Two parameterisation schemes of the turbulent surface fluxes and drag coefficients over the Arctic marginal sea ice zone (MIZ) are (further) developed, and their results are compared with each other. Although the schemes are based on different principles (flux averaging and parameter averaging), the resulting drag coefficients differ only slightly in case of neutral and stable stratification. For unstable stratification and sea ice conditions being typical for the north eastern Fram Strait, the drag coefficients resulting from the parameter averaging concept are 5-10 % larger than those of the flux averaging concept. At a sea ice concentration of 45 %, the parameter averaging method overestimates the heat fluxes by a factor of 1.2. An inclusion of form drag in the schemes, caused by floe edges and ridges, has a much larger effect on the drag coefficients and on the momentum fluxes than the choice between the parameter averaging or flux averaging method. Based on sensitivity studies with the flux averaging scheme, a simple formula for the effective drag coefficient above the Arctic MIZ is derived. It reduces the computational costs of the more complex parameterisations and could also be used in larger scale models. With the simple formula, the effective drag coeffcient can be calculated as a function of the sea ice concentration and skin drag coefficients for water and ice floes. The results obtained with this parameterisation differ only slightly from those from the more complex schemes. Finally, it is shown that in the MIZ, drag coefficients for sea ice models may differ strongly from the effective drag coefficients to be used in atmospheric models.