Modeling stochastic inflow patterns to a reservoir with hidden phase-type Markov model

Abstract

This paper proposes a new statistical framework for modelling precipitation patterns in a specific geographical region using Hidden Markov Models (HMMs). Unlike conventional HMMs, where the hidden-state process is Markovian, our approach introduces non-Markovian behaviour by incorporating phase-type distributions to model state durations. This extension allows for a more realistic representation of alternating dry and wet periods, providing deeper insight into the temporal structure of the local climate. Building on this framework, we model reservoir inflow patterns linked to the hidden states and explain observed water storage levels through a Moran model. The analysis uses historical rainfall and inflow records, where inflows are influenced by latent climatic conditions rather than rainfall alone. By integrating these unobserved dynamics, the proposed model captures system complexity that would be missed by direct observationbased modelling. To evaluate performance, we compare our model against several standard ARIMA alternatives. The proposed PH-HMM achieves a substantially lower AIC (204.38) than the best ARIMA specification (211.91) and reduces mean squared error from 185.74 to 183.10. These improvements demonstrate that explicitly modelling regime dynamics yields more accurate and parsimonious representations of inflow processes. Overall, the methodology enhances characterization of underlying climatic regimes and improves inflow modelling, offering a practical tool for water-resource management and climate-adaptation planning.