The paper starts with a classification of climate modeling in Big Data and presents research activities in DKRZ's two basic climate modeling workflows, the climate model development and the climate model data production. Research emphasis in climate model development is on code optimization for efficient use of modern and future multi-core high performance computing architectures. Complementary research is related to increase of I/O bandwidth between compute nodes and hard discs as well as efficient use of storage resources. Research emphasis in climate model data production is on optimization of the end-to-end workflow in its different stages starting from climate model calculations over generation and storage of climate data products and ending in long-term archiving, interdisciplinary data utilization research data publication for integration of citable data entities in scientific literature articles.