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The Tropospheric Emission Spectrometer (TES) is a high-resolution spaceborne sensor that is capable of observing tropospheric species. In order to exploit fully TES's potential for tropospheric constituent retrievals, an accurate and fast operational forward model was developed for TES. The forward model is an important component of the TES retrieval model, the Earth Limb and Nadir Operational Retrieval (ELANOR), as it governs the accuracy and speed of the calculations for the retrievals. In order to achieve the necessary accuracy and computational efficiency, TES adopted the strategy of utilizing precalculated absorption coefficients generated by the line-by-line calculations provided by line-by-line radiation transfer modeling. The decision to perform the radiative transfer with the highest monochromatic accuracy attainable, rather than with an accelerated scheme that has the potential to add algorithmic forward model error, has proven to be very successful for TES retrievals. A detailed description of the TES forward model and Jacobians is described. A preliminary TES observation is provided as an example to demonstrate that the TES forward model calculations represent TES observations. Also presented is a validation example, which is part of the extensive forward model validation effort.