The global radiosonde archives contain valuable weather data, such as temperature, humidity, wind speed and direction and atmospheric pressure. For climate studies, the quality control of this large dataset is essential and robust statistical methods are often needed. In this paper, we treat the wind profiles as bivariate functional data along pressure levels. Since the bivariate distribution of wind speeds at a given pressure level is not Gaussian but skewed and heavy-tailed, we propose the functional quantile envelopes to characterize the distribution as well as an outlier detection procedure to detect both magnitude and shape outliers. The proposed methods provide an informative visualization tool for multivariate functional data. We then develop two methods to predict these quantile envelopes, using the methods of directional quantile regression and kriging. In our simulation study, we show that our methods are robust against different types of outliers. For the application, we apply our methods to the radiosonde wind data to visualize the change in distribution across pressure levels, detect potential outliers and predict the distribution at unobserved pressure levels.