# WRF energy and moisture budget?

#### yhwong

##### New member
Hello,

I am trying to figure out how to get the correct variables to calculate energy and moisture budget in WRF in a radiative-convective equilibrium (RCE) setting. For moisture budget at RCE, I used the equation:

LH = P_e

where LH = Surface latent heat flux (W m-2), so basically evaporation; and Precipitation is the sum of cumulus and grid-scale (Large-scale) precipitation (P, in mm/day), converted to W m-2 using the formula P_e = Lv * P / 86400, where P is in mm/day, and Lv is the latent heat of evaporation.

This seems to work and for my RCE setting, it largely holds that LH = P_e

However, I am having problem getting the energy budget right. There seems to be many variables in WRF and I am not sure which ones I should use.

The equation I am currently using is:

Radiative cooling, Qc = SW + LW
Heating, Qh = LH + HFX

where
SW = SWDNT + SWUPB - SWUPT - SWDNB
LW = LWDNT + LWUPB - LWUPT - LWDNB
(SWDNT is instantaneous downwelling shortwave flux at top, SWUPB is instantaneous upwelling shortwave flux at bottom, SWUPT is upwelling SW flux at top, SWDNB is downwelling SW flux at bottom, and so on)

LH = Surface latent heat flux
HFX = Sensible heat flux ("Upward heat flux at the surface")

In principle, at RCE we should get Qc = Qh, but I am getting a discrepancy of around 10 W m-2 between Qc and Qh, with more heating than cooling. This makes me wonder if I am using the wrong variables to calculate my energy budget, or that my model has not reached RCE (although I doubt this is the case as the moisture budget seems to hold?).

Would anyone be able to advice?

Thank you

Hi,

If some of the variables are accumulated at every time step, and others are instantaneous values (such as GRDFLX, HFX, etc.), then when trying to calculate the budget, the results can be misleading and you probably won't get good energy balance​.

If you happen to be using the NoahMP LSM, then a calculation for the surface energy budget it already built-in. It will be output as NOAHRES. Otherwise, you can look in the file phys/module_sf_noahdrv.F to follow how it is done, to be used as a reference.

In general, the following calculations can be used for radiative flux calculations:

LWUPFLUX = STBOLT*TSK**4: where STBOLT is the Stefan-Boltzmann constant
netLW = EMISS*(GLW-LWUPFLUX): net long wave radiative flux

net radiative flux: RNET = GSW+netLW

Surface energy budget can be computed as RNET-GRDFLX-HFX-LH
All variables here (except RNET) are model variable names, and they represent instantaneous ground heat flux, sensible heat flux and latent heat flux.

Hi kwerner:

Can I use the net radiative flux (GSW+netLW) as a prediction of the surface solar radiation income? Dose this value consider the influence of the weather like cloud fraction? Any replies would be more than appreciated !

surface solar radiation income should be the sum of downward shortwave and longwave radiation at ground level. It should be calculated by
SWDNB + LWDNB

Thanks a lot

Hi,

If some of the variables are accumulated at every time step, and others are instantaneous values (such as GRDFLX, HFX, etc.), then when trying to calculate the budget, the results can be misleading and you probably won't get good energy balance.

If you happen to be using the NoahMP LSM, then a calculation for the surface energy budget it already built-in. It will be output as NOAHRES. Otherwise, you can look in the file phys/module_sf_noahdrv.F to follow how it is done, to be used as a reference.

In general, the following calculations can be used for radiative flux calculations:

LWUPFLUX = STBOLT*TSK**4: where STBOLT is the Stefan-Boltzmann constant
netLW = EMISS*(GLW-LWUPFLUX): net long wave radiative flux

net radiative flux: RNET = GSW+netLW

Surface energy budget can be computed as RNET-GRDFLX-HFX-LH
All variables here (except RNET) are model variable names, and they represent instantaneous ground heat flux, sensible heat flux and latent heat flux.
hi,
RNET is positive downward, and HFX and LH are positive upward ? is it right?
i am not sure weather GRDFLX is positive downward ?
if GRDFLX is positive downward, the surface energy budget should be computed as RNET+GRDFLX-HFX-LH ?
in my test, RNET+GRDFLX-HFX-LH is closed

Hi,
GRDFLX is negative download, which explains that RNET+GRDFLX-HFX-LH is closed in your case. Note the Surface energy budget can be computed by:
RNET+GRDFLX-HFX-LH

Hi Ming Chen,
I just need to follow up cibaouc question:
are HFX and LH positive upward ? or positive downwards?
Thank you!

HFX and LH both are positive upward.