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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 the Fill–Spill–Merge algorithm that utilizes our depression hierarchy data structure 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 and results from two sample study areas. In these case studies, the algorithm runs 90–2600 times faster (with a reduction in compute time of 2000–63 000 times) than the commonly used Jacobi iteration and produces a more accurate output. Complete, well-commented, open-source code with 97 % test coverage is available on GitHub and Zenodo. 

Abstract. Depressions – inwardly draining regions of digital elevation models – present difficulties for terrain analysis and hydrological modeling. Analogous “depressions” also arise in image processing and morphological segmentation, where they may represent noise, features of interest, or both. Here we provide a new data structure – the depression hierarchy – that captures the full topologic and topographic complexity of depressions in a region. We treat depressions as networks in a way that is analogous to surface-water flow paths, in which individual sub-depressions merge together to form meta-depressions in a process that continues until they begin to drain externally. This hierarchy can be used to selectively fill or breach depressions or to accelerate dynamic models of hydrological flow. Complete, well-commented, open-source code and correctness tests are available on GitHub and Zenodo. 

Climatic warming following the Last Glacial Maximum caused the southern Laurentide Ice Sheet (LIS) to begin ∼2,000‐year cycles of retreat and readvance whose cause remains ambiguous. By developing a marine‐calibrated chronology of southern LIS position, we counterintuitively demonstrate that between 17.6 and 11.3 ka, ice advanced during times of northern‐hemisphere warming and retreated during times of northern‐hemisphere cooling. Here we propose a cyclical feedback: Meltwater from ice retreat cooled the northern hemisphere by weakening the Atlantic Meridional Overturning Circulation (AMOC). This eventually lead to ice‐sheet readvance, which reduced and rerouted meltwater discharge, and thereby allowed the AMOC to strengthen and the northern hemisphere to warm. Our data suggest that this antiphased ice–climate interaction, paced by ice‐sheet response time, was initiated by synchronous warming and ice retreat ∼18.7–17.6 ka (corresponding to the Erie “Interstade”) and reached its apex during the Younger Dryas.

 

Abstract. Calculating flow routing across a landscape is a routine process in geomorphology, hydrology, planetary science, and soil and water conservation. Flow-routing calculations often require a preprocessing step to remove depressions from a DEM to create a “flow-routing surface” that can host a continuous, integrated drainage network. However, real landscapes contain natural depressions that trap water. These are an important part of the hydrologic system and should be represented in flow-routing surfaces. Historically, depressions (or “pits”) in DEMs have been viewed as data errors, but the rapid expansion of high-resolution, high-precision DEM coverage increases the likelihood that depressions are real-world features. To address this long-standing problem of emerging significance, we developed FlowFill, an algorithm that routes a prescribed amount of runoff across the surface in order to flood depressions if enough water is available. This mass-conserving approach typically floods smaller depressions and those in wet areas, integrating drainage across them, while permitting internal drainage and disruptions to hydrologic connectivity. We present results from two sample study areas to which we apply a range of uniform initial runoff depths and report the resulting filled and unfilled depressions, the drainage network structure, and the required compute time. For the reach- to watershed-scale examples that we ran, FlowFill compute times ranged from approximately 1 to 30 min, with compute times per cell of 0.0001 to 0.006 s.