Revisiting the Role of Vertical Shear in Analytic Ice Shelf Models

Abstract. Analytic modeling of ice shelf flow began when Weertman derived an expression for the strain rates within an unconfined shelf, of uniform thickness, extending only in one direction. Nearly two decades later, Thomas generalized Weertman's analysis to ice shelves of nonuniform thickness, deriving one of the most well-known analytic models in glaciology: . However, despite the prevalence of this model in both historical and contemporary texts, there remain persistent miscommunications regarding the role of vertical shear in its construction. In Thomas' original approach, vertical shear stress was considered negligible in the stress balance; in a significant contrast, the same model is typically derived in contemporary texts by the neglect of basal resistance. These two approaches are not equivalent, and yet, it remains common to misinterpret vertical shear stress as typically neglected in current ice shelf modeling studies. This manuscript provides clarification on this pervasive misconception. We emphasize that vertical shear stress should not be interpreted as negligible in the construction of general shallow shelf models. However, we also demonstrate that the vertical shear stress inherent in Thomas' expression does not give rise to a well-defined vertical shear strain rate. For situations in which vertical shear stress in shallow ice shelf models is of interest, we provide guidance on how to best calculate it.