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  Principle of sapflow measurements  Collection of environmental data  Statistical analysis of time series data  Descriptive statistics  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 cm 2 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 VPD 2 )

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 durbinWatsonTest(model_LA_2) lag Autocorrelation D-W Statistic p-value 1 0.5097381 0.9703643 0 Alternative hypothesis: rho != 0 H 0 : α = 0 → No Autocorrelation H 1 : α ≠ 0 → Autocorrelation

13. Determine the strength of the Autocorrelation Autocorrelation Function (ACF) Partial Autocorrelation Function (PACF) Y t = α Y t-1 + ε t

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 b j …regression coefficient S xj …standard deviation of x j S y …standard deviation of y

19. Optimal VPD for sapflow

20. Helpful R commands/features for using time series data: 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 !