On the Parameterization of Surface Roughness at Regional Scales

A parameterization for surface roughness and blending height at regional scales, under neutral atmospheric stability, is studied and tested. The analysis is based on a suite of large-eddy simulations (LES) over surfaces with varying roughness height and multiple variability scales. The LES are based on the scale-dependent Lagrangian dynamic subgrid-scale model, and the surface roughnesses at the ground are imposed using the rough-wall logarithmic law. Several patterns of roughness distribution are considered, including random tiling of patches with a wide distribution of length scales. An integral length scale, based on the one-dimensional structure function of the spatially variable roughness height, is used to define the characteristic surface variability scale, which is a critical input in many regional parameterization schemes. Properties of the simulated flow are discussed with special emphasis on the turbulence properties over patches of unequal roughness. The simulations are then used to assess a generalized form of the parameterization for the blending height and the equivalent surface roughness at regional scales that has been developed earlier for regular patterns of surface roughness (regular stripes). The results are also compared with other parameterizations proposed in the literature. Good agreement is found between the simulations and the regional-scale parameterization for the surface roughness and the blending height when this parameterization is combined with the characteristic surface variability scale proposed in this paper.

Effects of Land Use and Meteorological Conditions on Local and Regional Momentum Transport and Roughness for Midwestern Cropping Systems

Eddy covariance measurements of wind speed u and shear velocity u* from tower- and aircraft-based systems collected over rapidly developing corn- (Zea mays L.) and soybean [Glycine max (L.) Merr.] fields were used in determining the local and regional (effective) surface roughness length zo and 〈zo〉, respectively. For corn, canopy height increased from ∼1 to 2 m and the leaf area index changed from ∼1 to 4 during the study period, while for soybean, canopy height increased from ∼0.1 to 0.5 m and the leaf area index increased from ∼0.5 to 2. A procedure for the aggregation of local roughness values from the different land cover types based on blending-height concepts yielded effective surface roughness values that were from ∼1/2 to 1/4 of the magnitude estimated with the aircraft data. This indicated additional kinematic stress caused by form drag from isolated obstacles (i.e., trees, houses, and farm buildings), and the interaction of adjacent corn- and soybean fields were probably important factors influencing the effective surface roughness length for this landscape. The comparison of u* measurements from the towers versus the aircraft indicated that u* from aircraft was 20%–30% higher, on average, and that u* over corn was 10%–30% higher than over soybean, depending on stability. These results provide further evidence for the likely sources of additional kinematic stress. Although there was an increase in zo and 〈zo〉 over time as the crops rapidly developed, particularly for corn, there was a more significant trend of increasing roughness length with decreasing wind speed at wind speed thresholds of around 5 m s−1 for the aircraft and 3 m s−1 for the tower measurements. Other studies have recently reported such a trend. The impact on computed sensible heat flux H using 〈zo〉 derived from the aggregation of zo from the different land cover types, using the blending-height scheme, and that estimated from the aircraft observations, was evaluated using a calibrated single-source/bulk resistance approach with surface–air temperature differences from the aircraft observations. An underestimate of 〈zo〉 by 50% and 75% resulted in a bias in the H estimates of approximately 10% and 15%, respectively. This is a relatively minor error when considering that the root-mean-square error (rmse) value between single-source estimates and the aircraft observations of H was 15 W m−2 using the aircraft-derived 〈zo〉, and only increased to approximately 20 and 25 W m−2 using the 1/2 and 1/4 〈zo〉 values, as estimated from the blending-height scheme. The magnitude of the excess resistance relative to the aerodynamic resistance to heat transfer was a major contributing factor in minimizing the error in heat flux calculations resulting from these underestimations of 〈zo〉.

Applications of the Lagrangian Dynamic Model in LES of Turbulent Flow Over Surfaces With Heterogeneous Roughness Distributions

We study turbulent flow over surfaces with varying roughness scales, using large eddy simulation (LES). The goal is to use LES results to formulate effective boundary conditions in terms of effective roughness height and blending height, to be used for RANS. The LES are implemented with the dynamic Smagorinsky model based on the Germano identity. However, as is well-known, when this identity is applied locally, it yields a coefficient with unphysically strong fluctuations and averaging is needed for better realism and numerical stability. The traditional approach consists of averaging over homogeneous directions, for example horizontal planes in channel flow. This requirement for homogeneous directions in the flow field and the concomitant inability to handle complex geometries renders the use of this model questionable in studying the effect of surface heterogeneity. Instead, a new version of the Lagrangian dynamic subgrid-scale (SGS) model [1] is implemented. A systematic set of simulations of flow over patches of differing roughness is performed, covering a wide range of patch length scales and surface roughness values. The simulated mean velocity profiles are analyzed to identify the height of the blending layer and used to measure the effective roughness length. Extending ideas introduced by Miyake [2] and Claussen [3], we have proposed a simple expression for effective surface roughness and blending height knowing local surface patch roughness values and their lengths [4]. Results of the model agreed well with the LES results when the heterogeneous surface consisted of patches of equal sizes. The model is tested here for surfaces with patches of different sizes.