Using multinomial and imprecise probability for non-parametric modelling of rainfall in Manizales (Colombia)

This article presents a rainfall model constructed by applying non-parametric modelling and imprecise probabilities; these tools were used because there was not enough homogeneous information in the study area. The area's hydrological information regarding rainfall was scarce and existing hydrological time series were not uniform. A distributed extended rainfall model was constructed from so-called probability boxes (p-boxes), multinomiol probability distribution and confidence intervals (a friendly algorithm was constructed for non-parametric modelling by combining the last two tools). This model confirmed the high level of uncertainty involved in local rainfall modelling. Uncertainty encompassed the whole range (domain) of probability values thereby showing the severe limitations on information, leading to the conclusion that a detailed estimation of probability would lead to significant error. Nevertheless, relevant information was extracted; it was estimated that maximum daily rainfall threshold (70 mm) would be surpassed at least once every three years and the magnitude of uncertainty affecting hydrological parameter estimation. This paper's conclusions may be of interest to non-parametric modellers and decisions-makers as such modelling and imprecise probability represents an alternative for hydrological variable assessment and maybe an obligatory procedure in the future. Its potential lies in treating scarce information and represents a robust modelling strategy for non-seasonal stochastic modelling conditions.