## 2 Materials and Methods
### CO\({}_{2}\) Flux and Climate Data from the Eddy Flux Tower Site  
The EC instrument was established at the study site since 2008 (Figure 1), with the observation of CO\({}_{2}\) and water fluxes, wind speed, and wind direction. The EC tower equipped with an open path infrared CO\({}_{2}\)/H\({}_{2}\)O gas analyzer (Li 7500, LI-COR Inc., Lincoln, NE, USA) and ultrasonic anemometer (CSAT3, Campbell Scientific Inc., Jackson, MS, USA), which were installed 4.5 m above ground level. The sonic anemometer and the infrared CO\({}_{2}\)/H\({}_{2}\)O gas analyzer output were recorded at half-hour intervals by datalogger (CR5000, Campbell Scientific, Inc., Jackson, MS, USA), with high frequency of 10 Hz. Carbon and energy fluxes were calculated by using the half-hour covariance of vertical wind velocity and virtual temperature, water vapor density, and CO\({}_{2}\) density [15]. Figure 1: Study site location at the Yellow River Delta. The remote sensing data is derived from Google Earth. The eddy covariance system, including a flux tower and a weather station, was deployed at the coastal zone of Yellow River Delta Nature Reserve in 2008, with observation of CO\({}_{2}\) and water fluxes, air temperature, precipitation, photosynthetically active radiation (PAR), etc. We also measured some environmental factors that were used for gap filling calculations nearby the eddy tower. Photosynthetically active radiation (PAR) was observed by LI-190 SB sensors (LI-COR Inc., Lincoln, NE, USA). Relative humidity and air temperature were observed by humidity/temperature probes (HMP45C, VAISALA Woburn, MA, USA). Precipitation was measured at the height of 1.5 m above the ground level by a tipping bucket rain-gauge (TE525 MM, Campbell Scientific, Inc., Jackson, MS, USA). The copper-constantan thermocouples were installed at five depths (0.05, 0.10, 0.20, 0.50, and 1.0 m) below the ground to measure soil temperature. All data were saved in the digital datalogger (CR23X; Campbell Scientific, Inc., Jackson, MS, USA) [19]. For reducing the measurement-induced uncertainties, quality control was conducted for the observed data during 2009-2010. The CO\({}_{2}\) flux data observed during rainfall or snowfall or instrument failure (e.g., system maintenance, power outages, etc.) were eliminated as invalid data that has led to data gaps. To fill the CO\({}_{2}\) flux data gap, the gap filling methods, including mean diurnal variation (MDV), of previous periods and nonlinear regression were used in this study. For the MDV method, the means for different time interval (window size, usually 4-15 days) that were based on adjacent days were used to replace the missing flux data. Nonlinear regression method was interpolated by establishing the regression relationships between net ecosystem CO\({}_{2}\) exchanges (NEE) components and the associated environmental factors during the studied period [46]. Generally, the EC measured C fluxes represent NEE, which is the balance between ecosystem respiration (\(R_{\text{e}}\)) and GPP [47]. Therefore, GPP can be obtained by the difference between \(R_{\text{e}}\) and NEE. \(R_{\text{e}}\) is summed by the daytime (\(R_{\text{e,day}}\)) and nighttime (\(R_{\text{e,night}}\)) ecosystem respiration. \(R_{\text{e,night}}\) is derived from the nighttime NEE. Because \(R_{\text{e,night}}\) is relevant to the soil temperature (\(T_{\text{s}}\)) [15; 48], a temperature dependent model was derived from the observed \(R_{\text{e,night}}\) with \(T_{\text{s}}\)[19]. Then, we estimated the \(R_{\text{e,day}}\) rates and GPP by extrapolating the exponential relationship to the daytime periods. \[GPP=R_{\text{e}}-NEE \tag{1}\]  
\[R_{\text{e}}=R_{\text{e,day}}+R_{\text{e,night}} \tag{2}\]  
\[R_{\text{e,night}}=ae^{(bT_{\text{s}})} \tag{3}\]  
where \(T_{\text{s}}\) is soil temperature (\({}^{\circ}\)C) at the depth of 0.05 m, and \(a\) and \(b\) are coefficients.