The episodes of ice-rafted detritus (IRD) accumulation identified in N
orth Atlantic sediment cores indicate periods of abnormal iceberg prod
uction mainly of the Laurentide Ice Sheet. In this paper we develop fu
rther a scaling theory of these so-called Heinrich events, leading to
a general criterion for basal melting of an ice sheet which we take as
a necessary condition for Surging and streaming. This criterion depen
ds not only on the physical properties of ice sheets and the magnitude
of the geothermal and viscous heating but also on the history of chan
ges in ice elevation, atmospheric carbon dioxide, and sea surface temp
erature, the thermal effects of which at the top of an ice sheet are t
ransmitted with a time delay to the basal boundary by thermal advectio
n. We apply this criterion to various past and present ice sheets show
ing their general vulnerability to surging. In greater detail, we use
estimates of the time variations of ice volume (SPECMAP), carbon dioxi
de (Vostok), and North Atlantic sea surface temperature (site K708-1)
to estimate when basal melting conditions prevailed for the Laurentide
Ice Sheet over the past 140,000 years, thereby making it vulnerable t
o Heinrich-type surges. A reasonable level of agreement is obtained wi
th the observed record of North Atlantic IRD activity, including the s
ix numbered Heinrich events as well as earlier activity of this kind t
hat occurred when the ice volume was lower.