Identification and Filling of Surface Depressions in DEMs for Hydrologic Modeling

1
Identification and Filling of Surface Depressions
in DEMs for Hydrologic Modeling

• Lei Wang
• Department of Geography
• Texas AM University
• College Station, TX 77843

2
Talk Outline

• Research background
• New concept and method
• An application example
• Conclusions

3
GIS applications in hydrologic modeling
4
GIS-based terrain analysis in hydrologic modeling
Flow accumulation
Flow direction
Elevation Model
Flow Accumulation
Flow Direction
Watersheds
Stream network
5
Surface Depressions as Problems
Spurious internal Sub-watersheds
Discontinues stream segments
6
Surface Depressions

• Also known as pits or sinks
• Generally, the sink and its neighboring cells
  will form an internal basin, which drains into
  the sink cell

7
Numeric definition

• A single cell depression is a local minima with
  no defined outflow
• Eight flow direction

Flow direction
Elevation Model
Flow direction model
8
Methods for surface depression detection and
filling

• The earlier one by Marks et al. (1984)
• The most widely used algorithm, by Jenson and
  Domingue (1988) by many GIS software
• Arc/Info, GRASS, HEC GEO-HMS
• CRWR-PREPRO, TOPOZ ,TARDEM, TAPES-G, RiverTools

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Pour Point for Depression filling

• Water surface will increase when surface
  depression is filled by water

Pour Point

• Water will spill out through the lowest cell on
  the internal catchment boundary

• This cell is identified as Pour Point

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Depression-filling Algorithm By Marks et al. 1984
Time complexity is O(N2)
Elevation
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Depression-filling Algorithm By Jenson and
Domingue
Time complexity is O(N2)
Elevation
watershed 4 (by merging 1 and 2)
Merge looped pour points and find new pour point
Fill depression to pour point elevation
Partition of sub-watersheds
Locate pour points
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Running Time and Data Size
17 hours
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Disadvantages of Traditional Methods

• Time complexity is O(N2)
• Computationally intensive
• Very time-consuming for processing a large
  data set
• Many steps of operations involved
• Compute flow direction
• Label depression areas
• Build pour point table
• Merge looped pour points
• Fill to pour point elevation
• Requires large volume of intermediate storage
  space

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The Need for Better Algorithm

• High-quality DEMs from new technologies (LIDAR
  and IFSAR)

5m resolution LIDAR DEM
30 m resolution USGS DEM
Data volume increases by over 36 times
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The Need for Better Algorithm

• The number of surface depressions that are
  identified by the high-resolution DEMs is
  increased dramatically

e
Depressions detected from USGS DEM
Depressions detected from LIDAR DEM
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Talk Outline

• Research background
• New concept and method
• An application example
• Conclusions

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Two Cornerstones

• A new concept
• Spill Elevation
• Optimal flow path in 2D space
• Least-cost Search

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Concept of Spill Elevation

• Spill elevation for a cell is the minimum
  elevation required to spill water out of the cell
  to an outlet

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Definition of Spill Elevation (SE)
Spill Elevation
Elevation
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Calculation of Spill Elevation in one dimension
Elevation
c0
ci-1
ci
ci1
cn
SE (i) max SE (i-1) Elev (i)
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Searching in A Wrong Direction
SE (i) max SE (i-1) Elev (i)
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Search Paths in two-dimensional Space
3 3 Totally 8 different paths to reach the
outlet
5 5 Totally 1792 paths
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Searching for optimal flow path in
two-dimensional space

• Least-cost Search
• cost function
• SE(i) maxSE(i-1)Elev(i)
• Progressively determine optimal flow path from
  outlets to internal cells in a upstream direction

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Priority Queue
Least-cost Search with
15 2,1
13 3,1
15 1,1
5
Column
11 1,2
11 2,2
11 3,2
0
6
0
Row
Elevation Grid
12 3,3
11 2,3
16 1,3
Priority Queue
15 1,4
8 2,4
Spill Elevation
7 1,5
15 2,5
17 3,5
15 3,4
5 1,6
6 4,5
Filled Depth
Root
Root
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Derived Flow Direction and Watershed Partition
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Pseudo Codes

• For b ? cells on data boundary
• SEb ? Elevationb
• OPEN.push(b)
• While OPEN is not empty
• s ? OPEN.top()
• OPEN.pop()
• CLOSED.push(s)
• For n ? neighbors of s
• If n ? OPEN or n ? CLOSED
• Then do nothing
• Else
• SEn ? Max(Elevationn, SEs)
• OPEN.push(n)

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Performance Evaluation
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59,878
more than 130 times more time
Data Processing Time
Time Seconds
16,000
14,000
12,971
12,000
10,000
8,000
6,000
4,497
4,000
30
68
1,563
2,000
114
325
652
1
2
5
Traditional Method
0
11
23
48
100
210
456
250,000
500,000
1,000,000
2,000,000
My Method
4,000,000
8,000,000
16,000,000
32,000,000
64,000,000
Number of Pixels Doubling Data Volume
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Advantages

• Efficiency
• O ( NlogN) vs. O(N2)
• Over 30 times faster than traditional methods
• Multiple products from single-pass processing
• Depressionless DEM
• Surface depressions and filling-depths
• Flow direction
• Watershed partition
• Compact program code
• Easy to understand
• Easy to implement

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Talk Outline

• Research background
• New concept and method
• An application example
• Conclusions

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LIDAR DEM
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Detected Surface Depressions
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Geometric Attributes of Objects
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Classification Result
Large Detentions
Connected Linear Features
Linear Features
Small Detentions
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Detention Basins in White Oak Bayou Watershed,
Houston
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Comparison with Manually Derived Detention Basins
Average Delineation Difference 10.12 m
Storage Volume Error 4.6
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3D View of Detention Basins
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Conclusions

• The conventional depression-detection algorithm
  in GIS software packages is inefficient and
  inadequate to handle massive data sets

• I proposed a new concept Spill Elevation which
  is fundamentally important for hydrologic
  modeling of topography

• I developed a new algorithm to identify surface
  depressions in DEMs based on least-cost search
  and priority queue

• Detailed surface structures like detention basins
  can be detected and quantified by applying my
  method to LIDAR DEMs

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Acknowledgement

• NASA Earth Science Student Fellowship
• Academic advisor Dr. Hongxing Liu
• William B. Meyer
• Program manager
• Harris County Flood Control District
• Houston, Texas