# Osimorph

**Osimorph** (optimal statistical interpolation with morphing) is a Matlab package started by Jan Mandel when he was sitting in Prague in the office of Krystof Eben in June 2009 trying to quickly hack together some data assimilation with morphing on large weather simulation states on his laptop. He has decided to use as the state covariance a *negative power of the Laplace operator*, because

- it can be implemented quickly by FFT,
- it is invariant of the choice of spatial coordinates, esp. rotation invariant, so it will not cause artifacts or directional bias,
- it actually is the covariance of a smooth random field (i.e., a Gaussian measure, large enough negative powers are trace class operators)
- the Green's function already has the right covariance look, dropping off away from the diagonal,
- but, most importantly, the standard approach required decomposing a banded covariance matrix, which was just too much work both for Jan and for his laptop.

Since then, the Osimorph software has been developed by Jonathan Beezley and Jan. The idea branched into **FFT EnKF**, which estimates the ensemble covariance in the spectral domain by the diagonal of the covariance in the frequency domain. The original optimal statistical interpolation is still attractive, because it provides a good covariance model, so current developments include a covariance estimate by fitting a function of the laplacian to the ensemble. Jon has developed a matlab class framework for Osimorph.

The Osimorph/FFT EnKF approach is being used in wildfire, epidemic, and precipitation simulations.

## Repository

For authorized collaborators on request.

## Publications

- Jan Mandel, Jonathan D. Beezley, Loren Cobb, and Ashok Krishnamurthy, "Data Driven Computing by the Morphing Fast Fourier Transform Ensemble Kalman Filter in Epidemic Spread Simulations UCD",
*Procedia Computer Science, vol 1*, 1215–23, May 2010. ICCS 2010. Also available at arXiv:1003.1771.

- Jan Mandel, Jonathan D. Beezley, and Volodymyr Y. Kondratenko,
**Fast Fourier Transform Ensemble Kalman Filter with Application to a Coupled Atmosphere-Wildland Fire Model**. Anna M. Gil-Lafuente, Jose M. Merigo (Eds.) Computational Intelligence in Business and Economics (Proceedings of the MS'10 International Conference, Barcelona, Spain, 15-17 July 2010), World Scientific, pp. 777-784. Also available at arXiv:1001.1588.

- J. Mandel, J. D. Beezley, K. Eben, P. Jurus, V. Y. Kondratenko, and J. Resler,
*Data assimilation by morphing fast Fourier transform ensemble Kalman filter for precipitation forecasts using radar images*, CCM report 289, April 2010. Manuscript under development in**osimorph/papers/fftenkf-rain**

- J. Mandel,
*Optimal statistical interpolation and morphing*, working notes maintained in**osimorph/doc/osimorph.tex**.

- J. Mandel,
*Data assimilation by morphing FFT EnKF*, working notes maintained in**osimorph/doc/fftenkf.tex**.