Improving the Gross Primary Productivity Estimate by Simulating the Maximum Carboxylation Rate of the Crop Using Machine Learning Algorithms

The current regional-scale process-based photosynthesis models use biome-specified values of maximum carboxylation rate at 25 °C ( $V_{m25}$ ) in simulating ecosystem gross primary productivity (GPP). These models ignore the variations in $V_{m25}$ over time and space, resulting in substantial errors in regional estimates of cropland GPP. Thus, to resolve this problem, we used the ensemble Kalman filter (EnKF) to assimilate tower-based GPP from five maize flux sites into a process-based mode to obtain the “apparent” value of $V_{m25}$ and then modeled this parameter using machine learning (ML) algorithms. The results showed that $V_{m25}$ increased during the early growing season and then decreased after reaching a peak value in the middle of the growing season. The coefficient of determination ( $R^{2}$ ) root mean square error (RMSE) for satellite-driven coupled photosynthesis and evapotranspiration simulator (SCOPES)-Crop with EnKF-derived varied $V_{m25}$ in simulating daily GPP across all site-days increased (decreased) by 0.17 (5.63 $\mu \text {mol}\,\text {m}^{-2}\,\text {s}^{-1}$ ) on average compared to that for the model with fixed $V_{m25}$ . We used four ML algorithms, namely artificial neural network, random forest, extreme gradient enhancement, and convolutional neural network (CNN), to model the $V_{m25}$ of maize. The CNN algorithm yielded the best results. The average of the $R^{2}$ (RMSE) values of simulated GPP using CNN-based $V_{m25}$ over the three flux sites is 0.93 (1.95 $\mu \text {mol}\,\text {m}^{-2}\,\text {s}^{-1}$ ), higher (smaller) than that using fixed $V_{m25}$ . This study implies that representing the seasonal variations in $V_{m25}$ can facilitate improved estimates of GPP and the ML methods are useful tools for modeling the variation in $V_{m25}$ .