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Predictability: Forward and Backward

In a recently published paper in Advances in Atmospheric Sciences, two types of predictability are proposed: forward and backward predictability. Forward predictability mainly focuses on the forward evolution of initial errors superposed on the initial state over time, while backward predictability is mainly concerned with when the given state can be predicted before this state happens. These two predictability types are not independent but interconnected, according to Prof. DING Ruiqiang, the corresponding author of the study and a scientist at the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences.


"The problem of forward predictability for an initial state has been extensively investigated," says DING. "However, how to estimate the backward predictability of a given state is still unclear. To know the backward predictability in advance is very important for us, because it can tell us when specific states, especially extreme states, can be predicted before they happen."


Schematic diagram of local conservation of forward and backward predictability (Image by LI Xuan)


DING and his coauthors used the nonlinear local Lyapunov exponent method to quantitatively estimate the forward and backward predictability limits of initial states in the Lorenz63 and Lorenz96 models. They found that there is a negative correlation between the local forward and backward predictability limits. That is, the forward predictability limits are higher when the backward predictability limits are lower, and vice versa. They also found that the sum of forward and backward predictability limits tends to fluctuate around a constant value, which is dependent on the specific chaotic system.


"These new findings broaden the concept of predictability in theory, and enrich our knowledge of predictability," DING concludes. "It would be interesting to extend the current investigation to predictability studies of more realistic extreme weather and climate events, which we intend to examine in future research."



Li, X., R. Q. Ding, and J. P. Li, 2019: Determination of the backward predictability limit and its relationship with the forward predictability limit. Adv. Atmos. Sci., 36(6),

Media Conatct: Ms. LIN Zheng,


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