Estimation of Glacier Volume and Volume Change by Scaling Methods

Definition

Scaling relationship. A power-law exponential equation that relates two quantities such as volume and area.

Estimating volume

Glacier volume V can be estimated from the glacier surface area A using the scaling relationship

$$V = k{A^\gamma }$$

(1)

where γ and k are derived from either data or theory (Figure 1). Typical values are γ = 1.36 and k = 0.033 km^3–2γ for valley glaciers (Macheret et al., 1988; Chen and Ohmura, 1990; Bahr et al., 1997; Bahr, 1997). In many cases, measurements of the glacier volume would be preferable, but this has been done for relatively few glaciers (less than 200), and generally cannot be accomplished without considerable time or expense. The most common measurement technique uses ground-penetrating radar (see entry “ Ground Penetrating Radar Measurements Over Glaciers ”), but with crevasses and inaccessible terrain, hundreds of thousands of glaciers cannot be practically measured using this approach.

Estimation of Glacier Volume and Volume Change...