by Dan Hughes
It is not a boundary value problem.
The total energy equation is applied to Earth’s entire atmosphere and sub-systems to investigate requirements that the energy content of Earth’s climate system remains constant. The results are somewhat more complex than usually appears in the literature. The analysis method clearly illustrates the potential for physical phenomena and processes both within and between sub-systems to affect Earth’s energy balance.
Justification for the validity of very long-range climate change modeling and calculations is based solely on the notion that the problem is a Boundary Value Problem (BVP); and that solely radiative energy transport and trace gases in the atmosphere critically dominate and set the BVP. The results of this analysis show that modelling and calculation of Earth’s energy budget is not a Boundary Value Problem.
Due to coupling between sub-systems, the wide ranges of time scales involved, and the presence of non-linear physical phenomena and processes, the notion that Earth’s climate system represents a spatial-temporal chaotic system can be heuristically argued. This matter, however, is not directly addressed in these notes.
The objectives of these notes include a look into how natural internal variations within Earth’s climate system affect the radiative energy budget at the Top of the Atmosphere (ToA). The initial focus is on energy exchanges between sub-systems that make up Earth’s climate system. To this end, the local-instantaneous energy conservations equations, and averages of these, are examined in a little detail.
Unfortunately, no quantitative results are obtained or presented. The analysis is basically a general over-view of the energy-budget of the climate system with a focus on the significant potential for variations on a wide range of time and spatial scales. Maybe notes will provide food for thought and discussions.
Earth’s climate system is made up of several sub-systems, including:
- other inhabitants
- atmosphere, with condensing and non-condensing gases, liquid and solid particles,
- water vapor in the atmosphere
- non-condensing gases in the atmosphere
- solid particulate aerosols in the atmosphere
- oceans and other large bodies of liquid water,
- trees, plants, and other flora, on land and in water bodies,
- snow and ice solid phases of water, on both land and liquid water,
- organic materials that experience chemical interactions with adjacent materials,
- inorganic materials that experience chemical interactions with adjacent materials, and
- maybe a couple of others.
The solid, liquid, and vapor phases of water are present in the atmosphere, and are critically important relative to the radiative energy budget of Earth’s climate system. In this regard, clouds maybe should be a separate sub-system. Other, generally solid materials labeled aerosols, are also present in the atmosphere and also are critically important to the radiative energy budget. Non-condensing gases that interact with radiative energy transport, such as methane, are also relatively important. These are included as separate sub-systems in the above list.
The physical phenomena and processes occurring within the sub-systems can be significantly influenced by the activities of humans through the effects of these activities within and at the boundaries of the sub-systems. Darkening of the surface of snow and ice fields, for example, by solid aerosols produced by human activities and then precipitate out of the atmosphere.
We are interested in the biological, chemical, mass, momentum, and energy states of the entire climate system, the physical phenomena and processes occurring within each sub-system and at the interfaces between sub-systems. Many aspects of the phenomena and processes of an individual sub-system will be coupled to other sub-systems. The physical couplings involve a multitude of the biological, chemical, mass, momentum, and energy aspects that are of interest. Some of the phenomena and processes of interest will be affected by the interactions of humans with the systems.
In these initial notes we are primarily interested in the energy aspects of the physical phenomena and processes that occur both within the sub-systems and at the boundaries between sub-systems. Mass and energy aspects are coupled in the sense that mass exchanges occurring between sub-systems represent also exchanges of energy.
The atmosphere sub-system, for example, interfaces with just about all the other domains listed above. And the other sub-systems likewise interface with the atmosphere. The flora sub-system, for example, has interfaces with both the atmosphere and land; the canopy of forests and crops cultivated by humans, and the roots within the land sub-system.
The spatial variation and interactions of the sub-systems are the focus of these initial notes. Relative to Earth’s climate system, however, temporal variations both within and between sub-systems are also important. In this respect, the sub-systems identified above might be additionally divided relative to the Northern and Southern hemispheres of the planet, as well as by the local time-of-day and yearly seasonal variation. The Northern and Southern hemispheres experience the yearly seasonal variations at different times during the year. Additionally, the daily variations at a fixed location are among the largest temporal variations experienced by Earth’s climate system. The effects of the temporal variations will not be considered in detail in these notes. It is noted, however, that the significant temporal variations within Earth’s climate system, over a wide range of time scales, are potentially equally important as the spatial variations that are considered here.
Let’s consider that the total volume occupied by Earth’s climate system can be divided into the portions occupied by the sub-systems. The outer boundary of the total volume is at the Top of the Atmosphere (ToA). The inner, or lower, boundary can vary with the sub-system under consideration, and the physical phenomena and processes of interest. The deep oceans, for example, might be divided into: (1) the upper regions within which there are significant variations that interact with the mass and energy balances of the planet, and (2) the very deepest regions that might be taken to represent a more-or-less passive sink of energy. The portions of the total volume filled with the solid phases of water might consider that all the solid-water mass and some part of the material on which it rests should be included in the sub-system volume: the effects of the state of the water on which sea-ice floats, for example. Other examples are available for other sub-systems.
Generally, the deep details of all the sub-systems will not be necessary for these initial investigations.
The primary objective of this initial investigation is to attempt to get a handle on how variations within and between the sub-systems affect Earth’s overall energy budget. While we might eventually look into the thermal, kinetic, and potential energy budgets within a sub-system, the primary focus is on energy exchanges between the sub-systems and the effects of these exchanges on the ToA energy budget. The equations that govern fluid motions and thermodynamic processes are the primary tools of the work. Other aspects will be introduced as necessary.
[ The link below will load a pdf copy of the sections that have the development in them. The document is heavy of equations, and this is an easy way to get a usable copy of those sections. After you finish that document return to this blog post to leave/read comments.
If you arrange to have the pdf material open at the same time as the blog post is open, that will make for a good way to have the material at hand while you write your comments and read the comments of others. I think right/control/option/command-click will open the file in a new window. Whatever your case, carry it out for your fav browser. ]
Discussion and Conclusions
The concept that radiative energy transport at the Top of the Atmosphere will eventually obtain balance needs deeper study ( especially the part about carbon dioxide being the sole aspect of importance ). The results obtained herein clearly show that modeling and calculation of future states of Earth’s climate system is not a Boundary Value Problem. It is impossible for the problem to be set as a BVP because the physical domain does not allow that. The out-going radiative energy at the ToA is determined by the states of the sub-systems within Earth’s climate system.
Actually, the concept an equilibrium radiative-energy transport state for Earth’s climate systems is a little fuzzy, and is simply postulated to be attainable at some future time. The future time at which this state will be present is not well defined. Additionally, the time period over which the response metric should be measured in order to verify the postulate is also not well defined. It’s all kind of fuzzy.
A response function and its associated metric that averages out all the physical phenomena and processes occurring within the physical domain is not a valid measure of the state of Earth’s climate systems. It is also not useful for estimating the outcomes, both good and bad, at future time.
Instead the energy transport and exchanges within the climate system should also enter into considerations. The results show that in order for a purely radiative balance to obtain, energy and mass exchanges at the interfaces between sub-systems must also reach balance.
The developments discussed do not begin to address the nitty-gritty details of the multitude of physical phenomena and processes that enter into the interface exchanges. Unfortunately, the mathematical models and numerical solution methods for these details are potential sources for a lack of attaining balances.
Our day-to-day experiences indicate that variations in almost all aspects of the climate system change at a very wide range of time scales. Radiative balance between in-coming and out-going energy is said to be instantaneous. However, the states of the climate’s sub-system, all of which affect radiative energy transport do not change at that rate. The potential for temporal variations in mass and energy budgets both in and between sub-systems is such that it is very likely that temporal variations are the expected state. So far as I am aware, there are no damping mechanisms that act to ensure states of exact balance in the natural processes occurring in Earth’s climate system.
It has been known for a very long time that the over-simplified, purely radiative energy balance could not be the complete picture. Otherwise the expenditure of billions of funding on models, methods, and software developments, not to mention 100s of millions on dedicated super-computing hardware, would not be necessary. Maybe these notes have made that awareness more explicit and concrete.
Climate Science should re-consider using extremely over-simplified summaries such as Laws of Physics, Exact Equality of Radiative Energy Transport, and Boundary Value Problem. These proclamations are not only over-simplified, they border on being purposeful mischaracterizations.