Previous investigations proved the existence of local density enhancements in Europa's atmosphere, advancing the idea of a possible origination from water plumes. These measurement strategies, however, were sensitive either to total absorption or atomic emissions, which limited the ability to assess the water content. Here we present direct searches for water vapour on Europa spanning dates from February 2016 to May 2017 with the Keck Observatory. Our global survey at infrared wavelengths resulted in non-detections on 16 out of 17 dates, with upper limits below the water abundances inferred from previous estimates. On one date (26 April 2016) we measured 2,095 ± 658 tonnes of water vapour at Europa's leading hemisphere. We suggest that the outgassing of water vapour on Europa occurs at lower levels than previously estimated, with only rare localized events of stronger activity.