Functional derivatives applied to error propagation of uncertainties in topography to large-aperture scintillometer-derived heat fluxes

摘要

Scintillometer measurementsallow for estimations of the refractive index structure parameter C_n2over large areas in the atmospheric surface layer. Turbulent fluxes of heatand momentum are inferred through coupled sets of equations derived from theMonin–Obukhov similarity hypothesis. One-dimensional sensitivity functionshave been produced that relate the sensitivity of heat fluxes touncertainties in single values of beam height over flat terrain. However,real field sites include variable topography. We develop here, usingfunctional derivatives, the first analysis of the sensitivity ofscintillometer-derived sensible heat fluxes to uncertainties in spatiallydistributed topographic measurements. Sensitivity is shown to be concentratedin areas near the center of the beam path and where the underlying topographyis closest to the beam height. Relative uncertainty contributions to thesensible heat flux from uncertainties in topography can reach 20% of theheat flux in some cases. Uncertainty may be greatly reduced by focusingaccurate topographic measurements in these specific areas. A newtwo-dimensional variable terrain sensitivity function is developed forquantitative error analysis. This function is compared with the previousone-dimensional sensitivity function for the same measurement strategy overflat terrain. Additionally, a new method of solution to the set of coupledequations is produced that eliminates computational error.