Calculating inversion height

[leifdenby]

@annalea-albright had originally defined the inversion height by two means in her code (see https://github.com/eurec4a/eurec4a-environment/issues/11)

1. Gradient in relative humidity, requiring a large negative gradient (how large?)
2. Gradient in relative humidity and temperature, requiring ...?

NOTE: @annalea-albright please edit the above

On https://github.com/eurec4a/eurec4a-environment/pull/25 the conversion of how to define inversion height continued (https://github.com/eurec4a/eurec4a-environment/pull/25#issuecomment-667169317, https://github.com/eurec4a/eurec4a-environment/pull/25#issuecomment-667186107 and https://github.com/eurec4a/eurec4a-environment/pull/25#issuecomment-667248154)

@annalea-albright and @Geet-George would you be ok with quickly summarising what definitions of inversion height you think we should use? Thanks!

[annalea-albright]

I'd summarize our two main conclusions this way, and Geet please add what you think I've missed!

1. Choose a definition that encompasses two variables (since a definition finding max dRH/dz or max dT/dz seems prone to more error from noise) and test these definitions against each other:

   • static stability > 0.1 K/hPa and dRH/dz < 0 (Bony and Stevens, 2018)
   • dT/dz > 0, accompanied by dRH/dz < 0 (Grindinger 1992, Cao et al, 2007, etc)
   • another definition based on max N^2 that Geet has tested. N^2 by definition reflects both static stability and moisture

2. Limit the first inversion base height to 4km and then think about other definitions for additional inversions in the free troposphere. For the free tropospheric layering, the isotope measurements seem unique and promising. I, for one, know nothing about how to use these isotope measurements, but it would be great to collaborate with Adriana Bailey and others on these questions.

[Geet-George]

I think that's very well put..

I find inversion base heights hard to conceptualize because there can be multiple inversions of varying strengths, so I have a hard time understanding if we want to compare each day's strongest inversion, or the first inversion, or inversions occurring roughly in the same height range.

I also liked your comment here (partially quoted above), which is a very nice summary to the problem and a possible solution. It would depend on the objective of knowing the inversion, to decide which definition is more suitable. But like you said, I think the idea of testing these definitions against each other is a very good one and that should definitely tell us more. I'll push the function for max N<sup2 by evening today...

About point-2, should we define base of free troposphere as 700 hPa, which is the convention or the top of the cloud layer, which makes more physical sense? In case of the latter, I was thinking the cloud layer would be defined as the hydrolapse (the moisture gradient we are looking for in the inversion definition). But I am not sure of this. I have attached circle-mean q and T profiles for two HALO flights. For some profiles (q on 01-28) the hydrolapse-definition for cloud layer will be straightforward, while for others (e.g. q on 02-02) this would be very difficult.

For comparison, the T profiles show a stronger and higher first inversion on 02-02 than on 01-28. The latter's inversion also aligns well with the sudden drop in moisture. These plots should also give an idea of how different inversion definitions can possibly work out.

[annalea-albright]

About point-2, should we define base of free troposphere as 700 hPa, which is the convention or the top of the cloud layer, which makes more physical sense? In case of the latter, I was thinking the cloud layer would be defined as the hydrolapse (the moisture gradient we are looking for in the inversion definition). But I am not sure of this. I have attached circle-mean q and T profiles for two HALO flights. For some profiles (q on 01-28) the hydrolapse-definition for cloud layer will be straightforward, while for others (e.g. q on 02-02) this would be very difficult.

The plots are really interesting to see how much the q profiles differ, a smooth decrease with different gradients on 01-28 and much more variability on 02-02. And similarly, how the different strength and the height of the inversion can be seen clearly in the T profiles.

Good to know that 700 hPa is the convention for where the cloud layer ends, in general! What would you suggest as the lower and/or upper bounds for inversion base? I guess this also raises the question if we are defining the cloud layer itself (i.e. upper bound for cloud layer of 700hPa?), or the cloud layer as 'residual' between boundary layer top and inversion base. I'm not sure.

Somewhat relatedly, looking at the q profiles on 01-28, there are segments with different slopes: the boundary layer for ~600m, a rapid decrease from 15--> 11 g/kg, a less rapid decrease 11-->10 g/kg, and then another rapid decrease from 10--> ~1 g/kg. Do you have an idea how to interpret this physically? The highest segment decreasing from 10--> 1/kg seems to be the top of the cloud layer / inversion base when comparing with the T profiles? Where would you define the cloud layer in this case? Just anywhere in between the boundary layer and inversion base?

No rush with the N^2 script!

[Geet-George]

Sorry for the late response... Just saw this. I somehow missed your comment...

Somewhat relatedly, looking at the q profiles on 01-28, there are segments with different slopes: the boundary layer for ~600m, a rapid decrease from 15--> 11 g/kg, a less rapid decrease 11-->10 g/kg, and then another rapid decrease from 10--> ~1 g/kg. Do you have an idea how to interpret this physically?

For the moisture values for 01-28, my best guess of interpreting it physically would be as follows:

• The mixed layer being directly influenced by the surface fluxes would hold the moist moisture in the column (15 g/kg). Since the layer is also well-mixed by turbulence, the values are quite constant up to the mixed layer top (~600 m).
• Above the mixed layer, moisture would be transported via scattered updrafts and the amount of moisture transported would depend on the shallow convective mass flux, which once past the LCL, would form clouds. This moisture from clouds (given time and correct conditions) should detrain and like we see in 01-28, get a uniform moisture layer for a long time above the mixing layer.
• The moistening due to detrainment is probably aided by the inversion, which restricts the moisture to within this "cloud layer", and thus we get a nice, consistent value of ~10-11 g/kg.
• The slowly decreasing moisture as we go from ~0.6 to ~2 km, would probably be because of more detrainment at lower heights, since there is more moisture near cloud base than at cloud top.
• There isn't much moisture getting past the inversion, because of the stability, and thus we see a strong gradient there, with the layer being relatively devoid of moisture.

The sole difference I find between the q profiles of 01-28 and 02-02 is that there is a well-mixed and more steady "cloud layer" in 01-28.

As for defining the cloud layer, the more I look at profiles from several days, the more complicated it seems. I like your idea of defining the cloud layer as a residual between the mixed layer top and inversion base. As for the inversion, we can stick to the first inversion below 700 hPa (convention for where the free troposphere starts), for now? And then, get more feedback from other experts later...

[leifdenby]

Notes from Peter Blossey on calculating inversion height (email 8/6/2020)

For inversion height, I've had good luck with defining the inversion as the place where dRH/dz*dTHETAL/dz is minimized. In the LES, I use domain-average profiles for this, so that ERA columns should work fine. Using the RH helps find inversions even in places where there is no qt gradient across the inversion (e.g., in the Arctic). There is some danger that the inversion height might jump in places with multiple inversions, but I don't think this will happen too much in our region.