Graduate Research Course
Climate Science & Physics
From radiative transfer to hurricane dynamics — the physics of Earth's climate system, numerical models, and the science of prediction with Python and Fortran simulations.
Key Equations of Climate Physics
Stefan-Boltzmann Law
\( F = \sigma T^4, \quad T_{eq} = \left[\frac{S_0 (1-\alpha)}{4\sigma}\right]^{1/4} \)
Clausius-Clapeyron
\( \frac{de_s}{dT} = \frac{L_v\, e_s}{R_v\, T^2} \approx 7\%\;\text{K}^{-1} \)
Emanuel Potential Intensity
\( V_{PI}^2 = \frac{C_k}{C_D}\frac{T_s - T_o}{T_o}(k_0^* - k) \)
Navier-Stokes (Rotating Frame)
\( \frac{D\mathbf{v}}{Dt} + 2\boldsymbol{\Omega}\times\mathbf{v} = -\frac{1}{\rho}\nabla p + \nu\nabla^2\mathbf{v} + \mathbf{g} \)
Radiative Forcing
\( \Delta F = 5.35 \ln\!\left(\frac{C}{C_0}\right) \;\text{W m}^{-2} \)
Sverdrup Transport
\( \beta M_y = \hat{\mathbf{k}} \cdot \nabla \times \boldsymbol{\tau} \)
Video Lectures
Introduction to the Science of Climate Change
What Climate Science Says About Extreme Weather
Modeling Weather-Related Catastrophe Risk
Hurricane Physics & Risk in a Changing Climate
Heat Waves: Extreme Events in a Warming World
More on Climate Science
Connecting Global Climate Change to Local Impacts
Climate Change Perspectives
The Pacific SHOULD Be Warming, But It’s Not!
La Niña Is Doing Something It Shouldn’t This Year
The AMOC Collapse Scenario — Atlantic Meridional Overturning Circulation
About This Course
Earth's climate is governed by an intricate web of physical processes spanning radiative transfer, fluid dynamics, thermodynamics, and biogeochemistry. The atmosphere absorbs and re-emits infrared radiation according to the Stefan-Boltzmann law, while the Clausius-Clapeyron relation dictates that a warming atmosphere holds roughly 7% more water vapour per degree — amplifying both droughts and deluges.
This course takes a rigorous physics-first approach: we derive the primitive equations of atmospheric motion on a rotating sphere, build simplified general circulation models in Fortran and Python, analyse CMIP6 output, and apply extreme value statistics to real climate data. Every module includes MathJax derivations, SVG diagrams, and computational exercises.
Cross-links to our Climate & Biodiversity and Climatology courses connect the physical science to ecological impacts and paleoclimate records.
Nine Modules
M0
Radiative Transfer & Energy Balance
Solar spectrum, absorption bands, greenhouse effect, planetary energy budgets, and two-stream approximation models.
M1
Atmospheric Dynamics
Navier-Stokes on a rotating sphere, Rossby waves, baroclinic instability, jet stream meandering, and geostrophic balance.
M2
Ocean Circulation
Atlantic Meridional Overturning Circulation, ENSO dynamics, Gulf Stream transport, Ekman spirals, and Sverdrup balance.
M3
Tropical Cyclones
Emanuel potential intensity theory, eye wall dynamics, rapid intensification mechanisms, and warm-core vortex structure.
M4
Drought & Floods
Clausius-Clapeyron scaling of precipitation extremes, generalized extreme value distributions, and IDF curve construction.
M5
Climate Models & GCMs
Finite difference and spectral methods, parameterization schemes, CMIP6 model intercomparison, and Fortran implementations.
M6
Carbon Cycle & Feedbacks
Ocean carbon sink dynamics, permafrost thaw feedback, ice-albedo amplification, and climate tipping point analysis.
M7
Sea Level & Ice Sheets
Thermal expansion modeling, West Antarctic Ice Sheet instability, marine ice sheet instability (MISI), and glacier dynamics.
M8
Projections & Scenarios
Shared Socioeconomic Pathways, extreme event attribution, equilibrium climate sensitivity, and uncertainty quantification.
Recommended Textbooks
- [1] Hartmann, D.L. (2016). Global Physical Climatology, 2nd ed. Elsevier.
- [2] Vallis, G.K. (2017). Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation, 2nd ed. Cambridge University Press.
- [3] Trenberth, K.E. (ed.) (1992). Climate System Modeling. Cambridge University Press.
- [4] IPCC (2021). Climate Change 2021: The Physical Science Basis (AR6 WG1). Cambridge University Press.