  Today's scientific simulations require significant data volume reduction
because of the enormous amounts of data produced and the limited I/O bandwidth
and storage space. Error-bounded lossy compression has been considered one of
the most effective solutions to the above problem. However, little work has
been done to improve error-bounded lossy compression for Adaptive Mesh
Refinement (AMR) simulation data. Unlike the previous work that only leverages
1D compression, in this work, we propose an approach (TAC) to leverage
high-dimensional SZ compression for each refinement level of AMR data. To
remove the data redundancy across different levels, we propose several
pre-process strategies and adaptively use them based on the data features. We
further optimize TAC to TAC+ by improving the lossless encoding stage of SZ
compression to handle many small AMR data blocks after the pre-processing
efficiently. Experiments on 10 AMR datasets from three real-world large-scale
AMR simulations demonstrate that TAC+ can improve the compression ratio by up
to 4.9$\times$ under the same data distortion, compared to the state-of-the-art
method. In addition, we leverage the flexibility of our approach to tune the
error bound for each level, which achieves much lower data distortion on two
application-specific metrics.
