The eddy viscosity is an important parameter in the atmospheric boundary layer meteorology, and we usually cannot determine their exact values by direct measurements, but we can only obtain an approximate range by indirect approximate method. In this paper, the eddy viscosity in the stochastic general Ekman momentum approximation model is used for the retrieval research and uncertainty analysis. The main purpose of retrieval is to reduce the uncertainty and narrow the approximate range of eddy viscosity. First, the polynomial chaos-ensemble Kalman filter and the wind observations are used for eddy viscosity retrieval and uncertainty reduction. The main idea of this method is to replace the Monte-Carlo method with polynomial chaos in the uncertainty quantification of ensemble Kalman filter, and thusavoiding the consumption of computing resources brought by massive samples. The goal of uncertainty quantification is to investigate the effect of uncertainty in the eddy viscosity on the model and to subsequently provide a reliable distribution of simulation results. Then two numerical experiments are implemented, i.e. experiment I in which the eddy viscosity is assumed to be constant, and experiment Ⅱ in which the eddy viscosity is assumed to be a vertically varying random parameter. The uncertainty of eddy viscosity in experiment I is reduced quickly, at the same time the mean of eddy viscosity can converge to a reference value. The effect in experiment Ⅱ is also remarkable after 16 data assimilation steps. These results show that the polynomial chaos-ensemble Kalman filter is an effective and fast method of solving the posterior distribution of eddy viscosity and reducing the uncertainty of eddy viscosity. Finally, we calculate the prior distribution of wind speed according to the prior distribution of eddy viscosity and identify the heavy uncertainty area in wind speed. The results indicate that the posterior distribution of eddy viscosity solved with wind observations in the big uncertainty area is more accurate, which provides an important guidance for selecting the location of observation points.