Ian Grooms

Lucia Minah Yang, Ian Grooms

Using generative models from the machine learning literature to create artificial ensemble members for use within data assimilation schemes has been introduced in [Grooms QJRMS, 2020] as constructed analog ensemble optimal interpolation (cAnEnOI). Specifically, we study general and variational autoencoders for the machine learning component of this method, and combine the ideas of constructed analogs and ensemble optimal interpolation in the data assimilation piece. To extend the scalability of cAnEnOI for use in data assimilation on complex dynamical models, we propose using patching schemes to divide the global spatial domain into digestible chunks. Using patches makes training the generative models possible and has the added benefit of being able to exploit parallelism during the generative step. Testing this new algorithm on a 1D toy model, we find that larger patch sizes make it harder to train an accurate generative model (i.e. a model whose reconstruction error is small), while conversely the data assimilation performance improves at larger patch sizes. There is thus a sweet spot where the patch size is large enough to enable good data assimilation performance, but not so large that it becomes difficult to train an accurate generative model. In our tests the new patched cAnEnOI method outperforms the original (unpatched) cAnEnOI, as well as the ensemble square root filter results from [Grooms QJRMS, 2020].

Ian Grooms

It is proposed to use analogs of the forecast mean to generate an ensemble of perturbations for use in ensemble optimal interpolation (EnOI) or ensemble variational (EnVar) methods. A new method of constructing analogs using variational autoencoders (VAEs; a machine learning method) is proposed. The resulting analog methods using analogs from a catalog (AnEnOI), and using constructed analogs (cAnEnOI), are tested in the context of a multiscale Lorenz-`96 model, with standard EnOI and an ensemble square root filter for comparison. The use of analogs from a modestly-sized catalog is shown to improve the performance of EnOI, with limited marginal improvements resulting from increases in the catalog size. The method using constructed analogs (cAnEnOI) is found to perform as well as a full ensemble square root filter, and to be robust over a wide range of tuning parameters.

Gregor Robinson, Ian Grooms

A blurring algorithm with linear time complexity can reduce the small-scale content of data observed at scattered locations in a spatially extended domain of arbitrary dimension. The method works by forming a Gaussian interpolant of the input data, and then convolving the interpolant with a multiresolution Gaussian approximation of the Green's function to a differential operator whose spectrum can be tuned for problem-specific considerations. Like conventional blurring algorithms, which the new algorithm generalizes to data measured at locations other than a uniform grid, applications include deblurring and separation of spatial scales. An example illustrates a possible application toward enabling importance sampling approaches to data assimilation of geophysical observations, which are often scattered over a spatial domain, since blurring observations can make particle filters more effective at state estimation of large scales. Another example, motivated by data analysis of dynamics like ocean eddies that have strong separation of spatial scales, uses the algorithm to decompose scattered oceanographic float measurements into large-scale and small-scale components.