## 2 Study Area, Lake Model, and Data
### Data  
In this study, in situ observation data were utilized for both model input and evaluation, as presented in Table 1 and Figure 1. The lake characteristics, including depth, length, and area, were incorporated into the model. Additionally, datasets concerning various lake ecological processes, such as water nutrients, phytoplankton, and water quality, were gathered from the academic literature [16; 41; 47; 48; 49; 50; 51; 52; 53; 54], as shown in Table S1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Parameter** & **Value** & **Reference** \\ \hline \multirow{4}{*}{Lake characteristics} & Surface area & 1997.55 km\({}^{2}\) & [47] \\  & Mean depth & 40 m & [41] \\  & Maximum depth & 95 m & [41] \\  & Shortwave radiation & Figure 2a & [48; 49] \\ Local climate & Wind speed & Figure 2b & [48; 49] \\  & Water temperature & Figure 2d & [50; 51] \\ Lake thermodynamics & Water volume & Figure 2c & [47] \\  & Water evaporation & 27.52 int & [16] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main input parameters and setting values for the AQUATOX model.  
Figure 1: Geophysical location map of Lake Namco.  
The meteorological data used in our study encompassed downward shortwave radiation and wind speed, which exhibited a slight decreasing trend over the study period. Furthermore, lake thermodynamic data, comprising lake water temperature (WT), evaporation, lake water volume (WL), and lake water area (WA), were considered. Notably, both the lake volume and area of the lake exhibited rapid increases after the 2000s, as depicted in Figure 2.  
In our study, simulations were conducted for the period from 1980 to 2020, with a daily temporal resolution. To mitigate the effects of interannual fluctuations, the simulation results for each decade (1981-1990, 1991-2000, 2001-2010, and 2011-2020) were analyzed. In this paper, the main variables used to represent lake ecology are WTP, WTN, and Chl-a), and primary production (WGPP and WNPP).  
To elucidate the factors influencing lake ecological processes, long-term series data for meteorological and lake thermodynamic elements were employed to assess their respective impacts on lake ecological variations. Meteorological data were sourced from the multi-circle comprehensive observation and research station around Lake Namco [48; 49] and included downward shortwave radiation (DSR), air temperature (AT), specific humidity (SH), wind speed (WD), air pressure (AP), and precipitation (PC).  
To delineate the influence of meteorological elements on lake ecological indicators, including WTN, WTP, Chl-a, WGPP, and WNPP, a multiple linear regression model was employed using the SPSS software version 25. Generally, the relationship between the dependent and independent variables is expressed as shown in Equation (1):  
\[y=a_{1}x_{1}+a_{2}x_{2}+a_{3}x_{3+}\cdots+a_{1}x_{i}+b \tag{1}\]  
where \(y\) is the dependent variable, \(x_{i}\) (\(i=0\), \(1\),\(\ldots\), \(n\)) is the independent variable, \(a_{i}\) (i = 0, \(1\),\(\ldots\), \(n\)) is the regression coefficient, and \(b\) is the constant term. The relative contribution of the changes in lake water ecological indicators was estimated using multiple regression coefficients as shown in Equation (2):  
Figure 2: Variations in meteorological and lake thermal and dynamic elements of **(a)** downward shortwave radiation, **(b)** wind speed, **(c)** lake water volume, and **(d)** lake water temperature for Lake Namco.  
\[n_{\rm i}=a_{\rm i}/(\left\lfloor a_{\rm 1}\right\rfloor+\left\lfloor a_{\rm 2} \right\rfloor+\left\lfloor a_{\rm 3}\right\rfloor+\cdots+\left\lfloor a_{\rm i}\right\rfloor) \tag{2}\]  
where \(n_{\rm i}\) is the relative contribution coefficient. The larger this value, the greater the contribution from the independent variable to the dependent variable.