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Critical Test of the Validity of Monin–Obukhov Similarity during Convective Conditions

Cecilia JohanssonDepartment of Earth Sciences, Meteorology, Uppsala University, Uppsala, Sweden

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Ann-Sofi SmedmanDepartment of Earth Sciences, Meteorology, Uppsala University, Uppsala, Sweden

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Ulf HögströmDepartment of Earth Sciences, Meteorology, Uppsala University, Uppsala, Sweden

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James G. BrasseurDepartment of Mechanical Engineering, The Pennsylvania State University, University Park, Pennsylvania

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Samir KhannaDepartment of Mechanical Engineering, The Pennsylvania State University, University Park, Pennsylvania

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Abstract

A recent study of convective boundary layer characteristics performed with large eddy simulation technique (LES) has demonstrated unexpected influence of the depth of the boundary layer on surface layer characteristics. The present study tests some of the predictions from these simulations with field measurements from a summertime experiment in Sweden, which includes in addition to regular surface layer data also airborne measurements and numerous radio soundings, which enable accurate determination of boundary layer depth.

It is found that the measurements strongly support most of the conclusions draws from the LES study and give additional information over a wider stability range. Thus, the normalized wind gradient ϕm is found to depend on both z/L, where z is height above the ground and L is the Monin–Obukhov length, and zi/L, where zi is the height of the convective boundary layer. This additional dependence on zi/L explains much of the scatter between experiments encountered for this parameter. In the case of the normalized temperature gradient ϕh, the experimental data follow the generally accepted functional relation with z/L, but with an additional, slight ordering according to zi/L.

Analyses of nondimensional variances show (i) the horizontal velocity variance scales on mixed layer variables and is a function only of zi/L, in agreement with the LES results and with previous measurements; (ii) the normalized vertical velocity variance depends on the large-scale pressure gradient length scale for slight instability and is primarily a function of z/L for moderate and strong instability; (iii) the normalized temperature variance is a function of z/L, with a possible slight dependence on zi/L; and (iv) whereas mean temperature gradient is characterized by local shear scales, temperature variances are normalized by local buoyancy-driven scales.

Current affiliation: Corning, Inc., Corning, New York.

Corresponding author address: Prof. Ulf Högström, Department of Earth Sciences, Meteorology, Villavägen 16, S-752 36 Uppsala, Sweden. Email: ulf@big.met.uu.se

Abstract

A recent study of convective boundary layer characteristics performed with large eddy simulation technique (LES) has demonstrated unexpected influence of the depth of the boundary layer on surface layer characteristics. The present study tests some of the predictions from these simulations with field measurements from a summertime experiment in Sweden, which includes in addition to regular surface layer data also airborne measurements and numerous radio soundings, which enable accurate determination of boundary layer depth.

It is found that the measurements strongly support most of the conclusions draws from the LES study and give additional information over a wider stability range. Thus, the normalized wind gradient ϕm is found to depend on both z/L, where z is height above the ground and L is the Monin–Obukhov length, and zi/L, where zi is the height of the convective boundary layer. This additional dependence on zi/L explains much of the scatter between experiments encountered for this parameter. In the case of the normalized temperature gradient ϕh, the experimental data follow the generally accepted functional relation with z/L, but with an additional, slight ordering according to zi/L.

Analyses of nondimensional variances show (i) the horizontal velocity variance scales on mixed layer variables and is a function only of zi/L, in agreement with the LES results and with previous measurements; (ii) the normalized vertical velocity variance depends on the large-scale pressure gradient length scale for slight instability and is primarily a function of z/L for moderate and strong instability; (iii) the normalized temperature variance is a function of z/L, with a possible slight dependence on zi/L; and (iv) whereas mean temperature gradient is characterized by local shear scales, temperature variances are normalized by local buoyancy-driven scales.

Current affiliation: Corning, Inc., Corning, New York.

Corresponding author address: Prof. Ulf Högström, Department of Earth Sciences, Meteorology, Villavägen 16, S-752 36 Uppsala, Sweden. Email: ulf@big.met.uu.se

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