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Additionally, Equation (4) can be adjusted and rearranged to obtain the following equation (Schmidt et al. 2007):
formula
5
The one-dimensional heat steady-state transport model (Equation (5)) is undertaken using the parameters in January and July 2015 shown in Table 3, which can be directly applied to calculate the magnitudes of vertical hyporheic water exchange fluxes. The heat capacity of water and thermal conductivity are obtained by applying measured sediment and water samples. As well, the upper and lower boundary conditions are also significant (Yuan et al. 2008), and have been determined (Table 3) (Schmidt et al. 2007). , as the upper boundary condition, is the temperature value at 0.00 m depth (e.g., the interface between stream and streambed sediment). as the lower boundary condition, is a measured groundwater temperature value of a well close to the stream in the test site. Therefore, the input parameters of the physical properties and boundary conditions during two test periods are determined for the one-dimensional heat steady-state transport model to estimate the magnitudes of vertical hyporheic water exchange (Table 3).
Table 3

Input parameters for determining the physical properties and boundary conditions for one-dimensional heat steady-state transport model (Equation (5))

ParametersValues (winter)Values (summer)Units
Thermal conductivity,  1.695 1.765 J s−1 m−1 k−1 
Heat capacity of water,  4,223 4,224 J kg−1 K−1 
Density of water,  1,000 1,000 Kg m−3 
Upper boundary condition, a 5.2 27.7 °C 
Lower boundary condition, b 11.3 11.8 °C 
ParametersValues (winter)Values (summer)Units
Thermal conductivity,  1.695 1.765 J s−1 m−1 k−1 
Heat capacity of water,  4,223 4,224 J kg−1 K−1 
Density of water,  1,000 1,000 Kg m−3 
Upper boundary condition, a 5.2 27.7 °C 
Lower boundary condition, b 11.3 11.8 °C 

aLocated at the interface (0.00 m) between surface water and streambed.

bLocated at 10.5 m depth below the interface between surface water and streambed.

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