# Flow Duration Curves from Surface Reflectance in the Near Infrared Band
## 3 Results
### Comparison in Terms of River Discharge: Calibration Phase  
In the phase of calibration, the relationship between FDC and RDC is generated by associating the pairs with the same probability of exceeding and fitting a smoothing spline function. In the validation phase, the reflectance ratio calculated in the corresponding period is then used to derive the discharge values corresponding to the same probability by using the relationships established during the calibration phase (see Figure 3).  
Table 2 reports the performance indices for the calibration phase, while Figure 6 plots the time series. The two upstream sites of St. Cloud and St. Paul do not show good agreement with the observations. At St. Cloud, even if a double peak is detected by the satellite, often the magnitude is completely different, providing errors quite high (around 100% in terms of \(rRMSE\) and negative NSE). At St. Paul and Chester, the simulated discharges diverge more in the period 2003-2010, whereas the match is more evident in the period 2011-2015. At Grafton, disagreements are found along the overall period, both in terms of magnitude and in timing of the flood events. At Memphis, the unique year of simultaneous observations provides good performance with high correlations (0.88) and \(rRMSE\) rather low (around 25%). At the other stations (Prescott, Winona, McGregor, Clinton, St. Louis, Thebes, and Vicksburg), the simulated and observed river discharges agree: \(NSE\) are always positive, \(NRMSE\) are in the range of around 10-16%, whereas Spearman correlations are greater than 0.60.  
Figure 5: (**a,c**) show reflectance ratio duration curves (RDCs) calculated for (i) the entire period (tot), from 2003 to 2019, and (ii) for the selected calibration period (cal), from 2003 to 2015. (**b,d**) columns show differences in reflectance ratio C/M between the RDCs built considering the calibration and the total period, for all the sites analyzed.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Station**} & \(R_{p}\) & \(R_{s}\) & \(RMSE\) & \(rRMSE\) & \(NRMSE\) & \(\mathbf{N}\)\(\mathbf{E}\) \\  & [**–]** & [**–]** & [**–]** & **[**m\text{3/s}]** & **[**\%]** & **[**\%]** & **[**\%]** & **[**–]** \\ \hline St. Cloud & 0.29 & 0.37 & 1789 & 95.8 & 23.3 & \(-\)0.38 \\ \hline St. Paul & 0.37 & 0.36 & 5502 & 111.2 & 18.6 & \(-\)0.24 \\ \hline Prescott & 0.82 & 0.76 & 316 & 50.3 & 9.5 & 0.67 \\ \hline Winona & 0.66 & 0.62 & 571 & 61.3 & 14.1 & 0.36 \\ \hline McGregor & 0.78 & 0.71 & 5763 & 46.9 & 11.8 & 0.53 \\ \hline Clinton & 0.75 & 0.66 & 700 & 45.1 & 12.4 & 0.53 \\ \hline Keokuk & 0.46 & 0.49 & 1654 & 70.9 & 16.4 & \(-\)0.06 \\ \hline Below & & & & & & \\ Grafton & 0.16 & 0.17 & 35,301 & 88.0 & 27.8 & \(-\)0.64 \\ \hline St. Louis & 0.73 & 0.83 & 31,574 & 46.5 & 15.4 & 0.46 \\ \hline Chester & 0.30 & 0.40 & 4880 & 74.2 & 23.4 & \(-\)0.38 \\ \hline Thebes & 0.85 & 0.88 & 25,535 & 34.4 & 12.7 & 0.69 \\ \hline Memphis & 0.90 & 0.90 & 3854 & 24.4 & 14.0 & 0.77 \\ \hline Vicksburg & 0.80 & 0.88 & 7059 & 35.7 & 12.3 & 0.55 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Calibration phase: Performance indices of the comparison between the observed and simulated discharges: Pearson correlation coefficient, \(R_{p}\), Spearman correlation coefficient, \(R_{s}\), Root Mean Square Error, \(RMSE\), Relative \(RMSE\), \(rRMSE\) and Nash–Sutcliffe efficiency, \(N\)\(\mathbf{E}\).  
Figure 6: Calibration phase: Comparison between the observed and simulated discharges.