Errors in the determination of ablation using stakes: comments on Dr. Vallon's letter

Sir,

It may just be worth adding the following remark to M. Vallon’s letter. When the strain of the ice over the interval considered is large it is perhaps not immediately obvious how to calculate the correction term, because the length of stake buried in the ice, the gauge Length, is changing over the interval in an irregular way, as the ablation rate changes. But, if one assumes that the vertical strain-rate

is constant, it is easy to show that

where b is the true ablation, e is the length of stake exposed (the apparent ablation), Δt is the time interval, and

is the Lime average of the length of stake between the anchored point (which may be the bottom of the stake) and the surface. This holds for any variation in ablation rate, however irregular.

will not normally be known accurately, and must be estimated from the varying ablation rate over the interval.

21 August 1967