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# GEOG3839.9: Climate from trees

## on Feb 24, 2011

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## GEOG3839.9: Climate from treesPresentation 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