A multi-layer numerical model for calculating the daily dynamics of soil temperature for the conditions of Azerbaijan

The article presents the results of multilayer numerical modeling of the temperature regime of bare soil under natural climatic conditions. The proposed model assumes horizontal homogeneity of the soil cover, which makes it possible to treat the soil as a non-stationary one-dimensional system with a vertical spatial coordinate and time. Such an approach allows for a detailed study of heat transfer processes in the soil profile over time, considering both diurnal and seasonal variations. The model incorporates the effect of soil moisture on heat transfer by means of an effective thermal conductivity coefficient, which also accounts for the latent heat associated with phase transitions of water (freezing and thawing) within the soil. When determining the thermal conductivity coefficient, the volumetric heat capacity of soil and water, the specific heat of the soil skeleton, bulk density, and soil type characteristics are included to provide a realistic representation of the thermal regime. The upper boundary condition is set by the measured surface temperature, while the lower boundary assumes a constant soil temperature corresponding to the deep layer that is undisturbed by surface fluctuations. The initial condition is defined by a known temperature distribution within the soil profile at the beginning of calculations. A special computational algorithm has been developed to reconstruct this initial profile from limited observational data. The time integration step of the numerical scheme is generally 3 hours but is refined to 1 hour during precipitation events to capture rapid thermal changes caused by infiltration and evaporation processes. An additional procedure is introduced to compute the soil surface temperature dynamically throughout the simulation period. To verify the adequacy of the developed model, observed daily temperature values at the soil surface and at depths of 10 cm, 15 cm, 20 cm, 40 cm, and 80 cm were used. The simulation results were compared against field data collected over a five-year observation period in two distinct climatic regions of Azerbaijan—Ganja and Nakhchivan. The comparison demonstrated that the model accurately reproduces the temporal dynamics and vertical gradients of soil temperature, confirming its suitability for studying energy exchange between the soil and atmosphere, as well as for applications in agriculture, hydrology, and climate research.