Interpolation Techniques
The spatial distribution of the UK MET stations that measure global solar radiation provide an accurate cross-section of measured data. Data is measured at isolated points across the UK therefore an extrapolation or interpolation technique is necessary to provide data for simulation. The accuracy of extrapolation distances are very small for solar radiation, as stated by Suckling (1983) therefore an interpolation method is required to be evaluated for use in the hindcast model.
Inverse-Distance Weighting (IDW)
The IDW procedure is a type of deterministic method, where a particular input will always achieve the same output, for spatial interpolation. According to Burrough & McDonnell (1998) and Longley, et al., (2001) IDW and kriging have been
regarded as standard spatial interpolation techniques in GIS and have been implemented in many software packages. Additionally IDW is easy to program and understand but it does come with limitations.
The limitations of IDW have been listed in Watson & Philip (1985) where the major limitations is that calculated values are bounded by the extrema in the data set. Work performed by Goovaerts (2000), Lloyd (2005) and Lu & Wong (2008) shows that a constant distance-decay value, the spatial interaction declines as the distance increases, could be part of the reason that IDW provides less accurate predictions as compared to other interpolation methods.
Overall, according to Lam (1983) IDW is reasonably accurate under a wide range of conditions. Furthermore Kravchenko (2003), Burrough & McDonnell (1998) and Lu & Wong (2008) discuss IDW in comparison to Kriging. Burrough & McDonnell (1998) and Lu & Wong (2008) explain that IDW does not have the statistical advantages of kriging; IDW cannot estimate the variance for a predicted value in an unsampled location to what kriging can provide. On the other hand Kravchenko (2003) states that IDW is less labour intensive and there are no restrictions on the number of samples needed to perform the interpolation.
The limitations of IDW have been listed in Watson & Philip (1985) where the major limitations is that calculated values are bounded by the extrema in the data set. Work performed by Goovaerts (2000), Lloyd (2005) and Lu & Wong (2008) shows that a constant distance-decay value, the spatial interaction declines as the distance increases, could be part of the reason that IDW provides less accurate predictions as compared to other interpolation methods.
Overall, according to Lam (1983) IDW is reasonably accurate under a wide range of conditions. Furthermore Kravchenko (2003), Burrough & McDonnell (1998) and Lu & Wong (2008) discuss IDW in comparison to Kriging. Burrough & McDonnell (1998) and Lu & Wong (2008) explain that IDW does not have the statistical advantages of kriging; IDW cannot estimate the variance for a predicted value in an unsampled location to what kriging can provide. On the other hand Kravchenko (2003) states that IDW is less labour intensive and there are no restrictions on the number of samples needed to perform the interpolation.
Kriging
As stated in Bohling (2005), all interpolation techniques estimate the value at a given location as a weighted sum of the data values at surrounding locations. Additionally interpolation techniques usually assign weights in relation to functions that give a decreasing weight with increasing separation distance. Although studies by Mubiru, et al., (2006) and Isaaks & Srivastava (1989) show that weight factors in kriging are determined by calculating the variogram value for all distances between input points (MET stations) and also all distances between an output point (selected location) and all input points. Isaaks & Srivastava (1989) states that kriging will give very similar results to other interpolation techniques in many cases.
Based on reviews of Bohling (2005) and Kravchenko (2003), the following benefits and limitations of kriging were constructed from relating the interpolation method to the hindcast model. Kriging helps to compensate for the effects of data clustering by assigning individual points within the cluster less weight than isolated data points (Bohling, 2005). This benefit will help when interpolating between MET stations due to the spread of the stations. Another benefit includes giving an estimate of the estimation error (kriging variance).
Theory states that kriging is the optimal interpolation technique according to Isaaks & Srivastava (1989). On the other hand for it to be used in the correct way an accurate determination of the spatial structure is required this includes variogram construction and model fitting. In order to achieve a reliable variogram 50-100 samples are required to correctly describe the spatial structure (Webster & Oliver, 1992). However, even when enough stations are used, the sample variogram calculation and variogram model fitting can be tedious and time-consuming according to Kravchenko (2003).
Based on reviews of Bohling (2005) and Kravchenko (2003), the following benefits and limitations of kriging were constructed from relating the interpolation method to the hindcast model. Kriging helps to compensate for the effects of data clustering by assigning individual points within the cluster less weight than isolated data points (Bohling, 2005). This benefit will help when interpolating between MET stations due to the spread of the stations. Another benefit includes giving an estimate of the estimation error (kriging variance).
Theory states that kriging is the optimal interpolation technique according to Isaaks & Srivastava (1989). On the other hand for it to be used in the correct way an accurate determination of the spatial structure is required this includes variogram construction and model fitting. In order to achieve a reliable variogram 50-100 samples are required to correctly describe the spatial structure (Webster & Oliver, 1992). However, even when enough stations are used, the sample variogram calculation and variogram model fitting can be tedious and time-consuming according to Kravchenko (2003).
Graham Cairns
University of Edinburgh, 2013
University of Edinburgh, 2013