In this paper a nonlinear observer for a class of partial differential equations known as the advection equation is designed. The observer, that uses only boundary measurements, is developed based on the sliding mode method. The convergence of states of the observer to the actual system, in spite of possible mismatches between the model and the system, is proven through the Lyapunov stability techniques. In addition, a sliding mode method is employed to design an anomaly detection system that is able to identify parameters of the disturbance in the system such as intensity and location. The Lyapunov stability theorem has been used in order to guarantee the convergence of the anomaly detection system. The applications of observer and anomaly detector are illustrated through simulation.