a reply to: micromass
1) A polynomial curve of degree 3 or lower cannot describe cyclical behavior, which we know from experience exists in weather systems. The best and
most familiar example of such cyclical behavior is the seasons. A 4th degree polynomial can describe the continuous sinusoidal curve of the seasons
fairly well, but anything lower cannot. A third degree curve will always provide an extension that indicates a runaway system; a second degree more
I think you misinterpret my mention of the 90-year cycle. That is a complete guess and I have stated so many times in this thread. The actual period
cannot be ascertained by the data as presented without further analysis. I can state that the curve appears to be a portion of a sinusoidal curve.
Even that is not 100%, but I believe it to be a reasonable interpretation of the results.
In any analysis, the goal is always predictive. Knowing what the temperature was yesterday is easy; knowing what it will likely be tomorrow is much
more difficult. All of the climate models exist for the sole purpose of predicting future behavior from past behavior, and their veracity is not
assured until such time as they have successfully done so. In this case, some predictive indicators need to be stated so the analysis can be either
validated or invalidated depending on future events. If we continue to see rising temperatures for the next ten years, that will invalidate my
interpretation of the results; if we see a slowing of temperature rises and then a slow dropping of temperatures, that will validate my analysis and
lend credence to future predictions. I do not predict a 90-year cycle; I predict a cycle peaking within the next decade or so.
2) An autocorrelation would be helpful, but at the moment I do not have good access to the computer that handles all of the higher mathematical
functions (MatLab). In the interest of getting the data out, I went ahead and published the analysis minus the higher math functions. As I stated, my
intention is to soon continue the analysis using FFT methodology, which will give the same data. Any randomness will manifest itself as white noise in
the system, while cycles will show as a higher peak.
There is also a dynamic FFT analysis that will provide insight into deviations in frequency that are happening through time. That will be more useful
than an autocorrelation, as it can be analyzed with smaller portions of the dataset. The smaller sections will cause more uncertainty than a longer
section, but even with that uncertainty any deviation in cyclic frequency or amplitude will be evident.
3) I used mean inputation. Multiple inputation is indicated when the dataset is discontinuous. Temperature readings are continuous by their very
nature, and thus the difference between multiple inputation and mean inputation is negligible. As an example for other readers, mean inputation means
I make the assumption that the missing data will be close to the average of all data surrounding the missing data. For example, the data from July
1985 was missing; in it's place, I used the average (mean) of the months of July for 1980, 1981, 1982, 1983, 1984, 1986, 1987, 1988, 1989, and 1990.
While it is possible that July 1985 was exceptionally hot or cold, the likelihood is that July1985 was close to that average.
Luckily, there were no missing sections of data where the months averaged were missing as well. That would have required numerical methods in order to
achieve a reasonable approximation of the missing data. To use the above example, numerical methods would have been needed had July 1981 been missing
A similar result was used for missing single days. By adjusting the number of days in the month to reflect that the sums used were not inclusive of
the total number of days, the averages were maintained. The calculation inside Excel includes a separate column for the number of days in each month
instead of hardcoding it into the equations. This allows me to adjust for missing days. As above, it might e possible that a missing day was
exceptionally hot or cold, but the likelihood is that it was at least close to the average for that month.