Temperature for Convective velocity (WSTAR) in MYNN surface layer

[pareja]

Hello all,
I am working with the "gustiness" or free convection velocity scale (w*) over water based on Beljaars (1995) for the MYNN surface layer scheme. I wondered what temperature should go in the buoyancy parameter g/T in this scaling, for model coupling purposes.

Paper: https://rmets.onlinelibrary.wiley.com/doi/epdf/10.1002/qj.49712152203
Code: WRF/phys/module_sf_mynn.F at master · wrf-model/WRF

The Beljaars definition for WSTAR (equation 8) includes the buoyancy parameter g/T. Since this scaling comes from the buoyancy production term in the TKE budget, I assume T here would be a surface air temperature (e.g. T2 or T at level 1). However, I see that TSK (skin temperature?) is used:

!--------------------------------------------------------
         !  Calculate the convective velocity scale (WSTAR) and
         !  subgrid-scale velocity (VSGD) following Beljaars (1995, QJRMS)
         !  and Mahrt and Sun (1995, MWR), respectively
         !-------------------------------------------------------
         !  Use Beljaars over land and water
         fluxc = max(hfx(i)/RHO1D(i)/cp                    &
         &    + ep1*THVGB(I)*qfx(i)/RHO1D(i),0.)
         !WSTAR(I) = vconvc*(g/TSK(i)*pblh(i)*fluxc)**.33
         IF (xland(i).gt.1.5 .or. QSFC(i).le.0.0) THEN   !WATER
            WSTAR(I) = vconvc*(g/TSK(i)*pblh(i)*fluxc)**.33
         ELSE                                            !LAND
            !increase height scale, assuming that the non-local transoport
            !from the mass-flux (plume) mixing exceedsd the PBLH.
            WSTAR(I) = vconvc*(g/TSK(i)*MIN(1.5*pblh(i),4000.)*fluxc)**.33
         ENDIF

The Olson et al 2012 technical memorandum on MYNN surface layer (https://doi.org/10.25923/f6a8-bc75) suggests the temperature would be the potential temperature at level 1 (theta_1) for w*.

I wondered: Is TSK here a skin surface temperature (level 0) or an air temperature (level 1)? Would this make a difference in the value of w*? I will be working in very low mean wind conditions where free convection drives the surface heat fluxes.

---

For context: we are working on coupling an ocean model (ROMS) with WRF. When coupled, ROMS computes bulk fluxes, including w* (gustiness), based on the WRF air temperature at 2m (T2). The snippet below is from ROMS for gustiness (slightly modified for clarity)

!
!  Compute gustiness in wind speed.
!
            Bf=-g/TairK *Ustar *(Tstar +0.61 * TairK * Qstar)
         
IF (Bf.gt.0.0_r8) THEN

              Wgus = beta*(Bf*PBLh)^1/3
     
END

Thanks,
Fernando Pareja-Roman
Rutgers University

 

[Ming Chen]

TSK used in module_sf_mynn.F for WSTAR calculation is surface skin temperature. TSK and the first model level air temperature are definitely different.
I don't have an immediate answer how large the impact could be by using TSK instead of T(1).
Can you follow the description in the paper to replace TSK by T(1), and compare the results with your original run? Let's see how the model performs in this way.