Many problems in global climate and Earth systems science require know
ledge of regional- or global-scale distributions of glacier properties
, which includes mass balance, ice velocity, flux, thickness, volume,
and surface area, among others. With roughly 160,000 glaciers worldwid
e, obtaining information on the global probability distributions of mo
st ice properties is expensive and often infeasible. Only surface area
distributions are relatively easy to measure, either by direct observ
ation or remote sensing. While other properties are difficult to obser
ve, this work shows that scaling relationships from the continuum dyna
mics of ice can link the distribution of surface areas to the global a
nd regional distributions of any other continuum property. Some data i
nventories already exist for constructing reasonable distributions of
glacier sizes, and this analysis presents theoretical arguments based
on glacier network topologies (similar in concept to river networks) t
o suggest a power law times an exponential distribution of surface are
as (in agreement with the data). Therefore, by using existing data or
the theoretical distributions of surface areas, specific distributions
for other glacier properties in any region of the world can be constr
ucted. As an example, predictions (up to a scaling constant) are made
for the distribution of glacier volumes, characteristic thicknesses, c
haracteristic velocities, and characteristic response times in the Alp
s.