  The traditional method for estimating weather forecast sensitivity to initial
conditions uses adjoint models, which are limited to short lead times due to
linearization around a control forecast. The advent of deep-learning frameworks
enables a new approach using backpropagation and gradient descent to
iteratively optimize initial conditions to minimize forecast errors. We apply
this approach to forecasts of the June 2021 Pacific Northwest heatwave using
the GraphCast model, yielding over 90% reduction in 10-day forecast errors over
the Pacific Northwest. Similar improvements are found for Pangu-Weather model
forecasts initialized with the GraphCast-derived optimal, suggesting that model
error is not an important part of the initial perturbations. Eliminating small
scales from the initial perturbations also yields similar forecast
improvements. Extending the length of the optimization window, we find forecast
improvement to about 23 days, suggesting atmospheric predictability at the
upper end of recent estimates.
