Abstract
Abstract. Climate change is expressed as a climate system transiting from the initial state to a new state in a short time. The period between the initial state and the new state is defined as the transition process, which is the key part for connecting the two states. By using a piece-wise function, the transition process is stated approximately (Mudelsee, 2000). However, the dynamic processes are not included in the piece-wise function. Thus, we proposed a method (Yan et al., 2015, 2016) to fit the transition process by using a continuous function. In this paper, this method is further developed for predicting the uncompleted transition process based on the dynamic characteristics of the continuous function. We introduce this prediction method in detail and apply it to three ideal time sequences and the Pacific Decadal Oscillation (PDO). The PDO is a long-lasting El Niño-like pattern of Pacific climate variability (Barnett et al., 1999; Newman et al., 2016). A new quantitative relationship during the transition process has been revealed, and it explores a nonlinear relationship between the linear trend and the amplitude (difference) between the initial state and the end state. As the transition process begins, the initial state and the linear trend are estimated. Then, according to the relationship, the end state and end moment of the uncompleted transition process are predicted.
Highlights
A system transiting from one stable state to another in a short period is called abrupt change (Charney and DeVore, 1979; Lorenz, 1963, 1976)
We have developed a new method to predict the end state and the end moment of a transition process based on the quantitative relationship
In order to test the validity of this prediction method in a real climate system, we apply this method to predict the uncompleted transition process of the Pacific Decadal Oscillation (PDO)
Summary
A system transiting from one stable state to another in a short period is called abrupt change (Charney and DeVore, 1979; Lorenz, 1963, 1976). The abrupt change system has two or more states (Goldblatt et al, 2006; Alexander et al, 2012); the system swings between these states that are called equilibrium states in physics This phenomena is verified in many fields, including biology (Nozaki, 2001), ecology (Osterkamp et al, 2001), climatology (Thom, 1972; Overpeck and Cole, 2006; Yang et al, 2013a, b), brain science (Sherman et al, 1981), etc. The significant difference between the average values of the two sequences on both two sides of the turning point is defined as the index for measuring the abrupt change. It is difficult for these kinds of methods to detect the transition
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