After years of battling skeptics, you would think the climate change pundits would have a better source of boiler plate responses to commonly asked questions. How valid is the assumption of equilibrium gets brought up fairly often.

Radiant equilibrium is what is being assumed. This is Ein = Eout at the top of the atmosphere which is assumed to be approximately 20 kilometers in altitude. The energy in is predominately short wave electromagnetic and the energy out is predominately long wave electromagnetic. Since there is a constant flow of energy in and energy out, there is no assumption of thermodynamic equilibrium.

Ein is provided by an assumed constant power source, the Sun. The solar "constant" is about 1361 +/- 50 Wm-2 over one year and 1361 +/-0.5 Wm-2 over a solar cycle of approximately 11 years. Since Ein isn't completely constant, you need to define a period where the average of Ein over that time period would equal the average of Eout for the same period.

The current energy imbalance is ~ 0.6 +/- 0.4 Wm-2 or Ein = Eout + 0.6 +/- 0.4 Wm-2. So there is an assumed radiant equilibrium that doesn't exist. It is assumed that the imbalance is due to something, mainly greenhouse gases released into the atmosphere by man.

Some assumptions have to be made with any complex system and the radiant equilibrium assumption is not a bad choice. However, every assumption has the potential for error so it isn't a bad idea to revisit assumptions from time to time to determine how valid and useful they are.

Rosenthal et al. for example have done a great deal of paleo ocean research and found that ocean heat content varies on long time scales. Since the oceans would absorb/release most of the imbalance, a preexisting imbalance would need to be considered to see how much impact it would have on ALL the calculations and add on assumptions related to the radiant equilibrium assumption. Most of those would be small enough errors to ignore, but if the preexisting imbalance is 50% of the assumed mankind induced imbalance, that is more than enough to warrant some study.

To a lay person like myself, explaining the limits of an assumption would inspire more confidence in the person(s) using the assumptions to justify a trillion or so dollars worth of "mitigation" as opposed to adaption.

Now there are other issues with radiant versus thermodynamic equilibrium. The zeroth law isn't met, so assuming some average global surface temperature will always produce the require Eout is a bit of a stretch. It is quite likely that a range of surface temperatures can produce the desired Eout since the temperature range used to produce the average goes from ~-80C to +50 C and includes latent, convective and mechanical energy. This can easily be an uncertainty of 0.3 C or roughly 1 Wm-2 which is nearly 1/3 of the total estimated man made forcing produced to date.

Unfortunately, the early estimates of "sensitivity" ignored these issues so all warming is assumed to be "forced" by changes in the radiant energy budget. All of these potential errors would tend to reduce sensitivity much like estimates of transient climate sensitivity are currently indicating. A fairly small group of climate scientists have rather meekly pointed out the trend in reduced sensitivity, but the more vocal advocates still highlight the increasingly less probable "fat tail" extreme range.

To many, the math involved is a fun puzzle to ponder and they would like to see more debate over the most likely impact instead of horror stories about the least likely impact used to inspire political policy. If climate scientists want to have less rehashing, they should expand their frequently asked questions list to include uncertainty that is friggin' obvious.

## Thursday, April 20, 2017

## Wednesday, April 19, 2017

### They are still at it - Equilibrium

It is the 19th of April 2017 and there are still people discussing how useful an assumption of climate equilibrium happens to be. Many of the pro equilibrium crew are obviously liberal arts majors.

Equilibrium is very useful if the initial condition assume to be at equilibrium is valid to some degree of precision that is much more accurate than the change one is trying to measure.

At the Top of the Atmosphere you have Ein ~ 240 Wm-2 and Eout ~ 240 Wm-2 if you average both over a reasonable period of time. Both Ein and Eout vary by close to 5% over the course of a year and the change being made will be about 1% of the potential energy at the surface.

The surface energy is roughly 390 Wm-2 based on an average temperature of 288K degrees plus about 88 Wm-2 of latent energy on average plus around 20Wm-2 of energy related to convection. There is another 4 Wm-2 or so of mechanical energy related to ocean and atmospheric currents and several small sources of energy. Just using the bigger guys, you have 390 + 88 + 20 = 498 Wm-2 that will produce the ~240 Wm-2 at the top of the atmosphere. The uncertainty in that 498 Wm-2 is about +/- 17 Wm-2 based on Stephens et al 2015 I believe.

So the answer to is the equilibrium assumption useful question, depends on how many knock on assumptions are based on the initial assumption and how much error there can be because of the initial assumption multiplied by the sensitivity of knock on assumptions to that error.

The simple answer is still maybe it is valid, maybe it isn't. Time will tell.

Equilibrium is very useful if the initial condition assume to be at equilibrium is valid to some degree of precision that is much more accurate than the change one is trying to measure.

At the Top of the Atmosphere you have Ein ~ 240 Wm-2 and Eout ~ 240 Wm-2 if you average both over a reasonable period of time. Both Ein and Eout vary by close to 5% over the course of a year and the change being made will be about 1% of the potential energy at the surface.

The surface energy is roughly 390 Wm-2 based on an average temperature of 288K degrees plus about 88 Wm-2 of latent energy on average plus around 20Wm-2 of energy related to convection. There is another 4 Wm-2 or so of mechanical energy related to ocean and atmospheric currents and several small sources of energy. Just using the bigger guys, you have 390 + 88 + 20 = 498 Wm-2 that will produce the ~240 Wm-2 at the top of the atmosphere. The uncertainty in that 498 Wm-2 is about +/- 17 Wm-2 based on Stephens et al 2015 I believe.

So the answer to is the equilibrium assumption useful question, depends on how many knock on assumptions are based on the initial assumption and how much error there can be because of the initial assumption multiplied by the sensitivity of knock on assumptions to that error.

The simple answer is still maybe it is valid, maybe it isn't. Time will tell.

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