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Ablation cup
Equation
To calculate the ablation rate (melting speed), we\'ll assume that the glacier has a height h and is at a temperature $\Delta T$ below the melting point. The energy captured by a layer of height $\Delta x$ is partly conducted into the glacier, contributing to the melting of the layer and its warming. If l is the latent heat and $\rho_e$ the ice density, a volume element with surface $S$ and height $\Delta x$ will require the energy
$\Delta Ql = S\Delta x l \rho_e$
to melt.
To heat it up to the melting temperature $\Delta T_m$, it will require
$\Delta Q_c = S\Delta x\rho_ec\Delta T_m$
where c is the specific heat. Lastly, thermal conduction will remove heat
$\Delta Q_{\lambda}=\displaystyle\frac{\lambda S\Delta T_b}{h}\Delta t$
where $\lambda$ is the thermal conductivity, $\Delta T_b$ is the base-surface temperature difference, and $\Delta t$ is the elapsed time.
Therefore, the total heat will be
$\Delta Q_l + \Delta Q_c + \Delta Q_{\lambda} = (1 - a_{ev})(1 - \gamma_v)S I_s\Delta t$
which, after replacing with the expressions, becomes
$S\Delta xl\rho_e + S\Delta x\rho_ec\Delta T_m + (\lambda/h)S \Delta T_b \Delta t = (1 - a_{ev})(1 - \gamma_v)S I_s\Delta t$
Solving for
 $ v_a =\displaystyle\frac{(1 - a_{ev} )(1 - \gamma_v ) I_s - ( \lambda / h ) \Delta T_b }{ \rho_e (l + c \Delta T_m )}$ |
Hence, an increase in temperature leads to an increase in the ablation rate.
ID:(7432, 0)
Accumulation Rate
Equation
The accumulation rate, denoted as
| $ v_c =\displaystyle\frac{ \Delta x }{ \Delta t }$ |
ID:(7612, 0)
Mass balance rate
Equation
Solar radiation is partly reflected and partly absorbed by the surface. If $I_s$ is the radiation flux, $a_{ev}$ is the Earth\'s visible albedo, and $\gamma_v$ is the coverage factor, the absorbed fraction is
$(1 - a_{ev})(1 -\gamma_v)I_s$
The heat supplied is partly conducted into the glacier\'s interior and partly contributes to melting a layer of thickness $\Delta x$ in a time $\Delta t$.
In this way, the glacier\'s surface would decrease at an ablation rate (melting speed)
$v_a =\displaystyle\frac{\Delta x}{\Delta t}$
due to the melting effect, while it would grow at an accumulation rate $v_c$ (snow deposition speed) due to the effect of snow being deposited on its surface. Therefore, melting would occur if the total velocity
| $ v_b = v_c - v_a$ |
turns out to be negative.
ID:(7434, 0)
Glacier height variation
Equation
La taza de balance de masa que se calcula de la taza de acumulación y la taza de ablación
| $ v_b = v_c - v_a$ |
permite estimar la variación en la altura especifica del glaciar (en un lugar en particular)
| $\Delta h=v_b\Delta t$ |
ID:(8249, 0)