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

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 are used to calculate standardized regional L-moments.

$$\mathcal{A}\_r \mathcal{A}\_r^R = \frac{\sum\_{i=1}^N n\_i \lambda\_r^{(i)}}{\sum\_{i=1}^N n\_i} \tag{27}$$

analyzed in geostatistical studies. Some method of geostatistical studies are Inverse Distance Weighting (IDW), Global Polynomial (GP), Local Polynomial (LP), Radial Basis Functions

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

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

Use the Trend Analysis

Examine the semivariogram

Remove a trend

Adjust the lag size of the semivariogram model

Setup a MAP

Wind Speed Regionalization Under Climate Change Conditions

http://dx.doi.org/10.5772/55985

227

Create a surface

Explore the histogram

Explore the Normal QQ plot

None

None

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

Examine Predicted Values and sample points Account for directional influences

Speed Exact Interpolation

IDW Deterministic Prediction Fast Yes Little flexibility, few

GP Deterministic Prediction Fast No Little flexibility, few

fast

(RBF), Kriging (Simple, Ordinary, Universal, Disjunctive and CoKriging).

are summarized as follows in Figure 1.

Create a layout to show your results.

Clip the layers of the map to the state outline

Extrapolate values beyond the extent of the sample points

Display the prediction and probability surfaces

Use indicator kriging

Compare the cross validation results

Map quality of the prediction surface

Examine the quality of the models predictions

Figure 1. Spatial interpolation steps

**Figure 1.** Spatial interpolation steps

**18. Comparison of different methods** 

Model Type Output

LP Deterministic Prediction Fairly

Surfaces

where *λ<sup>r</sup> <sup>R</sup>* is the regional standardized L-moment of order *r*, *λ<sup>r</sup>* (*i*) is the standardized L-moment of order *r*in site *i*, *ni* is the number of years in site *i*, and *N* is the number of sites in the 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 subregions are calculated using Eq. (34)

$$\mathbb{Q}\_i(F) = \lambda\_1^{(i)} \eta(F) \tag{28}$$

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