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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.

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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 crossvalidation 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.

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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.

These methods are useful to detect underground hollow spaces but they provide limited information about spatial details with low levels of accuracy. Image-based photogrammetric surveying can also be used in cave studies but the difficulty of achieving homogeneous light conditions is a limiting factor