The episodes of ice-rafted detritus (IRD) accumulation identified in North Atlantic sediment cores indicate periods of abnormal iceberg production mainly of the Laurentide Ice Sheet. In this paper we develop further 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 depends not only on the physical properties of ice sheets and the magnitude of the geothermal and viscous heating but also on the history of changes in ice elevation, atmospheric carbon dioxide, and sea surface temperature, the thermal effects of which at the top of an ice sheet are transmitted with a time delay to the basal boundary by thermal advection. We apply this criterion to various past and present ice sheets showing their general vulnerability to surging. In greater detail, we use estimates of the time variations of ice volume (SPECMAP), carbon dioxide (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 to Heinrich-type surges. A reasonable level of agreement is obtained with the observed record of North Atlantic IRD activity, including the six numbered Heinrich events as well as earlier activity of this kind that occurred when the ice volume was lower.