Radiative-Equilibrium Models and the Weather Temperature
I started working on my own toy 0-D and 1-D models of the combined radiation-convection-conduction heat transfer problem aspect of energy balance approaches. I got to the point of assigning symbols to physical quantities and ran into a problem with some basic concepts. Details are discussed in the following paragraphs.
There are many examples of 0-D and 1-D radiative-equilibrium modeling approach both in the peer-reviewed literature, all in respectable journals of course, and in Web space. Professor Pielke Sr. has posted on some aspects of the problem and lucia has carried out some parameter-estimation exercises based on such a model. Raypierrie has an article published by Woods Hole, and Schwartz and Tung have also presented radiative-equilibrium models. You’ll find many such models in the archives of the journals of the AMS with the articles available for download. I’m not going to list these, but let me know if you would like to have additional information regarding them.
The following discussion has focused my thoughts and I’m now inclined to think that Paltridge, and Bejan and colleagues have presented the better way to address simple models. The key to success is to focus on the hydrodynamic and thermodynamic processes occurring on the surface of the planet. Radiative energy transport, of course will contribute to the model equations.
The following two guidelines are part of what got me thinking about the 0-D radiative-equilibrium model energy equation approach.
1. The quantities used in model equations must conform to the basic fundamentals of thermodynamics. I mention thermodynamics here because we’re talking about temperature and energy.
2. The symbols used in model equations must correspond exactly to specific quantities in the physical system of interest. You don’t call A the exit temperature from a turbine, say, and then measure something at the inlet as data for A.
For the 0-D radiative-equilibrium approach these mean that (a) whatever the quantity called temperature, T, is, it must have a thermodynamic connection with the quantity called energy, E, in the usual nomenclature. For a simple thermodynamic system comprised of a single pure substance, for example, temperature and energy are related through basic and fundamental thermodynamic relationships that cannot be violated. And that (b) measured data for the temperature must correspond to the radiative-equilibrium temperature. It is not clear to me that the radiative-equilibrium model energy balance equation approach satisfies either of these requirements. Consider the following arguments.
I think that the fundamentals of thermodynamics require that whenever energy is added into a material the temperature increases, and when energy is removed the temperature decreases. The subsystems present in the climate system, and the complete climate system itself are not closed systems comprised of a single simple material, of course.
The Measured Data
My interpretation of the situation is as follows. The temperature reported in some of the plots of the Surface temperature Record is some kind of (very) rough approximation of the temperature within the atmosphere near the surface of Earth. I’ll try to get back to those plots that have some kind of average for the Land + Ice + Ocean. But the temperature being measured is not an accurate reflection of the radiative-equilibrium balance approach. The 0-D radiative-equilibrium model energy balance equation cannot capture the physical phenomena and processes that dominate and control the quantity measured as T. The question of equilibrium is a whole nother open issue imo.
The plots of the quantity T do not show a monotonic dependence of the temperature with energy; taking the energy to be monotonically increasing as time increases. The smoothing and/or neglecting of the oscillatory nature of the temperature does give a more or less monotonic increasing of temperature. But maybe the time periods for which the temperature is decreasing are trying to tell us something. Plus something deep in the recesses keep saying to me that the specific heats must be positive numbers. The variability in the plotted temperature, when decreasing, means that energy has been removed from the system, if the temperature is the physical quantity associated with the energy. My understanding is that there is seldom an actual net reduction of energy in the Earth system. More is incoming than outgoing; let me know if that is not correct. So when a decrease in the temperature is measured, that actually means that the phenomena and processes down here have taken control of the temperature. The energy already added into the system has caused/been-a-part-of some transport/storage processes that result in changes in the temperature. Neglecting for a moment the cases for which energy does in fact get blocked/reflected back. By the same token, when the temperature is increasing that very likely is not an indication that an excess energy addition has occurred in contrast to that processes here that control the temperature have simply changed to other processes.
Whatever the case, the radiative transport problem/model in no ways reflects the actual physical system. The media through which the radiation, in both directions, passes is an interacting media, as you well know. Plus after the energy gets to the surface the surface is not a purely radiative body. All the radiative transport properties of the interacting surface vary all over the map (you might say). Covering the full ranges for about 0.0 to about 1.0. The energy is stored and transported in all the stuff here on the surface in addition to a part acting in a radiative-energy-transport way.
Thermo-and Hydrodynamical Physical Phenomena and Processes Determine the Surface Temperature
The Thermodynamic phenomena and processes present/undergoing down here are a heat engine in which the energy additions to the atmosphere provide the driving potentials required to move fluids from regions of higher temperature (energy) to regions of lower temperature (energy). Typically from the tropics toward the poles. The poles, being at lower temperature level, cannot reject all the energy transported to those areas. It would seem that as the driving potential for thermally induced motions decreases, the motions themselves will decrease and thus change the energy-transport mechanisms.
And here I’ll guess that the greater temperature increases at the North compared to the South is a reflection of the larger amounts of liquid and solid phases of water in the South. The liquid form, of course, has a high specific heat (and there’s tons of it around) and the solid form can absorbed energy at constant temperature after it reaches the melting temperature. Getting it up to the melting temperature might also require significant amounts of energy; I haven’t made an approximation.
I think the temperature measured in the atmosphere is more likely a function of the thermodynamic states of this heat engine at the locations where the measurements are made than a function of the energy additions to the system. There are of course simple systems for which energy additions act solely to increase the temperature. A closed system comprised of a pure homogeneous material initially at an equilibrium state internally is an example; the Earth is not such a system. Phase-change and energy storage and transport processes within the Earth system dominate the temperature here, I think.
The new operating states of the topics-to-polar heat engine will be a function of the relative temperature changes at the source and sink ends as excess energy accumulates. If both these increase the engine will operate at a higher temperature level, although I think the tropics end of the engine is controlled more by latent and sensible heat transfer thermodynamic processes rather than by excess energy additions. I don’t know if the power and dissipation will increase or decrease?
Plus, the various motions, large scale bulk motions in the atmosphere and oceans can, and do, affect the numbers reported to be the temperature of the day at all locations. All those Pacific Ocean hot and cold things, and all those shifts and oscillatory things. But, again, it is the motions and not the energy additions that have caused the variations in the temperature.
Equilibrium and Not Equilibrium
The lack of equilibrium both within and between the climate subsystems, causing interactions that effect the measured temperature are especially not functions of energy additions to the total system. The subsystems within the climate system have never been, and will never be in equilibrium either within a given subsystem and most certainly between subsystems. A thermally and mechanically static Earth is not going to happen. The daily and seasonal and yearly variations in the measured temperature are not stationary cyclical variations. The number of potential thermodynamic states internal to the total system seems to me to be quite large.
Some of the motions are of course a result of the energy additions. Many large-scale motions in both the atmosphere and oceans, however, are inherent in the basic properties of fluid motions on a rotating sphere. Additionally the exchanges of momentum at the interfaces between the subsystems can also induce motions in the respective subsystems. And finally, none of the subsystems is ever in equilibrium internally with respect to any of the driving potentials for either motion or energy transport/storage. Upwelling of deep liquid from deep within the oceans subsystems generally brings cooler material nearer the surface and thus affects the temperature on a large scale. Cool (sometimes really cold) air sometimes moves from the polar regions and causes significant changes in the temperature.
All the physical phenomena and processes active here at the surface are indications that attempts to tie the excess energy to the surface temperature record does not work in a straight-forward manner. The introduction of positive and negative feedbacks and forcings (my nomenclature here is not necessarily correct) is necessary in order to accommodate basing a technical analysis with an incomplete (or not the best approach, incorrect) basis.
Additionally, as Professor Pielke Sr. constantly reminds us, the effects of human and ‘natural’ processes are constantly making changes that significantly impact both the measured temperature and physical quantities that impact the radiative energy balance approach.
Isn’t it even possible that the lack of equilibrium and the available phenomena and processes internal to the system might even allow states of lower temperature level to be attained even as excess energy additions are occurring? Shouldn’t this possibility be investigated and eliminated before we assume that the Weather temperature will respond in only an increasing way to the excess energy additions?
In summary, the temperature here on the surface is a function of which way the wind is blowing, jet stream, macro (meso?)-scale motions in the oceans, as mentioned above, etc. And the macro-scale conditions near the measuring stations will significantly affect the reported values of the temperature (ocean-side vs. desert, for example); not to even begin consideration of micro-scale level issues. Again, all of these are functions of things other than energy additions.
The Weather Temperature
The quantity being measured near the surface is the Weather temperature. It has always been the Weather temperature. It will always be the Weather temperature. I think to take it to be the radiative-equilibrium temperature is not the right thing to do. I guess the assumption is that long-term averages of the Weather temperature are in fact the radiative-equilibrium temperature. Is that assumption sound? If the Weather temperature continues to decrease as well as increase while all the time the energy content is increasing, I think the assumption needs to be examined in a little more depth.
Short Partial Summary
I suspect that since part of the excess energy addition goes into changing the properties and characteristics of the Earth heat engine, the Weather temperature will not ever reflect the complete extent of the increase in the energy content of the system.
The typical 0-D model energy balance equations do not account for the heat engine processes, constant-temperature phase-change processes, dissipation, work. I certainly understand the concepts on which such an approach is based. And maybe everyone is happy even when they see a temperature decreasing, for whatever the time period, while the energy content of a system is increasing.
I suggest improved 0-D modeling based on
1. A radiative-equilibrium balance written for its more appropriate physical system in the overall scheme of things. I don’t know what this equation might include nor where in physical space it should be applied.
2. 0-D model energy balance equations that account for the heat-engine processes occurring down here on the surface; storage, phase change, transport, work, dissipation, and radiative energy additions.
I’m certain that this is in fact the approach taken in the early modeling days. However I think a good argument can be made that deeper understanding of the system and its responses might in fact be more readily available through study of these more simple approaches. Additionally there is software that will fit parameter values appearing in ODEs to data. So as the number of ODEs increases to be beyond hand/analytical work, the software can save the day.
That’s as far as I’ve gone on this, so it’s a very rough draft.
Raymond T. Pierrehumbert, “Lecture 6: energy Balance Models”, Woods Hole Oceanographic Institution, 2001. http://www.whoi.edu/cms/files/lect_06_2001_21420.pdf
G. W. Paltridge, “Global dynamics and Climate – A System of Minimum Entropy Exchange”, Quart. J. R. Met. Soc., Vol. 101, pp. 475-484, 1975.
G. W. Paltridge, “The Steady-State Format of Global Climate”, Quart. J. R. Met. Soc., Vol. 104, pp. 927-945, 1978.
Stephen E. Schwartz, “Heat Capacity, Time Constant, And Sensitivity Of Earth’s
Climate System”, Accepted for publication in Journal of Geophysical Research, Brookhaven National laboratory, June 2007.
Ka Kit Tung, “Simple Climate Modeling“, Discrete And Continuous Dynamical Systems–Series B, Vol. 7, No. 3, pp. 651–660, 2007.
Adrian Bejan and A. Heitor Reis, “Thermodynamic Optimization of Global Circulation and Climate”, Int. J. energy Res., Vol. 29, pp. 303–316, 2005. DOI: 10.1002/er.1058.
A. Heitor Reis and Adrian Bejan, “Constructal Theory of Global Circulation and Climate”, Int. J. Heat Mass Trans., Vol. xxx, pp. yyy-www, 2006.