A unified stochastic framework with memory for heat index and sea level dynamics

Abstract

Monitoring temperature-dependent events is critical for understanding their dynamics since these events have an impact on both animal and human habitation. It is common to see analysis of heat index and sea level that are described separately although these events have a direct connection to temperature. Often these analyses are less effective and less reliable in describing its dynamics vis-à-vis redundancy, flexibility, accounting of uncertainties and optimization. Since both are temperature-dependent events, a unified stochastic model with memory was derived. These events can be effectively described with a collective memory function (𝑇−𝑡)𝜇−12𝑒−𝛽2𝑡 𝑡𝜇+12, modifying the Brownian motion. A good match between the empirical and theoretical MSDs for both heat index and sea level was obtained with memory parameters 𝜇𝐻𝐼=1.0460 and 𝜇𝑆𝐿=1.0894 , respectively. With μ > 1, heat index and sea level exhibited long-term memory characteristics which have important implications for large timescale prediction. Similarly, analyses using a unified model are simplified and may provide the interrelatedness of these events.