GEOG3839.9: Climate from trees

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