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)

Arguments

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

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. The region is formed using distances in the space defined by parameters p.ungauged and p.gauged.

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.

References

Burn D. (1990) Evaluation of regional flood frequency analysis with a region of influence approach. Water Resources Research, 26, pp. 2257-2265.

Hosking, J.R.M. and Wallis, J.R. (1997) Regional Frequency Analysis: an approach based on L-moments, Cambridge University Pre ss, Cambridge, UK.

Viglione A. (2007) Metodi statistici non-supervised per la stima di grandezze idrologiche in siti non strumentati, PhD thesis, In press.

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)

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