Model-data integration such as model calibration and uncertainty quantification usually involves large ensemble model evaluations. Hydrological models and terrestrial ecosystem models (TEMs) often have lengthy simulation times making some model-data integration methods computationally infeasible. To reduce the computing cost, a surrogate model is usually constructed to approximate and replace the expensive model execution in the model-data integration analysis. For a complex model with a large number of model parameters and model outputs, constructing and evaluating the surrogate model itself is computationally intensive due to the “curse of dimensionality” and difficulties in data load and storage capacity. This study first uses singular value decomposition to reduce the data dimensionality and then uses advanced surrogate modeling methods such as Bayesian compressive sensing and Bayesian neural networks to build accurate surrogates in a reasonable amount of time. We apply the methods to a groundwater reactive transport model that simulates uranium (U(VI)) concentration at a uranium mill in Naturita, CO, and to a TEM that simulates GPP in the entire USA. Results indicate that our methods build accurate surrogates of the groundwater reactive transport model and the TEM efficiently, and fast evaluate the surrogates in uncertainty quantification to advance the U(VI) contaminant risk assessment and in model calibration to improve the GPP prediction.