### 2.6.2.2. Surface Water[¶](#surface-water "Permalink to this headline")

Phase change of surface water takes place when the surface water temperature, \\(T\_{h2osfc}\\), becomes less than \\(T\_{f}\\). The energy available for freezing is

(2.6.71)[¶](#equation-6-73 "Permalink to this equation")\\\[H\_{h2osfc} =\\frac{\\partial h}{\\partial T} \\left(T\_{f} -T\_{h2osfc}^{n} \\right)-\\frac{c\_{h2osfc} \\Delta z\_{h2osfc} }{\\Delta t} \\left(T\_{f} -T\_{h2osfc}^{n} \\right)\\\]

where \\(c\_{h2osfc}\\) is the volumetric heat capacity of water, and \\(\\Delta z\_{h2osfc}\\) is the depth of the surface water layer. If \\(H\_{m} =\\frac{H\_{h2osfc} \\Delta t}{L\_{f} } >0\\) then \\(H\_{m}\\) is removed from surface water and added to the snow column as ice

(2.6.72)[¶](#equation-6-74 "Permalink to this equation")\\\[H^{n+1} \_{h2osfc} =H^{n} \_{h2osfc} -H\_{m}\\\]

(2.6.73)[¶](#equation-6-75 "Permalink to this equation")\\\[w\_{ice,\\, 0}^{n+1} =w\_{ice,\\, 0}^{n} +H\_{m}\\\]

The snow depth is adjusted to account for the additional ice mass

(2.6.74)[¶](#equation-6-76 "Permalink to this equation")\\\[\\Delta z\_{sno} =\\frac{H\_{m} }{\\rho \_{ice} }\\\]

If \\(H\_{m}\\) is greater than \\(W\_{sfc}\\), the excess heat \\(\\frac{L\_{f} \\left(H\_{m} -W\_{sfc} \\right)}{\\Delta t}\\) is used to cool the snow layer.

