Surface Energy Balance in Complex Terrain: Accountingfor Three-Dimensional Fluxes

The surface energy balance (SEB) is a fundamental physical framework describing the distribution

of energy between the Earth’s surface and the lowest layer of the atmosphere. Its

understanding is essential not only for characterizing meteorological and climatological conditions

within the atmospheric boundary layer, but also for a wide range of applications, including

weather and climate modeling, agricultural and forest management, air quality studies, ecosystem

carbon budgeting, and biological processes. All these applications inherently rely on the

assumption of a closed energy balance. However, even under flat and horizontally homogeneous

conditions, closure of the SEB is rarely achieved.

For an idealized, massless surface layer, the SEB is expressed as the balance between net radiation

and the sum of sensible heat, latent heat, and ground heat fluxes (Rn = H + LE + G).

Previous studies attribute the persistent lack of closure either to measurement uncertainties or

to neglected processes. In practice, fluxes are not measured exactly at the surface interface but

at some distance above (for Rn, H, and LE) or below the ground (for G), implying that they

are representative of a volume rather than a surface. Accordingly, the storage of heat in the air

volume below the measurement height and the heat storage in the soil layer above the heat flux

plate have been identified as contributors to the SEB residual. More recently, non-turbulent

advective fluxes associated with surface heterogeneity have been recognized as a major driver

of SEB non-closure.

In this study, we investigate the role of additional three-dimensional terms (heat storage, vertical

advection, and horizontal advection) in the SEB using observational data from selected

complex terrain sites in the Inn Valley (Austria), including measurements collected during the

TEAMx Extended Observation Periods (EOPs). The magnitude of these fluxes is quantified

to assess their relative importance within the SEB. Furthermore, the SEB residual is evaluated

by incorporating all available terms and characterized under different environmental and

atmospheric conditions.