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## Sensible and Latent Heat Fluxes for Non-Vegetated Surfaces

For non-vegetated surfaces (bare soil, glaciers), the sensible heat flux (Hg) and water vapor flux (Eg) are calculated based on the fractions of exposed, snow-covered, and surface water-covered areas.

The sensible heat flux is calculated using the temperatures of the soil, snow, and surface water, along with the aerodynamic resistance to sensible heat transfer.

The water vapor flux is calculated using the atmospheric specific humidity, the specific humidities of the soil, snow, and surface water, and the aerodynamic and soil resistances to water vapor transfer. The soil surface specific humidity is based on the soil water matric potential.

The roughness lengths for momentum, sensible heat, and latent heat are calculated, including adjustments for accumulated snow melt.

The numerical solution iterates to determine the friction velocity, temperature and humidity scales, roughness lengths, wind speed, Monin-Obukhov length, and aerodynamic resistances, which are then used to compute the final sensible and latent heat fluxes.

The partial derivatives of the heat fluxes with respect to ground temperature are also provided for use in the soil temperature calculations and flux updates.