29.01.2015 Views

Volume 1 - The Atmospheric Studies Group at TRC

Volume 1 - The Atmospheric Studies Group at TRC

Volume 1 - The Atmospheric Studies Group at TRC

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

T (ºK)<br />

g (m/s 2 )<br />

temper<strong>at</strong>ure<br />

gravit<strong>at</strong>ional acceler<strong>at</strong>ion<br />

<strong>The</strong> constants A, B, and C have suggested values of 0.2, 2.5, and 8, respectively.<br />

Adjustments to He<strong>at</strong> Flux in Convective Mixing Height<br />

dh<br />

− ws<br />

dt<br />

=<br />

(<br />

( w'<br />

θv'<br />

) − ( w'<br />

θv'<br />

)<br />

2<br />

2<br />

h<br />

Cu*<br />

T γg<br />

+<br />

(1 + 2A)<br />

h − 2BκL<br />

(1 + A)<br />

h − BκL<br />

th<br />

)<br />

γ<br />

(3-35)<br />

where (w’θ v ’) th is the threshold kinem<strong>at</strong>ic he<strong>at</strong> flux <strong>at</strong> the surface.<br />

Observed positive values of the surface buoyancy flux over the Gulf of Mexico<br />

during summer time when the overw<strong>at</strong>er mixing layer is <strong>at</strong> equilibrium suggest th<strong>at</strong><br />

the warm surface destabilizing effect is balanced by dissip<strong>at</strong>ion.<br />

Although the equilibrium might be owing to various processes such as turbulence<br />

dissip<strong>at</strong>ion, radi<strong>at</strong>ive cooling <strong>at</strong> the top of marine str<strong>at</strong>ocumulus layer, or large scale<br />

subsidence, it is best modeled with a threshold surface buoyancy flux required to<br />

sustain convective mixing height growth over warm w<strong>at</strong>ers. Moreover it is intuitive<br />

th<strong>at</strong> this threshold should increase with the convective mixing height. <strong>The</strong>refore this<br />

threshold is expressed as a surface he<strong>at</strong> flux required to sustain convective mixing<br />

growth, per meter of mixing height. This ensures th<strong>at</strong> the convective mixing heights<br />

never grow ad infinitum and reach an equilibrium.<br />

A default value for the threshold parameter overw<strong>at</strong>er (THRESHW), based on the<br />

observed surface buoyancy flux <strong>at</strong> equilibrium st<strong>at</strong>e during summer months in the<br />

Gulf of Mexico, is set to 0.05 W/m 3 . THRESHW is rel<strong>at</strong>ed to (w’θ v ’) th by (w’θ v ’) th<br />

= (THRESHW)(h t-1 )/(ρc p ) where h t-1 is the convective mixing height <strong>at</strong> the previous<br />

time step. THRESHW is an user-input parameter and can therefore be adjusted so<br />

th<strong>at</strong> observed equilibrium conditions are best represented in the model. <strong>The</strong> threshold<br />

is implemented both in the Gryning and B<strong>at</strong>chvarova method (Equ<strong>at</strong>ion 3-35) and in<br />

the Maul-Carson method.<br />

A similar threshold (THRESHL) was implemented overland, although with the<br />

diurnal surface he<strong>at</strong>ing/cooling cycle and generally much larger values of surface<br />

he<strong>at</strong> flux over land surfaces, the threshold effect is normally much less important<br />

than over w<strong>at</strong>er where the positive he<strong>at</strong> fluxes may persist under cold air advection<br />

situ<strong>at</strong>ions for days <strong>at</strong> a time.<br />

Final Report Vol.1 15

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!