Deterministic, and still unpredictable
Why weather forecasts fail beyond about two weeks, why climate projections do not, and what deterministic chaos has to say about the limits of prediction in the atmosphere and ocean.
Every chapter pairs a short piece of text with one interactive notebook that runs in your browser — no installation, no server, no account. The numerics execute in your own tab via Pyodide, so you can move a slider and watch the forecast horizon move with it.
The book is organised around a single idea: apply a hierarchy of models to understand predictability in nonlinear dynamical systems. Predictability is never one number. It is a property of a system, a state, a lead time and a question — and the only convincing way to learn that is to turn the knob yourself.
What the word actually means before any mathematics: practical versus intrinsic limits, where numerical weather prediction came from, and why a three-variable model earns a place beside a coupled Earth system model.
Nonlinearity is not enough. A pendulum is thoroughly nonlinear and perfectly predictable; what has to be added before forecasts can fail is phase-space dimension.
Turning 'chaotic' into numbers: Lyapunov exponents and doubling times, fractal dimension and entropy, error growth past the linear regime, and predictability measured as information.
What changes when a system has forty variables instead of three, or a continuum of scales: the upscale error cascade and the case for a forecast limit no observing system can defeat.
The operational toolkit: tangent linear and adjoint models, optimal perturbations, ensemble design, variational and ensemble data assimilation, model error, and verification.
Predictability that comes from the boundaries rather than the initial state: the subseasonal-to-seasonal window, the ocean's memory, climate projection, and tipping points.
Two open questions: whether predictability itself is changing as the climate changes, and whether machine-learned emulators inherit the dynamics they were trained on.
The structure behind the results, for readers who want the why behind the why. Deliberately terminal and skippable.
A filled dot marks a chapter with a live interactive notebook; a hollow one marks a chapter that is planned and shows its abstract and knob. What the notebooks depend on →