Today's scientific simulations, for example in the high-performance exascale sector, produce huge amounts of data. Due to limited I/O bandwidth and available storage space, there is the necessity to reduce scientific data of high performance computing applications. Error-bounded lossy compression has been proven to be an effective approach tackling the trade-off between accuracy and storage space. Within this work, we are exploring and discussing error-bounded lossy compression solely based on adaptive mesh refinement techniques. This compression technique is not only easily integrated into existing adaptive mesh refinement applications but also suits as a general lossy compression approach for arbitrary data in form of multi-dimensional arrays, irrespective of the data type. Moreover, these techniques permit the exclusion of regions of interest and even allows for nested error domains during the compression. The described data compression technique is presented exemplary on ERA5 data.