## 3 Results
### Validation of FDR Measurements
#### 3.1.4 Validation of In Situ Recalibrated Functions  
For each layer four candidate recalibration models (LM and QM, with and without temperature correction, denoted LMTC and QMTC), are compared relatively to one another and the best and second-best models were selected based on lowest AICc value (Table A4). For 32 out of 60 layers, the simple LM proved to be the most parsimonious model and was supported over the LMTC or QM. Using the AICc, a LMTC was selected as the best model for 23% of all layers, more frequently than the QM (13% of all layers) and QMTC (10% of all layers). Evidence ratio's (ER) between the best and second-best model ranged from 1.01 (equally well) to 22.8 times better. Generally, the best model in the topsoil had no temperature correction which is remarkable for the layer where variation in soil temperature is greatest. By definition, recalibration of the standard functions eliminates bias so that overall prediction error is mainly determined by the SDPE (precision) composed of errors attributed to (short distance) spatial variation, sampling errors and random measurement error. Figure 4 shows the calibration gain of the overall prediction error for the best standard (i.e., with highest d\({}_{\rm r}\)) and recalibrated functions for all plots. Hence, compared to the standard functions, recalibration lowered the overall prediction error with a factor 1.8 (RAV) to 2.8 (GON). When comparing plots, the mean RMSPE is greatest at the GON plot, still double the allowable error of 0.03 m\({}^{3}\) m\({}^{-3}\) while on HOE the mean RMSPE equals the threshold while the means of the other plots are in between. For GON, not a single layer meets the threshold, whereas in HOE only three layers are exceeding the threshold when using the best recalibrated model. Apparently, accurate prediction of \(\theta_{\rm v}\) is most challenging for topsoil layers, whether they are organic (OFH) or mineral (M01) or most likely organo-mineral, with organic contents and bulk densities in between pure organic and mineral materials (Figure A1). However, some subsoil layers, such as M48 in GON show high prediction errors. From \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Site** & **Model** & **MPE** & **SDPE** & **RMSPE** & **d\({}_{\rm r}\)** \\ \hline WIJ & LM & 0.026 *** & 0.007 *** & \(-\)0.012 *** & 0.096 *** \\  & QM & 0.030 *** & 0.010 *** & \(-\)0.016 *** & 0.133 *** \\ RAV & LM & 0.014 *** & 0.002 ** & \(-\)0.002 \({}^{\rm NS}\) & 0.04 \({}^{\rm NS}\) \\  & QM & 0.013 *** & 0.002 \({}^{\rm NS}\) & \(-\)0.004 \({}^{\rm*}\) & 0.060 ** \\ BRA & LM & 0.011 *** & 0.0004 \({}^{\rm NS}\) & \(-\)0.005 \({}^{\rm NS}\) & 0.04 \({}^{\rm NS}\) \\  & QM & 0.010 *** & \(-\)0.0002 \({}^{\rm NS}\) & \(-\)0.006 \({}^{\rm*}\) & 0.05 \({}^{\rm NS}\) \\ GON & LM & 0.084 *** & 0.014 \({}^{\rm*}\) & 0.040 \({}^{\rm NS}\) & \(-\)0.06 \({}^{\rm NS}\) \\  & QM & 0.140 ** & 0.040 \({}^{\rm*}\) & 0.090 \({}^{\rm NS}\) & 0.01 \({}^{\rm NS}\) \\ HOE & LM & 0.044 *** & 0.004 \({}^{\rm NS}\) & 0.005 \({}^{\rm NS}\) & \(-\)0.013 \({}^{\rm NS}\) \\  & QM & 0.055 *** & 0.011 \({}^{\rm*}\) & \(-\)0.007 \({}^{\rm NS}\) & 0.012 \({}^{\rm NS}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Paired difference of validation indices without and with temperature correction of _PA_ signal for each model type. Validation index of model with TC minus index of same model without TC, using a paired _t_-test. Levels of statistical significance are \({}^{\rm*}\)_p_ \(<\) 0.05, **_p_ \(<\) 0.01 and ***_p_ \(<\) 0.001. Figure 44 it is clear that the recalibrated response for the B and C profiles in the M48 layer shows almost no variation in contrast to highly variable gravimetric measurements. We carefully checked whether all quadratic calibration models (QM and QMTC) selected as best models based on AICc (Table 44) were monotonically increasing functions (i.e., increasing output period should physically relate to higher soil water content). Five functions (WJJ-B-M12, RAV-C-M12, GON-B-M12, GON-C-M12, and GON-C-M48) did not meet this requirement.