Wind Erosion in Western Queensland Australia

Chapter 4 –Modelling Soil Erodibility DynamicsN() t0= (4.8) rt1 /[ N + ( K N ) e ] 0NK0where N 0 is the population size at time (t) = 0. To represent temporal changes in soilerodibility we can consider changes in the power b (Equation 4.4) to follow the logisticgrowth curve defined by Equation (4.8) and express the model as:b( t )( t) 150.(% clayQ = )(4.9)where Q(t) is the indicator of time-dependent soil erodibility (gm -1 s -1 ), %clay is thepercentage soil clay content and the power b(t) is defined by:C= (4.10)() t A +r( t M)b/1( 1+T exp ) Twhere A defines the lower asymptote (b min ), C equals the upper asymptote (b max ) minus thevalue of A, r defines the growth rate, M is the time of maximum growth, T affects near whichasymptote maximum growth occurs, and t equals the unit time. Parameter values for A and Ccan be assigned to Equation (4.10) assuming that b min can be defined by Equation (4.6) andb max is defined by the power (-0.05) providing a hypothetical Q max at ~150 gm -1 s -1 :2.29= (4.11)() t 2.34+r( t M)b/1( 1+T exp ) TFor the remaining parameters, the growth rate r can be defined based on soil texturalproperties and the disturbance intensity, and can be modulated by adjusting the parameters Tand M if changes in disturbance intensity take place through time (Bullock et al., 2001).Under this model, temporal changes in erodibility are constrained by the limits:min( t) bmaxb " b "(4.12)114