# Comparing two DEMs with RMSE?

I am relatively new to GIS. I am trying to compare a DEM that I developed through photos from an aerial drone and a DEM that we developed through traditional surveying methods.

Exactly how would I get the RMSE? I saw some similarly asked questions that explained how to use R to get it, but I am very unfamiliar with any sort of coding. Is there anyway to get the RMSE through Spatial Analyst or other already available tools?

There are numerous ways to examine the differences between two surfaces. A starting point would be:

1. Subtracting the two DEMs shows the differences as a map, which can indicate areas where one or both are erroneous.
2. Scatterplot with one on the X-axis and one on the Y-axis, to show correlation.
3. Calculate co-variance, RMSE, bimodality etc between the two datasets.
4. Creating contours from both layers and analyze those statistically.

Also, you could read Comparison of three contour lines or What is a good metric for mapping accuracy for ideas.

What specifically would you want to compare? There's lots of statistical methods you could use.

You could easily just compare histograms. These would show you the distributions of the elevation data for comparison. Key stats of a histogram could give you insight into how they differ, for example, comparing standard deviation values could show you if one has a higher spread from the mean and thus potentially differing systematic biases from the two surveying methods (i expect the photogrammetry method is more likely to have higher elevations if there is vegetation).

Hope that helps

Have you considered comparing the location of Ground Control Points (GCP) between the two DEMS in order to asses the accuracy of the UAV DEM and the one derived from traditional survey methods? By measuring the difference in x,y between GCPs identified in both images you could calculate the Root Mean Squared Error (RMSE) (http://gisgeography.com/root-mean-square-error-rmse-gis/)

Another relatively simple method of comparing how 'similar' the two DEMs are, would be to calculate the correlation between the two (assuming) raster datasets (Spearman correlation between two rasters in R)

My preference would certainly be to use a statistical software, such as R. That said, it is possible to do this in ArcGIS.

First, create a random sample using the "Create Random Points" tool in the Data Management toolbox. If the topography is highly variable you will need a bigger sample than if it is homogeneous. Just make sure that the sample is large enough to capture the variation in the data.

Second, assign the raster values to your random points using the "Extract Multi Values to Points" tool in the Spatial Analyst toolbox. To ensure that the sample distribution is adequate one would examine the empirical distribution, but in ArcGIS the histogram will do. Compare the histogram of the DEM to that of your samples to make sure that you are not missing sample variation.

Finally, you will have a table with the raster values from each raster assigned to your random points. To derive the Root Mean Squared Error (RMSE) you would calculate `sqrt(mean((predicted - observed)^2))` which, when exported, should be quite straight forward in in a spreadsheet such as Excel. Since it is designed to operate on attribute tables, the ArcGIS field calculator will not return a single value.

If you want to examine the scale dependent correlation or covariance, I have a tool in the Geomorphometry & Gradient Metrics Toolbox that will do exactly this. Sometimes looking at these patterns across multiple scales can reveal unexpected findings in your error structure.