In arid and semiarid systems of western North America, the most damaging invasive plants are winter annuals. These plants are destroying wildlife habitat, reducing livestock production, and increasing wildfires. Monitoring these plants for lasting population changes is challenging because their abundances vary widely from year to year. Some of this variation is due to weather, and quantifying effects of weather is important for distinguishing transcient from lasting population changes and understanding effects of climate change. Fall and spring weather affect germination and seed production of the current generation of plants and, therefore, impact population sizes of subsequent generations of plants. Extensive data are required to estimate effects of fall and spring weather on multiple generations of plants. We used Bayesian statistics to integrate experimental and long‐term (31 years) monitoring data and quantify invasive annual grass [downy brome (Bromus tectorum L.) and Japanese brome (Bromus japonicus Thunb.)] responses to weather. Bromes ranged from nearly absent to comprising half of total biomass depending on three previous years of weather. Brome biomass increased with precipitation one, two, and three falls prior to measurement. Fall precipitation is projected to increase, and a mere 6.5 mm increase, which is just 2% of mean annual precipitation, would increase brome biomass 40% (28%, 54%) (mean [95% CI]) according to our model. Increased fall precipitation could favor many invasive winter annual grasses and forbs. Dry spring conditions reduced brome biomass the current year but increased brome biomass one and likely two (p = 0.08) years later, perhaps because dry conditions weakened perennial competitors. This finding casts doubt on several one‐year precipitation experiments that concluded drier spring weather would reduce brome abundances. Integrating short‐term experiments and long‐term monitoring is useful for estimating invasive plant responses to the weather and characterizing their responses to climate change. Our research provides predictions of brome abundances that could improve monitoring efforts by helping land managers interpret population dynamics in the context of seasonal precipitation patterns.