Generating hollow or pit free DEMs

1
Generating hollow or pit free DEMs

• The How

2
The Problem As Stated By Chris

• From a cell in the channel of my DEM I need to be
  able to trace uphill and find every cell
• Another way to look at it is that from every cell
  in my DEM I need to be able to go downhill in any
  way and reach the channel and not get stuck in a
  hollow
• basically, my DEM has hollows and for a model I
  am using I effectively need to get rid of the
  hollows by filling them in
• actually what I need is for the maximum flow
  direction path from every cell to eventually end
  up in the channel

3
Immediate questions

• What constitutes a contiguity?
• What sort of neighbourhoods are we dealing with?
• In this case all cells in a 3x3 so diagonals are
  allowed
• NB. This is a special case of a circle so an
  extension might be to relax the contiguity
  condition to a neighbourhood defined by some
  function
• Is your DEM one block and does it roughly
  represent a catchment?
• If so pick a cell where to cal the outflow
• Why an earth would you want to do this?
• What is the result to be used for?
• Modelling floods?
• Concentrate on how

4
How to fill in the hollows?

• The first thing to do is find them
• This involves going through the entire dataset
  analysing differences height (flows)

10 9 8
11 10 9
12 6
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Identify the hollows

• A cell that is not noData and is surrounded by
  cells which are either higher or noData or the
  same height

10 10 11
11 10 12
12 11
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Fill hollows quickly and efficiently

• Easy?
• Simply raise all the hollows height to be equal
  to the minimum height of their neighbours plus a
  little bit
• Done?
• No because new hollows may have been created
• So repeat everything until there are no more
• That should work eventually, but it may take a
  very very long time!

7
Anyway what is a little bit?

• From now on lets call it tollerance
• The smallest number that can be added to
  (subtracted from) the number so that I have a
  number that is recognisably larger (smaller) than
  the number I started with given the precision of
  numbers I am dealing with
• The minimum y such that
• x y gt x and x - y lt x

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Ding dong hollows

• Consider the following part of the DEM

13 14 14 31
11 6 7 32
10 51 15 42
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An agent based approach

• If we knew that a hollow at this iteration is
  next to a hollow at the last iteration then they
  could be treated as part of the same hollow
• Likewise if we knew that a hollow at this
  iteration is next to another hollow then we can
  also treat them as part of the same hollow
• We can use cellular agents to trace out the
  bottom of each hollow and raise it to the height
  of its minimum neighbours adding those neighbours
  to the hollow until we find a downhill
• This can be explained with a wiggly line

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A wiggly line
Another Hollow
Top
3
2
1
4
Channel
Initial Hollows
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The basic algorithm

1. Calculate initial hollows and add these to a set
   of known hollows
2. Select a hollow that has not yet been treated
3. Trace the bottom of the hollow finding all
   adjoining hollows
4. Calculate the minimum height of the neighbours of
   the traced hollow and add these neighbours to the
   hollow set so long as they are not lower than the
   current height of the hollow
5. Raise all cells in the hollow set to the
   calculated minimum height tollerance
6. Repeat Steps 2 to 6 until all hollows treated
7. Check every cell visited to see if it is now a
   hollow
8. Repeat steps 2 to 8 until there are no more
   hollows

12
Simple?

• Easy to implement?
• When you know how
• The code was written in Java as part of a grids
  package that can do all sorts of other
  interesting and useful things
• The whole thing is based on collections
• These are what remember things (like where we
  have been and what the hollow set is) by
  containing the IDs of cells
• Think of the IDs as the row column index

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Java Collections

• What is so good about them?
• Convenience
• It is easy to add to them and remove from them
  other collections and individual objects
• It is easy to iterate through the elements
  (objects) in the collection
• It is easy to test whether they contain something
• They are fast, efficient and reliable
• There are many different sorts of collections
• HashTables
• HashTrees
• Lists etc
• The main collections used were HashSets and the
  following snippet ofJava code instantiates
  (creates a new) one
• HashSet hs new HashSet()
• The following Java code adds a cellID object to
  it
• hs.add( cell )
• The following Java code removes all the elements
  (objects) in hs from another collection c

14
Questions

• How fast is the implementation?
• Fast enough?
• Quantifying just how fast is a non-trivial task
  and to do it well we need
• A standard set of datasets for testing
• To test on different machines with different
  processors and different sizes and types of
  memory
• Is the implementation scaleable?
• Yes, you do not have to rely on that RAM stuff it
  works efficiently with files on disc
• What other methods for DEMs are in the grids
  package?

15
Discussion

• Would any extensions or modifications be useful?
• Identifying the catchments
• Identifying the channel etc like Peter Fisher
• Surely this agent based approach has been done
  and written about before
• If we think it is worth writing up we should
  refer to where and when
• Do we think it is worth writing up yet or do we
  need something more first, and if so what?