[RegCNET] calculation of Monin–Obukhov Length

[Travis O'Brien]

Hello Flyks,

The Obukhov length scale comes about from non-dimensionalizing the
turbulence kinetic energy budget equation.  Stull (2009; pg
181)<http://books.google.com/books?id=s-9zCT2bTr8C&lpg=PA180&vq=obukhov&pg=PA181#v=onepage&q&f=false>defines
it in equation 5.7c.  The length scale in the Holtslag code is
defined identically. I believe the dsign(...) part in the denominator is a
numerical trick to avoid dividing by zero (or overflow) when the buoyancy
flux becomes too small.

Regards,
-Travis-

On Thu, Nov 10, 2011 at 2:54 PM, flyks <flyyks at gmail.com> wrote:

> Dear all,
>
> I want to know the reference for calculating Monin–Obukhov Length in
> RegCM. Thank you.
>
> Following is code taken from PBL module,
>
>         sh10 = qx(i,kx)/(qx(i,kx)+1)
> c "virtual" potential temperature
>         if (sflux(i).ge. 0.) then
>            th10 = thvx(i,kx)
>         else
> c----   first approximation for obhukov length
>            oblen=-0.5*(thx(i,kx)+tg(i))
>     &           *(1.0+ep1*sh10)*ust(i)**3
>     &      /(g*karman*(sflux(i)+dsign(1.d-10,sflux(i))))
>            if (oblen.ge.za(i,kx)) then
>              th10=thvx(i,kx)+sflux(i)/(karman*ust(i))
>     &            *(dlog(za(i,kx)/10.)+5./oblen*(za(i,kx)-10.))
>            else if (oblen.lt.za(i,kx).and.oblen.gt.10.) then
>              th10=thvx(i,kx)+sflux(i)/(karman*ust(i))
>     &            *(dlog(oblen/10.)+5./oblen*(oblen-10.)
>     &                   +6*dlog(za(i,kx)/oblen))
>            else if (oblen.le.10.) then
>              th10=thvx(i,kx)+sflux(i)/(karman*ust(i))
>     &            *6*dlog(za(i,kx)/10.)
>            end if
>            th10=max(th10,tg(i))
>         end if
> c       compute obukhov length
>         oblen=-th10*ust(i)**3
>     &         /( g*karman*(sflux(i)+dsign(1.d-10,sflux(i))) )
>
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