1. Modeling BiOS? Why not.. Renzo Mosetti OGS

2. Main question: Is the pseudo-periodic reversal of the circulation in the Ionian sustainable only through internal dynamics? A feedback mechanism is the core of BiOS. Let’s try to do something in this direction….

3. Squeezing the theory to extract the simplest physical mechanism First : Ionian Sea Level Anomaly vs. ADW Salinity Anomaly The feedback state variables:

4. FACTS

5. The feedback: ANTICICLONICCICLONIC Enter AMWLower ADW sal.an.NO AMWIncrease ADW sal.an

6. Setting the Model Accumulation of salinity anomaly Feedback from SL anomaly Non linear damping/discharge S ADW salinity anomaly IONIAN sea level anomaly (Eq. 1) Feedback from Salinity anomaly Recharge oscillator: Fei-Fei Jin 1997, J. Atm. Sc. 54,811

7. Some math (*)… A-dimensional equation by scaling: Where: T= 2.592 X 10^6 H=200m *

8. By differentiating and substituting: Rearranging : This stuff has a familiar aspect…. (Eq.2)

9. and the winner is: The van der Pol equation has a unique, stable limit cycle for each > 0. The van der Pol equation has a unique, stable limit cycle for each > 0. We can rewrite Eq (2) in the standard form (3) by the following positions: (Eq. 3)

10. How to choose the parameters? A residence time of Adriatic deep water: 26 Months (Vilibic,sic!) C estimate from data: 1.13 x 10^(-9) B estimate from data : 1.58 x 10 ^(-10) D: estimate from data: 2.75 x 10^(-6) We do need better estimate from a deep statistical analysis of all available data Crude estimate: Nevertheless…

11. Salinity anomaly SL anomaly MONTHS Period T = 16 yrs ! (scaled to H)

12. Salinity anomaly SL anomaly MONTHS

13. Phase plane s - Limit cycle

14. Some comments and future developments This is a conceptual model: May be it is the simplest physical model based on the BiOS hypothesis; Over a wide range of coupling coefficients, the model can be self-excited with a robust decadal period; The role of an external seasonal /inter-annual forcing (Salinity flux; wind stress) should be investigated: what happens to the oscillations? What will be the effect of a stochastic forcing?

15. The forced, or driven, Van der Pol oscillator takes the 'original' function and adds a driving function: chaoschaos Lyapunov exponent There exist two frequencies in this system, namely, the frequency of self-oscillation determined by and the frequency of the periodic forcing. The response of the system is shown in Figure (upper) for Tin=10 and F=1.2. It is observed that the mean period Tout of x often locks to mTin/n, where m and n are integers. It is also known that chaos can be found in the system when the nonlinearity of the system is sufficiently strong. Figure (lower) shows the largest Lyapunov exponent, and it is observed that chaos takes place in the narrow ranges of. Lyapunov exponent chaosLyapunov exponent

16. a) Anneliese Van der Polb) Balthasar Van der Pol A QUESTION for you: Who is “right” Van der Pol ?