temperature water day length

THE PRINCIPLE OF

ECOLOGICAL AMPLITUDE

THE PRINCIPLE OF

SITE SELECTION

THE PRINCIPLE OF

AGGREGATE TREE GROWTH

THE PRINCIPLE OF

REPLICATION

STANDARDIZATION

THE PRINCIPLE OF

CROSS-DATING

White pine 1714

Photograph: Kurt Kipfmueller

C L I M AT E F R O M T R E E S

Photograph: RawheaD Rex

empirical Information gained by means of observation, experience or experiment.

Photograph: Minyoung Choi

h!p://sokar.geo.umn.edu/weather/

Single-site reconstruction

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

1900 1920 1940 1960 1980 2000

Year (A.D.)

-10

-5

0

5

10

PDSI

resolutionannual

chronological uncertaintysub-annual

time spanlast century

a statistical measure that describes how a set of numbers vary around their mean.

The second moment of a distribution.

variance

Variance

samplesize

variance observation

sample mean

1900 1920 1940 1960 1980 2000

Year (A.D.)

-10

-5

0

5

10

PDSI

empirical comparisons

Source: Hughes et al., 1999

tree rings

thermometers

Source: Hughes and Funkhouser, 1998

tree rings

rain gauges

correlation The Pearson product-moment correlation coefficient is probably the single most widely used statistic for summarizing the relationship between two variables.

Correlation Pearson’s product-moment correlation

covariance

product of both standard deviations

variable ‘X’

variable ‘Y’ r = +1.0

variable ‘X’

variable ‘Y’ r = -1.0

variable ‘X’

variable ‘Y’r = +0.85

Ring-width index

“SHARED”VARIANCE

1900 1920 1940 1960 1980 2000

Year (A.D.)

-10

-5

0

5

10

PDSI

-3

-2

-1

0

1

2

3

Ring

wid

th

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

r = 0.62 r2 = 0.622

r2 = 0.38

1900 1920 1940 1960 1980 2000

Year (A.D.)

-10

-5

0

5

10

PDSI

-3

-2

-1

0

1

2

3

Ring

wid

th

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

38% shared variance

Correlation Pearson’s product-moment correlation

covariance

product of both standard deviations

Source: Wikipedia

r = 0.816

Single-site reconstruction

CORRELATIONFUNCTION

Source: Kipfmueller, 2008

LINEARREGRESSION

yt = axt + b + ε

yt = axt + b + ε

the climate variable of interest (at year t)

yt = axt + b + ε

the tree-ring variable (at year t)

yt = axt + b + ε

regression weight for the tree-ring

variable

yt = axt + b + ε

constant

yt = axt + b + ε

error of the residual

yt = axt + b + ε

Ring-width index

CLIMATERECONSTRUCTION

never trust one tree

Multiple-site reconstruction

yt = a1x1t + a2x2t + a3x3t ... + b + ε

‘multiple’ linear regresson

Network reconstruction

yt = axt + b + ε

average tree-ring width at many sites

(in year t)

‘SHARED’ VARIANCE

CORRELATION FUNCTION

LINEAR REGRESSION

CLIMATE RECONSTRUCTION

Source: Woodhouse et al., 2006

Tree rings can provide extra-ordinarily good estimates (sometimes)

White pine 1714

Photograph: Kurt Kipfmueller