Table 1: Values of the parameters used in the simulations. The effect of some variables on the results was studied by altering their values within a plausible range. For example, several values of porosities, dust-to-ice ratios, and thermal inertia were used in the simulations.
Parameter Value(s) Units

Surface temperature 140, 150, 160 K

$R_{\rm {g}}$ 8.314 J K^-1 mol^-1

$\mu$ 18. g mol^-1

$\rho^{\rm {H_2O,c}}$ 920. kg m^-3

$\rho^{\rm {dust,c}}$ 2500. kg m^-3

$c^{\rm {H_2O}}$ 7.49 $\cdot$ T+90. J kg^-1 K^-1

$c^{\rm {dust}}$ 5. $\cdot$ T J kg^-1K^-1

$K_{\rm {am}}$ $7.1\times 10^{-5}T$ W m^-1K^-1

$K_{\rm {cr}}$ 567./T W m^-1K^-1

$K_{\rm {dust}}$ 2. W m^-1K^-1

T (initial)
30., 70 K

$\rho^{\rm {am}}$ (initial) 19-636 kg m^-3

$\rho^{\rm {dust}}$ 36-667 kg m^-3

p (initial porosity) 0.28-0.82

bulk density 250, 400, 700 kg m^-3

Thermal inertia 20, 100, 400 W K^-1 m^-2 s^1/2

dust-to-ice ratio 0.1, 1, 20

radius 1000 m

depth 5 m

**Table 1:** Values of the parameters used in the simulations. The effect of some variables on the results was studied by altering their values within a plausible range. For example, several values of porosities, dust-to-ice ratios, and thermal inertia were used in the simulations.
Parameter	Value(s)	Units
Surface temperature	140, 150, 160	K
$R_{\rm {g}}$	8.314	J K^-1 mol^-1
$\mu$	18.	g mol^-1
$\rho^{\rm {H_2O,c}}$	920.	kg m^-3
$\rho^{\rm {dust,c}}$	2500.	kg m^-3
$c^{\rm {H_2O}}$	7.49 $\cdot$ T+90.	J kg^-1 K^-1
$c^{\rm {dust}}$	5. $\cdot$ T	J kg^-1K^-1
$K_{\rm {am}}$	$7.1\times 10^{-5}T$	W m^-1K^-1
$K_{\rm {cr}}$	567./T	W m^-1K^-1
$K_{\rm {dust}}$	2.	W m^-1K^-1
T (initial)	30., 70	K
$\rho^{\rm {am}}$ (initial)	19-636	kg m^-3
$\rho^{\rm {dust}}$	36-667	kg m^-3
p (initial porosity)	0.28-0.82
bulk density	250, 400, 700	kg m^-3
Thermal inertia	20, 100, 400	W K^-1 m^-2 s^1/2
dust-to-ice ratio	0.1, 1, 20
radius	1000	m
depth	5	m

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