灾难能预测吗？

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对突变的预测一直是人们关心的问题，如果能测量的时间序列信息中提前预知系统的变化，就可能降低损失、甚至避免灾难发生。

网上已经有了总结得非常好的网站对这一问题进行介绍

http://www.early-warning-signals.org/home/

另外有一本科普书籍，Len Fisher-Crashes, Crises, and Calamities_ How We Can Use Science to Read the Early-Warning Signs

http://book.douban.com/subject/10598864/

也从历史上讲述了这一问题，可以在libgen上下载

先用一幅图说明什么是突发变化。

图中第三幅图就是突发变化，即在条件的微小变化可能会引发极端的不连续的变化，这种变化不可逆的（图C）。当在一个阈值，系统突然转向一个截然不同的状态。

再说为什么预测是可能的了

一个简单的方法来理解为什么我们应该期望预警前关键的转变是把一个系统的行为看做一个包含山谷和山顶的曲面上的一个球的运动。

上图中纵轴对应的是时间，横轴对应的是系统的状态，由于图的上部类似于系统的“表现型”，下部类似于系统的内在表现。故而我们可以从系统的可观察结果推出系统将要面临突发变化。

接下来说什么是可能预测信号

A. Early warning signals can be direct consequences of critical slowing down:

1. Slow recovery from perturbations: The recovery rate after small perturbations decreases when the system is close to the bifurcation。

   

2 .Critical slowing down—which might also be described as “today is the same as yesterday”—is another symptom of a nearby catastrophic shift. A progressively slower ability to recover from small perturbations as a crisis approaches is a characteristic of reduced resilience. The state of the system becomes more and more like its past state (panels a2,b2). The highly correlated time series close to the transition can be quantified as an increase in autocorrelation.

3.Increasing variance: The accumulating impact of the non-decaying shocks prior to the transition increases the variance of the state variable

4 Another significant statistical indicator of upcoming disaster is the occurrence of more extreme states. These can be easy to spot in relationships characterized by times of loving closeness interspersed with periods of violent argument.

5 One way in which complex systems achieve stability is through the
spontaneous emergence of spatial patterns, which develop when living conditions are improved by the presence of similar neighbors. One example from nature is the self-organized banding in beds of seagrass.

B. Early warning signals can also be associated with with asymmetries in the stability landscape or even jumps between alternative basins of attraction:

1. Increasing skewness: In the vicinity of saddles the rates of change are low (reflected in the asymmetry of the stability landscape, panels a,b). The system spends more time close to the saddle resulting in a highly skewed distribution of the state variable (panels a4,b4).
2. Flickering: The probability that stochastic forcing may temporarily shift a system back and forth between alternative basins of attraction is higher close to a bifurcation. As a result, the variance and skewness of the frequency distribution of the state variable increases.

接下来说说这个理论在生活中的应用：

下面来自 http://www.salon.com/2011/04/27/crashes_calamities/

One of the signs is more extreme conditions. In a relationship, for example, you might get a period when you have violent arguments and then periods when you’re lovey-dovey. If you get these extremes, or these things happen more frequently, that’s a warning sign that you’re getting very, very close to collapse.

Another thing that happens is quick fluctuation between different states, like, for example, when the cod fisheries collapsed in Newfoundland. The fishermen wouldn’t believe it because they had one or two years of good catches, but if they had been aware of [the warning signs] before that ultimate fluctuation between high fish stocks and low fish stocks, they would have said, “uh oh.”

The third warning sign is loss of resilience. When something happens to disturb the situation, it can be very hard to recover. I like to think of that in terms of a relationship: You think you’re getting along OK, you’re agreeing and you go out to a party. Then something happens. One person gets offered a drink and takes it, and the other gets mad. Rather than recover from the situation and apologize, they glower at one another all night, and it gets increasingly hard to recover from the disturbance.

举一个具体的例子，文中的我指Len Fisher

Just a month ago, I was playing five sets of tennis three times a week when I just happened to slip and sprung a small hernia. I saw a hernia surgeon, and he said, Oh by the way, if you’re going to have an operation, you’re probably going to need to have an examination first by a cardiologist. So I went and saw the cardiologist, and he did a few tests on me, and the result is that I am going to have a triple bypass because he found that I had two blocked arteries, and I didn’t have a clue.

But I might have noticed, applying the theories of my own book, that for a few months what’s been happening is, I’ve been having periods of extreme energy and then extreme lethargy, and swinging between extreme states.

那预测是否准确，针对不同的情景，要问以下这些问题

1. Are the data reliable?
2. Is the model reliable?
3. Are the calculations reliable?
4. Are the people reliable?

找到了预示突变机制的信号后，之后应该怎么办

1. Identify the potential wild-card scenarios where possible.
2. Learn to recognize the warning signs for upcoming critical
transitions, understanding that these signs can sometimes be
ambiguous and open to interpretation.
3. Share information about warning signs that have been
detected.
4. Use this information to prepare a plan that includes a builtin capacity for improvisation ifthe scenario should arise.

总结：

These are main warning signs for upcoming sudden and sometimes
disastrous change in personal, social, economic, physical, or environmental circumstances:

Unacceptable buildup of stress
Concentration of stress at weak points
Potential for uncontrolled runaway effects
Loss of resilience (the ability to recover rapidly from small
disturbances)
Increasing swings between different states
Increasing occurrence of extreme states
Changes in pattern

Just thinking about these signs in terms of our own personal relationships is sufficient to show their importance in warning us of disaster
ahead. In the hands of scientists, they are becoming an important quantitative tool to help forecast disasters of all kinds.

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