roi {nsRFA} | R Documentation |
Formation of clusters for Regional Frequency Analysis: region of influence (Burn, 1990).
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)
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 |
The Euclidean distance is used. Given p different classification variables, the distance between two elements i and j is:
d_ij = sqrt{1/p sum[h from 1 to p](x_hi - x_hj)^2}
where x_hi is the value of the h-th variable of the i-th element.
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
.
Alberto Viglione, e-mail: alviglio@tiscali.it.
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.
Robson, A. and Reed, D. (1999) Statistical procedures for flood frequency estimation. In Flood Estimation Handbook, volume 3. Institute of Hydrology Crowmarsh Gifford, Wallingford, Oxfordshire.
traceWminim
, AD.dist
, HOMTESTS
for the definition of the Hosking and Wallis "HW"
or Anderson-Darling "AD"
tests.
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)