## 2 Material and Methods
### Modeling-Based Uncertainty Analysis and Benchmarking  
To assess the efficacy and accuracy of the REddyProc-based gap filling algorithms on NEE and LE, we implemented a series of statistical/machine learning algorithms and benchmarked our results against REddyProc-produced results. In particular, NEE and LE were of primary interests, because both variables could be directly measured by EC systems and later used for GPP/ER partitioning and ET calculation, respectively. To complete this task, we first extracted the high-quality flux data according to the u-star filtering algorithm specified by REddyProc [22] and signal intensity associated with each flux data point, which retained the 30-min flux data that have a signal intensity of at least 60% and a u-star quality flag value of \"zero,\" indicating high-quality data point. Following that, the entire dataset was randomly and evenly partitioned into 10 subsets of similar size (10-fold cross validation, 10-fold CV). Each time, one subset of data were removed from the whole dataset to create artificial gaps and then gap-filled by REddyProc. This process was repeated 10 times until all ReddyProc predicted data were obtained and recombined to form a complete predicted dataset, which was then regressed with the original high-quality dataset for performance evaluation. In particular, we tested three different gap-filling conditions used by REddyProc [22]; including: only the target variables (NEE or LE) are missing but Rg, Tair, and VPD are available (Rg + Tair + VPD); both Tair and VPD are missing but Rg is available (Rg); and all three variables are missing (None) by artificially removing corresponding variable from the input dataset. Meanwhile, we also implemented our own least-square-based linear models (LSLM), artificial neural network models (ANN), and SVM models for gap-filling based on the same 10-fold CV regime. Additionally, 12 easy-to-measure EC-independent (without requiring IRGA or Sonic Anemometer) driver variables (features) were selected for this task, including hour readings, Rg, Tair, Tosoil, RH, VPD, Photosynthetic Photon Flux Density, Soil Heat Flux, Rn, wind speed, precipitation, and SWWC. The rationale for this was that we wanted to evaluate the possibility for accurately predicting high-resolution (30 min) flux data just based on easy-to-measure environmental variables without relying on high-cost IRGA or sonic anemometer. For the linear model, we used the least-square leaner, sparse-reconstruction-by-separable-approximation optimizer, and lasso-based regularization. For ANN, we constructed feedforward neural net with three hidden layers with ten, eight, and five neurons within each layer, respectively. For SVM, we used Gaussian kernel with grid-search optimizer identified hyper-parameters on standardized data. Additionally, instead of using the entire nine-subset training data,we also tested the performance of using just the 7- or 14-day flanking window (FW) around the artificial gap for model training processes, which closely mirror the gap-filling algorithms (dt \(\leq\) 7 or 14 days) used by REddyProc [22]. Modeling performances were evaluated based on simple linear regression analysis between the predicted data and original data, and the final R\({}^{2}\) and RMSE were presented. The overall data analysis scheme is summarized in Figure 2.