analysis of sapflow measurements of larch trees within the inner alpine dry inn-valley
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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 - PowerPoint PPT PresentationTRANSCRIPT
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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
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Overview
Background Principle of sapflow measurements Collection of environmental data
Statistical analysis of time series data Descriptive statistics Multiple linear regression Autocorrelation
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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
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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)
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Typical sesonal course of sapflow density
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Box plots I
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Box plots II
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Scatter plots
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Multiple linear regression (model VPD2)
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y vs. fitted and residuals vs. time
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What is Autocorrelation ?
Autocorrelation is the correlation of a signal with itself (Parr 1999).
part of the data:
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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
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Determine the strength of the Autocorrelation
Autocorrelation Function (ACF)
Partial Autocorrelation Function (PACF)
Yt = α Yt-1 + εt
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Time series model - ARIMA Elimination of the Autocorrelation Results:
Summary
Table with coefficients and standard errors
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Residual plots
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ACF and Partial ACF
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Multicollinearity
Variance Inflation Factors (vif)
tolerance = 1/vif
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Differential effect of the independent variables
bj…regression coefficient Sxj…standard deviation of xj Sy…standard deviation of y
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Optimal VPD for sapflow
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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")
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Thank you for your attention !