In this study, land surface temperature (LST) and leaf area index (LAI) observations are merged with a coupled two-source surface energy budget–vegetation dynamic model (TSEB–VDM) via a variational data assimilation (VDA) system to predict turbulent heat fluxes and gross primary productivity (GPP). The TSEB and VDM are coupled by relating photosynthesis in the VDM to transpiration in the TSEB equation. Unknown parameters of the VDA approach are the neutral bulk heat transfer coefficient (C_HN), evaporative fractions for soil and canopy (EF_S and EF_C), and specific leaf area (c_g). The VDA approach is evaluated at six AmeriFlux sites with distinct vegetative and climatic characteristics. The modeled sensible (H) and latent (LE) heat fluxes, and GPP agree well with the corresponding eddy covariance measurements in different environmental conditions. The six-site average root mean square error (RMSE) of estimated daily H, LE, and GPP is 42.2 W m⁻², 51.5 W m⁻², and 1.8 gC m⁻² d⁻¹, respectively. The outcomes show that the developed VDA approach is able to exploit the implicit information in the sequences of LST and LAI measurements to estimate H, LE, and GPP. Our findings also indicate that the estimates of the H and LE are more sensitive to uncertainties in LST measurements, while the GPP retrievals are more affected by uncertainties in the LAI observations.

中文翻译：

---

通过同化地表温度和叶面积指数估算湍流热通量和总初级生产力

在这项研究中，地表温度 (LST) 和叶面积指数 (LAI) 观测值与耦合的双源表面能量收支 - 植被动态模型 (TSEB-VDM) 通过变分数据同化 (VDA) 系统合并，以预测湍流。热通量和总初级生产力 (GPP)。TSEB 和 VDM 通过将 VDM 中的光合作用与 TSEB 方程中的蒸腾作用联系起来。VDA 方法的未知参数是中性体积传热系数 ( C _HN )、土壤和冠层的蒸发分数（EF _S和 EF _C）以及比叶面积（c _g）。VDA 方法在六个具有不同植被和气候特征的 AmeriFlux 站点进行了评估。模型化的理智（H ) 和潜热 (LE) 热通量，以及 GPP 与不同环境条件下相应的涡度协方差测量结果非常吻合。估计的每日H、LE 和 GPP的六站点平均均方根误差 (RMSE) 分别为 42.2 W m ^-2、51.5 W m ^-2和 1.8 gC m ^-2  d ^-1。结果表明，开发的 VDA 方法能够利用 LST 和 LAI 测量序列中的隐含信息来估计H、LE 和 GPP。我们的研究结果还表明，H的估计 和 LE 对 LST 测量的不确定性更敏感，而 GPP 反演更受 LAI 观测不确定性的影响。