## 4 Discussion
### Cow Respiration in Observed and Modeled CO\({}_{2}\) Fluxes  
Discrepancies between modeled and observed ER and NEE fluxes, on the grazed paddock, could be caused by the uneven repartition of dairy cows on the field and the variability of the flux footprint: i.e. dairy cows were under-represented in the flux footprint, causing an under-estimation of animal respiratory losses of CO\({}_{2}\) in EC data. Some large grazer respiration fluxes could have also been excluded through the filtering of NEE data to remove outliers (condition 1, 2 and 3 in Section 2.1.2). Moreover, because the Reichstein gap-filling algorithm does not explicitly include respiration from grazing animals (e.g., animals disturbance) to either fill gaps in NEE time series or in the partitioning of NEE into GPP and ER, substantial bias could be added to the dataset [56; 79]. For all measurements without grazing there was good agreement between the CenW model and EC observations, highlighting the correct parameterization of the model and confirming that most of the ecosystem processes were well embedded in the model. It also showed that large discrepancies were present during grazing periods because of the possible non or only partial capture of cows respiration in NEE data (Figures 7c, 9c and A1). A recent EC study of CO\({}_{2}\) fluxes on two paired sites under rotational and continuous grazing management, found that ER for the rotationally grazed paddock was greatly affected by cattle respiration and that grazing animal's respiration was correctly accounted for in EC measurements [95]. In this study, we showed that there is, during grazing events, a possible underestimation of observation-derived ER from the EC system placed on the grazed paddock (Figure 12), which is consistent with other studies on managed grassland that found no effect of animals' respiration on EC-derived ER [92; 93; 96]. By comparing daily EC-derived ER with their CenW modeled counterparts (Figure 12), we showed that, on a few cases (red dots around the one to one line), modeled and observation-derived ER agree very well, showing that cattle respiration was properly modeled and measured by the flux tower. However, for most of the grazing events recorded, a large proportion or all of cattle respiration was not captured by EC (red dots strongly deviating from the one to one line). This was likely caused by the uneven spatial repartition of animals on the paddock, shifts in flux footprint, specific site conditions, stocking densities, and the processing of EC data [75; 93]. In this study, we showed that the direct effect of grazing (i.e., the reduction of photosynthesizing biomass [22]) was properly captured in EC data but that the indirect effect (i.e., grazing animals' respiration [22]) was not captured by EC systems because of the stochastic position of cows and shifts in the flux footprint area. To fully understand why grazers' respiration is not accounted for and to find a way to correct EC data for this bias, using a biochemical, process-based ecosystem model incorporating management practices, like CenW, alongside dairy cows positioning devices and detailed flux footprint information, could be necessary [79; 94]. Another problem is also related to the gap-filling process since algorithm used for this task did not use any information on cows' position and their respiration rates. If actual data affected by the presence of cows in the footprint were used to fill gaps outside of grazing periods, the large (depending of the number of cows) respiration would bias gap filled fluxes [79]. We advocate that a better way to process EC data on rotationally grazed pasture would be to exclude measurements taken during grazing periods and fill the gaps outside and inside these periods with data acquired when there was no cows in the paddocks [97]. This would insure to get the flux from the pasture only [79; 94], and then calculate how much carbon is lost from the paddock due to grazers respiration based on stocking rates, grazing duration, and amount of ingested biomass.