Abstract
The idea of PARA is to improve the representation rain originating from the ice phase in climate models thanks to the information provided by polarimetric radar. Specifically, PARA will make rigorous use of subgrid-scale variability to revise the parameterisation of four relevant processes (illustrated in the Figure) in the ICON atmospheric general circulation model.


Figure 1: Schematic of investigated processes in PARA.

Current Status : 2021

Contribution of University Leipzig

A first goal of the Univ. Leipzig contribution to PARA was the evaluation of subgridscale
variability of cloud ice and its implementation in the aggregation parameterization. In the ICON general circulation model (Giorgetta et al., 2018), the cloud horizontal subgrid-scale variability is represented in terms of a “critical relative humidity” framework (Sundqvist et al., 1989) that corresponds to a uniform distribution of total-water specific humidity around its grid-box mean value (Quaas, 2012). In the present study, only ice clouds are considered, and the cloudy part of each grid box is isolated, i.e. the total-water amount that is beyond the saturation specific humidity with respect to ice. From this, the variance of the subgrid-scale variability is computed (Quaas, 2012) and analysed at several isobaric levels. As a reference for the global distributions, satellite retrievals from the raDAR-liDAR approach by Delanoë and Hogan (2010) are used. From the high-resolved satellite data along the track within each 2.8° length, the variance of the ice specific mass is computed on the isobaric surfaces. Since the modeled cloud ice content does not include precipitating and convective cloud ice, from the CloudSat 2B-CLDCLASS (Sassen and Wang, 2008) dataset information about the cloud classification and precipitation a comparable cloud ice content is calculated. Here, all data, which are flagged as “deep convection”, “cumulus” or “precipitation at the surface”, are removed. We provided this dataset for the partner PhD position in Bonn to compare different methods to remove snow (precipitation) from the cloud ice data. A multi-year mean of cloud ice variance is used to evaluate the modeled cloud ice distribution, which shows a good agreement in geographical pattern. The new specific cloud ice mass is now used for the aggregation parameterization of the ICON model, which describes the formation of snow by ice crystals. Due to the non-linearity of the aggregation process the process rate becomes stronger by using this stochastic approach. This leads to an overall small cloud ice loss. As a result of the higher aggregation rate the accretion of cloud ice by snow becomes smaller. Therefore, the cloud ice loss due to the stochastic aggregation parameterization is less strong. Compared to the DARDAR data the Model overestimates the cloud ice in lower levels and in the high latitudes (Fig. 1). As a further step, we will study the interactions of different cloud ice related process rates to improve the representation cloud ice in the model.

Figure 1: Comparison of vertical profiles of multi-year mean cloud ice mixing ratio for different regions: Global (80°S – 80°N), Tropics (30°S – 30°N), Mid-Lat N/S (30° - 60° N/S), High-Lat N/S (60° - 80° N/S). Black: Satellite DARDAR Dataset, green: ICON control run, red: ICON with the stochastical aggregation parameterization.

Contribution of University Bonn

The primary goal of improving the parameterizations of ICON-GCM subscale microphysical processes is being addressed at the University of Bonn using radar-based observations. First, the variability of the ice phase in stratiform and accordingly spatially nearly homogeneous cloud cover is investigated with the help of ice microphysical retrievals applied above the melting layer. Various polarimetric microphysical retrievals (e.g. Ryzhkov and Zrnić (2019), Murphy et al. (2020), Bukovčić et al. (2020), and Carlin et al. (2021)) for the total particle concentration Nt, the ice water content IWC and the mean volume diameter Dm were intercompared with respect to their means and standard deviations as a function of height and their respective accuracy. For this purpose, we use so-called QVPs (Quasi- Vertical Profiles), obtained via azimuthal averaging of polarimetric variables from PPIs (Plan Position Indicators) measured at an elevation angle of 18° (e.g. Trömel et al. (2017) and Ryzhkov et al. (2016)). In order to provide our partner in Leipzig with sub-grid scale variabilities of our retrievals as a function of height to improve the parameterizations, two related questions/challenges arise: 1) to what extent can the required window size (sector size) for the averaging process be reduced, while still guaranteeing that the statistical errors remain small enough, and 2) how can we distinguish between statistical errors in the retrievals resulting from statistical errors in the polarimetric variables on the one hand and the real temporal-spatial variability in the retrievals on the other hand. Therefore, we investigate the standard deviation of e.g. IWC as a function of the used azimuthal window (sector) size. First, we determine the statistical errors of the polarimetric variables in each bin individually, according to Ryzhkov and Zrnić (2019), then calculate the according statistical errors of our retrievals using Gaussian error propagation and finally compare their standard error of the mean with the azimuthal standard deviation for the different sector sizes (e.g. 15°, 30°, 45°). The real temporal-spatial variability (subgrid scale variability in ICON-GCM) is assumed to be the difference between the azimuthal standard deviation and the standard error of the mean. Thus, if the standard error of the mean is very small, the real temporal-spatial variability is equal to the azimuthal standard deviation. To quantify the influence of statistical errors, an error-ratio is defined as the ratio of the standard error of the mean and the azimuthal standard deviation: σmean/σstd. Figure 2 provides the error-ratio of the IWC(Zlin, ZDRlin, KDP,) retrieval from Carlin et al. (2021) for different window/sector sizes for a stratiform rain event observed on 7.10.2014 between 0:00 and 3:30 UTC with the polarimetric X-Band radar in Bonn (BoXPol). It can be seen that the error rate for most of the data set is below the value of about 100% for observed azimuthal sector sizes of 30° (corresponding to a subdivision of the PPIs into 12 sectors). In summary, the standard error of the mean is significantly smaller than the azimuthal standard deviation in the majority of the data (up to 12 sectors), so that subdivision for this case study is possible.

As a next step, the variability of ice and snow is investigated separately fitting an exponential distribution and using R = 100 μm, i.e. the smallest size a particle is assigned to snow/aggregates in the ICON-GCM. Due to the low sensitivity of weather radars to such small particles considered as ice, the data set of the TRIPEx-pol measurement campaign realized at the Jülich Observatory for Cloud Evolution Core Facility (JOYCE-CF) from November 2018 to February 2019 is now analyzed in synergy to evaluate the results obtained with the weather radars. Using cloud radars operating at three different wavelengths, it is also possible to determine the PSD (Particle Size Distribution) directly from the measured multifrequency Doppler spectrum via optimal estimation (e.g. Mróz et al. (2021)) and then compare the latter to the derived PSD from BoXPol. In summary, this may enable us to more accurately determine the variability or variance of the microphysical retrievals and analyze any differences/similarities and finally adapt or improve the parameterizations in ICON-GCM.

Figure 2: Boxplots representing the values of all time steps and heights for the IWC(Zlin, ZDRlin, KDP,) retrieval from Carlin et al. (2021). The y-axis represents the defined error ratio (σmean/σstd) and the x-axis the PPIs divided into different sectors sizes. The boxes representing the interquartile-range (IQR) and extend from the lower quartile (Q1) to the upper quartile (Q2) value, while the yellow line is the median. The whiskers extend from Q1-1.5*IQR to Q2+1.5*IQR.

References

• Bukovčić, P., Ryzhkov, A., & Zrnić, D. (2020): Polarimetric relations for snow estimation—Radar verification. Journal of Applied Meteorology and Climatology, 59(5), 991-1009.
  

• Carlin, J., Reeves, H., & Ryzhkov, A. (2021): Polarimetric Observations and Simulations of Sublimating Snow: Implications for Nowcasting. Journal of Applied Meteorology and Climatology.
  

• Delanoë, J., and R. J. Hogan, Combined CloudSat-CALIPSO-MODIS retrievals of the properties of ice clouds, J. Geophys. Res., 115, D00H29, doi:10.1029/2009JD012346, 2010.
  

• Giorgetta, M.A., R. Brokopf, T. Crueger, M. Esch, S. Fiedler, J. Helmert, C. Hohenegger, L. Kornblueh, M. Koehler, E. Manzini, T. Mauritsen, C. Nam, S. Rast, C. Reick, D. Reinert, M. Sakradzija, H. Schmidt, R. Schnur, L. Silvers, H. Wan, G. Zaengl, and B. Stevens, ICON-A, the atmospheric component of the ICON Earth System Model. Part I: Model Description, J. Adv. Model. Earth Syst., 10, 1613– 1637, doi:10.1029/2017MS001242, 2018.
  

• Kneifel, S., Kollias, P., Battaglia, A., Leinonen, J., Maahn, M., Kalesse, H., & Tridon, F. (2016): First observations of triple‐frequency radar Doppler spectra in snowfall: Interpretation and applications. Geophysical Research Letters, 43(5), 2225-2233.
  

• Kneifel, S., von Lerber, A., Tiira, J., Moisseev, D., Kollias, P., & Leinonen, J. (2015): Observed relations between snowfall microphysics and triple‐frequency radar measurements. Journal of Geophysical Research: Atmospheres, 120(12), 6034-6055.
  

• Mróz, K., Battaglia, A., Kneifel, S., von Terzi, L., Karrer, M., & Ori, D. (2021): Linking rain into ice microphysics across the melting layer in stratiform rain: a closure study. Atmospheric Measurement Techniques, 14(1), 511-529.
  

The work in the first year addresses the horizontal variability of cloud ice (WP 1) as well as accounting for this in the snow formation process via aggregation (WP 2).

Contribution of University Leipzig
A first goal of the Univ. Leipzig contribution to PARA was the evaluation of the subgrid-scale variability of cloud ice (Fig. 1, top). In the ICON general circulation model (Giorgetta et al., 2018), the cloud horizontal subgrid-scale variability is represented in terms of a “critical relative humidity” framework (Sundqvist et al., 1989) that corresponds to a uniform distribution of total-water specific humidity around its grid-box mean value (Quaas, 2012). In the present study, only ice clouds are considered, and the cloudy part of each grid box is isolated, i.e. the total-water amount that is beyond the saturation specific humidity with respect to ice.
From this, the variance of the subgrid-scale variability is computed (Quaas, 2012) and analysed at several isobaric levels. As a reference for the global distributions, satellite retrievals from the raDAR-liDAR approach by Delanoë and Hogan (2010) are used. From the high-resolved satellite data along the track within each 2.8° length, the variance of the ice specific mass is computed on the isobaric surfaces. The multi-year mean is compared to the ICON simulations (Fig. 2). The results show a relatively consistent geographical pattern between the model and the observations. However, some adjustments to the “critical relative humidity” parameter allow improving the simulation in the middle-to-upper troposphere. These new results will now be used to improve the representation of precipitation processes, and radar data will be used for an in-detail evaluation at a regional scale.

Figure 2: Geographical distributions of the annual-mean variance of the horizontal variability of specific cloud ice mass at different altitude levels from (top) 700 hPa to (bottom) 300 hPa at standard model resolution of about 2.8°. Left column: Standard ICON GCM; middle: ICON GCM with adjusted distribution width of the total-water variability; right: DARDAR satellite retrievals.

Contribution of University Bonn
At the University of Bonn the polarimetric radar measurements at C and X-band and the most recent ice microphysical retrievals (Murphy et al. 2018) for the ice particles number concentration N, the mean volume diameter Dm and the are used to investigate the ice variability above the melting layer. As an example Figure 3 shows for a rain event monitored with the polarimetric X-band radar in Bonn (BoXPol) the measured differential reflectivity ZDR and specific differential phase KDP in a time versus height display. Based on these measurements and horizontal reflectivity ZH, retrievals of number concentration Nt and mean volume diameter Dm are exstimated (Figure 4). Additional techniques are now implemented in order to disentangle statistical errors from spatial variability. Assuming an exponential distribution for ice particles aloft and distinguishing between cloud ice and aggregates/snow based on the smallest size a particle is assigned to snow in ICON-GCM (=100µm), observation-based retrievals of number concentration Nt, particle size Dm and ice water content IWC can, in extension to Figure 3, also be provided for ice and aggregates/snow particles separately. Together with the University of Leipzig, this information is subsequently used to assess the quality of the representation of cloud ice heterogeneity in the ICON GCM and suggest possible improvements.


Figure 3: Quasi-Vertical Profiles (QVPs) measured with the polarimetric X-band radar in Bonn on 7 October 2014 between 0 and 3:30 UTC. Panels show differential reflectivity ZDR (left) and specific differential phase KDP (right). Overlaid black solid and dashed lines indicate the 0, -5, -10 and -15°C temperature height level simulated with COSMO for the radar location


Figure 4: Estimated number concentration of ice particles (pristine crystals and snow) and mean volume diameter for 7 October 2014 between 0 and 3:30 UTC using the polarimetric X-band radar measurments in Bonn (see Figure 3).


References

• Delanoë, J., and Hogan R. J, Combined CloudSat-CALIPSO-MODIS retrievals of the properties of ice clouds, J. Geophys. Res., 115, D00H29, doi:10.1029/2009JD012346, 2010.
  

• Marshall, J. S., and Palmer, W., The distribution of raindrops with size. Journal of Meteorology, 5, 165–166, 1948.
  

• Mewes, D., Stochastic Parameterization of Precipitation in the ECHAM6 General Circulation Model, Master‘s thesis, University of Leipzig, 29 pp., available at Mewes Daniel Masterarbeit 2016
  

• Murphy, A., Ryzhkov, A., Zhang, P., McFarquhar, G., Wu, W., & Stechman, D., A polarimetric and microphysical analysis of the stratiform rain region of MCSs. In Annual American Meteorological Society Meeting, January 8–11, Austin, TX, 2018.
  

• Quaas, J., Evaluating the “critical relative humidity” as a measure of subgrid-scale variability of humidity in general circulation model cloud cover parameterizations using satellite data. J. Geophys. Res., 117, D09208, doi:10.1029/2012JD017495, 2012.
  

• Sundqvist, H., et al., Condensation and cloud parameterization studies with a mesoscale numerical weather prediction model, Mon. Weather Rev., 117, 1641–1657, 19
  

• Ulbrich, C., Natural variations in the analytical form of the raindrop size distribution. Journal of Climate and Applied Meteorology, 22, 1764–1775, 1983.
  

• Weber, T., and Quaas J., Incorporating the subgrid-scale variability of clouds in the autoconver¬sion parameterization. J. Adv. Model. Earth Syst., 4, M11003, doi:10.1029/2012MS000156, 2012.