Jielun Sun NCAR Earth System Laboratory Vertical Variations of Mixing Lengths under Neutral to Stable Conditions during CASES99 Jielun Sun NCAR Earth System Laboratory

Outline Various layers above the ground Monin-Obukhov similarity theory, the bulk formula for estimating turbulence fluxes Observations, CASES99 Comparison among the observed, MOST, and Blackadar neutral mixing lengths Summary

Various layers under neutral conditions

Mixing length under neutral conditions M-O similarity theory (MOST) Alternative MOST Prandtl mixing length The bulk formula Generalized MOST |τ|=u*2 H=-u*θ* If

Cooperative Atmosphere-Surface Exchange (CASES99) 1.5 m/0.5 m 55 m 50 m 40 m 30 m 20 m 10 m 5 m Sonic Poulos et al. 2002, BAMS 45 m 35 m 25 m 15 m Prop-vane ΔzTC=1.8m 34 levels of TC (0.2 m, 0.6 m, 2.3 m,…)

z/L vs local gradient Ri Based on MOST Businger (1971) & Dyer (1974) Holslag & De Bruin (1988) Beljaars and Holtslag (1991) Cheng & Brutsaert (2005)

Mixing length for momentum vs. local gradient Ri observation MOST Modified MOST

Mixing length for heat vs. local gradient Ri observation MOST Modified MOST

Mixing length under neutral conditions vs z Consistent with Mölder et al. (1999, AFM) and Dellwik and Jensen (2005, BLM)

lmN vs. z for a range of wind speed ---Pena et al. (2010, QJ) κz (MOST) Wind speed z lmN

Summary On average, MOST is approximately valid above 0.5 m and below 20 m during CASES99. The Blackadar formula works below 20 m for momentum and about 60 m for heat, l∞=15 m. Using MOST above the MOST layer to estimate turbulence fluxes would lead to overestimates of turbulent fluxes during CASES99. The stability functions developed for the MOST layer works reasonably well in the layer above and below it.