# How to calculate and compare RMSE between two DEMs? [duplicate]

I'm doing a project based on using Lidar point cloud data and I have access to a DEM that cover all of Sweden. But my goal is to produce several DEMs covering a small area using different interpolation methods. For this I'm working with the LAS dataset toolbox. When that's done I want to compare my own produced DEMs with the DEM that cover whole of Sweden and check for RMSE error.

I'm quite clueless how to solve this since I'm not a mathematician and I'm new to working with Lidar.

I'm using ArcGIS for this.

## 1 Answer

The Root Mean Square Error (RMSE) is one of those rare indices that is perfectly named, in that the name actually tells you how to calculate it. First difference the two DEMs ('error' or more properly in this case the deviation). Then square the differences. These first two steps can be calculated using a single expression in the Raster Calculator. Next, calculate the mean of your squared deviations for the image as a whole. For this you may want to use the Calculate Statistics tool, although there is likely several valid ways to get the average of a raster in ArcGIS. Lastly, take the square root of your mean squared deviation. That's it. That will give you the RMSD of the two rasters. Good luck.

• thanks for your answer. I don't really follow at the end when you say " Lastly, take the square root of your mean squared deviation." because Calculate Statistics don't give me a file just numbers. – Mutumba Oct 23 '14 at 20:28
• Yes, you will ultimately end up with just a single number for the entire dataset. Once you have your average (from Calculate Statistics), simply take the square root of it using Excel or a calculator. That's your RMSE. – WhiteboxDev Oct 23 '14 at 20:31
• Ah now I get it! Sorry but you sometimes get confused when you've worked with GIS too much I guess. Big thanks, this saved my project. – Mutumba Oct 23 '14 at 20:37
• I'm glad to have helped. – WhiteboxDev Oct 23 '14 at 20:39