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This study was carried out in the region of Taiwan, with a surface area covering around 36,000 km2. The country comprises 24 out of 30 meteorological stations, which are located in the territory of Republic of China. This implies a considerable restriction in the number of solar radiation information collection stations; therefore, it is impossible to provide spatially continuous set of data, which can be used in ecology, climate change studies and renewable energy systems (Diaz, Grosjean, & Graumlich, 2003; Nalder & Wein, 1998; & WU, 2001). To compensate for the missing data, this study used kriging methodology for the interpolation and the mapping of solar radiation distribution in Taiwan. As the study region exhibits high spatial variability, a particular interpolation procedure, namely residual or regression kriging (Hengl, 2007; Kollias, 2002), which enables incorporation of exterior sources such as geographical factors (i.e longitude, latitude and elevation) was selected as most appropriate. The experimental datasets included 10 years (2004-2013) of spatial data gathered by typical meteorological year method at 24 stations (23 used for validation). Cross validation was performed using 1SUFER 13, verification was carried out using the Geostatistical Analyst tool 2ArcGIS 10.3.
The least squares regression coefficients were computed by the standard Ordinary Least Squares (OLS) method using the statistical package 3EViews 8. A monthly map of 1 km ×1 km special resolution was assessed using ArcGIS 10.3. Two empirical models: a linear and an exponential variogram were computed to represent the distribution of spatial structures. Overall, both models performed similarly and showed satisfactory estimates, with a slight overestimation in MPE and ME for the exponential model. The proposed residual kriging was rated against the previous ordinary kriging study (Liu, C.W 2016), which was considered as the skill evaluator of the presumed residual kriging improvements. As expected, the results proved that residual kriging exhibits smaller statistical errors than ordinary kriging. The maximum improvement was found in July (maximum MAE value 1.84 versus 2.14, a 12% comparative improvement). The residual kriging error (MAPE) ranges from 8.3% in June to 11.5% in November as compared to 7% in June to 14% in November for OK, which represents a 3% relative improvement.

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1 http://www.goldensoftware.com/products/surfer
2 https://doc.arcgis.com/en/trust/
3http://www.eviews.com/home.html