Examine wet bulb temperature implementation

[dopplershift]

There was a poster at AGU comparing our implementation (among others) of wet bulb temperature and comparing to Davies-Jones 2008 and a new "NEWT" implementation--both of the latter showing better error characteristics. At some point, it would be worth seeing if there's low hanging fruit to improve ours.

[alioacar]

Hi @dopplershift ,
I've been tinkering the wet bulb temperature implementation for a bit. Here is the comparison of MetPy and the other two (Davies-Jones(Colin Raymond's DJ08) and NEWT).

It seems like MetPy has a bias compared the other two while they have a good agreement with each other. I think the difference comes from the temperature dependence of the latent heat of vaporization.(it should decrease if T increases and increase if T decreases). So I directly implemented it (Lv0 - (cpv-cpl)*(T-T0)) into to the moist lapse rate calculation and now it's really close what DJ08 and NEWT produce. Note that the different scales for the figure above and below.

However most tests related to the pseudo-adiabats(moist lapse) have failed now. So I'm not entirely sure it is correct.

[dopplershift]

I'm not shocked that updating the formula causes test failures; you are producing different values, and thus plots.

[alioacar]

I'm asking because I have no experience in this field—are there any validated datasets or measurements against which these calculations can be compared? (Not only for WBT but also like LCL or LFC ...) Also, I'm not sure if this level of accuracy is even desired but if it's needed, I can put in some effort here with some metrics and validation plots maybe.

[dopplershift]

None that I'm aware of. You could try comparing curves to e.g. those from the National Weather Service, but it's usually really hard to match since you don't know what set of assumptions is going into those curves.

[robwarrenwx]

Hi all,

I'm one of the authors on the poster that @dopplershift mentioned above. Cass Rogers (the lead author) and I have a paper in preparation on different methods of calculating wet-bulb temperature (Tw) and their accuracy. @alioacar is correct that the difference in results for MetPy compared with NEWT (our new highly accurate method) results mostly from the (rather inaccurate) assumption of constant latent heat in MetPy, which leads to errors in the pseudoadiabatic lapse rate. In the paper, we compare several approximate Tw calculation methods (MetPy, Davies-Jones, and NEWT) against an "exact" method, which accounts for the temperature dependence of the latent heat of vaporisation. The error magnitudes that we see for the MetPy method are consistent with those shown in the plot that Ali shared, though the sign is reversed (maybe a plotting error @alioacar?). Both NEWT and the Davies-Jones method have negligible errors; however, we identified a series of bugs in several open-source implementations of the Davies-Jones method. Colin Raymond's code was supposed to address these, but I think at least one of the bugs is still present. This likely explains why the results look so noisy when comparing that method with MetPy and NEWT in the plots above.

My initial recommendation would be for MetPy to implement the temperature dependence of the latent heat of vaporisation. This will lead to more accurate calculations not just for Tw but a whole range of quantities, including CAPE and CIN, the LFC and EL, and the lifted index. Down the line, you could look at implementing the NEWT or Davies-Jones method if you want to speed up the calculation of Tw. Details will be provided in the paper, but for now you can find an implementation in my Python library atmos (https://github.com/robwarrenwx/atmos/), specifically in the function thermo.pseudo_wet_bulb_temperature.

Another important thing that Cass and I cover in our paper is the fact that there are in fact two variants of Tw: pseudo (or adiabatic) and isobaric (see the AMS Glossary. All of the methods discussed above relate to the calculation of pseudo Tw. For isobaric Tw, there is a completely different iterative method, using Newton's method. This is again implemented in atmos, in the function thermo.isobaric_wet_bulb_temperature. It turns out that differences between pseudo and isobaric Tw are mostly small, except at very high temperatures and low relative humidities. Nevertheless, I think the distinction is important as isobaric Tw is more relevant when considering thermal comfort and heat stress, whereas pseudo Tw is more relevant in the analysis of moist instability and thermodynamic diagrams. As such, you may want to consider adding a function for isobaric Tw in the future.

[robwarrenwx]

Digging around a bit more, I see that the temperature dependence of the latent heats has already been implemented in #3725, along with the moist specific gas constant (Rm) and moist isobaric specific heat capacity (cpm). However, it doesn't appear that these variable "constants" are being used in the moist_lapse function. To rectify this, the pseudoadiabatic lapse rate in this function should be updated to match either Eq. 74 or Eq. 75 in Warren (2024). Note that the latter avoids the need to specifically calculate Rm and cpm.

It is worth noting that dry_lapse should also technically be using the moist air Poisson exponent (Rm/cpm). A parcel following this lapse rate will conserve its moist potential temperature, defined as theta_m = T (P_0 / P) ^ (Rm / cpm). It is pretty common to neglect the moisture dependence of the dry adiabatic lapse rate; however, doing so introduces an inconsistency if Rm and cpm are used in the moist (saturated) lapse rate. It might be worth modifying dry_lapse and potential_temperature to take dewpoint as an optional argument so that these more accurate moist variants can be calculated if desired.

[dopplershift]

@robwarrenwx I appreciate the feedback. I think using a temperature-dependent Lv in moist_lapse() is definitely something we can consider as we continue to refine our thermo calcs, e.g. implement Romps (2021) dewpoint and move our existing ODE-based moist_lapse to C++ (or change to a better method like Warren (2024) 😉 ).

It might be worth modifying dry_lapse and potential_temperature to take dewpoint as an optional argument so that these more accurate moist variants can be calculated if desired.

Yeah, that seems reasonable. We can make it a keyword-only argument to avoid confusion and any API-breaks.

[alioacar]

thanks @robwarrenwx for the feedback and you’re right, I think there was a sign mistake in my plots. Implementing the temperature-dependent latent heat shifted a lot of things slightly before and not sure what the current state of it. When I have some time, I will check again.
and a quick note - totally agree @dopplershift. updating the implementation to match Eq. 74 or Eq. 75 in Warren (2024) would avoid the current inconsistency and also remove the need to manually compute Rm and cpm in some cases.