Title: Linear Parametric Models Applied to Hydrological Series
Version: 3.2
Depends: R (≥ 3.5)
Date: 2024-06-15
Description: Apply Univariate Long Memory Models, Apply Multivariate Short Memory Models To Hydrological Dataset, Estimate Intensity Duration Frequency curve to rainfall series. NEW – Calculate the monthly water requirement for herbaceous and arboreal plants.
Imports: stats, graphics, grDevices, fracdiff, powdist, MASS
License: GPL-2
Maintainer: Corrado Tallerini <corrado.tallerini@gmx.com>
URL: http://www.corradotallerini.altervista.org/LPM.html
BugReports: http://www.corradotallerini.altervista.org/Contatti.html
Encoding: UTF-8
Author: Corrado Tallerini [aut, cre], Salvatore Grimaldi [aut]
NeedsCompilation: no
Packaged: 2024-06-15 15:01:37 UTC; Corrado
Repository: CRAN
Date/Publication: 2024-06-15 15:50:02 UTC

Intensity duration frequency curve

Description

Estimate IDF curve fitting a [mm/h], m ,n, b[h] parameters

Usage

IDFcurve(rain, g, s, tc, stvalue1 = 1, stvalue2 = fre, fre, Tr = 200,
                      MP=F, Trplot=F)

Arguments

rain

Observed Univariate rainfall series non cumulative

g

Maximum bound for cumulative series. For daily series g = 7 is recommended, for hourly series g=24 is racommended

s

Threshold for defining "event". If "10", only h > = 10 mm values are considered

tc

Time of concentration of Basin [h]

stvalue1, stvalue2

Starting values of estimation algorithm. Deault stvalue1=1, stvalue2=fre

fre

Series frequency [h]. For daily series fre=24, for hourly series fre=1

Tr

Return period [y]. Default Tr=200

MP

logical: TRUE for 3 parameters formula i=a/(b+t)^m , FALSE for 2 parameters formula i=a*t^(n-1), Default MP=False

Trplot

logical: TRUE for plotting Tr values of a(Tr) parameter. Default Trplot=False

Details

Estimate parameters of Intensity Duration Frequency curves

Value

par

List of estimated parameters: a(tr), m, b, h(t) [mm], i(t) [mm/h], Offset of least squares optimizer

Curve

IDF curve Scattered point matrix [mm/h]

Note

a(tr) is defined by Gumbel distribution.

Author(s)

Corrado Tallerini

See Also

IDFcurve2

Examples

##    data(hourly.rainfall.series)
##    res = IDFcurve(hourly.rainfall.series ,24, 15, 1, fre=1, Tr=200, MP=F)
## --> 2 parameters IDF curve estimation of a hourly rainfall series applying
## --> a Threshold "15 mm"  and Time of concentration t=1 h
##    res = IDFcurve(hourly.rainfall.series ,24, 15, 1, fre=1, Tr=200, MP=T)
## --> 3 parameters IDF curve estimation of a hourly rainfall series applying
## --> a Threshold "15 mm"  and Time of concentration t=1 h
## --> It's obvious the best performance of the 3 parameters formula

Intensity duration frequency curve for maximum annual rainfall series of different duration

Description

Estimate IDF curve fitting a [mm/h], m ,n, b[h] parameters of maximum annual rainfall series

Usage

IDFcurve2(rain, tc, stvalue1 = 1, stvalue2 = 1, t, Tr = 200, MP = F, Trplot = F)

Arguments

rain

Observed Maximum annual rainfall series [mm] of increasing duration

tc

Time of concentration of Basin [h] , maybe h(t) and i(t) duration must be calculated

stvalue1, stvalue2

Starting values of estimation algorithm. Deault stvalue1=1, stvalue2=1

t

observed rainfall series duration [h] example t=c(1,3,6,12,24) for durations 1,3,6,12,24 hours

Tr

Return period [y]. Default Tr=200

MP

logical: TRUE for 3 parameters formula i=a/(b+t)^m , FALSE for 2 parameters formula i=a*t^(n-1), Default MP=False

Trplot

logical: TRUE for plotting Tr values of a(Tr) parameter. Default Trplot=False

Details

Estimate parameters of Intensity Duration Frequency curves for maximum annual rainfall series of different duration

Value

par

List of estimated parameters: a(Tr), m, b, h(t) [mm], i(t) [mm/h], Offset of least squares optimizer

I

I(t) curve scattered point matrix [mm/h]

Curve

IDF curve scattered point matrix [mm/h]

Note

a(Tr) is defined by Gumbel distribution.

Author(s)

Corrado Tallerini

See Also

IDFcurve

Examples

##     data(milano)
##     ris=IDFcurve2(milano, 1, stvalue1 = 1, stvalue2 = 1,
##     t=c(0.25,0.5,0.75,1,1.25,1.5,2,2.5,3,4,6), Tr = 200, MP=F)
## --> 2 parameters IDF curve estimation of annual maximum rainfall
##     series recorded in Palazzo Marino - Milan (Italy)
##     ris=IDFcurve2(milano, 1, stvalue1 = 1, stvalue2 = 1,
##     t=c(0.25,0.5,0.75,1,1.25,1.5,2,2.5,3,4,6), Tr = 200, MP=T)
## --> 3 parameters IDF curve estimation of annual maximum rainfall
##     series recorded in Palazzo Marino - Milan (Italy)
## --> It's obvious the best performance of the 3 parameters formula

LPM

Description

Apply Univariate Long Memory Models, Apply Multivariate Short Memory Models To Hydrological Dataset, Estimate Intensity Duration Frequency curve to rainfall series. NEW – Calculate the monthly water requirement for herbaceous and arboreal plants.

Details

See ar.egls, lpm, mlpm rain.adapt WNeeds PWN

Author(s)

Authors: Salvatore Grimaldi and Corrado Tallerini

Maintainer: Corrado Tallerini

References

Grimaldi S., Tallerini C., Serinaldi F. (2004) 'Modelli multivariati lineari per la generazione di serie di precipitazioni giornaliere' Giornata di Studio: Metodi Statistici e Matematici per l'Analisi Idrologiche Napoli 2004

Grimaldi S. , Serinaldi F. & Tallerini C. (2004) 'Multivariate linear parametric models applied to daily rainfall time series' Mediterranean Storms, 6rd EGU Plinius Conference held in Mediterranean Sea, Italy, October 2004

Lutkepohl, H. (1993) Introduction to Multiple Time Series Analysis 2nd edition, Springer-Verlag, Berlin.

Grimaldi, S., 'Linear parametric models applied on daily hydrological series', Journal of Hydrologic Engineering, Vol. 9, No 5 , September 2004.

Brockwell, P.J and Davis, R.A. (1990) Time Series: Theory and Methods 2nd edition, Springer, NY.

Hipel, K.W. and McLeod, A.I., (1994) Time Series Modelling of Water Resources and Enviromental Systems, Reading, UK.

Hosking, J.R.M. (1980) 'The Multivariate Portmanteau Statistic' Journal of the American Statistical Association, Vol.75, N.371, 502-608.

United States Department of Agricolture (USDA - SCS). IRRIGATION - National Engineering handbook.

Fao irrigation and dreinage paper N. 24 - Crop water requirement, Food and agriculture organization of the united nations ROME, rivisited 1977

Moisello U. "Idrologia Tecnica" La Goliardica Pavese.

Genovesi R., Bottau D. "L'importanza della falda nell' alimentazione idrica delle colture nella pianura emiliano-romagnola."

Regione Campania - Assessorato Agricoltura - Settore S.I.R.C.A. La tessitura del suolo (foglio divulgativo novembre - dicembre 2002)

Crop Water requirement

Description

Calculate the monthly irrigation requirement of crops based on cumulative probability [p] and daily watering duration of irrigation [h]

Usage

PWN(x1, frvol, R, p, irr)

Arguments

x1

Bivariate series of monthly cumulative rainfall and average monthly temperatures

frvol

Volume fraction of the soil. It is 0.10 for sandy soil, 0.20 fpr loamy soil, 0.18 for clayey soil, 0.13 for medium-textured soil

R

Length of plant roots [cm] — see FAO-24 Mannini reworked, maximum extraction depth

p

Cumulative probability of plant's water requirement [percent]

irr

Daily watering duration of irrigation [h]

Value

Values

Monthly water requirement values [m3/ha] relating to the cumulative probability indicated (p)

Flow

Irrigation flow [l/s/ha] relating to the daily watering duration (irr) and cumulative probability (p)

Author(s)

Corrado Tallerini

References

United States Department of Agricolture (USDA - SCS). IRRIGATION - National Engineering handbook.

Moisello U. "Idrologia Tecnica" La Goliardica Pavese.

Genovesi R., Bottau D. "L'importanza della falda nell' alimentazione idrica delle colture nella pianura emiliano-romagnola."

Regione Campania - Assessorato Agricoltura - Settore S.I.R.C.A. La tessitura del suolo (foglio divulgativo novembre - dicembre 2002)

Fao irrigation and dreinage paper N. 24 - Crop water requirement, Food and agriculture organization of the united nations ROME, rivisited 1977

Grimaldi, S. Tallerini, C., Serinaldi, F., "Modelli multivariati lineari per la generazione di serie di precipitazioni giornaliere", Giornata di Studio: Metodi Statistici e Matematici per l'Analisi delle Serie Idrologiche, Napoli, maggio 2004

Examples

##---- data(Pistoia)
##---- PWN(Pistoia,0.13,40,75,16)
##---- Calculate the monthly irrigation requirement of a plant (Length of plant roots 40 cm in
##---- a medium-textured soil) based on a 75% cumulative probability and 16 hours daily irrigation

Dataset of Pistoia (Italy)

Description

Bivariate series of observed rainfall-temperature for Pistoia (Italy) during the period 1951-2012

Usage

data(Pistoia)

Format

A data frame with 744 observations on the following 2 variables.

V1

Monthly cumulative rainfall (mm)

V2

Average monthly temperature (degree)

Source

Ce.Spe.Vi. (Centro sperimentale per il vivaismo) Web: http://www.cespevi.it

Examples

data(Pistoia)
## maybe str(Pistoia) ; plot(Pistoia) ...

Crop water requirement

Description

Calculates the water requirement [m3/ha] of herbaceous or arboreal crops

Usage

WNeeds(x, frvol, R)

Arguments

x

Bivariate series of monthly cumulative rainfall [mm] and average monthly temperatures [degree]

frvol

Volume fraction of the soil. It is 0.10 for sandy soil, 0.20 fpr loamy soil, 0.18 for clayey soil, 0.13 for medium-textured soil

R

Length of plant roots [cm] — see FAO-24 Mannini reworked, maximum extraction depth

Author(s)

Corrado Tallerini

References

United States Department of Agricolture (USDA - SCS). IRRIGATION - National Engineering handbook.

Moisello U. "Idrologia Tecnica" La Goliardica Pavese.

Genovesi R., Bottau D. "L'importanza della falda nell' alimentazione idrica delle colture nella pianura emiliano-romagnola."

Regione Campania - Assessorato Agricoltura - Settore S.I.R.C.A. La tessitura del suolo (foglio divulgativo novembre - dicembre 2002)

Fao irrigation and dreinage paper N. 24 - Crop water requirement, Food and agriculture organization of the united nations ROME, rivisited 1977

Grimaldi, S. Tallerini, C., Serinaldi, F., "Modelli multivariati lineari per la generazione di serie di precipitazioni giornaliere", Giornata di Studio: Metodi Statistici e Matematici per l'Analisi delle Serie Idrologiche, Napoli, maggio 2004

Examples

## data(Pistoia)
## A1=WNeeds(Pistoia,0.13,60)
## edit(A1)

Subset Autoregressive Model

Description

Estimate VAR(p) model fixing some parameter values to zero

Usage

ar.egls(x, R, order.max , na.action = na.fail, series = NULL, ...)

Arguments

x

Univariate or multivariate series with nil mean

R

Matrices of parameters selection

order.max

Model order

na.action

Function to be called to handle missing values

series

Names for the series. Defaults to 'deparse(substitute(x))'

...

See ar.ols

Details

R matrix is a list of p matrices, with p the autoregressive order. In R value '1' allows parameter estimation, '0' fix the parameter value to zero.

Value

See ar.ols

Note

Function is created modifing ar.ols by Adrian Trapletti and Brian Ripley

Author(s)

Corrado Tallerini

References

Grimaldi S. , Serinaldi F. & Tallerini C. (2004) 'Multivariate linear parametric models applied to daily rainfall time series' Mediterranean Storms, 6rd EGU Plinius Conference held in Mediterranean Sea, Italy, October 2004

Lutkepohl, H. (1993) Introduction to Multiple Time Series Analysis 2nd Edition ._ Springer Verlag, NY

Examples

##	S1=matrix(0,3,3)
##	S1[1,1]=1
##	S1[1,2]=1
##	S=list()
##	S[[1]]=S1
##	S[[2]]=S1
##	ar.egls(series.rainfall[,1:3],S,order.max=2)
## --> Apply a Subset VAR(2) model restricted to 4 parameters (position (1,1)
## --> and (1,2) in both matrices) to first 3 series of series.rainfall 
## --> dataset

hourly rainfall series

Description

Hourly rainfall series recorded in Burlington (US) during the period 2012-2015.

Usage

data(hourly.rainfall.series)

Details

Dataset is available on The Iowa Environmental Mesonet (IEM) website

Source

https://mesonet.agron.iastate.edu/request/download.phtml?

Examples

data(hourly.rainfall.series)
## maybe str(series.rainfall) ; plot(series.rainfall) ...

Linear Parametric Model

Description

Estimate ARMA and FARMA models, make simulations and ed eventually apply a corrective procedure to rainfall synthetic series. Besides you can remove seasonal components with STL modified method.

Usage

lpm(x, p, q, n, smean, svar, outer=0, prob = 0.95, fre = 365, 
fractional = F, Plag = 20, lsign=0.05, n1 = 399, trasfo = F, des = T, rain = F, graph = F)

Arguments

x

Univariate series

p

AR order

q

MA order

n

Number of series to simulate

outer

Number of outer loops for STL modified method. Default outer = 0

smean, svar

Mean and Variance smoothing windows of STL modified method

prob

Parameter confidence interval. Default prob = 0.95

fre

Series frequency. Default fre = 365 (for daily series)

fractional

Logical variable: T to apply FARMA model. Default fractional = F

Plag

Maximum lag of ACF used in the Portmanteau test. Default Plag = 20

lsign

Portmanteau Test significance level. Default lsign = 0.05

n1

Number of parameters of infinite MA model . Default n1 = 399

trasfo

Logical variable: T for preventive logarithmical trasformation. Default trasfo = F

des

Logical variable: T to remove seasonal components. Default des = T

rain

Logical variable: T to apply the corrective procedure to daily rainfall simulated series. Default rain = F

graph

Logical variable: T to receive some graphics. Default graph = F

Details

Need integer periodical dataset. Function to complete modelling univariate series.

Value

para

List of estimated parameters

res

Residual series

simdes

List of simulated series without application of corrective procedure

sim

List of simulated series

BIC

Bayesian Information criterion index of estimated model

Note

Portmonteau test and BIC index are displaied during application. Portmonteau Test is positive if Q < chi square

Author(s)

Salvatore Grimaldi

References

Grimaldi, S., 'Linear parametric models applied on daily hydrological series', Journal of Hydrologic Engineering, Vol.9, No 5, September 2004.

Grimaldi S., F. Napolitano, L. Ubertini, 'A procedure to use linear parametric models for daily rainfall series simulation'

Brockwell, P.J and Davis, R.A. (1990) Time Series: Theory and Methods 2nd edition, Springer, NY.

Hipel, K.W. and McLeod, A.I., (1994) Time Series Modelling of Water Resources and Enviromental Systems, Reading, UK.

See Also

rain.adapt

Examples

##---  lpm(series.runoff,1,1,0,30,30,fractional=T,trasfo=T)
##--   Apply a FARMA(1,d,1) model to series.runoff after e preventive 
##     logarithmical trasformation and deseasonalization with smoothing 30.

Maximum annual rainfall series for different durations

Description

Maximum annual rainfall series for different durations recorded at the pluviograph of Palazzo Marino, Milan (Italy)

Usage

data(milano)

Details

Maximum annual precipitation series for 0.25, 0.5, 0.75, 1, 1.25, 1.50, 2, 2.5, 3, 4, 6 [h] 1931-1970

Source

dataset of Palazzo Marino pluviograph , Milan (Italy)

Examples

data(milano)
## maybe str(series.rainfall) ; plot(series.rainfall) ...

Multivariate Linear Parametric Model

Description

Multivariate modelling using VAR(p) and SVAR(p) different estimation methods, simulation, daily rainfall simulated series correction and deseasonalization are performed

Usage

mlpm(x, p, prob, nsim, smean, svar, fre = 365, outer = 0,plot = F, 
rain = T, over = T, estimate = "ols", CCFlag = 20, Plag = 20, lsign = 0.05, des = T)

Arguments

x

Multivariate series

p

Model order

prob

Condifidence interval used to fix parameters in SVAR(p) model

nsim

Number of series to simulated

smean, svar

Mean and Variance smoothing windows of STL modified method

fre

Series frequency. Default fre = 365

outer

Outer loops of STL modified method. Default outer = 0

plot

Logical variable: T to receive some graphics. Default plot = F

rain

Logical variable: T to apply rain adaptor to simulated series. Default rain = F

over

Logical variable: T to use SVAR(p) model estimated with EGLS method. Need estimate = 'ols' Default over = T

estimate

Define VAR(p) estimation method. 'ols', 'burg', 'yw' (Yule-Walker). Default estimate = 'ols'

CCFlag

Lag of (Partial) Auto-CrossCorrelation function graphics . Default CCFlag = 20

Plag

Maximum lag of A-CCF used in the Portmanteau Test. Default Plag = 20

lsign

Portmanteau Test significance level. Default lsign = 0.05

des

Logical variable: T to remove seasonal components

Details

Need integer periodical datasets. Simulation use Lutkepohl algorithm with a residuals vectorial permutation to obtain innovations. Parameters selections of EGLS method is defined by t-ratio approach.

Value

coeff

List of estimated coefficients matrix

coeffstd

List of estimated standard deviations coefficients matrix. Only for OLS and EGLS method

struct

List of 'structure' of SVAR(p) model (1 define position of estimated parameter). Only for EGLS method

res

Residual series

fit

Output List of ar function

aic

Akaike Information Criterion index

Q

Portmonteau statistic

sim

List of simulated series

Note

Portmonteau test, AIC e SBC index are displaied during application. Portmonteau test is positive if Q < chi square.

Author(s)

Corrado Tallerini

References

Grimaldi S., Tallerini C., Serinaldi F. (2004) 'Modelli multivariati lineari per la generazione di serie di precipitazioni giornaliere' Giornata di Studio: Metodi Statistici e Matematici per l'Analisi Idrologiche Napoli 2004

Grimaldi S. , Serinaldi F. & Tallerini C. (2004) 'Multivariate linear parametric models applied to daily rainfall time series' Mediterranean Storms, 6rd EGU Plinius Conference held in Mediterranean Sea, Italy, October 2004

Lutkepohl, H. (1993) Introduction to Multiple Time Series Analysis 2nd edition, Springer-Verlag, Berlin.

Grimaldi, S., 'Linear parametric models applied on daily hydrological series', Journal of Hydrologic Engineering, Vol. 9, No 5 , September 2004.

Brockwell, P.J and Davis, R.A. (1990) Time Series: Theory and Methods 2nd edition, Springer, NY.

Hipel, K.W. and McLeod, A.I., (1994) Time Series Modelling of Water Resources and Enviromental Systems, Reading, UK.

Hosking, J.R.M. (1980) 'The Multivariate Portmanteau Statistic' Journal of the American Statistical Association, Vol.75, N.371, 502-608.

See Also

lpm, ar.egls, rain.adapt

Examples

##-- Mrain=mlpm(series.rainfall,3,0.95,0,120,120)
##-- Apply a SVAR(3) model with selection probability 95 % to series.rainfall
##-- after preventive deseasonalization with smoothing 120.

Rainfall Adaptor

Description

Apply a corrective procedure to daily rainfall series to enforce actual caracteristics.

Usage

rain.adapt(x, a, ser)

Arguments

x

Observed series

a

Univariate series to modify (simulated series)

ser

Series identification number

Details

The no-rain frequency consequentally the total rainfall depth of the observed series are enforced on the synthetic series

Value

Corrected series

Author(s)

Salvatore Grimaldi

References

Grimaldi S., F. Napolitano, L. Ubertini, 'A procedure to use linear parametric models for daily rainfall series simulation'

Examples

##   rain=lpm(series.rainfall[,1],1,1,1,120,120)
##   rain.adapt(series.rainfall[,1],rain$sim[[1]],1)
##-- ==>  Apply rain adaptor to a simulated series with a ARMA(1,1) model

Support function

Description

Support function

Daily Rainfall Series

Description

Group of 5 daily rainfall series recorded in Tuscany region of Italy during the period 1958-1979.

Usage

data(series.rainfall)

Details

Dataset is created removing lacking years and replacing lacking days with the mean of previous and successive value. Beside 29 february day values are removed to obtain integer periodical dataset.

Source

Rudari, R. 'Predicibilita' del clima europeo ed influenze delle forzanti a scala sinottica su eventi regionali di precipitazione intensa', PDh Thesis 2001

Examples

data(series.rainfall)
## maybe str(series.rainfall) ; plot(series.rainfall) ...

Daily Runoff Series

Description

Daily runoff series of Tiber river observed to Ripetta station during the period 1930-1983

Usage

data(series.runoff)

Details

29 february day values are removed to obtain integer periodical dataset

Source

Available on the web site www.gndci.cnr.it. "Gruppo nazionale per la difesa delle catastrofi idrogeologiche"

Examples

data(series.runoff)
## maybe str(series.runoff) ; plot(series.runoff) ...