## 2 Materials and Methods
### Artificial Neural Network Modeling
In the ANN model, a hyperbolic tangent sigmoid transfer function (_tansig_) and linear transfer function (_purelin_) were used for hidden and output layers, respectively:  
\[\text{ansig}(\text{x})=\frac{2}{1\ +\ e^{-2x}}-1;\ \ \ \ \text{purelin}(\text{x})= \text{x} \tag{1}\]  
with _tansig_ and _purelin_ transfer function, general form of ANN model is presented as follow:  
\[ \begin{split}\left[\begin{array}{c}h_{k,1,1}\\ \vdots\\ h_{k,1,n}\end{array}\right]=\text{tan}\ \text{sig}\left(\left[\begin{array}{c} \overset{\rightarrow}{w}_{k,1,1}\\ \vdots\\ \overset{\rightarrow}{w}_{k,1,n}\end{array}\right]\times\left[\begin{array}[] {c}x_{1}\\ \vdots\\ x_{9}\end{array}\right]+\left[\begin{array}{c}b_{k},1,1\\ \vdots\\ b_{k,1,n}\end{array}\right]\right)\\ f_{k}=\text{purelin}\overset{\rightarrow}{w}_{2,k}\times\left[\begin{array}[] {c}h_{k,1,1}\\ \vdots\\ h_{k,1,n}\end{array}\right]+\ b_{2,k}\end{split}  \tag{2}\]  
where \(k\) is the order of output variables. \(f_{k}\) is the predicted value of \(k\)th output variable. The schematic structure of ANN model used in this study is illustrated in Figure 1.  
As an indicator of the optimal weights (\(w\)) and biases (\(b\)) and ANN topology, the mean squared error (MSE) was chosen (Equation (3)). Figure 1: Schematic structure of ANN model. \[\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}{(y_{i}-f_{i})} \tag{3}\]  
where \(y_{i}\) is the observed output value and \(f_{i}\) is the predicted value from ANN model. The _Levenberg-Marquardt_ algorithm was employed to optimize the ANN model by minimizing the MSE value [20]. While it would be nice to develop a model that can predict all output variables simultaneously, we developed a model separately for each output variable because we do not have all the data for all output variables in learning. Each dataset for a specific output variable was randomly divided into three subsets including training (60%), validating (20%), and testing (20%). Based on the _Levenberg-Marquardt_ algorithm, the ANN model was iterated to reduce MSE between the predicted values and observed values of the training subset by modifying and adjusting the w and b matrices. With adjusting the w and b matrices, MSE was calculated between the predicted and observed values of the validating subset. In this step, the w and b matrices with the lowest MSE from validating subset were chosen as the optimized values for the ANN model. After optimizing the ANN model, the testing subset was used to compare the predicted values with the observed values to assess the performance of the developed ANN model [21; 22]. This optimization process is performed in a certain topology. Since the topology is also a factor that greatly affects the predictability of ANN models, we optimized and compared ANN models for various topologies in this study. Using nine input variables and one output variable, the number of hidden layers and the number of hidden layer neurons were varied to determine the optimal topology. Initially, a single hidden layer with hidden layer neurons varying from five (9:5:1) to fifteen (9:15:1) was tested for the network topology. Based on the lowest MSE value, the best network topologies were selected as the best topology for each output variable. Further verification with the data not used for ANN model optimization was also performed to test the predictability of the developed ANN model. The dataset for further verification was chosen from our previous studies, as presented in Table 2.