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17. The “Hotspot”

Dr David Evans, 2 November 2015, David Evans’ Basic Climate Models Home, Intro, Previous, Next, Nomenclature.

Before applying data to the alternative model of the last post, which we shall do in the next post, we first dwell on one crucial aspect of the data.

Some notes on terminology before we begin:

• A concept of much concern in this post is the water vapor emission layer, which is such a mouthful that we frequently use its acronym WVEL (which we pronounce so as to rhyme with “bevel”).
• The “solar response” means the “response of the surface temperature to increased solar absorbed radiation” — that is, the response to the Sun, not the response of the Sun.
• The “CO2 response” is the “response of the surface temperature to an increased concentration of atmospheric carbon dioxide”  — the response to increasing CO2.

The solar and CO2 responses are perhaps best explained by Fig. 1 of post 13.

Overview

The “hotspot” is the informal name for a warming of the upper troposphere, caused by an ascent of the water vapor emission layer (WVEL).

• In the conventional model (see Fig. 2 of post 3), surface warming for any reason causes a hotspot. The water vapor amplification mechanism in the solar response causes a hotspot because it thickens the water vapor layer, causing the WVEL to ascend. The conventional model applies this solar response to every climate driver (post 9).
• In the alternative model (see Fig. 1 of post 13), the solar response causes the water vapor layer to thicken and thus the WVEL to ascend, while the CO2 response could either thicken or thin the water vapor layer, causing the WVEL to either ascend or descend (at this stage, before considering the data, we don’t know which). The water vapor responds to both responses, and both processes may be occurring simultaneously.

Given the apparent lack of a hotspot over the last few decades, coincident with a rapid rise in CO2 concentration, it would appear that (a) the CO2 response causes the WVEL to descend, which is consistent with the rerouting feedback, and (b) the descent of the WVEL due to the CO2 response outweighs the ascent of the WVEL due to the water vapor amplification caused by the increase in absorbed solar radiation (ASR) that also occurred over that time.

The Hotspot is Caused by an Ascending WVEL

The water vapor emission layer (WVEL) is effectively the upper optical boundary of the water vapor in the atmosphere, on average.  It is at about one optical depth as seen from space, on the wavelengths at which water vapor absorbs and emits. Its average height is ~8 km or ~360 hPa (post 14), which is in the upper troposphere. The most important part of the WVEL is in the tropics, where it is warmest and most of the radiation to space is occurring, and the WVEL, like the tropopause, is somewhat higher — maybe 10 km.

If the WVEL ascends, it creates the hotspot. The air above the WVEL is dry, but the air below the WVEL is moist and therefore warmer — because water vapor is condensing and releasing its latent heat. If the WVEL ascends it creates the hotspot, which is the warming of a volume that was dry and cool when just above the WVEL but which becomes moist and warmer as the WVEL ascends above it.

Conversely, a falling WVEL produce a volume of cooling (a “coolspot”?).

Because water vapor is quite dynamic in the upper troposphere, its upper boundary often moving up and down several kilometers over time at a given location, the “instantaneous WVEL” moves up and down. The (average) WVEL is the average of the instantaneous WVEL. Because of this dynamism, hotspot warming can extend for a couple of kilometers in height — as the WVEL moves up the instantaneous WVEL tends to move up, warming volumes over a couple of kilometers of vertical extent to some degree.

The traditional illustration of the hotspot comes in a diagram of atmospheric warming (color) by latitude (x-axis) and height (y-axis). If the instantaneous WVEL stayed very close to the WVEL (i.e. no dynamism), the hotspot would be a strip of strong warming in the upper troposphere somewhere around 300 to 400 hPa, and the height of the strip would be the amount by which the hotspot ascended. But the dynamism of the water vapor causes a cloud of instantaneous WVEL heights clustering around the WVEL, ensuring that the hotspot is smeared out over a couple of kilometers in height.

The hotspot is distinct from warming in the upper troposphere produced by a change in lapse rate. As the surface warms due to increased ASR, more evaporation causes a moister atmosphere and thus a lower lapse rate, which causes the atmosphere at a given height to warm. While this surface warming also causes the WVEL to ascend (next section), warming due to increased lapse rate is broadly and diffusely spread through the atmosphere with a shallow gradient, in contrast to the hotspot which is a smear of warming centered on the WVEL.

The Solar Response Causes the WVEL to Ascend

The conventional explanation for the hotspot is that surface warming causes more evaporation (70% of the surface is ocean), and the greater volume of water vapor in the atmosphere is assumed to push up the WVEL, which is the top layer of the water vapor. However, as noted by Paltridge, Arking, and Pook in 2009 ^[1], more water vapor in the atmosphere does not necessarily lead to more water vapor in the upper troposphere if the extra water vapor is mainly confined to a more stable lower troposphere with less overturning, as appears to be the case according to the better radiosonde data from 1973.

Note that the temperature at height h is

where Γ is the average lapse rate (about 6.5 °C per km).

Within the solar response (Fig. 1 of post 13), the surface warming due to increased ASR (that is, ΔT_S,A) is about twice the increase in radiating temperature (ΔT_R) because of amplification by the non-albedo solar feedbacks (Eq.s (3) and (4) of post 13). Because the radiating temperature is roughly the average of the warmings of the various emission layers, and because all the emission layers warm by about the amount of surface warming before the effects of changes to lapse rates and emission layer heights, one or more of the main non-surface emission layers must warm significantly less than the surface. The height of the CO2 emissions layer is determined by the concentration of CO2, so its height cannot change. The lapse rate changes slightly, but that works against the amplification of warming (the lapse rate feedback is negative). That leaves just the heights of the WVEL and the cloud tops, one or both of which must ascend to cooler places in the atmosphere. Clouds are not well understood, but it is generally thought that WVEL provides the bulk of the accommodation. Thus the WVEL ascends significantly in response to surface warming due to more ASR.

In the conventional model all climate drivers cause the solar response (Fig. 2 of post 3 or Fig. 2 of post 13), and all surface warming is due to the solar response, so the surface warming ΔT_S is equal to the surface warming due to ASR ΔT_S,A. Thus, the conventional explanation is that all warming influences cause the WVEL to ascend, thereby causing a hotspot. In the alternative model however, while extra ASR causes the WVEL to ascend as per the solar response in the conventional model (Fig. 1 of post 13), other climate drivers operating through their own responses might simultaneously cause the WVEL to descend.

The WVEL Has Not Ascended in the Last Few Decades

The only instruments with sufficient vertical resolution to measure the change in height of the WVEL over the last few decades (Δh_W) are the radiosondes. Satellites are not suitable because they aggregate information from several vertical kilometers into each data point.

Radiosonde-derived temperature and humidity data is used here. It is accepted that the latter especially must be treated with great caution, particularly at altitudes above the 500 hPa pressure level. Following the discussion in Paltridge, Arking, and Pook (2009), the humidity data is restricted to tropical and mid-latitude data at least ~0.5 g/kg, from 1973. While the data is not good enough to estimate changes in the average height of the WVEL, Δh_W, it is sufficient to at least distinguish the direction of movement.

Surface temperatures here are the midpoints of UAH and HadCrut4, 5-year smoothed and centered.

– Temperature Data

The temperatures measured by the radiosondes are shown in Fig. 1 below, for 1979 to 1999 (the only image as a function of height and latitude ever publicly released, apparently).

Over those two decades surface warming was ~0.120.20 °C per decade, which would have caused a similar warming at all levels of the troposphere had there been no change in the lapse rate (Eq. (1)). Lapse rate changes warm the atmosphere even more. Surface warming causes more evaporation and a damper atmosphere, and thus a lower lapse rate (our lapse rate is a positive number, about 6.5 °C per km). So, at a given height, there is warming due to the change in lapse rate (Eq. (1)). Working through the details*, at the WVEL height of ~8 km the atmosphere warmed by ~0.1627 ± 0.035 °C per decade over the period in Fig. 1, from a combination of surface warming (0.1220 °C per decade) and the attendant lapse rate change (0.047 ± 0.035 °C per decade). At 10 km, it would have warmed slightly more.

The real story in Fig. 1 is hidden between the lines. This graph is for the two decades that saw the most rapid surface warming of the last 50 years. It does not show the lowest 1.5 km, which would have been a yellow-orange color because the surface warmed by ~0.20 °C per decade. Yet it shows barely any upper tropospheric warming. The graph is putting it in the nicest possible way, but actually the numbers are devastating for the conventional models — because the warming observed around the WVEL height of 8 to 10 km is less than the warming merely due to the surface warming and lapse rate changes.

This tells us there was active cooling at work in the upper troposphere, some factor that countered the warming coming up from the ground. It’s like the dog that didn’t bark. If the structure of the troposphere stayed the same (that is, the WVEL did not move), then the surface warming and lapse rate changes would have warmed the upper troposphere at 8 km by ~0.1627 ± 0.035 °C per decade.  But the observed warming was about 0.1 °C per decade, as shown in the radiosonde data of Fig. 1. Therefore there was a  slight counteracting cooling, presumably due to structural changes in the upper troposphere. This suggests the WVEL fell slightly; it is not compatible with an ascending WVEL.

In other words, if you subtract out the warming in Fig. 1 that is simply due to surface warming and attendant lapse rate changes, what is left are the temperature changes for other reasons. This reveals a slight cooling in the upper troposphere around 8 km, or 10 km in the tropics. Again, this can only mean the WVEL descended, not ascended.

…

Figure 1: Atmospheric warming 1979 to 1999, as measured by the radiosondes. The horizontal axis shows latitude, the vertical axis height (km on the right, hPa on the left). From the US CCSP report of 2006, Fig. 5.7E in section 5.5 on page 116 (Santer 2006, ^[2]), see also Singer 2011 ^[3].

 

Dr Roy Spencer, who pioneered microwave sounding for measuring atmospheric temperatures from satellites, recently (May 2015) used a different mix of microwave channels to specifically look for the hotspot using the satellite data — see his graph of how broad the data collected is, or conversely, how low the vertical resolution is. He concludes: “But I am increasingly convinced that the hotspot really has gone missing. … I believe the missing hotspot is indirect evidence that upper tropospheric water vapor is not increasing, and so upper tropospheric water vapor (the most important layer for water vapor feedback) is not amplifying warming from increasing CO2.”

The cooling strips above 12 km are due to ozone depletion, and are too high to be of interest here.

– Temperatures Predicted by the Conventional GCMs

As something of an aside because this series is about basic climate models, the measured data in Fig. 1 is nothing like the picture predicted by the big computerized climate models, the general circulation models (GCMs).

The GISS Climate Model E, a prototypical GCM, makes many of its outputs public. From 1979 to 1999 the CO2 concentration went from 337 ppm to 368 ppm, an increase of 9%, or 13% of a doubling (ΔL=0.13). The nearest the GISS model will publicly simulate is for a 25% increase in CO2 (ΔL=0.32) with no change to solar irradiance, shown in Fig. 2. Obviously the intensity of warming will be different because the change in CO2 is different, but the pattern or quality of the heating is of interest here. Note the prominent heating in the tropics at ~10 km (250 hPa) — this is the “hotspot”. The GISS model would show roughly the same pattern, just with not as much warming, for a CO2 increase that was only 13% of a doubling, as occurred between 1979 and 1999.

Figure 3 shows what the GISS model predicts for a 2% increase in solar irradiance, with no change in CO2. It is roughly what the model predicts for a full doubling of CO2 (Fig. 2 is only for 32% of a CO2 doubling, so the pattern is similar but the warming is not as intense as for a full doubling). Fig. 3 has the same pattern of atmospheric warming as Fig. 2, because conventional models,  following the conventional basic climate model in Fig. 2 of post 9, essentially apply the solar response to all climate forcings — roughly the same sensitivity and the same feedbacks to surface warming, but with some smaller differences such as that incoming sunlight interacts with ozone (see post 9).

Figure 2: Atmospheric warming when the CO2 concentration increases by 25% (or 32% of a doubling) with no change in solar irradiance, as predicted by a typical conventional climate model (the GISS model E, 5/4 * CO2, 100 year response, Lat–Hgt). The “20”s on either end of the horizontal temperature scale are in error, so ignore them. Compare to reality in Fig. 1, but note that Fig.1 is for only a 9% increase in CO2 concentration (or 13% of a doubling). The dark red spot over the tropics at about 10 km (250 hPa, left vertical scale) is the hotspot; it amplifies the surface warming in the model, because it simulates the WVEL ascending and emitting less OLR, thereby requiring the surface to emit more OLR and thus be warmer than otherwise.

Figure 3: Atmospheric warming when the solar irradiance increases by 2% but CO2 is held constant, as predicted by the GISS model E (1.02 * solar irrad, 100 year response, Lat–Hgt). The “20”s on either end of the horizontal temperature scale are in error, so ignore them. Compare to Fig. 2: note the similar pattern of atmospheric warming, including the prominent hotspot, because conventional models roughly apply the solar response (similar sensitivity, same feedbacks to surface warming) to all climate influences. In the GISS model, a ~2% increase in solar irradiance produces the roughly same results as a full doubling of CO2 (Fig. 2 only shows 32% of a CO2 doubling).

 

Figures 2 and 3 are clearly nothing like Fig. 1. The supporters of the conventional model explain away this clash between GCMs and empirical evidence by ignoring or disputing the radiosonde data, and substituting vague satellite data instead — even though satellites, due to inadequate vertical resolution, are the wrong tool for the job. For example, see here or here or here.

A simpler explanation, that accords with the measured data in Fig. 1, lies in the alternative model presented in this series: simply don’t apply the solar response to the influence of CO2 (see post 13). Occam’s razor.

– Humidity Data

Consider the specific humidity data from the radiosondes, shown in Fig. 4. The more reliable data only goes to 400 hPa, but above 500 hPa the trend is one of drying. This agrees with the model in Fig.s 1b, 2b, 3 and 5 of Paltridge, Arking, and Pook (2009). The same trends are shown by the earlier radiosonde data from 1948 to 1973. Like the temperature data, this suggests a descending WVEL, and is not compatible with an ascending WVEL.

Figure 4: The atmosphere near the average WVEL height (around 360 hPa) shows a drying trend since 1973.

 

– Conclusion

The WVEL has descended in the last few decades, but we cannot determine how much:

 

Conclusion: The CO2 Response Causes the WVEL to Descend

In the last few decades there was surface warming yet the WVEL did not ascend — there is no hotspot. Therefore the conventional model is incorrect.

In the alternative model, the warming influences of ASR and CO2 are both considered. The albedo data discussed in post 10 indicates a small fall in reflected solar radiation from 1984 that is larger than the smoothed changes in TSI occurring in that period, so ASR presumably increased from 1984 — which caused some surface warming and invoked the solar response, thereby causing the WVEL to ascend. Yet the WVEL was observed to descend. Therefore the WVEL descended due to the CO2 response (to the increasing CO2), which outweighed the ascent due to the solar response (to the increased ASR). Hence the CO2 response to increasing CO2 causes the WVEL to descend. This is also supporting evidence for the rerouting feedback.

In other words, the strong rise in CO2 concentration and the lack of a hotspot together suggest that the effect of the CO2 response is to cause the WVEL to descend, and that this descent was only partly offset by the ascent caused by extra ASR and the solar response.

 

*Details of the effect of lapse rate change due to surface warming on the temperature at the WVEL height: Assuming that lapse rate change was uniform at all heights, the warming it caused can be estimated from the lapse rate feedback  in AR5 (f_LR, the increase in OLR per increase in surface temperature due to lapse rate change (∂R / ∂T_S), whose value is -0.6 ± 0.4 W/m² per °C  — see post 3) and the parameter g from the OLR model (the increase in OLR per increase in lapse rate (∂R / ∂Γ), whose value is  -13.5 W/m² per °C/km — see Eq. 14 of post 15). The increase in lapse rate per  increase in surface temperature (∂Γ / ∂T_S) is thus about  f_LR / g, or 0.044 ± 0.03 °C/km per °C. Hence the change in lapse rate for the observed surface warming of ~0.1220 °C per decade is 0.005388 ± 0.00366 °C/km per decade. At 8 km, the warming due to the change in lapse rate is thus about 0.047 ± 0.035 °C per decade.

 

References

[1^] Paltridge, G., Arking, A., & Pook, M. (2009). Trends in middle- and upper-level tropospheric humidity from NCEP reanalysis data. Theoretical and Applied Climatology, 98:351-359.

[2^] Santer, B. D. (2006). US Climate Change Science Program 2006, Temperature Trends in the Lower Atmosphere – Understanding and Reconciling Differences.

[3^] Singer, S. F. (2011). Lack of Consistency between Modeled and Observed Temperature Trends. Energy and Environment, Vol 22 No. 4, pp. 375 – 406.