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Modeling of Temperature Change using Random Walk

Recently, when we studied the possible impact of global warming on evolution of proteins from influenza A virus, we noticed the fluctuations in temperature. Although these fluctuations could be attributed to various factors, one thing is clear that the current climate models, which are based on differential equations, can produce only smooth curves, which can be viewed as trend of temperature.

Perhaps, we need a model based on random mechanism to describe the temperature change, thus we considered that the random walk model could be useful. Random walk is quite simple: if we toss a coin, then it will fall one side up in one time and the other side up in another time, these can be recorded as 1 and ?1. If we toss many times, and add 1, or -1 consequently, we will get a random walk. Similarly, when we ask if the temperature is higher or lower in this year than in the last previous year, we can record them as 1 and ?1, their addition would be the temperature walk.

With computer, we can find the seed that produces best similar random walk as temperature walk, this is the fit for temperature. Similarly, we can imagine that we toss a dice, which has many sides as we need, then the additions of tossing of dice would be a random walk, which can fit the real recorded temperature.

This way, we fitted the global temperature, and published it in a very small local journal, which can be downed in www.dreamscitech.com, we also fit the temperatures in many world cities.

If the underlined mechanism for model, which fits the temperature best, is the mechanism for global warming, then the temperature is more likely to be attributed to random mechanism. This is similar to use the random walk to describe the drunken man?s walk, he cannot walk directly to his final place, but takes several steps in one direction and some steps on another direction. Similarly, the temperature can increase for years, and then decreases for years. However, as no one can know how many steps a drunken man would take on each direction, no one could know how many years the temperature would go up or down.

Guang Wu Shaomin Yan
 
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