automated extraction of landforms from dem data
DESCRIPTION
Provides an overview of methods of automated landform classificationR. A. (Bob) MacMillanRemote Predictive Mapping (RPM) WebinarGovernment of Canada seriesTRANSCRIPT
Automated Extraction of Landforms from DEM data
R. A. MacMillanLandMapper Environmental Solutions Inc.
Outline• Rationale for Automated Landform
Classification– Theoretical, methodological, cost and
efficiency arguments• Classification of Landform Elements
– Conceptual underpinnings – hill slope segments
– Implementation methods – various examples• Classification of Landform Patterns
– Conceptual underpinnings – size, shape, scale, context
– Implementation methods – various examples• Miscellaneous Bits and Pieces
– Thoughts and ideas that may or may not prove useful
• Discussion and Conclusions– What works and what doesn’t?– Future developments & challenges to be
addressed
Rationale for Automated Landform Classification
Scientific and theoretical arguments
Business case – costs and efficiency
Rationale: Scientific and Theoretical
• Why Delineate Landforms?– Landforms define boundary
conditions for processes operative in the fields of:• Geomorphology• Hydrology• Ecology• Pedology• Forestry ... others
– Landforms control or influence the distribution and redistribution of water, energy and matterSource: MacMillan and Shary, (2009)
Rationale: Costs and Efficiency
• Why Automate the Delineation of Landforms?– Speed and cost of production
• Never likely to ever again see investments in large groups of human interpreters to produce global maps
• Governments can’t afford and are unwilling to pay for manual interpretation and delineation of landforms
– Consistency and reproducibility• Manual human interpretation can never
be entirely consistent or reproducible• Automated methods can be constantly
improved and re-run to produce updated products.
Source: MacMillan and Shary, (2009)
Conceptual Hierarchy of Landforms
• Focus here is on two main levels– Landform elements (facets here)– Landform patterns (repeating
landform types)
Source: MacMillan, 2005
Conceptual Hierarchy of Landforms
Source: MacMillan and Shary, (2009)
Rationale: Process-Form Relationships
• Landform Elements related to hill slope processes– Forms are related to processes and also
control them
Source: Skidmore et al. (1991)
Rationale: Process-Form Relationships
Source: Ventura and Irwin. (2000)
Rationale: Recognizing Landform Patterns
• Landform Patterns Establish Context and Scale– Different landform patterns exhibit
differences in• Relief energy available to drive processes
such as runoff, erosion, mass movement, solar illumination, energy flows
• Size and scale of landform features such as slope lengths, slope gradients, surface texture, complexity of slopes, degree of incision of channel networks
• Contextual position in the larger landscape– Runoff producing or runoff receiving area– Sediment accumulation or removal area– Elevated water tables or artesian conditions versus
recharge areas
Source: MacMillan, 2005
Classification of Landform Elements
Conceptual underpinningsImplementation examples
Landform Elements: Conceptual Underpinnings
• Many similar ideas on partitioning of hill slopes– Simplest and most basic
conceptualization– 2d not 3d partitioning of a hill slope into
elements
Landform Elements: Conceptual Underpinnings
• Many similar ideas on partitioning of hill slopes
Ruhe and Walker (1968)
Reprinted from Ventura and Irvin (2000)
Landform Elements: Conceptual Underpinnings
• 2D Concepts in 3D– Ventura & Irwin
(2000)• Ridge top• Shoulder• Backslope• Footslope• Toeslope• Floodplain
– Based solely on slope and curvature• No landform
position
Source: Ventura and Irvin (2000)
Landform Elements: Conceptual Underpinnings
• 3D concepts more comprehensive than 2D– Erosion, deposition, and transit are
influenced by both profile and plan (across-slope) curvature
Source: Shary et al., (2005)Concepts: Gauss, 1828
Landform Elements: Conceptual Underpinnings
• 3D concepts profile and plan curvature
Source: Shary et al., (2000)
Landform Elements: Conceptual Underpinnings
• 3D conceptualization
• 3D classes
Source: Pennock et al., (1987)Source: Pennock et al., (1987)
Landform Elements: Conceptual Underpinnings
• Complete system of classification by curvature
Source: Shary et al., (2005)
Landform Elements: Conceptual Underpinnings
• 3D conceptualization– Initially based
solely on local surface form• Convex, concave,
planar– In theory surface
form should reflect• Landscape
position• Hillslope
processes– Surface shape not
always sufficient• Need better
context
• 3D classes
Source: Dikau et al., (1989)
PEAK CELL
DIVIDECELL
PIT CELL
05 14 5 8 7 6 24 3 2 1
Downslope length - cell to pit (cells)
63
3 m
063 20100100 1080 88 75 50 38 25 12
Relative slope position as % length upslope
1
2
3
4
5
Downslope drainage direction (DDIR)
20
40
60
80
100
83 72 1 0 1 2 64 5 6 7
Upslope length - cell to peak (cells)
Upslope drainage direction (UDIR)
Relative slope position as % height above pit level
Elevation of each cell above pit elevation (m)
5 m
5 cells
3 cells
PEAK CELL
DIVIDECELL
PIT CELL
05 14 5 8 7 6 24 3 2 1
Downslope length - cell to pit (cells)
05 14 5 8 7 6 24 3 2 1
Downslope length - cell to pit (cells)
63
3 m
063 20100100 1080 88 75 50 38 25 12
Relative slope position as % length upslope
063 20100100 1080 88 75 50 38 25 12
Relative slope position as % length upslope
1
2
3
4
5
1
2
3
4
5
Downslope drainage direction (DDIR)Downslope drainage direction (DDIR)
20
40
60
80
100
83 72 1 0 1 2 64 5 6 7
Upslope length - cell to peak (cells)
Upslope drainage direction (UDIR)
83 72 1 0 1 2 64 5 6 7
Upslope length - cell to peak (cells)
83 72 1 0 1 2 64 5 6 7
Upslope length - cell to peak (cells)
Upslope drainage direction (UDIR)
Relative slope position as % height above pit level
Elevation of each cell above pit elevation (m)
5 m
5 cells
3 cells
Landform Elements: Conceptual Underpinnings
• Adding landform position to 3D improves 3D.
Source: MacMillan, 2000, 2005
Measures of Absolute Landform Position
Computed by LandMapR• Flow Length N
to Peak• Vertical Distance Z
to Ridge
FLOW UP TO RIDGE FROM EVERY CELLFLOW UP TO PEAK FROM EVERY CELL
Image Data Copyright the Province of British Columbia, 2003
Source: MacMillan et al., 2007
Measures of Relative Relief (in Z) Computed by
LandMapR• Percent Z Pit to Peak • Percent Z Channel to
Divide
MEASURE OF LOCAL CONTEXTMEASURE OF REGIONAL CONTEXT
Image Data Copyright the Province of British Columbia, 2003
Source: MacMillan et al., 2007
Measures of Relative Slope Length (L)
Computed by LandMapR• Percent L Pit to Peak • Percent L Channel to
Divide
MEASURE OF LOCAL CONTEXTMEASURE OF REGIONAL CONTEXT
Image Data Copyright the Province of British Columbia, 2003
Source: MacMillan et al., 2007
Image Data Copyright the Province of British Columbia, 2003
Measures of Relative Slope Position Computed
by LandMapR• Percent Diffuse
Upslope Area• Percent Z Channel to
Divide
RELATIVE TO MAIN STREAM CHANNELSSENSITIVE TO HOLLOWS & DRAWS
Source: MacMillan et al., 2007
Image Data Copyright the Province of British Columbia, 2003
Measures of Relative Slope Position Computed
by LandMapR• Percent Diffuse
Upslope Area• Percent Z Channel to
Divide
RELATIVE TO MAIN STREAM CHANNELSSENSITIVE TO HOLLOWS & DRAWS
Source: MacMillan et al., 2007
Multiple Resolution Landform Position
Source: Geng et al., 2012
What you see depends upon how closely you look
Different results with different window sizes and grid resolutions
Relative position is always relative to something and varies across an area
MRVBF: Multi-resolution valley bottom flatness
• Valley bottom flatness from:– Flatness (inverse of slope)– Local lowness (ranking in a 6 cell
circular region)• Multi-resolution:
– Compute valley bottom flatness at different resolutions• Smooth and subsample the DEM
Source: Gallant, 2012
MRVBF: Generalise DEMSmooth and subsample
Original: 25 m Generalised: 75 m Generalised 675 mFlatness
Bottomness
Valley Bottom Flatness
Valley Bottom Flatness
Bottomness
Flatness
Source: Gallant, 2012
MRVBF: Multi-ResolutionFlatness and bottomness at multiple
resolutions
25 m
75 m
675 m
Flatness Bottomness Valley Bottom Flatness
Source: Gallant, 2012
Calculating MRVBF
45555
23333
12222
)1(4
)1(2
)1(1
MRVBFWVBFWMRVBF
MRVBFWVBFWMRVBF
VBFWVBFWMRVBF
Weight function Wn gives abrupt transition,
depends on n
2*W2
5*W5
VBF
W
Source: Gallant, 2012
Multiple Resolution Landform Position MRVBF
Example Outputs
Source: Gallant, 2012
Broader Scale 9” DEM
MRVBF for 25 m DEM
Landform Elements: Other Measures of Landform
Position• SAGA-RHSP:
relative hydrologic slope position
• SAGA-ABC: altitude above channel
Source: C. Bulmer, unpublishedCalculation based on: MacMillan, 2005
Source: C. Bulmer, unpublished
Landform Elements: Other Measures of Landform
Position• SAGA-MRVBF:
valley bottom flatness index
• SAGA-Combined RHSP and MRVBF
Source: C. Bulmer, unpublished
Landform Elements: Other Measures of Landform
Position• SAGA-Combined
RHSP and MRVBF vs Soil Map
• SAGA-Combined RHSP and MRVBF vs Soil Map
Source: C. Bulmer, unpublishedCalculation based on: MacMillan, 2005
Source: C. Bulmer, unpublished
Landform Elements: Other Measures of Landform
Position• TOPHAT – Schmidt
and Hewitt (2004)• Slope Position –
Hatfield (1996)
Source: Hatfield (1996)Source: Schmidt & Hewitt, (2004)
Landform Elements: Other Measures of Landform
Position - Scilands
Source: Rüdiger Köthe , 2012
Landform Elements: Other Measures of Landform
Position - Scilands
Source: Rüdiger Köthe , 2012
Landform Elements: Other Measures of Landform
Position - Scilands
Source: Rüdiger Köthe , 2012
Landform Elements: Implementation Example -
Scilands
Source: Rüdiger Köthe , 2012
Landform Elements: Implementation Example -
Scilands
Source: Rüdiger Köthe , 2012
Landform Elements: Implementation Example -
Scilands
Source: Rüdiger Köthe , 2012
Landform Elements: Implementation Example -
Scilands
Source: Rüdiger Köthe , 2012
Landform Elements: Landform Elements:
Implementation Example - Scilands
Source: Rüdiger Köthe , 2012
Landform Elements: Implementation Example:
LandMapR• LandMapR 15 Default Landform
Classes
Source: MacMillan et al, 2000
Landform Elements: Implementation Example:
LandMapR• LandMapR 15 Default Landform
Classes
Source: MacMillan, 2003
LandMapR: Different Classes in Different Areas
Normal Mesic
Moist Foot Slope
Warm SW Slope
Shallow Crest
Organic Wetland
Wet Toe Slope
Cold Frosty Wet
Permanent Lake
Source: MacMillan et al., 2007
Example of Application of Fuzzy K-means Unsupervised
Classification
From: Burrough et al., 2001, Landscsape Ecology
Note similarity of unsupervised classes to
conceptual classes
Supervised Classification Using Fuzzy Logic
• Shi et al., 2004– Used multiple cases of
reference sites– Each site was used to
establish fuzzy similarity of unclassified locations to reference sites
– Used Fuzzy-minimum function to compute fuzzy similarity
– Harden class using largest (Fuzzy-maximum) value
– Considered distance to each reference site in computing Fuzzy-similarity
Fuzzy likelihood of being a broad ridge
Source: Shi et al., 2004
Classification of Landform Patterns
Conceptual underpinnings
Rationale: Identify Landscapes of Different Size,
Scale and Context
Source: MacMillan, 2005
Conceptualization of Landform Patterns
• Landform Patterns Tend to Repeat – Landform patterns are typically of
larger size and scale and display greater complexity and variation• Hills, mountains, plains, plateaus,
tablelands– Landform patterns usually, but not
always, exhibit full or partial cycles of repetition of forms• Hills and mountains exhibit a full range
of landform positions, slope gradients, curvatures (mostly positive)
• Valleys and plains can exhibit undulations or cyclic variations OR they may be asymmetric.
Considerations Used in Several Systems of
Classifying Landform Patterns• Hammond (Dikau,
1991)– Considerations
• Slope gradient; percentage of gentle slopes (4 classes) in search window
• Local relief within a search window of fixed dimensions (6 classes)
• Profile type; percentage of cells classed as gentle slope in lowland versus upland locations (4 classes)
• SOTER (van Engelen & Wen, 1995)– Considerations
• Dominant slope gradient• Relief intensity• Hypsometry (elevation asl)• Degree of dissection
• Iwahashi & Pike (2006)– Considerations
• Local slope gradient (3x3 window)
• Texture - Local relief intensity assessed as number of pits and peaks within a fixed window of 10 cells
• Curvature; calculated as percentage of convex cells in a 10 cell radius
• eSOTER (Dobos et al., 2005)– Considerations
• Majority slope gradient (of 7 classes in 900 m block, then smoothed)
• Relief intensity (max-min elevation within a radius of 5 cells, 990 m classified into 4 classes & smoothed)
• Hypsometry (elevation asl, 10 classes)
• Dissection (# channel cells in radius)
Rationale for Classifying Landform Patterns
• So, Why Consider These Attributes?– Slope Gradient
• Steepness relates to energy, erosion, deposition, context
– Relief Intensity (or texture or local relief)• Provides an indication of amplitude of
landscape, amount of energy available for erosion, slope lengths, size and scale of hill slopes
– Profile Type (or shape, curvature, hypsometry)• Helps to differentiate uplands (convex)
from lowlands• Helps to establish broader landscape
context
Conceptualization of Landform Patterns
Source: MacMillan, 2005
Classification of Landform Patterns
Implementation examples
Landform Patterns: Implementation Example of
the Hammond System• Hammond system; as per Dikau et al., 1991
Source: MacMillan and Shary, (2009)
Landform Patterns: Implementation Example of
the Hammond System• Hammond system; as per Dikau et al., 1991
Source: Zawadzka et al., in prep
9600m square window 9600m circular window 900m circular window
Nor
mal
Rel
ief I
ndex
Mod
ified
Rel
ief I
ndex
Landform Patterns: Implementation Example of
the Hammond System• Hammond system; as per Dikau et al., 1991
Source: Zawadzka et al., in prep
18000 m circular window
9200m circular window
900m circular window
Hammond approach tends to produce concentric rings related to how the search window observes the data
Hammond approach is very sensitive to differences in window size and shape or grid resolution
Landform Patterns: Implementation Example of
the Hammond System• Hammond system; as per Dikau et al., 1991
Source: MacMillan, (unpublished)
Landform Patterns: Implementation Example of
the Hammond System• Hammond landform underlying 1:650k soil map
Source: Reuter, H.I. (unpublished)
Landform Patterns: Implementation Example of
Iwahashi & Pike (2006)• Implemented by Zawadzka et al., (in prep)
Source: Zawadzka et al., in prep
8 classes 12 classes 16 classes
Iwahashi & Pike classes need to be labelled and interpreted
Landform Patterns: Implementation Example of
Iwahashi & Pike (2006)• Iwahashi landform underlying 1:650k soil map
Source: Reuter, H.I. (unpublished)
steep gentle
Terr
ain
Ser
ies
Fine texture,High convexityFine texture,
Low convexityCoarse texture,High convexityCoarse texture,Low convexity
Terrain Classes
1
4
5
8
9
12
13
2 6 10 14
3 7 11 15
16
Landform Patterns: Implementation Example of
eSOTER (Dobos, 2005)• Implemented by Dobos et al., (in 2005)
Source: Dobos et al., 20058 classes
Manual - yellow eSOTER - red
Manual - yellow eSOTER - red
Landform Patterns: Implementation Example of
Peak Shed Approach• Implemented by Zawadzka et al., (in prep)
Source: Zawadzka et al., in prep
Peak shed entities classified by clustering algorithm.
Resulting entities need to be labelled and interpreted
Landform Patterns: Implementation Example of
Peak Shed Approach• Implemented by Zawadzka et al., (in prep)
Source: Zawadzka et al., in prep
Peak shed entities labelled according to Hammond
Landform Patterns: Implementation Example of
Slope Break Approach• Implemented by Zawadzka et al., (in prep)
Source: Zawadzka et al., in prep
Run 2 Run 3
Landform Patterns: Implementation Example of
Homogeneous Objects (eCognition)• Implemented by Zawadzka et al., (in
prep)
Source: Zawadzka et al., in prep
Landform Patterns: Implementation Example -
Scilands
Source: Rüdiger Köthe , 2012
Source: http://eusoils.jrc.ec.europa.eu/projects/landform/
Landform Patterns: Implementation Example of Homogeneous Objects vs
Meybeck 2001• Implemented by Dragut, (unpublished)
Source: Drãgut & Eisank, 2011
Method: Meybeck et al., 2001
Implemented by: Reuter and Nelson
See: ai-relief.org
Landform Patterns: Implementation Example of
Meybeck 2001 vs Homogeneous Objects• Implemented by Dragut,
(unpublished)
Method: Meybeck et
al., 2001
Source: Reuter
and Nelson
Source: Drãgut , unpublished
See: ai-relief.org
Landform Patterns: Example of Multi-scale Nested Homogeneous Objects• Implemented by Dragut,
(unpublished)
Source: Drãgut, unpublished
Source: Reuter & Bock, 2012Scilands GMK ClassificationSee: ai-relief.org
Source: Reuter & Bock, 2012Hammond Classification (after Dikau, 1991)See: ai-relief.org
Source: Reuter & Bock, 2012Iwahashi & Pike Classification (16 classes)See: ai-relief.org
Source: Reuter & Bock, 2012Scilands GMK ClassificationSee: ai-relief.org
Source: Reuter & Bock, 2012Iwahashi & Pike Classification (16 classes)See: ai-relief.org
Source: Reuter & Bock, 2012Iwahashi & Pike Classification (8 classes)See: ai-relief.org
Source: Reuter & Bock, 2012Scilands GMK ClassificationSee: ai-relief.org
Source: Reuter & Bock, 2012Iwahashi & Pike Classification (16 classes)See: ai-relief.org
Source: Reuter & Bock, 2012Iwahashi & Pike Classification (8 classes)See: ai-relief.org
Miscellaneous Bits and Pieces
Some thoughts and ideas that may or may not prove useful
We are Really Looking for Discontinuities!
Source: Minar and Evans. (2008)
We are Really Looking for Discontinuities!
Source: MacMillan, unpublished
We are Really Looking for Discontinuities!
• The more I think about it the clearer it becomes– We are really looking to locate abrupt
boundaries where the slope, texture, relief and context change• If we are looking for boundaries it makes
sense to try to extract vector objects • It makes less sense to classify grid cells
then agglomerate them, then de-speckle them, then vectorize them
• This argues in favor of approaches like Object Extraction (Dragut) or perhaps Scilands (Kothe)
Source: Minar and Evans. (2008)
There are Special Cases that do not fit in a General
Classification (e.g River Valleys)
I like this!
Source: Rüdiger Köthe , 2012
There are Special Cases that do not fit in a General
Classification (e.g River Valleys)• Many General Purpose
Classifications Need to be Extended to Handle Special Cases– River Valleys are a case in point
• They have forms and patterns that are not cyclical
• They have special features that have special interpretation
– Active flood plain, levee, low terrace, high terrace, inter-terrace scarp, ox-bow lake, abandoned channel, dry islands
– Other Special Cases no doubt exist too• Think of mineral and organic wetlands,
deserts, playas
Multi-Scale and Multi-Resolution Calculations are Important but Problematic
No single fixed window size fits all landscapes – Need to be locally adaptive
Source: MacMillan, 2005
Multi-Scale and Multi-Resolution are Important but
Problematic• All algorithms and systems that
compute attributes within a fixed window are flawed– No single window fits all landscapes– User’s frequently adjust window size
subjectively to fit local landscape features – no longer universal!
– Windows that don’t fit the landscape produce artifacts and unrealistic classes or values
– Need to use multiple windows and average (like MRVBF) or make windows self-adjusting
I Like Top-Down, Divisive, Multi-scale Fully Nested
Hierarchical Objects• Multi-scale Objects of Dragut, (unpublished)
Source: Drãgut, unpublished
I Like Top-Down, Divisive, Multi-scale Fully Nested
Hierarchical Objects• Advantages of multi-scale,
hierarchical, nested vector objects– They nest, or fit, within higher level
objects exactly– There is less arbitrary sliver removal,
filtering, speckle removal, smoothing and manipulation
– They seem to produce fewer artifacts and outright errors
– They produce consistent and comparable results for all similar terrains
Source: Drãgut, unpublished
The World is Divided into Things that Stick Up and Things that Stick Down
As a first step we should always strive to separate erosional uplands from lowlands
Source: MacMillan, unpublished
The World is Divided into Things that Stick Up and Things that Stick Down
Extracting nested peaks may be a way to separate uplands from lowlands
Source: MacMillan, unpublished
Might work even better if applied to DEM of inverted Height Above Channel (Z2St)
The World is Divided into Things that Stick Up and Things that Stick Down
• In the First Instances Many Landform Pattern Classifications are Binary (upland vs lowlands)– Systems of Iwahashi and Pike, eSOTER,
Hammond Scilands all recognize this in their own way
– Maybe we should be making a point of finding ways to explicitly separate erosional uplands from aggrading lowlands as a first step in any classification
– I have fooled around with the idea of extracting nested pits from an inverted DEM as a way to extract uplands
Source: MacMillan, 2005
Are Landform Patterns and Landform Elements Really
Different Things??Maybe the only real difference is one of scale?
Source: MacMillan, unpublished
Many classifications of Landform Patterns look a lot like Hillslope Elements on a large scale
Source: Rüdiger Köthe , 2012
Are Landform Patterns and Landform Elements Really
Different Things?• The More I look, the more that
landform patterns begin to look like landform elements computed over larger areas and at a coarser scale– Maybe we need to look at approaches
like MRVBF that compute values at multiple scales then average them to produce a final value or class• Similarities to the work of Jo Wood.• We still want to first separate hills from
valleys and uplands from lowlands, then landform elements within these larger scale features.
Source: MacMillan, 2005
I Have Personally Found Hierarchical Classification
Useful to Set ContextI first classified areas into 3-4 relief classes
Then I developed and applied different classification rules for each relief class
Source: MacMillan, 2005
Discussion and Conclusions
What works and what doesn’t?
How can we tell what works? Challenges to be addressed
Future developments
What Works and What Doesn’t?
• All things being equal apply Ockham’s Razor– If you need to decide between several
competing methods and none is clearly superior to others• Pick the one that is simplest, fastest and
easiest to implement– Fewest input variables– Fewest processing steps– Fewest tuneable parameters– Fewest subjective decisions
• This points towards selection of one of the following
– Iwahashi and Pike, Dragut or Scilands
Source: MacMillan, 2005
How Can We Tell What Works?
• How can we evaluate “Truth” for subjective classifications?– Hard to decide objectively which
classification method to use when all classifications appear partly useful and partly incorrect• Need objective criteria and methods of
computing them to assess different classifications and identify the most useful
• Should be based on the ability of the classification to predict ancillary environmental properties or conditions of interest
Source: MacMillan, 2005
Challenges to be Addressed
• A diversity of methods and absence of standards– Classes and results need to be
comparable between different areas• This argues for selecting and applying one
method universally and not applying different methods in different regions
• Need to objectively compare methods and then select one to use widely (everywhere?).
• Method almost certainly has to be multi-scale, hierarchical and locally adaptive
• Method needs to be parsimonious and easy to apply
Source: MacMillan, 2005
Future Developments
• Global standards– We need global standards to compare
results• Free and open-source data and tools
on-line– I see both data & tools increasingly
available on-line• Incorporation of ancillary (remotely
sensed) data to infer parent material attributes for landforms– Once delineated, objects need to be
attributed for pm• Innovations in multi-scale hierarchical
analysis– Way forward will undoubtedly be multi-
scale
Source: MacMillan, 2005
Thank You
Extra Slides Follow
Classify Landforms by Size and Scale
Image Data Copyright the Province of British Columbia, 2003Source: MacMillan, 2005
Quesnel PEM Landform Classification
Image Data Copyright the Province of British Columbia, 2003Source: MacMillan, 2005
I Have Personally Found Hierarchical Classification
Useful to Set ContextI first classified areas into 3-4 relief classes
Source: MacMillan, unpublished
Then I developed and applied different classification rules for each relief class
Source: MacMillan, 2005
Quesnel PEM Landform Classification
Image Data Copyright the Province of British Columbia, 2003Source: MacMillan, 2005
The World is Divided into Things that Stick Up and Things that Stick Down
As a first step we should always strive to separate erosional uplands from lowlands
Source: MacMillan, unpublished