Climate Variable is Time-Averaged: Dealing with Uncertainty of Paleoclimatic Record Caused by Smoothening of Noisy Variations

Climate is the average of weather over some time period and shows characteristic behavior in each time scale. In paleoclimatic research, values of climate variables are measured from proxies that give time series of time-averaged variables. Therefore, understanding the dynamics of time-averaged variable is important to investigate climate variations thorough different time scales.

In our recent study, we formulated how stochastic dynamics changes corresponding to averaging time intervals using one dimensional first order stochastic differential equation which contains parametrically controlled terms of deterministic single-well or double-well potential force and random force. The dynamics of time-averaged variable is described by conditional probability density function. In the case of single-well, the function is analytically derived as normal distribution with scaling parameters. In the case of double-well potential, the function is obtained as skew generalized normal distribution function through numerical simulations. The mathematical framework of stochastic dynamics of time-averaged variable is general and applicable to analysis of many kinds of climate time series data.

In this study, we apply the above framework to the analysis of proxy data from ice core and discuss about time scaling of the past climate variations. We test several models to infer the optimal model description for the data.