Probability Distributions for the Inner Scale and the Refractive Index Structure Parameter and Their Implications for Flux Averaging

Abstract

Defining the averaging time required for measuring meaningful turbulence statistics is a central problem in boundary layer meteorology. Path-averaging scintillation instruments are presumed to confer some time-averaging benefits when the objective is to measure surface fluxes, but that hypothesis has not been tested definitively. This study uses scintillometer measurements of the inner scale (l0) and the refractive index structure parameter (C2n) to investigate this question of required averaging time. The first conclusion is that the beta probability distribution is useful for representing C2n and l0 measurements. Consequently, beta distributions are used to set confidence limits on C2n and l0 values obtained over various averaging periods. When the C2n and l0 time series are stationary, a short-term average of C2n or l0 can be as accurate as a long-term average. However, as with point measurements, when time series of path averaged C2n or l0 values are nonstationary, turbulent surface fluxes inferred from these C2n and l0 values can be variable and uncertain?problems that path averaging was presumed to mitigate. Because nonstationarity is a limiting condition, the last topic is quantifying the nonstationarity with a published nonstationarity ratio and also by simply counting zero crossings in the time series.