Local Warming

TL;DR

This paper presents a linear programming-based LAD regression model analyzing 55 years of local temperature data, successfully identifying temperature rise, seasonal effects, and the solar cycle, demonstrating accessible methods for climate data analysis.

Contribution

Introduces a LAD regression approach formulated as a linear programming problem to accurately extract temperature trends and solar cycle effects from archived temperature data.

Findings

Temperatures increased by about 2°F over 55 years.

The model correctly identified the solar cycle phase.

The linear trend and solar cycle effects were of comparable magnitude.

Abstract

Using 55 years of daily average temperatures from a local weather station, I made a least-absolute-deviations (LAD) regression model that accounts for three effects: seasonal variations, the 11-year solar cycle, and a linear trend. The model was formulated as a linear programming problem and solved using widely available optimization software. The solution indicates that temperatures have gone up by about 2 degrees Fahrenheit over the 55 years covered by the data. It also correctly identifies the known phase of the solar cycle; i.e., the date of the last solar minimum. It turns out that the maximum slope of the solar cycle sinusoid in the regression model is about the same size as the slope produced by the linear trend. The fact that the solar cycle was correctly extracted by the model is a strong indicator that effects of this size, in particular the slope of the linear trend, can be accurately determined from the 55 years of data analyzed. The main purpose for doing this analysis is to demonstrate that it is easy to find and analyze archived temperature data for oneself. In particular, this problem makes a good class project for upper-level undergraduate courses in optimization or in statistics. It is worth noting that a similar least-squares model failed to characterize the solar cycle correctly and hence even though it too indicates that temperatures have been rising locally, one can be less confident in this result. The paper ends with a section presenting similar results from a few thousand sites distributed world-wide, some results from a modification of the model that includes both temperature and humidity, as well as a number of suggestions for future work and/or ideas for enhancements that could be used as classroom projects.