# Category Archives: mathematics

## Trend and Cycle Together

Many climate signals show both trend and cycle (usually an annual cycle) together. A typical example is the concentration of carbon dioxide (CO2) in the atmosphere. If you look at the data (say, from the Mauna Loa atmospheric obsevatory) both the trend and the cycle are obvious.

## The Value of Data

On a cold January morning in 1986, the space shuttle Challenger lifted off its launch pad at the Kennedy Space Center in Florida. Morale was high, especially as the Challenger flight was to inaugurate the teacher-in-space program with astronaut/high school teacher Christa MacAuliffe in its crew. Alas, 73 seconds into the flight the shuttle disintegrated, destroying the spacecraft and killing all the astronauts on board. The cause of the accident was a leak of hot gas from one of the solid rocket boosters. The leak occured because of the failure of rubber “O-rings” which were supposed to seal the joints between rocket sections, and part of the reason they failed is that the temperature was so cold at the time of the launch — the O-ring material becomes more stiff at low temperature so it’s less likely to make a proper seal.

## Why Not Weighted?

The question arose on another blog, when analyzing the Berkeley data, why not use weighted least squares with weights determined by the uncertainty levels listed in the Berkeley data file?

## Decadal Variations and AMO — Part II

In this post I’d like to examine another claim made in one of the Berkeley papers, that there is a periodic fluctuation in the AMO (Atlantic Multidecadal Oscillation) with period about 9.1 years.

## Markov 2

In the last post we showed how Harold Brooks has applied a 1st-order Markov Chain model to the phenomenon of a significant tornado day (“STD”), in particular to explain the frequency of occurrence of long runs of consecutive STDs. An STD is defined as any day with at least one (possibly many more) tornados of strength F2 or greater (on the Fujita scale).

## Math Fun: the Markov Tornado

While looking around for tornado data, I found a fascinating page by Harold Brooks in which he builds a model of the likelihood of a “significant tornado day,” which I’ll call an “STD” (yeah, it’s a funny choice). This is defined as a day with at least one tornado of Fujita scale F2 or stronger.

## Mission Failure

As many of you are aware, the launch of the Glory satellite was a failure. The mission would have studied solar irradiance, aerosols, and clouds — all of which are important data for climate studies. Alas, the satellite failed to deploy and the mission — if it happens at all — will have to wait. It’s surely a demoralizing blow to the Glory team, and a blow to climate science since it follows hard upon the launch failure of the OCO satellite two years ago. RealClimate has a post on the subject.

## Ridge Regression

Since the subject of “ridge regression” came up in discussions on RealClimate recently, I thought I’d give a very brief description of what the heck it is.

I tried to keep the math to a minimum, but I failed. There’s no getting around that fact that this is a mathematical topic so there’s lots of math anyway. But it’s still only a peek at the subject — I hope that it at least gives a little perspective on what ridge regression is and why it’s used. Oh well, at least the “rigor police” have been banished.

## MLE

It’s routine practice in statistics to apply a statistical model to some process. Often (I’d even say, usually) the model depends on a certain number of parameters. Sooner or later, we’d like to know what the parameters are (or at least be able to estimate them). One of the most powerful methods in statistics for estimating the parameters of a model from a given set of data is called “MLE” for “Maximum Likelihood Estimation.”