This paper discusses the asymptotic covariance and outlier detection procedure in a linear functional relationship model for an extended circular model proposed by Caires and Wyatt. We derive the asymptotic covariance matrix of the model via the Fisher information and use the results to detect influential observations in the model. Consequently, an influential observation detection procedure is developed based on the COVRATIO statistic which has been widely used for similar purposes in ordinary linear regression models. We show via simulation that the above procedure performs well in detecting influential observations. As an illustration, the procedure is applied to the real data of the wind direction measured by two different instruments.