**17. Spatial interpolation**

In classic statistics, the samples derived from a population are usually considered as random sets and the recorded value of a particular variable in an individual sample cannot present any details about the value of that variable in another sample with specific distance. In geostatistics, it is possible to link the values of one variable in a population and distance and direction of samples relating to each other. Furthermore, in classic statistics, it is assuming that the variables are randomly changing, while in geostatistics, some parts of the variable is random and some other parts have structure and is a function of distance and direction. Thus, using geostatistics, first the existence or the absence of a spatial structure between data is considered and then, in presence of a spatial structure, the data will be analyzed. It is possible to adjacent data to be spatially dependent together in a certain distance. In such cases, as in the presence of spatial structure, the variations in a certain space have more chances to be effective on near spaces with regard to more far ones, it is clear that varia‐ bles are maybe more similar in closer samples.

Geostatistics is a field of statistics with the base of "local variables theory". Any variable distributed in 3d space with spatial dependence is called local variable and can be studied and analyzed in geostatistical studies. Some method of geostatistical studies are Inverse Distance Weighting (IDW), Global Polynomial (GP), Local Polynomial (LP), Radial Basis Functions (RBF), Kriging (Simple, Ordinary, Universal, Disjunctive and CoKriging).

Applying these methods needs to parallel application of spatial and statistical analysis, which is possible only in some environments like ArcMap. To visualize the above process, the steps are summarized as follows in Figure 1.

In above sections, all methods are separately presented but their comparison is very important to choose the most appropriate

parameter decision

parameter decision

No Some flexibility, more parameter decision

Flexibility Advantage Disadvantages Assumptions

Few decisions NO assessment of prediction errors, bull's-eyes around data location

Few decisions NO assessment of prediction errors, may be too smooth, edge points have large influence

Flexible NO assessment of prediction errors, may be hard to choose a good local neighborhood

None

None

None

method for analysis. However, a wrong selection in this step will lead to large amount of uncertainty in output results.

Speed Exact Interpolation

IDW Deterministic Prediction Fast Yes Little flexibility, few

GP Deterministic Prediction Fast No Little flexibility, few

fast

**18. Comparison of different methods Figure 1.** Spatial interpolation steps

Model Type Output

LP Deterministic Prediction Fairly

Surfaces

Figure 1. Spatial interpolation steps

**16. Estimation of the parameters of regional frequency distribution**

*λr R* = ∑ *i*=1 *N ni λr* (*i*)

*<sup>R</sup>* is the regional standardized L-moment of order *r*, *λ<sup>r</sup>*

*Qi* (*F*)=*λ*<sup>1</sup> (*i*)

are used to calculate standardized regional L-moments.

where *λ<sup>r</sup>*

respectively.

of order *r*in site *i*, *ni*

226 New Developments in Renewable Energy

subregions are calculated using Eq. (34)

**17. Spatial interpolation**

bles are maybe more similar in closer samples.

Four first orders L-moments for each site inside a homogeneous region is making dimension‐ less by dividing them by the average of the data. Weighted values of dimensionless L-moments

> ∑ *i*=1 *N ni*

homogenous region. The parameters of best fitted distribution are estimated using the relation between distribution parameters and L-moments presented by Hosking (1989). Then the quantile values corresponding to different return periods are estimated for under study variable as regional quantile. The quantiles for the sites in each sub-region are determined by multiplying the regional quantile with the site's mean. At any site, the *i*th quantiles for the

Where *Q*(*F* ) and *q*(*F* ) are the at-site *i* and regional quantiles with non-exceedance probability,

In classic statistics, the samples derived from a population are usually considered as random sets and the recorded value of a particular variable in an individual sample cannot present any details about the value of that variable in another sample with specific distance. In geostatistics, it is possible to link the values of one variable in a population and distance and direction of samples relating to each other. Furthermore, in classic statistics, it is assuming that the variables are randomly changing, while in geostatistics, some parts of the variable is random and some other parts have structure and is a function of distance and direction. Thus, using geostatistics, first the existence or the absence of a spatial structure between data is considered and then, in presence of a spatial structure, the data will be analyzed. It is possible to adjacent data to be spatially dependent together in a certain distance. In such cases, as in the presence of spatial structure, the variations in a certain space have more chances to be effective on near spaces with regard to more far ones, it is clear that varia‐

Geostatistics is a field of statistics with the base of "local variables theory". Any variable distributed in 3d space with spatial dependence is called local variable and can be studied and

(*i*)

*q*(*F* ) (28)

is the number of years in site *i*, and *N* is the number of sites in the

(27)

is the standardized L-moment
