Nighttime Validation and Local Sensitivity of a Reduced-Order Thermal Balance for Above-Ground Outdoor Pools

The paper presents a mathematical validation and a local sensitivity analysis of a reduced-order thermal balance model designed to predict nighttime heat losses from an above-ground outdoor pool. The model expresses the total heat flux as a linear function of the water–air temperature difference through an effective overall heat-transfer coefficient aggregating convective, evaporative, and radiative mechanisms, as well as cover-related effects. The analysis is explicitly restricted to quasi-steady nighttime conditions. Field data were segmented into 13 independent nighttime realizations (∆T ≈ 5.5–26.9 °C, wind ≈ 0.00–1.32 m∙s−1). Across the entire dataset, the model achieved a mean relative error of 0.39% and a maximum absolute deviation of 3.72%, with no monotonic error growth versus ∆T or wind speed. Normalized local sensitivities reveal that the convective (hc) and evaporative (he) components dominate the response, whereas the radiative contribution is smaller under typical nighttime boundaries; the cover-permeability factor gains influence as wind speed increases. The additive structure limits independent identifiability of individual mechanisms, supporting an interpretation in terms of effective parameters. The results delineate the domain where the reduced-order formulation is predictive without refitting and provide a compact, interpretable reference for analyzing energy-balance models of open-water systems under nighttime operation.