Antalife has written an article detailing the build of his a solar powered weather station:

To expand my microcontroller and programming knowledge I have decided to try and make a Solar Powered Weather Station. My goal is to record parameters like:
*Temperature
*Humidity
*Air pressure
*Air quality (something to do with CO or CO2)
I then hope to send (wirelessly) the data to a base station and log/display it on a simple website. To make things interesting I also aim to power the data gathering station from a large supercapacitor (~100F), and in keeping with my solar tradition the supercapacitor will be charged from a solar-cell.

See the full post on his blog.