# A Predictive Model of Chlorophyll a in Western Lake Erie Based on Artificial Neural Network
## 1 Introduction  
Eutrophication has been a serious global environmental problem in large lakes [1; 2; 3], including Lake Victoria in Africa, Lake Loosdrecht in Europe, and Lake Taihu in Asia. To investigate this water quality problem in these regions, different approaches have been applied including sampling field data, lab methods, and remote sensing [4; 5; 6]. Western Lake Erie (WLE) also has been suffering from eutrophication [7; 8; 9; 10], which was driven by climate change and excess nutrient loads, particularly phosphorus from agriculture [11]. With the implementation of phosphorus (P) abatement programs based on the Great Lakes Water Quality Agreement (GLWQA) in 1972 and the Lake Erie total phosphorus (TP) target load of 11,000 MTA in the 1978 Amendment to the GLWQA, P loads entering into WLE reduced, resulting in a decrease in algal blooms in WLE [12; 13]. However, since the mid-1990s, algal blooms have reoccurred resulted in increased spring runoff flushing more P from the Maumee River watershed into WLE [14; 15; 16]. In consideration of the long-term variations in algal blooms, to manage them efficiently, there is a need to develop a tool to reproduce the long-term development of algal blooms to implement better water resource management. To date, there are two commonly applied approaches to predict water quality, namely, process-based [17] and data-driven [18] models. Process-based models are based on known principles and theories of physics, biochemistry, and ecology with solving a series of mathematical equations, such as one-dimensional GLM-AED [19], two-dimensional CE-QUAL-W2 [20], and three-dimensional AEM3D [21]. Particularly, requiring less computational time than multi-dimensionalmodels, one-dimensional models are suitable for long-term predictions [22]. Unlike process-based models, data-driven models are based on data mining algorithms and statistical techniques that analyze patterns amongst the dataset about a specific system to explore the relationships between the input and output data without taking account of explicit knowledge of physical, biochemical, and ecological behavior of the system [23]. Various types of data-driven models have already been applied to water research, such as unit hydrograph method, statistical models, and machine learning models [24; 25]. Particularly, the artificial neural network method, one of the statistical methods, has been widely used in previous prediction cases [26; 27], showing the capability of this method in analyzing biogeochemical monitoring data [28; 29] and providing improved results compared to other modeling methods [30; 31]. Thus far, most previous studies associated with water quality predictions in WLE used process-based models and there are no current studies that apply ANN to predict WLE water quality. This study aims to establish an ANN model to predict water quality in WLE and compare its predictive performance with process-based GLM-AED. Chl-a is a US EPA-approved water quality evaluating criterion, which is regarded as a response variable used to measure biotic productivity indicating water impairment level by nutrients [32]. Hence, in this study, we evaluated water quality in WLE by using Chl-a concentrations as criteria. Firstly, based on historical meteorological forcing and monitoring nutrient concentrations, we developed a one-dimensional model GLM-AED and then calibrated it with the observed water temperature and Chl-a concentrations from 2002 to 2015. Secondly, based on the inputs of meteorological forcing and monitored nutrient concentrations, as well as the target of Chl-a concentrations generated by calibrated GLM-AED, we trained the ANN model from 2002 to 2010. Thirdly, we tested the ANN model with the inputs of meteorological forcing and monitoring nutrient concentrations as well as the target of the observed Chl-a concentrations from 2011 to 2015, and then computed the RMSE and MAE values between the predicted and observed Chl-a.