Calculate Topographic Position Index in Arcgis

The Topographic Position Index (TPI) is a terrain analysis tool used in geographic information systems (GIS) to identify landscape features such as ridges, valleys, and flat areas. This guide explains how to calculate TPI in ArcGIS, including the formula, practical examples, and interpretation of results.

What is Topographic Position Index (TPI)?

TPI is calculated by comparing the elevation of a cell to the average elevation of its surrounding cells. Positive values indicate ridges or peaks, negative values indicate valleys or depressions, and values close to zero indicate flat areas.

How to Calculate TPI in ArcGIS

Calculating TPI in ArcGIS involves several steps:

Prepare your digital elevation model (DEM) data
Use the Focal Statistics tool to calculate the average elevation of surrounding cells
Subtract the original elevation from the average elevation to get TPI values
Interpret the results to identify landscape features

Note: The neighborhood size for the Focal Statistics tool should be carefully chosen based on your specific analysis requirements.

TPI Formula

TPI = Elevation of cell - Average elevation of surrounding cells

The formula shows that TPI is calculated by subtracting the average elevation of surrounding cells from the elevation of the cell itself. This provides a measure of how much higher or lower the cell is compared to its neighbors.

Worked Example

Let's calculate TPI for a cell with an elevation of 500 meters, surrounded by cells with the following elevations:

Cell	Elevation (m)
Center cell	500
Surrounding cells	480, 490, 510, 520, 470, 485, 505, 515

First, calculate the average elevation of the surrounding cells:

Average elevation = (480 + 490 + 510 + 520 + 470 + 485 + 505 + 515) / 8 = 496.125 m

Then, apply the TPI formula:

TPI = 500 - 496.125 = 3.875

This positive TPI value indicates that the cell is higher than its surroundings, suggesting it may be part of a ridge or peak.

Interpreting TPI Results

Interpreting TPI results involves understanding the values and their implications for landscape features:

Positive TPI values (greater than 0) indicate ridges or peaks
Negative TPI values (less than 0) indicate valleys or depressions
Values close to zero indicate flat areas

The magnitude of TPI values can also provide information about the relative relief of landscape features. Larger positive or negative values indicate more pronounced features.

FAQ

What is the difference between TPI and other terrain analysis tools?: TPI focuses specifically on the relative position of a cell compared to its neighbors, while other tools like slope and aspect provide different types of terrain information.
How do I choose the appropriate neighborhood size for TPI calculation?: The neighborhood size should be chosen based on the scale of the landscape features you're interested in analyzing. Larger neighborhoods will smooth the results and highlight broader features.
Can TPI be used for hydrological analysis?: Yes, TPI can be useful for identifying potential drainage divides and flow paths in hydrological analysis.
What are the limitations of TPI?: TPI assumes that the landscape is isotropic (the same in all directions), which may not always be the case. Additionally, TPI may not capture all aspects of landscape complexity.
How can I visualize TPI results in ArcGIS?: You can use the Symbology tab in the Layer Properties to apply a color ramp to your TPI raster, making it easier to interpret the results.