Your suggestion that rampart craters penetrate deeply enough into the cryosphere to "access liquid water", seems to suggest that the isotherms of subsurface temperature are flat and horizontal. In fact, the isotherms will be concordant with surface topography, so at the walls and floors of craters, the isotherms are depressed just as much as the topography is. perhaps you're arguing that you can access these layers laterally, but you should make that clear with a diagram.

Don Musselwhite covered this ground in his 2001 GRL paper, but he was looking at CO2 liquid breakout. You can use the same treatment for liquid water, but I think you'll find it fails.

Your model of a multi-km dry dessicated (and poorly conducting) regolith on Mars is a bit suspect. One would expect subsurface ice to occur well above any possible liquid water, and once it does, it will push down the 273K isotherm remarkably. Although the regolith of Mars is likely fractured from sustained meteorite bombardment, it nevertheless appears to be moderately well-cemented, judging from the evident strength of crater rims and canyon walls. Modelling as fluffy dust is not a good idea and leads you to the same errors that Clifford and Fanale fell into.

I strongly question your figure 7. You have a mean annual surface temperature of 210K at 30 degrees lattitude. Yet you show a depth to the 273 K isotherm of ZERO. How on Earth (Mars) do you achieve this? If you cut out all the confusing numbers about conductivity and heat flow and just compare apples-with-apples. In Antarctica, the surface temperature is similar to this location on mars, yet the Icecap is 3 km thick. Mars should have about half the geothermal gradient, so you'd expect 5 or 6 km of ice-saturated regolith.

if I try to deconstruct your figure 7, I see that between 30 degrees and 60 degrees lattitude, surface temperature cools from 210K to 180K - a change of 25K. AT the same time, the depth to the 273K isotherm deepens by 7.5 km, implying a geothermal gradient of 3.3K/km. This is an adequately low figure for Mars (in fact, it may even be TOO low - I'd accept 5 or 10 K/km). Anyway, if we use THIS figure, then the depth to the 273K isotherm, when the surface temperature is 210 K is 63/3.3 km or 19 km!

The latitude dependence of the "depth" below crater rims where gullies "begin" (your figures 3 and 4) is really only measuring the behaviour of icepack, which requires more shelter below the crater rim at lower latitudes. In each case, we see a seasonal thaw of the icepack and when conditions are right, a CO2-gas-lubricated flow can be triggered.

The concept of a "depth below surface" for flows "beginning" is one of the most painfully wrong aspects of the interpretation of the Gullies on Mars. it is a way of thinking that presupposes an earth-like Mars with abundant shallow aquifers, rather than a Mars-like arid-surfaced icecube.

If you ASSUME a wet Mars, then your method shows you at what depth that liquid water is. Now you must show HOW liquid water can survive at that shallow depth on Mars. I don't think this paper goes any way towards explaining that, and it is riddled with inconsistencies and undeclared assumptions.

Sorry...