Alternating scanning orders and combining algorithms to improve the efficiency of flow accumulation calculation

Conventionally, a raster operation that needs to scan the entire image employs only one scanning order (i.e., single scanning order (SSO)), and the scan usually runs from upper left to lower right and row by row. We explore the idea of alternately applying multiple scanning orders (MSO) to raster operations that are based on the local direction, using the flow accumulation (FA) calculation as an example. We constructed several FA methods based on MSO, and compared them with those widely used methods. Our comparison includes experiments over digital elevation models (DEMs) of different landforms and DEMs of different resolutions. For each DEM, we calculated both single-direction FA (SD-FA) and multi-direction FA (MD-FA). In the theoretical aspect, we deducted the time complexity of an MSO sequential algorithm (MSOsq) for FA based on empirical equations in hydrology. Findings from the experiments include the following: (1) an MSO-based method is generally superior to its counterpart SSO-based method. (2) The advantage of MSO is more significant in the SD-FA calculation than in the MD-FA calculation. (3) For SD-FA, the best method among the compared methods is the one that combines the MSOsq and the depth-first algorithm. This method surpasses the commonly recommended dependency graph algorithm, in both speed and memory use. (4) The differences between the compared methods are not sensitive to specific landforms. (5) For SD-FA, the advantage of MSO-based methods is more obvious in a higher DEM resolution, but this does not apply to MD-FA.