How to realize the TVPDS method to add large-scale nudging in idealized simulation

[Mingling]

Onderlinde, M. J. and D. S. Nolan (2017), The tropical cyclone response to changing wind shear using the method of time-varying point-downscaling, J. Adv. Model. Earth Syst., 9, 908–931, doi:10.1002/2016MS000796.

I want to add vertical wind shear in my idealized WRF simulation. However, this paper didn't say clearly and I don't know where to modify "pert_coriolis".

 

[kwerner]

Hi, pert_coriolis is set in the namelist.input file in the &dynamics record. By default it is set to .false., so to turn it on, set it to .true.

 

[Mingling]

Thanks for your reply. However, according to the paper, if we want to add background winds in domain, we should also add a forcing term into the u-momentum equation and v-momentum equation? like this fomula:


Now I add the codes (marked by orange bold) into module_big_step_utilities_em.F. But I am not clear if it matchs the TVPDS method proposed by Onderlinde and Nolan (2017).

DO k=kts,ktf
DO i = i_start, i_end
ru_tend(i,k,j)=ru_tend(i,k,j) + (msfux(i,j)/msfuy(i,j))*0.5*(f(i,j)+f(i-1,j)) &
*0.25*(rv(i-1,k,j+1)+rv(i,k,j+1)+rv(i-1,k,j)+rv(i,k,j)) &
- 0.5*(e(i,j)+e(i-1,j))*0.5*(cosa(i,j)+cosa(i-1,j)) &
*0.25*(rw(i-1,k+1,j)+rw(i-1,k,j)+rw(i,k+1,j)+rw(i,k,j))
ru_tend(i,k,j) = ru_tend(i,k,j) - ru(i,k,j)/(sec_p_h*tao)
ENDDO
ENDDO

DO j=j_start, j_end
DO k=kts,ktf
DO i=its,MIN(ide-1,ite)

rv_tend(i,k,j)=rv_tend(i,k,j) - (msfvy(i,j)/msfvx(i,j))*0.5*(f(i,j)+f(i,j-1)) &
*0.25*(ru(i,k,j)+ru(i+1,k,j)+ru(i,k,j-1)+ru(i+1,k,j-1)) &
+ (msfvy(i,j)/msfvx(i,j))*0.5*(e(i,j)+e(i,j-1))*0.5*(sina(i,j)+sina(i,j-1)) &
*0.25*(rw(i,k+1,j-1)+rw(i,k,j-1)+rw(i,k+1,j)+rw(i,k,j))
rv_tend(i,k,j) = rv_tend(i,k,j) - rv(i,k,j)/(sec_p_h*tao)
ENDDO
ENDDO
ENDDO

 

[Mingling]

In my understanding, to realize smoothly adding background wind field into the domain, we should do two things simultaneously:

(1) Subtract the of Coriolis effect of u_ref, v_ref (i.e., PDS):

ru(i,k,j) = ru_in(i,k,j) - (c1h(k)*muu(i,j)+c2h(k))*u_ref(i,k,j)

ru_tend(i,k,j)=ru_tend(i,k,j) + (msfux(i,j)/msfuy(i,j))*0.5*(f(i,j)+f(i-1,j)) &

*0.25*(rv(i-1,k,j+1)+rv(i,k,j+1)+rv(i-1,k,j)+rv(i,k,j))

(2) Add momentum forcing to the u/v momentum tendency:

ru_tend(i,k,j) = ru_tend(i,k,j) - ru(i,k,j)/(tao)

And then, if we want to add background wind, we just activate "pert_coriolis = .true.". After 24-h nudging interval ,we just set "pert_coriolis = .false." and restart? So, after the nudging interval, we no longer need to substract the coriolis effect of background winds?

Base on my understanding，I have modified the SUBROUTINE perturbation_coriolis in module_big_step_utilities_em.F. But I am not clear if I am right.

 

[kwerner]

Hi, Apologies for the delay. I reached out to a colleague who is more of an expert in this area. This is their response:

Is the added wind horizontally uniform? It may be easier if it is.
u_base, v_base and z_base define the geostrophic wind and are normally constant but probably could be varied to be consistent.

 

[Mingling]

Thanks for your reply. I want to add horizontally non-uniform wind field, and now I am using the spectual nudging method in WRF fdda module to drive the simulation. In this case, as I simutanoeously nudging u/v wind, theta and geopotential (they are balanced in my algorithm), I don't need to substract background wind in coriolis force, am I right?