@tomszechy Most weather stations have the same design. They use a solar panel to run during the day and it also charges a battery or a capacitor (its like a battery). Then at night the capacitor runs the station when there is no solar energy. But there are times when there is not enough solar energy during the day to run the capacitor for the next night (rainy days...extreme cloudiness...extreme locations at the poles where there is minimal daylight...etc). Therefore for these reasons a good station besides the solar panel and capacitor will also have batteries to us in case of those extreme cases.
Typically the station will only deplete those batteries about every 2 to 3 years depending on how much those batteries need to be used as it will be different for every location. Certainly it should last a year. Even if using rechargable batteries they have a limit of charge cycles and just about any battery after 2 to 3 years starts to show signs of needing replacement.
But you should not think of a weather station that you can mount and forget. Because you should be servicing the station for other reasons. Sure if you only mount an anemometer on the roof you can get by with minimal maintenance, but if you also mount a rain gauge and temperature/humidity sensor you should be cleaning it out of debris, spider webs, and insects. Therefore a maintenance of at least every 6 months to at most a year is recommended.
The bottom line is that you can't mount a weather station and forget it. So battery depletion is the least of your worries.