Earth System Analysis is defined as the development of a mathematical-logical formulation of principles applicable to Earth Systems. A global overview of Earth Systems can be found on global earth systems
Scientific hypotheses and mathematical postulates must be refutable by the finding of contradictions with data or internal inconsistencies in a set of postulates. The systems principle of specification hierarchies will be used as an integrated analysis model for Earth systems Analysis.
The systems principle of specification hierarchies derives from science an intelligible understanding of our world and of our place in it, in short, a meaningful story of the world. From its inception it has had a developmental framework, beginning with origins, as the Big Bang theory for example. It features a role in the world for humans based on science, where stress should be put on the descriptors ‘intelligible and meaningful’.
Fig.1: An Example Specification Hierarchy
General properties of Specification Hierarchies
When used to model systems, higher levels (control, regulate, interpret, harness) lower levels, whose behaviors are made possible by properties generated at still lower levels. So behaviors of higher levels are initiated by lower level configurations. It is important to realize that few users of hierarchical forms would insist that particular levels exist in actuality. Levels are discerned from hierarchical analysis, aimed at constructing (discovering) Nature’s “joints” with respect to given projects.
Formal relations between Specification Hierarchy Levels
The specification hierarchy is one of classes and subclasses, as e.g., {material world {biological world {social world }}}, where {lower level(s) { highest level}}.
Style of growth of a Specification Hierarchy
In the specification hierarchy new levels can emerge. So this system can grow — but not in space. Growth here is by the accumulation of informational constraints, modeled as a process of refinement by way of adding subclasses.
Criteria for levels in Specification Hierarchies
Levels in the specification hierarchy mark the qualitative differences of different realms of being, as in ‘physical realm’ versus ‘biological realm’. It is an intensional construct, open at the top (the innermost level is unbounded above, and so free to give rise to ever higher levels).
Complexity of a level in a Specification Hierarchy
The specification hierarchy embodies intensional complexity, which characterizes a system to the degree that it is susceptible to many different kinds of analyzes.
Dynamical relations between levels in a Specification Hierarchy
Dynamics in the specification hierarchy are entrained by development, which is modeled as a process of refinement of a class or category. It is important to note that this process is open-ended in the sense that there could be many coordinate subclasses of a given class. That is, the potentials arising within any class form a tree. So, {physical realm { material realm { biological realm }}}, or {mammal { primate { human }}} each follow just one branch of a tree. Evolution (unpredictable change) is one -> many, and so we can picture organic evolution.
How is its direction into new subclasses insured (giving rise to the hierarchy)? In the material world by the fact that information, once in place (or once having had an effect), marks a system irrevocably. If a system continues to exist, it must march forward if it changes.
So, development of a specification hierarchy requires a two-level basic form. Yet these hierarchies involve more than just two levels. Why do not the more general levels prevent change, as by the weight of their accumulated information? Here we are led to note another aspect of development. The amount of change required to launch a new level is ever smaller as the hierarchy develops — refinements are just that. The more general levels do exert their influence; biology is a kind of chemistry, and humans are a kind of mammal. The key to understanding this situation is that in the specification hierarchy informational relations between levels are transitive. This means that there are functionally just two levels at work anywhere in the hierarchy — and new levels may branch off anywhere in the hierarchy, potentially giving rise to collections of coordinate classes.
Informational relations and semiotics
In the specification hierarchy the lower levels also make possible the emergence of a new realm. And here too the process is top-down, but in a different sense, involving finality. Thus, as organism sociality implies biology, and biology implies chemistry, so, because this is a process of refinement, only a very narrow set of possibilities could imply organism sociality. That is, chemistry could give rise to many kinds of super systems, biology to fewer, and sociality to even fewer. Developments (in distinction from evolution) are always entrained by final causes, and approach them asymptotically with each emergence of a new realm. Involved here, as in all developments, is the process of senescence, a condition of information overload (recall that information in this hierarchy is transitive across levels), leading to overconnectivity, leading in turn to functional underconnectivity, leading in its turn to inflexibility and habit driven responses (loss of requisite variety), leading ultimately to loss of adaptability (inability to produce interpretants of novel situations).
Mathematical Framework and Tool Support
A method with a mathematical framework for supporting modeling and analyzing a Complex System with a hierarchy of constraints given with a specification hierarchy was presented at the 23rd International Conference on Statistical Physics of the International Union for Pure and Applied Physics, IUPAP, http://www.statphys23.org
Fig.2: An Example Application of the Mathematical Framework and Tools
With the given method, the solution space of a complex system is determined, given the applicable constraints in the specification hierarchy, resulting in the applicable laws for the complex system under consideration. Below an application example of the presented framework is given. 
The method can be applied to all types of systems which can be constrained with a specification hierarchy, e.g. Information, Physical, Chemical, Biological, Ecological and Economical Systems. The calculation of the solution state-space of the complex system can be done symbolic and numeric.
Fig 3. A Mathematical Specification Hierarchy of the Physical General Relativity and Quantum Field Theory
Earth System Analysis Examples
Mathematical Ecology
Mathematical Ecology seeks to improve the understanding of the flow of energy and materials through ecosystems and the regulation of the distribution and abundance of organisms. It covers productivity and biogeochemical cycles in ecosystems, tropic dynamics, community structure and stability, competition and predation, evolution and natual selection, population growth and physociological ecology. In mathematical ecology, earth systems are analysed using the {Mathematical {Physical {Chemical {Biological {Psychological {Social}}}}}} specification hierarchy.
Mathematical Ecology examples can be found on mathematicalecology
Given the theory of specification hierarchies, richness is given by physical diversity. In our current society money is (virtual) credit money with no physical counter value when it is created. When (virtual) credit money is created physical diversity does not change. Richness in our current society is constrained by physical diversity and not by (virtual) credit money. Therefore physical diversity and not (virtual) credit money is the correct measure for richness of our society given the theory of specification hierarchies. To give an example, in mathematical ecology physical diversity is measured in biodiversity
Non-Renewable Energy Resource Analysis
The non-renewable fossil energy sources on earth can be regarded as stored solar energy. Given the earth systems specification hierarchy {Mathematical {Physical {Material {Economical}}}} we see the economical systems are constrained by the material systems.
http://renewenergy.wordpress.com/transition/energy-resources/non-renewable/ gives an analysis of the earth’s non-renewable material energy sources. It can easily be seen that the material fossil energy sources will last only for the coming decades. Given the specification hierarchy above, if the non-renewable fossil fuels remain the main physical energy source of the earth’s economical systems, these economical systems will also be severely disrupted. Since fossil fuels are formed on earth over million years and are currently used in several hundred years without being regenerated, it is easy to see that using these fossil fuels in a very short time compared with the time in which they formed causes massive disruptions in the earths systems specification hierarchy.
Climate Change Analysis
The earth surface temperature is a physical property. Given the above described specification hierarchy principles it is easy to see that the biological systems which evolved on earth are specified irreversibly with the historical gradual earth temperature fluctuations given by the {Mathematical {Physical {Material {Biological}}}} specification hierarchy.
If now the physical earth surface temperature is going to fluctuate more heavily given human caused increase of the earths atmospheric CO2 concentration many evolved biological systems on earth can not cope with these sudden fluctuations in physical temperature, because many material systems will change too quickly, given these temperature fluctuations. The historical physical temperature fluctuations with which material systems evolved during evolution on earth, were much more gradual then the current sudden fluctuations of the earth’s atmospheric temperature caused by human activity. Given the {Mathematical {Physical {Material {Biological}}}} specification hierarchy, biological systems depend heavily on the material systems on earth. When the earth’s material systems will change much more rapidly then during evolution caused by human activity, many biological systems on earth will not be able to adapt in time.
Renewable Energy Resource Analysis
Given the {Mathematical {Physical {Material {Biological {Social {Economical}}}}} specification hierarchy of the earth systems, we can see the earth’s specification hierarchy is in balance only if the economical systems use renewable physical energy sources and don’t use energy stored on earth which will not be regenerated again. With current state-of-the-art technology, usable renewable energy sources outside the earth on a large scale are the Sun (direct, e.g. PV / CSP and indirect e.g. Wind-, Bio- and Hydropower) and the Moon (e.g. Tidalpower).
On http://renewenergy.wordpress.com/transition/energy-resources/renewable/ an analysis is given of the renewable energy resources usable on earth. On earth enough renewable energy can be generated given all current and future constraints given the specification hierarchy above.
Energy System Transition Strategy Analysis
In order to analyze a transition strategy of the earths energy systems we can use the {Mathematical {Physical {Material {Biological {Legal {Economical }}}}}} system specification hierarchy. By using legal policies, we constrain the economical realm by making investments in renewable energy technologies more economical then investments in non-renewable energy technologies. This will result in replacement of non-economical non-renewable fossil energy technologies with economical renewable energy technologies.
Given this transition strategy, usage of non-renewable material energy resources on earth will decline, CO2 emission will decline, increase of physical temperature fluctuations of the earths temperature will decline and damaging biological systems will decline.
If we analyze biofuels with the {Mathematical {Physical {Material {Biological {Social {Economical}}}}} specification hierarchy, we see economical investments in biofuels are only justified when these investments don’t lead to more social inbalances.
