We have implemented a parameterization for contrail cirrus in the high resolution ICON-LEM model (resolution of 600m) to study the impact of contrail formation on cloud properties. In particular we study the modification of natural clouds due to contrail ice crystal formation within clouds. The number of ice crystals nucleating within the plume depends on soot number emissions and the atmospheric state. After ice crystal formation most of the contrail ice crystals are trapped within downward propagating vortices and depending on the atmospheric conditions a fraction of ice crystals sublimate due to adiabatic heating of the air volume. Contrail formation within cirrus introduces a large increase in the ice crystal number concentration of clouds. Ice water content, on the other hand, is not strongly disturbed since water vapor aircraft emissions are low relative to the atmospheric water vapor. The many small ice crystals lead to an increase in cloud optical depth. The modification in ice crystal numbers is especially pronounced in natural clouds that have low number concentrations and relative high in-cloud relative humidity. We study the modification of natural cloud properties induced by contrail formation within clouds, the resulting changes in microphysical process rates and the life time of those cloud perturbations.