Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models (1511.04463v1)

Abstract: Depressions (or pits) are low areas within a digital elevation model that are surrounded by higher terrain, with no outlet to lower areas. Filling them so they are level, as fluid would fill them if the terrain were impermeable, is often necessary in preprocessing DEMs. The depression-filling algorithm presented here---called Priority-Flood---unifies and improves on the work of a number of previous authors who have published similar algorithms. The algorithm operates by flooding DEMs inwards from their edges using a priority queue to determine the next cell to be flooded. The resultant DEM has no depressions or digital dams: every cell is guaranteed to drain. The algorithm is optimal for both integer and floating-point data, working in O(n) and O(n lg n) time, respectively. It is shown that by using a plain queue to fill depressions once they have been found, an O(m lg m) time-complexity can be achieved, where m does not exceed the number of cells n. This is the lowest time complexity of any known floating-point depression-filling algorithm. In testing, this improved variation of the algorithm performed up to 37% faster than the original. Additionally, a parallel version of an older, but widely-used depression-filling algorithm required six parallel processors to achieve a run-time on par with what the newer algorithm's improved variation took on a single processor. The Priority-Flood Algorithm is simple to understand and implement: the included pseudocode is only 20 lines and the included C++ reference implementation is under a hundred lines. The algorithm can work on irregular meshes as well as 4-, 6-, 8-, and n-connected grids. It can also be adapted to label watersheds and determine flow directions through either incremental elevation changes or depression carving. In the case of incremental elevation changes, the algorithm includes safety checks not present in prior works.

• The paper introduces the Priority-Flood algorithm, an optimal and efficient method for filling depressions and labeling watersheds in digital elevation models (DEMs).
• Using a priority queue approach, the algorithm achieves optimal time complexity of O(n) or O(n log n) for integer and floating-point data, respectively, outperforming previous methods empirically.
• Priority-Flood is versatile, applicable to watershed labeling and flow direction determination, with potential for integration into GIS for broader geospatial analysis.

An Overview of the Priority-Flood Algorithm for Digital Elevation Models

The paper "Priority-Flood: An Optimal Depression-Filling and Watershed-Labeling Algorithm for Digital Elevation Models" presents a detailed exploration of an algorithmic solution for handling depressions within digital elevation models (DEMs). This domain-specific concern arises due to depressions—low-lying areas enclosed by elevated regions that lack an outlet. The efficient preprocessing of DEMs necessitates the ability to fill these depressions to ensure that each cell can drain, thus supporting accurate hydrological and geomorphic analyses.

Algorithm Description and Complexity

The Priority-Flood algorithm emerges as a robust solution to the depression-filling problem. It uses a priority queue to manage cells based on elevation, initiating from the edges of the DEM. As the algorithm proceeds, it ensures that every cell is connected to the DEM's edge through an outlet. This method guarantees optimal performance for both integer and floating-point data, with time complexities of $O(n)$ and $O(n \log_2 n)$, respectively. Notably, for floating-point data, this complexity can be reduced further to $O(m \log_2 m)$ by utilizing a plain queue for depression cells, where $m$ is no greater than $n$.

The paper notes an empirical speed improvement of up to 37% over the original variant of the algorithm when using this improved approach. Additionally, the implementation simplicity is emphasized, with the pseudocode and reference implementations being relatively compact, making the algorithm both accessible and efficient.

Comparison with Other Algorithms

In comparing previous approaches, most notably the Planchon-Darboux algorithm, the Priority-Flood algorithm demonstrates superior performance. While competing methods require excessively complex operations or fail to scale efficiently with large data sets, Priority-Flood offers a consistent and optimal solution across varying DEM resolutions and data sizes.

Application and Adaptation

The Priority-Flood algorithm extends beyond depression filling. It is adaptable for watershed labeling and can facilitate the determination of flow directions in DEMs—either by exploiting incremental elevation changes or through an approach termed 'depression carving.' This flexibility significantly enhances its utility in terrain analysis tasks.

Implications and Future Directions

The mathematical rigor and practical utility of Priority-Flood have clear implications for geospatial analysis and hydrological modeling. By delivering a reliable mechanism for preprocessing DEMs, the algorithm substantially aids in the estimation of hydrological characteristics such as flow direction and accumulation.

Looking ahead, advancements in DEM resolution will likely escalate computational demands. Future research might explore the parallelization of the Priority-Flood Algorithm further, leveraging modern architectural capabilities to accommodate increasingly complex topographical data sets with even greater efficiency. Additionally, integrating Priority-Flood into comprehensive geographic information systems (GIS) could expand its impact across diverse applications in environmental monitoring and management.

Conclusion

The Priority-Flood algorithm provides an optimal and versatile solution to the depression-filling challenge in digital elevation models. The algorithm's robust performance across various data types and its adaptability for associated geospatial tasks make it a valuable tool in hydrological analysis, illustrating a significant advancement in terrain preprocessing methodologies.