Wavelet analyses of neural networks based river discharge decomposition

The problem of discharge forecasting using precipitation as input is still very active in Hydrology, and has a plethora of approaches to its solution. But, when the objective is to simulate discharge values without considering the phenomenology behind the processes involved, Artificial Neural Networks, ANN give good results. However, the question of how the black box internally solve this problem remains open. In this research, the classical rainfall-runoff problem is approached considering that the total discharge is a sum of components of the hydrological system, which from the ANN perspective is translated to the sum of three signals related to the fast, middle and slow flow. Thus, the present study has two aims (a) to study the time-frequency representation of discharge by an ANN hydrologic model and (b) to study the capabilities of ANN to additively decompose total river discharge. This study adds knowledge to the open problem of the physical interpretability of black-box models, which remains very limited. The results show that total discharge is adequately simulated in the time frequency domain, although less power spectrum is evident during the rainy seasons in the ANN model, due to fast flow underestimation. The wavelet spectrum of discharge represents well the slow, middle and fast flow components of the system with transit times of 256, 12–64 and 2–12 days, respectively. Interestingly, these transit times are remarkably similar to those of the soil water reservoirs of the studied system, a small headwater catchment in the tropical Andes. This result needs further research because it opens the possibility of determining MMT on a fraction of the cost of isotopic based methods. The cross-power spectrum indicates that the error in the simulated discharge is more related to the misrepresentation of the fast and the middle flow components, despite limitations in the recharge period of the slow flow component. With respect to the representation of individual signals of the slow, middle and fast flows components, the three neurons were uncapable to individually represent such flows. However, the combination of pairs of these signals resemble the dynamics and the spectral content of the aforementioned flows signals. These results show some evidence that signal processing techniques may be used to infer information about the hydrological functioning of a basin.