## 1. Introduction

[2] Snow surface roughness is a measurement of the variability of surface microtopographic features. It is a function of crystal type, deposition conditions, and age (metamorphism and temperature history). The roughness of the snow surface exerts an important control on the transfer of wind energy to the surface, with important effects on snow transport and redistribution and latent and sensible heat exchanges. Development and standardization of measurement and classification techniques for snow surface roughness would add a physical basis for estimation of the *z*_{0} roughness parameter used in energy balance computation, and could potentially increase the accuracy of snow transport, hydrologic, and climatic models.

[3] Roughness of different Earth surfaces has been measured at various scales, including the microtopography (millimeter to centimeter resolution) of soils related to tillage and erosion practices [e.g., *Kuipers*, 1957; *Currence and Lovely*, 1970] and the macrotopography (usually meter resolution) of seafloors related to their formation [e.g., *Swift et al.*, 1985; *Briggs*, 1989; *Lyons et al.*, 2002]. These investigations have developed several different surface profiling techniques and roughness analysis indices and measures. For soil, pin boards with either single or multiple probes measure vertical distance relative to an established datum in either one or two dimensions manually, electronically or with photography [*Currence and Lovely*, 1970]. These vertical distances have also been measured using laser scanners [*Huang et al.*, 1988] and stereoscopic imagery [*Welch et al.*, 1984; *Swift et al.*, 1985], and the digital data have been used to derive digital elevation models [*Rieke-Zapp et al.*, 2001]. *Munro* [1989] assessed snow roughness on a glacier using eddy correlation and physical measurements. *Herzfeld et al.* [2003] assessed snow surface patterns at a 0.1 mm resolution covering an area of 100 m by 100 m.

[4] Once surface data have been measured, various indices and measures are developed to describe roughness. A variety of roughness indices designed to describe surface variation as a single value have been outlined [*Currence and Lovely*, 1970; *Huang*, 1998]. These include the random roughness (RR) which is the standard deviation of the elevations from the mean surface [*Kuipers*, 1957], the sum of the absolute slopes (RM) between various distance intervals [*Currence and Lovely*, 1970], and the product of the microrelief index (MIF) (mean absolute deviation of elevation from a reference plane) and the peak frequency (number of elevation peaks per unit transect length) [*Romkens and Wang*, 1987].

[5] Roughness measures are designed to quantify the spatial structure of the surface. These include the semivariance [*Brown*, 1987], autocorrelation [*Huang*, 1998], and power spectral density [*Currence and Lovely*, 1970]. Semivariance is computed between elevation points of equal distance and the plot of the semivariance versus the lag distance between elevation pairs is called a variogram. In log-log space, linear segments indicate power law scaling, and the power law slope can be used to compute the fractal dimension (*D*), equal to the dimensional space plus one minus one half of the exponent or power of the relationship. A change in slope between power law variogram segments defines a scale break (SB), indicating a change in driving processes at that length scale [e.g., *Deems et al.*, 2006]. Often the semivariogram becomes random (*D* = 2 for a profile) at separation distances greater than a SB. To analyze larger snowpack roughness features (>0.1 m horizontal and >1 cm vertical), *Herzfeld* [2002] used variograms, called a first-order vario function, and subsequently a second-order vario function to investigate the variability of a variogram.

[6] To assess snowpack surface roughness, we captured digital images of the snow surface against a board partially buried into the snowpack, as has been done in some previous studies. For example, *Elder et al.* [2009] used 1.5-m-long boards that yielded a resolution of ±1 mm. *Löwe et al.* [2007] identified snow surface roughness at a subcrystal scale (∼0.1 mm) by defining the optimal gray scale threshold between the snow and a scaled target. This paper presents methods (1) to determine snowpack surface roughness from digital imagery and (2) to estimate several different roughness indices and measures. The snowpack surfaces derived from digital imagery are compared to manual measurements, and the sensitivities of various roughness metrics are examined.