Figure 1

(a) Lençóis Maranhenses dunes in northeastern Brazil (43° W, 2° S); a field of active barchan dunes (upper right corner) coexist with fixed vegetated parabolic dunes. Landsat Satellite image. [Landsat imagery courtesy of NASA Goddard Space Flight Center and USGS Center for Earth Resources Observations and Science.] (b) Satellite image (Google Earth) of the Israel-Egypt border area showing high contrast in albedo between the bright active Egyptian dunes and the darker fixed vegetated Israeli dunes. Arrows indicate the prevailing wind direction.Reuse & Permissions

Figure 2

(a) Stable states diagram showing vegetation cover $v$ vs DP. The gray area indicates the domain of bistability. The arrows indicate the hysteresis scenario, and the dash-dot vertical lines indicate the transition from fixed to active dune states and vice versa. Solid lines indicate stable states. Parameter values used are: $v_{\max }=1$, $v_c=0.2$, $ϵ=0.001$, $\alpha =0.1$, $\gamma =0.0008$, $\eta =0.2$. For these parameters, ${\mathrm{DP}}_1=139$ and ${\mathrm{DP}}_2=2828$. The vertical arrows indicate two examples shown in panels b and c. (b) An example of transition from a fixed dune to an active dune state (Netherlands case). Time evolution (in arbitrary time units) of vegetation cover $v$ for $\mathrm{DP}=1570$ for different initial conditions ($v=0.3$ and $v=0.1$). The upper curve converges to the fixed dune $F$ state, while the lower curve (that is associated with large disturbance) converges to the active dune $A$ state. (c) Same as b, but for different DP values, (Israel-Egypt border case), starting from $v=0.01$. For $\mathrm{DP}=50$ and $\mathrm{DP}=100$, the asymptotic state is the fixed dune state $F$, whereas for $\mathrm{DP}=200$, it is the active dune state $A$.Reuse & Permissions

Figure 3

(a) Active to fixed dune transition point ${\mathrm{DP}}_1$ [Eq. (6)] and fixed to active dunes transition point ${\mathrm{DP}}_2$ [Eq. (5)] as a function of critical vegetation cover $v_c$. The various gray shadings represent different stability regimes. As $v_c$ increases the fix-active and active-fix dune transitions occur for weaker winds (low DP) (b) Same as (a), but for different growth rates $\alpha$. As $\alpha$ decreases fix-active and active-fix dune transitions occur for weaker winds (low DP), suggesting that drought conditions are more favorable for transitions from fixed to mobile dune states (desertification process). Parameter values are as in Fig. 2.Reuse & Permissions