But surely the random sequences added together are just that random. Because they are random there will be random sequences that conform to any curve required, but outside the conformance the sequence will fall back to random = average zero.
Surely what is being proposed is that trees growths are controlled by many factors. no randomness just noise and a combination of factors.
Trees will not grow at -40C trees will not grow at +100c.
Trees do grow well at a temp in between (all else being satisfactory).
Choosing trees that grow in tune to the temperature means that if they extend beyond the temp record than the is a greater possibility that these will continue to grow in tune with the temp. If they grow to a different tune then they are invalid responders.
A long time ago I posted a sequence of pictures showing what can be obtained by adding and averaging a sequence of aligned photos - the only visible data was the church and sky glow. I added 128 of these images together and obtained this photo:
Note that it also shows the imperfections in the digital sensor (the window frame effect)
Image shack did have a single image with the gamma turned up to reveal the only visible image (Church+sky) but they've lost it!
The picture was taken in near dark conditions.
A flash photo of the same:
By removing all invalid data (pictures of the wife, the kids, flowers etc) that do not have the church and sky, a reasonable picture of the back garden appears from the noise.
Of course I may have included a few dark picture with 2 streetlights in those locations, but with enough of the correct image these will have a lessening effect.
This cap shape must have a dependence on temperature. It may not be linear but it must be there.
Somewhere between 15C and 100C the growth must start declining Did trees pass the optimum in the 60s?
Uncontrolled emissions in the 60s, 70s and 80s was known to cause acid rain (to an extent that some countries were forced to add lime to lakes to prevent damage) there was plenty of evidence that trees were being damage also.
Is it not true to say Damaged trees=slow growth
There are many factors that can slow tree growth but apart from over temperature these effects will be diminished by limited industrialisation (before 1900?).
Trees are rubbish thermometers, but in all the noise there MUST be a temperature signal. A large local sample will lower the noise from sickness, or damage. A large global sample will lower the noise from changes in soil fertility, etc.
Nothing will remove the noise from CO2 fertilisation, or other global events.
Some trees growing at the limit of their water needs may be negatively affected by rises in temperatures from their minimum growing value - growing in heat requires more water. these will always show a negative growth increase with temp. But if averaged with enough positive responders then these will be insignificant.
But the signal that remains must, when averaged contain a temperature signal (not necessarily linear)
"Overall, the Program's cap and trade program has been successful in achieving its goals. Since the 1990s, SO2 emissions have dropped 40%, and according to the Pacific Research Institute, acid rain levels have dropped 65% since 1976. However, this was significantly less successful than conventional regulation in the European Union, which saw a decrease of over 70% in SO2 emissions during the same time period.
In 2007, total SO2 emissions were 8.9 million tons, achieving the program's long term goal ahead of the 2010 statutory deadline.
The EPA estimates that by 2010, the overall costs of complying with the program for businesses and consumers will be $1 billion to $2 billion a year, only one fourth of what was originally predicted."
"However, the issue of acid rain first came to the attention of the international community in the late 1960s, having been identified in certain areas of southern Scandinavia, where it was damaging forests. The matter quickly became an international issue when it was discovered that the acid deposits in these areas were a result of heavy pollution in the UK and other parts of northern Europe.
Acid rain and air pollution emerged from the industrial boom of the early 1900s onwards and the increasing levels of chemical production associated with these processes. The building of taller industrial chimneys from the 1960s onwards was largely held to be responsible for pollutants generated in the UK blowing as far as Scandinavia. "