Probability distributions for scintillometer-derived values of the inner scale and the refractive index structure parameter and their implications for averaging

Knowing the probability distribution function of a turbulence variable guides the decision about how long to average data to obtain meaningful statistics. From indirect evidence, Andreas (1989) suggested that the refractive index structure parameter C_n² over Arctic sea ice follows a beta distribution in all seasons rather than the lognormal distribution often attributed to it. We now have available from measurements during SHEBA (the experiment to study the Surface Heat Budget of the Arctic Ocean) 600 hours of C_n² values measured with a 0.685-micrometer scintillometer and reported every minute. We also have simultaneous measurements of the inner scale of turbulence l₀ made with the same instrument. We will present the distribution functions for each of these variables and, from these results, evaluate appropriate averaging times.

Because l₀ is directly related to the dissipation rate of turbulent kinetic energy and because C_n² is related to the dissipation rate of temperature variance, these paired data yield path-averaged estimates of the friction velocity u_* and the sensible heat flux H_s. A long-standing hypothesis suggests that path-averaged scintillation measurements should produce estimates of u_* and H_s in a fraction of the time that single-point, eddy-correlation measurements can. We hope to evaluate this hypothesis by looking at the distribution functions of the SHEBA C_n² and u_* data.

References

Andreas, E. L, 1989: The refractive index structure parameter, C_n², for a year over the frozen Beaufort Sea. Radio Sci., 24, 667-679.