Most useful weather prediction for the public is near the surface. The processes that are most relevant for near-surface weather prediction are also those that are most interactive and exhibit positive feedback or have key role in energy partitioning. Land surface models (LSMs) consider these processes together with surface heterogeneity and forecast water, carbon and energy fluxes, and coupled with an atmospheric model provide boundary and initial conditions. This numerical parametrization of atmospheric boundaries being computationally expensive, statistical surrogate models are increasingly used to accelerated progress in experimental research. We evaluated the efficiency of three surrogate models in speeding up experimental research by simulating land surface processes, which are integral to forecasting water, carbon, and energy fluxes in coupled atmospheric models. Specifically, we compared the performance of a Long-Short Term Memory (LSTM) encoder-decoder network, extreme gradient boosting, and a feed-forward neural network within a physics-informed multi-objective framework. This framework emulates key states of the ECMWF's Integrated Forecasting System (IFS) land surface scheme, ECLand, across continental and global scales. Our findings indicate that while all models on average demonstrate high accuracy over the forecast period, the LSTM network excels in continental long-range predictions when carefully tuned, the XGB scores consistently high across tasks and the MLP provides an excellent implementation-time-accuracy trade-off. The runtime reduction achieved by the emulators in comparison to the full numerical models are significant, offering a faster, yet reliable alternative for conducting numerical experiments on land surfaces.