Rather the hotspot is predicted by the parameterizations of other processes ( probably convection ) and the lack of the hotspot appearance means the convection parameterization is likely quite erroneous.

The parameterization is wrong regardless of the source of the convection.

I was ready to dismiss the convection forces convergence argument until I reflected that hurricanes represent mutual feedback between convergence and convection – the inflow enhances convection while the convection ( and subsequent outflow aloft ) enhance converging inflow. The same probably occurs with the ITCZ – mutual feedback.

Still, ‘solar heating’ as theory runs into problems explaining why the ITCZ remains north of the equator year round in the Atlantic and the Eastern Pacific.

Further, tracing individual polar air masses by examining the total precipitable water demonstrates that polar air masses, greatly modified, do make their way to the equator and the instrusion of these air masses do show up as waves in the ITCZ.

That’s one problem I have with the ‘Hadley Cell’, which is not actually observed in nature. The ‘Cells’ don’t allow for air mass exchange across them. A better model, it seems to me, is that there is no such thing as the ‘sub tropical jet’, Hadley Cell, Ferrel Cell and the like, but polar air masses which spill underneath the baroclinic waves as part of the global circulation. There is an equatorial low in association with the ITCZ, but there is a large contribution of the convergence of polar air masses in driving the convection in the conditionally unstable air of the deep tropics.

The ITCZ is not something that dominates the tropical convection, it might be more correct to say that the tropical convection forces the existence of ITCZ. ITCZ represents the return flow of air when moist warm air rises as the uplift part of the Hadley cells. The reduced lapse rate is the consequence of this moist uplift, which is perhaps the most important driver of the global circulation. It drives almost everything, nothing drives it (except the solar heating of tropics).

This post tells about the role of IR in the local energy balance at various altitudes. The atmosphere is assumed to follow one of the AFGL standard atmospheres, that’s assumed not calculated. The only thing that’s calculated is the IR emission and absorption that results from the assumed atmospheric profiles under clear sky conditions.

In troposphere the imbalance of the IR terms is compensated by SW absorption and convection, in stratosphere by SW absorption alone.

I think that’s part of the failing of the parameterizations.

Were the lapse rate to actually decrease, that would imply less convection, meaning less heating reaching the upper troposphere (and less moisture).

Tropical convection is dominated by the ITCZ. But the ITCZ arises from air mass motion – non-linear dynamics – which are not well parameterized.

A tropical hot spot means that the temperature increases faster in the upper troposphere than near the surface. By definition that means a decrease in the lapse rate. But the average relative humidity in the tropical atmosphere above 10 km is less than 20%. I’m not sure why, if the RH remains that far below saturation, the lapse rate should decrease.

http://ajp.aapt.org/resource/1/ajpias/v24/i5/p303_s1

http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000024000005000303000001&idtype=cvips&doi=10.1119/1.1934220&prog=normal

As for the hotspot, doubling CO2 imposes close to zero change in the radiative cooling rate for any given level in the troposphere. ( Seems paradoxical until reflecting that it is the accumulation of energy for the troposphere as a whole that implies warming ).

Further, the hotspot appears in models for other forcings ( reducing albedo, increasing solar, etc. )

This implies that the hotspot is arising from modeled atmospheric response to energy increase. These other processes are parameterized, of course.
The failure of the models in this respect represents a serious error in the parameterizations which probably doesn’t get enough attention. This is no surprise, of course. Atmospheric motion is non-linear and not accurately represented by parameterization ( if it were, we wouldn’t need any meteorologists ).

He also arrives at an increase in downward flux of about 8 W/m^2, for a doubling of CO@, about four times the modern estimate. This is probably due to the poor quality of spectral data available, particularly the lack of data for H2O. He also shows in Fig 8 (upwards and downwards fluxes for three CO2 concentrations), that the flux change is entirely due to the 12-14 um and 16-18um bands, the 14-15 um band being saturated.

It would be interesting if you could reproduce his plots but with the modern spectral data. If you don’t have access to his paper I’d be happy to send you a scan of the two figures.

Your Figs 1 and 4 show a tropical tropospheric hotspot but Fig 5 doesn’t. Both Lindzen and Spencer point out that it is not observed in the ballon or satellite data. What is the source of the hotspot in your calculations?