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An Analysis for the Applicability of Monin–Obukhov Similarity Theory in Stable Conditions

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  • 1 Centre for Atmospheric Sciences, Indian Institute of Technology Delhi, New Delhi, India
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Abstract

An analysis in a plane of the stability parameters ζ = z/L (where z is a height above the ground surface and L is the Obukhov length) and bulk Richardson number RiB is proposed to examine the applicability of Monin–Obukhov similarity (MOS) theory in stable conditions. In this analysis, the data available from two different experimental datasets [(i) Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99) and (ii) Cardington] are divided into four quadrants. An unexpected behavior of decreasing ζ with increasing RiB was observed with both datasets in quadrant II characterized by ζ < 1 and RiB > 0.2 and in quadrant IV with ζ > 1 and RiB < 0.2. This is in contrast to a commonly expected monotonically increasing behavior between ζ and RiB. It is shown that the MOS theory is consistent for computing the surface fluxes corresponding to the data points lying in quadrants I (with ζ > 1 and RiB > 0.2) and III (with ζ < 1 and RiB < 0.2), whereas it may not be applicable for the points in quadrants II and IV. Thus, a breakdown of the relationship between observed ζ and RiB with growing stability in these quadrants may limit the applicability of MOS theory in stable conditions. Since quadrant IV has very few data points, the applicability of MOS theory needs to be substantiated further with the availability of sufficient data points in this regime.

Current affiliation: Center for Air Resource Engineering and Science, Clarkson University, Potsdam, New York.

Corresponding author address: Maithili Sharan, Centre for Atmospheric Sciences, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India. E-mail: mathilis@cas.iitd.ac.in

Abstract

An analysis in a plane of the stability parameters ζ = z/L (where z is a height above the ground surface and L is the Obukhov length) and bulk Richardson number RiB is proposed to examine the applicability of Monin–Obukhov similarity (MOS) theory in stable conditions. In this analysis, the data available from two different experimental datasets [(i) Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99) and (ii) Cardington] are divided into four quadrants. An unexpected behavior of decreasing ζ with increasing RiB was observed with both datasets in quadrant II characterized by ζ < 1 and RiB > 0.2 and in quadrant IV with ζ > 1 and RiB < 0.2. This is in contrast to a commonly expected monotonically increasing behavior between ζ and RiB. It is shown that the MOS theory is consistent for computing the surface fluxes corresponding to the data points lying in quadrants I (with ζ > 1 and RiB > 0.2) and III (with ζ < 1 and RiB < 0.2), whereas it may not be applicable for the points in quadrants II and IV. Thus, a breakdown of the relationship between observed ζ and RiB with growing stability in these quadrants may limit the applicability of MOS theory in stable conditions. Since quadrant IV has very few data points, the applicability of MOS theory needs to be substantiated further with the availability of sufficient data points in this regime.

Current affiliation: Center for Air Resource Engineering and Science, Clarkson University, Potsdam, New York.

Corresponding author address: Maithili Sharan, Centre for Atmospheric Sciences, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India. E-mail: mathilis@cas.iitd.ac.in
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