On Local
Warming and Climate
copyright © 2007 Paolo B. DePetrillo,
MD
Introduction
I learned how to develop and test nonlinear models as part
of my work in pharmacokinetics and pharmacodynamics. I have
absolutely no formal background in climate science, but I
can at least ask and attempt to answer very simple
questions using the tools and data at my disposal. In fact,
you could consider this a "pharmacodynamic" climate model,
with the sun as drug, the sunspots as dose, and the
temperature as a "drug" effect. If you are a climate model
expert reading this and have some time and pity, feel free
to contact me to let me know the features and flaws of the
following exercise. Even if I am completely wrong, I can
learn from the exchange. We start with Haskell, TX. Though
if you want a quick run down, go over to the
Wichita, KS station, where I have put in the most work so
far. It had the most complete data over the past hundred
years or so.
What are the
Questions?
Stated in a
somewhat informal fashion, here are my questions.
Is there a long term trend in annual average temperature
data from rural stations in the continental United States?
Do sunspot cycles influence local temperature?
Does the change in
estimated atmospheric carbon dioxide concentration
influence local temperature over time?
We are looking for patterns patterns in the temperature
time series that leave a mathematical signatures indicating
a recurring particular influence or influences. If we
discover the relationship, then we can test it against "the
real world" to see if it makes any sense.
Even random patterns of numbers can be mathematically
modeled if we allow ourselves enough parameters. For
mathematical modelers, parameters are like colors to an
artist. The general idea is to use the least amount of
"color" possible. Then at least we have some confidence
that the model is describing a relationship that might
exist in the 3D world, and not just a pretty colored
figment from the ethereal world of time series analysis.
Descriptions of some well studied climate
cycle oscillations can be found here.
Arctic Oscillation (AO)
North Atlantic Oscillation (NAO)
Pacific Decadal Oscillation (PDO)
El Nino-Southern Oscillation (ENSO)
Madden-Julian Oscillation (MJO)
Atlantic Multidecadal Oscillation
(AMO)
As a starting point, I have
modeled the Pacific Decadal Oscillation Index from data
published by Zhang et al and Mantua et al. and
copied here.
Data after the vertical line
which represents the year 2008 is extrapolated from the
model. It supports the hypothesis that we might be heading
into the cold phase of the PDO over the next 30 years.
This model is missing the higher frequencies, but you can
get a flavor for the interacting cycles. I have listed the
Period of each cycle in years:
The first four periods, ranging from about 59 years to
about 14 years are the main periods.
Years ± SEM
58.8 ± 1.4
25.7 ± 0.4
19.4 ± 0.3
13.6 ± 0.1
8.9 ± 0.1
5.7 ± 0.1
5.2 ± 0.1
4.6 ± 0.0
4.1 ± 0.0
3.5 ± 0.0
The PDO appears to exhibit regular periodic variations in
amplitude. Amazingly enough, so do the station temperature
data, where the major decadal cycles appear to match the
periods of the major cycles comprising the PDO.
I do not have the expertise to model anything more complex
than a single time series, so modeling a local temperature
time series is reasonable. I have no clue on how to model
something as complex as climate, a system that is partially
self-referential and behaves nonlinearly in four dimensions
[space + time]! Sounds like it should be better left to
experts. I would not know even the basics of how to proceed
to think about it.
If my technique is adequate, and the signal is strong
enough, I should be able to pick out an effect of recurring
climate oscillations, solar cycles, and perhaps CO2 on a
local temperature time series. Indeed a lot of ifs. I may
choose the wrong spots, I might be in the wrong part of the
hemisphere to pick out a strong signal. There may be lots
of reasons I might not be able to make sense of the data.
But it's worth a try. If some local predictive model of
temperature can be developed, it might even be useful to
folks like farmers and ranchers
It's a long
shot!
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