Estimating Cn^2 over snow and sea ice from meteorological data

Abstract

Because turbulent fluctuations in the atmospheric refractive index (n) at a wavelength λ are related to fluctuations in the temperature (t) and the humidity (q) by n = A(λ, P, T, Q)t + B(λ, P, T, Q)q it is possible to estimate the refractive-index structure parameter Cn2 from meteorological quantities. I describe and evaluate two such estimation procedures,one based on the velocity, temperature and humidity scales u*, t*, and q*and a second based on the routine meteorological quantities Uh, Ts − Th and Qs − Qh. The subscript h here denotes the wind speed (Uh), temperature (Th), or humidity (Qh) at a reference height h; the subscript s indicates the surface value. I also develop analytical expressions for the coefficients A and B as functions of λ, the atmospheric pressure (P), and the temperature and the humidity in four wavelength regions: visible (including near infrared), an infrared window, near millimeter, and radio. In a sensitivity analysis of the two estimation procedures, the core of the paper, I demonstrate that the accuracy of the Cn2 estimate is a strong function of the Bowen ratio (Bo). At two Bo values within the interval [−10, 10], one dependent on λ and the other dependent on meteorological conditions, the uncertainty in the Cn2 estimate becomes infinite.