## 3 Results
### Requirements for Optimal Calibration  
The practical question is raised how many field samples are required for adequate calibration of the FDR sensors. Figure 9 shows a simulation for the HOE site with the evolution of the overall prediction error (RMSPE in black), the bias (MPE in blue) and precision (SDPE in red) relative to an increasing number of calibration months, beginning from a three months period. Starting when soils are near field capacity (in February/March) extra calibration data is gained during spring and summer months when soils are gradually drying out. This substantially decreases the bias until August (i.e., eight months). Since the bias is eliminated by then, the overall error is converging with the precision error during this first calibration period.  
We considered the bias as sufficiently eliminated when the MPE is continuously below a 0.01 m\({}^{3}\) m\({}^{-3}\) threshold (i.e., the maximal error of the gravimetric reference measurement). The number of months required for each plot, profile and layer is given in Table 8. It is clear that for all plots a longer calibration period is needed to remove the bias in the topsoil (19\(-\)24 monthly observations) compared to subsoil layers, although some special layers also require almost two years of calibration.  
The precision error starts to decline substantially from 9 till 14 observation months, when soils are rewetting until field capacity in March, but raises again during the drying phase until driest conditions in August/September and declines again in the rewettingphase afterwards. For the M12 layers of the HOE site, the precision (and overall) error drops below the 0.03 m\({}^{3}\) m\({}^{-3}\) threshold after more than 22 observation months, but for the M01 layers in HOE and on the other sites much more than 25 observation months are required or will exceed a reasonable calibration period (see RMSPE Table A5). In that case, due to the high precision error (noise), reducing the prediction error will only be possible by increasing the number of sensors for these specific layers.  
Figure 9: Simulation of the number of monthly observations required to lower the total prediction error (black full dotted line), precision error (red open dotted line) and bias (blue open dotted line) for each of the profiles of the HOE site. Horizontal dashed lines indicate thresholds for total error and bias at 0.03 and 0.01 m\({}^{3}\) m\({}^{-3}\) volumetric water content respectively.  
For those layers where the sensor's precision error after calibration still exceeds the threshold of 0.03 m\({}^{3}\) m\({}^{-3}\), and assuming that the bias is near-zero and the observed precision error is of the same magnitude for other individual CS616 sensors used under similar (soil) conditions, the average measurement error can be reduced by the square root of the number of sensors installed in parallel in the given layer, following the classical central limit theorem.  
For each layer, we therefore estimated the number of sensors required to reduce the maximum SDPE found in the three profiles of that layer (data from three individual sensors) to a measurement error below 0.03 m\({}^{3}\) m\({}^{-3}\). So, the most difficult calibration environment per layer will determine the number of sensors needed for averaging soil moisture measurements of that layer at the plot level (Table 9).  
Table 9 suggests that the current number of three sensors is sufficient for all layers of the sites BRA and HOE. However, more sensors are required for the topsoils up to 20 cm of depth for WIJ and RAV, and also for the subsoil layers in GON, with up to 10 sensors in the clayey substrate if the required measurement accuracy has to be met.