Sensitivity of Entropy Method to Time Series Length in Hydrometric Network Design

The design of optimal hydrometric networks is an important starting point in water resources planning and management. Redundant or inappropriate networks may require unnecessary monitoring costs, while a sparse network may cause a lack of understanding of the process being monitored. Many studies employ information theory, which uses the Shannon entropy, as a measure of the information to design optimal hydrometric networks measuring various hydrologic parameters, such as streamflow and precipitation. The majority of entropy application methods in hydrometric network design have had two common objectives, i.e., maximizing joint entropy and minimizing total correlation. However, it is still unclear what data lengths should be adequate to properly use the entropy approach to network design and how the data lengths affect the entropy values. In this study, four different data lengths (e.g., 5, 10, 15, and 20 years) of daily time series are used to determine the optimal streamflow and precipitation networks using entropy theory coupled with multiobjective optimization. The spatial distributions of the optimal monitoring locations appeared similarly for each data length. Specifically, the hot-spots where the selection likelihood from optimization results is high were not significantly changed; this is more obvious when the data length of daily time series was 10 years or greater. Additionally, the joint entropy and total correlation of the optimal networks were calculated from 10 days to 20 years with a 10-day increment. The joint entropy increased significantly during the first 5 years and then gradually increased without significant change after 10 years. Similarly, the total correlation stabilized after 5 years of daily time series lengths with no major change after 10 years. Therefore, it is recommended to use at least 10 years of data for information theory–based hydrometric network design when using daily time series.