Five different planetary boundary layer (PBL) schemes in the Weather Research and Forecasting (WRF) model have been tested with respect to their capability to model boundary layer parameters relevant for offshore wind deployments. For the year 2005, model simulations based on the YSU, ACM2, QNSE, MYJ and MYNN2 PBL schemes with WRF have been performed for the North Sea and validated against measurements from the FINO1 platform. In part I, the investigations had focused on the key parameters 100 m mean wind speed and wind shear in terms of the power-law exponent. In part II, the focus is now set on the capability of the model to represent height and stability of the marine atmospheric boundary layer.Considerable differences are found among the PBL schemes in predicting the PBL height. A substantial part of this variation is explained by the use of different PBL-height definitions in the schemes. The use of a standardized procedure in calculating the PBL height from common WRF output parameters, in particular the temperature gradient and the wind shear, leads to reduced differences between the different schemes and a closer correspondence with the FINO1 measurements. The study also reveals a very clear seasonal dependency of the atmospheric stability over Southern North Sea. During winter time, the marine atmospheric boundary layer is more or less neutral with several episodes of unstable periods. During spring and early summer, the occurrence of periods with very stable stratification becomes dominant with stable conditions up to 40–45% of the time when warm continental air is advected from the South. In general, the results of part II confirm again that the MYJ scheme performs slightly better than the others and can therefore be suggested as first choice for marine atmospheric boundary layer simulations without a priori information of atmospheric stability in the region of interest. Copyright © 2014 John Wiley & Sons, Ltd.