Topographic, meteorologic, and canopy controls on the scaling characteristics of the spatial distribution of snow depth fields

[1] In this study, LIDAR snow depths, bare ground elevations (topography), and elevations filtered to the top of vegetation (topography + vegetation) in five 1-km 2 areas are used to determine whether the spatial distribution of snow depth exhibits scale invariance, and the control that vegetation, topography, and winds exert on such behavior. The one-dimensional and mean two-dimensional power spectra of snow depth exhibit power law behavior in two frequency intervals separated by a scale break located between 7 m and 45 m. The spectral exponents for the low-frequency range vary between 0.1 and 1.2 for the one-dimensional spectra, and between 1.3 and 2.2 for the mean twodimensional power spectra. The spectral exponents for the high-frequency range vary between 3.3 and 3.6 for the one-dimensional spectra, and between 4.0 and 4.5 for the mean two-dimensional spectra. Such spectral exponents indicate the existence of two distinct scaling regimes, with significantly larger variations occurring in the larger-scale regime. Similar bilinear power law spectra were obtained for the fields of vegetation height, with crossover wavelengths between 7 m and 14 m. Further analysis of the snow depth and vegetation fields, together with wind data, support the conclusion that the break in the scaling behavior of snow depth is controlled by the scaling characteristics of the spatial distribution of vegetation height when snow redistribution by wind is minimal and canopy interception is dominant, and by the interaction of winds with features such as surface concavities and vegetation when snow redistribution by wind is dominant.

[1]  Self-similarity in glacier surface characteristics , 2003, Journal of Glaciology.

[2]  Zhongwei Li,et al.  Temporal scaling of hydraulic head fluctuations: Nonstationary spectral analyses and numerical simulations , 2005 .

[3]  D. Tarboton,et al.  Modeling Snowmelt Over an Area: Modeling Subgrid Scale Heterogeneity in Distributed Model Elements , 2001 .

[4]  Kelly Elder,et al.  Comparison of spatial interpolation methods for estimating snow distribution in the Colorado Rocky Mountains , 2002 .

[5]  P. McSharry,et al.  Quantifying self-similarity in cardiac inter-beat interval time series , 2005, Computers in Cardiology, 2005.

[6]  Shaun Lovejoy,et al.  Causal space‐time multifractal processes: Predictability and forecasting of rain fields , 1996 .

[7]  Matthew Sturm,et al.  A snow-transport model for complex terrain , 1998 .

[8]  R. Pielke,et al.  Relationships between landscape, snowcover depletion, and regional weather and climate , 1999 .

[9]  G. Bloschl.  AN ANALYSIS OF SNOW COVER PATTERNS IN A SMALL ALPINE CATCHMENT , 2006 .

[10]  D. Gray,et al.  Synthesizing shallow seasonal snow covers , 1997 .

[11]  P. Molnar,et al.  Energy dissipation theories and optimal channel characteristics of river networks , 1998 .

[12]  P. Bernardara,et al.  Spectral analysis and modeling of space-time rainfall fields , 2005 .

[13]  D. Turcotte,et al.  Self-affine time series: measures of weak and strong persistence , 1999 .

[14]  Jürg Hosang,et al.  Evaluation of a water equivalent of snow cover map in a small catchment area using a geostatistical approach , 1991 .

[15]  Donald L. Turcotte,et al.  A fractal interpretation of topography and geoid spectra on the Earth, Moon, Venus, and Mars , 1987 .

[16]  J. Pomeroy,et al.  Boundary‐layer integration approach to advection of sensible heat to a patchy snow cover , 2002 .

[17]  R. Voss.  Random Fractals: characterization and measurement , 1991 .

[18]  D. Tarboton,et al.  Spatially Distributed Snowmelt Inputs to a Semi-Arid Mountain Watershed , 1997 .

[19]  Robert K. Crane,et al.  Space‐time structure of rain rate fields , 1990 .

[20]  Thomas M. Over,et al.  A space‐time theory of mesoscale rainfall using random cascades , 1996 .

[21]  David G. Tarboton,et al.  The Influence of the Spatial Distribution of Snow on Basin-Averaged Snowmelt , 1998 .

[22]  D. Turcotte.  Fractals in geology and geophysics , 2009, Encyclopedia of Complexity and Systems Science.

[23]  David G. Tarboton,et al.  Sub-grid parameterization of snow distribution for an energy and mass balance snow cover model , 1999 .

[24]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[25]  V. Gupta,et al.  MODELING SPACE-TIME RAINFALL AT THE MESOSCALE USING RANDOM CASCADES , 2004 .

[26]  Kelly Elder,et al.  Spatial Snow Modeling of Wind-Redistributed Snow Using Terrain-Based Parameters , 2002 .

[27]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[28]  John W. Pomeroy,et al.  Temporal Variation in Snowcover Area During Melt in Prairie and Alpine Environments , 1993 .

[29]  D. Gray,et al.  Small-Scale Spatial Structure of Shallow Snowcovers , 1996 .

[30]  Robert Kirnbauer,et al.  An analysis of snow cover patterns in a small alpine catchment , 1992 .

[31]  R. Voss.  Random Fractal Forgeries , 1985 .

[32]  K. Schilling,et al.  Temporal scaling of hydraulic head and river base flow and its implication for groundwater recharge , 2004 .

[33]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[34]  Kelly Elder,et al.  Snow accumulation and distribution in an Alpine Watershed , 1991 .

[35]  V. Iacobellis,et al.  Self‐similarity and multifractality of topographic surfaces at basin and subbasin scales , 1999 .

[36]  T. Erickson,et al.  Persistence of topographic controls on the spatial distribution of snow in rugged mountain terrain, Colorado, United States , 2005 .

[37]  Günter Blöschl,et al.  Scaling issues in snow hydrology , 1999 .

[38]  A. Rinaldo,et al.  On the spatial organization of soil moisture fields , 1995 .

[39]  Stephen R. Brown.  A note on the description of surface roughness using fractal dimension , 1987 .

[40]  Donald A. Walker,et al.  Spatial interrelationships between terrain, snow distribution and vegetation patterns at an arctic foothills site in Alaska , 1989 .

[41]  Ana P. Barros,et al.  Downscaling of remotely sensed soil moisture with a modified fractal interpolation method using contraction mapping and ancillary data , 2002 .

[42]  Jeffrey D. Niemann,et al.  Nonlinearity and self-similarity of rainfall in time and a stochastic model , 1996 .

[43]  Shaun Lovejoy,et al.  Universal Multifractals: Theory and Observations for Rain and Clouds , 1993 .

[44]  B. Mandelbrot.  How Long Is the Coast of Britain ? , 2002 .

[45]  R. Pielke,et al.  Improving first‐order snow‐related deficiencies in a regional climate model , 1999 .

[46]  Shaun Lovejoy,et al.  Generalized Scale Invariance in the Atmosphere and Fractal Models of Rain , 1985 .

[47]  Kelly Elder,et al.  Estimating the spatial distribution of snow water equivalence in a montane watershed , 1998 .

[48]  Reply [to “Comment on ‘Fractal mapping of digitized images: Application to the topography of arizona and comparison with synthetic images’ by J. Huang and D. L. Turcotte”] , 1990 .

[49]  D. Tarboton,et al.  The application of depletion curves for parameterization of subgrid variability of snow , 2004 .

[50]  Kelly Elder,et al.  Fractal Distribution of Snow Depth from Lidar Data , 2006 .

[51]  L. S. Kuchment,et al.  Statistical self‐similarity of spatial variations of snow cover: verification of the hypothesis and application in the snowmelt runoff generation models , 2001 .

[52]  Glen E. Liston,et al.  Interrelationships among Snow Distribution, Snowmelt, and Snow Cover Depletion: Implications for Atmospheric, Hydrologic, and Ecologic Modeling , 1999 .

[53]  I. Rodríguez‐Iturbe,et al.  The fractal nature of river networks , 1988 .