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Analysis of sapflow measurements of Larch trees within the inner alpine dry Inn-valley

Analysis of sapflow measurements of Larch trees within the inner alpine dry Inn-valley. PhD student: Marco Leo. Advanced Statistics WS 2010/11. Overview. Background Principle of sapflow measurements Collection of environmental data Statistical analysis of time series data

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Analysis of sapflow measurements of Larch trees within the inner alpine dry Inn-valley

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  1. Analysis of sapflow measurements of Larch trees within the inner alpine dry Inn-valley PhD student: Marco Leo Advanced Statistics WS 2010/11

  2. Overview • Background • Principleofsapflowmeasurements • Collectionof environmental data • Statistical analysisof time seriesdata • Descriptivestatistics • Multiple linear regression • Autocorrelation

  3. Principle of sapflow measurements • Two sensors installed into the sapwood • The top sensor is heated • Temperature difference between the sensors • Calculation of the sapflow density [ml cm2 min] • Relative sapflow for data interpretation ! • Dependent variable

  4. Dependence of environmental parameters • Collected environmental data: (independent variables)

  5. Typical sesonal course of sapflow density

  6. Box plots I

  7. Box plots II

  8. Scatter plots

  9. Multiple linear regression (model VPD2)

  10. y vs. fitted and residuals vs. time

  11. What is Autocorrelation ? Autocorrelation is the correlation of a signal with itself (Parr 1999). part of the data:

  12. Testing Autocorrelation Durbin Watson Test H0 : α = 0 → No Autocorrelation H1 : α ≠ 0 → Autocorrelation durbinWatsonTest(model_LA_2) lag Autocorrelation D-W Statistic p-value 1 0.5097381 0.9703643 0 Alternative hypothesis: rho != 0

  13. Determine the strength of the Autocorrelation • Autocorrelation Function (ACF) • Partial Autocorrelation Function (PACF) Yt = α Yt-1 + εt

  14. Time series model - ARIMA • Elimination of the Autocorrelation • Results: • Summary • Table with coefficients and standard errors

  15. Residual plots

  16. ACF and Partial ACF

  17. Multicollinearity • Variance Inflation Factors (vif) • tolerance = 1/vif

  18. Differential effect of the independent variables bj…regression coefficient Sxj…standard deviation of xj Sy…standard deviation of y

  19. Optimal VPD for sapflow

  20. Helpful R commands/featuresforusing time seriesdata: • Arima model: the output differs from a lm model • Residual diagnostic • plot(model_LA_2$resid,xlab="day of year",main="VPD2 model“) • Create lines to get an overview of diagnostic plots • abline(h=0,col="red") • abline(0,1,col="red")

  21. Thank you for your attention !

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