1. CP Hung, L Jouve, AS Brun, A Fournier, O Talagrand
Estimating the solar meridional flow and predicting the 11-yr cycle using advanced variational data assimilation techniques
CP Hung, L Jouve, AS Brun, A Fournier, O Talagrand

2. Contents Introduction Temporal variability of flow
Results and predictability
Summary

3. Magnetic observations
Monthly smoothed relative sunspot number R.
Phase lag in field reversal
Solar cycle is on average 11 +/- 3 years.
Amplitude is not constant and not exactly periodic.

4. Data assimilation Physical models produce dynamo model forecasts.
Sequential assimilation and Variational assimilation.
Jouve, ApJ 2011
Minimize an objective function within a time interval for which data is available before making a forecast : compute

5. Flux transport mean field dynamo
S. Sanchez, A. Fournier, and J. Aubert, ApJ 781, 8 (2014)
P. Charbonneau, Living Rev. Solar Phys., 7 (2010), 3
The meridional circulation is given by , .

6. Twin experiment
Synthetic observations are generated by the dynamo code, and we estimate the flow imposed in the model with the artificial observations. (Hung et al, ApJ, 2015)
The objective function is the misfit between the model (Aϕ, Bϕ) and observation data (Aϕo, Bϕo) is given by:

7. Reconstruction of a constant MC
Hung et al, ApJ, 2015

8. Stochastic time varying flow

9. Results
Estimation of the flow
Estimation of magnetic proxy

10. Summary
Data assimilation tool developed to estimate the meridional flow based on magnetic observations
We test the capability of the tool with twin experiment.
Predictability of the assimilation model is between 1 and 2 solar cycles.
Next step: (1) Inverting magnetic butterfly diagram of the past 40 years, (2) improve the modeling of the time dependency of the flow.

11. References L. Jouve and A. S. Brun, A&A 474, 239 (2007b).
L. Jouve, A. S. Brun, and O. Talagrand, ApJ 735, 31 (2011)
S. Sanchez, A. Fournier, and J. Aubert, ApJ 781, 8 (2014).
O. Talagrand, Proc. Conf. on Automatic Differentiation of Algorithms, ed. A. Griewank and G. G. Corliss (Philadelphia: Society for Industrial and Applied Mathematics) , 169 (1991).
M. Dikpati, G. de Toma, P. A. Gilman, C. N. Arge, and O. R. White, ApJ 601, 1136 (2004).
P. Charbonneau and M. Dikpati, ApJ 543: , 2000.
Dikpati et al, Geophysical Research Letters, Volume 41, Issue 15, pp
R. Ulrich, observations of meridional flow.

12. Predictability Free run Controlled run Free run Controlled run
Error in estimation of the field.
After 15 years without assimilation, the predictability is completely lost.