## 2 Materials and Methods
### Artificial Neural Network Model
#### 2.2.2 Learning Dataset and Normalization  
The learning data used in the ANN model were based on 14 items: freshwater discharge (discharge), water temperature (temperature), salinity, surface and bottom temperature difference (\(\Delta\)T), surface and bottom salinity difference (\(\Delta\)S), transparency, photosynthetically active radiation (PAR), duration of sunshine (DS), solar radiation (SR), NO\({}_{2}\)- + NO\({}_{3}\)-, NH\({}_{4}\)+, DSi, PO\({}_{4}\)3-, and dissolved inorganic nitrogen to dissolved inorganic phosphorus ratio (DIN/DIP) (Table 1).  
Figure 2: Structure of the artificial neural network model.  
Discharge is total amount of freshwater discharge for 4 days before sampling. The differences in water temperature and salinity in the surface water compared with the bottom samples indicated stratification and turbulence, and the DIN/DIP was used as an indirect indicator of nutrient limitation. The three items of output data were total chlorophyll \(a\) (total chl _a_) to indicate the total phytoplankton biomass [30], and size-fractionated (across 20 \(\upmu\)m) biomass as net-sized chlorophyll \(a\) (net chl _a_) and nano-sized chlorophyll \(a\) (nano chl _a_). The output values of the ANN model were obtained through the sigmoid function that produces values between 0 and 1, and for unifying the scale and units of the 17 environmental factors, normalization was applied to the input and output data. Equation (1) was used to convert the values to those between 0.05 and 0.95.  
\[\chi_{t}=0.05+0.9\left[\log_{\frac{\text{max}}{\chi_{min}}}\left(\frac{\chi_{ o}}{\chi_{min}}\right)\right] \tag{1}\]  
where  
\(\chi_{min}\): 5% minimum value  
\(\chi_{max}\): 95% maximum value  
\(\chi\): original data  
\(\chi_{t}\): transformed data.  
The examples of the histogram and cumulative distribution function of normalized and original input variable are shown in Figure 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter (unit)** & **Range** & **Mean \(\pm\) SD** \\ \hline Discharge (\(\times 10^{3}\) ton) & 1.00–52,621.00 & 7673.05 \(\pm\) 13,301.20 \\ Temperature (\({}^{\circ}\)C) & 2.78–26.54 & 13.05 \(\pm\) 7.16 \\ Salinity (psu) & 11.82–35.19 & 30.74 \(\pm\) 3.63 \\ \(\Delta\)T (\({}^{\circ}\)C) & 0.45–7.69 & 2.56 \(\pm\) 1.09 \\ \(\Delta\)S (psu) & 1.57–22.77 & 3.43 \(\pm\) 3.25 \\ Input data & Transparency (m) & 0.40–5.20 & 1.49 \(\pm\) 0.73 \\ PAR (\(\upmu\)m m\({}^{-2}\) s\({}^{-1}\)) & 1.81–1630.00 & 395.62 \(\pm\) 376.67 \\ Duration of sunshine (h) & 0.10–12.20 & 6.43 \(\pm\) 3.76 \\ Solar radiation (MJ m\({}^{-2}\)) & 1.06–28.42 & 14.33 \(\pm\) 6.79 \\ NO\({}_{2}\)\({}^{-}\) + NO\({}_{3}\)\({}^{-}\) (\(\upmu\)M) & 0.07–258.17 & 24.15 \(\pm\) 40.35 \\ NH\({}_{4}\) (\(\upmu\)M) & 0.21–88.29 & 9.11 \(\pm\) 11.30 \\ USi (MM) & 0.93–269.20 & 30.60 \(\pm\) 33.43 \\ PO\({}_{4}\)\({}^{3-}\) (\(\upmu\)M) & 0.02–31.23 & 1.24 \(\pm\) 3.19 \\ DIN/DIP & 0.54–1852.68 & 89.31 \(\pm\) 185.31 \\ \hline \multirow{3}{*}{Output data} & Total chl \(a\) (\(\upmu\) L\({}^{-1}\)) & 0.18–35.84 & 5.25 \(\pm\) 6.48 \\  & Net chl \(a\) (\(\upmu\) L\({}^{-1}\)) & 0.02–21.02 & 2.34 \(\pm\) 3.61 \\ \cline{1-1}  & Nano chl \(a\) (\(\upmu\) L\({}^{-1}\)) & 0.02–29.22 & 2.90 \(\pm\) 4.50 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Range and mean (standard deviation) of input and output data used in the artificial neural network model.  
Figure 3: Histogram and cumulative distribution function (CDF) of original and transformed data for the input variables. (**a**) water temperature, (**b**) salinity, (**c**) solar radiation, (**d**) DIN/DIP ratio.