Wind Erosion in Western Queensland Australia

Chapter 4 –Modelling Soil Erodibility Dynamicsand management factors, the slope gradient or rate of change in erodibility, and therefore theminimum period of time a soil may spend in this phase moving toward Q max .Gillette (1978) reported on the dependence of soils on drought to experience an increase inerodibility to wind (Chapter 2, Figure 2.5). His results show that the erodibility of sandy soilswith 40% clay are highly dependent ondrought to experience an increase in erodibility. This time dependence is driven by the soilparticle size distributions and particle shapes which affect the strength of inter-particle bonds.The final phase in the continuum, (iii) defines the condition of maximum erodibility (Q max ).In order for a soil to reach this condition moisture content (antecedent rainfall) must be at aminimum and disturbance to the soil surface at a maximum. Soils at Q max can be consideredto have an effective grain diameter d of 0.08 mm to position the soil at the u *t minima(Chapter 2, Figure 2.3) reported by Bagnold (1941).Mathematically the phase shifts through the soil erodibility continuum, from i to iii (Figure4.4), can be defined by a logistic (sigmoid) curve. Numerous expressions are available thatcan be used to delineate the shape of this curve (e.g. Richards, 1959; Turner et al., 1976). Thelogistic curve form can be approximated with few parameters, making it a good starting pointfor modelling temporal changes in soil erodibility to wind. The model framework presentedhere uses the Richard’s equation (Richards, 1959), selected for its wide application inmodelling vegetation growth dynamics (Tsoularis and Wallace, 2002) and more recentlydunefield activation and stabilisation (Hugenholtz and Wolfe, 2005). In differential form theRichard’s equation is expressed as:dNdt N = rN 1 (4.7) K where N is the population size, r is the growth rate, β is a positive real number and K is thepopulation carrying capacity reached as lim t→∞ N(t) = K. The integral of Equation (4.7) isthen:113