## 2 Data and Methods  
### In-Situ Data  
The daily observed GPP and ET data collected from the US-Ne1, US-Ne2, US-Ne3, US-Ro1, and US-Ro5 sites from the FLUXNET2015 dataset ([[http://fluxnet.fluxdata.org/](http://fluxnet.fluxdata.org/)]([http://fluxnet.fluxdata.org/](http://fluxnet.fluxdata.org/)), accessed on 7 October 2023) and AmeriFlux dataset ([[https://americflux.lbl.gov/](https://americflux.lbl.gov/)]([https://americflux.lbl.gov/](https://americflux.lbl.gov/)), accessed on 7 October 2023), which were planted with C4 maize and C3 soybean, were used for evaluating the GPP, ET, and eWUE estimates from the coupled PMLv2 and uncoupled MODIS products. The sites were selected by the following criteria: (1) the sites planted by C4 maize or C3 soybean or maize-soybean rotation, and (2) the land cover type extracted from the MODIS Land Cover Type Yearly L3 Global 500m product (MCD12Q1) corresponding to the site is croplands, which will affect the coefficients for estimating ET and GPP as well as eWUE. Please see Table 1 and Figure 1 for a detailed description of these five cropland sites. The daily daytime partitioning method-based GPP (termed 'GPP_DT_VUT_REF') and daily gap-filled ET using the Marginal Distribution Sampling (MDS) method (termed 'LE_F_MDS') were chosen for analysis. The provided daily quality control (QC) flag for observed GPP and ET (termed 'NEE_VUT_REF_QC' and 'LE_F_MDS_QC', respectively) was used to eliminate the poor-quality in-situ observations. Specifically, the daily GPP and ET were summed up to an eight-day scale, and the daily QC flag for observed GPP and ET (ranging from 0 to 1; the higher QC flag represents that the quality of daily observed GPP and ET data is higher) in every 8 days was averaged. Only the eight-day observed GPP and ET with eight-day average QC flags higher than 0.75 were collected for evaluating the eight-day GPP, ET, and eWUE from the RS products to avoid the uncertainty that might be introduced by the inaccurate in-situ observation as much as possible.  
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline
**Site ID** & **Site Name** & **Longitude** & **Latitude** & **Elevation** & **Time** & **Maize Year** & **Soybean Year** & **Dataset** \\ \hline \multirow{3}{*}{US-Ne1} & \multirow{3}{*}{\begin{tabular}{l} Mead—irrigated \\ continuous \\ maize site \\ \end{tabular} } & \multirow{3}{*}{\(-\)96.4766} & \multirow{3}{*}{41.1651} & \multirow{3}{*}{361 m} & \multirow{3}{*}{2001–2020} & \multirow{3}{*}{2001–2020} & \multirow{3}{*}{\(-\)} & AmeriFlux \\  & & & & & & & 2001, 2003, \\  & & & & & & 2005, 2007, & 2002, 2004, \\  & & & & & 2009, 2010, & 2006, 2008 \\ \multirow{3}{*}{US-Ne2} & \multirow{3}{*}{\begin{tabular}{l} Mead—rainfed \\ maize–soybean \\ rotation site \\ \end{tabular} } & \multirow{3}{*}{\(-\)96.4397} & \multirow{3}{*}{41.1797} & \multirow{3}{*}{363 m} & \multirow{3}{*}{2001–2012} & \multirow{3}{*}{2005, 2007,} & \multirow{3}{*}{2006, 2008,} & \multirow{3}{*}{FLUXNET} \\  & & & & & 2009, 2011, & 2010, 2012 \\ \multirow{3}{*}{US-Ro1} & \multirow{3}{*}{\
\begin{tabular}{l} Rosemount-G21 \\ Rosemount-G19 \\ \end{tabular} } & \multirow{3}{*}{\(-\)93.0898} & \multirow{3}{*}{44.7143} & \multirow{3}{*}{290 m} & \multirow{3}{*}{2004–2016} & \multirow{3}{*}{2009, 2011,} & \multirow{3}{*}{2008, 2010,} & \multirow{3}{*}{2012,} & \multirow{3}{*}{2014,} \\  & & & & & 2013, 2015 & 2016 \\ \multirow{3}{*}{US-Ro5} & \multirow{3}{*}{
\begin{tabular}{l} Rosemount-G19 \\ \end{tabular} } & \multirow{3}{*}{\(-\)93.0576} & \multirow{3}{*}{44.6910} & \multirow{3}{*}{283 m} & \multirow{3}{*}{2017–2020} & \multirow{3}{*}{2018, 2020} & \multirow{3}{*}{2017,} & \multirow{3}{*}{2019} & \multirow{3}{*}{2019} \\ \cline{1-1} \cline{6-6} \cline{