A Digital Elevation Model (DEM) with a vertical Root Mean Square Error (RMSE) of 2 m means that ___________.
Show Hint
Recall that RMSE is computed by squaring, averaging, and then root-extracting the elevation differences at checkpoints, so it summarises typical error magnitude.
the average magnitude of vertical error in the DEM is 2 m
the DEM has a horizontal accuracy of ±2 m
the slope values more than 2° cannot be derived from the DEM
only low relief can be analyzed using the DEM
Show Solution
The Correct Option isA
Solution and Explanation
Step 1: Write RMSE as a summary error statistic.
Suppose a DEM is checked at several ground control points where the true elevation is known very precisely, say from GNSS levelling. At each point $i$ the elevation difference is $e_i = z_{DEM,i} - z_{true,i}$. The vertical RMSE combines all these differences as $RMSE = \sqrt{\dfrac{\sum e_i^2}{n}}$.
Step 2: Reason about the units and meaning of this single number.
Squaring and then taking a square root brings the result back to the same unit as elevation, metres, and produces a value that behaves like a typical size of error, treating positive and negative deviations symmetrically and penalising larger errors more heavily. In practice, surveyors and GIS analysts read a quoted RMSE of 2 m as "the DEM's elevations are, on average, about 2 m off from the truth in magnitude."
Step 3: Match this reading to the given statement.
This is precisely what option A says, that the average magnitude of vertical error is 2 m, so it is the correct interpretation of a stated vertical RMSE.
Step 4: Show why the remaining statements fail.
The question explicitly labels the RMSE as vertical, so it carries no information about horizontal positional accuracy, ruling out option B. There is no fixed rule that a 2 m vertical RMSE blocks slope computation beyond some angular threshold like 2 degrees, slope accuracy instead depends jointly on vertical RMSE and grid cell size, so option C is a fabricated restriction. Likewise, nothing about the RMSE value itself restricts the DEM's use to flat or low relief terrain, a DEM can be applied to any relief class, just with correspondingly larger absolute height uncertainties in steep terrain, so option D is also incorrect.
\[ \boxed{\text{the average magnitude of vertical error in the DEM is 2 m}} \]
