PRINCIPAL COMPONENT ANALYSIS Global Sea Surface Temperatures

From voluntary ship observations:Colors show the percentage of monthswith at least one observation in a2 by 2 degree grid box.

From paper in Annual Review of Marine Science (2010)

PRINCIPAL COMPONENT ANALYSIS Global Sea Surface Temperatures

Climatology 1982-2008

Red areas mark regions with highestSST variability

PRINCIPAL COMPONENT ANALYSIS Global Sea Surface Temperatures

Principal Component Analysis (PCA)

(Empirical Orthogonal Functions (EOF))

The first leading Eigenvector Eigenvectors form nowgeographic pattern. Grids with highpositive values and large negative values are covarying out of phase (negative correlation). Green regionsshow small variations in this Eigenvector #1.

The Principal Component is a time seriesshowing the temporal evolution of the SST variations. This mode is associated with the El Niño - Southern Oscillation

ANOTHER EXAMPLE OF PCA: NORTH ATLANTIC OSCILLATION (NAO)

North Atlantic Sea Level Pressure (SLP) in winter season Dec-Mar

Explained varianceof the first EOF* mode:

41.9% of the gridded SLPvariability is representedby the first eigenvector.

Note: EOF (“Empirical Orthogonal Functions” is the more popular term in atmospheric sciences)= PCA

The eigenvector

Hurrell, James & National Center for Atmospheric Research Staff (Eds). Last modified 02 Dec 2013. "The Climate Data Guide: Hurrell North Atlantic Oscillation (NAO) Index (station-based)." Retrieved from https://climatedataguide.ucar.edu/climate-data/hurrell-north-atlantic-oscillation-nao-index-station-based

The temporal evolution (Principal Component)

CLIMATIC EFFECTS OF A THE NORTH ATLANTIC OSCILLATION (DURING WINTER)

(Timm 2003)

EFFECTS OF NAO ON WINTER TEMPERATURES

Source:http://www.climate.gov/news-features/climate-current-events/winter-temperatures-influenced-north-atlantic-oscillation-la (retrieved 2014-04-22)

A negative phase of the NAO (Weaker Island Low and weaker Azores High)causes cooler than normal winter temperature. But other modes of variability affect the NA winter climate(Polar vortex , blocking events etc.)

“This latest cold outbreak was one case where they [the Arctic Oscillation and NAO] were not in strong alignment; in early January 2014, the NAO index was near zero.” Quote from http://www.climate.gov/news-features/event-tracker/how-polar-vortex-related-arctic-oscillation (retrieved 2014-04-22)

WHAT IS NEEDED TO TEST A ‘HYPOTHESIS’ ?

A scientific proposition / hypothesis A ‘controlled’ experiment (if possible) A measurement (repeated samples) A statistical formalism including a

Null hypothesis Alternative hypothesis (or hypotheses)

THE STATISTICAL PROBLEM:Common phrases of hypotheses (propositions) : Are they suitable for statistical tests?

“Temperatures have gone up in the last 50 years!”

“Rainfall extreme events have increased in the recent years!”

“Smoking causes cancer!”

El Niño has an impact on NY winter climate!

“The start of the growing season has shifted over the last decades!”

“Winter temperatures at Albany are more variable than in New York City!”

“Man-made climate change is real!”

“There is a 50% chance that global warming is real!”

“We can expect a100-year extreme rainfall event to happen in the next 100 years!”

THE STATISTICAL PROBLEM:

“Temperatures have not changed in the last 50 years!”

“Rainfall extreme events have not changed in the recent years!”

“Smoking does not increase the risk of cancer!”

El Niño has no impact on NY winter climate!

“The start of the growing season has not shifted over the last decades!”

“Winter temperatures at Albany and in New York City have the same variance”

“Man-made climate change is real!” One can argue for it based on physical principles.How strong and what changes to expect is another issue]

“There is a 50% chance that global warming is real!”

“We can expect a100-year extreme rainfall event to happen in the next 100 years !”

“Statistical tests are designed to disprove a Null hypothesis”

THE STATISTICAL PROBLEM:

“We can expect a100-year extreme rainfall event to happen in the next 100 years!”

“Statistical tests are designed to disprove a hypothesis”

Let’s see what makes this propositions impossible to falsify statistically:

(1)First of all the phrase “we can expect” signals a subjective statement.

(Like last weeks false fire alarm in the building: Probably most of us expected a false alarm, but those who had sincere concerns were not wrong in ‘expecting’ a real emergency situation.[Or otherwise the fire alarm would be useless, if it was not able to set off alarms in case of a fire]

(2) A hundred-year extreme rainfall event does not mean it must happen within 100 years.(Like you cannot expect while throwing dices that ‘6’ appears on every 6th trial.)

THE STATISTICAL PROBLEM:“Statistical tests are designed to disprove a hypothesis”

Let’s see what makes this propositions impossible to falsify statistically:

(1)First of all the phrase “there is a chance” signals: We do not consider a priori thatone or the other statement is a certain event or fact.(2) The term ‘is real’ is too vague to express a null hypothesis that we could disprove and then accept the above hypothesis!(3) NOTE: Even if we had a 1% or 10 or 50% as a number, the problem would be the same.

But let’s assume we would try to falsify the null hypothesis: “There is not a 99.9% chance that global warming is real!” We would start looking for samples from around the worldand find ‘0.1%’ evidence against a global warming signal? The warming hiatus of the last 10-12 years would be one good piece of evidence. But is it sufficient? Is enough to argue there is more than 0.1% chance of global warming not being real? Not with any objective statistical measure.

“There is a 99.9% chance that global warming is real!”

THE STATISTICAL PROBLEM:“Statistical tests are designed to disprove a hypothesis”

This formulation (no matter how you choose the % number) in this type of proposition is very hard to approach with statistical methods. The problem is with the word ‘real’.What is ‘real’ or ‘not real’ is most often tied to a subjective ‘emotional’ a priori opinion.*

Better would be: “There is no warming trend in the global mean temperaturesfrom 1900-present.”

(* You are welcome to challenge this point of view!)

“There is a 50% (or 99.9%) chance that global warming is real!”

HYPOTHESIS TESTING

Example: http://video.pbs.org/video/2365222887/

From PBS NOVA: “Inside Animal Minds: Dogs & Super

Senses” (2014-04-22) How do birds avoid collisions with objects? (video from minute 27:30 to 33:00)

WHAT IS NEEDED TO TEST A ‘HYPOTHESIS’ ?

Watch the scientific experiment shown in the clip

What is the scientific ‘proposition’? How is the experimental setup

designed? What is the measurement? How often is the measurement

repeated?

ANSWERS:

ANSWERS:

Experiment

AverageSpeed

Sample size

StandardDeviation

Horizontal stripes

16.5ft/s 10 ? ???

Vertical stripes

15.3ft/s 10 ? ???

TESTING THE SIGNIFICANCE OF THE DIFFERENCES IN THE SPEEDExperimen

tSample

sizen

StandardDeviation

s(guessed)

H. stripes 16.5ft/s 10 1.5

V. stripes 15.3ft/s 10 1

The hypothesis is that there is a systematic difference between the average flight speedsin the two environments!Statistical tests are traditionally formulatedthe opposite way: “There is no difference in the speed”. All measured values are from the same statistical population (distribution)

THE STATISTICAL PROBLEM:

TESTING A NULL HYPOTHESIS

Hypothesis/Conclusion

Null hypothesis H0 true

Null hypothesis H0

false

Null hypothesis accepcted

Correct decision False decision(Type II error)

Null hypothesis rejected

False decision(Type I error)

Correct decision