Ruth Petrie


I currently work as a Senior Climate Data Scientist for the Centre for Environmental Data Analysis (CEDA) at the Rutherford Appleton Laboratory (RAL; Harwell, UK). I have a range expertise and including coding for complex dynamical systems,running and analysing state of the art Climate models, managing Petabytes of climate model output data, climate science, numerical weather prediction (NWP) and data assimilation for NWP.

I am particularly interested in the Arctic climate, how it may be affected by climate change and how changes in the Arctic may affect weather patterns in the extra-tropics. My interests in Meteorology are not limited to climate. I am also very interested in weather forecasting, in particular the ever fascinating process of data assimilation and how that has revolutionized weather forecasting since the 1980's.

I undergraduate degrees in Mathematics (Open University) and a joint degree in Accountancy and Computer Science (University of Stathclyde). I have a Masters and PhD in Meteorology from the University of Reading.

PhD Thesis

Background error covariance modelling for convective-scale variational data assimilation

An essential component in data assimilation is the background error covariance matrix (B). This matrix regularizes the ill-posed data assimilation problem, describes the confidence of the background state and spreads information. Since the B-matrix is too large to represent explicitly it must be modelled. In variational data assimilation it is essentially a climatological approximation of the true covariances. Such a conventional covariance model additionally relies on the imposition of balance conditions. These approximationsmay not be appropriate for convective-scale data assimilation and alternative ways of modelling the B-matrix are investigated in this thesis for such flows.

A toy model which is derived from the Euler equations (by making appropriate simplifications, and introducing tunable parameters) is used as a convective-scale system to investigate these issues. Its behaviour is shown to exhibit large-scale geostrophic and hydrostatic balance while permitting small-scale imbalance.

A control variable transform (CVT) approach to modelling the B-matrix where the control variables are taken to be the normal modes (NM) of the linearized model is investigated. This approach is attractive for convective-scale covariance modelling as it allows for unbalanced as well as appropriately balanced relationships. Although the NM-CVT is not applied to a data assimilation problem directly, it is shown to be a viable approach to convective-scale covariance modelling.

A new mathematically rigorous method to incorporate flow-dependent error covariances with the otherwise static B-matrix estimate is also proposed. This is an extension to the reduced rank Kalman filter (RRKF) where its Hessian singular vector calculation is replaced by an ensemble estimate of the covariances, and is known as the ensemble RRKF (EnRRKF). Ultimately it is hoped that together the NM-CVT and the EnRRKF would improve the predictability of small-scale features in convective-scale weather forecasting through the relaxation of inappropriate balance and the inclusion of flow-dependent covariances.

MSc Dissertation

Localization in the ensemble Kalman Filter

Data assimilation in meteorology seeks to provide a current analysis of the state of the atmosphere to use as initial conditions in a weather forecast. This is achieved by using an estimate of a previous state of the system and merging that with observations of the true state of the system. Ensemble Kalman filtering is one method of data assimilation.

Ensemble Kalman filters operate by using an ensemble, or statistical sample, of the state of a system. A known prior state of a system is forecast to an observation time, then observation is assimilated. Observations are assimilated according to a ratio of the errors in the prior state and the observations. An analysis estimate of the system and an analysis estimate of the of the errors associated with the analysis state are also produced.

This project looks at some problems within ensemble Kalman filtering and how they may be overcome. Undersampling is a key issue, this is where the size of the ensemble is so small so as to not be statistically representative of the state of a system. Undersampling can lead to inbreeding, filter divergence and the development of long range spurious correlations. It is possible to implement counter measures. Firstly covariance inflation is used to combat inbreeding and the subsequent filter divergence. Covariance localization is primarily used to remove long range spurious correlations but also has the benefit increasing the effective ensemble size.

Specifically this project uses an implementation of the ensemble Transform Kalman filter (ETKF) a deterministic ensemble, with a simple model, to demonstrate the behaviour of the filter when undersampling is present. Covariance inflation was implemented, and was found to increase the accuracy of the analysis state. A new method of covariance localization by Schur product for the ETKF was introduced and implemented. This method was not consistent with the equations of the ETKF. The analysis estimate was detrimentally affected by this technique. By using covariance inflation in conjunction with this localization the performance may be improved. In its current state this implementation does not function as desired.