# Evaluation of Five Reanalysis Products over France: Implications for Agro-Climatic Studies
## 2 Materials and Methods
### Comparison Approach  
To ensure a consistent comparison, the spatial coverage of climate RPs is matched to that of the reference data by extracting grid values at the coordinates of the selected SYNOP stations. For each station location, climate RP and, if necessary, ensemble members, daily time series of precipitation and mean temperature is calculated using bilinear interpolation of the four nearest neighbors (grid cells). In cases where bilinear interpolation is not suitable \begin{table}
\begin{tabular}{l l l} \hline \hline
**Crop** & **Indicator** & **Equation** \\ \hline \multirow{4}{*}{Vine} & Winkler Index & \(\sum_{01/04}^{31/10}\max(T_{d}-10,\ 0)\) \\  & (WI, \({}^{\circ}\)C) & \(\sum_{01/04}^{31/10}T_{m}\times P_{m}\) \\  & Hydrothermic index of & \(\sum_{01/04}^{31/08}T_{m}\times P_{m}\) \\  & (HyI, mm \({}^{\circ}\)C) & \(\sum_{15/04}^{31/08}\min(\max(T_{d}-6,\ 0),\ 30)\) \\ \multirow{4}{*}{ Maize} & Flowering date & \(\sum_{15/04}^{15/04}\min(\max(T_{d}-6,\ 0),\ 30)\) \\  & (FD, day of the year) & Date on which the threshold of 850 \({}^{\circ}\)C is reached \\ \multirow{4}{*}{Apple} & Dry days & \(\sum_{01/06}^{31/08}1_{T_{d}<1}\) \\  & (DDs, number of days) & \(\sum_{01/06}^{31/08}1_{T_{d}<1}\) \\ \multirow{4}{*}{Apple} & Dormancy breaking & \(CU(T)=\begin{cases}1-\left(\frac{|T-T_{c}|}{L}\right)&\text{if }T_{c}-l_{c}<T<T_{c}+l_{c}\\ &\text{otherwise}\\ &T_{c}=0\text{ and }lc=20.\end{cases}\) \\  & Date on which the threshold of 56 CU is used \\ \multirow{4}{*}{Water requirements (WR, mm)} & \(\sum_{01/06}^{31/08}p_{d}\) \\  & & \\ \hline \hline \end{tabular} \(P_{d}\) and \(P_{m}\) are respectively daily and monthly total precipitations (mm). \(T_{d}\) and \(T_{m}\) are respectively daily and monthly mean temperature (\({}^{\circ}\)C).  
\end{table} 
Table 2: Details of the agro-climatic indicators (Agcls) used in this study. within the gridded land dataset, nearest neighbor interpolation is used. The AgcIs were then calculated for each year using the interpolated data. The period of comparison is 1 January 1996 to 29 December 2012; this 17-year period is common among all the datasets. In the following, \(X_{rp}=\left(x_{1}^{rp},\ldots,\ x_{n}^{rp}\right)\) will represent RP-derived values and \(X_{ref}=\left(x_{1}^{ref},\ldots,\ x_{n}^{ref}\right)\) will represent the observed values from the reference dataset. The performance of the climate RPs was evaluated based on three metrics:  
1. [PERSON]'s concordance correlation coefficient (LCCC), first introduced by [56], quantifies the agreement between two continuous measures made by different observers/ methods of the same variable by measuring the variation of their linear relationship from the \(45^{\circ}\) line through the origin. The degree of concordance between \(X=X_{ref}\) and \(Y=X_{rp}\) is estimated using: \[\hat{\rho}_{c}=\frac{2\ S_{XY}}{S_{X}^{2}+S_{Y}^{2}+(\bar{X}-\bar{Y})^{2}}\,\] where \(\bar{X}=\frac{1}{n}\sum_{i=1}^{n}x_{i}\), \(S_{X}^{2}=\frac{1}{n}\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}\), and \(S_{XY}=\frac{1}{n}\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})\). \(\hat{\rho}\) will represent the degree of agreement between the climate RP and the reference dataset, with values ranging from \(-1\) to \(1\). A value of \(1\) indicates perfect agreement, \(0\) indicates no agreement, and \(-1\) indicates perfect disagreement. 2. Percent Bias (PBias) quantifies the average tendency of the RP-derived values to be larger or smaller compared to the observed values. \[PBias=100\times\frac{1}{n}\sum_{i=1}^{n}\left(\frac{x_{i}^{rp}-x_{i}^{ref}}{x_{ i}^{ref}}\right).\] A value close to zero indicates that the Agcl have similar average values, a positive value means that the evaluated product tends to overestimate the reference values, and a negative bias shows an underestimation against the reference values. 3. The integrated quadratic distance (IQD), introduced by [57], is defined as the integral over the squared difference between the corresponding cumulative distribution functions (CDFs).