Capturing critical behaviour in soil moisture spatio-temporal dynamics

A physical system is subject to a phase transition process when it shows a discontinuous change of a macroscopic feature of the system under a continuous change of a system’s state variable. For certain properties of physical systems subject to phase transition it is possible to observe a scale-invariant behaviour in the point of coexistence of the phases, which in that special case is defined “critical point”. Since the soil moisture spatial patterns in their seasonal time dynamics show the transition between spatially random to spatially connected appearances, we have investigated whether this process behaves as a critical point phenomenon. We have developed an algorithm working in analogy to the percolation theory [Bruce A, Wallace D. Critical point phenomena: the physics of the universality at large scales. In: Davis P, editor. The new physics. Cambridge: Cambridge University Press; 1989.]. The implemented methodology has been explored by applying to 365 soil moisture maps of daily data from a 507 km2 natural catchment in Southern Italy. We have investigated the relation between the occupation probability in the soil moisture spatial patterns and the normalized size of the largest cluster and the behaviour of the system under changing grid scales. The critical exponents have been also calculated. The undertaken analyses show that the process has a critical behaviour. The critical point for the examined river basin, expressed in terms of occupation probability, has a value of 0.88, which is maintained also after the coarse graining procedure. In order to evaluate the response of the model to the choice of its parameters, we have carried out a sensitivity analysis.