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.

pdoindex

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!



Dive


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