2:45 PM - 3:00 PM
[MIS16-05] How to analyze past global water cycle systems: a topological perspective
Keywords:global water cycle, earth system, topology, perturbation analysis, structural analysis
Background: Earth system science models the Earth as subsystems (S) and describes material exchange using a flux function (F). However, two observational problems exist: (1) lack of specific F values and (2) insufficient information on the functional form of F. Similar issues are found in biological reaction systems. Despite this, the topology of subsystems and fluxes remains stable over time, allowing for a structured mathematical approach to Earth system analysis.
Purpose: This study aims to analyze material cycles based solely on the Earth's topology without assuming specific values or functional forms of F. It applies mathematical methods from biological systems to structural analysis, focusing on the water cycle model.
Perturbation Analysis: Changes in F and S due to perturbations are considered without precise values. A linear constitutive law is used in numerical simulations to study system responses, yielding three key results:
1. Ocean S perturbations affect only directly related F.
2. Mantle S perturbations affect all F except those from continental crust S, indicating mantle water cycles are influenced more broadly than ocean cycles.
3. Continental crust S acts as an intermediary but only affects mantle S via input F from the ocean, with its direct influence localized.
Structural Analysis: Unlike perturbation analysis, structural analysis focuses solely on topology without assuming flux function types. Three key distinctions emerge:
1. Structural analysis has broader validity as it does not assume a specific flux function type.
2. It is purely analytical, requiring no numerical simulations, offering new theoretical insights.
3. It applies only to dynamic equilibrium states, unlike perturbation analysis, which can study non-equilibrium responses. The study also explores the relationship between structural analysis and KCC theory for non-equilibrium stability.
Purpose: This study aims to analyze material cycles based solely on the Earth's topology without assuming specific values or functional forms of F. It applies mathematical methods from biological systems to structural analysis, focusing on the water cycle model.
Perturbation Analysis: Changes in F and S due to perturbations are considered without precise values. A linear constitutive law is used in numerical simulations to study system responses, yielding three key results:
1. Ocean S perturbations affect only directly related F.
2. Mantle S perturbations affect all F except those from continental crust S, indicating mantle water cycles are influenced more broadly than ocean cycles.
3. Continental crust S acts as an intermediary but only affects mantle S via input F from the ocean, with its direct influence localized.
Structural Analysis: Unlike perturbation analysis, structural analysis focuses solely on topology without assuming flux function types. Three key distinctions emerge:
1. Structural analysis has broader validity as it does not assume a specific flux function type.
2. It is purely analytical, requiring no numerical simulations, offering new theoretical insights.
3. It applies only to dynamic equilibrium states, unlike perturbation analysis, which can study non-equilibrium responses. The study also explores the relationship between structural analysis and KCC theory for non-equilibrium stability.