Fractal Distribution of Snow Depth from Lidar Data

2006 ◽  
Vol 7 (2) ◽  
pp. 285-297 ◽  
Author(s):  
Jeffrey S. Deems ◽  
Steven R. Fassnacht ◽  
Kelly J. Elder
Keyword(s):  
Land Surface ◽  
Snow Depth ◽  
Multiple Scales ◽  
Driving Forces ◽  
Spatial Scales ◽  
Fractal Dimensions ◽  
Airborne Lidar ◽  
Surface Elevation ◽  
Fractal Distribution ◽  
Wide Range

Abstract Snowpack properties vary dramatically over a wide range of spatial scales, from crystal microstructure to regional snow climates. The driving forces of wind, energy balance, and precipitation interact with topography and vegetation to dominate snow depth variability at horizontal scales from 1 to 1000 m. This study uses land surface elevation, vegetation surface elevation, and snow depth data measured using airborne lidar at three sites in north-central Colorado. Fractal dimensions are estimated from the slope of a log-transformed variogram and demonstrate scale-invariant, fractal behavior in the elevation, vegetation, and snow depth datasets. Snow depth and vegetation topography each show two distinct fractal distributions over different scale ranges (multifractal behavior), with short-range fractal dimensions near 2.5 and long-range fractal dimensions around 2.9 at all locations. These fractal ranges are separated by a scale break at 15–40 m, depending on the site, which indicates a process change at that scale. Terrain has a fractal distribution over nearly the entire range of scales available in the data. Directional differences in the fractal dimensions for each parameter are also present at multiple scales, and are related to the wind direction frequency distributions at each site. The results indicate that different sampling resolutions may yield different results and allow rescaling in specific scale ranges. Resolutions of 10 m and finer are consistently self-similar, as are resolutions greater than 30 m, though the coarser resolutions show nearly random distributions.

scholarly journals Airborne lidar reflectance measurements at 1.57 μm in support of the A-SCOPE mission for atmospheric CO<sub>2</sub>

2009 ◽  
Vol 2 (2) ◽  
pp. 755-772 ◽  
Author(s):  
A. Amediek ◽  
A. Fix ◽  
G. Ehret ◽  
J. Caron ◽  
Y. Durand
Keyword(s):  
Land Surface ◽  
Atmospheric Carbon Dioxide ◽  
Western Europe ◽  
Signal To Noise Ratio ◽  
Spatial Scales ◽  
Airborne Lidar ◽  
Measurement Sensitivity ◽  
Airborne Measurements ◽  
Wide Range ◽  
Scope Project

Abstract. The characteristics of the lidar reflectance of the Earth's surface is an important issue for the IPDA lidar technique (integrated path differential absorption lidar) which is the proposed method for the spaceborne measurement of atmospheric carbon dioxide within the framework of ESA's A-SCOPE project. Both, the absolute reflectance of the ground and its variations have an impact on the measurement sensitivity. The first aspect influences the instrument's signal to noise ratio, the second one can lead to retrieval errors, if the ground reflectance changes are strong on small scales. The investigation of the latter is the main purpose of this study. Airborne measurements of the lidar ground reflectance at 1.57 μm wavelength were performed in Central and Western Europe, including many typical land surface coverages as well as the open sea. The analyses of the data show, that the lidar ground reflectance is highly variable on a wide range of spatial scales. However, by means of the assumption of laser footprints in the order of several tens of meters, as planned for spaceborne systems, and by means of an averaging of the data it was shown, that this specific retrieval error is well below 1 ppm (CO2 column mixing ratio), and so compatible with the sensitivity requirements of spaceborne CO2 measurements. Several approaches for upscaling the data in terms of the consideration of larger laser footprints, compared to the one used here, are shown and discussed. Furthermore, the collected data are compared to MODIS ground reflectance data.

scholarly journals Airborne lidar reflectance measurements at 1.57 μm in support of the A-SCOPE mission for atmospheric CO<sub>2</sub>

2009 ◽  
Vol 2 (3) ◽  
pp. 1487-1536 ◽  
Author(s):  
A. Amediek ◽  
A. Fix ◽  
G. Ehret ◽  
J. Caron ◽  
Y. Durand
Keyword(s):  
Land Surface ◽  
Atmospheric Carbon Dioxide ◽  
Western Europe ◽  
Signal To Noise Ratio ◽  
Spatial Scales ◽  
Airborne Lidar ◽  
Measurement Sensitivity ◽  
Airborne Measurements ◽  
Wide Range ◽  
Scope Project

Abstract. The characteristics of the lidar reflectance of the Earth's surface is an important issue for the IPDA lidar technique (integrated path differential absorption lidar) which is the proposed method for the spaceborne measurement of atmospheric carbon dioxide within the framework of ESA's A-SCOPE project. Both, the absolute reflectance of the ground and its variations have an impact on the measurement sensitivity. The first aspect influences the instrument's signal to noise ratio, the second one can lead to retrieval errors, if the ground reflectance changes are strong on small scales. The investigation of the latter is the main purpose of this study. Airborne measurements of the lidar ground reflectance at 1.57 μm wavelength were performed in Central and Western Europe, including many typical land surface coverages as well as the open sea. The analyses of the data show, that the lidar ground reflectance is highly variable on a wide range of spatial scales. However, by means of the assumption of laser footprints on the order of several tens of meters, as planned for spaceborne systems, and by means of an averaging of the data it was shown, that this specific retrieval error is compatible with the sensitivity requirements of spaceborne CO2 measurements.

scholarly journals Subgrid snow depth coefficient of variation spanning alpine to sub-alpine mountainous terrain

2021 ◽  
Author(s):  
Graham A. Sexstone ◽  
Steven R. Fassnacht ◽  
Juan I. López-Moreno ◽  
Christopher A. Hiemstra
Keyword(s):  
Coefficient Of Variation ◽  
Land Surface ◽  
Snow Depth ◽  
Mountainous Terrain ◽  
Mountainous Regions ◽  
Scale Modeling ◽  
Roughness Elements ◽  
Wide Range ◽  
Performance Statistics ◽  
Snowpack Properties

Given the substantial variability of snow in complex mountainous terrain, a considerable challenge of coarse scale modeling applications is accurately representing the subgrid variability of snowpack properties. The snow depth coefficient of variation (CVds) is a useful metric for characterizing subgrid snow distributions but has not been well defined by a parameterization for mountainous environments. This study utilizes lidar-derived snow depth datasets spanning alpine to sub-alpine mountainous terrain in Colorado, USA to evaluate the variability of subgrid snow distributions within a grid size comparable to a 1000 m resolution common for hydrologic and land surface models. The subgrid CVds exhibited a wide range of variability across the 321 km2 study area (0.15 to 2.74) and was significantly greater in alpine areas compared to subalpine areas. Mean snow depth was the dominant driver of CVds variability in both alpine and subalpine areas, as CVds decreased nonlinearly with increasing snow depths. This negative correlation is attributed to the static size of roughness elements (topography and canopy) that strongly influence seasonal snow variability. Subgrid CVds was also strongly related to topography and forest variables; important drivers of CVds included the subgrid variability of terrain exposure to wind in alpine areas and the mean and variability of forest metrics in subalpine areas. Two statistical models were developed (alpine and subalpine) for predicting subgrid CVds that show reasonable performance statistics. The methodology presented here can be used for characterizing the variability of CVds in snow-dominated mountainous regions, and highlights the utility of using lidar-derived snow datasets for improving model representations of snow processes.

scholarly journals Variability scaling and consistency in airborne and satellite altimetry measurements of Arctic sea ice

2020 ◽  
Vol 14 (2) ◽  
pp. 751-767
Author(s):  
Shiming Xu ◽  
Lu Zhou ◽  
Bin Wang
Keyword(s):  
Remote Sensing ◽  
Sea Ice ◽  
Snow Depth ◽  
Spatial Scales ◽  
Ice Cover ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
First Year ◽  
Noise Levels ◽  
Wide Range

Abstract. Satellite and airborne remote sensing provide complementary capabilities for the observation of the sea ice cover. However, due to the differences in footprint sizes and noise levels of the measurement techniques, as well as sea ice's variability across scales, it is challenging to carry out inter-comparison or consistently study these observations. In this study we focus on the remote sensing of sea ice thickness parameters and carry out the following: (1) the analysis of variability and its statistical scaling for typical parameters and (2) the consistency study between airborne and satellite measurements. By using collocating data between Operation IceBridge and CryoSat-2 (CS-2) in the Arctic, we show that consistency exists between the variability in radar freeboard estimations, although CryoSat-2 has higher noise levels. Specifically, we notice that the noise levels vary among different CryoSat-2 products, and for the European Space Agency (ESA) CryoSat-2 freeboard product the noise levels are at about 14 and 20 cm for first-year ice (FYI) and multi-year ice (MYI), respectively. On the other hand, for Operation IceBridge and NASA's Ice, Cloud, and land Elevation Satellite (ICESat), it is shown that the variability in snow (or total) freeboard is quantitatively comparable despite more than a 5-year time difference between the two datasets. Furthermore, by using Operation IceBridge data, we also find widespread negative covariance between ice freeboard and snow depth, which only manifests on small spatial scales (40 m for first-year ice and about 80 to 120 m for multi-year ice). This statistical relationship highlights that the snow cover reduces the overall topography of the ice cover. Besides this, there is prevalent positive covariability between snow depth and snow freeboard across a wide range of spatial scales. The variability and consistency analysis calls for more process-oriented observations and modeling activities to elucidate key processes governing snow–ice interaction and sea ice variability on various spatial scales. The statistical results can also be utilized in improving both radar and laser altimetry as well as the validation of sea ice and snow prognostic models.

Towards a scale-independent fractional snow-covered area parameterization for complex terrain

2020 ◽  
Author(s):  
Nora Helbig ◽  
Yves Bühler ◽  
Lucie Eberhard ◽  
César Deschamps-Berger ◽  
Simon Gascoin ◽  
...  
Keyword(s):  
Snow Depth ◽  
Hydrological Modeling ◽  
Spatial Scales ◽  
Ground Surface ◽  
Longwave Radiation ◽  
Data Sets ◽  
Depth Data ◽  
Snow Covered Area ◽  
Covered Area ◽  
Wide Range

&lt;p&gt;Whenever there is snow on the ground, there will be large spatial variability in snow depth. The spatial distribution of snow is significantly influenced by topography due to wind, precipitation, shortwave and longwave radiation, and even snow avalanches relocate the accumulated snow. Fractional snow-covered area (fSCA) is an important model parameter characterizing the fraction of the ground surface that is covered by snow and is crucial for various model applications such as weather forecasts, climate simulations and hydrological modeling.&lt;/p&gt;&lt;p&gt;We recently suggested an empirical fSCA parameterization based on two spatial snow depth data sets acquired at peak of winter in Switzerland and Spain, which yielded best performance for spatial scales larger than 1000 m. However, this parameterization was not validated on independent snow depth data. To evaluate and improve our fSCA parameterization, in particular with regards to other spatial scales and snow climates (or geographic regions), we used spatial snow depth data sets form a wide range of mountain ranges in USA, Switzerland and France acquired by 5 different measuring methods. Pooling all snow depth data sets suggests that a scale-dependent parameter should be introduced to improve the fSCA parameterization, in particular for sub-kilometer spatial scales. Extending our empirical fSCA parameterization to a broader range of scales and snow climates is an important step towards accounting for spatio-temporal variability in snow depth in multiple snow model applications.&lt;/p&gt;

scholarly journals A Continental-Scale Classification of Rainfall Seasonality Regimes in Africa Based on Gridded Precipitation and Land Surface Temperature Products

2011 ◽  
Vol 50 (12) ◽  
pp. 2504-2513 ◽  
Author(s):  
Stefanie M. Herrmann ◽  
Karen I. Mohr
Keyword(s):  
Surface Temperature ◽  
Land Surface Temperature ◽  
Land Surface ◽  
Driving Forces ◽  
Spatial Scales ◽  
Wet Season ◽  
Continental Scale ◽  
Rainfall Seasonality ◽  
The Stability

AbstractA classification of rainfall seasonality regimes in Africa was derived from gridded rainfall and land surface temperature products. By adapting a method that goes back to Walter and Lieth’s approach of presenting climatic diagrams, relationships between estimated rainfall and temperature were used to determine the presence and pattern of humid, arid, and dry months. The temporal sequence of humid, arid, and dry months defined nonseasonal as well as single-, dual-, and multiple-wet-season regimes with one or more rainfall peaks per wet season. The use of gridded products resulted in a detailed, spatially continuous classification for the entire African continent at two different spatial resolutions, which compared well to local-scale studies based on station data. With its focus on rainfall patterns at fine spatial scales, this classification is complementary to coarser and more genetic classifications based on atmospheric driving forces. An analysis of the stability of the resulting seasonality regimes shows areas of relatively high year-to-year stability in the single-wet-season regimes and areas of lower year-to-year stability in the dual- and multiple-wet-season regimes as well as in transition zones.

scholarly journals Discovering multiscale and self-similar structure with data-driven wavelets

2020 ◽  
Vol 118 (1) ◽  
pp. e2021299118
Author(s):  
Daniel Floryan ◽  
Michael D. Graham
Keyword(s):  
Multiple Scales ◽  
Spatial Scales ◽  
Building Blocks ◽  
Biological Tissues ◽  
Data Driven ◽  
Model Free ◽  
Starting Point ◽  
Wide Range ◽  
Direct Model ◽  
Self Similar

Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting, describing, and defining such features are difficult tasks, at least in part because each system has a unique set of features. Here, we introduce an analysis method that, given a set of observations, discovers an energetic hierarchy of structures localized in scale and space. We call the resulting basis vectors a “data-driven wavelet decomposition.” We show that this decomposition reflects the inherent structure of the dataset it acts on, whether it has no structure, structure dominated by a single scale, or structure on a hierarchy of scales. In particular, when applied to turbulence—a high-dimensional, nonlinear, multiscale process—the method reveals self-similar structure over a wide range of spatial scales, providing direct, model-free evidence for a century-old phenomenological picture of turbulence. This approach is a starting point for the characterization of localized hierarchical structures in multiscale systems, which we may think of as the building blocks of these systems.

scholarly journals A reduced-order modeling approach to represent subgrid-scale hydrological dynamics for land-surface simulations: application in a polygonal tundra landscape

2014 ◽  
Vol 7 (5) ◽  
pp. 2091-2105 ◽  
Author(s):  
G. S. H. Pau ◽  
G. Bisht ◽  
W. J. Riley
Keyword(s):  
Soil Moisture ◽  
Land Surface ◽  
Spatial Scales ◽  
Approximation Error ◽  
Reduced Order Modeling ◽  
Data Set ◽  
Reduced Order ◽  
Coarse Resolution ◽  
Wide Range ◽  
Study Sites

Abstract. Existing land surface models (LSMs) describe physical and biological processes that occur over a wide range of spatial and temporal scales. For example, biogeochemical and hydrological processes responsible for carbon (CO2, CH4) exchanges with the atmosphere range from the molecular scale (pore-scale O2 consumption) to tens of kilometers (vegetation distribution, river networks). Additionally, many processes within LSMs are nonlinearly coupled (e.g., methane production and soil moisture dynamics), and therefore simple linear upscaling techniques can result in large prediction error. In this paper we applied a reduced-order modeling (ROM) technique known as "proper orthogonal decomposition mapping method" that reconstructs temporally resolved fine-resolution solutions based on coarse-resolution solutions. We developed four different methods and applied them to four study sites in a polygonal tundra landscape near Barrow, Alaska. Coupled surface–subsurface isothermal simulations were performed for summer months (June–September) at fine (0.25 m) and coarse (8 m) horizontal resolutions. We used simulation results from three summer seasons (1998–2000) to build ROMs of the 4-D soil moisture field for the study sites individually (single-site) and aggregated (multi-site). The results indicate that the ROM produced a significant computational speedup (> 103) with very small relative approximation error (< 0.1%) for 2 validation years not used in training the ROM. We also demonstrate that our approach: (1) efficiently corrects for coarse-resolution model bias and (2) can be used for polygonal tundra sites not included in the training data set with relatively good accuracy (< 1.7% relative error), thereby allowing for the possibility of applying these ROMs across a much larger landscape. By coupling the ROMs constructed at different scales together hierarchically, this method has the potential to efficiently increase the resolution of land models for coupled climate simulations to spatial scales consistent with mechanistic physical process representation.

scholarly journals FRACTAL SURFACES: MEASUREMENT AND APPLICATIONS IN THE EARTH SCIENCES

Fractals ◽  
1993 ◽  
Vol 01 (01) ◽  
pp. 87-115 ◽  
Author(s):  
B. LEA COX ◽  
J. S. Y. WANG
Keyword(s):  
Earth Sciences ◽  
Spatial Scales ◽  
Measurement Techniques ◽  
Heterogeneous Systems ◽  
Fractal Dimensions ◽  
Fractal Surfaces ◽  
The Earth ◽  
Power Spectral ◽  
Wide Range ◽  
Map Data

Earth scientists have measured fractal dimensions of surfaces by different techniques, including the divider, box, triangle, slit-island, power spectral, variogram and distribution methods. We review these seven measurement techniques, finding that fractal dimensions may vary systematically with measurement method. We discuss possible reasons for these differences, and point to common problems shared by all of the methods, including the remainder problem, curve-fitting, orientation of the measurement plane, size and direction of the sample. Fractal measurements have been applied to many problems in the earth sciences, at a wide range of spatial scales. These include map data of topography; fault traces and fracture networks; fracture surfaces of natural rocks, both in the field and at laboratory scales; metal surfaces; porous aggregate geometry; flow and transport through heterogeneous systems; and various microscopic surface phenomena associated with adsorption, aggregation, erosion and chemical dissolution. We review these applications and discuss the usefulness and limitations of fractal analysis to these types of problems in the earth sciences.

scholarly journals Analysis and Reduction of Systematic Errors through a Seamless Approach to Modeling Weather and Climate

2010 ◽  
Vol 23 (22) ◽  
pp. 5933-5957 ◽  
Author(s):  
G. M. Martin ◽  
S. F. Milton ◽  
C. A. Senior ◽  
M. E. Brooks ◽  
S. Ineson ◽  
...  
Keyword(s):  
Time Scales ◽  
Land Surface ◽  
Large Scale ◽  
Climate Models ◽  
Spatial Scales ◽  
Full Range ◽  
Model Development ◽  
Model Performance ◽  
Systematic Errors ◽  
Wide Range

Abstract The reduction of systematic errors is a continuing challenge for model development. Feedbacks and compensating errors in climate models often make finding the source of a systematic error difficult. In this paper, it is shown how model development can benefit from the use of the same model across a range of temporal and spatial scales. Two particular systematic errors are examined: tropical circulation and precipitation distribution, and summer land surface temperature and moisture biases over Northern Hemisphere continental regions. Each of these errors affects the model performance on time scales ranging from a few days to several decades. In both cases, the characteristics of the long-time-scale errors are found to develop during the first few days of simulation, before any large-scale feedbacks have taken place. The ability to compare the model diagnostics from the first few days of a forecast, initialized from a realistic atmospheric state, directly with observations has allowed physical deficiencies in the physical parameterizations to be identified that, when corrected, lead to improvements across the full range of time scales. This study highlights the benefits of a seamless prediction system across a wide range of time scales.

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