roi: Region of influence

Description

Formation of clusters for Regional Frequency Analysis: region of influence (Burn, 1990).

Usage

roi (p.ungauged, p.gauged, cod.p, x=NULL, cod=NULL)
 roi.hom (p.ungauged, p.gauged, cod.p, x, cod,
   test="HW", limit=2, Nsim=500, index=2)
 roi.st.year (p.ungauged, p.gauged, cod.p, x, cod,
   test="HW", station.year=500, Nsim=500, index=2)

Value

roi returns the ‘region of influence’ for the site defined with p.ungauged. It the gauged sites ordered according to the euclidean distance against the site of interest (the distance is evaluated in the space defined by parameters p.ungauged and p.gauged). If x=NULL and cod=NULL (default), a data.frame with the ordered sites and the distances against the site of interest is returned. If x and cod are provided, the data.frame will contain also statistics of samples (number of data n and L-moments).

roi.hom returns the ‘region of influence’ for the site defined with p.ungauged. It returns codes of gauged sites that form an homogeneous region according to the Hosking and Wallis "HW" or Anderson-Darling "AD" tests. The region is formed using distances in the space defined by parameters p.ungauged and p.gauged.

roi.st.year returns the ‘region of influence’ for the site defined with p.ungauged. It returns codes of gauged sites that form a region and the risult of homogeneity tests, according to the station-year criterion. It also return the similarity ranking factor $S_i$, the weights $w_i$ and the regional L-moments as evaluated in the Flood Estimation Handbook (Robson and Reed, 1999). The region is formed using distances in the space defined by parameters p.ungauged and p.gauged.

Arguments

x: vector representing data from many samples defined with cod
cod: array that defines the data subdivision among sites
index: if index=1 samples are divided by their average value; if index=2 (default) samples are divided by their median value
p.ungauged: parameters of the ungauged site (1 row)
p.gauged: parameters of gauged sites
cod.p: code of gauged sites
test: homogeneity test to apply: "HW" (default) or "AD" (in roi.st.year you can choose "HW and AD" too
limit: limit over which regions must be considered heterogeneous: for example 2 for "HW" or .95 for "AD"
Nsim: number of simulations in "HW" or "AD" tests
station.year: number of station years to form the region

Details

The Euclidean distance is used. Given $p$ different classification variables, the distance between two elements $i$ and $j$ is: $$d_{i j} = \sqrt{\frac{1}{p} \sum_{h=1}^{p} (x_{h i} - x_{h j})^2}$$ where $x_{h i}$ is the value of the $h$-th variable of the $i$-th element.

Examples

Run this code

data(hydroSIMN)
parameters
summary(parameters)

annualflows
summary(annualflows)
x <- annualflows["dato"][,]
cod <- annualflows["cod"][,]

roi(parameters[5,3:5],parameters[-5,3:5],parameters[-5,1])
roi(parameters[5,3:5],parameters[-5,3:5],parameters[-5,1],x,cod)

# roi.hom
#roi.hom(parameters[5,3:5],parameters[-5,3:5],parameters[-5,1],x,cod)
                            # it takes some time
#roi.hom(parameters[5,3:5],parameters[-5,3:5],parameters[-5,1],x,cod,
#        test="AD",limit=.95)      # it takes some time

#roi.hom(parameters[8,3:5],parameters[-8,3:5],
#         parameters[-8,1],x,cod)    # it takes some time


# roi.st.year
roi.st.year(parameters[5,3:5],parameters[-5,3:5],
            parameters[-5,1],x,cod)
roi.st.year(parameters[5,3:5],parameters[-5,3:5],parameters[-5,1],
            x,cod,test="AD",station.year=100)