What is clear is that there has been no change in either greenhouse gas or global temperature trends since the Paris Agreement on Dec. 15, 2015. There has been no progress and there is none in sight. Given current trends, the question then is, when will global temperature reach the agreed upon 1.5°C limit. For this question a post at Tamino’s Open Mind blog is informative. He calculates that at 435 ppm CO2 in the atmosphere in about 2029 the earth would have reached it’s “carbon budget” for avoiding the 1.5°C limit. But estimates for the remaining “carbon budget” vary. Some uncertainty is due to vague definition. The reference period for the 1.5°C limit is poorly defined. There is disagreement on whether to use atmosphere or surface temperature. It was pointed out in discussion that other greenhouse gases should be included in the “budget” calculation. A reference was given to a NOAA/ESRL published graph showing how the mixture of all greenhouse gases have varied with time in units of the equivalent concentration of CO2 in ppm. There is also the question whether to allow for climate inertia, the lag time in temperature. It’s analogous to putting a roast in the oven. The oven heats the meat, but it takes time for the center of the roast to reach the right temperature for rare, medium, or well done. By reducing the heat energy radiated into space, greenhouse gases change the earth’s energy balance, but it takes time to heat the rocks, warm the oceans, and melt the ice. Maybe a better analogy is a bus traveling at 75mph. When will slamming on the brakes prevent it from going over the cliff and when would it otherwise go over the cliff?
I wondered what the no-lag time for reaching 1.5°C would be if current trends continue. For temperature I chose the NASA and Berkeley (first table) temperature records. Following the publication by Ed Hawkins, et. al., I referenced the period between 1986 and 2005 as being 0.68°C above the preindustrial period, referenced as the global temperature between 1765 and 1800. I used either the CO2 Keeling curve from NOAA or the “CO2 equivalent” for all greenhouse gases from NOAA/ESRL for fitting to global temperature.
I found that “trends” can lead to two different answers. As Tamino’s graph showed, the pattern of CO2 over the past 60 years has been very consistent. For this entire period global temperature can be fit within a standard deviation of 0.16°C to 2.5 times the base 2 logarithm of the concentration of CO2 in ppm divided by 301.2. If this relation and trend continue then we could expect to reach the 1.5°C limit by 2039 with 456 ppm CO2 in the atmosphere. However, that was ignoring all of the other greenhouse gases. The pattern or trend for the CO2 equivalent of all greenhouse gases combined has not been as consistent, but global temperature for the past 60 years can also be fit within a standard deviation of 0.16°C to 1.6 times the base 2 logarithm of the ppm CO2 equivalent for all greenhouse gases divided by 319.4. Extending this relationship and trend reaches the 1.5°C limit in 2062 with a 612 ppm CO2 equivalent mixing ratio of all greenhouse gases.
Here is the analysis.
CO2 data is surprisingly predictive. There’s a seasonal variation, which can be understood from the distribution of vegetation covered land on the planet, but the seasonal variation is superimposed on a near perfect quadratic. To model the trend, I used a least square fit of the 1958-2000 monthly data to a second order polynomial, i.e. a quadratic curve. For the seasonal variation I averaged the difference from the quadratic for each month. I also noticed and included that the magnitude of the seasonal trend gradually increased, maybe because it depends on the amount of in CO2 the atmosphere. The CO2 data and the trend are plotted below. Plotted with it is the CO2 equivalent and straight-line trend for all greenhouse gases over the same period. I estimated the points from the NOAA/ESRL graph. (Neither curve shows any tendency to a downward change after the Paris Agreement in 2015.)
The following graph compares the 225 monthly measurements at Mauna Loa since the year 2000 with the “predictions” from the model trend based on the 502 monthly measurements from 1958 to 2000. The 1958 to 2000 model “predicts” the measurements since the year 2000 to within 1 ppm.
There certainly is no sign that the trend in either CO2 or the CO2 equivalent of all the greenhouse gases has changed since the Paris Agreement in December 2015.
The next question is how this ever-increasing level of greenhouse gas will affect global temperature. Here is a graph showing the least squares fit of temperature to the log of CO2 for the past 60 years. As shown below, the fit is so good that one is tempted to extrapolate this relation to future years using the current trend of CO2.
This fit neglects, however, that the other non-aqueous greenhouse gases affect temperature. It’s probably more correct to instead use the CO2 equivalent for all greenhouse gases. Since I couldn’t find a table with the CO2 equivalent ppm values dating back to 1958, I estimated them from the graph. Below is the resulting analysis. For the previous 60 years the fit is just as good, but including other greenhouse gases bends the future trend downward.
For 60 years the trend in global temperature can also be very well fit to either the logarithm of just CO2, ignoring the other greenhouse gases, or the logarithm of the “CO2 equivalent” of all greenhouse gases in the atmosphere. Including other greenhouse gases changes the trajectory of the trend for future years. Using just CO2 predicts reaching the cliff in 2039 with 456ppm CO2. Using the CO2 equivalent for all greenhouse gases predicts reaching the cliff in 2062 with a CO2 equivalent of 612ppm or when CO2 concentration would be 530ppm.
In summary, for a cliff at 1.5°C, Tamino’s analysis suggests slamming on the brakes in 2029 at 435ppm CO2. My analysis looked at two trends, one for CO2 and one for the CO2 equivalent of all gases. The CO2 trend and fit to global temperature predicts the cliff in 2049 at 456ppm. The CO2 equivalent trend for all greenhouse gases predicts the cliff in 2062 at a CO2 equivalent 612ppm or a CO2 concentration of 530ppm. Using the Berkeley record showed similar results using CO2 or CO2 equivalent. Tamino’s result may be the best current estimate. Mine, based on trends, are not far removed. Prudence would dictate a moon shot size effort to eliminate human emissions of greenhouse gases.
I will be looking for a change in the trajectory for when measurements of CO2 and global temperature show actual progress in our goal to avoid the 1.5°C cliff.
hswildman 