While I agree that heat waves are not random events, that is really irrelevant to the argument.
You said "It would be entirely possible, for example, to see a spike in temps producing record high temps, then a return to normal. If "normal" were in fact, gradually rising temps, then we would see a long term increase in average temps (i.e. global warming) without any new record highs for much longer than your 200 days."
While this may be true, it is irrelevant to the statistical analysis of the situation.
For instance, let's use a shorter time frame to demonstrate statistically what I'm saying. If we just use the last five years of data for instance, then we will have five different temperature readings. There can be only one "highest" temperature, one "lowest" temperature, and three temperatures somewhere between the low and the high. This means there is a 20 percent chance that the "highest" temperature recorded occurred in year 1, there is a 20 percent chance it occurred in year 2, there is a 20 percent chance it occurred in year 3, there is a 20 percent chance it occurred in year 4, and there is a 20 percent chance it occurred in year 5. This also means that there is a 20 percent chance that a record high will be recorded each day, or a record high will be recorded, on average, once every five days. (record high meaning the highest ever recorded on this day, during this five-year period)
Whether global warming primarily causes changes in median temperatures, or not, does not change the above percentages. Whether heat waves are random events or not does not change the probability that a particular heat wave occurred in year 1,2, 3, 4 or 5. So, if records had only been kept for five years, you should see a maximum recorded temperature, on average, every five days. -- regardless of whether heat waves are random or not. Their probability of it occuring is equal for each of the years in question. The relevant information is only the period of time in which records have been kept.
For instance, if records were kept for 100 years, you would expect, without any global warming or cooling, a record high every 100 days. If records were kept for 500 years, you would expect to see a record high temperature recorded every 500 days. If records were kept for 2000 years, you would expect to see a record high temperature every 2000 days(on average).
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It would be entirely possible, for example, to see a spike in temps producing record high temps, then a return to normal.
While this is true, and it would be possible to see this happen, it would only happen if you were not talking about things happening on average. This "spike" in temperatures would have just as good of a chance of occurring now as it would have 10 years ago, 100 years ago, or 200 years ago (assuming no global warming). And if there was global warming, it would be more likely to occur today than in the past.
Also, you must consider the nature of global warming. Global warming is said to occur because the insulating affect of the atmosphere is increasing a small amount. If this is true, you would see a greater change in temperatures when it is hot.
For instance, lets assume that space is 200 degrees below zero. Now, let's look at what would happen at 2 different earth temperatures. To make things easy to demonstrate, let's use zero degrees for our cold temperature and 100 degrees for our warm temperature. Since there is a difference of 200 degrees (between Earth and space) using our cold temperature and a difference of 300 degrees using our warm temperature, what do you think would happen if we increased the insulating properties of our atmosphere? It is obvious that the high-temperature would go through a greater increase than the low temperature due to the fact that higher differences in temperatures will "benefit" more from added insulation. Because of this fact, global warming would cause greater increases during hot periods than it would during cooler periods. (assuming global warming is caused by the insulating effects of green-house gasses).
What matters in a global warming analysis is the average temperature, not the average high temperature.
While I agree that this is somewhat true, average temps. do matter a lot, I do not agree that the average high-temperatures will not be affected by global warming, due to the effects of insulators in a system as argued above. A much greater effect should be seen during temp. spikes, or heat waves, and this does not appear to be the case at all.
Rodney