## Case 1 Free Water Surface Wetland Prior to Ice Formation

Equation 6.25 is used to calculate the water temperature at the point of interest in the wetland. Experience has shown that ice formation commences when the bulk temperature in the liquid approaches 3°C (37°F) because of density differences and convection losses at the water surface (Ashton, 1986; Calkins, 1995). Equation 6.15 is therefore repeated until a temperature of 3°C is reached or until the end of the wetland cell is reached, whichever comes first. If a temperature of 3°C is reached prior to the end of the wetland, then Equation 6.17 is used to calculate the temperatures under an ice cover. If the wetland is composed of vegetated zones interspersed with deeper open water zones, Equation 6.15 must be used sequentially, with the appropriate heat-transfer coefficient (Us) to calculate the water temperatures:

where

Tw = Water temperature (°C; °F) at distance x (m; ft).

Tair = Average air temperature during period of interest (°C; °F).

T0 = Water temperature (°C; °F) at distance x0 (m; ft), the entry point for the wetland segment of interest. Us = Heat-transfer coefficient at the wetland surface (W/m2-°C; Btu/ft2-hr-°F).

= 1.5 W/m2-°C (0.264 Btu/ft2-hr-°F) for dense marsh vegetation. = 10-25 W/m2-°C (1.761-4.403 Btu/ft2-hr-°F) for open water; high value used for windy conditions with no snow cover. cp = Specific heat = 1.007 Btu/lb-°F (4215 J/kg-°C).

If the first iteration shows a temperature of less than 37°F (3°C) in the final effluent from the wetland, Equation 6.15 can be rearranged and solved for distance x at which the temperature becomes 37°F:

x - x0 = -[8yvcp/Us][ln(37 - Tak)/(T - Tak)] (6.16)

Example 6.1

Calculate the water temperature in a three-stage FWS constructed wetland:

Stage 1: Length 300 ft, depth 1 ft, densely vegetated, flow velocity 0.2 ft/hr Stage 2: Deep open-water zone, length 100 ft, depth 4 ft, flow velocity

0.1 ft/hr Stage 3: Same as stage 1

Air temperature, 49°F; influent wastewater temperature, 70°F Solution

1. Use Equation 6.15 to calculate the temperature at the end of stage 1: Tw = 49 + (70 - 49) exp[-0.264(300)/(62.4)(1)(11.7)(1.007)]

2. Calculate the water temperature at the end of stage 2:

Tw = 49 + (67.9 - 49) exp[-0.264(100)/(62.4)(4)(5.85)(1.007)] Tw = 49 + (18.9)(0.836) = 64.8°F

3. Calculate the water temperature at the end of the wetland: Tw = 49 + (64.8 - 49) exp[-0.264(300)/(62.4)(1)(11.7)(1.007)] Tw = 49 + (15.8)(0.9) = 63.2°F