Raster Analysis

Common Analytical Functions and Surface Analysis

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Jeff Jenness

jeffj@jennessent.com (928) 607-4638

Main Topics

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Main Topics

• Reminder of what Raster data is

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Main Topics

• Reminder of what Raster data is

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• A few common ways to analyze raster data

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Main Topics

• Reminder of what Raster data is

​

• A few common ways to analyze raster data
• Reclassification

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Main Topics

• Reminder of what Raster data is

​

• A few common ways to analyze raster data
• Reclassification
• Zonal Analysis

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Main Topics

• Reminder of what Raster data is

​

• A few common ways to analyze raster data
• Reclassification
• Zonal Analysis
• Neighborhood Analysis

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Main Topics

• Reminder of what Raster data is

​

• A few common ways to analyze raster data
• Reclassification
• Zonal Analysis
• Neighborhood Analysis
• Math with Raster Layers

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Main Topics

• Reminder of what Raster data is

​

• A few common ways to analyze raster data
• Reclassification
• Zonal Analysis
• Neighborhood Analysis
• Math with Raster Layers

​

• Analysis of the shape of the landscape

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Main Topics

• Reminder of what Raster data is

​

• A few common ways to analyze raster data
• Reclassification
• Zonal Analysis
• Neighborhood Analysis
• Math with Raster Layers

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• Analysis of the shape of the landscape
• Slope, Aspect, Insolation, Hillshade, Curvature

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Main Topics

• Reminder of what Raster data is

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• A few common ways to analyze raster data
• Reclassification
• Zonal Analysis
• Neighborhood Analysis
• Math with Raster Layers

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• Analysis of the shape of the landscape
• Slope, Aspect, Insolation, Hillshade, Curvature
• Special Issues with Geographic Data

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Spatial Data

• Two Broad Categories: Vector and Raster
• Vector Data:

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Spatial Data

• Two Broad Categories: Vector and Raster
• Vector Data:
• Precisely-defined spatial objects like Points, Lines and Polygons

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Spatial Data

• Two Broad Categories: Vector and Raster
• Vector Data:
• Precisely-defined spatial objects like Points, Lines and Polygons
• Defined by one or more points called Vertices.

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Spatial Data

• Two Broad Categories: Vector and Raster
• Vector Data:
• Precisely-defined spatial objects like Points, Lines and Polygons
• Defined by one or more points called Vertices.
• Each vertex has X, Y and sometimes Z coordinates.

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Spatial Data

• Two Broad Categories: Vector and Raster
• Vector Data:
• Precisely-defined spatial objects like Points, Lines and Polygons
• Defined by one or more points called Vertices.
• Each vertex has X, Y and sometimes Z coordinates.
• Points are composed of a single vertex.

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Spatial Data

• Two Broad Categories: Vector and Raster
• Vector Data:
• Precisely-defined spatial objects like Points, Lines and Polygons
• Defined by one or more points called Vertices.
• Each vertex has X, Y and sometimes Z coordinates.
• Points are composed of a single vertex.
• Lines (called Polylines in the GIS world) are linear features composed of a series of connected vertices.

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Spatial Data

• Two Broad Categories: Vector and Raster
• Vector Data:
• Precisely-defined spatial objects like Points, Lines and Polygons
• Defined by one or more points called Vertices.
• Each vertex has X, Y and sometimes Z coordinates.
• Points are composed of a single vertex.
• Lines (called Polylines in the GIS world) are linear features composed of a series of connected vertices.
• Polygons are areal features composed of connected vertices, where the last vertex is connected back to the first vertex.

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Vector Example

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Vector Example

• Good for Contiguous Regions with a Constant Value

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Vector Example

• Good for Contiguous Regions with a Constant Value
• Land Ownership, Named Features

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Vector Example

• Good for Contiguous Regions with a Constant Value
• Land Ownership, Named Features
• Not so good for Constantly Changing Values across the landscape

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Vector Example

• Good for Contiguous Regions with a Constant Value
• Land Ownership, Named Features
• Not so good for Constantly Changing Values across the landscape
• Elevation, Habitat Suitability, Solar Insolation

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Raster Data

• Remember Two Broad Categories: Vector and Raster
• Raster Data:

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Raster Data

• Remember Two Broad Categories: Vector and Raster
• Raster Data:
• Composed of square pixels that completely cover a region. Occasionally they have rectangular pixels.

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Raster Data

• Remember Two Broad Categories: Vector and Raster
• Raster Data:
• Composed of square pixels that completely cover a region. Occasionally they have rectangular pixels.
• Each pixel has a value (such as a color or number) which represents the general raster value within the pixel area.

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Raster Data

• Remember Two Broad Categories: Vector and Raster
• Raster Data:
• Composed of square pixels that completely cover a region. Occasionally they have rectangular pixels.
• Each pixel has a value (such as a color or number) which represents the general raster value within the pixel area.
• Not as precisely defined as vector data. The pixel value is a general descriptor of the cell, not the value at an exact location.

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Raster Data

• Remember Two Broad Categories: Vector and Raster
• Raster Data:
• Composed of square pixels that completely cover a region. Occasionally they have rectangular pixels.
• Each pixel has a value (such as a color or number) which represents the general raster value within the pixel area.
• Not as precisely defined as vector data. The pixel value is a general descriptor of the cell, not the value at an exact location.
• Good at describing constantly changing values over the landscape.

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Raster Example

• They are often images, but with spatial parameters so we know exactly where they are located.
• The pixel size is called the Resolution.

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More on Rasters

• All rasters are composed of either a single or multiple raster bands. Images commonly have at least three raster bands for different electromagnetic wavelengths.

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Numeric Rasters

• Rasters do not have to show imagery.

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Numeric Rasters

• Rasters do not have to show imagery.
• Many rasters contain some kind of numeric values that describe or measure the landscape in some way.

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Numeric Rasters

• Rasters do not have to show imagery.
• Many rasters contain some kind of numeric values that describe or measure the landscape in some way.
• DEM: Digital Elevation Model, containing elevation or bathymetric values

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Numeric Rasters

• Rasters do not have to show imagery.
• Many rasters contain some kind of numeric values that describe or measure the landscape in some way.
• DEM: Digital Elevation Model, containing elevation or bathymetric values
• Slope, Aspect, Curvature, Surface Area rasters

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Numeric Rasters

• Rasters do not have to show imagery.
• Many rasters contain some kind of numeric values that describe or measure the landscape in some way.
• DEM: Digital Elevation Model, containing elevation or bathymetric values
• Slope, Aspect, Curvature, Surface Area rasters
• Streamflow, flow direction, contributing area (watershed)

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Numeric Rasters

• Rasters do not have to show imagery.
• Many rasters contain some kind of numeric values that describe or measure the landscape in some way.
• DEM: Digital Elevation Model, containing elevation or bathymetric values
• Slope, Aspect, Curvature, Surface Area rasters
• Streamflow, flow direction, contributing area (watershed)
• Habitat quality

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DEM: Digital Elevation Model

• Each raster cell contains elevation or bathymetric values.

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Common Raster Analysis Methods

• We will look at 4 common methods in this lab.

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Common Raster Analysis Methods

• We will look at 4 common methods in this lab.
• Reclassification

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Common Raster Analysis Methods

• We will look at 4 common methods in this lab.
• Reclassification
• Zonal Statistics

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Common Raster Analysis Methods

• We will look at 4 common methods in this lab.
• Reclassification
• Zonal Statistics
• Neighborhood Focal Statistics

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Common Raster Analysis Methods

• We will look at 4 common methods in this lab.
• Reclassification
• Zonal Statistics
• Neighborhood Focal Statistics
• Math with Raster Layers

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Common Raster Analysis Methods�Reclassification

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Common Raster Analysis Methods�Reclassification

• Just means to assign a new value based on an old value.

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Common Raster Analysis Methods�Reclassification

• Just means to assign a new value based on an old value.
• Usually used to categorize regions on the landscape that lie within some range of values.

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Common Raster Analysis Methods�Reclassification

• Just means to assign a new value based on an old value.
• Usually used to categorize regions on the landscape that lie within some range of values.
• Produces a new raster.

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Common Raster Analysis Methods�Reclassification

• Just means to assign a new value based on an old value.
• Usually used to categorize regions on the landscape that lie within some range of values.
• Produces a new raster.
• Makes it easy to summarize an area based on proportion of cells that fall in each category.

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Reclassification

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Common Raster Analysis Methods�Zonal Statistics

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Common Raster Analysis Methods�Zonal Statistics

• Calculates general descriptive statistics (mean, minimum, maximum, etc.) on all raster cells within zones.

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Common Raster Analysis Methods�Zonal Statistics

• Calculates general descriptive statistics (mean, minimum, maximum, etc.) on all raster cells within zones.
• Produces a Table of statistics describing each zone (although there are variations that produce other output formats).

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Common Raster Analysis Methods�Zonal Statistics

• Calculates general descriptive statistics (mean, minimum, maximum, etc.) on all raster cells within zones.
• Produces a Table of statistics describing each zone (although there are variations that produce other output formats).
• Zones can be defined lots of ways.

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Common Raster Analysis Methods�Zonal Statistics

• Calculates general descriptive statistics (mean, minimum, maximum, etc.) on all raster cells within zones.
• Produces a Table of statistics describing each zone (although there are variations that produce other output formats).
• Zones can be defined lots of ways.
• Most commonly by a combination of vector objects (points, polylines, polygons) and associated attribute values.

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Common Raster Analysis Methods�Zonal Statistics

• Calculates general descriptive statistics (mean, minimum, maximum, etc.) on all raster cells within zones.
• Produces a Table of statistics describing each zone (although there are variations that produce other output formats).
• Zones can be defined lots of ways.
• Most commonly by a combination of vector objects (points, polylines, polygons) and associated attribute values.
• Also by categorical rasters, such as the reclassified elevation raster from last slide.

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Zonal Statistics

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Zonal Statistics for Polygon

Zonal Statistics for Points

Zonal Statistics

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Zones based on County Name

Zones based on State Name

Zonal Statistics: Caution!

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The tool doesn’t work with overlapping polygons!

Even worse, it won’t tell you there was a problem.

The solution is to select each polygon individually and run the tool on that single polygon.

Zonal Statistics: Another Caution!

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The internal methods don’t always give you the correct values!

Point zone value = 16.42?

Common Raster Analysis Methods�Neighborhood Focal Statistics

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Common Raster Analysis Methods�Neighborhood Focal Statistics

• Analyzes all raster cells in some neighborhood around each cell.

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Common Raster Analysis Methods�Neighborhood Focal Statistics

• Analyzes all raster cells in some neighborhood around each cell.
• Sometimes called a Moving Window analysis.

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Common Raster Analysis Methods�Neighborhood Focal Statistics

• Analyzes all raster cells in some neighborhood around each cell.
• Sometimes called a Moving Window analysis.
• Neighborhood analysis produces a new raster, where each raster cell value is a statistic (sum, mean, minimum, etc.) describing all cells in the neighborhood around the original cell.

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Neighborhood Focal Statistics

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Neighborhood Focal Statistics

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Neighborhood Focal Statistics

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Neighborhood Focal Statistics

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Neighborhood Focal Statistics

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Neighborhood Focal Statistics

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Neighborhood Focal Statistics

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Neighborhood Focal Statistics

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Neighborhood Focal Statistics

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Neighborhood Shapes

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Common Raster Analysis Methods�Math with Raster Layers

• Use any standard mathematical operators or functions.

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Common Raster Analysis Methods�Math with Raster Layers

• Use any standard mathematical operators or functions.
• For Example: Adding two raster layers produces a new raster where each cell is the sum of the overlapping cells from the two source raster bands.

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Common Raster Analysis Methods�Math with Raster Layers

• Remember you can apply any standard mathematical operators or functions.

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Common Raster Analysis Methods�Math with Raster Layers

• A common example: NDVI

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Common Raster Analysis Methods�Math with Raster Layers

• A common example: NDVI

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-

+

=

Done with these 4 common raster analysis methods

• Reclassification
• Zonal Statistics
• Neighborhood Focal Statistics
• Math with Raster Layers

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Any questions at this point?

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Surface Analysis

• All about describing the shape of the landscape based on a DEM.

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“Love has boundaries, like a map, and I guess that makes me a cartographer. Don’t take this the wrong way, but you’re too topographical for my taste.”

Jarod Kintz, Love quotes for the ages. Specifically ages 18-81

Surface Analysis

• All about describing the shape of the landscape based on a DEM.
• Also known as Terrain Analysis

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“Love has boundaries, like a map, and I guess that makes me a cartographer. Don’t take this the wrong way, but you’re too topographical for my taste.”

Jarod Kintz, Love quotes for the ages. Specifically ages 18-81

Surface Analysis

• All about describing the shape of the landscape based on a DEM.
• Also known as Terrain Analysis
• Also known as Geomorphology

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“Love has boundaries, like a map, and I guess that makes me a cartographer. Don’t take this the wrong way, but you’re too topographical for my taste.”

Jarod Kintz, Love quotes for the ages. Specifically ages 18-81

Surface Analysis

• We will look at slope, aspect, insolation (solar radiation), hillshade and curvature.

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Surface Analysis

• We will look at slope, aspect, insolation (solar radiation), hillshade and curvature.
• Technically, insolation does not describe the shape of the landscape directly, but it is almost entirely defined by the shape of the landscape.

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Surface Analysis

• We will look at slope, aspect, insolation (solar radiation), hillshade and curvature.
• Technically, insolation does not describe the shape of the landscape directly, but it is almost entirely defined by the shape of the landscape.
• There are many, many other ways to describe the shape of the landscape that we won’t go into.

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Slope

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Slope

• Slope is usually defined in either Degrees or Percent.

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Slope

• Slope is usually defined in either Degrees or Percent.

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• Percent Slope is defined as “Rise over Run”.

Slope

• Slope is usually defined in either Degrees or Percent.

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• Percent Slope is defined as “Rise over Run”.
• 100% slope means that you have climbed vertically as much as you have moved horizontally.

Slope

• Slope is usually defined in either Degrees or Percent.

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• Percent Slope is defined as “Rise over Run”.
• 100% slope means that you have climbed vertically as much as you have moved horizontally.
• Notice that 100% slope does not mean a vertical cliff!

Slope

• Slope is usually defined in either Degrees or Percent.

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• Percent Slope is defined as “Rise over Run”.
• 100% slope means that you have climbed vertically as much as you have moved horizontally.
• Notice that 100% slope does not mean a vertical cliff!
• Percent Slope ranges from 0% to Infinity.

Slope

• Slope is usually defined in either Degrees or Percent.

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• Percent Slope is defined as “Rise over Run”.
• 100% slope means that you have climbed vertically as much as you have moved horizontally.
• Notice that 100% slope does not mean a vertical cliff!
• Percent Slope ranges from 0% to Infinity.
• Slope in Degrees ranges from 0° to 90°

Slope

• Slope is usually defined in either Degrees or Percent.

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• Percent Slope is defined as “Rise over Run”.
• 100% slope means that you have climbed vertically as much as you have moved horizontally.
• Notice that 100% slope does not mean a vertical cliff!
• Percent Slope ranges from 0% to Infinity.
• Slope in Degrees ranges from 0° to 90°
• Conversion Factors:

Slope Statistics

• You cannot calculate the mean and standard deviation of slope values if they are in Percent!

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Slope Statistics

• You cannot calculate the mean and standard deviation of slope values if they are in Percent!

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• Given two slope values at 0° and 90°, clearly the average slope would be 45°.

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Slope Statistics

• You cannot calculate the mean and standard deviation of slope values if they are in Percent!

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• Given two slope values at 0° and 90°, clearly the average slope would be 45°.

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• If you tried this with % Slope values, your average slope would be a vertical cliff.

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Slope Statistics

• You cannot calculate the mean and standard deviation of slope values if they are in Percent!

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• Given two slope values at 0° and 90°, clearly the average slope would be 45°.

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• If you tried this with % Slope values, your average slope would be a vertical cliff.

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• If you want to calculate the average slope, your slope values must be in Degrees instead of Percent. You can always convert the average back to Percent if you want.

Aspect

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If you do not change direction, you may end up where you are heading. Lau Tzu

Aspect

• Aspect plays a major role in microclimate, vegetation density and species composition.

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What do you do with Aspect?

• Circular Variable:

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What do you do with Aspect?

• Circular Variable:
• The difference between 0° and 1° is the same as the difference between 0° and 359°!

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What do you do with Aspect?

• Circular Variable:
• The difference between 0° and 1° is the same as the difference between 0° and 359°!
• You can’t use arithmetic mean and standard deviation! The Focal Statistics and Zonal Statistics tools do not give you correct statistics.

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What do you do with Aspect?

• Circular Variable:
• The difference between 0° and 1° is the same as the difference between 0° and 359°!
• You can’t use arithmetic mean and standard deviation! The Focal Statistics and Zonal Statistics tools do not give you correct statistics.
• There are measures of dispersion and central tendency, though…

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What do you do with Aspect?

• Circular Variable:
• The difference between 0° and 1° is the same as the difference between 0° and 359°!
• You can’t use arithmetic mean and standard deviation! The Focal Statistics and Zonal Statistics tools do not give you correct statistics.
• There are measures of dispersion and central tendency, though…

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What do you do with Aspect?

• Mean Direction

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What do you do with Aspect?

• Mean Direction

Math was always my bad subject. I couldn't convince my teachers that many of my answers were meant ironically. Calvin Trillin

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What do you do with Aspect?

• Mean Resultant Length
• Component of several measures of dispersion

And by the same token, I appreciate math, because I can't do math. If I have to read a map or figure out the tip on a restaurant bill, I might start to tear up a little bit. Thomas Wilson

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• Some people decompose Aspect into Northness and Eastness values, using the sine and cosine of aspect.

• Make sure you convert Degrees to Radians first!

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What do you do with Aspect?

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• Some people decompose Aspect into Northness and Eastness values, using the sine and cosine of aspect.
• Or, from any direction of interest: See Trimble and Weitzman 1956 [SE/NW], or Beers et al. 1966 [Any Direction]

• Make sure you convert Degrees to Radians first!

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What do you do with Aspect?

Beers, T. W., P. E. Dress, and L. C. Wensel. 1966. Notes and Observations: Aspect Transformation in Site Productivity Research. Journal of Forestry 64:691–692.

Trimble, G. R., and S. Weitzman. 1956. Site Index Studies of Upland Oaks in the Northern Appalachians. Forest Science 2:162–173.

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• Some people decompose Aspect into Northness and Eastness values, using the sine and cosine of aspect.
• Or, from any direction of interest: See Trimble and Weitzman 1956 [SE/NW], or Beers et al. 1966 [Any Direction]
• Alternatively, simply convert aspect into a Deviation from some Direction of Interest.

• Make sure you convert Degrees to Radians first!

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• Green dashed line:
• If Aspect ≤ 180, then
• Deviation = Aspect
• Else if Aspect > 180, then
• Deviation = [360 – Aspect]

What do you do with Aspect?

Beers, T. W., P. E. Dress, and L. C. Wensel. 1966. Notes and Observations: Aspect Transformation in Site Productivity Research. Journal of Forestry 64:691–692.

Trimble, G. R., and S. Weitzman. 1956. Site Index Studies of Upland Oaks in the Northern Appalachians. Forest Science 2:162–173.

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What do you do with Aspect?

I am among those who think that science has great beauty. A scientist in his laboratory is not only a technician: he is also a child placed before natural phenomena which impress him like a fairy tale. Marie Curie

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What do you do with Aspect?

If you torture data sufficiently, it will confess to almost anything. Fred Menger

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Trivia Time!

• What famous statistician invented this type of graph?
• This person called it a Rose Plot, because the bars extended out like the petals of a flower.

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Trivia Time!

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Trivia Time!

Florence Nightingale!

In the Crimean War, she

convinced the queen to adopt

medical and sanitary standards

with this chart

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• A lot of people just reclassify it into general directions, then summarize their study area according to percentage in each general direction.

What do you do with Aspect?

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What do you do with Aspect?

• Some food for thought:
• Aspect obviously has a great influence on vegetation species composition, structure and microhabitat.

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What do you do with Aspect?

• Some food for thought:
• Aspect obviously has a great influence on vegetation species composition, structure and microhabitat.
• Why does Aspect have this influence?

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What do you do with Aspect?

• Some food for thought:
• Aspect obviously has a great influence on vegetation species composition, structure and microhabitat.
• Why does Aspect have this influence?
• Possibly because of prevailing wind direction.
• In large part because of how much sunlight hits the area, and at what angle.

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What do you do with Aspect?

• Some food for thought:
• Aspect obviously has a great influence on vegetation species composition, structure and microhabitat.
• Why does Aspect have this influence?
• Possibly because of prevailing wind direction.
• In large part because of how much sunlight hits the area, and at what angle.
• If aspect is important because of how it influences sun exposure, then perhaps solar insolation would be a better variable to use.
• Much easier to calculate summary statistics from solar insolation!

Solar Insolation

• In many cases, it may be a more direct driver for vegetation and microclimate than aspect.

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Solar Insolation

• In many cases, it may be a more direct driver for vegetation and microclimate than aspect.
• All about measuring how much sunlight hits the ground, based on topography.

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Solar Insolation

• In many cases, it may be a more direct driver for vegetation and microclimate than aspect.
• All about measuring how much sunlight hits the ground, based on topography.
• It does incorporate direct sunlight from the sun, plus diffuse radiation from the sky in general.

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Solar Insolation

• In many cases, it may be a more direct driver for vegetation and microclimate than aspect.
• All about measuring how much sunlight hits the ground, based on topography.
• It does incorporate direct sunlight from the sun, plus diffuse radiation from the sky in general.
• It does not incorporate reflection from the ground.

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Solar Insolation

• In many cases, it may be a more direct driver for vegetation and microclimate than aspect.
• All about measuring how much sunlight hits the ground, based on topography.
• It does incorporate direct sunlight from the sun, plus diffuse radiation from the sky in general.
• It does not incorporate reflection from the ground.
• Lots of cool options, like calculating for a specific time, day, season or year.

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Solar Insolation

• In many cases, it may be a more direct driver for vegetation and microclimate than aspect.
• All about measuring how much sunlight hits the ground, based on topography.
• It does incorporate direct sunlight from the sun, plus diffuse radiation from the sky in general.
• It does not incorporate reflection from the ground.
• Lots of cool options, like calculating for a specific time, day, season or year.
• It takes a long time to calculate, though.

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Solar Insolation

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Solar Insolation: Optional Output

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Hillshade

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The “Swiss Method”

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Beauty is the first test; there is no permanent place in the world for ugly mathematics. G. H. Hardy

The “Swiss Method”

• Light Source from Multiple Directions

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Beauty is the first test; there is no permanent place in the world for ugly mathematics. G. H. Hardy

The “Swiss Method”

• Light Source from Multiple Directions
• Atmospheric Adjustments

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Beauty is the first test; there is no permanent place in the world for ugly mathematics. G. H. Hardy

The “Swiss Method”

• Light Source from Multiple Directions
• Atmospheric Adjustments
• Blur the Final Hillshade

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Beauty is the first test; there is no permanent place in the world for ugly mathematics. G. H. Hardy

MDOW Hillshade��Multidirectional, Oblique-Weighted Hillshade

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4 illumination sources

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4 illumination sources

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Hypsometric Shading

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Blurring the hillshade

You can easily create this manually if you like, by:

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Blurring the hillshade

You can easily create this manually if you like, by:

1. Calculating a neighborhood mean of the DEM before creating the hillshade, or

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Blurring the hillshade

You can easily create this manually if you like, by:

1. Calculating a neighborhood mean of the DEM before creating the hillshade, or
2. Calculating a neighborhood mean of the hillshade after you’ve created it.

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Blurring the hillshade

You can easily create this manually if you like, by:

1. Calculating a neighborhood mean of the DEM before creating the hillshade, or
2. Calculating a neighborhood mean of the hillshade after you’ve created it.

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Option 1 usually looks a little better.

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Hillshade Trivia

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Is this a mountain range or a canyon?

Hillshade Trivia

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Here is what it looks like using the default sun direction.

Curvature

• Infinite number of variations. ArcGIS offers 3 types of curvature.

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Curvature

• Infinite number of variations. ArcGIS offers 3 types of curvature.
• It can be used as a measure of exposure because it identifies hills, ridges, valleys and depressions.

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Curvature

• Infinite number of variations. ArcGIS offers 3 types of curvature.
• It can be used as a measure of exposure because it identifies hills, ridges, valleys and depressions.
• Used a lot in hydrological projects because it shows whether water will converge, diverge, accelerate or decelerate as it flows over a cell.

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Curvature�This general curvature tells you whether the landscape is concave or convex. Values can be positive or negative.�

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Curvature

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Profile Curvature�Suggests whether running water will speed up or slow down as it flows over the point.�

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Intersect a vertical plane, in direction of aspect, with the surface

Profile Curvature

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Plan Curvature�Suggests whether water will converge or diverge as it flows over a point.

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Intersect a horizontal plane with the surface

Plan Curvature

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Curvature Units

• This is usually what curvature units mean, although some variations of curvature don’t really have understandable units.

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• Often landscape curvature is so flat that curvature is reported in units of

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• Curvature calculated on line of intersection between surface and a plane.

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Warning!�If your DEM is in Geographic coordinates, only use Geodesic methods to calculate surface rasters!

• Many standard ArcGIS surface tools are only accurate with projected data. Geographic (i.e. Latitude / Longitude) data violate important assumptions of the tools.

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Warning!�If your DEM is in Geographic coordinates, only use Geodesic methods to calculate surface rasters!

• Many standard ArcGIS surface tools are only accurate with projected data. Geographic (i.e. Latitude / Longitude) data violate important assumptions of the tools.
• Assumption 1: The tools assume the raster cells are square. Geographic raster cells are actually trapezoidal when viewed on the earth’s surface.

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Warning!�If your DEM is in Geographic coordinates, only use Geodesic methods to calculate surface rasters!

• Many standard ArcGIS surface tools are only accurate with projected data. Geographic (i.e. Latitude / Longitude) data violate important assumptions of the tools.
• Assumption 1: The tools assume the raster cells are square. Geographic raster cells are actually trapezoidal when viewed on the earth’s surface.
• Assumption 2: The X, Y and Z units are all the same.

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Here is the problem:

• All surface tools rely on both the east-west and north-south gradients over every cell.

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Given 9 elevation values…

Z1 ---- Z2 ---- Z3

| | |

| | |

| | |

Z4 ---- Z5 ---- Z6

| | |

| | |

| | |

Z7 ---- Z8 ---- Z9

Here is the problem:

• Unfortunately the cells are trapezoids, not squares!
• Therefore the cell size is different for the east-west and north-south gradients, and even for each row in the east-west calculations.

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Here is the problem:

• Consequently, ArcGIS underestimates the east-west gradient, which screws up all the other surface calculations.

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Another (more general) Problem with Units:

Remembering back to the

equations:

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Given 9 elevation values…

Z1 ---- Z2 ---- Z3

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Z4 ---- Z5 ---- Z6

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Z7 ---- Z8 ---- Z9

Another (more general) Problem with Units:

Remembering back to the

equations:

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• These equations also assume that the Z-units are the same as the X- and Y-units.

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Given 9 elevation values…

Z1 ---- Z2 ---- Z3

| | |

| | |

| | |

Z4 ---- Z5 ---- Z6

| | |

| | |

| | |

Z7 ---- Z8 ---- Z9

Another (more general) Problem with Units:

Remembering back to the

equations:

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• These equations also assume that the Z-units are the same as the X- and Y-units.
• If your elevation units are in Feet, but your raster coordinate system uses Meters (and therefore your cell sizes are in meters), then you must remember to set a correction factor in the tool to convert Feet to Meters!

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Given 9 elevation values…

Z1 ---- Z2 ---- Z3

| | |

| | |

| | |

Z4 ---- Z5 ---- Z6

| | |

| | |

| | |

Z7 ---- Z8 ---- Z9

Another (more general) Problem with Units:

Remembering back to the

equations:

​

​

​

​

​

​

​

​

• These equations also assume that the Z-units are the same as the X- and Y-units.
• If your elevation units are in Feet, but your raster coordinate system uses Meters (and therefore your cell sizes are in meters), then you must remember to set a correction factor in the tool to convert Feet to Meters!
• This is a common user error. ArcGIS lets you set an elevation correction factor (called a z-factor) to avoid this error, but it is up to you to remember to set it!

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Given 9 elevation values…

Z1 ---- Z2 ---- Z3

| | |

| | |

| | |

Z4 ---- Z5 ---- Z6

| | |

| | |

| | |

Z7 ---- Z8 ---- Z9

Surface Analysis: Major Points to Remember:�These are very common errors people make…

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Surface Analysis: Major Points to Remember:�These are very common errors people make…

• It is fine to calculate slope as either Percent Slope or Degrees Slope. However, you can’t calculate descriptive statistics if your slope values are in Percent.

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Surface Analysis: Major Points to Remember:�These are very common errors people make…

• It is fine to calculate slope as either Percent Slope or Degrees Slope. However, you can’t calculate descriptive statistics if your slope values are in Percent.
• Percent slope works fine if you want to reclassify into, say, harvestable vs. non-harvestable slopes.

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Surface Analysis: Major Points to Remember:�These are very common errors people make…

• It is fine to calculate slope as either Percent Slope or Degrees Slope. However, you can’t calculate descriptive statistics if your slope values are in Percent.
• Percent slope works fine if you want to reclassify into, say, harvestable vs. non-harvestable slopes.
• 100% Slope is not equal to a vertical cliff. It is equal to a 45° slope.

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Surface Analysis: Major Points to Remember:�These are very common errors people make…

• It is fine to calculate slope as either Percent Slope or Degrees Slope. However, you can’t calculate descriptive statistics if your slope values are in Percent.
• Percent slope works fine if you want to reclassify into, say, harvestable vs. non-harvestable slopes.
• 100% Slope is not equal to a vertical cliff. It is equal to a 45° slope.
• Aspect is a circular variable and therefore you can’t use traditional methods to calculate descriptive statistics.

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Surface Analysis: Major Points to Remember:�These are very common errors people make…

• It is fine to calculate slope as either Percent Slope or Degrees Slope. However, you can’t calculate descriptive statistics if your slope values are in Percent.
• Percent slope works fine if you want to reclassify into, say, harvestable vs. non-harvestable slopes.
• 100% Slope is not equal to a vertical cliff. It is equal to a 45° slope.
• Aspect is a circular variable and therefore you can’t use traditional methods to calculate descriptive statistics.
• Many surface variables require that your DEM be projected!
• Slope and Aspect exceptions in newer versions of software, but curvature and hillshades still require projected data.

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Neighborhood and Surface Analysis Tip

• Remember that all Neighborhood tools require all cells in the neighborhood to accurately calculate the new cell value.

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Neighborhood and Surface Analysis Tip

• Remember that all Neighborhood tools require all cells in the neighborhood to accurately calculate the new cell value.
• Most surface analysis functions (slope, aspect, hillshade and curvature) are neighborhood functions that use a 3x3 or 5x5 cell neighborhood.

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Neighborhood and Surface Analysis Tip

• Remember that all Neighborhood tools require all cells in the neighborhood to accurately calculate the new cell value.
• Most surface analysis functions (slope, aspect, hillshade and curvature) are neighborhood functions that use a 3x3 or 5x5 cell neighborhood.
• Therefore neighborhood and surface tools cannot accurately calculate values for the outermost rows and columns, or any cells next to “No Data” cells.

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Neighborhood and Surface Analysis Tip

• Remember that all Neighborhood tools require all cells in the neighborhood to accurately calculate the new cell value.
• Most surface analysis functions (slope, aspect, hillshade and curvature) are neighborhood functions that use a 3x3 or 5x5 cell neighborhood.
• Therefore neighborhood and surface tools cannot accurately calculate values for the outermost rows and columns, or any cells next to “No Data” cells.
• Consequently the new raster will either be smaller (fewer rows and columns) than the original raster, or the outermost cells will not be calculated with full data.

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Neighborhood and Surface Analysis Tip

• Remember that all Neighborhood tools require all cells in the neighborhood to accurately calculate the new cell value.
• Most surface analysis functions (slope, aspect, hillshade and curvature) are neighborhood functions that use a 3x3 or 5x5 cell neighborhood.
• Therefore neighborhood and surface tools cannot accurately calculate values for the outermost rows and columns, or any cells next to “No Data” cells.
• Consequently the new raster will either be smaller (fewer rows and columns) than the original raster, or the outermost cells will not be calculated with full data.

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Neighborhood and Surface Analysis Tip

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Neighborhood and Surface Analysis Tip

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Neighborhood and Surface Analysis Tip

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Neighborhood and Surface Analysis Tip

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Neighborhood and Surface Analysis Tip

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Neighborhood and Surface Analysis Tip

• Takeaway message: If you want to calculate neighborhood or surface rasters accurately within some area, make sure your original DEM or source raster is larger than that area!

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Neighborhood and Surface Analysis Tip

• Takeaway message: If you want to calculate neighborhood or surface rasters accurately within some area, make sure your original DEM or source raster is larger than that area!
• For Surface rasters (slope, aspect, hillshade, curvature), your original DEM should be at least 1 – 2 cells larger than your area (curvature requires a 5x5 neighborhood, so you need a 2-cell buffer).

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Neighborhood and Surface Analysis Tip

• Takeaway message: If you want to calculate neighborhood or surface rasters accurately within some area, make sure your original DEM or source raster is larger than that area!
• For Surface rasters (slope, aspect, hillshade, curvature), your original DEM should be at least 1 – 2 cells larger than your area (curvature requires a 5x5 neighborhood, so you need a 2-cell buffer).
• For other neighborhood rasters, your original raster should be larger than your area by at least ½-neighborhood size.

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Neighborhood and Surface Analysis Tip

• Takeaway message: If you want to calculate neighborhood or surface rasters accurately within some area, make sure your original DEM or source raster is larger than that area!
• For Surface rasters (slope, aspect, hillshade, curvature), your original DEM should be at least 1 – 2 cells larger than your area (curvature requires a 5x5 neighborhood, so you need a 2-cell buffer).
• For other neighborhood rasters, your original raster should be larger than your area by at least ½-neighborhood size.
• Solar Insolation requires a much larger region than your area (typically about 200 cells) because it accounts for shadows from far away.

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Issues with Directional Data

• If you are interested, I have attached a discussion on special issues with working with directional data.
• See Appendix to lab exercise document.

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