Variational Inference at Glacier Scale
This work addresses parameter inference in glaciology for researchers modeling ice sheet dynamics, but it is incremental as it applies existing variational inference techniques to a specific domain problem.
The authors tackled the problem of inferring basal traction and ice softness parameters of ice sheet models from surface speed observations using stochastic variational inference with natural gradient descent and Gaussian process priors. They demonstrated the method's ability to recover known parameters in synthetic tests and scaled it to real-world glacier applications, showing high posterior uncertainty in slow-flow regions.
We characterize the complete joint posterior distribution over spatially-varying basal traction and and ice softness parameters of an ice sheet model from observations of surface speed by using stochastic variational inference combined with natural gradient descent to find an approximating variational distribution. By placing a Gaussian process prior over the parameters and casting the problem in terms of eigenfunctions of a kernel, we gain substantial control over prior assumptions on parameter smoothness and length scale, while also rendering the inference tractable. In a synthetic example, we find that this method recovers known parameters and accounts for mutual indeterminacy, both of which can influence observed surface speed. In an application to Helheim Glacier in Southeast Greenland, we show that our method scales to glacier-sized problems. We find that posterior uncertainty in regions of slow flow is high regardless of the choice of observational noise model.