## 2 Materials and Methods
### Statistical Evaluation  
All statistical processing, evaluations and graphics were performed in the R environment, using R version 4.1.0 [29,30] in R Studio v1.3.1073. For time series manipulation and analysis, we used package _xts_ v0.12.1. Evaluation of models was performed both for their relative and absolute quality. Relative model selection among candidate models was evaluated using the Akaike Information Criterion (AIC) corrected for small sample sizes (AICc) using the _AICcmadag_ package v. 2.3-1 [31]. The AICc weights for each model are given and the evidence ratios (ER) quantifying the amount of support in favor of a model relative to a competing model. Absolute quality of models was judged using a set of complementary validation indices of their predictive quality by comparing their predicted \(P_{i}\) with observed (reference) values \(O_{i}\) (Equations (4)-(8)). \(R^{2}_{p}\) is the prediction coefficient of determination informing the explained variance of the model (4), MPE is the mean prediction error or bias (5), SDPE is the standard deviation of the prediction error or noise (precision) (6), RMPSE is the overall model prediction error or model accuracy (7) and is the general closeness of agreement between the FDR output measurement (\(\theta_{FDR}\)) and the reference observations (\(\theta_{v}\)). RMSPE is the square root of the mean square prediction error (MSPE). For large n, MSPE equals the sum of MPE\({}^{2}\) (bias) and SDPE\({}^{2}\) (noise) as shown in Equation (8). With effective calibration the MPE (bias) is removed and the precision component of accuracy dominates. \[R_{p}^{2}=\frac{[\text{cov}(P_{i},O_{i})]^{2}}{\text{var}(O_{i})\cdot\text{ var}(P_{i})} \tag{4}\]  
\[\text{MPE}=\frac{1}{n}\underset{i=1}{\overset{n}{\sum}}(P_{i}-O_{i}) \tag{5}\]  
\[\text{SDPE}=\sqrt{\frac{1}{n-1}\underset{i=1}{\overset{n}{\sum}}((P_{i}-O_{i} )-\text{MPE})^{2}} \tag{6}\]  
\[\text{RMSPE}=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\sum}}(P_{i}-O_{i} )^{2}} \tag{7}\]  
\[\text{MSPE}=\frac{1}{n}\underset{i=1}{\overset{n}{\sum}}(P_{i}-O_{i})^{2}= \text{MPE}^{2}+\frac{n-1}{n}\text{SDPE}^{2} \tag{8}\]  
The revised index of agreement (_dr_) is dimensionless and bounded by \([-1,1]\) with 1 indicating perfect agreement [32]. Principal component analysis was applied using the R \begin{table}
\begin{tabular}{c c c} \hline
**Attribute** & **Format/Unit** & **Description** \\ \hline TimeStamp & YYY-mm-dd hh-mm-ss & \begin{tabular}{c} Nearest FDR recording time to field \\ sampling event (in UTC + 1) \\ Period average raw sensor output for \\ \end{tabular} \\ \(PA_{i,j}\) & \(\upmu\)s & \begin{tabular}{c} Soil temperature measured in profile i = 1 \\ at depth j \\ \end{tabular} \\ ST\({}_{j}\) & \({}^{\circ}\)C & \begin{tabular}{c} Soil temperature measured in profile i = 1 \\ at depth j \\ \end{tabular} \\ \(\rho_{b,i,j}\) & kg m\({}^{-3}\) & \begin{tabular}{c} Fine earth bulk density of profile i and \\ depth j \\ \end{tabular} \\ \(\theta_{m,i,j}\) & g kg\({}^{-1}\) & \begin{tabular}{c} Soil water content by mass (gravimetric) \\ \end{tabular} \\ \(\theta_{v,i,j}\) & m\({}^{3}\) m\({}^{-3}\) & \
\begin{tabular}{c} Soil water content by volume \\ (volumetric) \\ \end{tabular} \\ Logger data & V, \({}^{\circ}\)C &
\begin{tabular}{c} Logger diagnostics: record ID, battery \\ voltage, logger temperature \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 4: Attributes of the calibration dataset. _precomp_ function, with data centered and scaled. The _ggbipid_ v.0.55 package was used to generate biplots using _ggplot2_ in order to plot both the position of each sample in terms of the principal components together with the initial variables mapped as vectors. In order to evaluate the importance of soil variables on the RMSPE, a generalized boosted regression tree model was built using the R package gbm v.2.1.8 with a gaussian distribution and following parameters: n.trees = 10,000, shrinkage = 0.01 and an interaction.depth = 4.