This paper presents a stochastical approach for the aggregation process rate in the ICON-GCM, which takes subgrid-scale variability into account. This method creates a stochastic parameterisation of the process rate by choosing a new specific cloud ice mass at random from a uniform distribution function. This distribution, which is consistent with the model's cloud cover scheme, is evaluated in terms of cloud ice mass variance with a combined satellite retrieval product (DARDAR) from the satellite cloud radar CloudSat and cloud lidar CALIPSO. For a realistic comparison with the simulated cloud ice, an estimate of precipitating and convective cloud ice is removed from the observational data set. The global patterns of simulated and observed cloud ice mixing ratio variance are in a good agreement, despite some regional differences. Due to this stochastical approach the yearly mean of cloud ice shows an overall decrease. As a result of the non-linear nature of the aggregation process, the yearly mean of the process rates increases when taking subgrid-scale variability into account. An increased process rate leads to a stronger transformation of cloud ice into snow and therefore, to a cloud ice loss. The yearly averaged global mean aggregation rate is more than 20 % higher at selected pressure levels due to the stochastical approach. A strong interaction of aggregation and accretion, however, lowers the effect of cloud ice loss due to a higher aggregation rate. The presented new stochastical method lowers the bias of the aggregation rate. [ABSTRACT FROM AUTHOR]