Table 1. Physical and chemical evaluation of the soil profile of a 1 ha fertirrigated cork oak plot in Avis, Portugal.
Horizon depth
(cm) 		Organic Matter
(%) 		P2O5
(mg kg–1) 		K2O
(mg kg–1) 		Total N
(g kg–1) 		texture
10 3.39 86 350 5.60 Loam
80 0.63 7 94 0.40 Sandy Clay loam
180 0.22 5 60 0.30 Sandy loam
1

Fig. 1. Irricork: The 1 ha experimental cork oak plot divided by fertirrigation treatments, in Avis, Portugal.

Table 2. Results of the trees’ dendrometric measurement performed in 2017 at a 1 ha fertirrigated cork oak plot in Avis, Portugal.
Trees CBH
(cm) 		TH
(m) 		HCB
(m) 		canopy projection
(m2)
Planted in 2003/05
(mean + S.D.) 		Debarked 75.11 ± 11.04 9.26 ± 1.06 6.43 ± 0.45 20.33 ± 8.03
Non-debarked 52.05 ± 17.21 7.18 ± 1.76 4.79 ± 0.49 8.52 ± 5.88
centenary (N. 13) (mean + S.D.) 214.16 ± 46.20 11.29 ± 1.10 7.88 ± 0.68 136.60 ± 56.87
CBH = trees’ circumference at breast height; TH = trees’ total height; HCB = trees’ height to canopy basis
2

Fig. 2. Monthly volume of total water – Precipitation and irrigation – supplied to the cork oak plot in Avis, Portugal over the study period. In 2017 and 2018 “Late fertirrigation” and “Fertirrigation ½” treatments were watered as Fertirrigation 1.

Table 3. Resume of daily fertirrigation by treatment during fertirrigation campaign at a 1 ha fertirrigated cork oak plot in Avis, Portugal, between 2017 and 2020.
Treatment Daily fertirrigation (mm)
Mean Maximum Minimum Standard Deviation
Fertirrigation 1 1.29 2.91 0.01 0.78
Fertirrigation ½ 0.55 1.31 0.01 0.36
Late Fertirrigation 1.01 2.65 0.01 0.76
Table 4. Resume of collected data and calculated parameters at a 1 ha fertirrigated cork oak plot in Avis, Portugal, between 2017 and 2020.
Variables Collected data Average values Calculated parameters Average values Periodicity
Dependent Trees’ Radial increment at 130 cm height (0.25 ± 0.21 mm) /15 days 15–30 days
Independent Meteorological Average Air Relative Humidity (raH) 71.35 ± 14.77 % air vapor pressure deficit (VPD) 1.39 ± 0.88 Kpa
Average Air Temperature (aT) 15.67 ± 5.60 °C
Average Solar Irradiance (SI) 179.26 ± 81.84 Wm–2
Sum of Precipitation (Prec) (23 ± 31 mm)/15 days
Treatment Sum of Irrigation (5.2 ± 7.6 mm)/15 days
Subject conditions Trees cork’ age Virgin: 16.40 ± 1.02 years
Secondary: 2.83 ± 1.30 years annual
Trees Circunference at Breast Height (CBH) 0.81 ± 0.03 m Tree Intraspecific Competition (index) 0.15 ± 0.01
Georreferencing lat, long initial
Table 5. Best fitting model of the curve estimation procedure for the relationship between daily stem increment (cm) at 130 height for each environmental factor, measured in a 1 ha fertirrigated cork oak plot in Avis, Portugal, between 2017 and 2020.
Factors Equation M. Summary Parameter estimates Tangential ≥ 0
R2 p-value b1 b2 b3
Av. raH (%) Quadratic 0.16 <0.001 0.050 –4.2E-04 ]-∞, 60.11%]
Av. aT (°C) Cubic 0.22 <0.001 –0.207 0.020 –4.9E-04 [6.95–20.33]
Av. SI (Wm–2) Quadratic 0.19 <0.001 2.2E-04 5.0E-06 [–22.46, +∞[
Av. VPD (Kpa) Quadratic 0.20 <0.001 0.004 –0.001 ]-∞, 2.05]
D. Prec (mm) Quadratic 0.11 <0.001 –0.005 0.001 [4.8, +∞[
Av. = Average; raH = relative air humidity; aT = air temperature; SI = solar irradiance; VPD = air vapor pressure deficit; Prec = precipitation; D. = Daily; M. = Model
3

Fig. 3. Pyramid frequency (number of time units) of cork oak daily stem increments under fertirrigated and non-fertirrigated trees at a 1 ha cork oak plot in Avis, Portugal, during fertirrigation campaigns from 2017–2020. Solid lines represent confidence interval for the medians.

Table 6.1. Generalized linear mixed model estimates of the Independent fixed effects on the daily stem increments (cm) at 130 height measured in a 1 ha fertirrigated cork oak plot in Avis, Portugal, between 2017 and 2020.
Model term Coefficient Std. Error t-student p-value 95% Conf. Interval
lower upper
Intercept –11.117 0.208 –53.351 <0.001 –10.708 –11.525
Cork age (year) –0.052 0.005 –10.608 <0.001 –0.042 –0.062
Initial CBH (cm) 0.018 0.002 8.12 <0.001 0.022 0.014
Av. SI (Wm–2) 0.006 0.001 11.923 <0.001 0.007 0.005
D. Prec (mm) 0.231 0.018 13.086 <0.001 0.266 0.196
(Daily Prec)2 –0.009 0.002 –5.119 <0.001 –0.005 –0.012
Av. VPD (Kpa) 2.588 0.129 20.093 <0.001 2.841 2.336
(Av. VPD)2 –0.646 0.031 –20.893 <0.001 –0.585 –0.706
D. fertirrigation 0.218 0.037 5.93 <0.001 0.291 0.146
(D. fertirrigation)2 0.019 0.014 1.385 0.166 0.045 –0.008
(D. fertirrigation)3 –0.018 0.004 –4.966 <0.001 –0.011 –0.025
IC Hh3 –0.395 0.163 –2.428 0.015 –0.714 –0.076
CBH = circumference at breast height; Av. = Average; SI: solar irradiance; Prec = precipitation; VPD = air vapor pressure deficit; D. = Daily; IC: Intra-competition; Hh3 = Hegyi Competition index based on competition light cone
Table 6.2. Generalized linear mixed model covariance estimates for residual and random effects (repetitions) with first-order autoregressive structure on the daily stem increments (cm) at 130 height measured in a 1 ha fertirrigated cork oak plot in Avis, Portugal, between 2017 and 2020.
Residual effect Coefficient Std. Error Z-test p-value 95% Conf. Interval
lower upper
AR1 Rho 0.320 0.016 19.797 <0.001 0.288 0.351
AR1 Diagonal 0.740 0.018 40.272 <0.001 0.705 0.777
Table 7.1. Generalized linear mixed model estimates of the Independent fixed effects on the daily stem increments (cm) at 130 height measured on non-fertirrigated trees from a cork oak plot in Avis, Portugal, during the 2017–2020 Fertirrigation campaigns.
Model term Coefficient Std. Error t-student p-value 95% Conf. Interval
lower upper
Intercept –4.237 0.53 –7.988 <0.001 –3.196 –5.279
Cork age (year) –0.052 0.007 –7.038 <0.002 –0.038 –0.067
Initial CBH (cm) 0.011 0.004 3.165 0.002 0.018 0.004
Av. SI (Wm–2) 0.013 0.001 8.947 <0.002 0.016 0.01
Av. VPD (Kpa) –4.142 0.405 –10.216 <0.003 –3.346 –4.938
(Av. VPD)2 0.682 0.079 8.641 <0.004 0.837 0.527
CBH = circumference at breast height; Av. = Average; SI = solar irradiance; VPD = air vapor pressure deficit
Table 7.2. Generalized linear mixed model covariance estimates for residual and random effects (repetitions) with first-order autoregressive structure on the daily stem increments (cm) at 130 height measured on non-fertirigated trees from a cork oak plot in Avis, Portugal, between 2017 and 2020.
Residual effect Coefficient Std. Error Z-test p-value 95% Conf. Interval
lower upper
AR1 Rho 0.338 0.045 7.591 <0.001 0.248 0.422
AR1 Diagonal 0.707 0.042 16.782 <0.001 0.629 0.794
Table 8.1. Generalized linear mixed model estimates of the Independent fixed effects on the daily stem increments at 130 height measured on fertirrigated trees from a cork oak plot in Avis, Portugal, during the 2017–2020 fertirrigation campaigns.
model term Coefficient Std. Error t-student p-value 95% Conf. Interval
lower upper
Intercept –8.512 0.95 –8.964 <0.001 –10.376 –6.648
Cork age (year) –0.044 0.006 –6.825 <0.001 –0.056 –0.031
Initial CBH (cm) 0.015 0.003 5.818 <0.001 0.01 0.02
Av. SI (Wm–2) 0.007 0 15.612 <0.001 0.006 0.008
Av. VPD (Kpa) 0.034 0.807 0.042 0.966 –1.549 1.618
(Av. VPD)2 –0.187 0.177 –1.058 0.291 –0.534 0.16
D. fertirrigation (mm) 0.662 0.072 9.246 <0.001 0.522 0.803
(D. fertirrigation)2 0.003 0.015 0.227 0.821 –0.025 0.032
(D. fertirrigation)3 –0.034 0.005 –7.388 <0.001 –0.042 –0.025
CBH = circumference at breast height; Av. = Average; SI = solar irradiance; VPD = air vapor pressure deficit; D. = daily
Table 8.2. Generalized linear mixed model covariance estimates for residual and random effects (repetitions) with first-order autoregressive structure on the daily stem increments (cm) at 130 height measured on fertirrigated trees from a cork oak plot in Avis, Portugal. between 2017 and 2020.
Residual effect Coefficient Std. Error Z-test p-value 95% Conf. Interval
lower upper
AR1 Rho 0.166 0.048 3.481 <0.001 0.071 0.258
AR1 Diagonal 0.436 0.025 17.289 <0.001 0.389 0.489
4

Fig. 4. Relationship between daily fertirrigation (mm) and predicted radial stem increments (cm) at a 1 ha fertirrigated cork oak plot in Avis, Portugal, calculated with the Model 3 “Fertirrigation campaign – fertirrigated trees”, separated by debarked vs non-debarked trees. Lines correspond to Kernel density using Epanechnikov function with 60% points to fit.