Easy weather forecasting

I remember reading somewhere that if you predicted the weather by saying simply that tomorrow's weather will be the same as today's, you'd be right about half the time. Since I now have a fair archive of detailed weather data for my own back yard (dating back to June 2003), I thought I'd give this notion a bit of a test.

Obviously, the accuracy of this method of forecasting depends on how you define "same". If you require all weather readings to be identical over both days, you will never get a match, so we need to define a tolerance. For starters, I have used the maximum, minimum and mean temperatures and the rainfall as indicators, and I've allowed tolerances to be set on each of these values so we can vary the definition of "same".

I've written a little C# program which reads in the data from my station and allows the user to define tolerances for the four key quantities in terms of how much the next day's data is allowed to vary from the current day in order for the two days to be judged as having the "same" weather. The results are rather interesting, so here's a taster.

The data cover a total of 2540 days, between 26 June 2003 and 10 June 2010. If we use the mean temperature as the only indicator, and allow a tolerance of plus/minus one degree C, the prediction is correct 44% of the time (that is, for nearly half the pairs of days, the mean temperature varied by less than 2 degrees C). If we use rainfall as the only indicator, and allow a tolerance of plus/minus 0.1 mm (which isn't very much - it's the smallest amount my weather station can measure), we get a correct prediction 36% of the time.
Requiring both mean temperature and rainfall (with the same tolerances) to match, the hit rate drops to 15%.

If we require all four indicators to match (with tolerances of plus/minus 1 degree for the three temperature readings, and plus/minus 0.1 mm for the rainfall), the rate drops to 4.4%.

I figure the results are interesting enough to merit expanding the program a bit. I could extend the prediction period (e.g. how good is a prediction of the weather n days in advance, rather than just one), produce some plots of accuracy versus tolerance or time lag, and perhaps even try some time series analysis to produce some curves that fit the data and allow more accurate predictions.

However, it does put the forecasts from the Met Office in perspective. If a simple little program that you could run on your mobile phone (well, you could if I wrote it for a mobile - this one runs on a desktop, but never mind) can get things like mean temperature and rainfall correct between a third and half the time just by looking one day ahead, is the met office's multi-million pound computer really giving us our money's worth?

It's a bit like playing the stock market based entirely on past performance of shares, rather than doing some research on the companies in which you want to invest.