Turning Our Attention to Stochastic Models in Hydrology: Average Discharges of the Pisco River - Peru as a Case Study

The stochastic modeling of the discharges of a river is important because it allows predicting its behavior in the future, becoming a planning tool to avoid social conflicts by the distribution of water resources in its different uses. In Peru, water scarcity and climatic variability are fundamental concerns in many basins, particularly those on the Pacific slope, where, despite its intense economic activity and high population density, it only accounts for 1.8 percent of the water resources. Such is the case of the Pisco River, which rises in the high Andes of the department of Huancavelica and whose total length is 472 km. It is the longest in the department of Ica, where it passes and then deposits its waters in the Pacific Ocean. Its irregular regime reaches the extensive coastal plain in a short but torrential route, being a river of great importance due to the intensive use of its waters in vine, cotton and fruit crops, which has fostered the development of an intense agricultural activity that demand greater amounts of water every day. Thus, the objective of the work was to model the average monthly discharges of the Pisco River with autoregressive models and models of probability distributions through the analysis of its time series, simulate and determine its availability in the hydrometric station of Letrayocc. To achieve the objectives we worked with the MATLAB software, establishing a sequence of commands with which the simulation was achieved through autoregressive models and their respective graphic outputs. Likewise, SAMS 2009 was used to calculate the statistics of the series of downloads. The results reveal that the periodic autoregressive model and first order mobile average PARMA (1) is the most appropriate because the goodness tests of statistical and graphical adjustment report equality between historical and simulated statistics, verifying the principle of randomness in the series simulated. In the validation stage of the model it was obtained that the simulated series are statistically and graphically equal to the discharges that occurred during periods subsequent to the modeling. It is concluded that using the PARMA model (1) could simulate the average monthly discharges and apply to possible scenarios of climate change in the Pisco river basin.