Traditional indexing techniques commonly employed in da\-ta\-ba\-se systems perform poorly on multidimensional array scientific data. Bitmap indices are widely used in commercial databases for processing complex queries, due to their effective use of bit-wise operations and space-efficiency. However, bitmap indices apply natively to relational or linearized datasets, which is especially notable in binned or compressed indices. We propose a new method for multidimensional array indexing that overcomes the dimensionality-induced inefficiencies. The hierarchical indexing method is based on $n$-di\-men\-sional sparse trees for dimension partitioning, with bound number of individual, adaptively binned indices for attribute partitioning. This indexing performs well on range involving both dimensions and attributes, as it prunes the search space early, avoids reading entire index data, and does at most a single index traversal. Moreover, the indexing is easily extensible to membership queries. The indexing method was implemented on top of a state of the art bitmap indexing library Fastbit. We show that the hierarchical bitmap index outperforms conventional bitmap indexing built on auxiliary attribute for each dimension. Furthermore, the adaptive binning significantly reduces the amount of bins and therefore memory requirements.