Weather is usually predictable only about a week ahead.
and about
December in the Northern hemisphere might be colder than this last.
Thats not exactly a prediction, It is a seasonal variation due to inclination of earth w.r.t. sun. Thats same as some product will have higher sale before Christmas, or there will be more traffic on roads before thanksgiving.
you are getting confused in semantics of word "prediction".
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.
I can barely understand what you're saying here, so I won't comment beyond this reply.
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.
You can always argue that you can predict weather for next milli or micro or femto seconds, why stop at weeks?
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.
Sometimes these smaller perturbations are called "sub-grid phenomena". I think practitioners think of them as, say, pressure waves or flows which average to zero when observed on a 10km x 10km grid. But it is possible that their ultimate origin is on a much finer grid ;-)
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).
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.
