Constant air density in turbulent exchange calculations

[bsu-wrudisill]

Hello,

I'm having trouble reconciling the treatment of air density in the computation of latent heat fluxes. It's possible that I'm missing part of a derivation where this cancels out, and apologies if that is the case. I'm only looking at latent heat flux for the ground, but this might matter elsewhere too.

The latent heat flux is computed using the vapor pressure gradient.

summa/build/source/engine/vegNrgFlux.f90

Line 2899 in 19a7f9c

latHeatGround = -latHeatSubVapGround*latentHeatConstant*groundConductanceLH*(satVP_GroundTemp*soilRelHumidity - VPair) ! (positive downwards)

The "latentHeatConstant" term is in there as a helper term that converts vapor pressure to specific humidity and then multiplies by the air density, $\rho$ to yield water vapor density (when multiplied by vapor pressure in the above equation).

summa/build/source/engine/vegNrgFlux.f90

Line 2768 in 19a7f9c

latentHeatConstant = iden_air*w_ratio/airpres ! latent heat constant for (kg m-3 Pa-1)

The $\rho$ term is treated as a constant and is defined here:

summa/build/source/dshare/multiconst.f90

Line 46 in 19a7f9c

real(rkind), PARAMETER :: iden_air = 1.293_rkind ! intrinsic density of air (kg m-3)

The value of 1.293 kg/m^3 is typical for sea level. I think that it is more appropriate to calculate the air density using the ideal gas law and the virtual temperature:

$\rho = \frac{p}{R_d \cdot T_v}$

[Petty, W. A First Course in Atmospheric Thermodynamics]. Where $R_d$ is the gas constant for dry air (287 J/kg/k).

So, to use some real numbers, a 0C atmosphere at 1000 hPa (sea level) has a density of close to 1.29, but an atmosphere also at 0C and at 700 hPa (around 10000 feet of elevation) will have an air density of about 0.8. So all else being equal, adjusting the air density in this case would yield about a 38% decrease in latent heat flux. Many climates where snow processes are important (and summa has lots of nice options for snow) are going to be well above sea level, so I think that this matters quite a lot.

Thanks

[wknoben]

Hi Will, thanks for your thoroughness in checking the code. We had some internal discussion about this and there's general agreement that you're right. This approach is a simplification and changing it would be good.