The values of the key atmospheric turbulence parameters (structure constants) for temperature and water vapor, i.e., CT2, and CQ2, are highly dependent upon the vertical height within the atmosphere thus making it necessary to specify profiles of these values along the atmospheric propagation path. The remote sensing method suggested and described in this work makes use of a rapidly integrating microwave profiling radiometer to capture profiles of temperature and humidity through the atmosphere. The integration times of currently available profiling radiometers are such that they are approaching the temporal intervals over which one can possibly make meaningful assessments of these key atmospheric parameters. These integration times, coupled with the boundary effects of the Earth’s surface are, however, unconventional for turbulence characterization; the classical Kolmogorov turbulence theory and related 2/3 law for structure functions prevalent in the inertial sub-range are no longer appropriate. An alternative to this classical approach is derived from first principles to account for the nuances of turbulent mechanics met with using radiometer sensing, i.e., the large-scale turbulence driven by the various possible boundary conditions within the buoyancy sub-range. Analytical expressions connecting the measured structure functions to the corresponding structure parameters are obtained. The theory is then applied to an experimental scenario involving radiometric profile measurements of temperature and shows very good results.
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The heat-loss anemometers have been used to study the turbulence previously, but in this work the radiometer is used. What are the advantages of radiometer over the heat-loss anemometer?
In your opinion, can the study of spectrum of the signal itself give us more information about the turbulence nature? Furthermore, may the instrumental preprocessing of the signal be beneficial?
The problem studied in the paper has been previously considered by the noted scientist A.M. Obukhov. But some of his approaches have been criticized by G. Batchelor. In your opinion, what is the main difficulty of this subject, which Obukhov had not been able to overcome? And how did you solve it?
This need to secure path profiles is the basis for this work. Although it was not my intent to enter too far into atmospheric turbulence dynamics, the nature of the problem necessarily required an investigation into the rather speculative region of large-scale turbulence. The work took an unexpected turn in the formulation of Eq.(33) of the manuscript. The equation gave me what I needed to complete the model for the radiometer measurements but, it looks as if it can be taken much further. I currently have several summer intern mathematics students working with the equation to investigate its other regions of applicability.
Knowledge of the form of the spectrum of the turbulent fluctuations is necessary in order to obtain the form of the corresponding structure function equation (i.e., Eqs.(52) and (53)) that is used to 'fit' the radiometer data.
I appreciate that this particular subject is indeed a bit controversial and that very well-known people such as Obukhov have considered it in the past. I feel rather privileged to be in such company and I can only hope that I can make some contribution. Hopefully, my summer intern math students can delve into the implications of Eq.(33) and we can report on this in the very near future.
Finally, related to your temperature measurement question, only the direct initial profiles of temperature and humidity are required using this radiometer method. That is, a temperature and humidity gradient must be secured (using, e. g., two such vertical measurements taken about 4 or 5 meters apart) in order to obtain an estimate of the prevailing Monin-Obukhov similarity scale from which the values of the two coefficients k_U and k_t can be obtained.