Let Us Change the Aerodynamic Roughness Length as a Function of Snow Depth

Abstract

A shallow, seasonal snowpack is rarely homogeneous in depth, layer characteristics, or surface structure throughout an entire winter. Aerodynamic roughness length ($z_0$) is typically considered a static parameter within hydrologic and atmospheric models. Here, we present observations showing $z_0$ as a dynamic variable that is a function of snow depth ($d_s$). This has a significant impact on sublimation modeling, especially for shallow snowpacks. Terrestrial LiDAR data were collected at nine different study sites in northwest Colorado from the 2019 to 2020 winter season to measure the spatial and temporal variability of the snowpack surface. These data were used to estimate the geometric $z_0$ from 91 site visits. Values of $z_0$ decrease during initial snow accumulation, as the snow conforms to the underlying terrain. Once the snowpack is sufficiently deep, which depends on the height of the ground surface roughness features, the surface becomes more uniform. As melt begins, $z_0$ increases, when the snow surface becomes more irregular. The correlation value of $z_0$ was altered by human disturbance at several of the sites. The $z_0$ versus $d_s$ correlation was almost constant, regardless of the initial roughness conditions that only affected the initial $z_0$.

1. Introduction

A shallow seasonal snowpack covers approximately 50% of the Northern Hemisphere, making the snowpack surface the primary land–atmosphere interface during the winter season [1,2]. Across Colorado, United States (U.S.), an important headwater state in the western United States, 60% of the annual precipitation falls as snow [3,4]. Accurate observations and modeling of snow water resources in the western United States is essential for water budgeting, recreation, wildfire management, and ecological resources [5].

The snowpack varies spatially and temporally [6], and is controlled by local, regional, and global weather and climate [7]. Consequently, snowpack conditions will vary between maritime and continental climates [8]. Due to the variability of the snowpack across these various regimes, a standard metric to quantify the snowpack surface and evolution is difficult to acquire. The aerodynamic roughness length, $z_0$, can be used as a measure of the snowpack surface [9,10]. The $z_0$ captures the variability that is produced by land cover characteristics as well as the underlying topography [2,6,11]. The variability is further enhanced by meteorological conditions [6], non-uniform distribution of snow cover during accumulation and ablation [6,9], snow-canopy interactions [12], and wind redistribution of snow [13]. Small-scale (<1 m) and large-scale (>1 m) variations within the snowpack can alter the overall $z_0$ value [10,14,15]. The effect of a single roughness feature coupled with non-uniform spatial arrangement among other elements affects all aspects of the snowpack surface [9,10]. A dynamic $z_0$ characterizes heterogeneity in snow–water equivalent, melt rates [9], redistribution, snow deposition [6], and surface energy fluxes [16].

The $z_0$ will decrease during accumulation as the snow initially conforms to the underlying terrain (Figure 1) [16]. Once a threshold snow depth, $d_s$, is reached, the snow surface has decoupled from the topography and becomes smoother, resulting in a smaller $z_0$ [9,16,17]. Quincey et al. [18] found that one new snowfall decreased $z_0$ by 75% since it covered small-scale feature variability and only large features were left to increase the roughness. As $d_s$ decreases due to compaction, metamorphism, and/or ablation, ground-based surface features and underlying topographical features are re-coupled with $z_0$, increasing its variability [16,19].

This relation of increasing $d_s$ and decreasing $z_0$ in some form has been observed previously [2,9,20]. This correlation of $d_s$ and $z_0$ is not considered within hydrologic, snowpack, or land surface models. The relation of these two factors is also expected to differ between periods of melt and accumulation as periods of melt are typically less uniform [16], so that the difference between accumulation and melt for $d_s$ versus $z_0$ is likely hysteretic (Figure 1b). Swenson and Lawrence [21] found that topography and land cover features have the most influence on the hysteresis. Once the snow cover has reached full coverage over these features, the snowpack will accumulate homogeneously [16]. These early-, mid-, and late-season snowpack surface changes have important impacts (Figure 1) on estimating an accurate $z_0$ value within hydrologic models [19].

To accurately understand and model the snowpack, variability of the surface needs to be considered at the local level. Otherwise, hydrologic models will either over or underestimate melt water availability and melt rates [19,22,23]. Currently, the same $z_0$ is used for an entire watershed, based on the assumption of 100% snow-covered area, undeviating melt throughout an area, despite the topographic or vegetation influences [6,23]. No spatial or temporal variation in $z_0$ is represented [24]. Therefore, we hypothesize that the incorporation of $z_0$ as a dynamic variable, rather than a static parameter, will improve meteorologic, snowpack, and hydrologic models [2,19,20,23,25]. To understand and observe the relation between $z_0$ and $d_s$, questions are asked as follows: (1) Does the snow surface roughness, defined here as $z_0$, change as a function of $d_s$? (2) Does the correlation between $z_0$ and $d_s$ vary over space? (3) Is the decrease in $z_0$ as $d_s$ increases consistent regardless of the initial ground roughness? (4) Is the correlation between increasing $d_s$ and decreasing snow surface $z_0$ a function of the initial roughness feature, such as dominate vegetation and topographic features? Also, (5) is there a difference between the $z_0$-$d_s$ correlation during periods of accumulation and melt, i.e., is it a hysteretic? Finally, we compare sublimation modeling, applying the bulk transfer approach, to compare using a constant $z_0$ value for snow with the dynamic $z_0$ versus $d_s$ correlation for one of our study sites.

2. Data and Methods

2.1. Site Descriptions

Sites were selected based on varying topography and vegetation cover, and abundance, elevation, and distribution throughout the watershed. This aided in determining spatial differences and the $z_0$ versus $d_s$ correlation. We selected nine sites near Meeker, Colorado (Figure 2), with an elevation range from 1885 to 2468 m, to evaluate the research questions. Land cover ranged from open, grassy fields to large Pinyon–Juniper- and shrub-dominated sites. Sites were chosen for land cover variability, size of the primary roughness feature, and winter accessibility (

Table 1. Description of the nine study sites within the White River watershed of Colorado U.S. during the 2019–2020 winter season, including the average scan frequency, primary roughness feature height, and initial/snow-free $z_0$.

Site Name	Scan Frequency	Primary Roughness Feature Height (m)	Initial ${\mathit{z}}_0$ ($\times {10}^{-3}$ m)
Yellow Jacket (YJ)	Tri-weekly	1.85	330
Trout Farm (TF)	Weekly	0.01	5.0
Julie Circle (JC)	Every storm	0.35	40
Lost Creek (LC)	Weekly	0.13	9.0
Spring Creek (SC)	Monthly	1.10	220
Cathedral Creek (CC)	Bi-weekly	1.30	570
Piceance (P)	Bi-weekly	0.68	110
CR11	Bi-weekly	0.46	66
Upper Piceance (UPC)	Bi-weekly	1.65	390

). Annual precipitation ranges from 391 to 631 mm [26].

Each site was equipped with a Bluetooth Blue Maestro Tempo Disc sensor [27] that recorded hourly air temperature, humidity, and dew point temperature. Three or four T-posts were installed with measuring tape to record $d_s$. A silver sphere was added to the north facing T-post for direction orientation. Additionally, the silver reflected well in the LiDAR scans to provide orientation within the processing software.

2.2. Field Data Collection

The snowpack surface was measured using a FARO Focus3D X 130 model Terrestrial LiDAR Scanner (TLS) [28]. This LiDAR instrument generates a point cloud scan of a given area with an error of +/− 2 mm and a resolution of approximately 7.5 mm. Three LiDAR scans from different locations were taken during each site visit to avoid shadowing from roughness features. TLS scan frequency ranged from every two days to monthly. Scan interruptions occasionally occurred due to extreme winter weather and/or inability to reach the site safely.

During each site visit, the Blue Maestro [27] air temperature ($T_a$) and relative humidity data were downloaded. The current weather conditions (sunny, cloudy, windy, etc.), upcoming storm forecasts, approximate new snow accumulation, and snow depths at each T-post were recorded. Photos were taken of the site. These data and photos were used to explore any inconsistencies among the $z_0$ calculations, or processing errors. Meteorological data ($T_a$) were used to explore any major temperature warming or cooling that may have altered melt rates.

2.3. Data Processing

The three LiDAR scans from each site visit were cropped, merged, and aligned with each other in the corresponding cardinal direction (Figure 3) in the open-source program Cloud Compare [29]. An area of interest (AOI) was chosen for each site within the middle of the T-posts that varied in size from 2 × 2 m to 8 × 8 m, and typically included a primary roughness feature such as a sagebrush or shrub (Figure 2). The AOI had a resolution from 1 to 10 mm for a total of approximately 1.3 million points. The AOI was cropped out of each merged/aligned scan and interpolated using kriging at a 0.01-m resolution in the Golden Software Surfer [30]. This created an interpolated, gridded AOI that was de-trended [11] in the x-y plane to remove the bias from the slope of the field or the angle of the LiDAR scanner [20].

For the AOI, the final geometric $z_0$ was calculated using the general approach of Lettau [31], specifically with the discretization and numerical method and code from Neville et al. [15]. This is a MATLAB code to apply Lettau’s equation to identify the mean obstacle height, $h^{*}$, by finding all local maxima and minima relative to each other across the surface. Then, the lot area, S, is calculated as the total area divided by the total number of maxima. Next, the silhouette area, s, is found as the profile of an obstacle, this is conducted at a predefined resolution step. These steps, applied within Equation (1), result in the average $z_0$ of the surface:

$$z_0={\displaystyle \frac{h^{*}s}{S}}$$

(1)

Note that Lettau [31] divides Equation (1) by 2, but Sanow et al. [20] found that halving $z_0$ was unnecessary since it was determined experimentally as a site-specific drag coefficient.

The $d_s$ for each LiDAR scan were calculated using Cloud Compare [29] by subtracting the initial snow-free scan from the snow-covered scan (Figure 3). The mean $d_s$ were computed across the AOI. Snow depths from site visits were cross-evaluated against LiDAR point clouds to ensure accuracy during post-processing. The snow depth observations at each T-post were also used to assess the LiDAR-derived snow depth estimate.

2.4. Data Analysis

Initial roughness LiDAR scans were taken with no snow on the ground. When snow was present throughout the season, the initial scans were subtracted from the snow-covered scans to find the average $d_s$. The corresponding $z_0$ values were calculated for each scan, including those with and without snow.

Resulting snow depths were plotted against the natural logs of $z_0$ for each site and grouped by slope. The coefficient of determination ($r^2$) was found for each site. One site, Julie Circle, was chosen to observe the hysteresis between periods of accumulation and melt due to the high temporal frequency of scans (Table 1). Melt versus accumulation was determined by $d_s$ of the previous scan. If $d_s$ had increased since the last scan, it was an accumulation time step. If it had decreased, it was a melt time step. This was verified using site photos, measured air temperature, as well as recorded hand measurements. However, it is important to note that snowpack depth can decrease due to densification and other metamorphism.

2.5. Sublimation Estimation

Sublimation was estimated with the bulk transfer formula [32] using both a constant $z_0$ of 2.4 × ${10}^{-4}$ m (the typical default value in models) [33] and a variable $z_0$. Specifically, the latent mass flux equation was simplified by assuming that the snowpack surface was saturated and that measured air temperature, could be used to estimate the snow surface humidity and, thus, the vapor pressure gradient [32,34]. For both scenarios, the height of the wind speed measurement was reduced by the depth of snow [34]. It is acknowledged that the bulk transfer formula is a simplification [35], yet this comparison, like Sanow et al. [25], illustrates the relevance of dynamic $z_0$ over a static $z_0$, as is used in most models.

The formulation from the Julie Circle (JC) site (Figure 3) was used since it had the most data (31 dates; Table 1). Sublimation was modeled using hourly meteorological data from the Meeker airport Automated Surface Observation Station (ASOS) [36]. The value of $z_0$ was computed from $d_s$, which was estimated from ASOS precipitation data, fresh snow density computed from by air temperature [37], and a first-order snowpack densification [38]. The simulated $d_s$ was evaluated from the $d_s$ measurements at the JC site (Figure A1).

3. Results

The height of the features was measured and ranged from 0.01 to 1.85 m (Table 1). The snow-free $z_0$ value corresponds to the $z_0$ of the underlying features (Figure 4). The feature $z_0$ is correlated to the feature height (Figure 4). While Trout Farm appears to be an outlier in the correlation (Figure 4), removing it reduces the $R^2$ value from 0.73 to 0.64. CC is actually more of a statistical outlier; removing it alone increases the $R^2$ value to 0.96.

Over the 2019–2020 winter season, 91 total site visits were conducted between October and April (

Table A1. Summary of the 91 measurement dates at the nine study sites (see Table 1) with the mean snow depth, geometric-based $z_0$, slope, and $R^2$ for the regressions in Figure 4.

Site	Date	Snow Depth (m)	${\mathit{z}}_0$ (× ${10}^{-3}$ m)	Regression Slope	Regression ${\mathit{R}}^2$
CR11	6 January 2020	0.32	10.9	−0.066	0.81
	29 January 2020	0.43	0.0724
	10 February 2020	0.49	0.176
	11 March 2020	0.05	20.0
	16 March 2020	0	65.8
Julie Circle	25 Nov 2019	0	40	−0.072	0.86
	26 November 2019	0.18	19.7
	27 November 2019	0.13	27.4
	27 November 2019	0.11	30.0
	28 November 2019	0.10	20.7
	28 November 2019	0.11	25.2
	30 November 2019	0.09	20.3
	8 December 2019	0.02	29.3
	14 December 2019	0.11	15.8
	25 December 2019	0.18	14.3
	26 December 2019	0.17	17.2
	27 December 2019	0.15	11.6
	28 December 2019	0.23	4.50
	29 December 2019	0.21	4.19
	2 January 2020	0.33	1.17
	6 January 2020	0.22	2.74
	7 January 2020	0.27	2.57
	10 January 2020	0.33	2.44
	13 January 2020	0.29	2.57
	15 January 2020	0.27	2.21
	20 January 2020	0.28	1.93
	23 January 2020	0.28	1.99
	24 January 2020	0.28	1.63
	28 January 2020	0.29	0.606
	4 February 2020	0.34	0.365
	6 February 2020	0.52	0.351
	10 February 2020	0.41	0.247
	2 March 2020	0.36	1.24
	4 March 2020	0.28	2.91
	5 March 2020	0.19	5.72
Trout Farm	26 December 2019	0.05	0.427	−0.034	0.23
	30 December 2019	0.13	1.49
	2 January 2020	0.18	0.0836
	6 January 2020	0.18	0.737
	19 January 2020	0.18	0.109
	24 January 2020	0.21	0.0562
	4 February 2020	0.27	0.467
	10 February 2020	0.29	0.631
	25 February 2020	0.29	0.246
	11 March 2020	0	4.76
Cathedral Creek	11 Oct 2019	0	563	−0.21	0.77
	3 January 2020	0.16	264
	16 January 2020	0.15	268
Piceance	15 November 2019	0	137	−0.24	0.99
	2 December 2019	0.16	120
	30 December 2019	0.34	124
	24 January 2020	0.36	58.3
	11 February 2020	0.50	28.8
	3 March 2020	0.38	51
	12 March 2020	0.14	121
Spring Creek	15 November 2019	0	222	−0.25	0.72
	3 January 2020	0.43	32.4
	11 February 2020	0.56	30.3
Upper Piceance	15 November 2019	0	389	−0.22	0.96
	2 December 2019	0.14	246
	8 January 2020	0.28	172
	24 January 2020	0.35	135
	11 February 2020	0.47	63
	25 February 2020	0.45	59.3
	12 March 2020	0.20	149
	24 March 2020	0.17	329
Lost Creek	8 Oct 2019	0	9.41	0.045	0.08
	27 November 2019	0.17	0.172
	28 November 2019	0.11	0.0476
	6 December 2019	0.17	0.203
	11 December 2019	0.17	0.231
	27 December 2019	0.33	0.281
	30 December 2019	0.39	0.0732
	7 January 2020	0.46	0.295
	14 January 2020	0.57	0.788
	28 January 2020	0.68	0.157
	26 February 2020	0.85	3.38
	4 March 2020	0.73	2.35
	11 March 2020	0.60	4.02
	26 March 2020	0.46	0.53
	31 March 2020	0.47	0.0976
	7 Apr 2020	0.29	0.598
Yellow Jacket	9 October 2019	0	328	−0.60	0.77
	21 October 2019	0.18	255
	27 November 2019	0.33	275
	30 December 2019	0.54	205
	28 January 2020	0.71	144
	26 February 2020	0.79	100
	4 March 2020	0.70	163
	26 March 2020	0.43	288
	31 March 2020	0.47	245

). All sites, except Lost Creek (Figure 5c), showed that as $d_s$ increased and enveloped roughness features, the corresponding $z_0$ decreased (Figure 5). For example, the Piceance site (P in Figure 5b) shows $d_s$ increasing and the corresponding decreasing in $z_0$ until 3 March 2020, when melt began. Furthermore, as $d_s$ starts decreasing, the $z_0$ values begin to increase. This relation developed quickly, and roughness feature size had an impact on the trend line slope. Lost Creek was disturbed during the spring and therefore did not follow this same temporal pattern (Figure 5c and Figure 6a,b).

To identify spatial and temporal patterns, the sites were grouped using the resulting slopes from the least square regression fit: CR11, Julie Circle, and Trout Farm (Figure 5a); Cathedral Creek, Piceance, Spring Creek, and Upper Piceance Creek (Figure 5b); Lost Creek (Figure 5c); and Yellow Jacket (Figure 5d). CR11 and Julie Circle have similar $r^2$ values (0.81 and 0.86, respectively), slope, roughness feature height, and initial $z_0$ values (Figure 5a). This result was seen despite the difference in data quantity between the two sites, i.e., five measurements (CR11) versus 30 measurements (JC). The primary roughness feature height (height of the tallest feature found within the AOI Table 1) at CR11 and Julie Circle are 0.46 m and 0.35 m; the slopes are quite similar at −0.066 and −0.072, respectively. Julie Circle had one notable outlier on 6 February 2020, with the deepest observed $d_s$ of 0.52 m and a $z_0$ value of 3.5 × ${10}^{-4}$ m (Figure 7). This occurred after an overnight storm deposited 0.18 m of new snow. Conversely, the lowest $z_0$ at the site occurred on 10 February 2020 with a $d_s$ of 0.41 m and a $z_0$ of 0.25 × ${10}^{-3}$ m. Similar to Julie Circle, the deepest $d_s$ at CR11 of 0.49 m on 10 February 2020 had a $z_0$ of 0.18 × ${10}^{-3}$ m, yet the lowest $z_0$ ($z_0$ of 0.07 × ${10}^{-3}$ m) at the site occurred during the second deepest $d_s$ of 0.43 m on 29 January 2020. Trout Farm had a similar slope to this pair (Figure 5a). Yet, compared to CR11 and Julie Circle with initial $z_0$ values of 66 × ${10}^{-3}$ m and 40 × ${10}^{-3}$ m, Trout Farm had the lowest roughness feature height (0.01 m for a grassy lawn) and initial $z_0$ of 4.8 × ${10}^{-3}$ m (Figure 6c,d). These initial $z_0$ values are an order of magnitude different between CR11 and Julie Circle. Separating TF into possible accumulation from the concurrent timing at JC (the four left, lower $z_0$ values in Figure 5a) yielded a slope of −0.049, leaving the possible melt points (the five right, higher $z_0$ values) yielding a slope of −0.11. These aligned better than the average slope of −0.034 at Trout Farm. Regressing with all three sites together (CR11, JC, and TF) produced a slope of −0.063 and an $r^2$ of 0.70.

The second grouping of sites includes Cathedral Creek, Piceance, Spring Creek, and Upper Piceance Creek (Figure 5b). These sites had the lowest number of site visits (three to eight) due to distance and difficult winter access. The slopes of all four sites were alike, with Cathedral Creek −0.21, Piceance −0.24, Spring Creek −0.25, and Upper Piceance Creek −0.22. The main variation among these sites is the $r^2$, primary roughness feature height, and initial $z_0$ values. Piceance and Upper Piceance Creek have very high $r^2$ values of 0.99 and 0.96, respectively. Spring Creek had the least amount of site visits and corresponding data. Upper Piceance has the highest amount of site visits in this grouping. Outliers from Cathedral Creek are from the two highest $d_s$ of 0.19 m and 0.23 m, and $z_0$ values 4.9 × ${10}^{-1}$ m and 4.4 × ${10}^{-1}$ m, respectively. Furthermore, the second group had the largest variation of roughness feature sizes ranging between 0.68 m at Piceance and 1.65 m at Upper Piceance Creek. Regressing with all four sites (CC, P, SC, and UPC) produced a slope of −0.22 and an $r^2$ of 0.77. It was initially thought that Piceance would correlate with group a (Figure 5a) due to the size of the primary roughness feature height. Yet, the initial $z_0$ was 1.1 × ${10}^{-1}$ m, which is much larger than the others within the group of group CR11, JC, and TF.

Spring Creek had a roughness feature height of 1.1 m and initial $z_0$ of 2.2 × ${10}^{-1}$ m which represents an average throughout the sites. Cathedral Creek had the highest initial $z_0$ value of 5.6 × ${10}^{-1}$ m, but it had only the third largest roughness feature (1.3 m), indicating the site had the highest quantity of roughness features. Upper Piceance Creek had the second-largest initial $z_0$ value and roughness feature height at 3.9 × ${10}^{-1}$ m and 1.65 m, respectively. However, both sites fell below Yellow Jacket, which was placed singularly into Figure 5d. Yellow Jacket had the largest roughness feature of 1.85 m (Aspen, large sage, and shrubbery). Though, it produced the third largest initial $z_0$ value of 3.3 × ${10}^{-1}$ m. Additionally, it had the steepest slope of any of the sites at −0.60. Yellow Jacket had two outliers that resulted in a higher $z_0$ value than the initial $z_0$ value. These instances occurred on 16 March 2020 and 7 April 2020, late in the season after peak $d_s$ had occurred (Figure 6e,f).

Lost Creek experienced heavy anthropogenic influence as shown in Figure 5c. Between 28 January and 26 February 2020, a snowmobile drove through the site which altered the natural progression of the snow (Figure 6a,b). Still, Lost Creek results show some similarities to the other sites. Prior to the snowmobile, Lost Creek was following the same hysteresis relation as the other sites. Lost Creek had the lowest $r^2$ at 0.08 likely due to the snowmobile tracks.

Since Julie Circle had the most data points of any site, it was used to analyze melt and accumulation values (Figure 7a). There are 11 accumulation points, 17 melt points, and 2 points with $d_s$ of 0 m, taken as the initial surface roughness scan (fall) and the final surface roughness scan (spring). The slopes were similar at −0.072 for accumulation and −0.075 for melt, both with high $r^2$ values (0.81 and 0.86, respectively).

It is possible that $z_0$ does not initially decrease as snow accumulates, or decreases less than once 0.1 m of snow is on the ground. Further, when the snow is deep, perhaps deeper than 0.4 m, $z_0$ no longer decreases and is disconnected from the ground surface $z_0$. As such, the rate of change in $z_0$ with $d_s$ is different (Figure 7b).

Cumulative Sublimation

The simulated snow depth matched the observed Julie Circle snow depth well (Figure A1a and Figure A2). The mean absolute error was 0.034 m, with a Nash–Sutcliffe Efficiency of 0.85 for the 31 sampling dates. The estimated cumulative sublimation using the dynamic $z_0$ was almost double the amount (24.9 versus 13 mm) estimated using the constant $z_0$ for snow (Figure 8). The dynamic $z_0$ reached its minimum of 0.00034 m later in February (Figure A1b) when the snowpack was deepest (Figure A1a), as per Figure 7b.

4. Discussion

The calculated $z_0$ changed as a function of observed $d_s$, although outliers of the relation existed. The first outlier was at the Julie Circle location (Figure 5a). The initial point on the x-axis indicates the highest $z_0$ value (4.0 × ${10}^{-2}$ m) due to the lack of snow, i.e., $d_s$ = 0 and this occurred prior to accumulation (Figure 7). The other point with a $d_s$ of 0 was at the end of the season after all the snow melted, and produced less than half the $z_0$ (16 × ${10}^{-1}$ m) of the initial $z_0$. This is likely attributed to the vegetation type, which is a regular lawn grass that was pushed down by the weight of the snow throughout the year. This scenario could happen to any type of thin, flexible vegetation, fluctuating $z_0$ values depending on time of year [10,18].

Another discrepancy at the Julie Circle site was that the highest $d_s$ did not correspond with the lowest $z_0$ value. A possible explanation for this observation is the large Cottonwood tree that overhangs the Julie Circle site. For example, within the point clouds, pock-marks were evident in the snowpack surface (Figure 3b) where accumulated canopy snow fell from the limbs and altered the roughness. No other sites in this study had canopy cover like Julie Circle. Although, most sites did have shrubbery present [39], so even small-scale canopy interception and deposition was possible [18]. Canopy interception and redeposition is a potential issue when correlating between $d_s$ and $z_0$. Therefore, to assume a uniform or linearly metamorphosing or melting snowpack could lead to errors [9,10,40]. A different explanation is that when the snowpack is deep enough, $z_0$ is disconnected from the ground $z_0$ (Figure 7b). This requires further investigation.

This lack of correlation is also noted at CR11 and Trout Farm. Similar to Julie Circle, the highest $d_s$ value did not correspond with the lowest $z_0$ value at CR11. This can be attributed to a recent snowfall event of about 10 cm that had fallen the day before the 29 January 2020 scan. On 10 February 2020, there was less fresh snow (approximately 5 cm) and conditions were sunny and warm. These differences in the snowpack were recorded in site notes and photos from the visits. Likewise, Trout Farm also experienced the same contradiction, since the highest $d_s$ value had a $z_0$ greater than double the lowest calculated $z_0$. This indicates that these small variations of the snowpack surface is key to addressing $z_0$ beyond simply considering the snow depth. Accounting for small surface variations is especially important on flat sites where initial $z_0$ may be surpassed by the development of surface features such as sun cups, sastrugi, surficial features, wildlife, and anthropogenic modifications [4,18,32,40].

Cathedral Creek (Figure 5b), followed the $d_s$ and $z_0$ relation until the 10 and 24 February 2020 scans. Between the scan dates of 16 January and 10 February 2020, temperatures were often warmer than earlier in the winter, with a maximum temperature of 19 °C. The interpolated surfaces of 16 January 2020 (lowest $z_0$) and 24 February 2020 (highest $d_s$) are shown in Figure 9, highlighting pock-marks and uneven melting. These elevated temperatures resulted in an increased, non-uniform melt [9]. So, even though additional snow fell between the scans, it did not completely cover the snow surface characteristics [9,16,17].

Yellow Jacket had one of the higher initial $z_0$ of the sites (Figure 6e,f, Table 1). Photos from the field visits late in the season show substantial recent melt, which revealed larger shrubs, as well as the development of sun cups within the AOI (Figure 6e,f). The late season increase in roughness likely produced two irregular points with a higher $z_0$ than for the initial after peak $d_s$ had occurred [2]. Another influence on the site was the anthropogenic modifications of snowmobile tracks. Combining these two factors led the roughness variations to be larger than the initial grassy, shrub-filled plot. This same anthropogenic disruption occurred at the Lost Creek site (Figure 5c and Figure 6a–d). This led to an extreme increase in $z_0$ after the disturbance, even with the deep snowpack 0.85 m (Figure 5d). The large increase in $z_0$ at the site was exacerbated by the very flat topography that contained one small, controlled roughness feature (railroad tie) in the middle.

We hypothesized that slopes would remain the same and the x-intercept would change. However, the initial ground roughness played a critical role in the slope of the data. The 0.13 m railroad tie at the Lost Creek site is an example of a feature responsible for the initial site $z_0$ value of 9.4 × ${10}^{-3}$ m. Without it, the $z_0$ would have been lower as the site was an open, grassy field. Due to this controlled roughness feature, none of the snowmobile-caused $z_0$ values were larger than the initial $z_0$. Lost Creek also had some of the highest $d_s$, which led to higher $z_0$ values, especially coupled with snowmobile tracks. Snowmobiling and other recreational activities are common throughout public lands during the winter [4]. Anthropogenic factors such as these are important to consider when evaluating a spatially and temporally dynamic $z_0$ [4]. Moreover, this could explain the discrepancies in sites like Yellow Jacket, also influenced by snowmobiles. Together, land cover type and function need to be considered when applying $z_0$ [4].

Figure 5b shows the grouping of Cathedral Creek, Piceance, Spring Creek, and Upper Piceance Creek. The slopes of all four sites were similar, ranging from −0.21 to −0.25. The $r^2$ values, roughness features (ranging between 0.68 and 1.65 m), and initial $z_0$ values (ranging from 1.1 to 5.7 × ${10}^{-1}$ m) varied among the sites. Based on the primary roughness feature heights, Piceance aligns better with the CR11, Julie Circle, and Trout Farm group than the one in which it was placed. Upper Piceance was more similar in initial $z_0$ and roughness feature size to Yellow Jacket, but their slopes have a difference of 0.38. However, as discussed, there were some values that skewed the slopes in these sites. Potential reasons for this were noted at several sites, such as overall changes in the surface of the snowpack throughout the season due to wind redistribution [41], surface energy fluxes [9], formation of surface features [2], and non-uniform melt and accumulation [9]. These influences metamorphize the snowpack and are very difficult to quantify or predict. The development of surface features is one reason why the slopes of Trout Farm and Julie Circle have only a slight difference despite the initial $z_0$ values being an order of magnitude different (4.8 × ${10}^{-3}$ and 40 × ${10}^{-3}$ m, respectively).

Julie Circle was used to compare accumulation and melt values (Figure 7). Yellow Jacket and Trout Farm had 9 or 10 measurement dates, respectively, but their measurements were not over a range of snow depths for both accumulation and melt. The slopes accumulation and melt slopes were similar, but the snow-free $z_0$ was less after snowmelt (16 × ${10}^{-3}$ m) than before accumulation (40 × ${10}^{-3}$ m). This could be due to the snow compacting the ground vegetation. Initially, accumulation versus melt hysteresis aspect of the study was to be conducted at Lost Creek and Yellow Jacket; however, these sites were anthropogenically altered and were thus not used. It was hypothesized that the melt versus accumulation at Yellow Jacket would yield a higher difference between the accumulation slope and the melt slope due to the higher initial roughness and quantity of roughness features to enhance melt (Figure 6e,f). Since Lost Creek was a flat, open site (Figure 6a), it was hypothesized that the slopes would be similar to Julie Circle. The primary influence of melt at Julie Circle was the addition of ecological factors from the tree near the site, and the proximity to a residential house, potentially increasing the effects of longwave radiation-induced melt. At Lost Creek, incoming solar radiation would dominate snowmelt. Therefore, slopes even more similar to each other were expected.

The method used to determine melt compared to accumulation values is also a source of potential error. Settling and metamorphism of the snowpack could have occurred, resulting in snow depth decreases without any actual snowmelt taking place [13,16,42]. Photos, atmospheric conditions, and visual assessments of the site were completed. For these shallow snowpacks where multiple melt cycles can occur, snow wetness sensors, soil moisture sensors, and other atmospheric/hydrologic monitoring equipment could aid in determining the exact periods of melt. In deeper snowpacks, that typically only have one melt period at the end of the winter, snowpack temperature sensors could assist in determining when the snowpack became isothermal and is beginning to melt.

4.1. Implications

The value of $z_0$ is not constant for snow [15,17,25,43]. It was observed to decrease as $d_s$ increased (Figure 5). When a dynamic $z_0$ is used as a function of $d_s$,

Table A2. Slope and y-intercept in the form $z_0$ = exp (SLOPE × $d_s$ + INTERCEPT) for the nine study sites (Figure 1). For Julie Circle, a minimum $z_0$ of 0.00034 m was used, as per Figure 7.

Site Name	Slope	Y-Intercept
CR11	−12.3	−2.7
Julie Circle (JC)	−12	−2.7
Trout Farm (TF)	−6.7	−6.7
Cathedral Creek (CC)	−4.8	−0.58
Piceance (P)	−4.1	−0.79
Spring Creek (SC)	−3.8	−1.6
Upper Piceance (UPC)	−2.9	−1.7
Yellow Jacket (YJ)	−1.3	−0.96
Lost Creek (LC)	1.8	−8.4

estimates sublimation can double (Figure 8), for a shallow snowpack. Since much of the world’s snowpack is shallow [44], land surface, meteorological, snowpack, and hydrological modeling should include a dynamic $z_0$, and possibly a hysteretic $z_0$ (Figure 7). This will initially change the sensible and latent heat fluxes, which would increase simulated sublimation and melt rates, decreasing snow water equivalent (SWE) [25].

4.2. Next Steps

This study consisted of 91 site visits, which produced a robust dataset for observing trends and correlations. While increased temporal scan frequency, preferably daily, would offer further insight into the snowpack surface evolution due to surface processes [6,7] and meteorological factors [2,45], the current dataset still captures the overall temporal changes. The scan areas represent a small portion of the White River watershed. Although this limits direct watershed-scale extrapolation, the findings highlight important local-scale processes and variability. Site-specific features, such as the cottonwood tree at Julie Circle which influenced surface conditions and canopy cover, reflect natural heterogeneity common in snow-covered landscapes [16]. However, some consistency was observed between sites with similar terrain and land cover. For example, Upper Piceance Creek and Cathedral Creek, since both are situated on old river terraces near cliffs, exhibited comparable initial roughness values (39 × ${10}^{-3}$ and 56 × ${10}^{-3}$ m) and similar feature heights (1.65 m and 1.3 m), producing nearly identical $z_0$ versus $d_s$ slopes (−0.22). This suggests that once a $z_0$ versus $d_s$ correlation is identified, it could be applied to other areas with similar characteristics.

Future studies could include larger plots within a smaller watershed that can be scanned with LiDAR for snow accumulation and melt more frequently [16,20]. Measuring and/or modeling meteorological data, such as (net) shortwave and longwave radiation, could provide more insight to determine melt periods and subsequent accumulation periods during mid- and late-season melt [42,46]. This could yield a change in one of $z_0$ or $d_s$ without a change in the other, i.e., hysteresis between blue and red lines in Figure 7 [47]. This study is a step toward understanding snowpack surface roughness dynamics and scaling roughness-based energy balance assessments, which will improve snowpack, hydrological, and meteorological modeling [2,19,20,23].

Furthermore, future studies could explore the uncertainty within the $z_0$ calculations. The current code [15] calculates $z_0$ based on the local maxima and minima within the scan area. This method is acceptable when roughness elements are homogeneously spaced and sized; however, that is not always the case in nature. The code could be reformed to calculate $z_0$ on a certain sized area (every 0.012 m, or 0.12 m, etc. depending on the size of the scan). This would give a distribution of $z_0$ values that would encompass the variations in terrain, vegetation, size, and/or distribution of roughness characteristics. This methodology could enhance the estimation of $z_0$ for an area that is larger, as a larger area (>100 m) will tend to have more variations than a small area (<10 m), such as sites used within this study.

Measuring more meteorological variables and modeling the snowpack would help guide additional data collection. This could consider sensible and latent heat fluxes [48], dust deposition [49], spatial and temporal distribution of incoming solar radiation [42], wind redistribution [40,50], longwave radiation [51], anthropogenic alterations [4,13], air temperature [45], spatial heterogeneity [52] of the snowpack [23], and vegetation cover [7]. Since melting occurred throughout the season, the environmental influences were also affecting accumulation rates, which supports the heterogeneity of the accumulation $z_0$ values. Melt rates influence atmospheric and hydrologic processes [13], and understanding the processes and rates that control melt water production is important for predicting the timing and magnitude of peak melt in a watershed [22,23,53].

5. Conclusions

At all study locations that were undisturbed, as $d_s$ increased, $z_0$ decreased, from the initial snow-free $z_0$ of the underlying ground. There were two groupings of similar $d_s$ versus $z_0$ correlations: three sites (CR11, JC, and TF) had a mean slope of −0.063 while four sites (CC, P, SC, and UPC) had a mean slope of −0.22. The initial roughness features played a large role in determining the slope f the $z_0$ versus $d_s$ correlation. We observed limited hysteresis between the $z_0$ versus $d_s$ correlation from periods of melt and accumulation, and this needs further investigation. When sites were disturbed over the winter, usually by snowmobile or other human traffic, $z_0$ increased by orders of magnitude. Incorporating a dynamic $z_0$ as a function of $d_s$ will dramatically impact, and likely improve, modeling outcomes, specifically energy fluxes, sublimation, and melt rates, and thus SWE.