# A Predictive Model of Chlorophyll a in Western Lake Erie Based on Artificial Neural Network
## 3 Results and Discussion  
### Performance of Predictive Models  
The simulations provided by GLM-AED were compared with the observed surface water temperature and Chl-a from 2002 to 2015. The time-series of surface water temperature showed that the model reproduced the annual variations of water temperature, varying between \(-5\)\({}^{\circ}\)C in winter and 25 \({}^{\circ}\)C in summer (Figure 3). The RMSE and MAE were 2.95 and 2.75 \({}^{\circ}\)C, respectively, which were comparable to previous studies with the applications of the one-dimensional model with an RMSE value of 1-6 \({}^{\circ}\)C [53] and three-dimensional model with an RMSE value of 1-3 \({}^{\circ}\)C [54] to Lake Erie. In Figure 4, both predicted and observed Chl-a peaks occurred in 2011, with high cyanobacteria in summer (optimum temperature of 25 \({}^{\circ}\)C) and diatoms in early spring (optimum temperature of 9.8 \({}^{\circ}\)C) [55]. The Chl-a RMSE and MAE were 19.61 and 18.23 \(\mathrm{\SIUnitSymbolMicro g}\)\(\mathrm{L}^{-1}\), respectively. These errors are comparable to previous studies; for example, [PERSON] et al. (2008) have obtained an RMSE of 10.4-12.76 \(\mathrm{\SIUnitSymbolMicro g}\)\(\mathrm{L}^{-1}\) in Lake Ravn in Denmark with the application of the one-dimensional DYESM-CAEDYM (Dynamic Reservoir Simulation Model-Computational Aquatic Ecosystem Dynamics Model) [56]. [PERSON] et al. (2014) underestimated about 110 \(\mathrm{\SIUnitSymbolMicro g}\)\(\mathrm{L}^{-1}\) in Rio de la Plata with the application of the three-dimensional ELCOM-CAEDYM (Estuary, Lake and Coastal Ocean Model-Computational Aquatic Ecosystem DYnamics Model) [57]. Disparities still occurred between predictions and observations, which may be due to the simplification of the complicated ecological processes; for example, our model GLM-AED assumes there is no horizontal variability (horizontally averaged) [37]. The parameters used in this model during calibration were listed in Appendices C and D.  
In the training process of the ANN model, to obtain the smallest errors, the number of the hidden layer was selected as 15. The sigmoid function was used as the activation function between layers. The learning rate, momentum, and batch size were 0.3, 0.2, and 100. With trying different percentages of the database for training, 66% of the total data (2002-2010) and 34% of the total data (2011-2015) were used for training and testing, respectively. Figure 5 showed the scatter density plots for Chl-a concentrations between the predictions from the ANN model (\(y\)-axis) and the targets from GLM-AED (\(x\)-axis) from 2002 to 2010. The value of R\({}^{2}\) was 0.83; thus, compared to the value of approximately 0.73 in the previous study [46], our ANN model can reproduce the target Chl-a concentrations. The RMSE and MAE values during the training process were 3.20 and 2.53 \(\mu\)g L\({}^{-1}\), respectively. Figure 4: Comparison between depth-averaged simulations and observed total Chl-a from sampling at GLENDA stations for 2002–2015 (ER 58, 59, 60, 61, 91, 92); The GLENDA data have been converted from biovolume to biomass using the conversions in [PERSON] et al. (2016). Figure 5: Performance of ANN in modeling Chl-a concentrations simulated by GLM-AED (Targets) in WLE from 2002 to 2010. Figure 3: The simulated and observed surface water temperature comparison at Sta. 45005 (ECCC & NOAA) for 2002–2015. During the testing period, predicted Chl-a concentrations obtained from the ANN model were compared with GLENDA observations from 2011 to 2015, and the RMSE and MAE values were 21.29 and 15.58 \(\upmu\) L\({}^{-1}\), respectively. Compared with the RMSE and MAE values of 23.27 and 19.08 \(\upmu\) L\({}^{-1}\) between GLM-AED simulations and GLENDA measurements during 2011 and 2015, the ANN model has a better predictive performance.