Analysis of applicability of Granier’s original equation for calculating the stem sap flux density—Take Populus tomentosa as an example

doi:10.17521/cjpe.2022.0321

Abstract

Abstract:

Aims Thermal dissipation probes (TDP) have been extensively applied in studying forest transpiration. The calculation accuracy of TDP data directly affects the precise quantification of water consumption of trees and stands. Granier’s original equation (F_d = 0.0119K^1.231, F_d is the sap flux density (cm·s^-1), K is the temperature difference coefficient) is a standard method for calculating the data measured by TDP, but its accuracy is questioned. The objective of this study is to systematically understand the applicability of Granier’s original equation to Populus tomentosa and clarify the need for calibration.

Methods With P. tomentosa as the experimental material, this study used the stem-weighing and the whole-tree potometer methods to evaluate the accuracy of Granier’s original equation for different types of TDP probes, and compared the applicability of equations calibrated by various methods.

Important findings Compared with the values measured by the stem-weighing method, the sap flux density calculated by Granier’s original equation was underestimated by 52.3%-61.4% on average. The calibrated equations by the stem-weighing method and the whole-tree potometer method were F_d= 0.0362K^1.870 and F_d = 0.0105K^0.976, respectively. The calibrated equation by one method produced a large deviation when applied to calculate the sap flux density measured by other methods. Relative to the values estimated by Granier’s original equation, the average sap flux density of seven field-grown trees calculated using the whole-tree potometer calibrated equation did not change significantly, but that calculated using the equations calibrated by the stem-weighing method or in other studies became significantly larger. Compared with the sap flux density measured by the whole-tree potometer method, the calculation precision of Granier’s original equation is considerably higher than that of other calibrated equations, and its relative average absolute error and root mean square error were 10% and 0.000 5 cm·s^-1, respectively. In addition, the coefficients of the calibrated equation differed greatly across different trees, but their values were negatively correlated with the length ratio of the probe inserted into the water conducting sapwood. To sum up, it may be necessary to calibrate original Granier’s equation when applying TDP to measure sap flux density. However, the application effects of calibrated equations by different methods varied considerably, indicating that the calibrated equations derived in previous studies have great limitations. Meanwhile, this study did not find sufficient evidence to support the viewpoint that it is necessary to use a calibrated equation for accurately estimate the sap flux density of P. tomentosa, especially considering that no significant difference was observed when using the calibrated equation by the whole-tree potometer method and Granier’s original equation to estimate the sap flux density of field-grown P. tomentosa. Therefore, continued application of Granier’s original equation is recommended for this tree species.

Key words: transpiration, water use, water relation, heat dissipation, poplar

ZHAO Xiao-Ning, TIAN Xiao-Nan, LI Xin, LI Guang-De, GUO You-Zheng, JIA Li-Ming, DUAN Jie, XI Ben-Ye. Analysis of applicability of Granier’s original equation for calculating the stem sap flux density—Take Populus tomentosa as an example[J]. Chin J Plant Ecol, 2023, 47(3): 404-417.

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URL: https://www.plant-ecology.com/EN/10.17521/cjpe.2022.0321

https://www.plant-ecology.com/EN/Y2023/V47/I3/404

Figures/Tables 11

Table 1 Basic information on the stems and their discs where the sap flux density was measured in the stem-weighing method experiment

茎段编号 Stem number	直径 Diameter (cm)	安装探针类型 Sensor type	圆盘面积 Disc area (cm²)	平均边材厚度 Average sapwood depth (cm)	具有导水能力的边材面积 Area of water conducting sapwood (cm²)
1	9.80	TDP-20, TDP-30	72.7	1.2	32.5
2	10.50	TDP-20, TDP-30	86.1	0.9	25.4
3	10.20	TDP-20, TDP-30	87.2	1.5	43.8
4	10.91	TDP-20, TDP-30	97.6	1.9	54.8
5	11.20	TDP-20, TDP-30	103.3	1.2	38.9
6	12.00	TDP-20, TDP-30	111.9	1.1	36.6
7	11.80	TDP-30	106.8	0.8	25.0

Fig. 1 Schematic diagram of the laboratory device used for the stem-weighing method.

Fig. 2 Cross-section of different stem segments after dyeing of Populus tomentosa. The red area in the cross sections indicates the water-conducting sapwood.

Fig. 3 Comparison between the calculated sap flux density by Granier’s original equation and the actual sap flux density measured with the stem-weighing method. R2 and p values represent the linear regression results of stems with data points having corresponding color.

Fig. 4 Degree of underestimation for sap flux density predicted with Granier’s original equation and compared with the actual value measured by the stem-weighing method.

Fig. 5 Calibrated equations for estimating sap flux density of Populus tomentosa using different methods.

Fig. 6 Calibrated equations for estimating sap flux density of Populus tomentosa for different stem azimuth.

Fig. 7 Relationship between the calibrated parameters of Granier’s original equation and the proportion of probe inserted into water-conducting sapwood.

Fig. 8 Verification of Granier’s original equation and other calibrated equations of Populus tomentosa using the data of the stem-weighing method. M1, Granier’s original equation; M2, calibrated equation of stem-weighing method; M3, calibrated equation of whole-tree potometer method; M4, calibrated equation of Ma et al. (2020); M5, calibrated equation of Xie & Wan (2018).

Fig. 9 Verification of Granier’s original equation and other calibrated equations of Populus tomentosa using the data of the whole-tree potometer method. M1, Granier’s original equation; M2, calibrated equation of stem-weighing method; M3, calibrated equation of whole-tree potometer method; M4, calibrated equation of Ma et al. (2020); M5, calibrated equation of Xie & Wan (2018).

Fig. 10 Comparison of sap flux density predicted with Granier’s original equation and other calibrated equations for field grown Populus tomentosa (mean ± SE). Different lowercase letters indicate a significant difference at p <0.05, according to Tukey’s test. M1, Granier’s original equation; M2, calibrated equation of stem-weighing method; M3, calibrated equation of whole-tree potometer method; M4, calibrated equation of Ma et al. (2020); M5, calibrated equation of Xie & Wan (2018).

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