Course content

The course provides an advanced theoretical and methodological framework for the quantitative study of Earth’s geosystems across all scales, from the inner core to the magnetosphere. It introduces mathematical methods for describing, modeling, and analyzing interactions within and between geosystems, emphasizing the use of differential equations, system dynamics, and statistical inference.

Topics include:

• Classification and examples of geosystems and their characteristic parameters.
• Universal quantitative laws and differential equations governing geophysical, geochemical, and geobiological processes.
• Scale‐dependent and scale‐independent phenomena analyzed through Fourier methods, dimensional analysis, and fractal geometry.
• Dynamical behavior of geosystems, including phase transitions, Hopf bifurcations, chaotic dynamics, and catastrophe theory.
• The representation of geosystems through forward and inverse modeling, and the epistemological transition between the two.
• Problems of model construction in systems ranging from micromagnetics and mantle convection to plate tectonics and the global climate system.
• Statistical and probabilistic representations of geosystems using Bayes’ theorem and logical inference.
• Self-organization, emergence, and the role of life in the global geosystem.

Throughout the course, emphasis is placed on the identification of relevant parameters, the characterization of uncertainty, and the epistemological limits of prediction in complex Earth systems.Students will develop both theoretical and applied modeling experience through analytical, computational, or experimental investigations of selected geosystems.

Learning outcome

Competence

After completing the course, the candidate will be able to:

• Formulate, analyze, and evaluate mathematical models of geosystems using advanced differential equations and dynamical systems theory.
• Critically assess the epistemological and methodological foundations of quantitative geoscience, including the role of uncertainty, inference, and model assumptions.
• Integrate analytical, numerical, or experimental approaches to produce original insights into the dynamics and predictability of geosystems.
• Communicate complex quantitative and conceptual aspects of geosystem behavior to both specialists and interdisciplinary audiences.

Knowledge and skills

After completing the course, the candidate will be able to:

• Explain the governing equations and characteristic parameters describing the Earth’s main spheres and coupled geosystems.
• Derive, classify, and analyze systems of differential equations representing geophysical and geochemical processes.
• Identify characteristic scales, dimensional relationships, and fractal or self-similar behaviors in natural systems.
• Evaluate the stability and potential for bifurcation or chaotic behavior in nonlinear dynamical systems.
• Apply advanced methods of forward and inverse modeling, and assess the resulting uncertainties and predictive limitations.
• Design and conduct computational or experimental studies of a selected geosystem, interpret the results quantitatively, and compare them with theoretical predictions.
• Reflect critically on the epistemological implications of model construction, parameterization, and statistical inference in geoscience.

Learning methods and activities

The course will be taught according to direct agreement with the teacher if at least three students participate. The activities include lectures, laboratory work, seminars, and self-study.

Specific conditions

Required previous knowledge

The course requires either to be accepted as PhD student in engineering at NTNU or individual acceptance by the lecturer. A high level of mathematical and physical background is required: Calculus (up to partial differential equations), linear algebra, experimental and basic theoretical physics.

Course materials

Selected journal articles and textbooks.