workflow.tex

% Options for packages loaded elsewhere
\PassOptionsToPackage{unicode}{hyperref}
\PassOptionsToPackage{hyphens}{url}
%
\documentclass[
]{article}
\usepackage{amsmath,amssymb}
\usepackage{lmodern}
\usepackage{iftex}
\ifPDFTeX
  \usepackage[T1]{fontenc}
  \usepackage[utf8]{inputenc}
  \usepackage{textcomp} % provide euro and other symbols
\else % if luatex or xetex
  \usepackage{unicode-math}
  \defaultfontfeatures{Scale=MatchLowercase}
  \defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1}
\fi
% Use upquote if available, for straight quotes in verbatim environments
\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
\IfFileExists{microtype.sty}{% use microtype if available
  \usepackage[]{microtype}
  \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
}{}
\makeatletter
\@ifundefined{KOMAClassName}{% if non-KOMA class
  \IfFileExists{parskip.sty}{%
    \usepackage{parskip}
  }{% else
    \setlength{\parindent}{0pt}
    \setlength{\parskip}{6pt plus 2pt minus 1pt}}
}{% if KOMA class
  \KOMAoptions{parskip=half}}
\makeatother
\usepackage{xcolor}
\usepackage[margin=1in]{geometry}
\usepackage{color}
\usepackage{fancyvrb}
\newcommand{\VerbBar}{|}
\newcommand{\VERB}{\Verb[commandchars=\\\{\}]}
\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
% Add ',fontsize=\small' for more characters per line
\usepackage{framed}
\definecolor{shadecolor}{RGB}{248,248,248}
\newenvironment{Shaded}{\begin{snugshade}}{\end{snugshade}}
\newcommand{\AlertTok}[1]{\textcolor[rgb]{0.94,0.16,0.16}{#1}}
\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}}
\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.77,0.63,0.00}{#1}}
\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}}
\newcommand{\BuiltInTok}[1]{#1}
\newcommand{\CharTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}}
\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}}
\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}}
\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}}
\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}}
\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{#1}}
\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}}
\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}}
\newcommand{\ErrorTok}[1]{\textcolor[rgb]{0.64,0.00,0.00}{\textbf{#1}}}
\newcommand{\ExtensionTok}[1]{#1}
\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}}
\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}}
\newcommand{\ImportTok}[1]{#1}
\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}}
\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}}
\newcommand{\NormalTok}[1]{#1}
\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.81,0.36,0.00}{\textbf{#1}}}
\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{#1}}
\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}}
\newcommand{\RegionMarkerTok}[1]{#1}
\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}}
\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}}
\newcommand{\StringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}}
\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}}
\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}}
\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}}
\usepackage{longtable,booktabs,array}
\usepackage{calc} % for calculating minipage widths
% Correct order of tables after \paragraph or \subparagraph
\usepackage{etoolbox}
\makeatletter
\patchcmd\longtable{\par}{\if@noskipsec\mbox{}\fi\par}{}{}
\makeatother
% Allow footnotes in longtable head/foot
\IfFileExists{footnotehyper.sty}{\usepackage{footnotehyper}}{\usepackage{footnote}}
\makesavenoteenv{longtable}
\usepackage{graphicx}
\makeatletter
\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth\else\Gin@nat@width\fi}
\def\maxheight{\ifdim\Gin@nat@height>\textheight\textheight\else\Gin@nat@height\fi}
\makeatother
% Scale images if necessary, so that they will not overflow the page
% margins by default, and it is still possible to overwrite the defaults
% using explicit options in \includegraphics[width, height, ...]{}
\setkeys{Gin}{width=\maxwidth,height=\maxheight,keepaspectratio}
% Set default figure placement to htbp
\makeatletter
\def\fps@figure{htbp}
\makeatother
\setlength{\emergencystretch}{3em} % prevent overfull lines
\providecommand{\tightlist}{%
  \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\setcounter{secnumdepth}{-\maxdimen} % remove section numbering
\ifLuaTeX
  \usepackage{selnolig}  % disable illegal ligatures
\fi
\IfFileExists{bookmark.sty}{\usepackage{bookmark}}{\usepackage{hyperref}}
\IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available
\urlstyle{same} % disable monospaced font for URLs
\hypersetup{
  pdftitle={Data Processing Example},
  pdfauthor={ROBIN Network},
  hidelinks,
  pdfcreator={LaTeX via pandoc}}

\title{Data Processing Example}
\author{ROBIN Network}
\date{2023-03-21}

\begin{document}
\maketitle

\hypertarget{plan}{%
\section{Plan}\label{plan}}

This R Markdown document is part of the ROBIN hydrometric data pipeline.
It takes daily and sub-daily data, extracting statistics of high, low
and mean flows, including estimates of trend and aridity indices.

The present script only runs the work for a single station.

\hypertarget{outline-of-script}{%
\subsection{Outline of script}\label{outline-of-script}}

\begin{itemize}
\tightlist
\item
  Data format (columns: Agency, Station, Day, Flow, Flag)
\item
  Check for Level-1/Level-2 status based on completeness.
\item
  Summary statistics

  \begin{itemize}
  \tightlist
  \item
    Monthly thresholds
  \item
    POT series
  \item
    30-day/10-day/7-day rolling totals
  \item
    Annual/monthly/quarterly quantiles/mean
  \item
    Annual 1-day/10-day/30-day maxima
  \item
    Annual 7-day/30-day minima
  \end{itemize}
\item
  Tests

  \begin{itemize}
  \tightlist
  \item
    Pettitt breakpoint test
  \item
    Seasonal Mann-Kendall
  \item
    Rolling Mann-Kendall-Snyers Indicators
  \end{itemize}
\item
  SSI
\item
  Intermittence
\item
  Mean Annual Flow (Standardised)
\item
  Aridity Index
\end{itemize}

\hypertarget{read-in-data}{%
\section{Read in data}\label{read-in-data}}

First the data must be read in, hopefully in the pre-specified format.
The only addition required is the addition of any other flags to the
\texttt{Flag} field. Currently there are:

\begin{itemize}
\tightlist
\item
  M: Missing value. Should correspond to an \texttt{NA}, \texttt{0}, or
  empty value \texttt{""} in the Value column.
\item
  E: Estimated (or modelled) value
\item
  S: Suspect value, may have high associated error.
\end{itemize}

Dates should be consistent, either with a full date
(e.g.~\texttt{2022-04-01}), or a full date and time
(e.g.~\texttt{2022-04-01T09:00:00Z})

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{filein\_path }\OtherTok{\textless{}{-}} \StringTok{"./41022\_gdf.csv"}
\NormalTok{date\_format }\OtherTok{\textless{}{-}} \StringTok{"date"} \CommentTok{\# state "date" or "datetime"}

\NormalTok{data\_in }\OtherTok{\textless{}{-}} \FunctionTok{read\_in\_robin}\NormalTok{(filein\_path, }\AttributeTok{skip=}\DecValTok{21}\NormalTok{)}

\NormalTok{Agency }\OtherTok{\textless{}{-}} \StringTok{"EA"}
\NormalTok{Station }\OtherTok{\textless{}{-}} \DecValTok{41022}

\NormalTok{data\_in}\SpecialCharTok{$}\NormalTok{Agency }\OtherTok{\textless{}{-}}\NormalTok{ Agency}
\NormalTok{data\_in}\SpecialCharTok{$}\NormalTok{Station }\OtherTok{\textless{}{-}}\NormalTok{ Station}
\end{Highlighting}
\end{Shaded}

\hypertarget{check-data-type}{%
\subsection{Check data type}\label{check-data-type}}

All the data should be gauged daily flow.

\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{check\_for\_level}\NormalTok{(data\_in, }\StringTok{"M"}\NormalTok{)}
\end{Highlighting}
\end{Shaded}

\begin{verbatim}
## [1] "Suitable for trend analysis"
\end{verbatim}

\begin{verbatim}
## $stationLevel
## [1] 1
## 
## $trendFlag
## [1] TRUE
\end{verbatim}

\hypertarget{reformat-data}{%
\section{Reformat data}\label{reformat-data}}

Dates are reformatted into a datetime variable, and a numerical record
ordering is added. QA flags are converted to a factor form. Data without
issue should have empty \texttt{QA\_Flag} fields.

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{data\_in}\SpecialCharTok{$}\NormalTok{id }\OtherTok{\textless{}{-}} \FunctionTok{seq}\NormalTok{(}\DecValTok{1}\NormalTok{, }\FunctionTok{nrow}\NormalTok{(data\_in)) }\CommentTok{\# does not account for missing rows in the data}
\NormalTok{data\_in}\SpecialCharTok{$}\NormalTok{Flag }\OtherTok{\textless{}{-}} \FunctionTok{factor}\NormalTok{(data\_in}\SpecialCharTok{$}\NormalTok{Flag)}

\CommentTok{\# Make the lfstat object}
\NormalTok{lf\_flow\_raw }\OtherTok{\textless{}{-}}\NormalTok{ data\_in}
\FunctionTok{colnames}\NormalTok{(lf\_flow\_raw)[}\DecValTok{1}\NormalTok{] }\OtherTok{\textless{}{-}} \StringTok{"Date"}
\NormalTok{lf\_flow\_raw}\SpecialCharTok{$}\NormalTok{day }\OtherTok{\textless{}{-}} \FunctionTok{day}\NormalTok{(lf\_flow\_raw}\SpecialCharTok{$}\NormalTok{Date)}
\NormalTok{lf\_flow\_raw}\SpecialCharTok{$}\NormalTok{month }\OtherTok{\textless{}{-}} \FunctionTok{month}\NormalTok{(lf\_flow\_raw}\SpecialCharTok{$}\NormalTok{Date)}
\NormalTok{lf\_flow\_raw}\SpecialCharTok{$}\NormalTok{year }\OtherTok{\textless{}{-}} \FunctionTok{year}\NormalTok{(lf\_flow\_raw}\SpecialCharTok{$}\NormalTok{Date)}
\NormalTok{lf\_flow }\OtherTok{\textless{}{-}}\NormalTok{ lf\_flow\_raw[,}\FunctionTok{c}\NormalTok{(}\StringTok{"day"}\NormalTok{, }\StringTok{"month"}\NormalTok{, }\StringTok{"year"}\NormalTok{, }\StringTok{"Flow"}\NormalTok{)]}
\FunctionTok{colnames}\NormalTok{(lf\_flow) }\OtherTok{\textless{}{-}} \FunctionTok{c}\NormalTok{(}\StringTok{"day"}\NormalTok{, }\StringTok{"month"}\NormalTok{, }\StringTok{"year"}\NormalTok{, }\StringTok{"flow"}\NormalTok{)}
\NormalTok{year\_start\_month }\OtherTok{\textless{}{-}} \DecValTok{1}
\NormalTok{lf\_flow }\OtherTok{\textless{}{-}} \FunctionTok{createlfobj}\NormalTok{(lf\_flow, }\AttributeTok{hyearstart=}\NormalTok{year\_start\_month)}
\FunctionTok{flowunit}\NormalTok{(lf\_flow) }\OtherTok{\textless{}{-}} \StringTok{"m\^{}3/sec"}
\NormalTok{lf\_flow}\SpecialCharTok{$}\NormalTok{date }\OtherTok{\textless{}{-}}\NormalTok{ lf\_flow\_raw}\SpecialCharTok{$}\NormalTok{Date}
\end{Highlighting}
\end{Shaded}

\hypertarget{derive-flow-statistics}{%
\section{Derive flow statistics}\label{derive-flow-statistics}}

\hypertarget{high-flow}{%
\subsection{High Flow}\label{high-flow}}

\hypertarget{amax}{%
\subsubsection{AMAX}\label{amax}}

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{MIN\_DAYS\_PER\_YEAR }\OtherTok{\textless{}{-}} \DecValTok{300} \CommentTok{\# Need to agree on.}
\CommentTok{\# This value might be different by indicator}
\NormalTok{amax\_raw }\OtherTok{\textless{}{-}} \FunctionTok{as.data.frame}\NormalTok{(lf\_flow) }\SpecialCharTok{\%\textgreater{}\%}
  \FunctionTok{group\_by}\NormalTok{(year) }\SpecialCharTok{\%\textgreater{}\%}
  \FunctionTok{summarise}\NormalTok{(}\AttributeTok{count=}\FunctionTok{n}\NormalTok{(), }\AttributeTok{amax=}\FunctionTok{max}\NormalTok{(flow, }\AttributeTok{na.rm=}\NormalTok{T),}
            \AttributeTok{doy=}\FunctionTok{which.max}\NormalTok{(flow), }\AttributeTok{date=}\NormalTok{date[doy]) }\SpecialCharTok{\%\textgreater{}\%} 
\NormalTok{  dplyr}\SpecialCharTok{::}\FunctionTok{filter}\NormalTok{(count }\SpecialCharTok{\textgreater{}}\NormalTok{ MIN\_DAYS\_PER\_YEAR)}

\NormalTok{amax\_out }\OtherTok{\textless{}{-}}\NormalTok{ amax\_raw[,}\FunctionTok{c}\NormalTok{(}\DecValTok{1}\NormalTok{,}\DecValTok{3}\NormalTok{,}\DecValTok{5}\NormalTok{,}\DecValTok{4}\NormalTok{)]}
\FunctionTok{colnames}\NormalTok{(amax\_out) }\OtherTok{\textless{}{-}} \FunctionTok{c}\NormalTok{(}\StringTok{"YEAR"}\NormalTok{, }\StringTok{"AMAX"}\NormalTok{, }\StringTok{"DATE"}\NormalTok{, }\StringTok{"DOY"}\NormalTok{)}

\FunctionTok{write\_csv}\NormalTok{(amax\_raw, }\FunctionTok{paste0}\NormalTok{(}\StringTok{"./Data/AM\_raw\_"}\NormalTok{, Station, }\StringTok{"\_"}\NormalTok{, Agency, }\StringTok{".csv"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}

\includegraphics{workflow_files/figure-latex/amaxplot-1.pdf}

\hypertarget{peaks-over-threshold}{%
\subsubsection{Peaks-over-Threshold}\label{peaks-over-threshold}}

Here a monthly threshold is determined by taking the POT3 threshold (an
average of 3 POT events per year) which equated to an annual probability
of exceedence of 0.81\%.

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{vmt\_pot }\OtherTok{\textless{}{-}}\NormalTok{ lfstat}\SpecialCharTok{::}\FunctionTok{vary\_threshold}\NormalTok{(lf\_flow,}
                      \AttributeTok{varying=}\StringTok{"monthly"}\NormalTok{,}
                      \AttributeTok{fun=}\ControlFlowTok{function}\NormalTok{(x)\{}\FunctionTok{quantile}\NormalTok{(x, }\AttributeTok{probs=}\FunctionTok{c}\NormalTok{(}\FloatTok{0.992}\NormalTok{), }\AttributeTok{na.rm=}\NormalTok{T)\})}

\NormalTok{lf\_flow}\SpecialCharTok{$}\NormalTok{threshold }\OtherTok{\textless{}{-}} \FunctionTok{as.vector}\NormalTok{(vmt\_pot)}

\NormalTok{vmt\_summary }\OtherTok{\textless{}{-}}\NormalTok{ lf\_flow }\SpecialCharTok{\%\textgreater{}\%} 
  \FunctionTok{group\_by}\NormalTok{(month) }\SpecialCharTok{\%\textgreater{}\%} 
  \FunctionTok{summarise}\NormalTok{(}\AttributeTok{threshold=}\FunctionTok{mean}\NormalTok{(threshold))}

\NormalTok{lf\_flowPOT }\OtherTok{\textless{}{-}}\NormalTok{ lf\_flow}
\NormalTok{lf\_flowPOT}\SpecialCharTok{$}\NormalTok{flow[}\FunctionTok{is.na}\NormalTok{(lf\_flowPOT}\SpecialCharTok{$}\NormalTok{flow)] }\OtherTok{\textless{}{-}} \SpecialCharTok{{-}}\DecValTok{9999}
\NormalTok{peaks }\OtherTok{\textless{}{-}}\NormalTok{ ilaprosUtils}\SpecialCharTok{::}\FunctionTok{extractPeaks}\NormalTok{(}\AttributeTok{vecObs=}\NormalTok{lf\_flowPOT}\SpecialCharTok{$}\NormalTok{flow, }\AttributeTok{mintimeDiff=}\DecValTok{7}\NormalTok{)}
\NormalTok{pot\_raw }\OtherTok{\textless{}{-}}\NormalTok{ lf\_flow[((lf\_flow}\SpecialCharTok{$}\NormalTok{flow }\SpecialCharTok{\textgreater{}}\NormalTok{ lf\_flow}\SpecialCharTok{$}\NormalTok{threshold) }\SpecialCharTok{\&}\NormalTok{ (peaks}\SpecialCharTok{==}\DecValTok{1}\NormalTok{)), ]}
\FunctionTok{write\_csv}\NormalTok{(pot\_raw, }\FunctionTok{paste0}\NormalTok{(}\StringTok{"./Data/POT\_raw\_"}\NormalTok{, Station , }\StringTok{"\_"}\NormalTok{, Agency, }\StringTok{".csv"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}

\includegraphics{workflow_files/figure-latex/potplot-1.pdf}

\hypertarget{low-flow}{%
\subsection{Low flow}\label{low-flow}}

\hypertarget{percentiles-of-flow}{%
\subsubsection{Percentiles of flow}\label{percentiles-of-flow}}

We calculate the annual and seasonal maximum and minimum, and the 5th,
70th, 90th, and 95th percentiles of flow. Seasons are actually just
yearly quarters (JFM, AMJ, JAS, OND) to allow for seasonal comparability
across the network.

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{lf\_seas\_fun }\OtherTok{\textless{}{-}} \ControlFlowTok{function}\NormalTok{(lf\_flow, }\AttributeTok{qxx=}\FloatTok{0.9}\NormalTok{)\{}
  \FunctionTok{apply.seasonal}\NormalTok{(lf\_xts, }\AttributeTok{fun=}\NormalTok{\textbackslash{}(x)\{}\FunctionTok{quantile}\NormalTok{(x,qxx,}\AttributeTok{na.rm=}\NormalTok{T)\},}
                 \AttributeTok{varying=}\FunctionTok{c}\NormalTok{(}\StringTok{"Qu1"}\OtherTok{=}\StringTok{"1999{-}01{-}01"}\NormalTok{,}\StringTok{"Qu2"}\OtherTok{=}\StringTok{"1999{-}04{-}01"}\NormalTok{,}
                           \StringTok{"Qu3"}\OtherTok{=}\StringTok{"1999{-}07{-}01"}\NormalTok{,}\StringTok{"Qu4"}\OtherTok{=}\StringTok{"1999{-}10{-}01"}\NormalTok{)) }\SpecialCharTok{\%\textgreater{}\%}
    \FunctionTok{as.data.frame}\NormalTok{() }\SpecialCharTok{\%\textgreater{}\%}
    \FunctionTok{mutate}\NormalTok{(}\AttributeTok{year=}\FunctionTok{rownames}\NormalTok{(.), }\AttributeTok{Qxx=}\DecValTok{1}\SpecialCharTok{{-}}\NormalTok{qxx) }\SpecialCharTok{\%\textgreater{}\%}
    \FunctionTok{pivot\_longer}\NormalTok{(}\AttributeTok{cols=}\DecValTok{1}\SpecialCharTok{:}\DecValTok{4}\NormalTok{, }\AttributeTok{names\_to=}\StringTok{"Season"}\NormalTok{, }\AttributeTok{values\_to=}\StringTok{"Flow"}\NormalTok{)}
\NormalTok{\}}

\NormalTok{lf\_year\_fun }\OtherTok{\textless{}{-}} \ControlFlowTok{function}\NormalTok{(lf\_flow, }\AttributeTok{qxx=}\FloatTok{0.9}\NormalTok{)\{}
    \FunctionTok{apply.yearly}\NormalTok{(lf\_xts, }\AttributeTok{FUN=}\NormalTok{\textbackslash{}(x)\{}\FunctionTok{quantile}\NormalTok{(x,qxx,}\AttributeTok{na.rm=}\NormalTok{T)\}) }\SpecialCharTok{\%\textgreater{}\%}
    \FunctionTok{as.data.frame}\NormalTok{() }\SpecialCharTok{\%\textgreater{}\%}
    \FunctionTok{mutate}\NormalTok{(}\AttributeTok{year=}\NormalTok{lubridate}\SpecialCharTok{::}\FunctionTok{year}\NormalTok{(}\FunctionTok{rownames}\NormalTok{(.)), }\AttributeTok{Qxx=}\DecValTok{1}\SpecialCharTok{{-}}\NormalTok{qxx)}
\NormalTok{\}}

\NormalTok{lf\_month\_fun }\OtherTok{\textless{}{-}} \ControlFlowTok{function}\NormalTok{(lf\_flow, }\AttributeTok{qxx=}\FloatTok{0.9}\NormalTok{)\{}
    \FunctionTok{apply.monthly}\NormalTok{(lf\_xts, }\AttributeTok{FUN=}\NormalTok{\textbackslash{}(x)\{}\FunctionTok{quantile}\NormalTok{(x,qxx,}\AttributeTok{na.rm=}\NormalTok{T)\}) }\SpecialCharTok{\%\textgreater{}\%}
    \FunctionTok{as.data.frame}\NormalTok{() }\SpecialCharTok{\%\textgreater{}\%}
    \FunctionTok{mutate}\NormalTok{(}\AttributeTok{year=}\NormalTok{lubridate}\SpecialCharTok{::}\FunctionTok{year}\NormalTok{(}\FunctionTok{rownames}\NormalTok{(.)),}
           \AttributeTok{month=}\NormalTok{lubridate}\SpecialCharTok{::}\FunctionTok{month}\NormalTok{(}\FunctionTok{rownames}\NormalTok{(.)),}
           \AttributeTok{Qxx=}\DecValTok{1}\SpecialCharTok{{-}}\NormalTok{qxx)}
\NormalTok{\}}

\NormalTok{lf\_xts }\OtherTok{\textless{}{-}} \FunctionTok{as.xts}\NormalTok{(lf\_flow)}

\NormalTok{percentiles }\OtherTok{\textless{}{-}} \FunctionTok{list}\NormalTok{(}\AttributeTok{max=}\DecValTok{1}\NormalTok{, }\AttributeTok{Q95=}\FloatTok{0.05}\NormalTok{, }\AttributeTok{Q90=}\FloatTok{0.10}\NormalTok{, }\AttributeTok{Med=}\FloatTok{0.5}\NormalTok{, }\AttributeTok{Q70=}\FloatTok{0.30}\NormalTok{, }\AttributeTok{Q05=}\FloatTok{0.95}\NormalTok{, }\AttributeTok{min=}\DecValTok{0}\NormalTok{)}
\NormalTok{lf\_year }\OtherTok{\textless{}{-}} \FunctionTok{lapply}\NormalTok{(percentiles, \textbackslash{}(x)\{}\FunctionTok{lf\_year\_fun}\NormalTok{(lf\_xts, x)\})}
\NormalTok{lf\_year\_long }\OtherTok{\textless{}{-}} \FunctionTok{as.data.frame}\NormalTok{(}\FunctionTok{do.call}\NormalTok{(rbind,lf\_year))}
\NormalTok{lf\_year }\OtherTok{\textless{}{-}}\NormalTok{ lf\_year\_long }\SpecialCharTok{\%\textgreater{}\%} 
  \FunctionTok{pivot\_wider}\NormalTok{(}\AttributeTok{id\_cols=}\FunctionTok{c}\NormalTok{(year), }\AttributeTok{names\_from=}\NormalTok{Qxx, }\AttributeTok{names\_prefix=}\StringTok{"Q"}\NormalTok{,}
              \AttributeTok{values\_from=}\StringTok{"discharge"}\NormalTok{)}
\FunctionTok{colnames}\NormalTok{(lf\_year) }\OtherTok{\textless{}{-}} 
  \FunctionTok{c}\NormalTok{(}\StringTok{"Year"}\NormalTok{, }\StringTok{"MAX"}\NormalTok{, }\StringTok{"Q95"}\NormalTok{, }\StringTok{"Q90"}\NormalTok{, }\StringTok{"Q70"}\NormalTok{, }\StringTok{"Median"}\NormalTok{, }\StringTok{"Q05"}\NormalTok{, }\StringTok{"MIN"}\NormalTok{)}
\FunctionTok{write\_csv}\NormalTok{(lf\_year, }\FunctionTok{paste0}\NormalTok{(}\StringTok{"./Data/yearlyPercentiles\_"}\NormalTok{, }
\NormalTok{                          Station, }\StringTok{"\_"}\NormalTok{, Agency, }\StringTok{".csv"}\NormalTok{))}
\NormalTok{lf\_year\_long}\SpecialCharTok{$}\NormalTok{Qxx }\OtherTok{\textless{}{-}} \FunctionTok{factor}\NormalTok{(lf\_year\_long}\SpecialCharTok{$}\NormalTok{Qxx, }\AttributeTok{levels=}\FunctionTok{c}\NormalTok{(}\DecValTok{0}\NormalTok{,}\FloatTok{0.05}\NormalTok{,}\FloatTok{0.5}\NormalTok{,}\FloatTok{0.7}\NormalTok{,}\FloatTok{0.9}\NormalTok{,}\FloatTok{0.95}\NormalTok{,}\DecValTok{1}\NormalTok{),}
                           \AttributeTok{labels=}\FunctionTok{c}\NormalTok{(}\StringTok{"MAX"}\NormalTok{,}\StringTok{"Q05"}\NormalTok{, }\StringTok{"Med"}\NormalTok{, }\StringTok{"Q70"}\NormalTok{, }\StringTok{"Q90"}\NormalTok{, }\StringTok{"Q95"}\NormalTok{, }\StringTok{"MIN"}\NormalTok{))}

\NormalTok{lf\_seasonal }\OtherTok{\textless{}{-}} \FunctionTok{lapply}\NormalTok{(percentiles, \textbackslash{}(x)\{}\FunctionTok{lf\_seas\_fun}\NormalTok{(lf\_xts, x)\})}
\NormalTok{lf\_seasonal\_long }\OtherTok{\textless{}{-}} \FunctionTok{as.data.frame}\NormalTok{(}\FunctionTok{do.call}\NormalTok{(rbind,lf\_seasonal))}
\NormalTok{lf\_seasonal }\OtherTok{\textless{}{-}}\NormalTok{ lf\_seasonal\_long }\SpecialCharTok{\%\textgreater{}\%} 
  \FunctionTok{pivot\_wider}\NormalTok{(}\AttributeTok{id\_cols=}\FunctionTok{c}\NormalTok{(year, Season), }\AttributeTok{names\_from=}\NormalTok{Qxx, }\AttributeTok{names\_prefix=}\StringTok{"Q"}\NormalTok{,}
              \AttributeTok{values\_from=}\StringTok{"Flow"}\NormalTok{)}
\FunctionTok{colnames}\NormalTok{(lf\_seasonal) }\OtherTok{\textless{}{-}} 
  \FunctionTok{c}\NormalTok{(}\StringTok{"Year"}\NormalTok{, }\StringTok{"Season"}\NormalTok{, }\StringTok{"MAX"}\NormalTok{, }\StringTok{"Q95"}\NormalTok{, }\StringTok{"Q90"}\NormalTok{, }\StringTok{"Q70"}\NormalTok{, }\StringTok{"Median"}\NormalTok{, }\StringTok{"Q05"}\NormalTok{, }\StringTok{"MIN"}\NormalTok{)}
\FunctionTok{write\_csv}\NormalTok{(lf\_seasonal, }\FunctionTok{paste0}\NormalTok{(}\StringTok{"./Data/seasonalPercentiles\_"}\NormalTok{, }
\NormalTok{                          Station, }\StringTok{"\_"}\NormalTok{, Agency, }\StringTok{".csv"}\NormalTok{))}

\NormalTok{lf\_monthly }\OtherTok{\textless{}{-}} \FunctionTok{lapply}\NormalTok{(percentiles, \textbackslash{}(x)\{}\FunctionTok{lf\_month\_fun}\NormalTok{(lf\_xts, x)\})}
\NormalTok{lf\_monthly\_long }\OtherTok{\textless{}{-}} \FunctionTok{as.data.frame}\NormalTok{(}\FunctionTok{do.call}\NormalTok{(rbind,lf\_monthly))}
\NormalTok{lf\_monthly }\OtherTok{\textless{}{-}}\NormalTok{ lf\_monthly\_long }\SpecialCharTok{\%\textgreater{}\%} 
  \FunctionTok{pivot\_wider}\NormalTok{(}\AttributeTok{id\_cols=}\FunctionTok{c}\NormalTok{(year, month), }\AttributeTok{names\_from=}\NormalTok{Qxx, }\AttributeTok{names\_prefix=}\StringTok{"Q"}\NormalTok{,}
              \AttributeTok{values\_from=}\StringTok{"discharge"}\NormalTok{)}
\FunctionTok{colnames}\NormalTok{(lf\_monthly) }\OtherTok{\textless{}{-}} 
  \FunctionTok{c}\NormalTok{(}\StringTok{"Year"}\NormalTok{, }\StringTok{"Month"}\NormalTok{, }\StringTok{"MAX"}\NormalTok{, }\StringTok{"Q95"}\NormalTok{, }\StringTok{"Q90"}\NormalTok{, }\StringTok{"Q70"}\NormalTok{, }\StringTok{"Median"}\NormalTok{, }\StringTok{"Q05"}\NormalTok{, }\StringTok{"MIN"}\NormalTok{)}
\FunctionTok{write\_csv}\NormalTok{(lf\_monthly, }\FunctionTok{paste0}\NormalTok{(}\StringTok{"./Data/monthlyPercentiles\_"}\NormalTok{, }
\NormalTok{                          Station, }\StringTok{"\_"}\NormalTok{, Agency, }\StringTok{".csv"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}

\includegraphics{workflow_files/figure-latex/monthlymean-1.pdf}

\hypertarget{drought-events}{%
\subsubsection{Drought events}\label{drought-events}}

Using the \texttt{lfstat} package, we calculate the monthly varying 20\%
threshold, and use that to find periods of drought where this threshold
is not exceeded for a length of time.

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{vmt\_drought }\OtherTok{\textless{}{-}} \FunctionTok{vary\_threshold}\NormalTok{(lf\_flow,}
                      \AttributeTok{varying=}\StringTok{"monthly"}\NormalTok{,}
                      \AttributeTok{fun=}\ControlFlowTok{function}\NormalTok{(x)\{}\FunctionTok{quantile}\NormalTok{(x, }\AttributeTok{probs=}\FunctionTok{c}\NormalTok{(}\FloatTok{0.2}\NormalTok{))\})}
\NormalTok{droughts }\OtherTok{\textless{}{-}} \FunctionTok{find\_droughts}\NormalTok{(lf\_flow, vmt\_drought, }\AttributeTok{varying=}\StringTok{"monthly"}\NormalTok{)}
\FunctionTok{write\_csv}\NormalTok{(}
  \FunctionTok{summary}\NormalTok{(droughts), }\AttributeTok{file=}\FunctionTok{paste0}\NormalTok{(}\StringTok{"./Data/droughts\_"}\NormalTok{, Station, }\StringTok{"\_"}\NormalTok{, Agency, }\StringTok{".csv"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}

\hypertarget{n-day-minima}{%
\subsubsection{N-day minima}\label{n-day-minima}}

We also calculate the mean annual flow minima based on 7 and 30 day
accumulations.

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{mean\_annual\_min\_7 }\OtherTok{\textless{}{-}} \FunctionTok{MAM}\NormalTok{(lf\_flow, }\DecValTok{7}\NormalTok{, }\AttributeTok{yearly=}\ConstantTok{TRUE}\NormalTok{)}
\NormalTok{mean\_annual\_min\_30 }\OtherTok{\textless{}{-}} \FunctionTok{MAM}\NormalTok{(lf\_flow, }\DecValTok{30}\NormalTok{, }\AttributeTok{yearly=}\ConstantTok{TRUE}\NormalTok{)}
\NormalTok{mean\_flow }\OtherTok{\textless{}{-}} \FunctionTok{meanflow}\NormalTok{(lf\_flow, }\AttributeTok{yearly=}\ConstantTok{TRUE}\NormalTok{)}

\NormalTok{mean\_lowflow }\OtherTok{\textless{}{-}} \FunctionTok{data.frame}\NormalTok{(}\AttributeTok{Year=}\FunctionTok{min}\NormalTok{(lf\_flow}\SpecialCharTok{$}\NormalTok{year)}\SpecialCharTok{:}\FunctionTok{max}\NormalTok{(lf\_flow}\SpecialCharTok{$}\NormalTok{year),}
                           \AttributeTok{MAM7=}\NormalTok{mean\_annual\_min\_7}\SpecialCharTok{$}\NormalTok{MAn,}
                           \AttributeTok{MAM30=}\NormalTok{mean\_annual\_min\_30}\SpecialCharTok{$}\NormalTok{MAn,}
                           \AttributeTok{MAF=}\NormalTok{mean\_flow}\SpecialCharTok{$}\NormalTok{flow)}

\FunctionTok{write\_csv}\NormalTok{(mean\_lowflow, }\FunctionTok{paste0}\NormalTok{(}\StringTok{"./Data/mean\_lowflow\_"}\NormalTok{, Station, }\StringTok{"\_"}\NormalTok{, Agency, }\StringTok{".csv"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}

\hypertarget{trend-analysis-and-plots}{%
\section{Trend analysis and plots}\label{trend-analysis-and-plots}}

We test the yearly quantile data for significant breakpoints (examining
daily data gives very high likelihood of breakpoints being detected due
to very narrow confidence bands conferred by large datasets.)

\hypertarget{check-for-breakpoints}{%
\subsection{Check for breakpoints}\label{check-for-breakpoints}}

\begin{longtable}[]{@{}lrrrrr@{}}
\toprule()
& Pettitt.bp.1 & Pettitt.p & Chow.test.F & Chow.test.p & CPT.max.bp \\
\midrule()
\endhead
MAX & 1988 & 0.6984209 & 0.4832118 & 0.6198294 & 1 \\
Q95 & 1997 & 0.0212907 & 0.0204811 & 0.9797359 & 1 \\
Q90 & 1997 & 0.0169167 & 0.0553620 & 0.9462042 & 1 \\
Q70 & 1987 & 0.6243279 & 0.0105043 & 0.9895530 & 1 \\
Median & 1997 & 0.3391481 & 0.3322652 & 0.7189682 & 1 \\
Q05 & 1992 & 0.1092478 & 0.4322425 & 0.6516058 & 1 \\
MIN & 1996 & 0.0305652 & 1.0635907 & 0.3533753 & 1 \\
amax & 1970 & 1.0000000 & 0.8946598 & 0.4158916 & NA \\
MAn\_30 & 1997 & 0.0111583 & 0.0811588 & 0.9221762 & 1 \\
MAn\_7 & 1996 & 0.0169167 & 0.4911516 & 0.6150268 & 1 \\
\bottomrule()
\end{longtable}

\hypertarget{check-for-autocorrelation}{%
\subsection{Check for autocorrelation}\label{check-for-autocorrelation}}

We plot the autocorrelation of the different percentiles of flow, AMAX
and POT data.

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{daily\_autocor }\OtherTok{\textless{}{-}} \FunctionTok{acf}\NormalTok{(lf\_flow}\SpecialCharTok{$}\NormalTok{flow, }\AttributeTok{ci.type=}\StringTok{"ma"}\NormalTok{, }\AttributeTok{plot=}\NormalTok{F)}
\NormalTok{amax\_autocor }\OtherTok{\textless{}{-}} \FunctionTok{acf}\NormalTok{(amax\_raw}\SpecialCharTok{$}\NormalTok{amax, }\AttributeTok{ci.type=}\StringTok{"ma"}\NormalTok{, }\AttributeTok{plot=}\NormalTok{F)}
\NormalTok{pot\_autocor }\OtherTok{\textless{}{-}} \FunctionTok{acf}\NormalTok{(pot\_raw}\SpecialCharTok{$}\NormalTok{flow, }\AttributeTok{ci.type=}\StringTok{"ma"}\NormalTok{, }\AttributeTok{plot=}\NormalTok{F)}
\NormalTok{low\_ac\_monthly }\OtherTok{\textless{}{-}}\NormalTok{ lf\_monthly\_long }\SpecialCharTok{\%\textgreater{}\%}
\NormalTok{  dplyr}\SpecialCharTok{::}\FunctionTok{filter}\NormalTok{(Qxx}\SpecialCharTok{==}\FloatTok{0.95} \SpecialCharTok{\&} \SpecialCharTok{!}\FunctionTok{is.na}\NormalTok{(discharge)) }\SpecialCharTok{\%\textgreater{}\%}
  \FunctionTok{select}\NormalTok{(discharge) }\SpecialCharTok{\%\textgreater{}\%}
  \FunctionTok{acf}\NormalTok{(}\AttributeTok{ci.type=}\StringTok{"ma"}\NormalTok{, }\AttributeTok{plot=}\NormalTok{F)}
\NormalTok{low\_ac\_q1 }\OtherTok{\textless{}{-}}\NormalTok{ lf\_seasonal\_long }\SpecialCharTok{\%\textgreater{}\%} 
\NormalTok{  dplyr}\SpecialCharTok{::}\FunctionTok{filter}\NormalTok{(Qxx}\SpecialCharTok{==}\FloatTok{0.95} \SpecialCharTok{\&}\NormalTok{ Season}\SpecialCharTok{==}\StringTok{"Qu1"} \SpecialCharTok{\&} \SpecialCharTok{!}\FunctionTok{is.na}\NormalTok{(Flow)) }\SpecialCharTok{\%\textgreater{}\%}
  \FunctionTok{select}\NormalTok{(Flow) }\SpecialCharTok{\%\textgreater{}\%}
  \FunctionTok{acf}\NormalTok{(}\AttributeTok{ci.type=}\StringTok{"ma"}\NormalTok{, }\AttributeTok{plot=}\NormalTok{F)}
\NormalTok{low\_ac\_Jan }\OtherTok{\textless{}{-}}\NormalTok{  lf\_monthly\_long }\SpecialCharTok{\%\textgreater{}\%}
\NormalTok{  dplyr}\SpecialCharTok{::}\FunctionTok{filter}\NormalTok{(Qxx}\SpecialCharTok{==}\FloatTok{0.95} \SpecialCharTok{\&}\NormalTok{ month}\SpecialCharTok{==}\DecValTok{1} \SpecialCharTok{\&} \SpecialCharTok{!}\FunctionTok{is.na}\NormalTok{(discharge)) }\SpecialCharTok{\%\textgreater{}\%}
  \FunctionTok{select}\NormalTok{(discharge) }\SpecialCharTok{\%\textgreater{}\%}
  \FunctionTok{acf}\NormalTok{(}\AttributeTok{ci.type=}\StringTok{"ma"}\NormalTok{, }\AttributeTok{plot=}\NormalTok{F)}
\end{Highlighting}
\end{Shaded}

\includegraphics{workflow_files/figure-latex/autocorplots-1.pdf}

\hypertarget{mann-kendall-tests}{%
\subsection{Mann-Kendall Tests}\label{mann-kendall-tests}}

We perform Mann-Kendall tests, using significance derived from
block-bootstrapping

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{mk\_yearly }\OtherTok{\textless{}{-}} \FunctionTok{lapply}\NormalTok{(lf\_data[,}\SpecialCharTok{{-}}\DecValTok{1}\NormalTok{], MKZ\_blockboot)}

\NormalTok{mk\_yearly }\OtherTok{\textless{}{-}} \FunctionTok{as.data.frame}\NormalTok{(}\FunctionTok{do.call}\NormalTok{(rbind, mk\_yearly))}

\NormalTok{mk\_yearly}\SpecialCharTok{$}\NormalTok{pwmkZ }\OtherTok{\textless{}{-}} \ConstantTok{NA}
\NormalTok{mk\_yearly}\SpecialCharTok{$}\NormalTok{pwmkP }\OtherTok{\textless{}{-}} \ConstantTok{NA}
\NormalTok{mk\_yearly}\SpecialCharTok{$}\NormalTok{pwmkTSE }\OtherTok{\textless{}{-}} \ConstantTok{NA}

\ControlFlowTok{for}\NormalTok{(i }\ControlFlowTok{in} \DecValTok{1}\SpecialCharTok{:}\FunctionTok{ncol}\NormalTok{(lf\_data[,}\SpecialCharTok{{-}}\DecValTok{1}\NormalTok{]))\{}
\NormalTok{  z }\OtherTok{\textless{}{-}} \FunctionTok{pwmk}\NormalTok{(lf\_data[,i])}
\NormalTok{  mk\_yearly}\SpecialCharTok{$}\NormalTok{pwmkZ[i] }\OtherTok{\textless{}{-}}\NormalTok{ z[}\DecValTok{1}\NormalTok{]}
\NormalTok{  mk\_yearly}\SpecialCharTok{$}\NormalTok{pwmkP[i] }\OtherTok{\textless{}{-}}\NormalTok{ z[}\DecValTok{4}\NormalTok{]}
\NormalTok{  mk\_yearly}\SpecialCharTok{$}\NormalTok{pwmkTSE[i] }\OtherTok{\textless{}{-}}\NormalTok{ z[}\DecValTok{2}\NormalTok{]}
\NormalTok{\}}
\end{Highlighting}
\end{Shaded}

\begin{longtable}[]{@{}
  >{\raggedright\arraybackslash}p{(\columnwidth - 14\tabcolsep) * \real{0.0614}}
  >{\raggedright\arraybackslash}p{(\columnwidth - 14\tabcolsep) * \real{0.0965}}
  >{\raggedright\arraybackslash}p{(\columnwidth - 14\tabcolsep) * \real{0.1053}}
  >{\raggedright\arraybackslash}p{(\columnwidth - 14\tabcolsep) * \real{0.1140}}
  >{\raggedright\arraybackslash}p{(\columnwidth - 14\tabcolsep) * \real{0.1404}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 14\tabcolsep) * \real{0.1404}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 14\tabcolsep) * \real{0.2018}}
  >{\raggedleft\arraybackslash}p{(\columnwidth - 14\tabcolsep) * \real{0.1404}}@{}}
\toprule()
\begin{minipage}[b]{\linewidth}\raggedright
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
MKZ
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
MKZ 2.5\%ile
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
MKZ 97.5\%ile
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
MKZ significant
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
prewhitened MKZ
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
prewhitened MKZ pvalue
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedleft
prewhitened TSE
\end{minipage} \\
\midrule()
\endhead
MAX & 1.177837 & -1.951177 & 1.870372 & FALSE & 10.239 & 0.000 &
0.059 \\
Q95 & 1.982648 & -2.423779 & 2.423886 & FALSE & 1.104 & 0.270 & 0.038 \\
Q90 & 2.559538 & -2.28483 & 2.360951 & TRUE & 1.071 & 0.284 & 0.000 \\
Q70 & -0.3817817 & -2.381615 & 2.260013 & FALSE & 1.640 & 0.101 &
0.000 \\
Median & 0.9586317 & -2.350707 & 2.228526 & FALSE & -0.636 & 0.525 &
-0.001 \\
Q05 & 1.998064 & -1.845427 & 1.845467 & TRUE & 0.301 & 0.763 & 0.000 \\
MIN & 1.593145 & -2.418073 & 2.438346 & FALSE & 1.506 & 0.132 & 0.011 \\
amax & 0.7241469 & -1.992184 & 1.905833 & FALSE & 1.046 & 0.296 &
0.000 \\
MAn\_30 & 2.745307 & -2.413863 & 2.536362 & TRUE & 0.880 & 0.379 &
0.032 \\
MAn\_7 & 1.908909 & -2.464365 & 2.45523 & FALSE & 1.355 & 0.175 &
0.000 \\
\bottomrule()
\end{longtable}

\hypertarget{theil-sen-slope}{%
\subsection{Theil-Sen slope}\label{theil-sen-slope}}

\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\# Trends in high/mid/low percentiles}

\NormalTok{lf\_data }\OtherTok{\textless{}{-}}\NormalTok{ plyr}\SpecialCharTok{::}\FunctionTok{join\_all}\NormalTok{(}\AttributeTok{dfs=}\FunctionTok{list}\NormalTok{(lf\_year\_temp, amax\_raw[,}\FunctionTok{c}\NormalTok{(}\DecValTok{1}\NormalTok{,}\DecValTok{3}\NormalTok{)], mean\_annual\_min\_30, mean\_annual\_min\_7), }\AttributeTok{type=}\StringTok{\textquotesingle{}full\textquotesingle{}}\NormalTok{, }\AttributeTok{by=}\StringTok{"year"}\NormalTok{)}

\NormalTok{MKp }\OtherTok{\textless{}{-}} \FunctionTok{t}\NormalTok{(}\FunctionTok{apply}\NormalTok{(lf\_data[,}\SpecialCharTok{{-}}\DecValTok{1}\NormalTok{], }\DecValTok{2}\NormalTok{ , \textbackslash{}(x)}\FunctionTok{unlist}\NormalTok{(}\FunctionTok{MannKendall}\NormalTok{(x))[}\DecValTok{1}\SpecialCharTok{:}\DecValTok{2}\NormalTok{]))}
\NormalTok{TSEp }\OtherTok{\textless{}{-}} \FunctionTok{t}\NormalTok{(}\FunctionTok{sapply}\NormalTok{(}\FunctionTok{colnames}\NormalTok{(lf\_data)[}\SpecialCharTok{{-}}\DecValTok{1}\NormalTok{],\textbackslash{}(x)\{}
  \FunctionTok{zyp.sen}\NormalTok{(}\FunctionTok{as.formula}\NormalTok{(}\FunctionTok{paste0}\NormalTok{(x,}\StringTok{"\textasciitilde{}year"}\NormalTok{)), }\AttributeTok{data=}\NormalTok{lf\_data)}\SpecialCharTok{$}\NormalTok{coefficients\}))}
\end{Highlighting}
\end{Shaded}

\begin{longtable}[]{@{}llrrrr@{}}
\toprule()
& quantile & MKZ & MK\_pvalue & TSE & TSE\_intercept \\
\midrule()
\endhead
MAX & MAX & 0.1146448 & 0.2388616 & 0.0500000 & -90.6000000 \\
Q95 & Q95 & 0.1930676 & 0.0474068 & 0.0003056 & -0.5516111 \\
Q90 & Q90 & 0.2489192 & 0.0104811 & 0.0003913 & -0.7157826 \\
Q70 & Q70 & -0.0376914 & 0.7026232 & -0.0003437 & 0.9081562 \\
Median & Median & 0.0935537 & 0.3377442 & 0.0002936 & -0.4750894 \\
Q05 & Q05 & 0.1937255 & 0.0457097 & 0.0136333 & -24.8335333 \\
MIN & MIN & 0.1557361 & 0.1111277 & 0.0002308 & -0.4195385 \\
amax & amax & 0.0723713 & 0.4689755 & 0.0288902 & NA \\
MAn\_30 & MAn\_30 & 0.2658823 & 0.0060455 & 0.0004007 & -0.7349847 \\
MAn\_7 & MAn\_7 & 0.1853162 & 0.0562739 & 0.0003077 & -0.5629341 \\
\bottomrule()
\end{longtable}

\hypertarget{temporal-clustering}{%
\subsection{Temporal clustering}\label{temporal-clustering}}

\hypertarget{droughts}{%
\subsubsection{Droughts}\label{droughts}}

Here we examine whether there are any significant clusters or prolonged
absences of drought events, only looking at start dates.

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{summdrought }\OtherTok{\textless{}{-}} \FunctionTok{summary}\NormalTok{(droughts)}
\NormalTok{drght\_per\_yr }\OtherTok{\textless{}{-}} \FunctionTok{findHydrolYr}\NormalTok{(}\FunctionTok{ymd}\NormalTok{(summdrought}\SpecialCharTok{$}\NormalTok{time), }\AttributeTok{starttime=}\StringTok{"2000{-}10{-}01"}\NormalTok{) }\SpecialCharTok{\%\textgreater{}\%}
  \FunctionTok{group\_by}\NormalTok{(yr) }\SpecialCharTok{\%\textgreater{}\%} 
  \FunctionTok{summarise}\NormalTok{(}\AttributeTok{Nlow=}\FunctionTok{n}\NormalTok{())}
\end{Highlighting}
\end{Shaded}

\begin{verbatim}
## Warning: All formats failed to parse. No formats found.
\end{verbatim}

\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{MannKendall}\NormalTok{(drght\_per\_yr}\SpecialCharTok{$}\NormalTok{Nlow)}
\end{Highlighting}
\end{Shaded}

\begin{verbatim}
## tau = -0.0573, 2-sided pvalue =0.5988
\end{verbatim}

\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{var}\NormalTok{(drght\_per\_yr}\SpecialCharTok{$}\NormalTok{Nlow)}\SpecialCharTok{/}\FunctionTok{mean}\NormalTok{(drght\_per\_yr}\SpecialCharTok{$}\NormalTok{Nlow)}
\end{Highlighting}
\end{Shaded}

\begin{verbatim}
## [1] 1.856085
\end{verbatim}

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{lf\_year }\OtherTok{\textless{}{-}} \FunctionTok{left\_join}\NormalTok{(lf\_year, drght\_per\_yr, }\AttributeTok{by=}\FunctionTok{c}\NormalTok{(}\StringTok{"Year"}\OtherTok{=}\StringTok{"yr"}\NormalTok{))}

\NormalTok{DC }\OtherTok{\textless{}{-}} \FunctionTok{denclust}\NormalTok{(summdrought}\SpecialCharTok{$}\NormalTok{time, }\AttributeTok{bwi=}\DecValTok{365}\SpecialCharTok{*}\DecValTok{4}\NormalTok{,}
    \AttributeTok{plotfilename=}\FunctionTok{paste0}\NormalTok{(}\StringTok{"./droughtclustering\_"}\NormalTok{, Station,}\StringTok{"\_"}\NormalTok{, Agency, }\StringTok{".png"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}

\begin{verbatim}
## [1] "2 significant clusters and 1 significant absences."
\end{verbatim}

\includegraphics{workflow_files/figure-latex/droughtclust-1.pdf} Here we
see that the dispersion of droughts is 1.8560847. If this is a lot less
than 1, then it shows signs of under dispersion compared to a Poisson
process (independent arrivals).

\hypertarget{pot-events}{%
\subsubsection{POT events}\label{pot-events}}

clustering: over/underdispersion

Here we examine whether there are any significant clusters or prolonged
absences of POT events.

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{pot\_per\_year }\OtherTok{\textless{}{-}}\NormalTok{ pot\_raw }\SpecialCharTok{\%\textgreater{}\%} \FunctionTok{group\_by}\NormalTok{(year) }\SpecialCharTok{\%\textgreater{}\%}\NormalTok{ dplyr}\SpecialCharTok{::}\FunctionTok{summarise}\NormalTok{(}\AttributeTok{Npots=}\FunctionTok{n}\NormalTok{())}
\FunctionTok{MannKendall}\NormalTok{(pot\_per\_year}\SpecialCharTok{$}\NormalTok{Npots)}
\end{Highlighting}
\end{Shaded}

\begin{verbatim}
## tau = -0.00168, 2-sided pvalue =1
\end{verbatim}

\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{var}\NormalTok{(pot\_per\_year}\SpecialCharTok{$}\NormalTok{Npots)}\SpecialCharTok{/}\FunctionTok{mean}\NormalTok{(pot\_per\_year}\SpecialCharTok{$}\NormalTok{Npots)}
\end{Highlighting}
\end{Shaded}

\begin{verbatim}
## [1] 1.359763
\end{verbatim}

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{lf\_year }\OtherTok{\textless{}{-}} \FunctionTok{left\_join}\NormalTok{(lf\_year, pot\_per\_year, }\AttributeTok{by=}\FunctionTok{c}\NormalTok{(}\StringTok{"Year"}\OtherTok{=}\StringTok{"year"}\NormalTok{))}

\NormalTok{DC\_pot }\OtherTok{\textless{}{-}} \FunctionTok{denclust}\NormalTok{(pot\_raw}\SpecialCharTok{$}\NormalTok{date, }\AttributeTok{bwi=}\DecValTok{365}\SpecialCharTok{*}\DecValTok{2}\NormalTok{, }\AttributeTok{daysNotSeconds=}\ConstantTok{FALSE}\NormalTok{,}
    \AttributeTok{plotfilename=}\FunctionTok{paste0}\NormalTok{(}\StringTok{"./droughtclustering\_"}\NormalTok{, Station,}\StringTok{"\_"}\NormalTok{, Agency, }\StringTok{".png"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}

\begin{verbatim}
## [1] "1 significant clusters and 2 significant absences."
\end{verbatim}

\includegraphics{workflow_files/figure-latex/potclust-1.pdf}

Here we see that the dispersion of droughts is 1.3597627. If this is a
lot less than 1, then it shows signs of under dispersion compared to a
Poisson process (independent arrivals).

\hypertarget{trends-in-timing}{%
\subsection{Trends in timing}\label{trends-in-timing}}

\hypertarget{day-minimadroughts}{%
\subsubsection{7-day minima/droughts}\label{day-minimadroughts}}

In this section we briefly look at whether there are trends in when in
the year droughts and 7-day minima are happening.

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{drt\_yday }\OtherTok{\textless{}{-}}\NormalTok{ ((}\FunctionTok{yday}\NormalTok{(summdrought}\SpecialCharTok{$}\NormalTok{time)}\SpecialCharTok{+}\DecValTok{180}\NormalTok{) }\SpecialCharTok{\%\%} \DecValTok{365}\NormalTok{) }\SpecialCharTok{{-}} \DecValTok{180}
\NormalTok{drght\_circular }\OtherTok{\textless{}{-}} \FunctionTok{circular}\NormalTok{(}\FunctionTok{yday}\NormalTok{(summdrought}\SpecialCharTok{$}\NormalTok{time)}\SpecialCharTok{*}\DecValTok{2}\SpecialCharTok{*}\NormalTok{pi}\SpecialCharTok{/}\DecValTok{365}\NormalTok{)}
\NormalTok{rm\_circ }\OtherTok{\textless{}{-}} \FunctionTok{rollapply}\NormalTok{(drght\_circular, }
                     \AttributeTok{FUN=}\NormalTok{\textbackslash{}(x)\{}\FunctionTok{suppressWarnings}\NormalTok{(}\FunctionTok{mean.circular}\NormalTok{(x))\}, }\AttributeTok{width=}\DecValTok{50}\NormalTok{)}
\NormalTok{rm\_circ2 }\OtherTok{\textless{}{-}} \FunctionTok{rollmean}\NormalTok{(}\FunctionTok{yday}\NormalTok{(summdrought}\SpecialCharTok{$}\NormalTok{time), }\DecValTok{50}\NormalTok{)}
\end{Highlighting}
\end{Shaded}

\includegraphics{workflow_files/figure-latex/droughtcircplots-1.pdf}
\includegraphics{workflow_files/figure-latex/droughtcircplots-2.pdf}

\begin{verbatim}
## NULL
\end{verbatim}

\includegraphics{workflow_files/figure-latex/droughtcircplots-3.pdf}
\includegraphics{workflow_files/figure-latex/droughtcircplots-4.pdf}

\hypertarget{amaxpot}{%
\subsubsection{AMAX/POT}\label{amaxpot}}

In this section we briefly look at whether there are trends in when in
the year AMAX events and other POT events are happening.

\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{fhy\_pot }\OtherTok{\textless{}{-}}\NormalTok{ (}\FunctionTok{yday}\NormalTok{(pot\_raw}\SpecialCharTok{$}\NormalTok{date)}\SpecialCharTok{+}\DecValTok{180}\NormalTok{)}\SpecialCharTok{\%\%}\DecValTok{365} \SpecialCharTok{{-}} \DecValTok{180}
\NormalTok{pot\_circular }\OtherTok{\textless{}{-}} \FunctionTok{circular}\NormalTok{(fhy\_pot}\SpecialCharTok{*}\DecValTok{2}\SpecialCharTok{*}\NormalTok{pi}\SpecialCharTok{/}\DecValTok{365}\NormalTok{)}
\NormalTok{rm\_pot }\OtherTok{\textless{}{-}} \FunctionTok{rollapply}\NormalTok{(pot\_circular, }
                    \AttributeTok{FUN=}\NormalTok{\textbackslash{}(x)\{}\FunctionTok{suppressWarnings}\NormalTok{(}\FunctionTok{mean.circular}\NormalTok{(x))\}, }\AttributeTok{width=}\DecValTok{50}\NormalTok{)}
\NormalTok{rm\_pot2 }\OtherTok{\textless{}{-}} \FunctionTok{rollmean}\NormalTok{(fhy\_pot, }\DecValTok{50}\NormalTok{)}

\NormalTok{fhy\_am }\OtherTok{\textless{}{-}}\NormalTok{ (}\FunctionTok{yday}\NormalTok{(amax\_raw}\SpecialCharTok{$}\NormalTok{date)}\SpecialCharTok{+}\DecValTok{180}\NormalTok{)}\SpecialCharTok{\%\%}\DecValTok{365} \SpecialCharTok{{-}} \DecValTok{180}
\NormalTok{am\_circular }\OtherTok{\textless{}{-}} \FunctionTok{circular}\NormalTok{(fhy\_am}\SpecialCharTok{*}\DecValTok{2}\SpecialCharTok{*}\NormalTok{pi}\SpecialCharTok{/}\DecValTok{365}\NormalTok{)}
\NormalTok{rm\_am }\OtherTok{\textless{}{-}} \FunctionTok{rollapply}\NormalTok{(am\_circular, }
                    \AttributeTok{FUN=}\NormalTok{\textbackslash{}(x)\{}\FunctionTok{suppressWarnings}\NormalTok{(}\FunctionTok{mean.circular}\NormalTok{(x))\}, }\AttributeTok{width=}\DecValTok{10}\NormalTok{)}
\NormalTok{rm\_am2 }\OtherTok{\textless{}{-}} \FunctionTok{rollmean}\NormalTok{(fhy\_am, }\DecValTok{10}\NormalTok{)}
\end{Highlighting}
\end{Shaded}

\includegraphics{workflow_files/figure-latex/potcircplots-1.pdf}
\includegraphics{workflow_files/figure-latex/potcircplots-2.pdf}
\includegraphics{workflow_files/figure-latex/potcircplots-3.pdf}
\includegraphics{workflow_files/figure-latex/potcircplots-4.pdf}
\includegraphics{workflow_files/figure-latex/potcircplots-5.pdf}
\includegraphics{workflow_files/figure-latex/potcircplots-6.pdf}
\includegraphics{workflow_files/figure-latex/potcircplots-7.pdf}
\includegraphics{workflow_files/figure-latex/potcircplots-8.pdf}

\hypertarget{yearly-output}{%
\subsection{Yearly output}\label{yearly-output}}

\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{write\_csv}\NormalTok{(lf\_year, }\AttributeTok{file=}\FunctionTok{paste0}\NormalTok{(}\StringTok{"./Data/yearlystats\_"}\NormalTok{, Station,}\StringTok{"\_"}\NormalTok{, Agency, }\StringTok{".csv"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}


\end{document}