# Analysis of the Water Circulation Structure in the Paldang Reservoir, South Korea
## 2 Materials and Methods
### Water Stability Analysis  
This study examined multiple parameters, such as water temperature, water temperature gradient with depth (DT/DZ), flow velocity, the Richardson number (Ri), and stratification coefficient, to analyze the stability of the water mass. The Richardson number is the dimensionless ratio of the flow velocity  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Kriging type & Point \\ Transformation method & Linear (use z values directly) \\ Break line filtering & Not in use \\ Polynomial drift order & 0 \\ Kriging standard deviation grid & 0 \\ Semi-variogram model: & \\ Component type & Linear \\ Anisotropy angle & 0 \\ Anisotropy ratio & 1 \\ Variogram slope & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters for gridding utilized in the Kriging interpolation.  
gradient to the density gradient and is used as an indicator of vertical mixing in a stratified fluid; this number can be expressed as follows:  
\[\text{Ri}=-\frac{g}{\rho}\frac{\partial\rho/\partial z}{\partial u/\partial z)^{ 2}}\, \tag{1}\]  
\[\begin{array}{l}\rho=999.842594+\Big{(}6.793952\times 10^{-2}\Big{)}T-\Big{(}9.095290\times 10^{-3}\Big{)}T^{2}\\ +\Big{(}1.001685\times 10^{-4}\Big{)}T^{3}-\big{(}1.120083\times 10^{-6}\Big{)}T^{4 }+\Big{(}6.536332\times 10^{-9}\Big{)}T^{5},\end{array} \tag{2}\]  
where g is the gravity acceleration (m/s\({}^{2}\)), \(\rho\) is the density (kg/m\({}^{3}\)), z is the vertical position (m), u is the flow velocity (m/s), and T is the water temperature (\({}^{\circ}\)C). Similar to flow velocity, water temperature was averaged at an interval of 10 min, and density was calculated based on these data. Flow velocity was measured at an interval of 0.2-0.5 m, while water temperature was measured at an interval of 1 m; accordingly, the calculation was performed based on the water layer in which the water temperature was measured. For the analysis of measured data, flow velocity data (1 m intervals) were used in the same position as the water temperature data. The density and flow velocity differences between the upper and lower layers were computed and defined at a point between layers. Therefore, the Richardson number was also defined at the midpoint of the water layers where the water temperature was measured.  
For the analysis of water stratification, the stratification coefficient was calculated [39; 40; 41; 42]. The stratification coefficient, defined as the work per unit volume required to fully mix a water layer, can be represented as the potential energy anomaly (PEA; J/m\({}^{3}\)) [40] due to differences between the potential energy currently present in the water layer and the potential energy present in the water layer when fully mixed in a vertical direction. If density inversion occurs vertically, then negative values are produced. [PERSON] et al. [43], [PERSON] et al. [44], [PERSON] et al. [45], and [PERSON] and [PERSON] [46] defined a stratification coefficient, log(PEA), of less than 1 as a value indicative of vertical mixing or density inversion and a log(PEA) greater than 1 as a value indicative of stratification. Based on this, they analyzed the stratification characteristics of the reservoir in their study area.  
\[\text{PEA}\ =\ \frac{g}{H}\int_{-H}^{0}(\overline{\rho}-\rho(z))z\,dz, \tag{3}\]  
where H is the total water depth (m) and \(\overline{\rho}\) is the depth-averaged density (kg/m\({}^{3}\)). Similar to the Richardson number calculation, the water temperature data averaged at 10 min intervals were used. The ADCP data observed at an interval of 10 min, from the same monitoring site, were used to examine the water depth. Moreover, density was computed in the same manner as the Richardson number calculation, and the results were employed for the PEA calculations.