An analytical slab model for the growth of the coastal thermal internal boundary layer under near-neutral onshore flow conditions

Analytical parameterisations of the thermal internal boundary-layer (TIBL) height based on the slab approach are widely used in coastal dispersion models. However, they tend to a singular behaviour when the stability of the onshore flow is close to neutral. Assuming that convective turbulence dominates mixing, we derive a more general analytical model that is valid for both stable and neutral onshore flows. The model is based on the existing framework for the slab approach but involving the Zilitinkevich correction (or the 'spin-up' term). The height variation of the onshore flow lapse rate is accounted for in the model by including an initial TIBL height. An algebraic form of the model also includes the mechanical mixing contribution to the TIBL growth and is, therefore, suitable for use when the overland surface heat flux is small and friction velocity large. The new analytical model is tested with field measurements taken under near-neutral onshore how conditions. The performance of the model is shown to be better than a commonly used TIBL parameterisation scheme.