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

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.

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

Earth Surface Dynamics ◽

10.5194/esurf-9-105-2021 ◽

2021 ◽

Vol 9 (1) ◽

pp. 105-121

Author(s):

Richard Barnes ◽

Kerry L. Callaghan ◽

Andrew D. Wickert

Keyword(s):

Data Structure ◽

Water Conservation ◽

Source Code ◽

Planetary Science ◽

Topographic Complexity ◽

Flow Models ◽

Detailed Explanation ◽

Jacobi Iteration ◽

Flow Through ◽

Compute Time

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.

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Computing water flow through complex landscapes, part 1: Incorporating depressions in flow routing using FlowFill

10.5194/esurf-2019-11 ◽

2019 ◽

Author(s):

Kerry L. Callaghan ◽

Andrew D. Wickert

Keyword(s):

Water Flow ◽

Water Conservation ◽

Planetary Science ◽

Rapid Expansion ◽

Hydrologic Connectivity ◽

Drainage Network ◽

Flow Routing ◽

Data Errors ◽

Hydrologic System ◽

Flow Through

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 longstanding problem of emerging significance, we developed FlowFill, an algorithm that routes a prescribed amount of runoff across the surface in order to flood depressions, but only 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. Typical FlowFill calculations take minutes to perform and permit more realistic analyses of water flow across landscapes.

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Computing water flow through complex landscapes – Part 1: Incorporating depressions in flow routing using FlowFill

Earth Surface Dynamics ◽

10.5194/esurf-7-737-2019 ◽

2019 ◽

Vol 7 (3) ◽

pp. 737-753 ◽

Cited By ~ 2

Author(s):

Kerry L. Callaghan ◽

Andrew D. Wickert

Keyword(s):

Water Conservation ◽

Planetary Science ◽

Rapid Expansion ◽

Hydrologic Connectivity ◽

Drainage Network ◽

Watershed Scale ◽

Flow Routing ◽

Data Errors ◽

Hydrologic System ◽

Flow Through

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.

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