The society is strongly influenced by precipitation, which forms by cloud microphysical processes, e.g., sedimentation and aggregation. These processes determine where and how clouds precipitate relevant for the global water cycle, freshwater availability, and flooding. However, the precipitation forming processes are poorly understood and pose a significant challenge to earth system modeling. Challenges arise from the difficulties of deriving parameterizations from laboratory experiments or observations. Even if accurate process parameterizations could be derived, implementing them into numerical models poses additional challenges due to computational cost and unresolved scales. In the last decades, rapid progress has been made in modeling and observing microphysical processes, which enables or even necessitates further studies that exploit the synergy between both fields. In this thesis, microphysical models are employed that either resolve the microphysical processes up to the single particle level (3D snowflake model and Lagrangian particle model) or are computationally efficient (bulk scheme). The explicit models are used to derive parameterizations and provide detailed insights into the processes that can be used in the less explicit models. Improving the less explicit but computationally efficient bulk schemes is particularly important, as they are indispensable for weather and climate prediction. Output from all models is compared to observations that provide information either on individual particle properties (in situ particle observations) or average properties of large particle ensembles (multi-frequency Doppler radar observations). These model-observation combinations are used to improve the knowledge about the microphysical processes and their representation in the microphysical models. 3D snowflake models simulate the complex shape of ice particles, the representation of which presents a major difficulty for microphysical schemes. In Study I, such a 3D snowflake model is used to derive parameterizations of particle properties, such as mass as a function of size, monomer number and shape. Hydrodynamic models are used to additionally derive the particle velocity. The most detailed parameterizations are used to assess the effect of aggregate composition on the particle properties, which is challenging to do with observations alone. It is found that aggregate properties change smoothly with increasing monomer number but differ substantially depending on the monomer shapes that constitute the aggregates. Other, less detailed parameterizations can be readily applied in bulk microphysical schemes to improve the physical consistency of these schemes. In simulations with a Lagrangian particle model, it can be shown that these less detailed parameterisations are very accurate even if they only distinguish between the two classes of monomers and aggregates. Comparing the parameterization with in situ observations ensures that they are physically realistic in size ranges where observations are available. In addition, the physical principles of the 3D snowflake and hydrodynamic models help to ensure that the parameterizations are realistic even in size ranges for which it is difficult to obtain observations. In Study II, parameters that are important for the microphysical description of sedimentation and aggregation in a two-moment scheme bulk microphysics scheme are constrained by observations. Traditionally, microphysical parameterizations are tuned to improve the prediction of few variables of interest, such as the precipitation rate. This procedure likely introduces compensating errors, since adjusting one parameter may improve the prediction of these variables even if that change leads away from the most physically meaningful value of the parameters. Therefore, a different approach is used in this study that uses several variables from multi-frequency Doppler radars simultaneously and focuses on single or few processes to avoid this issue of underdetermined parameters. First, the observed statistics are used to evaluate microphysical parameters in an idealized 1D model, which allows efficient testing of all key parameters. These simulations reveal that the simulation of aggregation is most sensitive to the aggregate particle properties, the aggregation kernel formulation and the size distribution width and less sensitive to the monomer habit and the sticking efficiency. A statistical comparison between 3D large-eddy simulations with the default and the new scheme setup and the observations show that previously existing large biases of too fast and too large particles in the scheme could be substantially reduced. This bias reduction can be attributed to the improved simulation of sedimentation and aggregation. Since a large portion of precipitation reaches the ground as rain but forms in the ice phase, processes in the melting layer are an essential part of precipitation modeling. In Study III, an approach is used to infer the dominance of growth or shrinkage processes through the relationship of reflectivity flux at the melting layer boundaries. In addition, radar Doppler spectra and multi-frequency observations are used to evaluate assumptions of the approach and to classify profiles according to the degree of riming. For unrimed profiles, growth processes increase the mean mass only slightly. For rimed profiles, shrinking processes lead to a substantial decrease the mean mass probably caused by particle breakup. Simulations using a Lagrangian particle model reveal that breakup processes for which parameterizations are available can not reproduce the observed decrease of the mean mass for rimed profiles and suggest that further laboratory studies of collisional breakup of melting particles are needed.