I am beginning to explore how land surface temperature is used in weather forecast models. However, as beginner in the field, have no idea of where to start. Any advice on basic references on this topic would be much appreciated.
In order to obtain a realistic representation of the surface temperature in our models we have to consider multiple couplings in the Earth system. In addition to clouds and radiative transfer equations we need the soil model including vegetation and hydrological processes at the surface. This coupling leads to a complex, nonlinear dynamical system being an integral part of the numerical weather prediction model. The excellent review of all relevant topics is presented in the deck of "slides" from ECMWF
Basically, LST needs to be assimilated into land surface model (WFM) component of weather forecast model. So I would like to suggest that you can start from LST assimilation firstly (generally into land surface model, rather than WFM), and then focus on how to couple land surface model and WFM together.
There are two ways to build a weather forecast model. As commonly used and advised in earlier replies to your question, one way is to build an analytical model. This model can be precise but suffers from high computational cost and you should know about the relation between the elements, i.e. white box modelling approach. On the other hand there is yet another method that does not require in depth knowledge of the elements of the systems and the model itself can automatically extract related elements dependent on the accuracy at the output required and the computational cost that you are willing to pay. In this approach feature selection as elements in the weather system is performed without knowing their effect on the output of the model, i.e. black box approach. You may find more about this approach in my laboratory website. One of my Ph.D. students completed his thesis on this subject area last year. One major publication of his is accepted in ISI journal and it will be published at any time in the "Intelligent Data Analysis - An International Journal".
Mohsen Moshki, Peyman Kabiri, Alireza Mohebol-Hojeh, “Scalable Data-Driven Modelling of Spatio-Temporal Systems: Weather Forecasting”, Intelligent Data Analysis - An International Journal, Vol. 21, No. 3, To be published around May 2017, (DOI: 10.3233/IDA-150494). (ISI IF for 2016 = 0.631)