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Julien, we would have to dig deep into the continuum equations, off the top of my head I fail to see how this could produce an energy leak (but yes, my intuition could be wrong.
is correct if you assume that the water is free of any air bubble. The value from Luethi et al. (2002) is indicative of the presence of air, so you probably would have to write
with the air volume virtually unknown. From our current understanding of temperate ice, I don't think we are able to calculate beta from first principles, as you suggest. I see is as a tuning parameter. But again, I could be wrong. |
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Julien, I agree with Andy that I don't think this issue is a energy-conservation leak. (There are other leaks I am more worried about, like at ice sheet margins.) In PISM, and in Aschwanden et al (2012), we are defining internal energy a certain way, and in particular we assume the ice mixture is incompressible. This means our approximation of conservation is less-than-physical, but we can still conserve this defined energy. Yes, pressure does affect pressure-melting temperature. Consider a chunk of ice/water mixture which is experiencing no conductive losses (i.e. take the empirical conductivity to be zero). Suppose it is advected from one pressure level (depth) to a different one. Then the enthalpy does change according to the pressure-melting temperature (and thus Note that a better enthalpy-based conservation of energy model would be compressible. In that compressible theory we would want the Clapeyron equation to hold, and then we would have to decide how air bubbles would shift the value. But we don't have that now. By the way, I am not very confident in my understanding of conservation of energy! I would love to see a critical re-analysis of the theory in Aschwanden et al (2012). You? |
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Extract from the current default config in dev:
According to the Clapeyron equation,
we have:
But using the above values for
T
,L
andrho_i
, andrho_w = 1000
, we getbeta = 8.088e-8 K Pa-1
. I came accross this inconsistence when writing my thesis and wonder if, although small, it may cause energy "leaks" in the model.If this is the case, perhaps the most rigorous fix would be to remove one of these parameters from the configuration file and instead compute it from the three other ones. Arguably that would be the "Clapeyron constant"
beta
. On the other hand, I see the rationale behind using the experimental valuebeta = 7.9e-8
from Lüthi et al. (2002). Maybe the default for ice density should be changed? I am not sure what would be the best fix here...Beta Was this translation helpful? Give feedback.
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