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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Year (A.D.)
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PDSI
1900 1920 1940 1960 1980 2000
Year (A.D.)
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PDSI
resolutionannual
1900 1920 1940 1960 1980 2000
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PDSI
chronological uncertaintysub-annual
1900 1920 1940 1960 1980 2000
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PDSItime spanlast century
Variance
samplesize
variance observation
sample mean
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PDSI
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Ring
wid
th
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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Ring
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Ringwidthlag-0 autocorrelation
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Ring
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Ringwidthlag-1 autocorrelation
1900 1920 1940 1960 1980 2000
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Ring
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Ringwidthlag-2 autocorrelation
1900 1920 1940 1960 1980 2000
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Ring
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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
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