Improving the performance of water balance equation using fuzzy logic approach

- Fuzzy Logic models (FLMs) reduced the error in the Water Balance Equation (WBE).
- Best developed FLM reduced the mean absolute error in the WBE up to 79%.
- Fuzzy coefficients correct over- and underestimation error in WBE components.

SummaryIt is a common practice to conduct the water budget or water balance analysis in a given area within a specified time in order to investigate the balance between the inputs and outputs of the water system. Such an analysis can be used for water management and water allocation in a designated study area. Due to appearance of an error in water balance equation because of difficulty in accurate estimation of its individual components, the main objective of the current paper was to apply a set of fuzzy coefficients to the components of the water balance equation in order to reduce this error. The fuzzy coefficients reflect the uncertainty and imprecision in evaluating each component, and minimize the overall error of the water balance equation. These coefficients are adjusted by an error minimization procedure, based on fuzzy regression concepts and using available recorded data for a given study area within a specified time scale. The adjusted coefficients can effectively estimate the water balance components in the future. In this study, four different models, representing different types of fuzzy coefficients, were considered and used for annual water balance of Azghand catchment in Khorasan Razavi Province, Iran as a case study. Analysis of results showed that all models were effective in reducing water balance error in Azghand catchment. The best model reduced the error up to 79% in terms of mean absolute error compared with error in water balance equation when conventional (with no correction coefficients) water balance analysis was conducted. Moreover, the results indicated that the performance of the proposed fuzzy models was not significantly sensitive to selection of confidence level in data (h) and improved slightly as h increased.