CM and Q time series are, therefore, trained with the aforementioned formulations. To check the best-fit solution from the selected distribution, a model evaluation criterion has been set considering Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Pearson correlation coefficient ( r ). The best fit of any site has been obtained by lower values of AIC and BIC with a higher value of r ; thus, a composite index (CI) is formulated to evaluate the overall model scores to determine the best-fit model for the selected site.
Eq.15a AIC = 2k – 2ln L’ BIC = k*ln n – 2ln L’ CI = r + (1-AIC) + (1-BIC) Eq.15b Eq.15c where k equals to the number of parameters used in the model; n equals to the sample size, and is the maximum value of the likelihood function for the model. 6.4.2 Uncalibrated Approach In the absence of coincident observations of Q and CM time series, the uncalibrated procedure uses the same framework proposed by Tourian et al. (2013). Here, the available discharge and retrieved CM signal time series are sorted independently in descending order.
Subsequently, the corresponding exceeding probability of each value in the time series is computed for both Q and CM time series individually by considering their percentage of the observation periods. Here, for each site, the basic assumption is that the insitu Q and CM signals have the same exceedance probability. Developing the joint probability distribution by considering the individual cumulative distribution function (CDF) of Q and CM, the river discharge could be estimated from the standalone CM signals for any gauging sites. Thus, the CDF curves are calculated and compared to generate the percentiles associated with the discharges.
With the relative correspondences between percentiles, it is possible to generate river discharge from the reflectance time series. Following this principle, the uncalibrated approach is performed along the selected gauging sites to estimate the long-term river discharge time series from the CM signals. For generating long-term discharge time series using the CM signals, the calibrated procedure is based on the coincident observations of in situ Q and CM. The absence of CM signals during flood events due to the presence of cloud cover in the images may affect the model parameterization to capture the high flow dynamics both in Best Fit and Copula Fit solutions.
Although the uncalibrated procedure is independent of the coincident observations of in situ Q and CM, the availability of the in situ Q data period is still a key concern. For instance, the hydrograph generated from a short event may not be representative of the long-term period; thus, derived CDF cannot find the proper solution while deriving the joint distribution, which also may add significant uncertainties while deriving long-term discharge time series. In both calibrated and uncalibrated procedures, there are possibilities to lose the flood information due to the unavailability of CM signals in the presence of cloud cover, which is very often too. D.3 River Discharge ATBD. Reference:
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