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Data assimilation (DA) in the geophysical sciences remains the cornerstone ofrobust forecasts from numerical models. Indeed, DA plays a crucial role in thequality of numerical weather prediction, and is a crucial building block thathas allowed dramatic improvements in weather forecasting over the past fewdecades. DA is commonly framed in a variational setting, where one solves anoptimization problem within a Bayesian formulation using raw model forecasts asa prior, and observations as likelihood. This leads to a DA objective functionthat needs to be minimized, where the decision variables are the initialconditions specified to the model. In traditional DA, the forward model isnumerically and computationally expensive. Here we replace the forward modelwith a low-dimensional, data-driven, and differentiable emulator. Consequently,gradients of our DA objective function with respect to the decision variablesare obtained rapidly via automatic differentiation. We demonstrate our approachby performing an emulator-assisted DA forecast of geopotential height. Ourresults indicate that emulator-assisted DA is faster than traditionalequation-based DA forecasts by four orders of magnitude, allowing computationsto be performed on a workstation rather than a dedicated high-performancecomputer. In addition, we describe accuracy benefits of emulator-assisted DAwhen compared to simply using the emulator for forecasting (i.e., without DA).

Efficient high-dimensional variational data assimilation with machine-learned reduced-order models