# Flow Duration Curves from Surface Reflectance in the Near Infrared Band
## 3 Results
### FDCs in the Validation Phase: Evaluation of the Performances  
Conscious of such potential performances (expected and in line with previous investigations when trying to reproduce the discharge dynamic in time), the main purpose of the study is not to reproduce the temporal variation of the discharges, rather their frequency distributions over a period of reference. Thus, Figure 8 shows the FDCs built by using the C/M ratio, here called \(\text{FDC}_{\text{val}}\) sim, compared to the FDCs built by the ground-observed data in the same period of validation, \(\text{FDC}_{\text{val}}\) obs. According to the k-s test (significance level alpha equal to 0.01), the flow duration curves simulated for Below Grafton, Thebes, Memphis, and Vicksburg are from the same distribution of those observed. For the other  
Figure 7: Validation phase: Comparison between the observed and simulated discharges.  
sites, the k-s test failed (k-s rejects the null hypothesis). However, considering the FDCs reconstructed annually for the entire period (2013-2019), we show that the FD\({}_{\text{val}}\) sim fall within the range of variability of the FDCs (see light gray curves in Figure 8). Thus, although not perfectly in agreement with the observations, FD\({}_{\text{val}}\) sim can be associated with the natural variability expected for the annual flow duration curves. For McGregor, because in the validation period the data are missing, we compare the simulated FDCs with the annually reconstructed FDCs in the calibration period.  
Figure 8: Simulated and observed FDCs for the period of validation (2016-2019). For comparison, the FDC built on single years of the entire observation period, 2003–2019, are also represented.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Station** & \(\mathbf{R_{p}}\) **[-]** & \(\mathbf{R_{s}}\) **[-]** & **RMSE [m\({}^{3}\)/s]** & **rRMSE [\%]** & **NRMSE [\%]** & **NSE [-]** \\ \hline St. Cloud & 0.39 & 0.55 & 17,843 & 69.2 & 29.5 & \(-\)0.53 \\ \hline St. Paul & 0.14 & 0.31 & 83,784 & 96.5 & 27.2 & \(-\)1.20 \\ \hline Prescott & 0.85 & 0.90 & 3815 & 33.7 & 10.7 & 0.79 \\ \hline Winona & 0.73 & 0.74 & 6725 & 43.7 & 15.5 & 0.36 \\ \hline McGregor & - & - & - & - & - & - \\ \hline Clinton & 0.57 & 0.58 & 9768 & 39.7 & 18.3 & 0.32 \\ \hline Keokuk & 0.40 & 0.35 & 20,709 & 57.6 & 22.1 & \(-\)0.31 \\ \hline Below & 0.44 & 0.33 & 326,920 & 54.2 & 23.1 & \(-\)0.03 \\ \hline St. Louis & 0.57 & 0.74 & 489,400 & 51.7 & 19.6 & \(-\)0.03 \\ \hline Chester & 0.58 & 0.65 & 47,113 & 51.2 & 20.0 & \(-\)0.04 \\ \hline Thebes & 0.69 & 0.79 & 382,943 & 37.4 & 15.3 & 0.44 \\ \hline Memphis & 0.81 & 0.84 & 61,406 & 27.8 & 14.7 & 0.66 \\ \hline Vicksburg & 0.72 & 0.82 & 82,228 & 33.8 & 17.9 & 0.52 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Validation 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, _NSE_.  
Figure 9 shows the distribution of the errors expressed as differences between the observed and estimated discharges, for all the sites except for McGregor (due to the missing data during the validation period), removing the temporal dimension (i.e., the variability of the discharge in time at a given section). The highest errors are detected for high flows, with a spread distribution of the errors in the low durations range. For medium and high durations (medium and low discharges, respectively), the differences tend towards 0, meaning a higher potential capacity to estimate the discharges associated with medium-low flow conditions.