Analysis of the applicability of the original Granier formula for stem sap flow in Pinus tabuliformis

Background Accurate measurement of tree transpiration is critical for understanding plant-water interactions and ecosystem water budgets. The Granier equation, widely used in thermal dissipation probe (TDP) systems and developed for temperate conifers, brings significant errors when applied to other species. Pinus tabuliformis, a keystone species in northern China's ecological restoration, lacks validation of TDP accuracy under field conditions. This study, conducted in Baoding, Hebei province, a region characterized by a warm-temperate monsoon climate, aimed to evaluate and recalibrate the original Granier formula for P. tabuliformis to address systematic underestimation issues in sap flow measurements.

Methods Three healthy P. tabuliformis trees with similar morphological characteristics were selected and transplanted into root-control containers to minimize root disturbance. Sap flow was monitored using TDP (model AV-3665R), while transpiration was simultaneously measured using a whole-tree container weighing method (precision: 20 g) from July 11 to 15, 2023. Sapwood area was measured to standardize flow rates. The thermal dissipation coefficient (K) derived from TDP was regressed against gravimetric transpiration to recalibrate the original Granier equation. Data were processed using Excel 2022 and Origin 2021, with ANOVA used to assess significance (α = 0.05).

Results 1) Continuous measurements from 11–13 July showed that TDP-derived and gravimetric time series shared the same diurnal pattern, both peaking at 11:00–12:00, but the original Granier equation (F_d = 0.0119 K^1.231) produced substantially lower magnitudes than whole-tree weighing. Across three experimental trees, the original formula underestimated sap flux density by an average of 69.1% (mean absolute difference 0.691 cm³/(cm²·s), indicating a large, systematic negative bias in TDP estimates for P. tabuliformis despite matching temporal dynamics. 2) Regression of the thermal dissipation coefficient K against gravimetric transpiration (nonlinear fitting) yielded a species-specific calibration: F_d = 0.0126 K^0.6697 (R² = 0.7059, P < 0.01). The fitted coefficient α = 0.0126 is close to the original constant, whereas the fitted exponent β = 0.6697 differs markedly from the original 1.231, reflecting altered K–F_d sensitivity for this species and implying the influence of P. tabuliformis xylem/thermal properties on the K–flux relationship. 3) Validation using an independent dataset (14–15 July) demonstrated the calibrated model's superior predictive performance: corrected TDP estimates closely matched weighing-derived transpiration (model fit R² > 0.95; mean relative error −0.43%), while residual analysis showed standardized residuals within ± 2. Comparison of daily patterns across the three calculation methods also produced high synchronicity (daily R² > 0.85, P < 0.01), confirming that the calibration primarily corrected magnitude bias and substantially improved quantitative agreement between TDP-based fluxes and whole-tree gravimetric measurements.

Conclusions The corrected Granier quation substantially improves the accuracy of sap flow measurements in P. tabuliformis, resolving the 69.1% underestimation observed with the original model. This validated calibration provides a reliable methodological framework for assessing transpiration in conifer species and enhances the precision of ecohydrological evaluations and soil-water conservation planning.