In the previous three sections, the results of applying mathematical modelling techniques to the study of various aspects of both the atmospheric and oceanic components of the monsoon have been described. These studies exploit a wide range of mathematical methods ranging from those of classical mathematical analysis, for example wave perturbation theory, to those of numerical analysis. The development of the techniques themselves is an activity which is necessary if models are to be improved, and the five chapters in this section deal with particular areas of importance. The incorporation of orography into numerical prediction models is one of the major technical problems in the field of numerical modelling. Substantial advances have been made, particularly through the device of computing the meteorological parameters on surfaces which generally follow the orographic features. However, difficult problems still remain, associated with the inability of these models to properly resolve small-scale circulations in the neighbourhood of mountain ranges. Nowhere is this problem more acute than over the Indian subcontinent where the Himalayan range has such an enormous influence. A review of the technical problems associated with this phenomenon is given in Chapter 39. The estimation of vertical motion in the monsoon circulation, a dynamical feature to which the rainfall is intimately related, is described in Chapter 40. In Chapter 41, the use of a turbulence closure scheme in the context of the planetary boundary layer is described: the use of this new technique, or some modification of it, may well prove to be of importance in the difficult problem of dealing with the unresolved small scales of motion in numerical models.