Course Description:

Primary Activities

The course provides an in-depth overview of the advanced data assimilation methods. It covers theory and techniques, as well as possible drawbacks and strategies to overcome them. For major methods, student project and presentation are assigned to gain practical experience.

Guest Lectures on Special Topics

Some lectures will be given by guest speakers who are the leading experts of data assimilation.

Suggested Textbooks: [Not Required]

Data Assimilation

	Atmospheric Modeling, Data Assimilation and Predictability by Kalnay, 2003.
	Dynamic Data Assimilation: A Least Squares Approach (Encyclopedia of Mathematics and its Applications) by John M. Lewis. S. Lakshmivarahan, and Sudarshan Dhall, 2006.
	Atmospheric Data Analysis (Cambridge Atmospheric and Space Science Series) by Roger Daley, 1993.
	Data Assimilation: The Ensemble Kalman Filter by Geir Evensen, 2007.

Related Topics

	Sequential Monte Carlo Methods in Practice by Arnaud Doucet, Nando de Freitas, Neil Gordon, (Eds.) 2001.
	Stochastic Processes and Filtering Theory by Andrew H. Jazwinski, 1974.
	Inverse Problem Theory and Methods for Model Parameter Estimation by Albert Tarantola, 2005.

Classic Research Articles

	NMC Method for Background Covariance Matrix Construction
		Parrish, D. F. and J. C. Derber, 1992: The national-meteorological-centers spectral statistical interpolation analysis system. Mon. Wea. Rev., 120, 1747–1763.
	Correlation Function for Covariance Matrix
		Gaspari, G. and S.E. Cohn, 1999: Construction of correlation functions in two and three dimensions, Quat. J. Roy. Meteor. Soc, 125, 723-757.
	Data assimilation diagnostics in observation space
		Desrozier, G., L. Berre, B. Chapnik, and P. Poli, 2005: Diagnosis of observation, background and analysis-error statistics in observation space, Quat. J. Roy. Meteor. Soc, 131, 3385–3396.
	Predictability and Probability Evolution
		Epstein, E.S., 1969: Stochastic dynamic prediction, Tellus, 21, 739-759.
		Leith, C.E., 1974: Theoretical skilll of Monte Carol Forecasts, Mon. Wea. Rev., cal102, 409-418.
		Ehrendorfer, M., 1994: The Liouville equation and its potential usefulness for the prediction of forecast skill, Part I & II, J. Atmos. Sci., 122, 703-713 & 714-728.
		Legras, B. and R. Vautard, 1995: A Guide to Liapunov Vectors, ECMWF Seminar Series "Predictability".
	Ensemble Kalman Filters
		Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic ocean model, JGR Ocean, 97, 17905-17924.
		Houtekamer, P.L., H.L. Mitchell, 1998: Data assimilation using an ensemble Kalman filter technique, Mon. Wea. Rev., 126, 796-811.
		Burgers, G., P.J. van Leewen, G. Evensen, 1998: Analysis scheome in the ensemble Kalman filter, Mon. Wea. Rev., 126, 1719-1724.
		Bishop, C.H. B. Etherton, and S. J. Majumdar, 2001: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129, 420–436.
		Whitaker, J.S., T.M. Hamill,2002: Ensemble data assimilation without perturbed observations, Mon. Wea. Rev., 130, 1913-1934.
		Tippett, M.K., J.L. Anderson, C.H. Bishop, T.M. Hamill, J.S. Whitaker, 2003: Ensemble square-root filters, Mon. Wea. Rev., 131, 1485-1490.
		Hunt, B.R., E.J. Kostelich, I. Szunyogh, 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter, Physica D, 230, 112-126.
	Hybdrid Schemes
		Hamill, T. M., and C. Snyder, 2000: A hybrid ensemble Kalman filter-3D variational analysis scheme. Mon. Wea. Rev., 128, 2905–2919.
		Lorenc, A. 2003: A hybrid ensemble Kalman filter-3D variational analysis scheme. Mon. Wea. Rev., 128, 2905–2919.
		Buehner, M. 2005: Ensemble-derived stationary and flow dependent background error covariances: Evaluation in a quasi-operational NWP setting. Quart. J. Roy. Meteor. Soc., 131, 1013–1043.
		Wang, X., C. Snyder, and T.M. Hamill. 2007: On the Theoretical Equivalence of Differently Proposed Ensemble–3DVAR Hybrid Analysis Schemes. Mon. Wea. Rev., 135, 222–227.
	Particle Filters
		TBA

Prerequisite/Corequisite and Credits:

Prerequisite: AOSC 614 is preferred but not strictly required.

Grading Policy:

	Students are responsible for checking the UMD Honor code.
	Credits are based on: attendance/participation: 30%; projects/assignment: 50%; & final presentation/report: 20%.

Schedule

Weekly

	Class	PLS 1164	TuTh 12:30pm-1:45pm
	Office hour	CSS 3403	By appointment

Course Syllabus:

1. Introduction 2. Background 3. "3D" Methods 4. Uncertainty Evolution 5. "4D" Methods 6. Advanced Methods 7. Special Topics

Suggested Project Models:

	Lorenz 3 variable model
		Ref:	(i)	Lorenz, E. N., 1963: Deterministic non-periodic flow. J. Atmos. Sci., 20, 130-141.
			(ii)	Kalnay, E. and co-authors, 2007: 4-D-Var or Ensemble Kalman filter? Tellus, 59A, 758-773.
	Lorenz 40 variable model
		Ref:	(i)	Lorenz, E. N., 1995: Predictability: a problem partly solved. ECMWF proceedings for Seminar on Predictability, 1-18.
			(ii)	Lorenz, E. N. and K. Emanuel, 1998: Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model, J. Atmos. Sci. 45, 399-414.
	Lorenz 960 variable model
		Ref:	(i)	Lorenz, Ed 2005: Designing Chaotic Models, JAS, 62, 1574-1587
	Point Vortex Model
		Ref:	(i)	Aref, H.. 2007: Point vortex dynamics - A classical mathematics playground. J. Math. Phys., 48, 065401. [Tracer dynamics is obtained by treating tracers as point vortices with zero circulation.]
			(ii)	Kuznetsov, L., K. Ide, CKRT Jones, 2003: A Method for Assimilating Lagrangian Data. MWR, 131, 2247-2260.

Exercises and Projects:

Exercises [Expected for Projects]

1.	[Self Practice]	No Due.	Implementation of Optimization Algorithms
2.	[Self Practice]	No Due.	Construction of Background Covariance Matrix
3.	[Self Practice]	No Due.	Preconditioning for Optimization (3D-Var)
4.	[Self Practice]	No Due.	Tangent Linead and Adjoint Models
4.	[Self Practice]	No Due.	Diagnostics in Observation Space

Projects and Exercises

Ia.	Project	Feb 04, 5pm.	Model and Language selection
Ib.	Project	Feb 11, 5pm	Basic framework of Data Assimilation [with Analysis=Forecast]
II.	Presentation	Mar 03.	3D Methods: 3D-Var and OI
	Report	Mar 04, 5pm
III.	Presentation	Mar 29 & 31	Extended Kalman Filter:
	Report	April 01, 5pm
IV.	Presentation	April 12 & 14	Ensemble Kalman Filter:
	Report	April 15, 5pm
V.	Presentation	May 03	4DVar:
	Report	May 06, 5pm
VI.	Presentation	May 10	Final:
	Report	May 13, 5pm