Data Assimilation

National Centre for Earth Observation, University of Reading

Research Projects Reports Demos Posters
Talks Research Day Public Understanding Teaching
Maths in Data Assim Met Office Info Miscellaneous Info References
Research Projects

Simultaneous Nadir Overpases

Calibration of HIRS to IASI data.

Enter the 'SNO'
project page

Reduced rank Kalman filter at high resolution

Data assimilation with models that include small-scale flow needs a new machinery to represent the background error covariance statistics. This project will develop a toy model that will have qualitative properties of the atmosphere (viz convective non-hydrostatic flow at the small scales) and will investigate the use of the RRKF in a 4d-Var setting.

Enter the 'reduced-rank Kalman filter'
project page

Inference of tracer source and sink fields using data assimilation

Data assimilation provides the machinery to infer information about a system that cannot be measured directly. The estimation of sources and sinks of trace gases is an important example with application to environmental science and pollution control. This project investigates how accurately atmospheric sources and sinks of a trace gas can be dermined by combining measurements of the gas with long-time-window 4d-VAR.

Enter the 'sources and sinks'
project page

Forecast errors for convective-scale variational data assimilation

Data assimilation relies heavily on a 'first guess' that is provided by a forecast model. This forecast is not perfect and has systematic and random errors, and each requires a separate treatment. The random errors are considered here and are meant to be accounted for by the 'B-matrix'. These errors are assumed to mirror the properties of the forecast equations. Until now, efforts in modelling the B-matrix have focused on its properties on synoptic scales where familiar meteorological balances provide a guide on how the B-matrix should be formed (e.g. see potential vorticity project below). High-resolution models (of order 1km grid length) are increasingly being used for data assimilation where the existing methods for modelling the B-matrix are less appropriate. This project assesses the properties of forecast errors from high-resolution models.

Enter the 'convective scale'
project page

Assimilation in the presence of sharp features and cloud in the boundary layer

The success of a weather forecast can be sensitive to the way that the data assimilation is done, because it determines the forecast model's initial conditions. The boundary layer presents many complications in the weather forecasting problem due to the presence of the temperature inversion, which is sometimes present at the top of the boundary layer and the presence of the associated stratocumulus cloud. This Ph.D. project (student Alison Fowler) looks at how positional errors in prior forecasts of the inversion, and cloud can be treated in the data assimilation problem.

Enter the 'boundary layer'
project page

Potential Vorticity Based Control Variables in Variational Data Assimilation

Data assimilation schemes used in numerical weather prediction try to determine the current state of the atmosphere. To do this they require a background state (a forecast) whose errors must be estimated. This is done presently in operational schemes with a catalogue of approximations and assumptions. One simplifying assumption is that the errors in the balanced part of the fields are decoupled from errors in unbalanced parts. Currently in all schemes known to the author, the partitioning into balanced and unbalanced components is not done in the best way. In this project, a new method of partitioning based on potential vorticity - expected to be better - is developed and tested. (Collaborator, Mike Cullen, Met Office).

Enter the 'PV control variable'
project page

Waveband summation transformation in Variational Data Assimilation

Spatial correlations of the errors within meteorological fields need to be captured realistically in data assimation for accurate estimation of the initial conditions for weather forecasting. Spatial error structures are complicated and exact methods of capturing them cannot be used due to the prohibitive size of the problem. Existing methods reproduce either the variations of errors with scale, but not position, or the variations of errors with position, but not scale. The waveband summation transform is a wavelet-like approach to error modelling and is designed to do both simultaneously.

Enter the 'WS transform'
project page

Assimilation of Ozone, Temperature and Humidity Retrievals from ENVISAT

The simplest way of assimilating satellite data is to deal with retrievals. The retrievals that we are using consist of vertical profiles of ozone, temperature and humidity inferred from measurements made from the ENVISAT satellite. The profiles comprise of data at a number of discrete levels which are representative of the atmosphere in a layer. This project is to develop and implement code in the Met Office variational data assimilation system that will accept these profiles, taking into account approximately the broad extent of the data in the vertical.

Enter the 'layer averaging'
project page
Ross's DARC Technical Reports
Elementary 4d Var. (DARC technical report #2)
Layer averaging operators for 3dVar - T, O3, RH (DARC technical report #3)
On control variable transforms in the Met Office 3d and 4d Var., and a description of the proposed waveband summation transformation (DARC technical report #5)
The implementation of a PV-based leading control variable in variational data assimilation. Part 1: transforms (DARC technical report #6, written with Mike Cullen)
Collection of results on background error covariance models (DARC technical report #7)
Demos and Software
'4d-Var' demo with the double pendulum system (original page)
'4d-Var' demo with the double pendulum system (page with MatLab plotting)
Kepler equation inversion (code+user guide)
Ensemble Square Root Kalman Filter (user guide + interactive demo)
Selected DARC Posters
Milestones in atmospheric data assimilation
Data assimilation, southern vortex split and the tape recorder
Background error modelling and satellite retrieval assimilation
A Potential Vorticity (PV) based control variable control parameter for background error covariance modelling. Added April 2005.
Multi-scale methods to model forecast error covariances in variational data assimilation. Added Sept. 2005.
Data Assimilation for Multi-Scale Atmospheric Flow. Added May 2012.
Model errors for MetUM winds - can we estimate these well with dense observations? Added June 2017.
Selected Conference and Seminar Talks
ECMWF talk, 'New observations and novel ways of assimilating', January 2002
EGS talk, 'New observations and novel ways of assimilating', April 2002
Departmental Seminar, 'Some fundamentals of inverse modelling', October 2002
Statistics workshop, 'Statistical considerations in atmospheric data assimilation', October 2002
Earth observation conference, 'Building a better B with balance', Swansea, April 03
RMS Maths in Meteorology meeting, 'Two wrongs can make a right: combining models and data', 16th April 03
Preconditioning in the Met Office variational scheme
PI meeting overview, 'The implementation of potential vorticity as a leading control variable in Var', November 2002
RMS Conference, 'Building a better B with balance', UEA, September 2003 (plus extra slides)
'Wavelets' talk, 'Wavelets: what and why?', September 2003
Earth observation conference, 'Gauging uncertainty in data assimilation', Plymouth, June 2004
PI Meeting, Oct. 05, Science Update
ECMWF Workshop on Flow Dependence in Data Assim, June 2007. Talk and paper for proceedings available.
ECMWI talk, June 2008.
Departmental Seminar, Oct. 2008.
ESA Living Planet Symposium, Edinburgh, Sep. 2013 (Ensemble analysis)
ESA Living Planet Symposium, Edinburgh, Sep. 2013 (Ensemble localization)
Warwick data assimilation workshop, May 2014
Leeds maths seminar, Oct. 2014
NCEO Conference, Warwick, June 2016
Research Day Slides
Research Day 2001 (a)
Research Day 2001 (b)
Research Day 2003
Research Day 2006
Public Understanding of Science Talks
Public understanding of science talk, 'Predictability, chaos & the weather'
National Science Week talk, 'Chaos and weather prediction', March 2003
Oxford-RAL spring school, 'Using prior knowledge in data assimilation', March 2004
QUEST ES4 summer school, 'Observations and data assimilation', Sept. 2006
NCAS measurement summer school, Isle of Arran, Sept. 2010
DAIMG module list with links (2015/16)
Part I of M.Sc. module MTMD02
Guest lectures in M.Sc. module (pre 2011)
NCEO Training in Data Assimilation
Satellites for Meteorology and Weather Prediction (ES4)
Mathematics in Data Assimilation
Summary of mathematical tools for data assimilation (added March 2011)
Some vector algebra and the generalized chain rule
Vorticity and divergence equations
Notes and questions on variational calculus
Error covariance propagation and 4d Var
The Lanczos method for Hermitian and non-Hermitian operators
Vector derivatives
Personal notes on derivatives, inner products and adjoints (added March 2003)
Finite linear vector spaces (added August 2003)
Iterative solvers/minimization algorithms (updated August 2006)
Geostrophic covariances (added February 2004, modified January 2011)
Adjoint coding of summations (added June 2004)
Some adjoint properties of the Laplacian in spherical co-ordinates (added August 2004)
Polar points in spherical coordinates (added August 2004)
Linearized PV of the vertical normal modes (added September 2004)
The Legendre Transform (added May 2005)
Separable correlation functions in real and spectral spaces (added December 2005)
Single and double observation tests (added October 2006)
How do observations affect background error covariance lengthscales? (added January 2007)
Localization in the EnKF (added August 2008)
Combining data notes (added September 2010)
Particle filter formulae (added December 2010)
Statistical assimilation diagnostics (added March 2011)
Deriving EnKF and square-root EnKF (added April 2012)
PDF symmetry of difference between two iid variables (added May 2013)
Moore-Penrose generalized inverse (added August 2015)
Gaussian anamorphosis and rank-based transforms (added August 2016)
Regression formulae (added August 2016)
Advection of loclization (added November 2017)
Forecast and analysis error covariance identity (added March 2019)
Lagrange multipliers in strong constraint 4DVar (added February 2020)
Why the N-1 (Bessel's correction in sample variance calculations)? (added January 2022)
Met Office System Information
Summary of equations - Met Office scheme
Inner loop control
Outer loops without the T-transform (added February 04)
Met Office grids and some STASH codes
Miscellaneous Information
DARC Science Meetings
HRAA High Resolution Atmospheric Assimilation
Earth observation and data assimlation acronyms
Meanings of the different levels in satellite data products NASA WMO
News items
List of papers
Review list

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