**3. Results**

The unplowed versus plowed field yielded different *z*0*A* values (Figure 1). On average, the plowed field was almost 20 times as rough as the unplowed field, ye<sup>t</sup> the coefficient of variation (COV) was essentially the same (0.67 and 0.62, respectively) (Figure 1). The smallest *z*0*A* values for the plowed field were of the same magnitude as some of the largest *z*0*A* values for the unplowed field, in the range of 1 to 3 × 10−<sup>3</sup> m.

The Counihan method estimated *z*0*G* values that were 1.39 times larger and had greater variation than the estimated *z*0*A* values (Figure 2). We used the Nash-Sutcliffe coefficient of efficiency (NSCE), which is a performance statistic based on a comparison of the data fit to the 1:1 line, to evaluate how estimates of *z*0*G* compared with *z*0*A* [43]. The NSCE of the Counihan *z*0*G* was −1.18, and the Lettau *z*0*G* was 0.14, indicating the Lettau method compared more favorably with the *z*0*A*. A linear regression between both *z*0*G* estimates (Counihan *z*0*G* and Lettau *<sup>z</sup>*0*G*) and *z*0*A* was fit through the data origin to evaluate if the bias between the two methods could be removed through simple linear scaling (Figure 2). When the Counihan *z*0*G* values were scaled by 0.721 (1/1.39), the NSCE value only increased to 0.07. However, the NSCE increased to 0.88 when the Lettau *z*0*G* values were scaled by 2.34 (1/0.428).

**Figure 1.** Histogram showing range and distribution of anemometric *z*0 (*<sup>z</sup>*0*A*) values for the unplowed and plowed field from anemometric data, based on 28 and 125 wind-speed profiles, respectively. The summary statistics (mean, standard deviation (std.dev.), and coefficient of variation (COV)) are presented in the legend. A logarithmic scale is shown on the x-axis to highlight the large difference for *z*0*A* values among fields with varying characteristics.

**Figure 2.** Comparison of Lettau and Counihan geometric methods to the anemometric method. A linear regression between the geometric-based Lettau and Counihan methods (*<sup>z</sup>*0*G*) and the anemometric method (*<sup>z</sup>*0*A*) fit through the origin are presented. The Nash-Sutcliffe coefficient of efficiency [43] fit statistic is also presented. When the Lettau method is scaled by 2.34 (1/0.428), the NSCE increases to 0.88. For the Counihan comparison, when it is scaled by 0.721 (1/1.39), NSCE increases to 0.07.

The estimated *z*0 values were found to vary as a function of the amount of SCA present (Figure 3). As SCA increases, *z*0 decreases, with variability based on the calculation method (Figure 3a). A linear regression between SCA and each of the *z*0 estimates showed r2 values that were 0.01, 0.7, and 0.88 for the Counihan, anemometric, and Lettau methods of *z*0 calculation, respectively. There were noticeable differences in *z*0 depending whether SCA was increasing because snow was accumulating versus when SCA was decreasing because the snow was melting. For periods of snow accumulation, removing snow measurements that were not immediately following a snow event (the yellow boxes in Figure 3b that represent non-accumulation values) improved the linear relation between accumulating SCA and *z*0 (R<sup>2</sup> = 0.94).

**Figure 3.** Linear relation between *z*0 and snow-covered area (SCA as a %) for (**a**) all datasets (scaled Lettau and Counihan geometry-based and anemometric-based) with anemometric-based *z*0 for the pre-plowed (orange circles) and plowed fields (green triangles) highlighted, and (**b**) the scaled Lettau geometry-based *z*0 using a factor of 2.34 (see Figure 2). Lettau geometry-based *z*0 measurements with non-accumulation snow measurements were removed. Lines are based on the best-fit linear regression of the data. Snow had been on the ground for numerous days prior to the two concurrent measurements (yellow squares) taken on 22 March 2014 (SCA = 100%) and 13 April 2014 (SCA = 70%). The snowfall was fresh for all other measurements.
