Hydrological system modeling: Approach for analysis with dynamical systems

Abstract

Recent methods for sustainability analysis have involved the methodology of system dynamics for the representation of different landscape components that are analyzed. This document proposes a mathematical model based on system dynamics for the hydrological component in the sustainability analysis that includes the processes between precipitation and runoff. Additionally, the stability of the equilibrium point found with the theory of dynamic systems is studied. The modeling is carried out from a diagram of levels and flows, in order to obtain a system of ordinary differential equations of first order, linear, non smooth, that takes as state variables static and capillary storage, superficial storage, higher gravitational storage, lower gravitational storage (aquifer) and storage in the channel. The model was validated with time series of the Chinchina basin (Caldas, Colombia). From dynamical systems point of view, the system behavior has an equilibria point that depends on the saturation value in the static and capillary storage.