Before revision:  In the two dimensional case our analysis shows that both the local and global shift of the front exhibit intermittent dynamics and follow the same scaling laws as in one dimension, apart from a logarithmic correction for global shifts. In one dimension, we show that determining the front position is related to an extremal problem of random walks, shedding further light on the origin of the jumps. Our results are in stark contrast to the behavior of the model without disorder, suggesting that current observations might misleadingly show little to no climate response for an extended period of time, concealing the long-term effects of climate change.
After revision:  Our results suggest that current observations might misleadingly show little to no climate response for an extended period of time, concealing the long-term effects of climate change.