Interpolation by regularized spline with tension: II. Application to terrain modeling and surface geometry analysis

A general approach to the computation of basic topographic parameters independent of the spatial distribution of given elevation data is developed. The approach is based on an interpolation function with regular first and second order derivatives and on application of basic principles of differential geometry. General equations for computation of profile, plan, and tangential curvatures are derived. A new algorithm for construction of slope curves is developed using a combined grid and vector approach. Resulting slope curves better fulfill the condition of orthogonality to contours than standard grid algorithms. Presented methods are applied to topographic analysis of a watershed in central Illinois.     

The consequences of land-cover changes on soil erosion distribution in Slovakia

Soil erosion is a complex process determined by mutual interaction of numerous factors. The aim of erosion research at regional scales is a general evaluation of the landscape susceptibility to soil erosion by water, taking into account the main factors influencing this process. One of the key factors influencing the susceptibility of a region to soil erosion is land cover. Natural as well as human-induced changes of landscape may result in both the diminishment and acceleration of soil erosion. Recent studies of land-cover changes indicate that during the last decade more than 4.11% of Slovak territory has changed. The objective of this study is to assess the influence of land-cover and crop rotation changes over the 1990–2000 period on the intensity and spatial pattern of soil erosion in Slovakia. The assessment is based on principles defined in the Universal Soil Loss Equation (USLE) modified for application at regional scale and the use of the CORINE land cover (CLC) databases for 1990 and 2000. The C factor for arable land has been refined using statistical data on the mean crop rotation and the acreage of particular agricultural crops in the districts of Slovakia. The L factor has been calculated using sample areas with parcels identified by LANDSAT TM data. The results indicate that the land-cover and crop rotation changes had a significant influence on soil erosion pattern predominately in the hilly and mountainous parts of Slovakia. The pattern of soil erosion changes exhibits high spatial variation with overall slightly decreased soil erosion risks. These changes are associated with ongoing land ownership changes, changing structure of crops, deforestation and afforestation.     

Multivariate Interpolation of Precipitation Using Regularized Spline with Tension

Regularized Spline with Tension (RST) is an accurate, flexible and efficient method for multivariate interpolation of scattered data. This study evaluates its capabilities to interpolate daily and annual mean precipitation in regions with complex terrain. Tension, smoothing and anisotropy parameters are optimized using the cross-validation technique. In addition, smoothing and rescaling of the third variable (elevation) is used to minimize the predictive error. The approach is applied to data sets from Switzerland and Slovakia and interpolation accuracy is compared to the results obtained by several other methods, expert-drawn maps and measured runoff. The results demonstrate that RST performs as well or better than the methods tested in the literature. The incorporation of terrain improves the spatial model of precipitation in terms of its predictive error, spatial pattern and water balance.     

Modelling topographic potential for erosion and deposition using GIS

Abstract

Modelling of erosion and deposition in complex terrain within a geographical information system (GIS) requires a high resolution digital elevation model (DEM), reliable estimation of topographic parameters, and formulation of erosion models adequate for digital representation of spatially distributed parameters. Regularized spline with tension was integrated within a GIS for computation of DEMs and topographic parameters from digitized contours or other point elevation data. For construction of flow lines and computation of upslope contributing areas an algorithm based on vector-grid approach was developed. The spatial distribution of areas with topographic potential for erosion or deposition was then modelled using the approach based on the unit stream power and directional derivatives of surface representing the sediment transport capacity. The methods presented are illustrated on study areas in central Illinois and the Yakima Ridge, Washington.     

A New 3‐D Solar Radiation Model for 3‐D City Models

Estimates of solar radiation distribution in urban areas are often limited by the complexity of urban environments. These limitations arise from spatial structures such as buildings and trees that affect spatial and temporal distributions of solar fluxes over urban surfaces. The traditional solar radiation models implemented in GIS can address this problem only partially. They can be adequately used only for 2‐D surfaces such as terrain and rooftops. However, vertical surfaces, such as facades, require a 3‐D approach. This study presents a new 3‐D solar radiation model for urban areas represented by 3‐D city models. The v.sun module implemented in GRASS GIS is based on the existing solar radiation methodology used in the topographic r.sun model with a new capability to process 3‐D vector data representing complex urban environments. The calculation procedure is based on the combined vector‐voxel approach segmenting the 3‐D vector objects to smaller polygon elements according to a voxel data structure of the volume region. The shadowing effects of surrounding objects are considered using a unique shadowing algorithm. The proposed model has been applied to the sample urban area with results showing strong spatial and temporal variations of solar radiation flows over complex urban surfaces.     

A New GIS-based Solar Radiation Model and Its Application to Photovoltaic Assessments

The solar radiation model r.sun is a flexible and efficient tool for the estimation of solar radiation for clear‐sky and overcast atmospheric conditions. In contrast to other models, r.sun considers all relevant input parameters as spatially distributed entities to enable computations for large areas with complex terrain. Conceptually the model is based on equations published in the European Solar Radiation Atlas (ESRA). The r.sun model was applied to estimate the solar potential for photovoltaic systems in Central and Eastern Europe. The overcast radiation was computed from clear‐sky values and a clear‐sky index. The raster map of the clear‐sky index was computed using a multivariate interpolation method to account for terrain effects, with interpolation parameters optimized using a cross‐validation technique. The incorporation of terrain data improved the radiation estimates in terms of the model's predictive error and the spatial pattern of the model outputs. Comparing the results of r.sun with the ESRA database demonstrates that integration of the solar radiation model and the spatial interpolation tools in a GIS can be especially helpful for data at higher resolutions and in regions with a lack of ground measurements.     

Spatial Interpolation of Elevation Data With Variable Density: A New Methodology to Derive Quality DEMs

A new methodology for spatial interpolation of elevation data with variable density is proposed. The method is based on two-step interpolation and data processing to minimize interpolation artifacts caused by variable data density. In the first step, the parameterization of the spline interpolation method is focused on areas with sparse data that need smoother interpolation. Then, the resulting surface in these areas is randomly sampled to densify the original data set. In the second step, the parameterization of the interpolation method is focused on areas with a required high level of detail. The final resulting surface contains the properties of surfaces optimized for different data densities and levels of detail