The Parameterisation of Scalar Transfer over Rough Ice

We test a surface renewal model that is widely used over snow and ice surfaces to calculate the scalar roughness length (zs), one of the key parameters in the bulk aerodynamic method. For the first time, the model is tested against observations that cover a wide range of aerodynamic roughness lengths (z0). During the experiments, performed in the ablation areas of the Greenland ice sheet and the Vatnajökull ice cap in Iceland, the surface varied from smooth snow to very rough hummocky ice. Over relatively smooth snow and ice with z0 below a threshold value of approximately 10−3 m, the model performs well and in accord with earlier studies. However, with growing hummock size, z0 increases well above the threshold and the bulk aerodynamic flux becomes significantly smaller than the eddy-correlation flux (e.g. for z0 = 0.01 m, the bulk aerodynamic flux is about 50% smaller). Apparently, the model severely underpredicts zs over hummocky ice. We argue that the surface renewal model does not account for the deep inhomogeneous roughness sublayer (RSL) that is generated by the hummocks. As a consequence, the homogeneous substrate ice grain cover becomes more efficiently ‘ventilated’. Calculations with an alternative model that includes the RSL and was adapted for use over hummocky ice, qualitatively confirms our observations. We suggest that, whenever exceedance of the threshold occurs (z0  >  10−3 m, i.e., an ice surface covered with at least 0.3-m high hummocks), the following relation should be used to calculate scalar roughness lengths, ln (zs/z0)  =  1.5  − 0.2 ln (Re*)  − 0.11(ln (Re*))2.