Modified parameterization of the vertical water temperature profile in the FLake model

Table 1.

AuthorsParameterizationApplicationAnderson and Munk 1947 (cited from Mironov 2008)Verbal mention of the ‘almost constant shape’ of the temperature profile beneath the upper mixed layerLake water columnKitaigorodskii and Miropolsky (1970)$T^{\ast }(\zeta )=\frac{8}{3}·\zeta -2·{\zeta }^2+\frac{1}{3}·{\zeta }^4$(8)Oceanic active layer Arsenyev and Felzenbaum (1977)T*(ζ) = 1 – (1 – ζ)³(9)Oceanic active layerMalkki and Tamsalu (1985)$T^{\ast }(\zeta )=\begin{array}{ccc}1-{(1-\zeta )}^3\hfill & \text{at}\hfill & \text{d}h/\text{d}t>0\hfill \\ 1-4·{(1-\zeta )}^3+3·{(1-\zeta )}^4\hfill & \text{at}\hfill & \text{d}h/\text{d}t\le 0\hfill \end{array}$(10)Baltic Sea active layer, water column of lakesGolosov et al. (2003)T*(ζ) = (2 – B(t)) ⋅ ζ + (B(t) – 1) ⋅ ζ²(11)Water column of lakes at ice cover periodMironov (2008)T*(ζ) = ζ(12)Water column of lakes at ice cover period, snow and ice cover Golosov et al. (1998); Golosov and Kirillin (2010)$\begin{array}{ccc}{T}_1^{\ast }({\xi }_1)=2·{\xi }_1-{\xi }_1^2\hfill & \text{at}\hfill & D\le z\le H\hfill \\ T_2^{\ast }({\xi }_2)=3·{\xi }_2^2-2·{\xi }_2^3\hfill & \text{at}\hfill & H\le z\le L\hfill \end{array}$(13)Bottom sediments of lakes

Table 2.

AuthorsParameterizationValues of A(t) and B(t) in new parameterizationKitaigorodskii and Miropolsky (1970)$T^{\ast }(\zeta )=\frac{8}{3}·\zeta -2·{\zeta }^2+\frac{1}{3}·{\zeta }^4$(8)$\begin{array}{c}A=2.85\hfill \\ B=0\hfill \end{array}$Arsenyev and Felzenbaum (1977)T*(ζ) = 1 – (1 – ζ)³(9)$A=3,B=0$Malkki and Tamsalu (1985)$T^{\ast }(\zeta )=\begin{array}{ccc}1-{(1-\zeta )}^3\hfill & \text{at}\hfill & \text{d}h/\text{d}t>0\hfill \\ 1-4·{(1-\zeta )}^3+3·{(1-\zeta )}^4\hfill & \text{at}\hfill & \text{d}h/\text{d}t\le 0\hfill \end{array}$(10)$\begin{array}{cc}A=3,\hfill & B=0\hfill \\ A=?,\hfill & B=?\hfill \end{array}$Golosov et al. (2003)T*(ζ) = (2 - B(t)) ⋅ ζ + (B(t) – 1) ⋅ ζ²(11)A(t) ∊ [0, 2], B(t) ∊ [0, 2]Mironov (2008)T*(ζ) = ζ(12)A = 1, B = 1Golosov et al. (1998); Golosov and Kirillin (2010)$\begin{array}{ccc}{T}_1^{\ast }({\xi }_1)=2·{\xi }_1-{\xi }_1^2\hfill & \text{at}\hfill & D\le z\le H\hfill \\ T_2^{\ast }({\xi }_2)=3·{\xi }_2^2-2·{\xi }_2^3\hfill & \text{at}\hfill & H\le z\le L\hfill \end{array}$(13)$\begin{array}{cc}A=2,\hfill & B=0\hfill \\ A=0,\hfill & B=0\hfill \end{array}$