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[ACG33-08] An Interpretation of ENSO as an Information Channel with Feedback
Keywords:Atmosphere–Ocean Interaction, Information Theory, Information Thermodynamics, Non-Equilibrium Physics
The interaction, or information transmission, between the atmosphere and the ocean is essential for the El Niño Southern Oscillation (ENSO). Recently, information thermodynamics [1], an emerging field in non-equilibrium physics, has facilitated the analysis of information transmission in stochastic processes [2]. This study applies these methods to a recharge oscillator system, interpreting the atmosphere-ocean coupling as an information channel with feedback. We will discuss the stochastic nature of ENSO from this perspective.
We investigate a bivariate dynamical system, comprising regional mean variables (120E-80W, 5S-5N) of wind stress and the depth of the 20-degree isothermal surface (Eqs. 1 and 2). Each positive coefficient in these equations was determined through regression analysis of reanalysis data. In Eqs. 1 and 2, f(t) represents external forcings, such as the annual cycle, while the last terms denote white Gaussian noise. The atmospheric noise is an order of magnitude greater than the oceanic noise, and the atmospheric relaxation time scale is an order of magnitude shorter than that of the ocean. This system is regarded as a recharge oscillator for a decaying mode [3,4].
Following Ito and Sagawa [2], we derive Eq. 3 by applying the second law of information thermodynamics to the wind stress variable. The left-hand side of this equation represents the negative dissipation rate for wind stress, while the right-hand side includes the transfer entropy, which we will discuss later. The dissipation rate, defined in Eqs. 4 and 5, represents the difference between the variances of wind stress and noise, with the former variance based on the instantaneous equilibrium value (Eq. 5). A lower dissipation rate suggests more deterministic variation in wind stress.
Based on the noisy-channel coding theorem [5], Eq. 3 provides an interpretation as an information channel with feedback [2] (Fig. 1). Here, the atmosphere encodes an external forcing as input and transmits it to the ocean, which decodes the received signal and provides feedback to the atmosphere. With its longer relaxation time, the ocean acts as a memory, enhancing the efficiency of information transmission through feedback [2]. The upper bound of this efficiency is given by the transfer entropy, I tr (Eq. 3). The negative dissipation rate is the actual efficiency and suggests that information on the forcing is transmitted more efficiently as the variation in wind stress becomes more deterministic. However, this actual efficiency cannot exceed I tr. Equation 3 implies that the randomness of noise limits the clarity of transmitted information and sets an upper bound on transmission efficiency.
Transforming Eq. 3 into Eq. 6 reveals that atmospheric randomness (i.e., the wind stress variance) has a lower bound. Information transmission between the atmosphere and ocean reduces this lower bound by the amount of transfer entropy, I tr, which can be theoretically determined using the parameters in Eqs. 1 and 2. Figure 2 shows the dependence of I tr on a and rh. The magnitude of I tr increases with stronger feedback from the ocean to the atmosphere (i.e., larger a) or slower oceanic relaxation (i.e., smaller rh). This result implies that stronger atmosphere-ocean coupling or longer ocean memory enhances information transmission efficiency, reducing atmospheric randomness. In our presentation, we will further explore Eq. 6 from the perspective of atmospheric and ocean sciences.
References:
[1] Shiraishi, 2023, Springer.
[2] Ito and Sagawa, 2015, Nat. Commun.
[3] Jin, 1997, J. Atmos. Sci.
[4] Jin et al., 2007, Geophys. Res. Lett.
[5] Cover and Thomas, 2006, Wiley.
We investigate a bivariate dynamical system, comprising regional mean variables (120E-80W, 5S-5N) of wind stress and the depth of the 20-degree isothermal surface (Eqs. 1 and 2). Each positive coefficient in these equations was determined through regression analysis of reanalysis data. In Eqs. 1 and 2, f(t) represents external forcings, such as the annual cycle, while the last terms denote white Gaussian noise. The atmospheric noise is an order of magnitude greater than the oceanic noise, and the atmospheric relaxation time scale is an order of magnitude shorter than that of the ocean. This system is regarded as a recharge oscillator for a decaying mode [3,4].
Following Ito and Sagawa [2], we derive Eq. 3 by applying the second law of information thermodynamics to the wind stress variable. The left-hand side of this equation represents the negative dissipation rate for wind stress, while the right-hand side includes the transfer entropy, which we will discuss later. The dissipation rate, defined in Eqs. 4 and 5, represents the difference between the variances of wind stress and noise, with the former variance based on the instantaneous equilibrium value (Eq. 5). A lower dissipation rate suggests more deterministic variation in wind stress.
Based on the noisy-channel coding theorem [5], Eq. 3 provides an interpretation as an information channel with feedback [2] (Fig. 1). Here, the atmosphere encodes an external forcing as input and transmits it to the ocean, which decodes the received signal and provides feedback to the atmosphere. With its longer relaxation time, the ocean acts as a memory, enhancing the efficiency of information transmission through feedback [2]. The upper bound of this efficiency is given by the transfer entropy, I tr (Eq. 3). The negative dissipation rate is the actual efficiency and suggests that information on the forcing is transmitted more efficiently as the variation in wind stress becomes more deterministic. However, this actual efficiency cannot exceed I tr. Equation 3 implies that the randomness of noise limits the clarity of transmitted information and sets an upper bound on transmission efficiency.
Transforming Eq. 3 into Eq. 6 reveals that atmospheric randomness (i.e., the wind stress variance) has a lower bound. Information transmission between the atmosphere and ocean reduces this lower bound by the amount of transfer entropy, I tr, which can be theoretically determined using the parameters in Eqs. 1 and 2. Figure 2 shows the dependence of I tr on a and rh. The magnitude of I tr increases with stronger feedback from the ocean to the atmosphere (i.e., larger a) or slower oceanic relaxation (i.e., smaller rh). This result implies that stronger atmosphere-ocean coupling or longer ocean memory enhances information transmission efficiency, reducing atmospheric randomness. In our presentation, we will further explore Eq. 6 from the perspective of atmospheric and ocean sciences.
References:
[1] Shiraishi, 2023, Springer.
[2] Ito and Sagawa, 2015, Nat. Commun.
[3] Jin, 1997, J. Atmos. Sci.
[4] Jin et al., 2007, Geophys. Res. Lett.
[5] Cover and Thomas, 2006, Wiley.