Richard,

About the simulatons, you could just take actual datra from weather station sampled over a limited time span, say ten years. The statistical distribution can be studied. And then you can let a computer generate simulated data that simulates any trend on top of which there are random fluctuations and short term natural variations like El Ni?o etc.

The simulation does not have to be very acurate, because what you are testing is if the data analysis algorithm can subtract the random fluctuations plus any short term variations to obtain the long term trend. So, if you simulate the smame trend and add a hypothetical 20 year period oscillation, the algorithm should still produce the same result. The algorthm may only fail if you feed it with unrealistic data.