Obtaining ELA from AAR method

I am trying to understand how to obtain ELA using Accumulation area ratio method. My understanding is:

• Accumulation area/ ablation area is assumed to be constant.
• Empirical data of long term annual mass balance, Bn and corresponding AAR is needed to obtain steady state AAR of a particular glacier.(For the graph of AAR vs Bn, corresponding AAR value for Bn = 0)
• Total area of the glacier should be known.

Now, with AARo and total glacier area, how do I obtain ELA?

The ELA (Equilibrium Altitude) is related to the AAR (Accumulationa Area relationship). But before exploring the realationship we must establish what these entities mean.

First, AAR, relates the area occupied by the accumulation area to the total area by the glacier. The accumulation area is by definition the area showing a surplus of mass by the end of the season. This means that the snow falling during the year survives the melt season. Hence we relate the total area of the glacier to the area experiencing a net surplus of mass at the end of the mass balance year to yield a percentage value indicating what percentage of the glacier is experiencing a surplus.

The area experiencing surplus of mass is defined as the accumulation area and the area experiencing a deficit of mass is defined as the ablation area. On any glacier, the line separating the areas of surplus and deficit of mass is defined as the equilibrium line. This means that the total mass gain equals the mass loss along this line and on each side there will be a net gain or loss of mass.

The equilibrium line will ideally divide the glacier into two areas experiencing net total mass loss and mass gain, respectively. Because mass gain is commonly occuring at higher altitude and mass losses occuring at lower altitudes due to snow distribution and the decrease of temperature and hence melting with altitude, areas of mass loss occur at lower elevation while areas of mass gain occurs at higher elevation.

The equilibrium line altidude (ELA) is usuually a calculated entity dependent on where the net balance curve of the glacier crosses the zero balance, i.e. the altitude where the glacier net balance changes sign or goes from loss to gain or vice versa.

Based on this we can see that ELA and AAR are related but calculated in different ways from the same original data. AAR is simply the relationship between the area of positive and negative mass change whereas the ELA is the altitude where the elevation dependent mass balance turns from postive to negative or vice versa.

References

[Cogley et al., 2011] [1]

[Kaser et al. 2003] [2]