# Quantum Neural Networks Approach for Water Discharge Forecast
## 2 Methodology and Data Series
### Study Area and Data Series  
The Buzau River is a significant watercourse in southeastern Romania, flowing through the Curvature Carpathians and the Buzau Plateau to the Siret River. Its catchment (Figure 1) covers 5264 km\({}^{2}\) and includes diverse landscapes, from the mountains in the Curvature Carpathians to the lower plateau regions. The mean elevation of the Buzau River is 1043 m above sea level.  
This variation in terrain affects the river's flow, with heavy rainfall in the higher regions often causing significant runoff during storms. The river basin is located within a temperate continental climate zone, which results in distinct seasonal shifts in temperature, precipitation, and runoff. Over 80% of the river's annual flow comes from the basin's upper reaches, especially from tributaries upstream of the town of Nehoui. The region has experienced severe flooding, particularly in the mid-20 th century, with the most notable occurring in 1975 when the Buzau River reached a peak discharge of 2100 m\({}^{3}\)/s. These  
Figure 1: (**a**) The Romanian map and the Buzü catchment—inside the ellipse in red, and (**b**) the data series (S). The vertical red line represents the delimitation between the two series—S1 (before 1 January 1984) and S2 (January 1984).  
floods prompted the development of flood control infrastructure, including the construction of dams. To address flood risks, regulate the river's flow, and provide electricity, the Siriu Dam was built on the Buzau River (partially put into function on 1 January 1984). Its apparition has been instrumental in reducing flood risks and altering the river's natural flow, improving surrounding communities' life conditions [58; 59].  
The studied series is formed by monthly river flow from January 1955 to December 2010. For modeling purposes, the entire series, denoted by S, was divided into the subseries S1 (January 1955-December 1983) and S2 (covering the rest of the period). The series were standardized before applying QNN. Each series (S, S1, and S2) was divided into training and test sets. The training sets were before January 2005 (before January 1984) for S (for S1) and between January 1984 and December 2005 for S2. The test one was the same in all cases, i.e., after January 2006. It is the series for which the forecast was conducted after the model learned the data on the training sets. Modeling was also performed on the same series after removing the anomalies, which are mainly the extreme values with respect to their neighbors (Figure 2). These series will be denoted by So, S1o, and S2o. We shall not present the methodology utilized for anomaly detection because it is presented in detail in our articles [60; 61]. The statistical analysis of the series and an extended description of the study region can be found in [62].  
Anomalies are occurrences in a dataset that are in some way unusual and do not fit the general patterns. In hydrology, they are generally associated with high water discharges (appearing in the case of high precipitations, for example) with extreme values (maxima). When interested only in extremes, the theory of extreme values can be applied. In hydrology, the Peak over Threshold (POT) [64] is generally used to model the distributions of extreme values and find the return period. However, only the values above a certain threshold are utilized in such a case. The anomalies should be kept when determining a model for the entire data series. In this article, in the first stage, the models were built in each scenario without eliminating the extremes. In the second stage, we removed the outliers and reran the algorithm to address the algorithm's performance.  
Figure 2: S series and anomalies represented by blue circles. The table contains the values of anomalies and the corresponding apparition month [63].