3.6 Stream temperature modeling
Stream temperature data were analyzed using the one-dimensional heat
transfer model HFLUX (Glose, Lautz, & Baker, 2017).
The following describes a model
modification introduced in this study, while a brief summary of HFLUX is
presented in an electronic supplement.
In previous studies the direct precipitation flux has been calculated
using:qp = 1.16 yp(Tp – Tw ) (1)
where qp is the precipitation flux (W
m-2), yp is precipitation (mm
h-1), Tp is precipitation
temperature (°C), Tw is stream temperature (°C),
and 1.16 is a unit conversion factor including the specific heat of
liquid water (4.2 × 103 J kg-1°C-1) (Hebert et al., 2011; Marcotte & Duong, 1973).
Precipitation temperature is assumed to be equal to air temperature
(Marcotte & Duong, 1973).
At high elevation sites and in winter, precipitation often falls in the
solid state and melts in streams. To account for the latent heat of
fusion in the energy balance calculation, Equation (1) is modified in
this study as:qp = 1.16 yp(Tp – Tw ) + 92.8yp (2)
where the second term represents the effect of the latent heat of fusion
(= 3.34 × 105 J kg-1 at 0 °C) and
unit conversion.
The HFLUX model was calibrated for 12:00 August 14 to 12:00 August 20,
2019, which included a snowfall event. The model was then validated for
12:00 August 20 to 12:00 August 26, 2019. Shading (SF ),
groundwater temperature (TL-gw ) and view to sky
coefficient (VTS ) were estimated during the calibration process,
whilst considering field observations and aerial photographs, as the
parameters were not measured directly. Parameter estimation was carried
out using a nonlinear, multivariable optimization solver known as
fminunc (MathWorks, 2020a) which was integrated with the original code.
The objective function was set to minimize the root-mean-squared-error
(RMSE) between the measured and modeled stream temperatures.