  Scintillometer measurements allow for estimations of the refractive index
structure parameter $C_n^2$ over large areas in the atmospheric surface layer.
Turbulent fluxes of heat and momentum are inferred through coupled sets of
equations derived from the Monin--Obukhov similarity hypothesis.
One-dimensional sensitivity functions have been produced that relate the
sensitivity of heat fluxes to uncertainties in single values of beam height
over flat terrain. However, real field sites include variable topography. We
develop here, using functional derivatives, the first analysis of the
sensitivity of scintillometer-derived sensible heat fluxes to uncertainties in
spatially distributed topographic measurements. Sensitivity is shown to be
concentrated in areas near the center of the beam path and where the underlying
topography is closest to the beam height. Relative uncertainty contributions to
the sensible heat flux from uncertainties in topography can reach 20\,\% of the
heat flux in some cases. Uncertainty may be greatly reduced by focusing
accurate topographic measurements in these specific areas. A~new
two-dimensional variable terrain sensitivity function is developed for
quantitative error analysis. This function is compared with the previous
one-dimensional sensitivity function for the same measurement strategy over
flat terrain. Additionally, a~new method of solution to the set of coupled
equations is produced that eliminates computational error.
