Unresolved atmospheric processes can introduce history dependence beyond the short input windows used by many weather forecasting models. We introduce GraphCast--Mamba, which augments a frozen, pretrained $1^\circ$ GraphCast backbone with a trainable Mamba correction branch combining graph message passing and Mamba layers. The branch retains a temporal memory state across successive six-hour forecast steps, learning corrections informed by temporal context beyond GraphCast's two-frame input. Training is confined to the correction branch, using ERA5 data from 2015--2021. After 2,500 optimizer updates, including warm-up, the selected model achieves substantial improvements relative to the uncorrected GraphCast backbone. It reduces the GraphCast loss (normalized weighted mean-squared error; MSE) by 14.42% when aggregated over the full ten-day forecast and by 21.66% at day 10 (240 h after forecast initialization). At this final forecast lead time, root-mean-square error (RMSE) decreases by 7.09--14.60% across all 11 evaluated variable groups, spanning temperature, wind, pressure, geopotential, specific humidity, and precipitation. These results demonstrate broad improvements in ten-day weather forecasts through a short correction-training schedule while retaining the pretrained backbone.

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