A fuzzy logic framework to handle uncertainty in remote sensing‐based hydrological data for water budget improvement across mid‐ and small‐scale basins

Abstract

In recent years, the efficacy of remote sensing (RS) products for water budget (WB) analysis has been widely tested and implemented in global and regional basins. Although RS products provide high temporal and spatial resolution images with near‐global coverage, uncertainty is still a significant problem. Fuzzy logic is a powerful technique for dealing with uncertainty in different engineering problems. In this study, the annual residual error (r$$ r $$) in the WB equation arising from the uncertainties of the RS products was minimized by applying fuzzy correction coefficients to each WB component. For analysis, three different fuzzy linear regression (FLR) models with 14 different sub‐models were used in the two basins having different spatial characteristics, namely Sakarya and Cyprus basins. Although FLR sub‐models produce similar findings in the Sakarya basin, they generated more complex results in the Cyprus basin. This is mainly due to the higher uncertainty of the RS products in the Cyprus basin. The Cyprus basin is too small for some low‐resolution RS‐based products to resolve, and it has a higher leakage error due to across ocean/land boundary. In addition, the general performance of sub‐models is better in the Sakarya basin than that in the Cyprus basin. The best fuzzy sub‐models reduced the error up to 68% and 52% in terms of mean absolute error compared with the non‐fuzzy model in the Sakarya and Cyprus basins, respectively. Further evaluations showed that the best sub‐model precipitation well captured the temporal patterns of gauge observations in both basins. Moreover, they have the best consistency with gauge observations in terms of root mean square error, Kling‐Gupta efficiency, and percent bias in both basins. The results proved that this study will provide valuable insights into WB analysis in ungauged basins by incorporating the fuzzy logic approach into hydrological RS products.

Fuzzy Regression Analysis with a proposed model

“…For this purpose, measurement theory offers an axiomatically based, easy to use method. For any given variable, the best and worst values are determined, and the remaining values are assigned a degree of membership by comparison with the best and the worst [6]. On real variables, however, this would require an infinite number of questions.…”