Droughts and floods are two opposite but related hydrological events. They both lie at the extremes of rainfall intensity when the period of that intensity is measured over long intervals. This paper presents a new concept based on stochastic calculus to assess the risk of both droughts and floods. An extended definition of rainfall intensity is applied to point rainfall to simultaneously deal with high intensity storms and dry spells. The meanreverting Ornstein-Uhlenbeck process, which is a stochastic differential equation model, simulates the behavior of point rainfall evolving not over time, but instead with cumulative rainfall depth. Coefficients of the polynomial functions that approximate the model parameters are identified from observed raingauge data using the least squares method. The probability that neither drought nor flood occurs until the cumulative rainfall depth reaches a given value requires solving a Dirichlet problem for the backward Kolmogorov equation associated with the stochastic differential equation. A numerical model is developed to compute that probability, using the finite element method with an effective upwind discretization scheme. Applicability of the model is demonstrated at three raingauge sites located in Ghana, where rainfed subsistence farming is the dominant practice in a variety of tropical climates.
the paper develops a mathematical model of duct air heating process, as widely used in drying of different materials in the form of powder. In this work, a mathematical model of the duct air heating system containing resistive heating element has been developed for simulation study, by considering one dimensional forced convective heat transport phenomena. Then a Continuous Time (CT) model identification technique based on Instrumental Variation (IV) approach has been applied to the actual duct air heating process, in order to identify the model parameters. The model was intended to evaluate dynamic changes in outlet air temperature corresponds to changes in current through the heating coils, air flow velocity and ambient temperature. The proposed mathematical model has been validated by a set of simulated models obtained from the experimental data collected from the actual setup, involving duct air heating under open loop conditions.The obtained responses of the mathematical model as well as identified system were found to be closely correlated with the experimental responses. Index Terms-Mathematical model of heating and flow control process, Open loop identification, Instrumental Variable methods (IV), Simplified refined instrumental variable (SRIVC) method, CT Transfer function model.
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