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Quantifying Landscape Pattern

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Quantifying Landscape Pattern

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    1. Quantifying Landscape Pattern ESM 215 Feb 3, 2003

    2. Changes in forest cover, Cadiz Township, Wisconsin (Curtis 1956)

    3. Landscapes over time

    4. Analysis of Model Outputs

    5. Western boundary, Yellowstone National Park (Turner et al. Fig 5-2)

    6. Why quantify pattern? Investigate pattern <> process Landscape monitoring Comparison across landscapes Compare and contrast management strategies Sampling and experimental design

    7. Classification and Pattern

    9. Metrics of landscape composition: categorical maps Number of classes (richness, S) Proportion of area occupied by class i (pi) Diversity (evenness) SHEI = (-?[pi * ln (pi)] ) / ln (S) Dominance D = (ln(S) + ?[pi * ln(pi)]) / ln(S)

    10. Measures of spatial configuration Adjacency (cell-based) Contagion and Interspersion (cell-based) Perimeter-area (patch) Connectivity (patch) Proximity (patch) Patch size distribution (e.g., area-weighted patch size)

    11. Contagion C = 1 + ??? Pij ln (Pij) 2 ln (S) P = probability that 2 randomly chosen adjacent cells are the same cover type S = # of cover types

    12. Connectivity/Fragmentation Patch cohesion (Schumaker 96)

    13. Fractals Fractals: objects or patterns that have non-integer dimensions self-similarity: pattern at coarse scales is repeated at finer and finer scales scale-dependence

    14. Fractal curves

    15. Fractal Patches

    17. Box analysis of fractal dimension of lattices

    18. Procedure for box analysis map is superimposed with a grid > the grain size. Boxes which contain class of interest (in any small amount) are counted. The process is repeated with different box sizes until 1-2 orders of magnitude in box size has been explored (say boxes of size 1 to 100). the logarithm of the number of occupied boxes of each length is regressed against the logarithm of box length. The slope of the regression is the exponent in the power law N(L) = kL-Db

    20. Converting box counts to areas A(L) = kL2-Db assuming self-similarity at scales below the grain size, the scaling relation for area could be used to estimate the area of a feature at sub-grain scales k : lacunarity; used to estimate N(L) for box size L

    21. Multiple metrics

    22. Which metrics? # types, contagion, fractal dimension, mean patch perimeter-area ratio, relative patch area (Riiters et al. 1995) Patch shape and edge contrast, patch density, patch size (McGarigal and Marks (1995) # types, proportion of each type, spatial arrangement of patches, patch shape, contrast between neighboring patches (Li and Reynolds 1994)

    23. Pattern in continuous variables and point processes Trend surface analysis Spatial autocorrelation Semivariance 1-d and 2-d spectral analysis wavelets

    24. Morans I, Gearys C Two general measures of spatial autocorrelation wij - weight at distance d, that is, wij=1 if point j is within distance class d from point i, else wij=0; z's are deviations (i.e., zi=yi-ymean for variable y), W is the sum of all the weights. The summation is done for all i not equal to j

    26. Semivariograms N = # point (location) pairs f1i = value of variable at location 1 f2i = value of variable at location 2

    28. Variograms and correlograms

    29. Example application of landscape pattern metrics G. Darrel Jenerette 2001. Analysis and simulation of land-use change in the central Arizona Phoenix region, USA. Landscape Ecology 16(7): 611-626.

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