environmental modeling advanced weighting of gis layers (2)

Environmental ModelingEnvironmental ModelingAdvanced Weighting of Advanced Weighting of

GIS Layers (2)GIS Layers (2)

1. Issue1. Issue► Modeling the habitat of red squirrel in Modeling the habitat of red squirrel in the Mt. Graham areathe Mt. Graham area

► Red squirrel prefer a shaded and humid Red squirrel prefer a shaded and humid environment and feed on pine cones, that environment and feed on pine cones, that are offered by Mt. Grahamare offered by Mt. Graham

► The issue is whether the construction of The issue is whether the construction of an astronomy observatory will affect the an astronomy observatory will affect the habitat habitat

Pereira, J.M.C., and R.M. Itami, 1991. GIS-based habitat modeling using Pereira, J.M.C., and R.M. Itami, 1991. GIS-based habitat modeling using logistic multiple regression: a study of the Mt. Graham Red Squirrel. logistic multiple regression: a study of the Mt. Graham Red Squirrel. Photogrammetric Engineering and Remote Sensing, 57(11):1475-1486. Photogrammetric Engineering and Remote Sensing, 57(11):1475-1486.

2. Factors2. Factors

a. Topography:a. Topography: b. Vegetation:b. Vegetation:

ElevationElevation Land Land covercover

SlopeSlope Canopy Canopy closureclosure

Aspect (e-w)Aspect (e-w) Food Food productivityproductivity

Aspect (n-s) Aspect (n-s) Tree dbh Tree dbh

Distance to openness (canopy closure Distance to openness (canopy closure and roads)and roads)

3. Spatial Sampling3. Spatial Sampling

► The 200 presence sites are observed The 200 presence sites are observed in the fieldin the field

► The 200 absence sites can be The 200 absence sites can be randomly randomly

generated using Hawth’s tool generated using Hawth’s tool ► OR systematically sampled every nOR systematically sampled every nthth cell,cell,

Then n=? Then n=?

At each of the 400 locations, collect both dependent and the independent variables

3. Spatial Sampling .. 3. Spatial Sampling ..

►Moran’s I

► Cij = 1, if xi and xj are adjacent, Cij=0 otherwise

I n

2a

Cij (x i x )(x j x )j1

n

i1

n

(x i x )2

i1

n

2a Cijj1

n

i1

n

3. Spatial Sampling .. 3. Spatial Sampling ..

Moran’s I ..Moran’s I ..

► I = 1 indicates a positive spatial I = 1 indicates a positive spatial autocorrelationautocorrelation

► I = -1 indicates a negative spatial I = -1 indicates a negative spatial autocorrelationautocorrelation

► I = 0 indicates a random spatial I = 0 indicates a random spatial pattern pattern

3. Spatial Sampling .. 3. Spatial Sampling ..

Ileft = 0.94, Imiddle = -1, Iright = 0.168

3. Spatial Sampling .. 3. Spatial Sampling ..

► The spatial lag can be any value, e.g. 1, 2, 3, 4, …. The spatial lag can be any value, e.g. 1, 2, 3, 4, ….

► When the lag value increases, the pairs of i and j When the lag value increases, the pairs of i and j locations are further apartlocations are further apart

► The I value decreases with an increasing lag value, The I value decreases with an increasing lag value, indicating increasing differences between values at i and j indicating increasing differences between values at i and j locations locations

3. Spatial Sampling .. 3. Spatial Sampling ..

► Moran’s I is applied to each variableMoran’s I is applied to each variable

► lag = 1, 2, 3, … 7lag = 1, 2, 3, … 7► When lag = 1, I is close to 1When lag = 1, I is close to 1► When lag= 7, I = 0.16 – 0.34 among the ind variablesWhen lag= 7, I = 0.16 – 0.34 among the ind variables► Every 7Every 7thth cell is selected cell is selected ► 259 absence cells, compatible to the 212 presence cells259 absence cells, compatible to the 212 presence cells

independent variablesindependent variables

► Independent variables (14)Independent variables (14)

the continuous variables (1-5, ratio the continuous variables (1-5, ratio data)data)

1. Elevation1. Elevation

2. slope 2. slope

3. aspect (e-w)3. aspect (e-w)

4. aspect (n-s)4. aspect (n-s)

5. distance to openness 5. distance to openness (buffer to roads or to land cover)(buffer to roads or to land cover)

ind var ..ind var ..

The categorical ind variables 6-14 The categorical ind variables 6-14 (nominal, ordinal, or interval(nominal, ordinal, or interval data)data)

6-8. Food productivity 6-8. Food productivity

9-11. Canopy closure9-11. Canopy closure

12-14. Tree dbh12-14. Tree dbh

5. Model 1 - the Logistic 5. Model 1 - the Logistic ModelModel

YY = = 0.0020.002ele ele - 0.228- 0.228slope slope + + 0.6850.685canopy(high) canopy(high)

+ 0.443+ 0.443canopy(medium) canopy(medium) + + 0.4810.481canopy(low) canopy(low)

+ 0.009+ 0.009aspect(e-w)aspect(e-w)

P P (Y) = 1/[1 + exp (Y) = 1/[1 + exp (-(-YY)] )]

PP - The probability of red squirrel - The probability of red squirrel habitathabitat

Accuracy AssessmentAccuracy Assessment

► Error Matrix Error Matrix

for the 150 presence and 150 absence for the 150 presence and 150 absence sites that are used to develop the sites that are used to develop the logistic modellogistic model

ModeledModeled presence absence total presence absence total

accuracyaccuracy presence presence 123123 27 150 27 150

absence 36absence 36 114114 150 150

300300

Trut

Trut

hh

82%82%76%76%

Overall accuracy = (123+114)/300 Overall accuracy = (123+114)/300 = 79%= 79%

Model ValidationModel Validation

► Error Matrix Error Matrix

for the 50 presence and 50 absence sites for the 50 presence and 50 absence sites that are put aside for model validationthat are put aside for model validation

ModeledModeled presence absence total presence absence total

accuracyaccuracy presence presence 3737 13 50 13 50

absence 16absence 16 3434 50 50

100 100

Trut

Trut

hh

74%74%

68%68%

71%71%

5. Model 2 - Trend Surface 5. Model 2 - Trend Surface AnalysisAnalysis

► A dependent variable and two A dependent variable and two independent variables – x and y independent variables – x and y coordinatescoordinates

► Linear (1Linear (1stst order) : z = a order) : z = a00 + a + a11x + x + aa22yy

► Quadratic (2nd order): Quadratic (2nd order):

z = az = a00 + a + a11x + ax + a22y + ay + a33xx22 + a + a44xy + axy + a55yy22

► Cubic etc. Cubic etc.

► Least square methodLeast square method

Trends of one, two, and three independent variables for polynomial equations of the first, second, and third orders (after Harbaugh, 1964).

5. Trend Surface 5. Trend Surface Analysis ..Analysis ..

► Assuming that the presence and Assuming that the presence and absence depend on coordinates x and absence depend on coordinates x and yy

► A 4A 4thth order polynomial multiple order polynomial multiple logistic regression model is used logistic regression model is used

► Dependent variable: presence and Dependent variable: presence and absenceabsence

► Independent variables: x and yIndependent variables: x and y► Prediction accuracy: 57%Prediction accuracy: 57%

5. Model 3 - Bayesian Model5. Model 3 - Bayesian Model► A Bayesian model is used to A Bayesian model is used to combine the environmental model and combine the environmental model and the trend surface modelthe trend surface model

► to reach a predictive accuracy of to reach a predictive accuracy of 87% 87%

6. Habitat Loss Estimate6. Habitat Loss Estimate

► Total number of cells lost to the Total number of cells lost to the observatory:observatory:

Overlay the predicted suitable cells and Overlay the predicted suitable cells and construction cellsconstruction cells

► Density of red squirrel in each Density of red squirrel in each suitability class: suitability class:

number of presence in the class / acreage number of presence in the class / acreage of the classof the class

► Total habitat loss: Total habitat loss: density * acreage density * acreage per classper class