Class 9, Statistics in paleoclimatology

GEOG5426 Statistics in paleoclimatology

November 24

Brief (15-minute) summaries of project topics.

(1) What are the most important features of the modern climate in your region?

(2) What proxies are available in your region, over the time interval specified? How are they related to climate? and

(3) How different were past climates from modern conditions? Why is that important?

GEOG5426 Statistics in paleoclimatology

A time series is a set of observations ordered in time.

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PDSI

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PDSI

resolutionannual

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chronological uncertaintysub-annual

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PDSItime spanlast century

Variance

samplesize

variance observation

sample mean

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Ring

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PDSI Ringwidth

drought-sensitive tree-ring records Eastern Canadian Rockies

St. George et al., (2009), Journal of Climate

Correlation Pearson’s product-moment correlation

covariance

product of both standard deviations

Source: Wikipedia

r = 0.816

statisticalsignificance

practicalsignificance

nnumber of observations

Source: Wikipedia

T I M E S E R I E S T E R M I N O L O G Y

Trends are progressive increases or decreases in the levels of a particular climate variable.

Bartlein 2006

Trends Bartlein (2006)

Steps are abrupt transitions from one level to the other, relative to the timescale of variations under investigations.

Bartlein 2006

Steps Bartlein (2006)

Oscillations are either periodic or quasi-periodic variations about a stationary or slowly changing level.

Bartlein 2006

Oscillations Bartlein (2006)

Fluctuations are aperiodic variations of climate that appear at all timescales (but tend to be more evident at shorter timescales).

Bartlein 2006

Fluctuations Bartlein (2006)

Events are variations that return rapidly to a previous state. Because events are reversible, they are distinct from steps.

Bartlein 2006

Events Bartlein (2006)

A U T O C O R R E L AT I O N

Correlation Pearson’s product-moment correlation

covariance

product of both standard deviations

Autocorrelation describes the correlation of a time series with its own past and future values.

Autocorrelation

covariance

product of the standard deviation

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Ringwidthlag-0 autocorrelation

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Ringwidthlag-1 autocorrelation

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Ringwidthlag-2 autocorrelation

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Ringwidthlag-3 autocorrelation

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10PDO index Mexican PDSI

IF a time series (of length N) is significantly autocorrelated, then:

The series is not random in time

Each observation is not independent from other observations

The number of independant observations is fewer than N

The “effective sample size” is an estimate of the “real” number of observations a!er adjusting for the effects of autocorrelation.

Effective sample size

samplesize

effectivesample

sizefirst-order

autocorrelation

T H E S P E C T R U M O F C L I M AT E

The spectrum of a time series is the distribution of variance of the series as a function of frequency.

redorangegreenbluevioletyellow

redorangegreenbluevioletyellow

shortwavelengths

longwavelengths

redorangegreenbluevioletyellow

Fastchanges

slowchanges

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example of a ‘white’ time series

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example of a ‘red’ time series

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example of a ‘blue’ time series

“White”

“Red”

“Blue”

Schematic variance spectrum of climate variations Bartlein 2006

Schematic variance spectrum of climate variations Bartlein 2006

BIG changes

LITTLE changes

Schematic variance spectrum of climate variations Bartlein 2006

FASTSLOW

S P E C T R A L A N A LY S I S

Source: Burroughs, Weather Cycles: Real or Imaginary?

Source: Burroughs, Weather Cycles: Real or Imaginary?

Source: Burroughs, Weather Cycles: Real or Imaginary?

Source: Burroughs, Weather Cycles: Real or Imaginary?

frequency (cpy)

Source: Burroughs, Weather Cycles: Real or Imaginary?

Source: Burroughs, Weather Cycles: Real or Imaginary?

Source: Burroughs, Weather Cycles: Real or Imaginary?

Source: Burroughs, Weather Cycles: Real or Imaginary?

Source: Burroughs, Weather Cycles: Real or Imaginary?

evolutive spectra

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4 Imagine a ‘window’ passing through your data

Evolutionary spectra for the global 018 record Bartlein 2006

Evolutionary spectra for the global 018 record Bartlein 2006

Evolutionary spectra for the global 018 record Bartlein 2006

Evolutionary spectra for the global 018 record Bartlein 2006

Evolutionary spectra for the global 018 record Bartlein 2006

cone ofinfluence

cone ofinfluence

what?compared to

“Red”

Source: Shanahan et al., 2009, Science

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example of a ‘white’ time series

X

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example of a ‘red’ time series

Source: Shanahan et al., 2009, Science

statisticalsignificance

physicalsignificance

The history of meteorology is li"ered with whitened bones of claims to have demonstrated the existence of reliable cycles in the weather.

“”

William James Burroughs