Random Errors in Turbulence Measurements in the Atmospheric Surface Layer: Implications for Monin–Obukhov Similarity Theory

Scott T. Salesky The Pennsylvania State University, University Park, Pennsylvania

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Marcelo Chamecki The Pennsylvania State University, University Park, Pennsylvania

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Abstract

An error propagation analysis is conducted to estimate random errors in the friction velocity u* and the Monin–Obukhov similarity theory (MOST) stability variable z/L from estimated random errors in the turbulent fluxes. Errors in the dimensionless mean wind shear φm and mean temperature gradient φh are also estimated. To the authors’ knowledge, this is the first time that errors in calculated values of z/L, φm, and φh have been systematically analyzed. Random errors in z/L are found to be large for unstable conditions, reaching values of 40% or greater. It is shown through statistical hypothesis tests that random errors cannot explain departures of calculated values of φm and φh from theory. The deviation of calculated values of φm from empirical curves is found to have a strong diurnal variation that increases with height; deviations of φh from theory are not found to have clear diurnal variation. These results support the findings of previous studies, which have suggested that additional dimensionless parameters representing additional physical processes need to be included in the set of governing parameters for surface layer similarity. Implications for atmospheric surface layer turbulence are also discussed.

Corresponding author address: Marcelo Chamecki, Department of Meteorology, The Pennsylvania State University, University Park, PA 16802. E-mail: chamecki@meteo.psu.edu

Abstract

An error propagation analysis is conducted to estimate random errors in the friction velocity u* and the Monin–Obukhov similarity theory (MOST) stability variable z/L from estimated random errors in the turbulent fluxes. Errors in the dimensionless mean wind shear φm and mean temperature gradient φh are also estimated. To the authors’ knowledge, this is the first time that errors in calculated values of z/L, φm, and φh have been systematically analyzed. Random errors in z/L are found to be large for unstable conditions, reaching values of 40% or greater. It is shown through statistical hypothesis tests that random errors cannot explain departures of calculated values of φm and φh from theory. The deviation of calculated values of φm from empirical curves is found to have a strong diurnal variation that increases with height; deviations of φh from theory are not found to have clear diurnal variation. These results support the findings of previous studies, which have suggested that additional dimensionless parameters representing additional physical processes need to be included in the set of governing parameters for surface layer similarity. Implications for atmospheric surface layer turbulence are also discussed.

Corresponding author address: Marcelo Chamecki, Department of Meteorology, The Pennsylvania State University, University Park, PA 16802. E-mail: chamecki@meteo.psu.edu
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