We propose the first weather-based algorithmic trading strategy on a continuous intraday power market. The strategy uses neither production assets nor power demand and generates profits purely based on superior information about aggregate output of weather-dependent renewable production. We use an optimized parametric policy based on state-of-the-art intraday updates of renewable production forecasts and evaluate the resulting decisions out-of-sample for one year of trading based on detailed order book level data for the German market. Our strategies yield significant positive profits, which suggests that intraday power markets are not semi-strong efficient. Furthermore, sizable additional profits could be made using improved weather forecasts, which implies that the quality of forecasts is an important factor for profitable trading strategies. This has the potential to trigger an arms race for more frequent and more accurate forecasts, which would likely lead to increased market efficiency, more reliable price signals, and more liquidity.