Table 1. Measurements from SMEAR II station. The Manual selection indicates subjective pre-selection to the any time model by LARS (see 2.4.2).
Manual
selection 		Variable Abbreviation Units Specifications Missing
values
√ Precipitation Prec mm includes snow 1%
√ Air temperature T °C   –
  Atmospheric pressure P hPa   –
√ Air relative humidity RH %   –
  CO2 concentration in air CO2 ppm   –
  Water vapour in air H2O ppth   –
  Soil volumetric water content MO m3 m–3 O horizon 50%
√ Soil volumetric water content MA m3 m–3 A horizon 50%
  Soil volumetric water content MB m3 m–3 B horizon 50%
  Soil volumetric water content MC m3 m–3 C horizon 50%
  Soil temperature TO °C O horizon 1%
  Soil temperature TA °C A horizon 1%
√ Soil temperature TB °C B horizon 1%
  Soil temperature TC °C C horizon 1%
√ Net ecosystem exchange NEE μmol m–2 s–2 for CO2 –
√ Total ecosystem exchange TER μmol m–2 s–2 for CO2 –
√ Gross primary production GPP μmol m–2 s–2 for CO2 –
√ Evapotranspiration ET μmol m–2 s–2   1%
  Sensible heat flux H W m–2   –
  Vapour Pressure Deficit VPD kPa   –
√ Global shortwave radiation SW W m–2   9%
  Reflected shortwave radiation SWR W m–2   10%
√ Photosynthetically active radiation PAR μmol m–2 s–2 400–700 nm –
  Reflected PAR PARR μmol m–2 s–2   11%
  Ultraviolet A UVA W m–2 320–400 nm 6%
  Ultraviolet B UVB W m–2 280–320 nm 7%
√ Snow depth dsnow cm   3%
√ Snow presence Snow present/absent   3%
  Wind speed WS m s–1   –
  wind direction E–W WDEW ° cos of direction 8%
  wind direction N–S WDNS ° sine of direction 8%
1

Fig. 1. Standardized response variables i.e. indices for ring width (RWI) and height increment (HII).

2

Table 2a. Predictive accuracies of explanatory variables for the ring width indices. Cons. indicates the consistency index for the best time, R2 fit the coefficient of determination of the model fit on all data and R2 test the coefficient of determination of leave-one-out cross-validation testing. The abbreviations are introduced in Table 1.
Feature Best time Cons. R2 fit R2 test
Prec. Dec 4 – Dec 31 [y-1] 1 0.44 0.35
T Jan 2 – Jan 29 [y-1] 0.9 0.37 –0.17
P Dec 4 – Dec 31 [y-1] 0.9 0.3 –0.91
RH May 22 – Jun 18 [y-1] 0.4 0.22 –2.23
CO2 Aug 13 – Sep 9 0.8 0.02 –0.62
H2O Aug 14 – Sep 10 [y-1] 0.8 0.3 –0.48
MO Jul 3 – Jul 30 [y-1] 0.8 0.14 –0.73
MA May 22 – Jun 18 [y-1] 0.8 0.12 –0.56
MB May 22 – Jun 18 [y-1] 0.9 0.23 –0.13
MC May 22 – Jun 18 [y-1] 0.9 0.26 –0.04
TO Jul 2 – Jul 29 0.3 0.17 –1.28
TA Jan 16 – Feb 12 [y-1] 0.9 0.34 –0.68
TB Jan 16 – Feb 12 [y-1] 0.9 0.43 –0.07
TC Jan 2 – Jan 29 [y-1] 0.8 0.3 –0.37
NEE Apr 9 – May 6 1 0.38 0.2
TER Aug 13 – Sep 9 0.6 0.25 –0.98
GPP Apr 9 – May 6 1 0.42 0.26
ET Jan 2 – Jan 29 [y-1] 0.6 0.12 –1.45
H Jan 2 – Jan 29 [y-1] 0.9 0.39 –0.06
VPD May 22 – Jun 18 [y-1] 0.4 0.16 –1.23
SW Nov 20 – Dec 17 [y-1] 0.6 0.3 –1.33
SWR Apr 23 – May 20 1 0.4 0
PAR May 22 – Jun 18 [y-1] 0.8 0.22 –0.66
PARR Aug 28 – Sep 24 [y-1] 0.8 0.26 –0.96
UVA Nov 20 – Dec 17 [y-1] 0.7 0.28 –0.93
UVB Nov 20 – Dec 17 [y-1] 0.4 0.26 –1.31
dsnow Apr 24 – May 21 [y-1] 0.8 0.24 –5.28
Snow Apr 24 – May 21 [y-1] 0.7 0.15 –3.77
WS Apr 9 – May 6 0.6 0.2 –1.29
WDEW Jun 5 – Jul 2 [y-1] 0.9 0.18 –1.74
WDNS Sep 25 – Oct 22 [y-1] 0.9 0.09 –1.22
Table 2b. Predictive accuracies of explanatory variables for height growth indices. Columns as in Table 2a.
Feature Best time Cons. R2 fit R2 test
Prec. Jan 16 – Feb 12 [y-1] 0.8 0.25 –1.24
T Jul 3 – Jul 30 [y-1] 0.4 0.26 –2.19
P Feb 12 – Mar 11 0.4 0.32 –0.66
RH Jun 4 – Jul 1 0.9 0.36 –0.84
CO2 Aug 13 – Sep 9 0.5 0.01 –0.92
H2O Apr 23 – May 20 0.9 0.3 –0.82
MO Jun 4 – Jul 1 0.6 0.14 –1.19
MA Jun 4 – Jul 1 0.3 0.12 –1.32
MB May 8 – Jun 4 [y-1] 0.4 0.17 –1.15
MC May 22 – Jun 18 [y-1] 0.8 0.13 –1.2
TO Jan 16 – Feb 12 [y-1] 0.9 0.29 –0.84
TA Jan 2 – Jan 29 [y-1] 0.8 0.25 –1.21
TB Jan 2 – Jan 29 [y-1] 0.9 0.22 –0.62
TC Nov 20 – Dec 17 [y-1] 0.3 0.08 –1.2
NEE Jul 31 – Aug 27 [y-1] 0.9 0.42 0.14
TER Mar 26 – Apr 22 0.6 0.29 –0.83
GPP Jul 31 – Aug 27 [y–1] 0.9 0.38 –0.27
ET Jun 18 – Jul 15 0.8 0.22 –0.71
H Jan 2 – Jan 29 [y-1] 0.8 0.34 –0.76
VPD Jun 4 – Jul 1 0.7 0.4 –0.78
SW Jul 31 – Aug 27 [y-1] 0.7 0.31 –0.78
SWR Sep 25 – Oct 22 [y-1] 0.6 0.31 –1.59
PAR Jul 3 – Jul 30 [y-1] 0.9 0.39 –0.14
PARR Nov 20 – Dec 17 [y-1] 0.9 0.46 –0.09
UVA Jan 29 – Feb 25 0.9 0.43 –0.79
UVB Apr 10 – May 7 [y-1] 1 0.51 0.31
dsnow Nov 6 – Dec 3 [y-1] 0.4 0.17 –5.13
Snow Apr 9 – May 6 0.9 0.38 –0.6
WS Mar 12 – Arp 8 0.6 0.21 –1.02
WDEW Sep 25 – Oct 22 [y-1] 0.8 0.29 –0.2
WDNS Jun 19 – Jul 16 [y-1] 0.9 0.28 –0.34
Table 3. Predictive accuracy of selected models with 1–4 predictors for the ring width and height growth indices by the greedy approach. The abbreviations are introduced in Table 1. The used periods are as in Table 2 a and b.
  Predictor R2 fit R2 test
1 2 3 4
Ring width Prec. MC GPP H 0.81 0.52
H2O MC TB NEE 0.92 0.48
Prec. TB TC ET 0.70 0.41
T MB MC SWR 0.75 0.38
H2O H SWR - 0.67 0.36
Prec. NEE - - 0.59 0.35
H2O MB TC GPP 0.28 0.84
MO TB SWR - 0.17 0.57
Height growth PARR UVB dsnow Snow 0.81 0.63
MA GPP H UVB 0.89 0.60
H2O TB NEE PAR 0.74 0.46
Prec. RH TER UVB 0.84 0.38
PAR UVB - - 0.63 0.33
H2O GPP SWR PARR 0.77 0.31
MB TA NEE H 0.17 0.79
NEE PARR WD - 0.15 0.64
3

Fig. 3. Accuracy of fit and test models by LARS (see 2.4.2) as a function of the number of included variables.

4

Fig. 4. Analysis of variable selection by LARS in three types of any-time models with different number of candidate predictors (BB, MS and TR). The vertical axis lists variables and the horizontal axis times of year. Black-lined rectangles indicate the most probable actual growing period (Schiestl-Aalto et al. 2015). For time reference, the mean temperature over time is plotted in the middle of the models. Each square is an average over 15–16 models obtained using leave-one-out cross-validation procedure. Blue squares indicate negative relations, and red squares indicate positive relations. Darker colours encode more stable (consistent) performance over multiple trials. Abbreviations are introduced in Table 1. View larger in new window/tab.