Why Weather Forecasts Don't Turn into Nonsense ✎

Original: "Data Assimilation in Operator Algebras"
arXiv:2206.13659 · 2022-06-27 · arXiv non-exclusive · independent analysis · 1 min
A new way to combine measurements and models treats probabilities with care.

A weather forecaster combines data from weather stations with a computer model to say whether it will rain tomorrow. But the model can be wrong, and data doesn't come from everywhere. If you combine them incorrectly, the forecast can produce nonsense: a temperature below absolute zero or a probability greater than one.

The new method solves this problem. It borrows rules from quantum mechanics, where the state of a system is described by special tables of numbers. These rules are designed so that correct values never become incorrect. It's like a translator who condenses the text without changing its meaning.

Tests on a chaotic atmospheric model and on El Niño data showed that forecasts come out accurate, and the uncertainty estimate honestly reflects how much you can trust the prediction.

This approach is useful for weather, climate, and ocean forecasting, where it's important not only to guess the value but also to understand how reliable it is. In the future, it could run on quantum computers, which are especially good at such tasks.

The Lorenz-96 model was proposed by Edward Lorenz as a simplified model of atmospheric circulation on a latitude circle, and its chaotic regime at F=10 has become a standard test bed for data assimilation algorithms.

The idea of representing probabilistic states as quantum operators resonates with Greg Egan's novel 'Permutation City', where consciousness is modeled as a quantum state evolving according to the laws of quantum mechanics.

Concepts
data assimilation koopman operator product operator gaussian process prior distribution Bayesian inference posterior distribution automated analysis nested sampling data processing database nonlinear laplacian spectral analysis quantum operation density matrix ensemble forecast hamiltonian generalization summation bayesian hierarchical model probabilistic model