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

2. 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

3. Various layers under neutral conditions

4. 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

5. 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,…)

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

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

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

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

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

11. 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.