Simulations are often used to investigate the flow structures and system dynamics of complex natural phenomena and systems, which are significantly harder to obtain from experiments or theoretical analyses. Surrogate models are employed to mimic the results of simulations by reducing computational costs. In order to reduce the amount of computational time consumed, a novel framework for building efficient surrogate models is proposed in this work. The novelty lies in that the new framework runs simulations using the different simulation time spans for different inputs and builds a comprehensive surrogate model through the fusion of non-homogeneous spatio-temporal data by integrating the temporal and spatial correlations in parametric space. This differs from the existing works in the literature, which only consider the situation of spatio-temporal data with a consistent time span during simulations under different inputs. Some simulation studies and real data analysis concerning the pollution of the river in the Sichuan Province of China are used to demonstrate the superior performance of the proposed methods.