eventually masked with a threshold of 35 dBZ. Because of different spatial resolutions of satellite and radar data, as well as increasing apparent shifts due to cloud growth effects, it was found necessary to realign the radar data. We therefore successively performed image registration techniques that use maximum correlation to correct for apparent spatial shifts in the masked radar data. The realigned and masked radar data are smoothed in time, and precipitation clusters are determined by a combination of automatic clustering and manual selection described in the following.
In a first step, a 3D connectivity cluster algorithm was applied to the smoothed and realigned radar data. The cluster algorithm is built on a binary mask using a threshold of 35 dBZ. The cluster center position that was closest to the parallax-corrected satellite-based track and with meaningful temporal length was chosen as first guess of the 3D radar-based precipitation cluster. In a second step, a manual correction was performed to ensure a high quality of the precipitation cell dataset. We developed an interactive application in which radar fields and marked cell objects are visualized and highlighted simultaneously at different time instances. By hand, a human expert added missing or removed wrongly assigned parts of the radar fields.
APPENDIX B
Relationship between Updraft Strength and Anvil Expansion
A large body of literature exists showing the utility of the normalized anvil expansion rate 
APPENDIX C
Anvil Expansion for Constant Vertical Mass Flux
Now, choosing the values that attach the theoretical curve to the median observation of Fig. 5a at 
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