Reservoir inflow Classification of Jamishan reservoir by K-means method and its effect on stochastic dynamic programming

One of the Principles of water resources management is the optimal use of the reservoirs as the main sources of surface water, and this issue has a special importance in the science of water engineering. In this research, the new K-means clustering method to discretize reservoir inflow has been presented for the Stochastic Dynamic Programming(SDP). In addition, the Moran's method is used to discretize the reservoir storage. By the programming in the Python environment, the historical reservoir inflow in each season is classified to different clusters and obtained the best inflow cluster for each season. The effects of this clustering is also considering in the SDP of Jamishan reservoir. In general, the change in inflow classification will lead to a fundamental change in the transition probability matrix. Thus, the use of K-means method for the reservoir inflow discretization, due to the possibility of optimizing the number of clusters in each time period, can be very useful for the SDP. finally, it is strongly recommended to use K-means method to discretize reservoir inflow for reservoir operation by SDP.

K-means is an object-based algorithm that selects representative clusters from the data itself rather than averaging them. K-means of a cluster is the most central element of a cluster. The purpose of this method is to reduce sensitivity to large values in the data set. Each cluster is introduced with one of the data close to the centers. According to the number of data categories (k), the value of the least squares function is minimized and the data are categorized in the best way. In addition, the Moran's method is used to discretize the reservoir storage. In this method, the upper and lower limit of the range of changes and the upper limit of each category are used as indicators of discretization of the reservoir volume. The study area includes Jamishan reservoir sub-basin with an area of 527.07 km2 located in the southwest of Sanghar city near the Pirsalman hydrometric station. This watershed is the part of Kermanshah province which is between 32-34° to 34-53° North latitude and 47-22° to 47-52° East longitude. The annual average of rainfall, evaporation and temperature are 441 mm, 1534 mm and 10 degrees Celsius, respectively.

Evaluating the performance of the K-means model in 4 different seasons, showed that among the 19 considered clusters, the best result in seasonalclassification is obtained by the 5 inflow clusters according to the performance rate in fall, winter, spring and summer seasons - 142.57, -176.90,-475.36 and -2.10, respectively. The results of the First-order Markov chain, the possible values are given in Table 1 for 4 seasons in 5 clusters,and in this table, the specified numbers indicate the probability of moving each cluster for each season.In thefollowing, using the backward recursive function, the calculations are continued until reaching the stationary state condition. Finally, the value of l* was obtained for all 4 periods and different combinations of k and i as Fig.1. The results of Steady-state condition showed that l* happened mostly in spring up to 5 clusters of the reservoir storage and the least happened in summer with onecluster. Then, the calculations of the reservoir release probability in each period for each class of inflow and storage have been made. The highest value has occurred for reservoir storage class 4 in the autumn, winter, and spring seasons but in the summer season, due to less inflow and high water demand, it has happened in reservoir storage class 5.

In this research, the Stochastic Dynamic Programming (SDP) of the Jamishan dam reservoir is discussed using the K-means method in classifying the inflow discharge seasonally for the 41 years of historical data. Moran's method is also used to classify the storage volume of the reservoir into 7 classes. To calculate the transition probability matrix during the first-order Markov chain process, it is necessary to have the flow class in each period. For this purpose, the k-means method is used. The reservoir inflow in each season is classified from 2 to 20 classes by programming in the Python environment and especially with the Scikit-learn library. Evaluating the performance of the K-means model in 4 different seasons, showed that among the 19 considered clusters, the best result in seasonal classification is obtained by the 5 inflow clusters. Changing the number of inflow clusters leads to changes in the transition probability matrix and this process would change the results of reservoir operation. It can be said that the use of this flow classification method can have a significant impact on the management and optimization of dam reservoir performance. In general, the use of new classification methods such as the K-means method in the discretization of reservoir inflow for the reservoir stochastic dynamic programming can be very beneficial and effective.