Black-Shoes-Merton Model and Neural Networks in River Level Prediction: Case Study on La Leche River - Peru

The rugged relief of Peru determines a particular hydrological regime. This geographical context includes our region, which is also affected by meteorological phenomena, e.g., El Niño and La Niña, that occur unpredictably and whose effects we feel with heavy rains and floods in the north of Peru. For that reason, the capability of being able to forecast river levels, in particular the river La Leche, is essential. For this purpose, we use the Black-Sholes-Merton stochastic differential equation of the river level and other parameters achieved from meteorological stations within the area of influence of the La Leche river basin as inputs to an LSTM Neural Network, which was trained with downloaded data and can forecast the river level 6, 12, 18, and 24 h in advance. The performance tests of the obtained neural networks demonstrated a high adaptation of the solution to the hydrological model since the NSE is very close to unity. Besides that, the average error is minimal, RMSE is of the order of 0.002, and the absolute error is of the order of 0.007.