How to Set Maximum Water Content?

[andrewdnolan]

How do we determine where the maximum water content should be the value for glacier ice (~3%) versus firn (~10%)?

For now I've set the maximum water content based on density:

thermal-structure/src/elmer_UDF/Thermodynamics.f90

Lines 92 to 98 in a4faedd

	! If density less than poreclose off, allow more water content
	if (rho .lt. rho_f) then
	! Eqn. (10) from Aschwanden et al. 2012
	H_max = H_f + w_max_aq*L_heat
	else
	H_max = H_f + w_max_en*L_heat
	endif

From a prescribed surface density profile if the nodal density rho is less than pore close off rho_f then allow the maximum water content to correspond to firn.

Gwenn made a good point that maybe firn values of maximum water content should be confined to the "firn aquifer". The firn aquifer thickness is a free parameter which we need to set and have been using a reference value of ~3 m for experiments . So in practice, because of our vertical grid cell spacing, this means only the surface nodes would have firn water content values.

My thought process was given the higher porosity of firn we should allow for more water content. That being said the whole idea of setting firn aquifer thickness is that's the depth over which melt percolates, below which some unmodeled physical processes initiate instantaneous run-off. From the tests I was running with sample data using the firn model, rarely did melt actually reach an impermeable layer (i.e. the ice base) more often in my tests all the melt was consumed to heat the snow pack. I didn't allow for ice lenses when testing the firn model, but that seems beyond our needed level of complexity.

Not really sure about this one, guess some test to see how important this actually is would be useful.

[andrewdnolan]

From a closer rereading of Wilson and Flowers (2013) it appears as though Nat used to the firn aquifer thickness to prescribe the maximum englacial water content. While it's not explicitly stated, the second row of Figure 7. makes it clear that the maximum aquifer water content is coupled to the firn aquifer thickness.

Given that $h_{\rm aq}$ is the denominator

$$ \begin{equation} Q_{\rm lat} = (1 - r) \frac{\rho_{\rm w}}{h_{\rm aq} \Delta t} L M , \end{equation} $$

but Figure 7. from W&F (2013) show increasingly warmer glaciers with larger firn aquifers; the maximum aquifer water content must be coupled to the thickness.

Given our currently approach, using the pore close off density to set the maximum firn water content, $h_{\rm aq}$ has no physical meaning and actually have an inverse relationship than the W&F (2013). Given that it's in the denominator, the amount of heat added is inversely proportional to $h_{\rm aq}$.

The problem with using the firn aquifer thickness to prescribe the maximum water contents means we need <1 m vertical mesh resolution at the surface, which we definitely aren't achieving with 15 vertical layers. Looks like in Wilson et al. 2013, Nat used 50 vertical layers. This becomes extra challenging to deal with as we scale up to Kluane glacier which is considerably thicker, so would need even MORE vertical layers.