Estimates of turbulence from numerical weather prediction model output with applications to turbulence diagnosis data assimilation

Estimates of small-scale turbulence from numerical model output are produced from local estimates of the spatial structure functions of model variables such as the velocity and temperature. The key assumptions used are the existence of a universal statistical description of small-scale turbulence and a locally universal spatial filter for the model variables. Under these assumptions, spatial structure functions of the model variables can be related to the structure functions of the corresponding atmospheric variables. The shape of the model spatial filter is determined by comparisons with the spatial structure functions from aircraft data collected at cruising altitudes. This universal filter is used to estimate the magnitude of the small-scale turbulence, that is, scales smaller than the filter scale. A simple yet universal description of the basic statistics (such as the probability density function and the spatial correlation) of these small-scale turbulence levels in the upper troposphere and lower stratosphere is proposed. Various applications are presented including 1) predicting the statistics of turbulence experienced by aircraft at upper levels, 2) diagnosing and forecasting turbulence for aviation safety, and 3) estimating the total observation error for optimal data assimilation and for improving operational weather prediction models. It is determined that the total observation error for typical rawinsonde measurements of velocity are dominated by the sampling error or " error of representativeness" resulting from the effects of small-scale turbulence.