Modeling BiOS?

Why not..

Renzo Mosetti OGS

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….

Squeezing the theory to extract the simplest physical mechanism

First :

Ionian Sea Level Anomalyvs.

ADW Salinity Anomaly

The feedback state variables:

FACTSFACTS

The feedback:The feedback:

ANTICICLONIC CICLONIC

Enter AMW Lower ADW sal.an. NO AMW Increase ADW sal.an

DSdt

d

CSBASdt

dS 3

Setting the ModelSetting the ModelAccumulation 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

Some math (*)…

A-dimensional equation by scaling:

dst~d

~d

cs~bast~d

ds 3

H/~;month/tt~

H/DTd

CTc

;BHTb

;ATa

Where:T= 2.592 X 10^6

H=200m

*

t~d

dscs3sbd

t~d

dsa

t~d

sd 22

2

0sbdt~d

ds)cs3a(

t~d

sd 22

2

By differentiating and substituting:

Rearranging :

This stuff has a familiar aspect….

(Eq.2)

and the winner is:

We can rewrite Eq (2) in the standard form (3) by the following positions:

(Eq. 3)

c3

ap

;bd

1a

;pxs

;bd

1t~t

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…

Salinity anomaly

SL anomaly

MONTHS

Period T = 16 yrs !

(scaled to H)

Salinity anomaly

SL anomaly

MONTHS

Phase plane s -

Limit cycle

~

Some comments and future developments

This is a conceptual model: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?

The forced, or driven, Van der Pol oscillator takes the 'original' function and adds a driving function:

There exist two frequencies in this system, namely, the frequency of self-oscillation determined by ϵ 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 ϵ .

a) Anneliese Van der Pol b) Balthasar Van der Pol

A QUESTION for you: Who is “right” Van der Pol ?