Adaptive Neuro‐Fuzzy Inference System integrated with solar zenith angle for forecasting sub‐tropical Photosynthetically Active Radiation

Abstract Advocacy for climate mitigation aims to minimize the use of fossil fuel and to support clean energy adaptation. While alternative energies (e.g., biofuels) extracted from feedstock (e.g., micro‐algae) represent a promising role, their production requires reliably modeled photosynthetically active radiation ( PAR ). PAR models predict energy parameters (e.g., algal carbon fixation) to aid in decision‐making at PAR sites. Here, we model very short‐term (5‐min scale), sub‐tropical region's PAR with an Adaptive Neuro‐Fuzzy Inference System model with a Centroid‐Mean ( ANFIS ‐ CM ) trained with a non‐climate input (i.e., only the solar angle, θ Z ). Accuracy is benchmarked against genetic programming ( GP ), M5Tree, Random Forest ( RF ), and multiple linear regression ( MLR ). ANFIS ‐ CM integrates fuzzy and neural network algorithms, whereas GP adopts an evolutionary approach, M5Tree employs binary decision, RF employs a bootstrapped ensemble, and MLR uses statistical tools to link PAR with θ Z . To design the ANFIS ‐ CM model, 5‐min θ Z (01–31 December 2012; 0500H–1900H) for sub‐tropical, Toowoomba are utilized to extract predictive features, and the testing accuracy (i.e., differences between measurements and forecasts) is evaluated with correlation ( r ), root‐mean‐square error ( RMSE ), mean absolute error ( MAE ), Willmott ( WI ), Nash–Sutcliffe ( E NS ), and Legates & McCabes ( E LM ) Index. ANFIS ‐ CM and GP are equivalent for 5‐min forecasts, yielding the lowest RMSE (233.45 and 233.01μ mol m −2 s −1 ) and MAE (186.59 and 186.23 μmol m −2 s −1 ). In contrast, MLR , M5Tree, and RF yields higher RMSE and MAE [( RMSE = 322.25 μmol m −2 s −1 , MAE = 275.32 μmol m −2 s −1 ), ( RMSE = 287.70 μmol m −2 s −1 , MAE = 234.78 μmol m −2 s −1 ), and ( RMSE = 359.91 μmol m −2 s −1 , MAE = 324.52 μmol m −2 s −1 )]. Based on normalized error, ANFIS ‐ CM is considerably superior ( MAE = 17.18% versus 19.78%, 34.37%, 26.39%, and 30.60% for GP , MLR , M5Tree, and RF models, respectively). For hourly forecasts, ANFIS ‐ CM outperforms all other methods ( WI = 0.964 vs. 0.942, 0.955, 0.933 & 0.893, and E LM = 0.741 versus 0.701, 0.728, 0.619 & 0.490 for GP , MLR , M5Tree, and

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