## Methods
### Eddy Covariance Data and Footprint Analysis  
Carbon dioxide (CO\({}_{2}\)), water and energy fluxes were measured using the EC technique. Wind velocity components were measured using an ultra-sonic anemometer (SA-Gill R3-50; Gill Instruments Limited, Lymington, UK) and water vapor and CO\({}_{2}\) fluctuations with an enclosed-path infrared gas analyzer (LI-7200, LI-COR Biosciences Inc., Lincoln, NE, USA) positioned at 15 m. EC raw data--including the three dimensional wind velocities (\(u,v,w\) in m/s), sonic temperature (\(T_{\mathrm{s}}\) in K), and dry CO\({}_{2}\)/H\({}_{2}\)O mixing ratios--were collected at 20 Hz. Data were processed with EddyPro software (version 5.2.0, LI-COR Biosciences Inc., Lincoln, NE, USA) as described in [PERSON] et al. [32].  
A quality flag was assigned to each half-hourly flux according to [PERSON] [44] and [PERSON] [45]; data flagged as low quality or during rain events were removed from the dataset. Data with low turbulent mixing were identified and discarded from analysis according to the algorithm developed by [PERSON] et al. [46] and implemented in the REddyProc R Package [47; 48]. The procedure was applied separately to all the towers and a friction-velocity (\(u^{\star}\)) threshold of 0.14 m/s was used for further filtering. CO\({}_{2}\) fluxes were corrected for CO\({}_{2}\) storage using the single point correction according to [PERSON] and [PERSON] [49]. The resulting Net Ecosystem Exchange (_NEE_) estimates were then partitioned in \(GPP\) and ecosystem respiration (\(R_{\mathrm{eco}}\)) according to [PERSON] et al. [50] using the REddyProc R Package [47; 48]. From the final dataset, only high-quality \(GPP\) data coming from daytime (Global incoming radiation, \(R_{\mathrm{g}}\) > 10 W\(\cdot\)m\({}^{-2}\)) were used.  
As surrogate of the uncertainty in the \(GPP_{\mathrm{hh}}\) (\(\sigma_{GPP_{\mathrm{hh}}}\)) was used the random uncertainty of _NEE_ (\(e\)) derived from the standard deviation of the marginal distribution sampling of the gap-filling procedure [50]. This methodology represents one way to assess the random error of the _NEE_[46; 51; 52]. \(\sigma_{GPP_{\mathrm{hh}}}\) should account also for the formal propagation of the uncertainty introduced by the determination of the \(u^{\star}\) threshold used to filter the data with low turbulence conditions (e.g., [46]). However, in this study we did not formally propagate this uncertainty because we are focusing on daytime and mainly on midday fluxes measured with high \(PAR\) and; in these conditions, \(e\) and _NEE_ are strongly correlated because _NEE_ is dominated by photosynthesis [53]. Additionally, under daytime/midday conditions the \(u^{\star}\) threshold is usually exceeded and no filtering is applied. \(\sigma_{GPP_{\mathrm{hh}}}\) was calculated in order to weight a cost function which includes prior information on the model parameters (see Section 2.5). Therefore, for this purpose, the uncertainties in _NEE_ and \(GPP\) are comparable because they are strongly correlated.  
Footprint climatology was computed using a modified version of the 2-D model developed by [PERSON] et al. [54] and updated by [PERSON] et al. [12]. Footprints were integrated in periods of 30 min, similarly as the EC variables. Specific details can be found in [55] and [PERSON] et al. [36].