A New Sensitivity Analysis and Solution Method for Scintillometer Measurements of Area-Averaged Turbulent Fluxes

Abstract

Scintillometer measurements of the turbulence inner-scale length $l_o$ and refractive index structure function $C_n^2$ allow for the retrieval of large-scale area-averaged turbulent fluxes in the atmospheric surface layer. This retrieval involves the solution of the non-linear set of equations defined by the Monin-Obukhov similarity hypothesis. A new method that uses an analytic solution to the set of equations is presented, which leads to a stable and efficient numerical method of computation that has the potential of eliminating computational error. Mathematical expressions are derived that map out the sensitivity of the turbulent flux measurements to uncertainties in source measurements such as $l_o$. These sensitivity functions differ from results in the previous literature; the reasons for the differences are explored.