Wind turbine wake and blockage effects can reduce the energy yield in wind farms and fast models are required to mitigate these effects by wind farm layout optimization. However, most fast models do not account for important physics that impact wake and blockage effects, as for example atmospheric stability. In this work, we propose a surrogate model of a Reynolds-averaged Navier-Stokes (RANS) wind farm model including atmospheric surface layer stability that is about five orders of magnitude faster than the original model. The surrogate model is based on a single wake database of stream-wise velocity deficit and wake-added turbulence intensity, generated by a RANS model. The surrogate model is evaluated against the RANS model for different inflow conditions and wind farms. The errors of the surrogate model are reduced by a factor two to four when taking into account wake-added turbulence intensity and the use of a rotor-averaging model in combination with a momentum-based wake superposition method. However, the computational effort of the surrogate model is still an order of magnitude larger compared to traditional engineering wake models and more research is required to reduce it.