Calculating relative humidity at reference height (RHREFHT)

[sur23beeb]

How is RHREFHT calculated in CAM? Is there a link that displays the equation? The relevant line in the code is:

      ! Calculate and output reference height RH (RHREFHT)

      call qsat(cam_in%tref(:ncol), state%ps(:ncol), tem2(:ncol), ftem(:ncol))
      ftem(:ncol) = cam_in%qref(:ncol)/ftem(:ncol)*100._r8

but instead of trawling through multiple subroutines, it would be easier to just see the equation. The manual does not seem to provide this information.

 

[nusbaume]

Hi ST,

The equation for RHREFHT is the following:

RHREFHT = QREFHT / Qsat(TREFHT) * 100

Where "QREFHT" is the specific humidity at two meters above the surface, and "TREFHT" is the air temperature at two meters.

"Qsat" is then a function of the air temperature which represents the saturation specific humidity at the reference height (two meters). This is calculated from the saturation vapor pressure like so:

qsat(TREFHT) = epsilo * es(TREFHT) / [pres - (1-epsilo)*es(TREFHT)]

where "epsilo" is the ratio of the molecular weight of H2O over the molecular weight of dry air, and "pres" is the atmospheric pressure at one's location (which for the reference height is just the surface pressure, PS). Finally, "es" is the saturation vapor pressure at the provided reference height temperature value. There are multiple different ways this can be calculated in the model, but for CESM2.1.3 it defaults to the Goff-Gratch method, which can be found online here:

Goff–Gratch equation - Wikipedia

en.wikipedia.org

Anyways, I hope that helps, and if you need any additional details just let me know.

Thanks, and have a great day!

Jesse

 

[sur23beeb]

Thanks for the detailed reply!

 

[sur23beeb]

Hi ST,

The equation for RHREFHT is the following:



Where "QREFHT" is the specific humidity at two meters above the surface, and "TREFHT" is the air temperature at two meters.

"Qsat" is then a function of the air temperature which represents the saturation specific humidity at the reference height (two meters). This is calculated from the saturation vapor pressure like so:



where "epsilo" is the ratio of the molecular weight of H2O over the molecular weight of dry air, and "pres" is the atmospheric pressure at one's location (which for the reference height is just the surface pressure, PS). Finally, "es" is the saturation vapor pressure at the provided reference height temperature value. There are multiple different ways this can be calculated in the model, but for CESM2.1.3 it defaults to the Goff-Gratch method, which can be found online here:

Goff–Gratch equation - Wikipedia

en.wikipedia.org

Anyways, I hope that helps, and if you need any additional details just let me know.

Thanks, and have a great day!

Jesse

Hi Jesse:
I was trying to rederive this and noticed a typo. The parameter "epsilo" is the ratio of the molecular weight of dry air to that of water vapor, not the other way round.

 

[nusbaume]

Hi ST,

I went back into the code, and confirmed that "epsilo" is the following:

epsilo = molecular_weight_H2O / molecular_weight_dry_air

Is that not what you got in your derivation? If not, can you send your derivation to us? You can just attach a PDF or something equivalent if you don't want to type it all out on the forum itself. If we have a bug in the code it would be great to get it rectified.

Thanks!

Jesse

 

[sur23beeb]

I am at work right now and don't have the sheet of paper on which I rederived it. But here's a link that is saying the same thing.

Is it possible that in the actual equation, they are using 1/epsilo and not epsilo?

 

[sur23beeb]

Here is another link. The parameter epsilon is defined in the section "Mixing Ratio" as the ratio of the mass of dry air to that of water vapor and is equal to 0.622. If you scroll down to the "specific humidity" section, you can see how q_s is being calculated.

I am still wondering if somehow the actual parameter entering the equation in the code is 1/epsilo and not epsilo.

 

[sur23beeb]

Or it could be a mistake just in the documentation and the right number (0.622) is entering the equation for q_s.

 

[nusbaume]

Hi ST,

I double-checked the values and epsilo is ~0.622, which is the ratio of the molecular weight of H2O over the molecular weight of dry air (i.e. the equation above). Please note that in the equations you sent they are using the gas constants and not the molecular weights, hence the difference in the order. So it looks like everything is correct as-is, at least in the model code. Thanks for helping me double check though!

Jesse

 

[sur23beeb]

oops, that was a miss on my part! sorry for the confusion and thanks for double checking.

 

[lufiedler]

Hi Jesse, Hi ST,

sorry for re-opening this discussion more than one year later. I recently stumbled across RHREFHT fields as well. In some first investigations with the CESM2 Single Forcing Experiment RHREFHT seems to go up to 200 and is often higher than 100 which I can not explain with the equation at the top of this thread or the common definition of relative humidity. Could you help me out, what am I missing to understand the physical meaning of RHREFHT?

Cheers,
Lukas