# Atmosphere Ocean Science Colloquium

#### Ensemble Kalman Filters in High Dimensions

**Speaker:**
Xin Tong, University of Singapore

**Location:**
Warren Weaver Hall 1302

**Date:**
Wednesday, May 10, 2017, 3:30 p.m.

**Synopsis:**

Ensemble Kalman filter (EnKF) is a data assimilation method for high dimension systems. With a few hundred samples, EnKF can provide accurate forecast for weather models of 10^{8} dimensions. Yet, how does the EnKF beat the curse of dimensionality remains much of a mystery. It is known that for numerical matrix operations, the computation can be efficient if either the matrix is low rank or sparse. Interestingly, a similar statement can be made for EnKF as well. One heuristic explanation of EnKF's success is that there is an small effective dimension p for forecast uncertainty. With a proper EnKF augmentation and formulation of the effective dimension, we can show the necessary sample size indeed depends linearly on p. Another fundamental reason of EnKF's success is the localization technique, which taps into a special sparse structure in the covariance matrix. Yet, an intrinsic inconsistency rises with the localization technique. Fortunately, it can be controlled by the localized covariance structure. This leads to a small necessary sampling size for the EnKF, which scales linearly with log d.