A high altitude platform station (HAPS) based communications scenario for providing Internet access and broadband multimedia services to the passengers on board of a high speed train (traveling up to 300km/h) is proposed. Regarding the addressed scenario, when the propagation link between HAPS and train is blocked by obstacles, a three-dimensional (3-D) geometrical single cylinder spatial-temporal channel model is presented, in which closed form, mathematically tractable space-time correlation functions are obtained. It shows that the correlation functions determined by the 3-D model are of significant difference with those of the conventional 2-D model. Based on the analysis model, the paper derives a realized simulation model using sum-of-sinusoids approach, and applies method of equal areas (MEA) and modified method of equal areas (MMEA) to determine the model parameters. The fitting performance of the simulation model with the analysis one is evaluated by two means-square error (MSE) performance criteria. Finally, numerical simulation results verify the mathematical analysis conclusion, when N≥21, simulation model has an excellent fitness with the analysis one.