More on the Atmospheric R-value

The R-value used to rate the insulation quality of construction materials and clothing is pretty simple. R=delta T/delta Q where T is the temperature, Q is the heat flow and delta is the difference of rate of change in either. If you have a room you want to be at 72 degrees with an outside air temperature of 32 degrees and only what to use 12.0 MBTH, then R=40/12=3.33 minimum R-value for the space. 3.33 is about the R value of a 3/4" airspace with some of that radiant reflective barrier stuff added. Not a very high R-value, but that was just an example. The atmosphere can have an R-value from one point to another. Since there are seldom dead air spaces, it is pretty low. It is like a house with no walls or roof, pretty hard to air condition. Adding greenhouse gases is supposed to increase the R-value of the atmosphere. If there were dead air spaces, the GHGs would do a fine job. Without dead air spaces, it is s touch more difficult to figure out how good a job they will do. Part of the R-value calculation is delta T. Since we have pretty good temperature data for the atmosphere at differing altitudes, we can get part of the R-value information.

That plot is for the University of Alabama, Huntsville, middle troposphere data minus the lower stratosphere data for the Northern and Southern extents. Adding CO2, CH4 and other gases and particles while change the temperature relationship between these atmospheric layers. As you can see, the differential for both is increasing with time. Since the delta T part of the equation between these two layers is increasing, the R-value would be increasing if the delta Q part remained the same or decreased. For global warming theory, delta Q should decrease as delta T increases.

This plot is just for the Northern Extent from 1995 with the estimated R-value included in yellow. I based the flux on a surface temperature of 273K (zero C degrees or 32 degrees F) and the differential based on 255K degrees. This is not an actual value of R but should give a trend. In this case the R estimate decreases very slightly. There would not be a radical change in the R-value, but it should be increasing. Of course these are only two regions with large assumptions made, but it could be an indication that the R-value is not linear with altitude. Which is what I suspect.

Making Data Dance

The Microwave Sounding Unit (MSU) data appears to be pretty reliable. While the fits are far from perfect, some indication of the CO2 forcing change, Solar forcing change and even changes in mean sea level can be teased out of the data. That should mean that even more can be coaxed out of all the noise.

That is a chart of the UAH southern extent, tropics and northern extent lower stratosphere data from 1994. I chose 1994 because there appears to be a general shift from cooling to neutral in the global stratosphere temperatures. The stratosphere should cool as the lower troposphere warms. In the lower troposphere, the 1998 super El Nino was a huge temperature event. It is not so huge in the troposphere. In the chart above, 2003 appears to be the largest stratospheric temperature event. That gave me an idea, possibly not the smartest idea I have ever had, but one that may be worth pursuing.

In this chart I plotted the mid-troposphere temperature divided by the lower stratosphere temperature for both the northern extent and the southern extent, again using the UAH data. By dividing by the lower stratosphere temperature, spikes should show when the monthly temperature approaches the mean anomaly. Depending on the sign of each, there would be positive ore negative spikes. It both data sets were fluctuation around their mean, the spikes would be evenly distributed, there would be more noise. In the chart above, there is much less noise than I expected. There was also more interesting noise than I expected. Since the mean for the data sets are based on the 1981 to 2010 period, most of the record, I would have expect no spikes at all prior to the 1994 to 95 leveling off of the stratospheric cooling with lot more noisy spikes after 1994 similar to the Sothern extent Orange curve. Since the Northern extent has more surface warming, I would have expected it to have more noise early in the series and less later, not fairly well distributed as it appears to be. That may mean that is could be possible to adjust the base line periods for the two data sets to establish similar noise patterns. That would give some indication of the relationship of "average" for each set with common events. With similar patterns, it could be possible to "slide" the relative timing of each series to isolate lag times.

Here, by adding 0.25C to the Northern extent lower stratosphere average, I was able to get the 1998 spike, the tropics 1998 spike is based on the 1978 to 1998 average of the tropical stratosphere and the Southern extent get a large negative spike with -0.02 used to adjust the average. I need a more logical method to adjust for optimum correlation, but there seems to be some potential here. I also am trying the differential of the lower troposphere and the lower stratosphere to compare changes in the emissivity of the atmosphere. Also a fairly crude method, but interesting.

This is the differential temperature for the entire UAH series.

And this is the temperature differential from 1995. The slopes of the regressions are much closer since 1995. With the short data series this will be a major challenge, but the average slope that best compares to Greenhouse gas forcing may be found by removing solar forcing change. It possible, then I may be able to estimate the land use impact. A lot of ifs and mays here, but the nearly double slope of the northern extent is fairly close to what I would expect for land use impact amplified by CO2 forcing. This is all probably a glorious waste of time. Still, there appears to be an outside chance of teasing out some useful information. This is more of a personal note than a real post.

It's Moving!

The change in the altitude of a parcel of air does whacky things. If you have ever looked at a thunder cloud you have seen the anvil top. That is where high velocity air is moving over the cloud, shearing off the top of the cloud. That is a big deal for guys like me living in hurricane country. I want to know better whether I need to plan on visiting relatives out of state or not. Low shear winds mean bigger storms which means Kansas here I come! With thunder storms, the greater the shear, the weaker the storm. Warmer rising air creates a downdraft of colder air which feeds the storm circulation. If the warmer air displaces colder air further down the road, there is less local energy to push more air into the base of the storm. Radiantly, the same thing happens. If the air above the warmer air is stationary, both masses approach the same temperature so there is radiant feedback allowing the warm air to cool slower. If the air above the warmer air is at a fixed temperature, the warmer air would continue to cool at the same rate and never be able to warm the layer above it. Try to visualize a three dimensional model with the surface, one sphere and the tropopause an outer concentric sphere. Now adjust the shape of the outer sphere so that it contours with the average tropopause temperature, say -60 degrees centigrade. It would have a large bulge at the equator and hug the surface as it approaches the poles. At one pole, it would actually intersect the inner surface sphere, leaving that pole open to the stratospheric temperatures. Now insert a sphere in the middle at the average temperature between the surface and outer spheres. Allow the surface sphere to remain fixed, rotate the middle sphere at some velocity near the average velocity of the surface wind speed and the outer sphere to rotate at the average velocity of the jet stream. You now have a basic radiant model of the coupled Earth atmosphere system. To tweak the model, include hexagonal shapes turning the spheres into "Bucky" ball geodesic shapes. Allow the middle sphere shape to rotate in simulation of the atmospheric vorticies. Now you have a model that may be able to do some good. For some reason Blogger is not allowing paragraphs, sorry.