Reading Assignment: Bolstad Chapters 10 & 11

Spatial Analysis (Raster)

• Spring Break Next Week!• During break fill out address form for ~ 20 places

– Will be used later in lab for Home Range analysis

Raster Data Model

Uses grid cells of a given dimension to represent the value or attribute of a real world entity or phenomenon.

• In a raster layer, the cells are arranged in rows and columns.

• All cells in a raster layer are the same size.

• Cell Size = Spatial Resolution: the dimension of the area covered on the ground and represented by a single cell (e.g., 10m).

• The value may be a measurement or a code.

• Cell values are numeric: can be either positive or negative, integer, or floating point.

Applications– Predictive modeling– The fate of pollutants– Fire spread– Determine erosion potential – Estimates of forest growth– Change detection

Map Algebra: • Dana Tomlin and Joseph Berry (1970’s)• A method of treating individual raster layers as

members of algebraic expressions.

2 * LayerA

Raster is Faster!Vector is corrector

Arithmetic Operators (+, -, *, /)

Mathematical Functions (Sqr, Sqrt, Log, Abs, exp, int, etc.)Comparison Operators (>, >=, =, <>, <, <=)Boolean Operators (AND, OR, NOT, XOR)

Map Algebra: LayerA + LayerB

Map Algebra:

Input

Output

LayerA * LayerB

Raster Calculator(for map algebra)

Spatial Analyst (extension for working

with raster data)

Converting feet to meters

Probability of encountering the cascade treefrog (Litoria pearsoniana) within the forests of eastern Australia:

1 / (1 + exp(10.48 – 2.204 * log10(RAINFALL) – 2.037 * PALMS))

RAINFALL= the annual volume of rain falling in the watershed above the stream PALMS = 1 if palms are present at the site and 0 otherwise.

Map Algebra Examples:

Fire Hazard:[Fuel Density Hazard] + [Slope Hazard] + [Veg Type Hazard]

Probability of success for entrepreneurs in Mendocino County

1 / (1 + exp(-(1.010e + 0) + (6.409e-02 * acreage) + (-7.100e-06 * land_value) + (-2.797e-01 * CE_count) + (-1.234e-02 * tot_pop))))))

Green = suitable aspect (cell value = 1)Red = unsuitable aspect (cell value = 0)

Slope < 20 degrees South facing slopes aspect between 150 and 200 degrees.

Identifying suitable habitat

Green = suitable slope (cell value = 1)Red = unsuitable slope (cell value = 0)

“suitable aspect” * “suitable slope”

suitable_habitat

Cell value = 1…Suitable slope & Suitable aspect

1 0 0 1

1 1 0 0

0 0 0 1

0 1 0 1

0 0 0 0

0 1 1 0

1 1 0 1

1 1 0 1

0 0 0 0

0 1 0 0

0 0 0 1

0 1 0 1

* =

Slope < 20 degrees South facing slopes aspect between 150 and 200 degrees.

?

Reclassification

Reclassification:

Assigns new output values that depend on the specific sets of input values (usually defined by a range of values)

1

1 1

1

1 1

1

1 2

2

1

2 3

44

4

2

3

4

0

Identify Slope < 20 degrees

Reclassify

Comparison operators

<

Layer 1 Layer 2

=

Comparing the cell value in one layer to the cell value in another layer.N = No Data

(>, >=, =, <>, <, <=)

Identify Slope < 20 degrees

(Alternative method)

“Slope” < 20

Boolean operatorsLayer 1 Layer 2

Output = 1 whereboth input cells aresomething other than0 or “N” (No Data)

Output = 1 whereone input cell or the other is something other than 0 or “N”

Output = 1 where input cell is a 0

(AND, OR, NOT, XOR)

XOR

[RAINFALL] > 20 XOR [SLOPE] < 35

Boolean operators

If the rainfall value is 21 and the slope value is 34 at a particular location, what would the output cell value be at that location?

0

Finding cells within a specific elevation range (500 -1000m)

Combining Boolean & Comparison Operators (1 raster layer)

1

0

"dem" > 500 and "dem" < 1000

Finding elevations between 20 and 500m where slope is less than 30 degrees

Combining Boolean & Comparison Operators (2 raster layers)

"DEM" > 20 and "DEM" < 500 and "slope" < 30

1

0

• Elevation• Slope• Aspect• Viewshed• Hillshade

Deriving terrain variables (e.g., slope, aspect) from a DEM

The direction (in compass angles) that a cell’s slope faces.

Determines …

1) Which way water will flow

2) amount of sunlight a site may receive

3) which portion of a landscape is visible from a

viewing point

N

The viewshed for a point is the collection of areas visible from that point.