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\title[Benefits of forecasting for flood warning]{Estimating the benefits of single value and probability forecasting
for flood warning}
%\subtitle[short subtitle]{long subtitle}
\author[Verkade and Werner]{Jan Verkade \thanks{Delft University of Technology} \thanks{Deltares} and Micha Werner $^2$ \thanks{Unesco-IHE Institute for Water Education}}
\date[18-04-2012]{Statistics Community, Deltares, April 18, 2012}
\institute[StatCom]{}
%\logo{\includegraphics[width=2cm]{tudelft-logo.jpg}}
\titlegraphic{\vspace{3cm}}

\graphicspath{{./figures/}}


\begin{document}



\begin{frame}[plain]
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\titlepage
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\begin{frame}
\frametitle{Presentation outline}
\tableofcontents[hideallsubsections]
\end{frame}



\section{Introduction}



\begin{frame}{Introduction}
\begin{block}{Estimating the benefits --- rationale}
\begin{itemize}
\item Reduction of flood risk can be done in many ways $\rightarrow$ investment decision
\item Structural versus non--structural measures 
\item Single value forecasts versus probability forecasts

\pause
\item[$\rightarrow$] framework for evaluating alternatives is necessary
\item[$\rightarrow$] inclusion of forecasting uncertainty required
\end{itemize}
\end{block}
\end{frame}



\section{Materials and methods}
\subsection{Flood risk}



\begin{frame}{Estimating flood risk}
\begin{itemize}
	\item Flood risk is a measure for expected annual flood-related costs and damage
	\pause
	\item Flood risk is a combination of:
	\begin{enumerate}
		\item the frequency of occurrence of floods and their characteristics (extent, depth, $\ldots$)
		\item the consequences of floods
	\end{enumerate}
	\pause
	\item In this research: direct, tangible damage as a function of inundation depth only!
	\bigskip \pause
	\item Flood risk: $\textnormal{EAD}~=~\int_{0}^{1}~D(P)~dP$
	\item Estimate risk using a `hydro--economic EAD--model'
\end{itemize}
\end{frame}



\begin{frame}[plain]{Hydro-economic EAD model}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics<1>[width=\paperwidth]{EAD-model-no-ffwrs-1of4.pdf}
	\includegraphics<2>[width=\paperwidth]{EAD-model-no-ffwrs-2of4.pdf}
	\includegraphics<3>[width=\paperwidth]{EAD-model-no-ffwrs-3of4.pdf}
	\includegraphics<4>[width=\paperwidth]{EAD-model-no-ffwrs-4of4.pdf}
	};
\end{tikzpicture}
\end{frame}



\subsection{FFWRS}



\begin{frame}{Flood forecasting, warning and response systems}
\begin{itemize}
	\item Flood warning systems increase time available to respond to a flood before it actually occurs
	\item[] \centerline{ \includegraphics[width=.5\textwidth]{hess-2011-205-discussions-f01.pdf} }
	\item Increased mitigation time $\rightarrow$ increased potential for damage mitigation
\end{itemize}

\end{frame}



\begin{frame}[plain]{Hydro-economic EAD model}
\framesubtitle{Damage and risk reduction as a result of FFWRS}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics<2>[width=\paperwidth]{hess-2011-205-discussions-f02.pdf}
	};
\end{tikzpicture}
\end{frame}



\begin{frame}[plain]{Hydro-economic EAD model}
\framesubtitle{FFWRS costs}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics<2>[width=\paperwidth]{EAD-model-ffwrs-warning-costs.pdf}
	};
\end{tikzpicture}
\end{frame}



\subsection{Relative Economic Value}


\begin{frame}{Costs of forecasting uncertainty}
\begin{itemize}
	\item Water level forecasts are inherently uncertain
	\item Increasing lead time $\rightarrow$ increasing uncertainty
	\item Forecasting uncertainty manifests itself through misses, false alarms
	\item Frequency of occurrence of these determines expected cost
	\item Tool for expressing these costs: \textit{relative economic value}
	\item `Relative' to:
	\begin{itemize}
		\item no warning $\rightarrow$ flood losses: yes, loss mitigation: no
		\item perfect warning $\rightarrow$ loss mitigation, no misses, no false alarms
	\end{itemize}
\end{itemize}
\end{frame}



\begin{frame}{Relative Economic Value}
\begin{itemize}
	\item Forecasting system's performance can be captured in `contingency table'
\end{itemize}

{\scriptsize
\begin{block}{Contingency table}
\begin{center}
\begin{tabular}{llll}
\hline
& Event observed & Event NOT observed & $\sum$ \\
\hline
Warning issued & hits $h \left( C + L_u \right)$ & false alarms $f \left( C \right) $ & $w$ \\
Warning NOT issued & missed events $m \left( L_a + L_u \right)$ & quiets/correct negatives $q \left( - \right) $ & $w'$ \\
\hline
$\sum$ & $o$ & $o'$ & $N$ \\
\hline
\end{tabular}
\captionof{table}{Contingency table. The consequences of the items listed are in brackets.}
\end{center}
\end{block}
}
\end{frame}



\begin{frame}{Relative Economic Value}
\begin{itemize}
	\item Value of a system where forecasting uncertainty is present:
	\begin{itemize}
		\item is likely to be less than `perfect warning'
		\item is hopefully higher than in the `no warning' situation
		\item but could be lower, as false alarms introduce additional cost
	\end{itemize}
	\pause
	
	\item REV uses 2 benchmarks:
	\begin{itemize}
		\item perfect forecasts $\rightarrow$ REV = 1
		\item no warning $\rightarrow$ REV = 0
		\item REV can be less than 0
	\end{itemize}
	\pause
	
	\item Warning system performance is scaled between these two benchmarks:
	$\textnormal{REV} = \dfrac{ \textnormal{EAD(reference)} - \textnormal{EAD(myFWS)}}
						 {\textnormal{EAD(reference)} - \textnormal{EAD(perfect system)}}$
	
\end{itemize}
\end{frame}



\begin{frame}{Relative Economic Value}
\begin{block}{Expressing REV in elements of contingency table}
\begin{itemize}
	\item $\textnormal{REV} = \dfrac{ \textnormal{EAD(reference)} - \textnormal{EAD(myFWS)}}
						 {\textnormal{EAD(reference)} - \textnormal{EAD(perfect system)}}$

	\pause \bigskip
	\item $\textnormal{EAD}_{\textnormal{nowarn}}~=~o~\left(~L_{\textnormal a}~+~L_{\textnormal u}~\right)$
	\item $\textnormal{EAD}_{\textnormal{perfect}}~=~o~\left(C~+~L_{\textnormal u}\right)$
	\item $\textnormal{EAD}_{\textnormal{FFWRS}}~=~h~\left(C~+~L_{\textnormal u}\right)~+~f~C~+~m~\left(L_{\textnormal a}~+~L_{\textnormal u}\right)$
	
	\pause \bigskip
	\item REV can thus be expressed in elements of contingency table: $V~=~\frac{o~L_{\textnormal a}~-~\left(h~+~f\right)~C~-~m~L_{\textnormal a}}{o~L_{\textnormal a}~-~o~C}$

\end{itemize}
\end{block}
\end{frame}



\begin{frame}{Relative Economic Value = f (cost / loss ratio)}
\begin{example}\small
	You're going for a job interview, wearing an expensive suit. If it rains when you're outside, it'll cost \EUR 100 to have the suit dry-cleaned. You can prevent this `damage' by using an umbrella, which you'll have to buy.
	
	\medskip 
	If the umbrella costs \EUR 5, it's not that important whether or not it'll rain.
	
	\medskip
	If the umbrella costs \EUR 95, you'd want to be quite sure it'll rain.
	
	\pause \medskip
	\begin{itemize}
	\item[$\rightarrow$] False alarms are not so expensive if cost/loss is small (e.g. \EUR 5 / \EUR 100, r=.05)
	
	\item[$\rightarrow$] False alarms are relatively expensive if cost/loss is high (e.g. \EUR 95 / \EUR 100, r=.95)
	
	\item[$\rightarrow$] Relative Economic Value thus depends on the user's cost--to--loss ratio.
	
	\pause \medskip
	\item[$\rightarrow$] Optimal decision rule: warn if probability of the event $ \geq $ cost-loss ratio $r$	
	\end{itemize}

\end{example}
\end{frame}



\begin{frame}{Combining the EAD--model with REV}
\begin{itemize}
\item Rewrite equation for REV:
\begin{math}
	V~=~\frac{o~L_{\textnormal a}~-~\left(h~+~f\right)~C~-~m~L_{\textnormal a}}{o~L_{\textnormal a}~-~o~C} 
	=~\frac{o~-~\left(h~+~f\right)~r~-~m}{o~-~o~r} 
	=~\frac{o~-~\left(h~+~f\right)~r~-~m}{o~\left(1~-~r\right)}. 
\end{math}

\item Subsequently use to scale between `no warning' and `perfect warning' cases:
\begin{math}
	\textnormal{EAD}_\textnormal{FFWRS}~=~\textnormal{EAD}_\textnormal{nowarn}~-~V~\left(\textnormal{EAD}_\textnormal{nowarn}~-~\textnormal{EAD}_\textnormal{perfect}\right)
\end{math}

\end{itemize}

\centerline{ \includegraphics[width = .5\textwidth]{EAD-model-scale-REV.pdf} }
\end{frame}



\section{Case study}



\subsection{White Cart basin}



\begin{frame}{Case study}
\begin{enumerate}
\item no warning
\item perfect forecasts
\item deterministic forecasts
\item probabilistic forecasts
\end{enumerate}
\end{frame}



\begin{frame}{White Cart basin}
\begin{itemize}
\item Location: South of Glasgow, Scotland
\item Tributary of Clyde
\item Approx. 100 km$^2$, time of concentration approx. 3 hours
\item Geology: mostly impermeable limestone, steep
\item Climate: moderate, approx. 1,400 mm a$^{-1}$
\item Flooding occurs quite frequently
\item Forecasting-warning system in place
\end{itemize}
\begin{overprint}
\centerline{ \includegraphics[width = .8\textwidth]{figures/Picture1.png} }
\end{overprint} 
\end{frame}


\subsection{Cases One and Two}


\begin{frame}[plain]{Cases One and Two: No Warning and Perfect Forecasts}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics<2>[width=.9\textwidth]{hess-2011-205-discussions-f04.pdf}
	};
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\end{frame}



\begin{frame}{Cases One and Two: No Warning and Perfect Forecasts}



\begin{block}{Loss reduction}
	\begin{center}
	\footnotesize
	\begin{tabular}{lcccr}
	\hline
	Case & mitigation time [h] & EAD [GBP] & $\Delta$ EAD [GBP] & $\Delta$ EAD [\%] \\
	\hline
	No Warning        &   & 394\,695 &            & \\
	Perfect forecasts & 1 & 386\,871 & $-$ 7\,824 & $-$2\% \\
	Perfect forecasts & 2 & 384\,640 & $-$10\,055 & $-$3\% \\
	Perfect forecasts & 3 & 384\,129 & $-$10\,566 & $-$3\% \\
	Perfect forecasts & 4 & 359\,473 & $-$35\,221 & $-$9\% \\
	Perfect forecasts & 5 & 349\,913 & $-$44\,782 & $-$11\% \\
	Perfect forecasts & 6 & 349\,913 & $-$44\,782 & $-$11\% \\
	\hline
	\end{tabular}
	\captionof{table}{Loss reduction in terms of expected annual damage (response costs not included)}
	\end{center}
\end{block}
\end{frame}




\begin{frame}[plain]{Perfect forecasts--case: flood risk}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics[width=.9\paperwidth]{hess-2011-205-discussions-f05.pdf}
	};
\end{tikzpicture}
\end{frame}



\subsection{Case Three: deterministic forecasts}



\begin{frame}{Case Three: deterministic forecasting}
\begin{itemize}
	\item predictive uncertainty $\rightarrow$ imperfect system
	\item contingency table populated with results from re-forecasting exercise
	\item one contingency table for each lead-time considered
\end{itemize}
\pause
\begin{block}{Forecasting system performance}
	\begin{center}
	\small
	\begin{tabular}{cccccc}
	\hline
	lead-time $[$h$]$ & $h$ $[-]$ & $m$ $[-]$ & $f$ $[-]$ & $q$ $[-]$ & $N$ $[-]$ \\
	\hline
	1 & 10 & 2 & 0 & 15\,860 & 15\,872
	\\
	2 & 10 & 4 & 2 & 15\,856 & 15\,872
	\\
	3 & 6 & 9 & 2 & 15\,855 & 15\,872
	\\
	4 & 7 & 7 & 2 & 15\,856 & 15\,872
	\\
	5 & 8 & 6 & 2 & 15\,856 & 15\,872
	\\
	6 & 6 & 9 & 3 & 15\,854 & 15\,872
	\\ \hline
	\end{tabular}
	\captionof{table}{Performance of the FFWRS based on deterministic forecasts, expressed in the elements of a contingency table.}
	\end{center}
\end{block}
\end{frame}



\begin{frame}[plain]{Deterministic forecasts: REV}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics[width=\paperwidth]{hess-2011-205-discussions-f06.pdf}
	};
\end{tikzpicture}
\end{frame}



\begin{frame}[plain]{Deterministic forecasts: flood risk}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics[width=\paperwidth]{hess-2011-205-discussions-f07.pdf}
	};
\end{tikzpicture}
\end{frame}



\subsection{Case Four: probabilistic forecasting}



\begin{frame}[plain]{Case Four: probabilistic forecasts}
\framesubtitle{Sample forecast}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics[width=\paperwidth]{hess-2011-205-discussions-f03.pdf}
	};
\end{tikzpicture}
\end{frame}



\begin{frame}{Case Four: probabilistic forecasts}
\begin{block}{Forecasting system performance}
	\begin{center}
	\small
	\begin{tabular}{lccrcc}
	\hline
	threshold $[-]$ & $h$ $[-]$ & $m$ $[-]$ & $f$ $[-]$ & $q$ $[-]$ & $N$ $[-]$
	\\
	\hline
	0 & 15 & 0 & 15\,857 & 0 & 15\,872
	\\
	0.1 & 15 & 0 & 17 & 15\,840 & 15\,872
	\\
	0.2 & 13 & 2 & 7 & 15\,850 & 15\,872
	\\
	0.3 & 13 & 2 & 6 & 15\,851 & 15\,872
	\\
	0.4 & 11 & 4 & 5 & 15\,852 & 15\,872
	\\
	0.5 & 11 & 4 & 5 & 15\,852 & 15\,872
	\\
	0.6 & 8 & 7 & 2 & 15\,855 & 15\,872
	\\
	0.7 & 6 & 9 & 2 & 15\,855 & 15\,872
	\\
	0.8 & 3 & 12 & 1 & 15\,856 & 15\,872
	\\
	0.9 & 3 & 12 & 1 & 15\,856 & 15\,872
	\\
	1 & 0 & 15 & 0 & 15\,857 & 15\,872
	\\
	\hline
	\end{tabular}
	\captionof{table}{Probabilistic forecasting system performance at 3h leadtime.}	
	\end{center}
\end{block}
\end{frame}



\begin{frame}[plain]{Probabilistic forecasting: REV}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics[width=\paperwidth]{hess-2011-205-discussions-f08.pdf}
	};
\end{tikzpicture}
\end{frame}



\begin{frame}[plain]{Probabilistic forecasting: flood risk}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics[width=\paperwidth]{hess-2011-205-discussions-f09.pdf}
	};
\end{tikzpicture}
\end{frame}



\subsection{Summary of results}



\begin{frame}[plain]{Summary of results}
\begin{tikzpicture}[remember picture,overlay]
	\node[at=(current page.center)] {
	\includegraphics<1>[width=\paperwidth]{hess-2011-205-discussions-f10.pdf}
	\includegraphics<2>[width=\paperwidth]{ead-prob-envelopes-only.pdf}	
	};
\end{tikzpicture}
\end{frame}



\section{Discussion and conclusions}
\begin{frame}{Discussion and conclusions}
\begin{block}{Discussion}
\begin{itemize}
\item Probabilistic versus deterministic forecasting
\item Limitations and assumptions
\item Possible implications for policy--makers
\item Open questions and future research
\end{itemize}
\end{block}

\pause

\begin{block}{Main conclusions}
\begin{itemize}
\item Lower values of residual flood risk when using probabilistic forecasts
\item Optimal lead-time for warning is not necessarily \textit{longest} possible lead-time
\end{itemize}
\end{block}
\end{frame}


\section{Closing remarks}


\begin{frame}{These slides are based on $\ldots$}
\href{http://www.hydrol-earth-syst-sci.net/15/3751/2011/hess-15-3751-2011.html}{
\fbox{ \includegraphics[width = .95\textwidth]{verkade2011benefits.pdf} }
}
\end{frame}



\begin{frame}{\centerline{Contact details}}
\centerline{ \textbf{Jan Verkade} }
\centerline{ \href{mailto:jan.verkade@deltares.nl?SUBJECT=Your presentation at StatCom}{jan.verkade@deltares.nl} }
\bigskip
\centerline{ \textbf{Micha Werner} }
\centerline{ \href{mailto:micha.werner@deltares.nl?SUBJECT=Your presentation at StatCom}{micha.werner@deltares.nl} }
\bigskip
\centerline{ Slides are available via \href{http://twitter.com/janverkade}{twitter.com/janverkade} }
\end{frame}



\end{document}