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We know and use the statistics but cannot model the process each carbon atom undergoes.

Figure 1, shows the Earth climate going back 540 million years spanning the entire Phanerozoic Era.

A primitive cite can be dated by measuring the ratio of carbon 14 to carbon 12.

Both isotopes of carbon have the same atomic number, i.e., the same number of protons and electrons but carbon 14 has 8 neutrons compared to only 6 for carbon 12.

Another good example is carbon 14 dating [wiki-rcdating] used in archaeology, history and other fields.

Weather models assume a horizontal grid size of a few kilometers (or miles) covering the Earth surface while climate models have a horizonal grid size of a few hundred kilometers. Figure 3 shows some of the physical phenomena which are calculated at each grid point.

Weather simulations recompute parameters every few minutes while climate models compute them every tens of minutes. Snyder, Evolution of global temperature over the past two million years, Nature, 2016 [wiki-nwp] https://en.wikipedia.org/wiki/Numerical_weather_prediction.

Scientists can estimate the annual local climate based on the thickness of tree ring. The only way to hindcast weather is if somebody observed it and wrote it down.

Scientists simulate past climates but they cannot simulate past weather.

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