не в моей компетенции, конечно

[juan_gandhi]

Но я наслаждаюсь аргументами противников теории ГП. Красиво гонят, такое ощущение, что это какая-то умственная паника.

Типа почему никакого ГП нету вообще:

- да последние пять лет самые холодные за наблюдаемую историю вообще;

- у нас на Магадане морозы надоели уже, пусть уже потеплее будет;

- в 1500-м 97% ученых считали, что Земля неподвижна, а кто был не согласен, того на костре сжигали;

- на Марсе тоже ледники тают;

- всех интересует только температура на поверхности, а что творится на высоте 10км, никого не интересует;

- при динозаврах вообще стояла жарища;

- инерция поведения океана: вода, что сейчас выходит к поверхности на Бермудах (и дальше идет в качестве Гольфстрима), шла от Антарктиды, вдоль Южной Америки, примерно тысячу лет;

- Грета Тунберг в школу давно не ходила;

- Индии и Китаю вообще пофиг какая температура стоит, им первым делом надо народ накормить;

- так нам в Калифорнии чего конкретно ожидать-то, засухи или наводнений? А то каждый год новости;

- кто-нибудь вообще изучал вопрос изменения поведения Солнца за последние 50-100 лет?

Comments

[chaource]

Yes, this is a very good analogy. What is the trend of T = sin(t) at t=2019? We can compute that by averaging over some period of time (e.g. between 2019 and 2019.001) and find the "trend". But it will have little predictive power if we do that over such a small interval. If we compute the trend of sin(x) over a very long interval, we will get approximately zero trend.

Now, of course, sin(t) is a highly repetitive function, so if M(t) = sin(t) is the correct model of temperature, we would have a lot of predictive power. But this is not the case with temperature: we can't even predict ordinary weather for more than a week in advance, let alone for 100 years. We don't have M(t).

I am asking a very limited question: given the observed T(t), can we see a growth trend, and can we say with certainty that the temperature is growing, and that it is growing faster after 1950 than it was growing before 1950?

If somebody says that today we have "global warming" and that it has accelerated in recent years, can we verify this with observational data? What exactly do these words mean, "the temperature is growing" and "it is growing faster than before", in terms of observational data? That's all I'm asking. And we can answer that question simply by doing statistical analysis on the observed data for T(t), with no need for complicated physics.

Now, of course, that analysis will tell us nothing about predicting T(t) for the next 1000 years. It will have no predictive power for the next 1000 years. But predicting for the next 1000 years is a very hard question - and not the question I'm asking.

[sassa_nf]

Ok, I understand your intent. Now can we go back to the meaning of fitting "b"? Further up you mentioned that if we find "b" for different intervals, at some point it starts looking like "2 sigma different". What are you comparing to what? "b"s before 1950 and "b"s after 1950? But are "b"s before 1950 independent and identically distributed? I am not sure in what sense we can treat "b"s as a quantity to which we can apply the methods that we want to apply.

[chaource]

So, we are back to the original question - estimate "b" from a given dataset T(t) using the assumption that T(t) = a + b*t + U(t) where U is unknown noise with zero mean.

You performed a calculation where you estimated "b" linearly from different time intervals. Let us first assume that the true value "b" is the same for all time from 1900 to 2020. Then you can perform linear fit for "b" with different time intervals. For example, take the 20-year intervals 1900-1920, 1901-1921, 1902-1922 and so on until 2000-2020. The result will be 100 different estimates of "b". They are not independent, of course, but highly correlated. Nevertheless, you can look at the resulting distribution of estimates and see if there is evidence that the mean of "b" is not zero.

You can compute the mean and the standard deviation of the set of 100 estimates of "b". Roughly, if the mean is > 2 stdev then the mean is nonzero with high confidence. You can also use other statistical tests for nonzero mean, of course.

[sassa_nf]

I see. I think I understand now.

I think the criticism remains in force. If the "b"s are not iid, then "the mean is > 2 stdev" may not apply. The problem is not only the correlation between "b"s (one flavour of "dependent"), but also how they are going to be distributed (another flavour of "dependent"). Put differently, if you were to draw samples of 20 normally distributed values, and computed "b"s, would such "b"s be distributed normally? If not, then why would the two-sigma rule be meaningful?

[chaource]

The two-sigma rule is very rough. Of course, the 100 values of "b" are not independent (although they are identically distributed). To be correct, you need to calculate the correlation between all of them. But as a very rough guide, you can take two sigma. In a more precise calculation, such as in my Fourier-based analysis, you can exactly account for correlations.