Question

A Digital Elevation Model (DEM) with a vertical Root Mean Square Error (RMSE) of 2 m means that ___________.

• A. the average magnitude of vertical error in the DEM is 2 m
• B. the DEM has a horizontal accuracy of ±2 m
• C. the slope values more than 2° cannot be derived from the DEM
• D. only low relief can be analyzed using the DEM

Hint:

Recall that RMSE is computed by squaring, averaging, and then root-extracting the elevation differences at checkpoints, so it summarises typical error magnitude.

Answer 1

The Correct Option is A

Step 1: Recall the definition of Root Mean Square Error.
For a Digital Elevation Model, the vertical accuracy is usually reported as a Root Mean Square Error (RMSE), computed by comparing the DEM elevation \(z_{DEM,i}\) with an independently surveyed, more accurate reference elevation \(z_{ref,i}\) at a set of \(n\) checkpoints: \( RMSE_z = \sqrt{\dfrac{1}{n}\sum_{i=1}^{n}\left(z_{DEM,i}-z_{ref,i}\right)^2} \).
Step 2: Interpret what this number represents physically.
Because the individual errors are squared before averaging and then a square root is taken, RMSE behaves like a typical or characteristic magnitude of the vertical error across the checkpoints, it summarises how far, on average, the DEM elevations deviate from the true elevations, giving more weight to larger errors than a simple mean absolute error would. So a vertical RMSE of 2 m tells the user that the DEM elevation values are typically in error, up or down, by about 2 m compared to the true ground surface.
Step 3: Confirm this matches option A.
Stating that "the average magnitude of vertical error in the DEM is 2 m" is exactly this interpretation, RMSE is the accepted standard statistic used precisely to summarise the overall magnitude of vertical error in a DEM.
Step 4: Eliminate the other options.
Option B is wrong because RMSE here is explicitly stated to be vertical, it says nothing about horizontal (planimetric) accuracy, which would need a separate horizontal RMSE computed from horizontal checkpoint coordinates. Option C is wrong because slope is a derivative of elevation, RMSE does not put any fixed cap of "2 degrees" on derivable slope values, slope error propagation from a 2 m vertical RMSE actually also depends on the DEM's horizontal grid spacing, not a fixed angular cutoff. Option D is wrong because RMSE is a statistic about accuracy, not about terrain relief category, a DEM with 2 m vertical RMSE can still be used, with appropriate caution, over higher relief terrain, it does not restrict analysis strictly to low relief areas.
\[ \boxed{\text{Option (A): the average magnitude of vertical error in the DEM is 2 m}} \]