1) Physical Basis: The sim ulation rules were not derived from fundam ental equa tions, b u t introduced phenomenologically, based on observations and aerody nam ic considerations. For example, if wind blows in a desert, sand is tran sp o rted in th e wind direction. The stronger th e wind, the greater distance sand is trans ported. These form the physical background of the slab tra n sp o rt in th e model. A nother exam ple is th a t avalanching occurs in n a tu re if th e angle of a sandy slope exceeds th e angle of repose of ab ou t 32°. In th e m odel avalanching dynam ics has been introduced in th e same m anner, w ithout discussing its microscopic origin, hence th e phenomenological basis of the model. O th er dynam ics such as wind speedup, slab bouncing and th e shadow zone have also been introduced phenomenologically, though the origins of all these processes can be discussed in some detail.
2) Simplicity: T he sim ulation rules are simple. T his is evident when comparing to models w ith th e Navier-Stokes equation, where in teractin g air pressure and three com ponents of wind velocity are defined on a three-dim ensional continuous space { x ,y ,z ) . Consequently, th e com putational burden for such conventional models is very heavy. In the present model on th e oth er hand, slab tran sp o rt length (L) is defined on a two-dimensional discrete space, and tra n sp o rt length is simply a function of local num ber of slabs at a location.
3) G enerality and Richness: It has already been shown th a t a lattice model can be effective for vegetated dune fields (de C astro, 1995) (section 2.7.2). The present study has assum ed a fiat hard surface, on which slabs are piled up. By creating undulations on th is hard surface, the effects of existing topography could be sim ulated. Sim ulations are expected to reproduce, for exam ple, climbing and falling dunes (Lancaster, 1995, pp82-83) (generality). The m odel has been shown to mimic some of a variety of dune p attern s (dome, barchan, transverse, linear and star-like dunes), and to enable system atic understanding of m any different envi ronm ents, according to wind environm ent (strength and directional complexity)
and sand availability (richness).
4) P o ten tial for Scaling Up and Down: The model m ay apply to an inhomoge- neous dune field by introducing regionally different p aram eters {i.e. a distributed model), if m ore com putational capacity were to be available (scaling up). The use of discrete dynam ics has already been recognised to be effective in th e study of ripples (N ishim ori and Ouchi, 1993; Anderson and B unas, 1993; Landry and W erner, 1994) (section 2.7.2) (scaling down).
In short, b o th m odels are generally satisfactory in th e light of these four criteria. Still, th e first m odel suffers lack of richness, in th a t it cannot go beyond two- dim ensional, equilibrium bedforms. The physical basis of th e second model is still not secure. However, by sim ulating m any other types of dune {i.e. collecting more circum stantial evidence), th e model may become more convincing.
7.2.3
E ngineering asp ects
In respect of engineering, th e m ost notable success is th e estim ation of dune mi gration speed. Civil engineers will benefit from the first m odel when exploiting deserts w ith roads or pipelines for oil and gas. The ability to predict responses in shape and m igration speed to environm ental change is im p o rtan t. More specifi cally, it is im p o rta n t to investigate th e dynamics of dunes under rare high winds. Engineers are th o u g h t to be interested in how dunes th a t have been developed in m odest w ind conditions change in shape and in m igration speed during a storm, which is a sh o rt-term event of a day or a few days. In such conditions, the as sum ption of equilibrium is clearly inappropriate, and th e dune field model may be able to take over th e predictive role from the kinem atic model. In th e dune field model, as b o th sp atial and tem poral scales can be estim ated, a storm event of a certain d u ratio n can easily be sim ulated. In th e ‘sto rm ’, th e slab tran sp o rt length is increased for a certain period of tim e such th a t sand flux in th e model conforms to th e n a tu ra l behaviour a t a considered w ind speed (section 6.3.2).
Also using th e dune field model, effects of pre-existing topography such as rocks on dune dynam ics can be investigated.