Uncertainty in computed turbulent heat fluxes over seasonal snow arising from roughness length and similarity theory assumptions

Abstract. Aerodynamic roughness lengths are a key source of uncertainty in modeling turbulent heat fluxes over snow-covered surfaces, particularly in complex terrain. We investigate the influence of instrumental and measurement uncertainties and terrain complexity on roughness length estimates and MOST-based turbulent flux calculations using data from twelve eddy-covariance (EC) stations across the European Alps, covering slopes from 0.5° to 27°. Two stations with multiple measurement levels allow for a detailed analysis of vertical wind profiles. Several bulk aerodynamic  methods and roughness length parameterizations are evaluated.

Roughness lengths derived from logarithmic wind profiles under near-neutral conditions vary by up to an order of magnitude between measurement heights, indicating a strong sensitivity to sensor height and potential violations of the law of the wall. Instrumental and measurement uncertainties, especially under predominantly near-neutral or stable conditions with weak vertical gradients, lead to large relative errors in scalar roughness lengths and propagate into modeled turbulent fluxes, resulting in relative errors of up to 38.9% for turbulent sensible heat flux and up to 56.5% for turbulent latent heat flux.

Roughness lengths for momentum and scalars vary substantially among sites, and commonly assumed fixed ratios between them do not hold. No systematic degradation in bulk aerodynamic method performance with increasing slope is observed, suggesting that limitations arise from the general application of MOST in complex terrain. When EC-derived roughness lengths are unavailable, prescribing a constant roughness length (0.61 mm) for momentum and scalars provides the most robust EC-independent results.