Solar energy in progress and future research trends

# Linear interpolation

The essence of the spatial interpolation is to transfer available information in the form of data from a number of adjacent irregular sites to the estimation site through a function that represents the spatial weights according to the distances between the sites. Generally, changes in the measurement site number, or especially, the location of the estimation site will cause changes in the weightings due to change in the distances. In the linear interpolation technique, as presented by Gandin [43], the value at an uninstrumented site is assumed to be the linear combination of the records at the adjacent sites which can be expressed as

n

SE = £ w& (60)

i=1

where SE is the solar irradiance estimation, n is the number of the measurement sites, and wi is the weighting factor which shows the contribution from the ith site with its measured solar irradiation value, Sj. Unbiased estimation requires that the summation of all weights is equal to 1 as a restriction. Of course, such an estimation will give rise to an error, E, defined as the difference between the solar irradiance estimation, SE, and the measured values Si (i = 1,2,n). The error estimation variance VE, can be written as,

1n

Ve = - X (Se - Si)2 (61)

n =

where R is the radius of influence and is determined subjectively depending on personal experience.

3. take the successive summation of the half-squared differences starting from the smallest distance rank to

the biggest. This procedure yields a non-decreasing function as

m m

gduj) = Dij (67)

i=l i=1

where y(dij) represents CSV value at distance dj, and finally,

4. plotting of y(dij) versus the corresponding distance d(j appears similar as a representative CSV functions in Fig. 26. The sample CSV functions are free of subjectivity because no a priori selection of distance classes is involved in contrast to the analysis as suggested by Perrie and Toulany [99] in which the distance axis is divided into subjective intervals, and subsequently, average is taken within each interval as the representative value.

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