In this paper, an adaptive Kalman filtering procedure is developed and applied to 2-metre temperature and 10-metre wind-speed forecasts in Iceland. The goal is to reduce the systematic bias and improve the accuracy of the local forecasts derived from a numerical weather prediction model and, in addition, to produce reliable prediction intervals. The method consists of adding two algorithms to the traditional Kalman filter procedure that adaptively estimate the noise statistics individually at each forecast location and each time step. The tested data set shows that the method is able to remove the systematic errors and to quantify the prediction uncertainty in a consistent manner.