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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 !