# Transient temperature change estimation under varying radiative forcing change scenarios, part one

The estimation of transient climate sensitivity (TCS, defined below) has been in the back of my mind since writing a couple of posts a couple of months ago (here and here) on expected future global mean temperatures over this century. This post, and the one to follow, is thus a methods oriented post resulting from that thought process investigation. This one just introduces the basics of the problem and in the next one I’ll get into methods.

I use TCS here to refer to the realized, global mean, surface temperature change, at any given time point, resulting from a change in radiative forcing (RF) up to that point, regardless of whether either the thermal, or radiation, environments have re-equlibrated in response to this forcing change or not. It is a generalization of the transient climate response (TCR), which is defined as the expected mean surface temperature change at t = 70 years, of a 1% per year CO2 increase. Such a rate gives a CO2 doubling (1.01^69.66 = 2), and since CO2 RF is well-approximated by a logarithmic function of the CO2 concentration ratio at two time points, this results in a constant annual RF change rate (= 5.35 * ln(CO2.2/CO2.1)/70 = 0.053 W/m^2/yr). So, TCS is just a generalization of TCR, in that the time span needn’t be exactly 70 years, nor the forcing rate exactly 0.053 W/m^2/yr. Linear scaling, based on other delta RF rates, is allowed, but the reference time should be within, say, a couple decades or so of 70 years. In the CMIP5 climate model experiments, which form the input to the IPCC AR5 report, the 1% increase is extended over 140 years, reaching 4X CO2 (from pre-industrial), and the transient response at that point is simply divided by 2, to estimate TCR as just defined.

Although the concept itself is straight-forward, TCS estimation from empirical data is not, because of the several important time delays and/or feedbacks, not to mention forcing agents, in the climate system, for which the available data are not sufficient to this highly important task. Generally, global mean time series output for idealized, modeled RF scenarios is thus required, in particular the 1% per year, and instantaneous 400%, CMIP5 CO2 increase scenarios. For whatever reason, the annual time series output for these, and more importantly for the four more realistic Representative Concentration Pathway (RCP) scenarios analyzed, are rarely reported. Why this is so baffles me; it’s not hard and the AR5 seemingly should have done it, but whatever, I’m not in charge. To get them, one thus has to analyze each climate model’s raw output data. Finding these data, downloading them, aggregating them from native temporal and spatial scales to obtain yearly global means, etc., is a time-consuming process, and one requiring a fair bit of programming; it’s a lot of work. But useful and important work.

The equilibrium climate sensitivity (ECS) is the temperature change expected after this same RF increase (3.7 Watts/m^2, allowing for stratospheric/tropospheric adjustment) has been imposed, but only after both radiation and temperatures have reached equilibrium. What’s missing from most reported ECS estimates however, is the time scale over which the full temperature increase is realized. In a few cases, model-estimated ECS time scales have been determined by running models having lower spatio-temporal resolutions than typical AOGCMS, for one to five thousand years, to equilibrium. But that costs a lot of supercomputer computing time, and full resolution runs cost even more, so most often it is computed from shorter AOGCM model runs (~ 150 to 300 years). An important method for so doing involves linear regressions of delta T on the planetary, top-of-atmosphere radiative flux, extrapolated to the point where that flux is estimated to be zero: the so-called “Gregory method”, after it’s originator. ECS estimates vary, with the consensus central tendency value, for 35 years or more now, being estimated at around 3.0 degrees C, with a likely range between 1.5 and 4.5. But that issue is not the point of these posts.

But ECS, which while important, is not fully realized for several hundred years after the cessation of a RF increase, and why it should receive (typically) more attention than estimates for the next few decades, is another big puzzler (albeit one that CMIP5 addressed directly with its decadal forecasts). However, the main point of this post is that the idealized CMIP5 experiments mentioned above can be used to predict the annual time series of the expected warming for any imposed, realistic RF change, even though the idealized experiments are themselves decidedly unrealistic. An instantaneous 4X CO2 increase is obviously wildly unrealistic–nobody’s ever argued such a thing could actually happen short of some planetary natural disaster scenario. Even the 1% per year increase from pre-industrial for 70, or even 140, years is clearly too high; even from a 1950 baseline the mean annual CO2 increase has been only (400/310)^(1/64) = 1.004, or 0.4% per year. Only in the last couple decades has it exceeded 0.5% per year, although it’s certainly possible to hit 1% per year in the near future, from either a continuing increase in emission rates, decrease in aerosol production rates, strong carbon cycle feedback (or forcing, via land cover changes), or some combination of these. [Edit:referring to the equivalent RF here, not necessarily via CO2 increases.]

By any account, whether purely scientific or as policy input information, the estimated TCS for any given year, i.e. a time series, is an important thing to know, (of higher practical significance than is knowing ECS and/or it’s time scale, I would argue). I haven’t seen it commonly estimated however; in the IPCC AR5 report for example, just the TCR and ECS are reported, and decadal resolution estimates for the four RCP scenarios, in which several forcing agents are changing simultaneously, including various well-mixed greenhouse gases, non well-mixed atmospheric agents (e.g. aerosols, surface ozone), land cover, surface albedo, and sometimes other things.

TBC. Fire away if you have any comments/questions. I’ll do my best to answer the easy ones and dodge or obfuscate on the hard ones.