Characterization of the Surface Energy Balance Residual in Complex Terrain

The closure of the surface energy balance (SEB) in complex terrain remains a persistent challenge. We present a multi-site analysis based on the i-Box network in the Inn Valley, Austria, to characterize the SEB residual (<i>Res</i>) normalized by net radiation (<i>Rn</i>) across different conditions. Diurnal cycles of <i>Res</i>/<i>Rn</i> and turbulent fluxes show a significant residual, positive (i.e., an energy gain) during the day and negative (i.e., an energy loss) during the night. Large <i>Res</i>/<i>Rn</i> is observed during nighttime stable conditions, and minimum values are found under convective mixing. Annual cycles show a distinct pattern for most of the sites, with warmer months displaying the smallest <i>Res</i>/<i>Rn</i> during daytime and largest values during nighttime, while colder months are associated with the opposite behaviour. The study examines the influence of atmospheric stability, turbulent mixing and flow conditions on <i>Res</i>/<i>Rn</i>. Results reveal that unstable conditions, associated with higher vertical mixing, tend to reduce the magnitude of <i>Res</i>/<i>Rn</i>. In contrast, stable conditions are linked to larger residuals. Especially for certain stations, foehn events and valley wind days introduce additional variability. Our findings thus point out not only the need to account for atmospheric stability, turbulence structure, and flow regimes, but also the site-specific response of <i>Res</i>/<i>Rn</i> to the above conditions which highlights the importance of collecting spatially distributed complex terrain observations.