When evaluating the accuracy of a terrain model, two common metrics are the **Average Error** and the **Root Mean Square Error (RMSE)**. Both metrics provide insight into how well the terrain model matches the actual observed values, but they do so in different ways. The Average Error is easy to understand but is less effective as a metric, while the RMSE is more difficult to understand than the average error, but a more effective metric. We'll cover what both of these metrics are and what they mean for your drone data.

**Overview**

# Understanding Average Error and RMSE

**The Average Error:** The Average Error represents the mean of the differences between your terrain elevation (modeled values) and the measured control points (actual values). A lower average error often suggests that your control points are closely aligned with the elevation terrain, this is usually the case, but the reality can be more nuanced. If you have a lot of large errors that average each other out e.g., errors being on opposite ends of the spectrum but give an average error close to 0, you still might not have acceptable results. In contrast, a high average error might be caused by a constant vertical shift due to the wrong vertical reference datum being used on your elevation terrain. I.e., the Average Error is easy to interpret and treats all errors equally—regardless of their magnitude and direction—and makes it easy to see how far off the terrain measurement is on average.

**The RMSE:** The Root Mean Square Error (RMSE) is a more reliable measure of terrain model accuracy because it considers both the magnitude and direction of errors. Unlike the Average Error, where positive and negative errors can cancel each other out, the RMSE accounts for their effects. Larger errors have a greater impact on the RMSE than smaller ones, making it a better indicator of typical error ranges in a terrain model. However, it is also more sensitive to outliers.

## Error Cases

Here are some theoretical cases that will help you understand the difference. The 0 line in the graph images below represent the terrain measurement, and the dots represent the field measurements. The errors are the difference between the terrain measurement and each measured control point.

A - Low Average Error Low RMSE | B - Low Average Error High RMSE | C - High Average Error High RMSE | D - High Average Error High RMSE | |
---|---|---|---|---|

Average Error | 0.010 | -0.003 | 0.122 | 0.160 |

RMSE | 0.016 | 0.064 | 0.079 | 0.053 |

**Case A: **Normal case with minor errors. This is what you want your data to look like with errors being close together.

**Case B:** Normal case with slightly higher errors. Flying the drone higher can create opposing errors at a wider margin resulting in a low average error and a higher RMSE.

**Case C: **In cases where there is a high average error and RMSE, it can often be challenging to immediately identify the cause. Such situations can have multiple underlying reasons. A common scenario is when you're working in a local coordinate system, which Terrain Creator does not support yet. In this case, the ground points have a scaling factor applied, while the project's coordinate system is defined without that scaling factor, leading to discrepancies in accuracy. Read our troubleshooting for errors or validating your elevation model for additional insight and information.

**Case D:** A unique case where the wrong vertical datum is used, causing a large vertical shift of errors.

This unique scenario (Case D) has a solution. If you process your drone data through our Terrain Creator app, it will recognize and fix this offset for you. If you load an orthophoto and DSM from another program into the Virtual Surveyor app, you can use the Offset Z function to lower both your Average Error and RMSE by correcting your terrain measurement to your field measurements. Read more about how to do this in our Offset Z article.

# Benefits of Your Drone Data

The drone elevation model gives you a continuous surface and information over the entire site, while a traditional survey only gives you a small sample of points to work with—which may be fairly accurate—but doesn't tell you anything about the locations of the project site in between the points. There is a lot of value using a drone elevation model simply due to the density of its data and how much information (both visuals and metrics) you have to work with.