An important challenge faced by wind farm operators is to reduce operation and maintenance cost. Structural health monitoring provides a means of cost reduction through minimising unnecessary maintenance trips as well as prolonging turbine service life. Population-based structural health monitoring can further reduce the cost of health monitoring systems by implementing one system for multiple structures (i.e.~turbines). At the same time, shared data within a population of structures may improve the predictions of structural behaviour. To monitor turbine performance at a population/farm level, an important initial step is to construct a model that describes the behaviour of all turbines under normal conditions. This paper proposes a population-level model that explicitly captures the spatial and temporal correlations (between turbines) induced by the wake effect. The proposed model is a Gaussian process-based spatial autoregressive model, named here a GP-SPARX model. This approach is developed since (a) it reflects our physical understanding of the wake effect, and (b) it benefits from a stochastic data-based learner. A case study is provided to demonstrate the capability of the GP-SPARX model in capturing spatial and temporal variations as well as its potential applicability in a health monitoring system.