Uncertainty modeling and analysis of surface area calculation based on a regular grid digital elevation model (DEM)

In the field of digital terrain analysis (DTA), the principle and method of uncertainty in surface area calculation (SAC) have not been deeply developed and need to be further studied. This paper considers the uncertainty of data sources from the digital elevation model (DEM) and SAC in DTA to perform the following investigations: (a) truncation error (TE) modeling and analysis, (b) modeling and analysis of SAC propagation error (PE) by using Monte-Carlo simulation techniques and spatial autocorrelation error to simulate DEM uncertainty. The simulation experiments show that (a) without the introduction of the DEM error, higher DEM resolution and lower terrain complexity lead to smaller TE and absolute error (AE); (b) with the introduction of the DEM error, the DEM resolution and terrain complexity influence the AE and standard deviation (SD) of the SAC, but the trends by which the two values change may be not consistent; and (c) the spatial distribution of the introduced random error determines the size and degree of the deviation between the calculated result and the true value of the surface area. This study provides insights regarding the principle and method of uncertainty in SACs in geographic information science (GIScience) and provides guidance to quantify SAC uncertainty.