## 2 Theoretical Model for Water Temperature Field
### Cold Skin Layer Calculation Model of Water  
By combining the water-air interface flux model with the vertical temperature profile calculation model, it is evident that the vertical temperature structure of the water body is primarily governed by shear-driven horizontal turbulence and the heat, moisture, and momentum fluxes at the water-air interface. During daylight hours, solar radiation causes significant warming in the upper few meters of the water body. When the temperature stratification induced by solar radiation becomes sufficiently strong to inhibit shear-induced mixing, the stratification intensity can reach magnitudes of up to 3 K/m. Furthermore, a distinctive phenomenon in the vertical temperature distribution of the water body is the \"cold skin\" effect. The \"cold skin\" refers to a surface temperature boundary layer resulting from the combined cooling effects of net longwave radiation, sensible heat flux, and latent heat flux. The temperature difference between the \"cold skin\" and the underlying water typically ranges from 0.1 to 0.5 K, with a thickness generally on the order of millimeters. Although the overall impact of the \"cold skin\" may be offset by warmer water layers, this effect is nearly always present. [PERSON] [42] outlined the fundamental principles of the \"cold skin\" effect. The cooling flux at the water-air interface is described by Equation (34), and the temperature gradient at this interface \(\psi\) is governed by molecular heat conduction, satisfying the following equation:  
\[\psi=\left.k\frac{\partial T}{\partial z}\right|_{z=0} \tag{34}\]  
where \(k\) denotes the thermal conductivity of water. Away from the water-air interface, the temperature gradient is rapidly disrupted by turbulent mixing. The temperature variation of the \"cold skin\" is confined to a region with a thickness of \(\delta\), expressed as follows:  
\[\Delta T_{c}=\frac{\psi\delta}{k} \tag{35}\]  
The thickness of the \"cold skin\" boundary layer is proportional to the Kolmogorov scale, satisfying the following equation:  
\[\delta:\left(v^{3}/\varepsilon\right)^{1/4} \tag{36}\]where \(\epsilon\) denotes the turbulent dissipation rate. For turbulence induced by surface shear, \(\epsilon:u_{*}^{3}/z\); for turbulence generated by convection, \(\epsilon:ag\psi/(\rho c_{p})\), where \(a\) represents the thermal expansion coefficient of water;  
Therefore, for turbulence generated by shear, the dissipation rate in the diffusion sublayer can be determined by setting \(\delta=z\). Substituting the corresponding turbulent dissipation rate into Equations (37) and (38) yields the following equations:  
\[\delta_{s}=\frac{\lambda v}{u_{*}} \tag{37}\]  
\[\Delta T_{\rm cs}=\frac{\lambda\psi v}{ku_{*}} \tag{38}\]  
Similarly, for turbulence generated by convection, the following condition is satisfied:  
\[\delta_{b}=\left(\frac{k^{2}v}{A^{3}ga\rho c_{p}\psi}\right)^{1/4} \tag{39}\]  
\[\Delta T_{cb}=\left(\frac{v}{A^{3}ga\rho c_{p}k^{2}}\right)\psi/\psi^{1/4} \tag{40}\]  
where \(A\) is an empirical constant; the subscript \(s\) refers to the shear-driven state, and the subscript \(b\) refers to the convection-driven state.