start:hype_model_description:hype_tracer
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start:hype_model_description:hype_tracer [2018/10/11 17:42] cpers [Lake and river ice] |
start:hype_model_description:hype_tracer [2020/04/29 15:09] cpers [Lake and river ice] |
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| === Black ice growth === | === Black ice growth === | ||
| - | Black ice growth (<m>dH_i/dt</m> (cm/s)) is derived from the modified Stefan’s equations as described by Leppäranta (1983): | + | Black ice growth (<m>dH_i/dt</m> (cm/s)) is derived from the modified Stefan’s equations as described by Leppäranta (1983) reduced by heat flow from water. |
| - | <m> dH_i/dt = {k_i/{rho_i * L_f}}*{(T_f - T_a)/(H_i+H_s*{k_i/k_s}+k_i/k_a)} </m> | + | <m> dH_i/dt = {k_i/{rho_i * L_f}}*{(T_f - T_a)/(H_i+H_s*{k_i/k_s}+k_i/k_a)}- qh*100/rho_i/T_f </m> |
| The first part is constant in HYPE. //k<sub>i</sub>// is thermal conductivity of ice (0.022 J/°C/cm/s), //ρ<sub>i</sub>// is density of ice (0.917 g/cm<sup>3</sup>), and //L<sub>f</sub>// is latent heat of freezing (334 J/g). | The first part is constant in HYPE. //k<sub>i</sub>// is thermal conductivity of ice (0.022 J/°C/cm/s), //ρ<sub>i</sub>// is density of ice (0.917 g/cm<sup>3</sup>), and //L<sub>f</sub>// is latent heat of freezing (334 J/g). | ||
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| where //ρ<sub>s</sub>// is density of snow (g/cm<sup>3</sup>). Snow density changes over time depending on a change parameter (//sndens//). | where //ρ<sub>s</sub>// is density of snow (g/cm<sup>3</sup>). Snow density changes over time depending on a change parameter (//sndens//). | ||
| + | |||
| + | qh is heat flow from water during the time step (MJ/m2/day). For rivers it is calculated depending on river velocity (//vel//) and depth (Hw), but for lake it is constant, (parameter //liceqhw//, W/m2). The river equation is | ||
| + | |||
| + | <m> qh = (Tw-Tf)*{{Cwi*vel^0.8}/{Hw^0.2}} * unitf </m> | ||
| + | |||
| + | but limited by minimum and maximum parameters (//riceqhmn, riceqhmx//). Cwi is the heat exchange coefficient, a parameter. A unit transformation (//unitf//) is made from W/m2 to MJ/m2/day. | ||
| + | |||
| The heat released when the black ice is formed at the bottom of the ice layer (<m>rho_i * L_f * {dH_i/dt}</m>) is conducted through the ice and the overlaying snow layer to the atmosphere. This heat flow is driven by the temperature gradient between the air above the ice or snow surface and the freezing temperature of the water assumed at the bottom of the ice layer, and is governed by the depths and thermal conductivities in the ice and snow layers, and the heat exchange coefficient in the air. It should also be noted that a term representing the heat flow from the water has been neglected compared to Leppäranta (1983). | The heat released when the black ice is formed at the bottom of the ice layer (<m>rho_i * L_f * {dH_i/dt}</m>) is conducted through the ice and the overlaying snow layer to the atmosphere. This heat flow is driven by the temperature gradient between the air above the ice or snow surface and the freezing temperature of the water assumed at the bottom of the ice layer, and is governed by the depths and thermal conductivities in the ice and snow layers, and the heat exchange coefficient in the air. It should also be noted that a term representing the heat flow from the water has been neglected compared to Leppäranta (1983). | ||
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| <m> dH_i/dt=-p_m * T_a </m> | <m> dH_i/dt=-p_m * T_a </m> | ||
| - | Ice can be melted from below if the water contain enough heat. This process is limited by a melt efficiency parameter (//me//). | + | Ice can be melted from below if the water contain enough heat. This process is limited by a melt efficiency parameter (//meff//). |
| Final ice break-up is defined as the time step when //H<sub>i</sub>//=0. Although it is well known that ice tend to fall apart before it is completely melted, this is not considered by the present model. | Final ice break-up is defined as the time step when //H<sub>i</sub>//=0. Although it is well known that ice tend to fall apart before it is completely melted, this is not considered by the present model. | ||
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| |:::|//sndens//|//ricesndens, licesndens//|:::| | |:::|//sndens//|//ricesndens, licesndens//|:::| | ||
| |:::|<m>p_m</m>|//ricetmelt, licetmelt//|:::| | |:::|<m>p_m</m>|//ricetmelt, licetmelt//|:::| | ||
| + | |:::|//meff//|//ricewme, licewme//|:::| | ||
| |Surface water processes|//tcf//|//tcfriver, tcflake//|[[start:hype_file_reference:par.txt|par.txt]]| | |Surface water processes|//tcf//|//tcfriver, tcflake//|[[start:hype_file_reference:par.txt|par.txt]]| | ||
| |:::|//scf//|//scfriver, scflake//|:::| | |:::|//scf//|//scfriver, scflake//|:::| | ||
start/hype_model_description/hype_tracer.txt · Last modified: 2024/01/25 11:37 (external edit)
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