Bounding linear rainfall-runoff models with fractional derivatives applied to a barren catchment of the Jordan Rift Valley

A new concept is developed to mathematically understand the dynamics of rainfall-runoff events in a barren catchment Jordan Rift Valley. Time series data rainfall and runoff have been acquired at an observation point catchment. Due extreme arid environment, water current as from ephemeral, are clearly distinguishable each other. Firstly, pair linear autoregressive models with exogenous input (ARX models) identified tightly bound time using simplex method programming. The part compatible conventional unit hydrograph method, while regarded discretized differential operator fractional orders. Then, equation determined approximate ARX model, which restricts perturbation actual causal relationship between intensity discharge. resulting lower upper bounding derivatives examined system-theoretic framework. Finally, nominal model nonlinear stochastic phenomena perturb arranged envelope all frequency domain, leading formulation challenging optimal control problem involving processes.