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\documentclass[20pt,a4paper]{article}
\setlength{\parskip}{6pt}
\newcommand{\unit}[1]{\ensuremath{\, \mathrm{#1}}}
\usepackage{graphicx}
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\usepackage[utf8]{inputenc}
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\usepackage[colorlinks, urlcolor=blue, linkcolor=black]{hyperref}
\begin{document}
\title{A comparison of AROME wind to the wind observations on the sea}
\author{Saeed Falahat}
\maketitle

\section{Introduction}
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In this study, we make a comparison between the wind data from the atmospheric model called AROME and the wind observation. The wind observations stem from mora database. 
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The objective of this study is to investigate how well AROME performs in predicting the wind over the sea. The wind is a mechanical driving force to the ocean by exerting a stress to the ocean surface. Hence, this is of paramount importance in connection with the ocean circulation model such as NEMO ocean model when run in the forced mode. NEMO ocean model is run operationally in SMHI, predicting the sea surface height, sea surface temperature, salinity, ice extent, ice thickness and some other oceanic variables.   
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The model and observational data span from the January 1, 2018 to April 1, 2018 with a hourly temporal resolution. We do a comparison between the model and the observation by plotting the time series, scatter plots, and calculating the correlation coefficients. 
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\section{Model data}
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AROME is a regional atmospheric model running operationally for the short range forecast at SMHI. The current resolution of the model is ${2.5}$ km. AROME uses the lambert canonical conformal projection. A more detailed information on AROME is given by Lisa Bengstson et al (2017), which can be obtained from \href{https://journals.ametsoc.org/doi/pdf/10.1175/MWR-D-16-0417.1}{here}. 

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We use the model wind data at ${10}$ meter. Model data in the GRIB format are retrieved for the period January 1, 2018 and April 1, 2018 from mars archiving system. They have an hourly temporal resolution. Note that we only use the hourly average wind not the gust wind. The effect of the gust wind on the average wind are very interesting but it is beyond the scope of this study. 
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The model wind data is first interpolated to the regular grid and then their values at the observational points are obtained using the inverse distance weight interpolation method. It should be mentioned that since the wind data are relative to the model grid, before doing the interpolation, we rotate them back to the geogrid, .i.e. west-east and south-north direction on the earth.
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Inverse distance weighted (IDW) interpolation assumes that the points close to the observation point have more influence on that and the influence decreases further away from the observation point, depending on a defined weighted function such as the inverse of the distance between the observation point and the model point. The interpolation is done for both wind components in the west-east and south-north directions, namely ${U}$ and ${V}$ components.
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Figure \ref{uw}, showing  ${U}$ wind component, is an example of model data used in this study. The latitude of model data is in a range $53.5$N-${67.725}$N and their respective longitude lies between ${7.0}$E-${27.958}$E. Note, however, that AROME grid covers a bit larger domain than that in Figure \ref{uw}.   
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\section{Observational data}
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Observational data comes from mora database. The information on mora database can be found \href{http://mora-apps/}{here}. We only use WMO stations which are located on the sea or close to the coast. Figure \ref{station} shows the location of the $64$ mora stations on the sea. Note that not all these stations measure the wind exactly at the height $10$ m above the ground. That is, we only use those stations having a height comparable to $10$ m. The wind data is retrieved from mora website in a json format which are then processed and converted to CSV format, making them convenient for comparing to the model data.   
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\section{Results}
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In the comparison between the model and observation, we inspect the time series of the $U$ and ${V}$ wind components, as well as the scatter plots. We also calculate the correlation coefficient between the model and observation. We only show the results of few stations as there are many stations.

 
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\section{Conclusion and future perspective}
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In this study, we have compared the wind data from AROME atmospheric regional model to the observational data for the wind obtained from mora database. This is done only for the stations located on the Baltic sea and the north sea which are very crucial for the NEMO ocean circulation model which is run operationally in SMHI. 
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The model data is interpolated to the observational point using the inverse distance weight interpolation method. The validation period was between January 1, 2018 and April 1, 2018. The comparison between the model and observational data in terms of the time series, scatter plots and correlation coefficients reveals that AROME model does a good job in predicting the wind on the sea. 
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A follow up to this study is to do a comparison for other years than 2018 and also other periods of a year. The best possible scenario is to look at the data for at least few consecutive years. Also, it is interesting to find out how the interpolation method can affect the results. For instance, we can use the bilinear or the nearest point interpolation method. These warrant a motivation for the follow up study.     
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\clearpage
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\section{Figures}

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\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{uwind.png}
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\caption{10 meter U wind from AROME model}
\label{uw}
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\end{figure}

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\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{stationmap.png}
\caption{WMO stations located on sea}
\label{station}
\end{figure}

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\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{uwindarome_wmo_mora_id493_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}


\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{uwindarome_wmo_mora_id721_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}


\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{uwindarome_wmo_mora_id751_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{uwindarome_wmo_mora_id794_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{uwindarome_wmo_mora_id907_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{uwindarome_wmo_mora_id97_type0_block10.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{uwindarome_wmo_mora_id980_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{uwindarome_wmo_mora_id992_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}
\clearpage 
%%%%vwind

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{vwindarome_wmo_mora_id493_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}


\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{vwindarome_wmo_mora_id721_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}


\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{vwindarome_wmo_mora_id751_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{vwindarome_wmo_mora_id794_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{vwindarome_wmo_mora_id907_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{vwindarome_wmo_mora_id97_type0_block10.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{vwindarome_wmo_mora_id980_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{vwindarome_wmo_mora_id992_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}
\clearpage 

%scatter uwind

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_uwindarome_wmo_mora_id493_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}


\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_uwindarome_wmo_mora_id721_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

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\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_uwindarome_wmo_mora_id751_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_uwindarome_wmo_mora_id794_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_uwindarome_wmo_mora_id907_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_uwindarome_wmo_mora_id97_type0_block10.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_uwindarome_wmo_mora_id980_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_uwindarome_wmo_mora_id992_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}
\clearpage
%%scatter V
%scatter uwind
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\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_vwindarome_wmo_mora_id493_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}


\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_vwindarome_wmo_mora_id721_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}


\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_vwindarome_wmo_mora_id751_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_vwindarome_wmo_mora_id794_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_vwindarome_wmo_mora_id907_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_vwindarome_wmo_mora_id97_type0_block10.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_vwindarome_wmo_mora_id980_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}

\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{scatter_vwindarome_wmo_mora_id992_type0_block2.png}
\caption{10 meter U wind from AROME model}
\label{uw}
\end{figure}
\clearpage
\pagebreak
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%station              Experiment                               RMS        RMSD       Correlation
%               OBSERVATION                              5.979      0.0        1.0
%NYHAMN               AROME                                    5.704      1.552      0.966
%station              Experiment                               RMS        RMSD       Correlation
%            OBSERVATION                              5.478      0.0        1.0
%ULKOKALLA            AROME                                    5.401      1.561      0.959
%station              Experiment                               RMS        RMSD       Correlation
%KOKKOLATANKAR        OBSERVATION                              5.033      0.0        1.0
%KOKKOLATANKAR        AROME                                    4.909      1.592      0.949
%station              Experiment                               RMS        RMSD       Correlation
%PORITAHKOLUOTO       OBSERVATION                              5.237      0.0        1.0
%PORITAHKOLUOTO       AROME                                    4.814      1.341      0.968
%station              Experiment                               RMS        RMSD       Correlation
%KIRKKONUMMIMAKILUOTO OBSERVATION                              5.647      0.0        1.0
%KIRKKONUMMIMAKILUOTO AROME                                    5.445      1.597      0.959
%station              Experiment                               RMS        RMSD       Correlation
%PERNAJAORRENGRUND    OBSERVATION                              5.557      0.0        1.0
%PERNAJAORRENGRUND    AROME                                    5.432      1.501      0.963
%station              Experiment                               RMS        RMSD       Correlation
%SöderarmA            OBSERVATION                              5.929      0.0        1.0
%SöderarmA            AROME                                    5.988      1.797      0.955


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\section{Tables}
\begin{table}[h!]
\centering
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\begin{tabular}{l|c}
Station& Correlation Coefficient \\
\hline
NYHAMN & 0.966  \\
\hline
ULKOKALLA  & 0.959  \\
\hline
KOKKOLA TANKAR & 0.949 \\
\hline
PORI TAHKOLUOTO  & 0.968 \\
\hline
KIRKKONUMMI MAKILUOTO & 0.959 \\
\hline 
PERNAJA ORRENGRUND & 0.963 \\
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\hline
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SöderarmA    & 0.955\\
\hline 
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\end{tabular}
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\caption{Correlation coefficient between ${U}$ wind component of model and the observation for some stations over the sea}
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\label{tabstation}
\end{table}
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\end{document}