Check out these two recent publications on drivers and indicators of state change and recovery. This is pretty interesting. Although the models and empirical data are mostly from mesic systems, these ideas definitely apply to aridland systems as well.
Ratajczak, Z., P. D’Odorico, J.B. Nippert, S.L. Collins, N.A. Brunsell and S. Ravi. 2017. Changes in spatial variance during a grassland to shrubland state transition. Journal of Ecology 105: 750-760.