How does surface roughness affect the accuracy of the elevation measurement?

Over most of the ice sheets, the accuracy of each elevation measurement will be 15 cm. Average ice elevation changes less than 1 cm will be detected by averaging the elevation differences observed at many points in selected regions of the ice sheets. Over land, the vertical accuracy of the elevation measurements will be better than a meter in regions of low slope and up to 10 m in regions of large slopes.

Areas of high roughness and/or slope produce a broadening (or even multiple peaks) in the returned energy (y) vs. time (x) waveform from a single laser pulse. This broadening has the effect of increasing the uncertainty in assigning a single average elevation to the area within the GLAS footprint without independent estimates of both the slope and roughness.

Researchers can measure the level of surface roughness by studying the waveform. The broader the received pulse, the greater the roughness (Brenner et al. 2000, Schutz 2002). Surface roughness and slope are interrelated. The following equation for surface roughness of a rough, flat surface assumes zero slope:

where:

Δξ = surface roughness (m)
SP = RMS received pulse width (s)
Sl = RMS transmitted pulse width (s)
Sh = RMS width of receiver impulse response (s)
c = effective velocity of light (m/s)
E = laser energy (millijoules)

The following equation for surface slope of a flat, smooth surface assumes zero roughness:

where:

S = slope
c = effective velocity of light (m/s)
z = altimeter height above the terrain (m)
qT = halfwidth divergence angle of the laser beam
E = laser energy (millijoules)
SP = RMS received pulse width (s)
Sl = RMS transmitted pulse width (s)
Sh = RMS width of receiver impulse response (s)

Surface slope and roughness values are only accurate for single-pulse waveforms.

Land surface relief is the range of elevations within the footprint caused by slope and roughness. For footprints lacking vegetation or cultural features, the interpretation of the land surface elevation is similar to that of ice sheets, sea ice, and oceans. For footprints that contain vegetation or cultural features, the surface height distribution created by slope and roughness is combined with the height distribution of those features.