No, FSNT - FLNT is the radiative imbalance at the top of the model. This is related to the radiative forcing, but is not typically called ERF. If the system's imbalance is sustained in some way, this is the radiative forcing, but under typical conditions an imbalance will tend toward zero as the climate system establishes equilibrium by changing temperature.
Usually it is the change in (FSNT - FLNT) associated with a perturbation that is ERF.
One common experiment is to run the global atmosphere-land model (fixed SST and sea-ice) twice: first with aerosols and second with pre-industrial aerosols. Taking (FSNT-FLNT)_present - (FSNT-FLNT)_preindustrial provides the "aerosol ERF" (ERF_aer). See, for example, Pincus et al. 2016:
GMD - The Radiative Forcing Model Intercomparison Project (RFMIP): experimental protocol for CMIP6
Other references:
- Forster, P. M., T. Richardson, A. C. Maycock, C. J. Smith, B. H. Samset, G. Myhre, T. Andrews, R. Pincus, and M. Schulz (2016), Recommendations for diagnosing effective radiative forcing from climate models for CMIP6, J. Geophys. Res. Atmos., 121, 12,460–12,475, doi:10.1002/2016JD025320.
- Smith et al. 2020,
Effective radiative forcing and adjustments in CMIP6 models
- Tang, T., Shindell, D., Faluvegi, G., Myhre, G., Olivié, D., Voulgarakis, A., et al. (2019). Comparison of effective radiative forcing calculations using multiple methods, drivers, and models. Journal of Geophysical Research: Atmospheres, 124, 4382–4394.
https://doi.org/10.1029/2018JD030188