Journal de Chaource

https://amazon.com/Carbon-Dioxide-Theory-Climate-Change/dp/3030168794/

This book provides a complete review of the role of CO2 in the Earth’s atmosphere and reveals detailed information about the subject of climate change. Many different science disciplines are visited and discussed and each area is introduced with a brief summary written to appeal to a broader audience. The logic of CO2 involvement in changing the climate is investigated from every perspective: reviewing the historical data record of Ice Ages with vast ice sheets, noting the interglacial periods of little or no ice, examining in further detail the 20th century data record and evaluating the radiation role of CO2 in the atmosphere. The radiation calculations, using the appropriate equations and data are reviewed in great detail. The results of this review and examination reveal no role of CO2 in any change of the Earth’s climate.

Можно-ли надѣяться, что этого приспѣшника мiровой закулисы, проплаченнаго нефтегазовыми лоббистами, этого такъ называемаго ученаго, будутъ слушать?

Я увѣренъ, что въ этой книгѣ - неправильная наука. Ну не можетъ быть, что испускаемый промышленный СО2 (около 1% отъ всего CO2: около 30*10^9 изъ 3*10^12 тоннъ) не играетъ никакой роли въ климатѣ. Даже движенiе Луны играетъ роль.

Послѣдняя моя надѣжда найти методъ, которымъ климатологи пользуются для оцѣнки ошибокъ, - это прочитать материалы доклада IPCC. Священная Википедiя говоритъ, что потеплѣнiе оцѣнивается такъ:

In the period from 1906 to 2005, Earth's average surface temperature rose by 0.74±0.18 °C. The rate of warming almost doubled in the last half of that period (0.13±0.03 °C per decade, against 0.07±0.02 °C per decade).[27]

Вотъ онѣ, оцѣнки ошибокъ. Идемъ по горячему слѣду!

Ссылка [27] - это докладъ "Climate Change 2007: Working Group I: The Physical Science Basis". IPCC AR4. https://en.wikipedia.org/wiki/Global_warming#cite_note-29
Это талмудъ на 1000 страницъ съ десятками тысячъ ссылокъ на статьи. На страницѣ 336 читаемъ (выдѣленiе жирнымъ шрифтомъ мое):

The time series used in this report have undergone diverse quality controls that have, for example, led to removal of outliers, thereby building in some smoothing. In order to highlight decadal and longer time-scale variations and trends, it is often desirable to apply some kind of low-pass filter to the monthly, seasonal or annual data. In the literature cited for the many indices used in this chapter, a wide variety of schemes was employed.
...
Another low-pass filter, widely used and easily understood, is to fit a linear trend to the time series although there is generally no physical reason why trends should be linear, especially over long periods. The overall change in the time series is often inferred from the linear trend over the given time period, but can be quite misleading. Such measures are typically not stable and are sensitive to beginning and end points, so that adding or subtracting a few points can result in marked differences in the estimated trend. Furthermore, as the climate system exhibits highly nonlinear behaviour, alternative perspectives of overall change are provided by comparing low-pass-filtered values (see above) near the beginning and end of the major series.

The linear trends are estimated by Restricted Maximum Likelihood regression (REML, Diggle et al., 1999), and the estimates of statistical significance assume that the terms have serially uncorrelated errors and that the residuals have an AR1 structure. Brohan et al. (2006) and Rayner et al. (2006) provide annual uncertainties, incorporating effects of measurement and sampling error and uncertainties regarding biases due to urbanisation and earlier methods of measuring SST. These are taken into account, although ignoring their serial correlation.

The error bars on the trends, shown as 5 to 95% ranges, are wider and more realistic than those provided by the standard ordinary least squares technique. If, for example, a century-long series has multi-decadal variability as well as a trend, the deviations from the fitted linear trend will be autocorrelated. This will cause the REML technique to widen the error bars, reflecting the greater difficulty in distinguishing a trend when it is superimposed on other long-term variations and the sensitivity of estimated trends to the period of analysis in such circumstances. Clearly, however, even the REML technique cannot widen its error estimates to take account of variations outside the sample period of record. Robust methods for the estimation of linear and nonlinear trends in the presence of episodic components became available recently (Grieser et al., 2002).
As some components of the climate system respond slowly to change, the climate system naturally contains persistence. Hence, the statistical significances of REML AR1-based linear trends could be overestimated (Zheng and Basher, 1999; Cohn and Lins, 2005). Nevertheless, the results depend on the statistical model used, and more complex models are not as transparent and often lack physical realism. Indeed, long-term persistence models (Cohn and Lins, 2005) have not been shown to provide a better fit to the data than simpler models.

Appendix 3.B: Techniques, Error Estimation and Measurement Systems: See Supplementary Material
This material is included in the supplementary material. Please note that the many references that are cited only in Appendix 3.B have not been included in the list above, but are just as valuable in formulating the report.

Здѣсь наступаетъ засада. Эти дополнительные матерiалы (Appendix 3.B), гдѣ объясняются методы расчетовъ и оцѣнки ошибокъ - напрочь отсутствуютъ! Якобы они должны быть въ файлахъ ПДФ, но ихъ нигдѣ нѣтъ!
https://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch3sappendix-3-b.html

Итакъ, предварительный отвѣтъ найденъ - они пользуются методомъ REML, который какъ-то учитываетъ корреляцiи во времени. Это уже плюсъ. Однако, остаются многочисленные вопросы и проблемы.

1. Результаты расчетовъ по REML указаны въ таблицѣ на стр. 243. Эта таблица показываетъ темпъ роста температуры за перiоды 1850-2005, 1901-2005, и 1979-2005, причемъ съ разбивкой по суше, океану, сѣверному, южному полушарiямъ, и по даннымъ разныхъ группъ ученыхъ. Цифры темпа роста разнятся очень сильно - отъ 0.04 до 0.4 С за декаду. Какъ это интерпретировать, не очень ясно. Океаны утѣпляются очень медленно, а сѣверное полушарiе на сушѣ - очень быстро. Усредненiемъ по всѣй поверхности Земли получается "средняя температура по больницѣ" - т.е. лишенная физическаго смысла величина, полученная усредненiемъ совершенно разныхъ, физически не связанныхъ другъ съ другомъ процессовъ. Такая величина будетъ флуктуировать безъ какой-либо закономѣрности, подъ влiянiемъ непредсказуемыхъ факторовъ.

2. "A wide variety of schemes was employed". Это значитъ, они не знаютъ, что они вычисляютъ. Это чистое упражненiе въ статистикѣ - какъ "лучше" усреднить и сгладить временной рядъ. Отвѣта на такъ поставленный вопросъ не будетъ никогда, отсюда и "wide variety of schemes".

3. "there is generally no physical reason why trends should be linear", "adding or subtracting a few points can result in marked differences in the estimated trend", "the results depend on the statistical model used" - это свидѣтельствa того, что вычисляется лишенная физическаго смысла величина ("trend").

4. Явно сказано, что игнорируются корреляцiи временного ряда въ опредѣленныхъ мѣстахъ вычисленiй.

5. Однако, также сказано, что используется методъ REML, который, съ одной стороны, учитываетъ корреляцiи, но, съ другой стороны, "the statistical significances of REML AR1-based linear trends could be overestimated" въ присутствiи корреляцiй ("the climate system naturally contains persistence"). Это значитъ, что методъ REML не учитываетъ полностью эффектовъ корреляцiй. Надо будетъ прочитать статью про методъ REML, а также про другiе методы, которые вродѣ бы должны исправить этотъ недочетъ.

6. "the statistical significances of REML AR1-based linear trends could be overestimated" - "Nevertheless, the results depend on the statistical model used". Фраза построена такъ, какъ будто "nevertheless" смягчаетъ проблему недостаточной точности REML. Однако, на дѣлѣ эта проблема лишь усугубляется, если результаты еще и зависятъ отъ выбора статистической модели.

PS

Ура, найденъ Appendix 3.B.
https://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-chapter3-supp-material.pdf
Разочарованъ - ни слова о корреляцiяхъ или методѣ REML.

Слѣдующiе шаги - найти и прочитать источники, упомянутые въ связи съ проблемами REML:

The linear trends are estimated by Restricted Maximum Likelihood regression (REML, Diggle et al., 1999)
Diggle, P.J., K.Y. Liang, and S.L. Zeger, 1999: Analysis of Longitudinal Data. Clarendon Press, Oxford, UK, 253 pp. (А это уже книга, не статья.)

...the statistical significances of REML AR1-based linear trends could be overestimated (Zheng and Basher, 1999; Cohn and Lins, 2005)
Zheng, X., and R.E. Basher, 1999: Structural time series models and trend detection in global and regional temperature series. J. Clim., 12, 2347– 2358.
Cohn, T., and H.J. Lins, 2005: Nature’s style: Naturally trendy. Geophys.
Res. Lett., 32, L23402, doi:10.1029/2005GL024476.

Robust methods for the estimation of linear and nonlinear trends in the presence of episodic components became available recently (Grieser et al., 2002)
Grieser, J., S. Trömel, and C.-D. Schönwiese, 2002: Statistical time series decomposition into significant components and application to European temperature. Theor. Appl. Climatol., 71, 171–183.

Summary: Out of about 3200 scientists surveyed, 5% were climate scientists. Out of these 160 climate scientists, 79 have published more than 50% of their recent peer-reviewed papers on the subject of climate change. 77 out of these 79 agreed that human activity is a “significant contributing factor” to global warming; that's the "97%" of scientists. However, everybody else's opinions were not counted in this figure.

A 2012 poll of American Meteorological Society members reported a diversity of opinion. Of the 1,862 members who responded (a quarter of the organization), 59 percent stated that human activity was the primary cause of global warming, and 11 percent attributed the phenomenon to human activity and natural causes in about equal measure, while just under a quarter (23 percent) said enough is not yet known to make any determination.

Read more at: http://www.nationalreview.com/article/425232/climate-change-no-its-not-97-percent-consensus-ian-tuttle

Previous posts - http://chaource.livejournal.com/135561.html and http://chaource.livejournal.com/135899.html

Suppose that the temperature T(t) has the form

T(t) = β t + R(t),

where R(t) is a stationary random process with zero mean and correlation function

C(x) = E [ R(t) R(t+x) ].

Also suppose that we only observe T(t) during the interval [ - D/2, D/2 ]. We can estimate β from these observations by the method of least squares: we approximate T(t) by a linear function,

T(t) = a + b t + error,

and we choose a and b such that the integral of square error over [ -D/2, D/2] is at the minimum.

The result is that a and b become random variables with standard deviation that we can compute by the same method as in my previous post. If R(t) is an oscillating function that makes n oscillations of amplitude M, the standard deviation of both a and b*D is of order M/n. The mean of "a" is zero, and the mean of "b" is β (i.e. these estimators are unbiased). The quantity b*D is the mean change in the temperature (i.e. the estimated amount of "climate change") during the observation interval.

I estimated the value of M/n to be of order 1 °C. So, for the Wikipedia-quoted data:

... a 15-year period starting in 1996 shows a rate of increase of 0.14 [0.03 to 0.24] °C per decade, but taking 15 years from 1997 the rate reduces to 0.07 [–0.02 to 0.18] °C per decade.
https://en.wikipedia.org/wiki/Global_warming_hiatus

we find that the total amount of climate change during the observation interval is of order 0.2 °C. This is below 1 sigma and not statistically significant.

In other words, this value could be 0.1 °C or -0.5 °C just as likely, due to random fluctuations, and so we cannot conclude that the temperature has increased or decreased during that interval.

My estimate is of course rough, but it can be made precise by a numerical calculation of the correlation function C(t). How do meteorologists estimate the uncertainty in their global warming?

"Global warming" means that the surface temperature grows with time, on the average. How can we define the average temperature? What is the precision of the definition of this value?

For simplicity, let us first assume that we know how to average the temperature over the entire Earth to obtain a single value. So, after this averaging we find a value T(t) as a function of time. This function typically exhibits large oscillations, both regular (daily, seasonal) and irregular. We can certainly choose a particular time interval [a,b] and compute the average of T(t) over that interval. However, the results may depend on the interval quite sensitively. Here is what happens when one takes different intervals and fits a line to the data, computing the rate of increase:

... a 15-year period starting in 1996 shows a rate of increase of 0.14 [0.03 to 0.24] °C per decade, but taking 15 years from 1997 the rate reduces to 0.07 [–0.02 to 0.18] °C per decade. https://en.wikipedia.org/wiki/Global_warming_hiatus

If we take other periods for analysis, we might conclude that there is a global cooling.
https://en.wikipedia.org/wiki/Global_cooling

So it is clear that, if we are to talk sensibly about the rate of increase of T, we first need to define the "time-averaged" value of T, and estimate the inherent uncertainty in the definition of the time-averaged T.

Suppose that T(t) were a stationary random process with zero mean and a fixed correlation function C(t):

E [ T(t) ] = 0
E [ T(t_1) T(t_2) ] = C(t_1 - t_2) .

Suppose further that we can only observe a single sample of T(t), and only for t within a fixed interval of duration D. Let us denote by A(D) the average of T over the observed interval. The value of A(D) is a random variable with zero mean and nonzero standard deviation. Can we estimate its standard deviation from a single available sample of T(t)?
( Read more... )

Watched some more discussions and debates about man-made climate warming. My initial conclusions are unchanged (we don't know if it's man-made). There are several aspects of this debate that to me quite obviously indicate that the issue is not settled, in part because it's too technically complicated, in part because it's politically driven.

( Read more... )