Hybrid Modeling Combining Neutrosophic Logic and Bayesian Deep Learning for Modelling Precipitation in Northern Iraq

Abstract

This paper proposes a hybrid model combining neutrosophic logic and Bayesian deep learning to enhance the accuracy of precipitation forecasting in northern Iraq. Precipitation does not depend on a single climatic factor but results from the simultaneous interaction of several physical factors. The model depends on the specific humidity (QV2M), temperature at a height of 2 meters (T2M), soil moisture (GWETTOP), wind speed at 2 meters (WS2M), and their interactions and lagged variables. Because of data skewness, we applied the Yeo–Johnson transformation to reduce it. Neutrosophic logic was used to transform the climatic variables into three levels: truth (T), indeterminacy (I), and falsity (F). A Bayesian Neural Network (BNN) was then trained using the proposed Bayesian neural network architecture. A deep ensemble strategy was employed, using three models to generate the final estimates. The proposed model achieved high forecasting accuracy. The results indicate that the model explained approximately 89.30% of the variance in actual precipitation data. NSE and R2 yielded very similar values, both ≈ 0.90. The values (RM SE = 8.4081, M AE = 4.9232) indicate relatively low forecasting errors, given precipitation variability exceeding 100 mm, suggesting high forecasting accuracy. Therefore, combining neutrosophic logic with Bayesian neural networks offers a promising way to understand climate variability better and support sustainable water resources management.