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Gayana (Concepción)

versión impresa ISSN 0717-652Xversión On-line ISSN 0717-6538

Gayana (Concepc.) v.68 n.2 supl.TIProc Concepción  2004

http://dx.doi.org/10.4067/S0717-65382004000200010 

 

Gayana 68(2) supl. t.I. Proc. : 60-61, 2004 ISSN 0717-652X

A PBL MODEL WITH ORGANIZED LARGE EDDIES FOR MESOSCALE-SYNOPTIC-GLOBAL WINDS

 

Robert A. Brown

Dept. Atmospheric Sciences, Box 351640, University of Washington Seattle, WA 98105. rabrown@atmos.washington.edu


ABSTRACT

The University of Washington PBL model is a nonlinear similarity model (with organized large eddies in an equilibrium mean flow) suitable for km-scale to General Circulation Model or Climate numerical models. The theory and verification for this solution are now well established. Researchers who work with winds in the boundary layer with scales from point to 20-km regimes must be aware of this horizontal inhomogenuity in the PBL flow to avoid significant errors. Since the OLE contribute advectively to the mean flow there can be 10-20% (or more) increase in surface winds and fluxes over K-theory models. The model is described and several applications have been made.


 

INTRODUCTION

Since Ekman found his wonderful logarithmic spiral solution for a Planetary Boundary Layer (PBL) in 1904, it has been used widely to model the boundary layer in a rotating frame of reference.

The analytic solution for a PBL

f V + K Uzz - pz/r = 0

f U - K Vzz + pz/r = 0

where K is an eddy viscosity, and f is the Coriolis parameter . The solution, U (f, K,Ñp ) was found by Ekman in 1904.

Unfortunately, the classic Ekman spiral velocity profile has rarely, if ever, been observed. The winds do spiral, turning clockwise from surface to geostrophic, as do the oceanic PBL flows. But they are not consistent, steady, or logarithmic.

Most researchers assumed that the problem was variable turbulence, resulting in a highly variable eddy diffusivity, K(x,y,z,t). But for most large-scale numerical modelers, the great simplification of using a constant K overcame any worries about the problems with variable turbulence.

In the 1960s it was found that the PBL solution was unstable to infinitesimal perturbations, hence the prescribed K solutions were not valid. In 1970 it was found that the perturbation grew to a state of equilibrium, where energy into the perturbation equaled energy back to the mean flow. This 'Coherent Structure' solution treated the finite perturbation explicitly as organized large eddies (OLE) in the form of longitudinal alternating vortices, or 'Rolls'. The nonlinear solution used K-theory for small eddies whereas the PBL size eddies, the Rolls, are part of the mean flow.

f V + K Uzz - pz/r = 0

f U - K Vzz + pz/r = A(v2w2)

where u2, v2, w2 are finite perturbations an organized secondary flow. The solution, U (f, K, Ñ p ) was found in 1970 (Brown, 1970); completed in 1996. K is the eddy viscosity for small eddies only.

This solution predicts that OLE are part of the solution for 80% of the observed conditions (slightly stably stratified to convective conditions). Unfortunately, it was difficult to observe and consequently it was not accepted as the solution for decades.

By the 1990s, Synthetic Aperture Radar (SAR) data from the Canadian Radarsat was showing linear effects on the ocean surface that corresponded to the nonlinear PBL solution. A statistical study showed these signatures to be present about 50% of the time. This is a sufficient, but not necessary, condition for the presence of Rolls. It is now apparent that the nonlinear solution is the prevailing solution for planetary boundary layer flow. This has profound consequences on 'surface truth' measurements and satellite wind applications. The effects are illustrated in Figure 1.

Figure 1. The nonhomogenuities from Rolls.

CONCLUSIONS

1. The winds are non-homogeneous at the surface over a 0.1-5 km horizontal distance. Upper high velocity wind is advected to the surface in lines. OLE must be taken into account in surface truth measurements (In the average and point values). (Brown, 2002)

2. The average wind profile is different from the Ekman solution ­and from a profile 100m away ­ the nonlinear wind solution (and hence fluxes of momentum, heat, CO2 etc.) is 10-50% different, depending on stratification and thermal wind. In a satellite's 25-km footprint there will be 10-OLE so the periodic effect will be the average. Not true at 6-km or less the SAR resolution. (Brown & Foster, 1994.)

3. The PBL contains advecting flow not amenable to diffusion modeling. Numerical models cannot portray correct physics of the mean flow without extreme increase in resolution (Brown, R.A., in press).

REFERENCES

Brown, R.A., 1970; A Secondary Flow Model for the Planetary Boundary Layer. J. Atmos. Sciences , 27, 742-757. [         [ Links ]1]

Brown R.A. & Ralph Foster, 1994; On PBL Models for general circulation models, The Global Atmos.-Ocean System, 2, 163-183. [         [ Links ]2]

Brown, R.A., 2002; Scaling Effects in Remote Sensing Applications and the Case of Organized Large Eddies, Canadian Jn. Remote Sensing, 28, 340-345. [         [ Links ]3]

Brown, R.A. 2004; Comments on the synergism between the analytic PBL model and remote sensing data, Bound.-Layer Meteor., in press. [         [ Links ]4]

 

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