An algorithm for developing a roughness map from a digital elevation model of a sediment bed

The roughness of a sediment bed is an important bed characteristic used for modeling processes occurring in a stream or an open channel. Surface roughness is usually measured for the entire channel; however, roughness can vary significantly throughout a channel, changing fluid dynamics. An algorithm is created to provide a spatially varying roughness estimate for any location of a sediment bed from a digital elevation model by using a moving sample window. Three different roughness measurements were used: standard deviation of the absolute value of detrended elevations, peak frequency, and microrelief frequency. All three roughness measurements resulted in a roughness map that represented the spatial variability in the channel roughness. The standard deviation and microrelief frequency produced similar maps with roughness measurements increasing with sediment sizes. The peak frequency did not correlate with sediment size, perhaps due to the resolution of the digital elevation model. Once the peak frequency is corrected for the resolution, then the peak frequency decreases with sediment size. The roughness maps can be altered by adjusting the sample window size and the decay rate of the weighting matrix. A larger sample window and a smaller decay rate results in a smoother roughness map. A smaller sample window and a larger decay rate results in a more sensitive roughness map. The roughness maps are applicable to any application where the spatial or temporal change in channel roughness may be of interest. The values in the roughness maps agreed with observations made during flume experiments under a variety of conditions.