Computing water flow through complex landscapes, Part 3: Fill-Spill-Merge: Flow routing in depression hierarchies

Abstract

Abstract. Depressions – inwardly-draining regions – are common to many landscapes. When there is sufficient moisture, depressions take the form of lakes and wetlands; otherwise, they may be dry. Hydrological flow models used in geomorphology, hydrology, planetary science, soil and water conservation, and other fields often eliminate depressions through filling or breaching; however, this can produce unrealistic results. Models that retain depressions, on the other hand, are often undesirably expensive to run. In previous work we began to address this by developing a depression hierarchy data structure to capture the full topographic complexity of depressions in a region. Here, we extend this work by presenting a Fill-Spill-Merge algorithm that utilizes our depression hierarchy to rapidly process and distribute runoff. Runoff fills depressions, which then overflow and spill into their neighbors. If both a depression and its neighbor fill, they merge. We provide a detailed explanation of the algorithm as well as results from two sample study areas. In these case studies, the algorithm runs 90–2600× faster (with a 2000–63 000× reduction in compute time) than the commonly-used Jacobi iteration and produces a more accurate output. Complete, well-commented, open-source code is available on Github and Zenodo.

Computing water flow through complex landscapes – Part 2: Finding hierarchies in depressions and morphological segmentations

“…Likewise, in image processing and segmentation, regions of differing image intensity and color can be modeled as depressions that represent either noise or features of interest. In this context, geomorphological algorithms for depression handling (e.g., Barnes et al, 2014b) have been applied to cosmic microwave background radiation (Giri et al, 2017), nanoparticle chemistry (Svoboda et al, 2018), biological membranes (Kulbacki et al, 2017), road-car segmentation (Beucher, 1994), murder and crime statistics (Khisha et al, 2017), remote sensing of buildings (Golovanov et al, 2018), neuron mapping (Iascone et al, 2020), and metal defect mapping (Blikhars'kyi and Obukh, 2018). This multidisciplinary set of uses demonstrates the broad potential of a generalized algorithm that can compute depressions and their topology.…”

“…This problem is similar to one in image processing, in which a computer must reassemble multiple distinctlooking features into a meaningful whole. For example, oversegmentation can cause features such as cars to be fragmented into many small pieces (Beucher, 1994). Understanding the relationships between topographic depressions can aid the general goal of building relational hierarchies among adjacent objects and in so doing can reduce oversegmentation by providing a principled way of merging small features and extracting composite features of interest.…”

“…Prior researchers have developed structures with similar purpose -and in some cases, function -as depression hierarchies, but these either yield nondeterministic results, are not developed in a way to permit dynamic water flow through a set of nested depressions, or are prohibitively slow. Beucher (1994) presents a hierarchical segmentation algorithm for images using a "waterfall" approach that merges adjacent features by filling smaller local minima while maintaining significant minima that can act as a sink over larger regions. However, this waterfall algorithm does not produce a persistent data structure to be used in subsequent operations nor does it construct a full hierarchy as an intermediate product.…”