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Fig. 1. Schematic showing experimental set-up with sensor (S1–S24) layout (red arrows). View larger in new window/tab.

Table 1. Independent predictor variables used to model bark surface temperature.
Independent Variable   Unit Data Source
Max temperature (Tmax) Maximum daily temperature °C In situ measurements
Min temperature (Tmin) Minimum daily temperature °C In situ measurements
Mean air temperature (Tmean) Mean daily temperature °C In situ measurements
Sunshine (Sun) Daily sum of sunshine hours hr DWD 2015
Cloud cover (Cloud) Mean daily cloud cover Okta DWD 2015
Wind speed (Wind) Mean daily wind speed m sec–1 DWD 2015
Relative humidity (RH) Mean daily relative humidity % DWD 2015
Solar elevation (Elev) Maximum daily solar elevation Degrees from horizontal NOAA 2015
Height Height on tree bole m In-situ measurements
Table 2. Model parameters: maximum and minimum daily bark surface temperature as a function of max. temperature (Tmax), min. temperature (Tmin), mean air temperature (Tmean), sunshine duration (Sun), cloud cover (Cloud), wind speed (Wind), relative humidity (RH), solar elevation (Elev) and Height.
  Model Included Variables F df R r2adj p AIC
Maximum 1.1 Tmax 23052.0 1,4979 0.907 0.822 <0.001 15543.9
1.2 Tmax, Sun 22205.0 2,4978 0.948 0.899 <0.001 12723.7
1.3 Tmax, Sun, Height 15746.7 3,4977 0.951 0.905 <0.001 12447.3
1.4 Tmax, Sun, Height, Wind 12162.4 4,4976 0.952 0.907 <0.001 12315.7
1.5 Tmax, Sun, Height, Wind, Elev 9944.2 5,4975 0.953 0.909 <0.001 12218.3
1.6 Tmax, Sun, Height, Wind, Elev, RH 8296.5 6,4974 0.953 0.909 <0.001 12214.1
Minimum 2.1 Tmin 113926.5 1,4979 0.979 0.958 <0.001 2151.5
2.2 Tmin, Cloud 59781.8 2,4978 0.980 0.960 <0.001 1921.8
2.3 Tmin, Cloud, Tmean 45176.1 3,4977 0.982 0.965 <0.001 1322.0
2.4 Tmin, Cloud, Tmean, RH 34677.8 4,4976 0.983 0.965 <0.001 1211.5
2.5 Tmin, Cloud, Tmean, RH, Wind 28256.3 5,4975 0.983 0.966 <0.001 1124.2
2.6 Tmin, Cloud, Tmean, RH, Wind, Elev 24164.9 6,4974 0.983 0.967 <0.001 1000.5
2.7 Tmin, Cloud, Tmean, RH, Wind, Elev, Height 20730.5 7,4973 0.983 0.967 <0.001 997.5
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Fig. 2. Stem discs (at 1.3 m above ground level) taken from sun damaged Prunus avium grown within an AFS. True colour images (a and c) and false colour images to highlight tree rings and damaged regions (b and d).

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Fig. 3. Enlarged image displaying primary (red) cambium damage with associated decay, also with secondary (green) and tertiary (blue) damages to cambium tissues in subsequent years.

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Fig. 4. Average maximum and minimum bark surface temperature values with absolute maximum and minimum temperature records between sensor direction and height (Tukey HSD, significance level p < 0.05, Maximum: p-values: a = 0.159, b = 0.172, c = 0.054, d = 0.999 e = 1.000; Minimum: p-values: z = 0.998). View larger in new window/tab.

Table 3. Regression parameters Model 1.6: maximum SW bark surface temperature and model 2.7: minimum SW bark surface temperature using max. temperature (Tmax), min. temperature (Tmin), mean air temperature (Tmean), sunshine duration (Sun), cloud cover (Cloud), wind speed (Wind), relative humidity (RH), solar elevation (Elev) and Height as predictor variables.
Dependent Variable Independent Variables Unstandardised coefficients t p
β SE
Max. Daily Bark Surface Temp.
Model 1.6 Intercept 5.786 0.653 8.863 <0.001
Tmax 0.990 0.010 94.914 <0.001
Sun 0.798 0.017 46.097 <0.001
Height –0.455 0.026 –17.351 <0.001
Wind –0.444 0.038 –11.576 <0.001
Elev 0.041 0.004 9.325 <0.001
RH –0.016 0.006 –2.489 0.013
Min. Daily Bark Surface Temp.
Model 2.7 Intercept –6.361 0.225 –28.291 <0.001
Tmin 0.663 0.011 59.100 <0.001
Cloud 0.222 0.011 19.924 <0.001
Tmean 0.301 0.011 26.327 <0.001
RH 0.037 0.002 17.039 <0.001
Wind 0.148 0.013 11.759 <0.001
Elev 0.018 0.002 11.284 <0.001
Height 0.019 0.008 2.252 0.024
Table 4. Summary of extreme temperature measurements.
Parameter Bark Surface Temp. (Air Temp.*) (°C) Height on tree bole (m) Sensor(s) Nr. Date and Time of occurrence
Unpainted Trees
Max. (SW) 49.1 (31.1) 3.0 12 22.07.13 / 14:25
Max. (NE) 42.3 (34.8) 5.5 14 27.07.13 / 14:30
Min. (SW) –11.8 (–10.5) 5.5 13 29.12.14 / 05:35
Min. (NE) –11.7 (–10.6) 3.0 22 29.12.14 / 05:45
Greatest difference (SW/NE) 14.7 (10.2) 1.0 5/6 02.03.14 / 14:45
Max. range within 24hrs (SW) 38.0 (17.1) 1.0 5 17.04.14 / 24hrs
Painted Trees
Max. (SW) 45.6 (31.1) 3.0 3 22.07.13 / 14:55
Max. (NE) 41.4 (34.8) 3.0 4 27.07.13 / 14:30
Min. (SW) –11.4 (–10.5) 3.0 3 29.12.14 / 05:35
Min. (NE) –11.3 (–9.9) 3.0 4 29.12.14 / 06:25
Greatest difference (SW/NE) 10.2 (4.0) 3.0 17/18 15.03.13 / 14:50
Max. range within 24hrs (SW) 33.8 (22.6) 1.0 1 15.04.15 / 24hrs
Air temperature during study period: mean 10.7 °C, maximum 35.4 °C, minimum: –10.6 °C
* Concurrent air temperature measurement
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Fig. 5. Comparison of painted (sensor 1) vs. unpainted (sensor 5) tree boles in regards to bark surface temperature. View larger in new window/tab.

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Fig. 6. Extreme values for SW (sensor 5) and NE (sensor 6) surface temperature during selected 24 hour periods: a) maximum recorded temperature; b) maximum range; c) large SW temperature variation including sub-zero temperatures. View larger in new window/tab.

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Fig. 7. Model validation: predicted vs. observed values.

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Fig. 8. Modelled daily temperature range for the three successive winters (Nov–Apr) in 2008/09, 2009/10 and 2010/11. View larger in new window/tab.