Landscape Metrics
Prof. Dr. Adrienne Grêt-Regamey
Sibyl Brunner
Ana Stritih
Landscape structure
Block 2: Landscape assessment
(1) Descriptive analysis
(2) Comparison of landscapes
(3) Comparison of alternatives
(4) Monitoring
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Overview
“Clearly, the objective of applying landscape metrics goes beyond describing and
measuring patterns: its aim is to explain and understand the processes that occur.”
(Haines-Young, 1999)
From last time:
(1) Data classification
Arable land
Forest
Intensive grassland
Matrix: Extensive grassland
(2) Scale
100m x 100m
(3) Patch definition
=> (4) Selection and (5) Interpretation of landscape metrics
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Landscape metrics
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Lang und Blaschke, 2007
Area metrics
Example: Patch area = 9 raster cells 25m x 25m
= 5’625 m2
Lang and Blaschke, 2007
𝐴𝑟𝑒𝑎 =
𝑅𝑎𝑠𝑡𝑒𝑟_𝐶𝑒𝑙𝑙𝑠
Patch Size (PS) =
Patch area
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𝐴𝑟𝑒𝑎 = 𝐴𝑟𝑒𝑎𝑂𝐴𝐵 +𝐴𝑟𝑒𝑎𝑂𝐵𝐶 +
𝐴𝑟𝑒𝑎𝑂𝐶𝐷 + 𝐴𝑟𝑒𝑎𝑂𝐷𝐸 - 𝐴𝑟𝑒𝑎𝑂𝐴𝐸
Meaning
Habitat,
minimal size
Lynx, single individual:
100 – 400 km2
Lynx, viable population:
20’000 km2
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Area metrics
Short exercise: Calculate Patch Size for the selected patches.
100m x 100m
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Edge metrics
Lang und Blaschke, 2007
Total Edge
= Total length of edges
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Edge Density
= Edge length per unit area
Meaning
Connectivity
Complexity
Ground-nesting
birds:
skylark, lapwing,
gray partridge
Michel and Walz, 2012
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Caution
Human impacts:
Road construction
"good" versus "bad"
Digitalized data:
Artificial identification of boundary
lines
"real" versus "artificial"
Quality of the edge lines!
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Edge metrics
Short exercise: Calculate Total Edge and Edge Density for the selected patches.
Which metric is more meaningful?
100m x 100m
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Core area metrics
Lang and Blaschke, 2007
Core Area (CA)
= Core area of a patch
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Core area metrics
Lang und Blaschke, 2007
Core Area Index (CAI)
= Percentage of the patch that is comprised of core area
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Core area metrics (landscape)
𝑁𝑃 − 𝑁𝐶𝐴𝐼=0
𝐶𝑌 =
𝑁𝐶𝐴
NP = Number of patches
NCAI=0 = Cases without core areas
NCA = Number of core areas
Lang und Blaschke, 2007
Cority (CY)
= Fragmentation with respect to a core area distance
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Meaning
Effective
habitat area
Erosion risk
Habitat edge
area
Red kite
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Core area metrics
Short exercise: Calculate the landscape-level Core Area Index and the Cority for the
yellow patches and for a core area distance of 100m. What values can Cority have?
100m x 100m
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Shape metrics
Area/Perimeter or
Perimeter/Area?
Lang und Blaschke, 2007
Area-Perimeter Ratio
= Ratio of area to perimeter
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Shape metrics
Short exercise: Calculate the Area-Perimeter-Ratio for the two highlighted patches.
What jumps out, and how can you address it?
100m x 100m
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Shape metrics
p = perimeter, a = area
Shape Index
= Deviation from a circular shape
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Application
Forest planning: Minimization of shape index
Korosue et al., 2014
Habitat
fragmentation
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Shape metrics
Fractal dimension (D)
= Irregularity of a patch
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Shape metrics
p = perimeter, a = area
Lang and Blaschke, 2007
Ex. Fractal dimension (D)
= Irregularity of a patch
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Compactness metrics
Radius of gyration
= largest circle around the patch
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Lang und Blaschke, 2007
Meaning
Habitat
suitability
Landscape
scenery
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Mean patch metrics
Mean Patch Size (MPS)
= average patch size
n
j=1 a ij
MPS =
ni
Patch Size Standard
Deviation (PSSD)
= spread of the patch size
n
j=1
PSSD =
n
j=1 a ij
aij −
ni
ni
n = number of patches, a = area
Patch Density (PD)
= number of patches per ha
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2
Application
Bielsa et al. 2005
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Mean patch metrics
Short exercise: Calculate the MPS, PSSD and PD for the class forest (green patches).
Which metric gives the most information?
100m x 100m
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Mean patch metrics
Problem: PSSD large absolute differences, even when relative similar variance
PSSD
= 2 ha
100m x 100m
PSSD
= 2 m2
1m x 1m
Patch Size Coefficient of Variation (PSCV)
= standardized spread of the patch sizes
= (PSSD/MPS) *100
PSCV
= 50%
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PSCV
= 50%
Proximity metrics
Euclidean Distance (d)
= shortest distance between two patches
Nearest-Neighbor-Distance
= minimal distance to target patch in the
same class
Mean-Nearest-Neighbor-Distance
= mean distance to target patch in the same
class
Question: Why are these metrics
problematic?
Lang and Blaschke, 2007
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Proximity metrics
Proximity buffer
Various possibilities for the
combination of
Distance
Area
Proximity index (PX)
= Patch isolation and fragmentation of the patch type
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Proximity metrics
Distance: all patches in PB
Area: both
Area: Focal patch
Lang and Blaschke, 2007
Area: Target patch
Distance: nearest neighbor
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At = Area target patch
d = Distance
Af = Area focal patch
𝐴𝑓
𝑉𝑎𝑟𝑖𝑎𝑛𝑡𝑒 𝐷: 𝑃𝑋94 =
+
𝑑
𝑛
𝑖=1
𝐴𝑡
𝑑
Meaning
Habitat
connectivity
Isolation
Hamster:
Radius of activity 195m
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Lizard:
Maximum dispersion distance 300m
Proximity metrics
Short exercise: Calculate the Proximity Index PXfg for the two indicated patches
(Assumption: all visible patches are within the Proximity Buffer).
100m x 100m
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Diversity metrics
𝑅=
𝑠
𝑠𝑚𝑎𝑥
s = number of classes
smax = maximum number of classes
pi = proportional coverage of class "i"
∙ 100
Relative Richness (R)
= number of patch types (classes)
𝑠
𝐻=−
(𝑝𝑖 ) ∙ ln(𝑝𝑖 )
𝑖=1
Shannon diversity (H)
= distribution of patch types
𝐸𝑉𝐸𝑁 =
𝐻
ln(𝑠)
Evenness (EVEN)
= standardized diversity, even distribution
of area between patch types
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𝐷𝑂𝑀 = ln 𝑠 − 𝐻
Dominance (DOM)
= deviation from maximum
diversity
Meaning
Biodiversity
Landscape
scenery
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Diversity metrics
Short exercise: Calculate the Shannon-Diversity-Index, Evenness and Dominance for the
exercise landscape.
100m x 100m
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Lang and Blaschke, 2007
Diversity metrics
6% Forest, 25% Water, 69% Agriculture
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6% Agriculture, 25% Forest, 69% Water
Diversity Limmattal
Based on "Arealstatistik" (100 x 100 m Raster), 4
Categories
Shannon Diversity: 1.12
Shannon Evenness: 0.81
Based on "Arealstatistik" (100 x 100 m Raster), 72
Categories
Shannon Diversity: 2.98
Shannon Evenness: 0.72
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Fragmentation metrics
Ftotal = total area
n = number of patches
Fi = area of a patch
Jaeger, 2006
Lang and Blaschke, 2007
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Effective Mesh Size (meff)
= Size of remaining residual areas; expresses the probability that two
points chosen randomly in a region are connected.
Urban sprawl metrics
Urban sprawl (DE: "Zersiedelung")
= Extent of buildings in the landscape and
their dispersion
New metrics:
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Schwick et al., 2010
Settlement units per km2
Urban sprawl metrics
DIS = Dispersion, TS = Total settlement
(Siedlungsfläche = settlement area;
Grösse der Landschaft = size of the landscape)
Jaeger et al., 2008
Urban Penetration (UP)
= Penetration of urban area in the landscape
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Settlement units per km2
Urban sprawl metrics
DIS = Dispersion, TS = Total settlement
(Siedlungsfläche = settlement area;
Grösse der Landschaft = size of the landscape)
Jaeger et al., 2008
Dispersion (DIS)
= Scattering / dispersion of the urban area
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Urban sprawl Limmattal
Dispersion
High! > 46 DSE/m2 (similar to Bern, Lausanne, Lugano…)
Area utilization per person
Small! < 200 m2/person (similar to Bern, Lausanne, Lugano…)
Jaeger et al., 2008
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Significance
Habitat loss
Barrier effect
Fragmentation
Mortality
Species loss
Recreation
Aesthetics
Emissions
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Fragmentation metrics
Short exercise: Calculate the Effective Mesh Size for the landscape, which is divided by
two roads into three areas; assume that an animal can move around in all natural
habitats. What are the maximum and minimum values of the metric?
100m x 100m
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Application
Landscape indicators
The state and evolution of the environment in the landscape are illustrated and
evaluated based on selected characteristics
Indicator: landscape fragmentation
Indicator: urban sprawl
BAFU Schweiz, Indikatoren der Umwelt
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Learning goals and materials
Leaning goals: You…
… have a sense for LSM and can interpret formulae for previously unknown LSM
… know the strengths and weaknesses of different LSM at various levels
… can design a LSM for a given problem statement
… can apply and calculate LSM in exercise landscapes
… know the significance and applicability of different LSM
… understand extreme values (max, min) of LSM
… do not have to learn by heart the exact formula of all LSM, but rather
understand which metrics are necessary for certain purposes
Slides and background literature will be available for
download on the course website …
... as well as the answers to the short exercises
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