## 2 Materials and Methods
### Flux and Meteorological Observations  
#### 2.1.1 FLUXNET Data  
This study collected FLUXNET data to provide meteorological and ET information. The half-hourly FLUXNET data include net radiation (Rn, W/m\({}^{2}\)), air temperature (TA, \({}^{\circ}\)C), relative air humidity (RH, %), vapor pressure deficit (VPD, kPa), soil water content of different depths (SWC1, SWC2, %), CO\({}_{2}\) concentration (CO2, umol/mol), wind speed (WS, m/s), friction velocity (UST, m/s), solar radiation (Rg, W/m\({}^{2}\)), latent/sensible/soil heat flux (LE/H/FG, W/m\({}^{2}\)), barometric pressure (PRESS, kPa), and precipitation (PREC, mm). Using the eddy covariance observations FLUXNET dataset and three distinct \(T\) partitioning methods (see Section 2.1.2 for details), site-based \(G_{\rm s}\) was derived, and its controlling factors were analyzed. Constrained by the spatial overlap of the above-mentioned datasets, eight FLUXNET sites (60 site-years) were meticulously selected to ensure representativeness and accuracy of the data, including one Evergreen Broadleaf Forest (EBF) site, four Grassland (GRA) sites, one Cropland (CRO) site, and two Woody Savanna (WSA) sites (Figure 1, Table 1). Each site's characteristics include latitude (\({}^{\circ}\)N), longitude (\({}^{\circ}\)E), plant functional type (PFT), K\({}^{\circ}\)open-Geiger climate classification (CLIM), measurement height (Z, m), measurement depths and integration depths for SWC1, and Depth2 is measurement depths and integration depths for SWC2), and recording period. The PFTs were taken from the International Geosphere-Biosphere Program (IGBP) Land cover classification scheme (EBF = Evergreen Broadleaf Forest, GRA = Grasslands, CRO = Croplands, WSA = Woody Savannas). The details of the climatic classification are described in [PERSON] and Kottek [40]. Figure 1: Locations of the study sites. The hydrometrological conditions expressed as environmental factors were also collected from FLUXNET sites. Those factors can be broadly categorized into four types: radiation (Rn and Rg), water (SWC1, SWC2, RH, and VPD), temperature (TA), and atmospheric conditions (CO2 and WS). All these observations went through the following quality control steps. Data quality control of the half-hourly/hourly flux data was performed according to similar screening methods described by [PERSON] et al. [22] and [PERSON] et al. [23], [PERSON] et al. [49], and [PERSON] et al. [50]: (1) Exclude defective entries such as missing values or values set to missing by Carbon Dioxide Information Analysis Center (CDIAC) denoted by \(-9999\) and parameters not reported by the field investigator denoted by \(-6999\). (2) Exclude entries if the energy budget is not closed (i.e., the sum of the net radiative less latent, sensible, and soil heat fluxes exceeded 300 W/m\({}^{2}\)). (3) Exclude rainy period entries, i.e., only retain entries with simultaneous PREC entries that were 0 for the whole day. (4) Exclude nighttime period entries, i.e., only retain entries with Rg greater than 50 W/m\({}^{2}\). (5) Aggregate the data to the daily average and use only daily-scale sample data where the number of valid entries for a single day was more than 2/3 (16 entries) of the total number of entries. Meanwhile, this study used the statistical 3-sigma, i.e., standard deviation method, to identify outliers. \[\mathrm{P}(|\mathrm{x}\,-\,\mu|>\,3\sigma)\,\leq\,0.003 \tag{1}\]  
As the US-ARM site is in fallow cropland, it is important to determine whether the dates correspond with the typical cultivation period. When the land is fallow and lacks typical vegetation, it does not accurately represent the characteristics of its land class. Thus, only flux data from the interval between planting and harvesting periods were considered. The Biological, Ancillary, Disturbance, and Metadata database (BADM) ([[https://fluxnet.org/](https://fluxnet.org/)]([https://fluxnet.org/](https://fluxnet.org/)), accessed on 7 August 2024) [51] provides such information.