Skewness of the Prior Through Position Errors and Its Impact on Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 143

Chapter 7
Skewness of the Prior Through Position Errors
and Its Impact on Data Assimilation

Daniel Hodyss and Alex Reinecke

Abstract Uncertainty in the position of a feature is a ubiquitous influence on data
assimilation (DA) in geophysical applications. This chapter explores the properties
of distributions arising from the uncertainty of the location of a flow feature. It is
shown that distributions arising from phase uncertainty have surprisingly complex,
non-Gaussian characteristics. These non-Gaussian characteristics are explored from
an ensemble DA perspective in which the skewness (third-moment) is shown to
be a significant contributor to the state-estimates obtained through Bayesian state
estimation. Idealized examples, as well as an example in a real tropical cyclone
using a state-of-the-art numerical weather prediction model, will be shown.

7.1 Introduction

Data assimilation (DA) is the combining of information from a model forecast and
an observation to obtain an estimate of the state of a physical system that is generally
better than either individually. One way DA is accomplished is through ensemble
(Monte-Carlo) methods. The basic idea in this perspective is to perform regression
of the state variables in need of updating against the observations of the state. This
form of DA is rapidly becoming the technique of choice for the estimation of the
state of a geophysical system. This popularity is largely due to the significant ease of
implementation afforded by the use of Ensemble-based Kalman Filter (EnKF) DA
systems. The EnKF is a state-estimation technique that makes use of the ensemble
to estimate the first and second moments of the prior distribution, which are then
used to estimate the posterior mean. This reliance upon just the first and second
moments of the prior distribution allows for significant computational advantages