GEOG3839.9: Climate from trees
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GEOG3839.9: Climate from trees

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    GEOG3839.9: Climate from trees GEOG3839.9: Climate from trees Presentation Transcript

    • temperature water day length
    • THE PRINCIPLE OF CROSS-DATING THE PRINCIPLE OFAGGREGATE TREE GROWTH THE PRINCIPLE OF REPLICATION STANDARDIZATION THE PRINCIPLE OFECOLOGICAL AMPLITUDE THE PRINCIPLE OF SITE SELECTION
    • White pine 1714Photograph: Kurt Kipfmueller
    • C L I M AT E F R O M T R E E SPhotograph: RawheaD Rex
    • empirical Information gained by means ofobservation, experience or experiment.
    • Photograph: Minyoung Choi
    • h p://sokar.geo.umn.edu/weather/
    • Single-site reconstruction
    • A time series is a set of observationsordered in time.
    • time span resolution 10 last century annual 5PDSI 0 chronological uncertainty -5 sub-annual -10 1900 1920 1940 1960 1980 2000 Year (A.D.)
    • variance a statistical measure that describes how a set of numbers vary around their mean. The second moment of a distribution.
    • variance observation sample mean sample size Variance
    • 10 5PDSI 0 -5 -10 1900 1920 1940 1960 1980 2000 Year (A.D.)
    • empirical comparisons
    • thermometers tree ringsSource: Hughes et al., 1999
    • rain gauges tree ringsSource: Hughes and Funkhouser, 1998
    • correlation The Pearson product-momentcorrelation coefficient is probably the singlemost widely used statistic for summarizingthe relationship between two variables.
    • covariance product of both standard deviationsCorrelation Pearson’s product-moment correlation
    • variable ‘Y’ r = +1.0 variable ‘X’
    • variable ‘Y’ r = -1.0 variable ‘X’
    • variable ‘Y’ r = +0.85 variable ‘X’
    • Ring-width index
    • “SHARED”VARIANCE
    • 10 3 2 5 Ringwidth 1PDSI 0 0 -1 -5 -2 -10 -3 1900 1920 1940 1960 1980 2000 Year (A.D.)St. George et al., (2009), Journal of Climate
    • r = 0.62r2 = 0.62 2r2 = 0.38
    • 38% shared variance 10 3 2 5 Ringwidth 1PDSI 0 0 -1 -5 -2 -10 -3 1900 1920 1940 1960 1980 2000 Year (A.D.)St. George et al., (2009), Journal of Climate
    • covariance product of both standard deviationsCorrelation Pearson’s product-moment correlation
    • r = 0.816Source: Wikipedia
    • Single-site reconstruction
    • CORRELATION FUNCTION
    • Source: Kipfmueller, 2008
    • LINEARREGRESSION
    • yt = axt + b + ε
    • the climate variableof interest (at year t) yt = axt + b + ε
    • yt = axt + b + ε the tree-ring variable (at year t)
    • regression weightfor the tree-ring variable yt = axt + b + ε
    • constantyt = axt + b + ε
    • yt = axt + b + ε error of the residual
    • yt = axt + b + ε
    • Ring-width index
    • CLIMATERECONSTRUCTION
    • never trust one tree
    • Multiple-site reconstruction
    • ‘multiple’ linear regressonyt = a1x1t + a2x2t + a3x3t ... + b + ε
    • Network reconstruction
    • yt = axt + b + ε average tree-ring width at many sites (in year t)
    • ‘SHARED’ VARIANCECORRELATION FUNCTION LINEAR REGRESSIONCLIMATE RECONSTRUCTION
    • Tree rings can provide extra-ordinarily good estimates (sometimes)Source: Woodhouse et al., 2006
    • White pine 1714Photograph: Kurt Kipfmueller