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 Descriptive statistics Multiple linear regression Autocorrelation

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

Dependence of environmental parameters

Collected environmental data: (independent variables)

Air temperature [°C] (TAIR)

Soil temperature [°C] (TSOIL)

Solar radiation [W m-2] (RAD)

Wind velocity [m s-1] (VWIN)

Soil water potential [MPa] (SWP)

Vapour pressure deficit [hPa] (VPD)

Typical sesonal course of sapflow density

Box plots I

Box plots II

Scatter plots

Multiple linear regression (model VPD2)

y vs. fitted and residuals vs. time

What is Autocorrelation ?

Autocorrelation is the correlation of a signal with itself (Parr 1999).

part of the data:

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

H0 : α = 0 → No AutocorrelationH1 : α ≠ 0 → Autocorrelation

Determine the strength of the Autocorrelation

Autocorrelation Function (ACF)

Partial Autocorrelation Function (PACF)

Yt = α Yt-1 + εt

Time series model - ARIMA Elimination of the Autocorrelation Results:

Summary

Table with coefficients and standard errors

Residual plots

ACF and Partial ACF

Multicollinearity

Variance Inflation Factors (vif)

tolerance = 1/vif

Differential effect of the independent variables

bj…regression coefficient Sxj…standard deviation of xj Sy…standard deviation of y

Optimal VPD for sapflow

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")

Thank you for your attention !