Is Inference in Position and Amplitude Subspaces Useful for Estimating State and Uncertainty?

Sai Ravela


Contemporary state estimation is based on amplitude adjustment. Adjusting amplitudes can produce unacceptable 'distortions' when fields exhibit "mesoscale" coherence with relative position errors. Although there are several sources of "position error," finding and fixing all of them is non-trivial. Yet, correcting position errors can be essential for localized meteorological structures. In contrast to a "comfortable world," where forecast fields have no position errors and are Gaussian distributed, in the "real world" position errors introduce bias, variance or both, and this is the fundamental reason for worsening performance. So, we propose a quadratic optimization problem that considers both position and amplitude errors and construct methods to solve it. One of these methods can be used as a handy tool in contemporary practice. In this two-step approach, the first step is field alignment, where the current model field is aligned with observations by adjusting a continuous field of local displacements, subject to certain constraints. The second step is amplitude adjustment, where contemporary approaches are used. Our approach does not rely on the detection of "features," and can be used with sparse "station observations." It has been implemented with multivariate fields, and extensions to 3D is straightforward. Preliminary work on using this method with the WRF-VAR system and other advances, including the development of a generalized filter will, time permitting, be discussed. Our method has also been used for velocimetry (velocity from tracer observations), pattern recognition, and new applications continue to develop which, time permitting, I will highlight.