Are you really saying that everyone from pre-historic hunter-gatherer societies tracking the seasons to modern meteorologists with their supercomputers and satellites have been engaging in something theoretically and practically impossible? That would surely be staggering news to everyone involved.
That said, there are larger trends that can be predicted. For instance the seasons which come from astronomical facts. Or the several year El Niño/La Niña oscillation. Not to mention relatively slow moving Rossby waves in the jet stream. (One of which is bringing hot weather to Russia and monsoons to Pakistan right now.) These give useful information about what is likely to happen and keep happening over periods of weeks, months, and to some extent years.
But none of this brings us any closer to the idea of being able to give an exact weather forecast for a day 6 months in the future. That goal is impossible. And has been known to be impossible for several decades. Furthermore I assure you that this fact is well-known to every competent modern meteorologist. (The word "competent" does not necessarily cover people chosen primarily for their appearance to deliver the weather report for local TV stations.)
http://www.ecmwf.int/about/programmatic/strategy/strategy.pd...
the forecast skill for ECMWF and NOAA have been improving pretty steadily over the last 15 years. Basically, we're seeing two days farther into the future now than 20 years ago.
I agree that chaotic dynamics and various noise sources limit the time horizon for weather predictions to perhaps 2 weeks.
To his surprise the weather that the machine began to predict was completely different from the weather calculated before. Lorenz tracked this down to the computer printout. The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 0.506127 was printed as 0.506. This difference is tiny and the consensus at the time would have been that it should have had practically no effect. However Lorenz had discovered that small changes in initial conditions produced large changes in the long-term outcome.[43] Lorenz's discovery, which gave its name to Lorenz attractors, showed that even detailed atmospheric modelling cannot in general make long-term weather predictions. Weather is usually predictable only about a week ahead.[25]
Weather is usually predictable only about a week ahead.
December in the Northern hemisphere might be colder than this last.
(1) "Predicting Weather is near impossible in theory forget the practice."
and
(2) Quoting wikipedia, "Weather is usually predictable only about a week ahead."
These two remarks are not quite opposites, but almost.
Weather in theory is an Chaotic system thus there is no simple laws such as F = Ma to predict it.
Time frames of week , seconds and years are meaningless. You can always argue that you can predict weather for next milli or micro or femto seconds, why stop at weeks? but that does not proves that chaos theory is wrong or that there is some generative law which can be used to predict weather without relying on data.
Also from a utilitarian perspective, a long term accurate weather forecast would be so much useful rather than just a week long range [Assuming that is accurate right now,]. But you dont find accurate prediction for monsoon in January, or even of say a hurricane a fortnight before.
There are plenty of simple mechanical systems governed by mechanical laws that exhibit chaotic behaviour. You said a silly thing about weather prediction, it happens. There's really no need to dig yourself into some deeper hole of gibberish.
The reason that I've heard for stopping at weeks is that that is the time frame for perturbations to work their way up from the quantum scale to the macro scale. We cannot, even in principle, measure what is happening everywhere on the quantum scale.
Of course as soon as you merge quantum mechanics and chaos theory, life gets very, very weird. See http://www.iqc.ca/publications/tutorials/chaos.pdf for more.
Another problem, separate from these effects, is getting closure on the variables in the model. Things like evaporation from soils and vegetation, for example, which ECMWF is trying to include in their models. You put them in the weather model to improve accuracy, and all the sudden you need a time-dependent model for soil and vegetation water content. And also, sensors to satisfy the boundary conditions for your model (e.g., to estimate plant vegetation type).
The time scale is critical. If you look at any review of numerical weather prediction accuracy, such as the one I linked to above, you will see it's a key parameter. It's why 3-day forecasts are excellent and 7-day forecasts are not very good. Good 3-day predictability does not imply good 7-day predictability.
This is no different than the pictures of the state trajectories of the Lorenz system (http://en.wikipedia.org/wiki/Lorenz_attractor) starting from two nearby states, which stay together for a time, and then diverge suddenly.
It's true, the relevant laws are the Navier-Stokes differential equations, not simple laws like F = m a. But, we can observe the boundary conditions and propagate the system state forward in time. These equations do constrain the future dynamics.