Parameterization of the structure function time lag for resolving ramp characteristics in scalar time series data

Turbulent coherent structures dominate the total turbulent exchange of energy and mass between the surface and the atmosphere. Ramp-like patterns in scalar time series data are attributed to these structures. The amplitude and the frequency of the ramps (i.e., the ramp characteristics) are commonly derived from structure functions of the scalar data using the linearized Van Atta model, especially for use in surface renewal analysis. Van Atta proposed the model for a limited range of structure function time lags, but the range was not clearly defined. The power of the model to resolve the coherent structure signals from the random fluctuations has not been well quantified. Uncertainties in the Van Atta model contribute to uncertainties in surface renewal analysis. In this paper, both model and real time series data were used to investigate the limitations of the linearized Van Atta model. We hypothesize that the appropriate range of time lags can be determined a priori according to ramp characteristics. The range can also be determined a posteriori according to interrelationships between odd- and even-order structure functions.