From dc5f2ca1dbdb5db2c216793de18f6e9c077345a9 Mon Sep 17 00:00:00 2001 From: yvesdeville Date: Fri, 29 Dec 2023 14:30:06 +0100 Subject: [PATCH] README and guide --- .Rbuildignore | 11 ++- R/GPtail.R | 14 ++-- README.Rmd | 27 ++++--- inst/doc/Rgraphics/figBrestAsympt1-1.pdf | Bin 48479 -> 48479 bytes inst/doc/Rgraphics/figBrestAsympt2-1.pdf | Bin 46640 -> 46640 bytes inst/doc/Rgraphics/figBrestConv0-1.pdf | Bin 25508 -> 25508 bytes inst/doc/Rgraphics/figBrestConv1-1.pdf | Bin 25703 -> 25703 bytes inst/doc/Rgraphics/figBrestConv15-1.pdf | Bin 25710 -> 25710 bytes inst/doc/Rgraphics/figBrestConv2-1.pdf | Bin 25682 -> 25682 bytes inst/doc/Rgraphics/figBrestConv3-1.pdf | Bin 24489 -> 24489 bytes inst/doc/Rgraphics/figBrestConv4-1.pdf | Bin 27749 -> 27749 bytes inst/doc/Rgraphics/figBrestConvGEV-1.pdf | Bin 23122 -> 23122 bytes inst/doc/Rgraphics/figBrestFitSurge-1.pdf | Bin 19683 -> 19683 bytes inst/doc/Rgraphics/figBrestTide-1.pdf | Bin 7951 -> 7951 bytes inst/doc/Rgraphics/figSplineDens1-1.pdf | Bin 39835 -> 39835 bytes inst/doc/Rgraphics/figSplineDens1-2.pdf | Bin 39850 -> 39850 bytes inst/doc/Rgraphics/figSplineDens2-1.pdf | Bin 65548 -> 65548 bytes inst/doc/Rgraphics/figSplineDens2-2.pdf | Bin 4846 -> 4846 bytes inst/doc/Rgraphics/figSplineDens3-1.pdf | Bin 18142 -> 18142 bytes inst/doc/Rgraphics/figempirical-1.pdf | Bin 23255 -> 23255 bytes inst/doc/Rgraphics/figempirical1-1.pdf | Bin 23283 -> 23283 bytes inst/doc/SeaLevGuide.Rnw | 82 ++++++++++------------ inst/doc/SeaLevGuide.pdf | Bin 1239301 -> 1265922 bytes 23 files changed, 71 insertions(+), 63 deletions(-) diff --git a/.Rbuildignore b/.Rbuildignore index 022f3fc..434cb0c 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -6,4 +6,13 @@ doc/images doc/cache doc/figures doc/Rgraphics -doc/Old \ No newline at end of file +doc/Old +^\.github +^\.git +^.*\.Rproj$ +^\.Rproj\.user$ +README.Rmd +README.md +^_pkgdown\.yml$ +^docs$ +^pkgdown$ \ No newline at end of file diff --git a/R/GPtail.R b/R/GPtail.R index 4522a61..177d488 100644 --- a/R/GPtail.R +++ b/R/GPtail.R @@ -53,7 +53,6 @@ ##' the \code{ret.lev} table. A NULL value correspond to a default ##' vector of values. ##' -##' ##' @param pred.period If not \code{NULL}, a vector giving periods at ##' which predictions (return levels and confidence limits) should be ##' computed and returned in the \code{ret.lev} data.frame. @@ -75,8 +74,7 @@ ##' table where only rounded return periods are used after ##' an interpolation. ##' -##' -##' @return A list. +##' @return A list similar to that returned by \code{\link{convSL}}. ##' ##' @author Yves Deville ##' @@ -88,6 +86,14 @@ ##' "shape" = 0.2 * runif(1)) ##' res <- GPtail(x = SD.Brest, par.y = par.y, lambda = 1) ##' +##' ## change variable names +##' varnames(res) <- c(x = "Tide", y = "Skew surge", z = "Sea level") +##' +##' ## plot the densities +##' plot(res) +##' +##' ## plot the return level +##' plot(res, which = 3) GPtail <- function(x, threshold.y = NA, distname.y = "GPD", @@ -118,7 +124,7 @@ GPtail <- function(x, mc <- match.call() - if (class(x) != "SplineDensity") { + if (!inherits(x, "SplineDensity")) { stop("'x' must be an object with class \"SplineDensity\".", " Use the 'SplineDensity' function to create such an object.") } diff --git a/README.Rmd b/README.Rmd index 53da8b5..c90e247 100644 --- a/README.Rmd +++ b/README.Rmd @@ -1,23 +1,22 @@ --- -title: "README" +title: "R Package SeaLev" author: "Yves Deville" date: "2023-05-22" output: github_document --- - -# The SeaLev package +# Scope The **SeaLev** package is a R package funded by IRSN/Behrig. It is devoted to the distribution of a Sea Level random variable (r.v.) say -$Z$ viewed as the sum of two independent r.vs $X$ and $Y$ representing -the astronomical tide and the surge. More precisely the r.vs relate to -a *tide interval* defined as the time interval separating two -consecutive astronomical low tides. Then $X$ is the astronomical -*high-tide* level and $Y$ is the so-called *skew surge* representing -the difference between the observed highest level and the astronomical -high tide level. +$Z$, viewed as the sum of two independent r.vs $X$ and $Y$ +representing the astronomical tide and the surge. More precisely the +r.vs relate to a *tide interval* defined as the time interval +separating two consecutive astronomical low tides. Then $X$ is the +astronomical *high-tide* level and $Y$ is the so-called *skew surge* +representing the difference between the observed highest level and the +astronomical high tide level. - The distribution of $X$ can be regarded a perfectly known. More precisely, the support of $X$ is an interval $[x_{\texttt{min}}, \, @@ -41,17 +40,15 @@ In an R session use ```{r, eval=FALSE} library(remotes) -install_github("IRSN/SeaLev", dependencies = TRUE, auth_token = myToken) +install_github("IRSN/SeaLev", dependencies = TRUE) ``` - -where `myToken` is *your* GitHub token. This should install the -package and make it ready to use. +This should install the package and make it ready to use. Mind that by default this does not build the vignette shipped with the package (long-form documentation). To build the vignette, use instead ```{r, eval=FALSE} -install_github("IRSN/SeaLev", dependencies = TRUE, auth_token = myToken, build_vignettes = TRUE) +install_github("IRSN/SeaLev", dependencies = TRUE, build_vignettes = TRUE) ``` The installation will then take a longer time but the vignette will be accessible from the help of the package (link above the "Help Pages" diff --git a/inst/doc/Rgraphics/figBrestAsympt1-1.pdf b/inst/doc/Rgraphics/figBrestAsympt1-1.pdf index fe7d5b4b5788e75ed8438b76716640f57bc91fa1..ad208138fedfe9ee44868c5d64ba7739424eeae2 100644 GIT binary patch delta 59 zcmccri|PI^rU@qM#)d{lmWGCg=Ei24T>8HGDK3d6sR|k{Rz?O!NOBXSb(oFy3^#UN G-2(tAYZ2W5 delta 59 zcmccri|PI^rU@qMMh2$Fh6WY}mL`^(T>8HGDK3d6sR|k{Rz?O!NOBXSb(oFx3^sOM G-2(tBO%de) diff --git a/inst/doc/Rgraphics/figBrestAsympt2-1.pdf b/inst/doc/Rgraphics/figBrestAsympt2-1.pdf index ec529215bccae0fe05599d60268e7def4153ad17..3416b5c99e015f012a22a7bad892e345d14ccbca 100644 GIT binary patch delta 59 zcmdn+hH1karU@qM#)d{lmWGCg=Ei24T>8HGDK3d6sR|k{Rz?O!NOBXSb(oFy3^#Ty G+X?^;yAdq_ delta 59 zcmdn+hH1karU@qMMh2$Fh6WY}mL`^(T>8HGDK3d6sR|k{Rz?O!NOBXSb(oFx3^sNx G+X?^u<#tA0s#)d{lmWGCg=ElaFT>8HGDK3d6sR|k{Rz?O!NOBXSb(oFy3^#U3 GB?AEUeh=jU delta 59 zcmZ2-oN>u<#tA0sMh2$Fh6WY}mL?{eT>8HGDK3d6sR|k{Rz?O!NOBXSb(oFx3^sO2 GB?AEU_z&p- diff --git a/inst/doc/Rgraphics/figBrestConv1-1.pdf b/inst/doc/Rgraphics/figBrestConv1-1.pdf index 0102245bbe04bfd65162a1400ebb74ccdd787daa..f012852638365cea4abd4c80729df02de2095990 100644 GIT binary patch delta 58 zcmaEUg7NtY#t9~B#)d{lmWGCg=Ef$PT>8HGDK3d6sR|k{Rz?O!2)T(-y3EFUh8w%? 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More information +on the context can be found in the books by David +Pugh~\cite[chap.~8]{PUGHBOOK1}, \cite[chap.~6]{PUGHBOOK2}, or that (in french) +of Bernard Simon~\cite[chap.~VIII]{SIMON}. The method concerns a \textit{still water} sea level, and relies on a -decomposition of it as the sum of a \textit{tide} part, and a -\textit{non-tidal} part --~or \textit{surge} part. The two components -are considered as independent random variables, and the probability -distribution of the sea level can then be computed by -convolution. Note that the surge part can not be observed by itself -and is obtained as the difference between the observed level and -its tidal prediction. The surge is sometimes called the \textit{tide residual}. - -The assumption of independence between the tide and the surge is best -supported when the modelled sea level is recorded at or near high -tide~\cite{COLESBAYES}. The \index{skew surge} \textit{skew surge} is -computed as minus the difference of the predicted (astronomical) tide -and the nearest experimented high water. Modelling high tide sea levels -and skew surges (rather than, say, hourly levels and surges) is a valuable -option as far as the interest is on extreme \textit{high} sea -levels. The time between two successive high tides is about $12$ hours and $26$ -minutes for semi-diurnal tides, corresponding to a sampling rate of -\index{rate, sampling for high tides} -about $705.8$ high tides by year. The method of convolution applied -with Skew Surges is sometimes called the \textit{Skew Surge Joint Probability -Method} (SSJPM). +decomposition of it as the sum of a \textit{tide} part, and a \textit{non-tidal} +part --~or \textit{surge} part. The two components are considered as independent +random variables, and the probability distribution of the sea level can then be +computed by convolution. Note that the surge part can not be observed by itself +and is obtained as the difference between the observed level and its tidal +prediction. The surge is sometimes called the \textit{tide residual}. + +The assumption of independence between the tide and the surge is best supported +when the modelled sea level is recorded at or near high +tide~\cite{COLESBAYES}. The \index{skew surge} \textit{skew surge} is computed +as minus the difference of the predicted (astronomical) tide and the nearest +experimented high water. Modelling high tide sea levels and skew surges (rather +than, say, hourly levels and surges) is a valuable option as far as the interest +is on extreme \textit{high} sea levels. The time between two successive high +tides is about $12$ hours and $26$ minutes for semi-diurnal tides, corresponding +to a sampling rate of \index{rate, sampling for high tides} about $705.8$ high +tides by year. The method of convolution applied with Skew Surges is sometimes +called the \textit{Skew Surge Joint Probability Method} (SSJPM). \subsection{Limitations} %--------------------- @@ -298,8 +294,8 @@ This condition can be useful in the numerical convolution. tides will often be bi-modal. \item The conditions (\ref{eq:FX0}) are not always fulfilled by an arbitrary - periodic oscillation with range $(\Low{x},\,\Up{x})$, - see the example in~\cite{PUGHVASSIE80}, p.~975. + periodic oscillation with range $(\Low{x},\,\Up{x})$, see the example + in~\cite{PUGHVASSIE80}, p.~975. \item In practice, the distribution of the tide must be computed from ``observations'' $X_t$, that is \textit{predictions} arising from a @@ -1921,9 +1917,9 @@ are used in the \verb@momGen@ and \verb@GPtail@ functions. \frac{(-1)^{j+1}}{t^{j+1}} \left[ f^{[j]}_X(\zeta_i+) - f^{[j]}_X(\zeta_i-) \right] \right\} \, e^{t \zeta_i}. $$ - \item If $Y \sim \mathtt{GPD}(\mu_Y,\,\sigma_Y,\,\xi_Y)$, and - $1/\xi_Y$ is not equal to any of the integers $1$, $2$, $\dots$, $k$ then - the survival function of $Z$ is given by + \item Assume that $Y \sim \mathtt{GPD}(0,\,\sigma_Y,\,\xi_Y)$ is independent + of X. Then provided that $1/\xi_Y$ is not equal to any of the integers $1$, + $2$, $\dots$, $k$ the survival function of $Z = X + Y$ is given by \begin{equation} \label{eq:SSplineGPD} S_Z(z) = \sum_{i=0}^{\ell} \, \sum_{j=k-\nu_i}^{k-1} a_j d_i^{[j]} @@ -1953,10 +1949,10 @@ derived w.r.t. the parameters of the GPD, this allows the determination of confidence intervals for the return levels based on the delta method. \index{delta method} -A remarkable point in the theorem is that the coefficients $a_j$ are -not positive. If only simple knots are used, it can be shown that -$\sum_i a_i \zeta_i^j = 0$ for $0 \leqslant j \leqslant k-1$ hence -the coefficients $a_j$ sum to zero. +A remarkable point in the theorem is that the coefficients $a_j$ are not +positive, so the tail of $Z$ is a \textit{signed mixture} of GPD tails. If only +simple knots are used, it can be shown that $\sum_i a_i \zeta_i^j = 0$ for +$0 \leqslant j \leqslant k-1$ hence the coefficients $a_j$ sum to zero. \subsection{Practical consequences} %%--------------------------------------- @@ -1967,11 +1963,11 @@ The first statement of the theorem can be used for exponential surges, since the cumulant generating function for the tide gives the shift between the sea level tail and the surge tail, see section~\ref{ExpSurges}. -The second statement of the theorem is used for the general case $\xi_Y \neq 0$. It -allows the accurate determination of the sea level tail distribution -without using discrete convolution or quadratures. Since the formula -for $S_Z(z)$ only works for $z > \Up{x} + \mu_Y$, a discrete -convolution must be used to compute the bulk of the distribution. +The second statement of the theorem is used for the general case $\xi_Y \neq +0$. It allows the accurate determination of the sea level tail distribution +without using discrete convolution or quadratures. 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