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\usepackage{acro} |
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\DeclareAcronym{rmse}{ |
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short=RMSE, |
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long=Root-Mean-Square Error, |
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} |
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\newcommand{\rmse}{\ac{rmse}} |
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\DeclareAcronym{hpc}{ |
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short=HPC, |
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long=High-Performance Computing, |
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} |
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\newcommand{\hpc}{\ac{hpc}} |
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\DeclareAcronym{obc}{ |
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short=OBC, |
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long=Open Boundary Condition, |
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} |
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\newcommand{\obc}{\ac{obc}} |
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\newcommand{\obcs}{\acp{obc}} |
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\DeclareAcronym{esm}{ |
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short=ESM, |
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long=Earth System Model, |
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} |
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\newcommand{\esm}{\ac{esm}} |
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\DeclareAcronym{cmip6}{ |
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short=CMIP6, |
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long=Coupled Model Intercomparison Project 6, |
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} |
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\newcommand{\cmip}{\ac{cmip6}} |
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\DeclareAcronym{nm}{ |
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short=nm, |
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long=nautical miles, |
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} |
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\newcommand{\nm}{\ac{nm}} |
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\DeclareAcronym{ergom}{ |
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short=ERGOM, |
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long=Ecological ReGional Ocean Model, |
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} |
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\newcommand{\ergom}{\ac{ergom}} |
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\DeclareAcronym{gcm}{ |
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short=GCM, |
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long=Global Climate Model, |
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} |
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\newcommand{\gcm}{\ac{gcm}} |
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\newcommand{\gcms}{\acp{gcm}} |
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\DeclareAcronym{sst}{ |
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short=SST, |
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long=Sea Surface Temperature, |
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} |
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\newcommand{\sst}{\ac{sst}} |
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\DeclareAcronym{mom5}{ |
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short=MOM5, |
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long=Modular Ocean Model 5, |
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} |
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\newcommand{\mom}{\ac{mom5}} |
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\DeclareAcronym{cclm}{ |
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short=CCLM, |
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long=COSMO model in CLimate Mode, |
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} |
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\newcommand{\cclm}{\ac{cclm}} |
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\DeclareAcronym{ssp}{ |
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short=SSP, |
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long=Shared Socioeconomic Pathway, |
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} |
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\newcommand{\ssp}{\ac{ssp}} |
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\newcommand{\ssps}{\acp{ssp}} |
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\DeclareAcronym{bsap}{ |
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short=BSAP, |
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long=Baltic Sea Action Plan, |
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} |
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\newcommand{\bsap}{\ac{bsap}} |
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\DeclareAcronym{dkrz}{ |
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short=DKRZ, |
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long=Deutsches Klimarechenzentrum, |
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} |
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\newcommand{\dkrz}{\ac{dkrz}} |
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\DeclareAcronym{mpi}{ |
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short=MPI, |
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long=Message Passing Interface, |
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} |
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\newcommand{\mpi}{\ac{mpi}} |
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\DeclareAcronym{iow}{ |
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short=IOW, |
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long=Leibniz-Institut für Ostseeforschung Warnemünde, |
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} |
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\newcommand{\iow}{\ac{iow}} |
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\DeclareAcronym{sh}{ |
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short=SH, |
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long=Sensible Heat, |
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} |
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\newcommand{\sh}{\ac{sh}} |
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\DeclareAcronym{lh}{ |
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short=LH, |
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long=Latent Heat, |
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} |
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\newcommand{\lh}{\ac{lh}} |
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\DeclareAcronym{bbr}{ |
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short=BBR, |
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long=Black-Body Radiation, |
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} |
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\newcommand{\bbr}{\ac{bbr}} |
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\DeclareAcronym{sw}{ |
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short=SW, |
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long=Short-Wave, |
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} |
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\newcommand{\sw}{\ac{sw}} |
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\DeclareAcronym{lw}{ |
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short=LW, |
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long=Long-Wave, |
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} |
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\newcommand{\lw}{\ac{lw}} |
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awk ' |
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BEGIN{ |
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entries = 0 |
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if(NF==0){ |
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next |
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if(author ~ /^[a-zA-Z]+$/ && year ~ /^[0-9]+$/){ |
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key = author year |
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key = original_key |
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} |
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double_counter++ |
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} |
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if(double_counter > 1){ |
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key = key"-"double_counter |
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} |
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keys[entries++] = key |
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print l[0]key"," |
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print l[i] |
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print "}\n" |
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open = false |
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if(open==true){ |
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if(c==0){ |
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author=b[2] |
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} |
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if($1=="year"){ |
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split($3,b,"{") |
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year=b[1] |
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} |
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l[c++]=$0 |
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} |
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} |
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}' all_endnote.bib > all.bib |
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if [ -f "lib.bib" ]; then |
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cat lib.bib >> all.bib |
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fi |
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\documentclass[a4paper,titlepage]{article} |
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\usepackage[english]{babel} |
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\usepackage{amsmath} |
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\usepackage{amsfonts} |
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\usepackage{amssymb} |
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\usepackage{graphicx} |
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\usepackage{fourier} |
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\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry} |
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%\usepackage{graphicx} |
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\usepackage{float} |
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\usepackage{caption} |
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%\captionsetup{width=0.88\textwidth} |
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\captionsetup{font=small} |
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\usepackage{subcaption} |
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\usepackage{color} |
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\usepackage{hyperref} |
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\hypersetup{ |
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colorlinks, |
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citecolor=black, |
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filecolor=black, |
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linkcolor=black, |
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urlcolor=black |
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} |
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\usepackage{lipsum} |
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\include{accronyms} |
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\include{useful_commands} |
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\usepackage{authblk} |
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\title{The IOW Earth System Model for the Baltic Sea region} |
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\author[1]{Sven Karsten} |
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\author[1,*]{Hagen Radtke} |
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\author[1]{Hossein Mashayekh} |
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\author[1]{Matthias Gröger} |
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\author[1]{Thomas Neumann} |
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\author[1]{H. E. Markus Meier} |
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\affil[1]{Leibniz Institute for Baltic Sea Research Warnem\"unde (IOW), Seestraße 15, 18119 Rostock, Germany} |
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\affil[*]{Corresponding author: hagen.radtke@io-warnemuende.de} |
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%\affil[2]{Leibniz Institute for Baltic Sea Research Warnem\"nde (IOW), Seestraße 15, 18119 Rostock, Germany} |
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\begin{document} |
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\maketitle |
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\renewcommand{\abstractname}{Abstract} |
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\begin{abstract} |
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% |
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In this article the development and the validation of a high-resolution regional \esm\ is described, to downscale reanalysis or \gcm\ simulations to the Baltic Sea region. |
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% |
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Currently, the model consists of the \mom\ for the ocean and the \cclm\ for the atmosphere. |
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% |
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This model allows to study regional climate phenomena and to produce climate data appropriate for end users and policy makers. |
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% |
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Technically, the model is driven by the atmospheric boundary conditions that are a priory generated from reanalysis data \gcm\ simulation. |
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% |
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The data stemming from a run that is forced reanalysis data can be used to validate the quality of the model by comparison to the same reanalysis or observation data. |
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% |
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The bi-directional ocean-atmosphere coupling allows allows for a realistic air-sea feedback which clearly outperforms the traditional approach of using uncoupled standalone models as typically pursued with the \EC\ protocol. |
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% |
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The coupling of model components is implemented such that is highly scaleable and can potentially be used on \hpc\ centers world-wide. |
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% |
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In order to address marine environmental problems (e.g. eutrophication and oxygen depletion), the ocean model encompasses a marine biogeochemistry model setup suitable for the Baltic Sea's hydrographic conditions. |
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% |
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The model might be driven by reasonable \ssps\ including different assumptions for nutrient load scenarios. |
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% |
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Beside these applications of high societal relevance, the \esm\ can be used for various scientific questions such as climate sensitivity experiments, reconstruction of ocean dynamics, study of past climates and natural variability as well as investigation of ocean-atmosphere interactions. |
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% |
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Hence, it can serve for better understanding of natural processes via attribution experiments that relate observed changes to mechanistic causes. |
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\end{abstract} |
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\renewcommand{\abstractname}{Kurzfassung} |
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\begin{abstract} |
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% |
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\open{\lipsum[1-2]} |
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\end{abstract} |
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\newpage |
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\tableofcontents |
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\newpage |
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\printacronyms |
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\newpage |
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\section{Introduction} |
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\open{\lipsum[1-3]} |
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\section{Theoretical background and methodology} |
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One basic problem when dealing with regional climate models system is that the individual components (atmosphere, ocean, land etc.) are described by different models (realized as computer programs) that act on different grids, see \Fig{fig:grids2D} and \Fig{fig:grids1D}. |
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% |
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Still, the components have to be coupled in order communicate their state to each other and exchange fluxes as given by nature itself. |
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% |
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\begin{figure} |
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\centering |
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\begin{subfigure}[t]{0.45\textwidth} |
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\centering |
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\includegraphics[width=\linewidth]{"./figures/grids.pdf"} |
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\caption{ |
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\label{fig:grids2D} |
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Overlaying grids of atmospheric and ocean model for the Baltic Sea. |
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} |
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\end{subfigure} |
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\hfill |
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\vspace{1em} |
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\begin{subfigure}[t]{0.45\textwidth} |
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\centering |
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\includegraphics[width=\linewidth]{"./figures/grids1D.pdf"} |
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\caption{ |
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\label{fig:grids1D} |
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Abstraction of figure \ref{fig:grids2D} in one spatial horizontal dimension. Bottom model can support different surface types as water (blue) and ice (white). |
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} |
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\end{subfigure} |
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\caption{The different grids of the different models.} |
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\end{figure} |
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\subsection{Introducing the exchange grid and the flux calculator} |
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\label{sec:exchange_grid_and_flux_calculator} |
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To exemplify the aforementioned problem let us consider the calculation of a flux of something from the atmosphere to the bottom. |
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% |
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Usually, if the flux depends on the state of the ocean, some state variables have to be communicated first to the atmosphere. |
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% |
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Since the atmospheric grids are normally larger, the information has to be averaged (weighted by areas) over several bottom cells, |
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over different surface types, see \Fig{fig:conservative_mapping1}. |
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With this averaged state information and its own internal state, the atmospheric model can now calculate the flux as a field on the atmospheric grid. |
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% |
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It is noteworthy that the flux cannot be calculated for the different surface types differently, since the atmospheric model does not know about that (at least not without changing the code significantly). |
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% |
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Finally, the flux field then has to be redistributed on the bottom cells (again in a area-weighted manner such that flux variable is overall conserved), |
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see \Fig{fig:conservative_mapping2}. |
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% |
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Since the flux is only calculated from averaged information and not surface-type-dependent, this approach locally not consistent and can become inaccurate. |
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% |
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This is especially true if many bottom grid cells are covered by one atmospheric grid cell. |
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% |
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\begin{figure} |
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\centering |
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\begin{subfigure}[t]{0.45\textwidth} |
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\centering |
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\includegraphics[width=\linewidth]{"./figures/conservative_mapping1.pdf"} |
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\caption{ |
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\label{fig:conservative_mapping1} |
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Average of ocean's state variables communicated to the atmosphere. |
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} |
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\end{subfigure} |
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\hfill |
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\begin{subfigure}[t]{0.45\textwidth} |
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\centering |
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\includegraphics[width=\linewidth]{"./figures/conservative_mapping2.pdf"} |
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\caption{ |
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\label{fig:conservative_mapping2} |
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Calculation of fluxes in the atmospheric model and remapping on to the ocean's grid. |
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} |
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\end{subfigure} |
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\captionsetup{width=\linewidth} |
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\caption{The standard way of coupling.} |
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\end{figure} |
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% |
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The alternative approach chosen within the developed \esm\ is the introduction of a third component, i.e. the flux calculator that acts on the exchange grid. |
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% |
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This grid is the set of intersections between the atmospheric and the bottom grid and thus has, by construction, |
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a higher resolution than all involved model components, see \Fig{fig:grids1D_plus_exchange}. |
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% |
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\begin{figure} |
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\centering |
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\captionsetup{width=\linewidth} |
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\includegraphics[width=0.45\linewidth]{"./figures/grids1D_plus_exchange.pdf"} |
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\caption{ |
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\label{fig:grids1D_plus_exchange} |
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Introduction of the exchange grid on which the flux calculator is acting. |
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} |
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\end{figure} |
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% |
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The example from above, i.e. a flux shall be communicated from the atmosphere to the ocean, is then treated as follows. |
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First, the physical components of the coupled model send their necessary state variables to the flux calculator. |
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% |
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The variables are thereby mapped onto the exchange grid, see \Fig{fig:exchange_grid_mapping1}. |
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% |
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Importantly, since the exchange-grid cells are always smaller or equal to the „physical“ grid cells, this mapping does not feature any averaging and, |
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% |
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thus, no information is lost. |
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% |
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Moreover, different surface types can be treated individually since the flux calculator might know about these feature of the bottom model. |
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Second, with all the state information, the flux calculator is now able to calculate the flux of interest. |
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% |
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Any formula can be used that maps the given state variables onto the desired flux field. |
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% |
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The calculation only requires local information and can be surface-type-dependent. |
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% |
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The resulting flux has to be finally mapped onto the bottom grid, see \Fig{fig:exchange_grid_mapping2}. |
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% |
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Note that, although not shown in the figures, the very same fluxes are communicated to the atmospheric model as well. |
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% |
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This ensures a conservative and locally consistent exchange of mass, energy and momentum between the different model components. |
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% |
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\begin{figure} |
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\centering |
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\begin{subfigure}[t]{0.45\textwidth} |
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\centering |
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\includegraphics[width=\linewidth]{"./figures/exchange_grid_mapping1.pdf"} |
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\caption{ |
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\label{fig:exchange_grid_mapping1} |
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Communication of state variables to the flux calculator. Importantly no averaging is performed while mapping. |
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} |
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\end{subfigure} |
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\hfill |
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\begin{subfigure}[t]{0.45\textwidth} |
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\centering |
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\includegraphics[width=\linewidth]{"./figures/exchange_grid_mapping2.pdf"} |
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\caption{ |
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\label{fig:exchange_grid_mapping2} |
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Fluxes are calculated and subsequently communicated to the bottom model. |
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} |
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\end{subfigure} |
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\captionsetup{width=\linewidth} |
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\caption{Coupling the models via the exchange grid and the flux calculator.} |
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\end{figure} |
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% |
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Some fluxes that are not simply determined by surface variables, however, do not fit into this concept. |
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% |
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In particular, precipitation and (downward shortwave and longwave) radiative fluxes will still be determined by the atmospheric model and the resulting fluxes will be sent to the flux calculator executable. |
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% |
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Subsequently, radiation and precipitation is then simply passed to the bottom models. |
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% |
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Still, there is no direct communication between the two physical components and this simplifies ultimately interchangeability of the models. |
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\subsection{Current implementation} |
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As the first step, a working version of the coupled \esm\ is developed that consists of the \mom~\citesqr{neumann2021} ocean model and the \cclm~\citesqr{cclm2020} atmospheric model. |
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% |
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In contrast to other coupled models, the developed \iow\ \esm\ involves a \textit{flux calculator} executable that mediates the coupling between these models via the so-called \textit{exchange grid}. |
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% |
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How the coupling is implemented is described in detail in \Secs{\ref{sec:coupling_cycle} and \ref{sec:flux_formulas}}. |
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Importantly, as mentioned in \Sec{sec:exchange_grid_and_flux_calculator} the \esm\ is designed such, that other models are added and the current configuration might be extended or replaced by other suitable models. |
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\subsubsection{Coupling cycle} |
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\label{sec:coupling_cycle} |
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\open{See \Fig{fig:coupling_cycle}... |
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\begin{itemize} |
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\item describe which quantities are exchanged |
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\item detailed description of flux calculation is written \Sec{sec:flux_formulas} |
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\end{itemize} |
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} |
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|
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\begin{figure} |
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\centering |
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\captionsetup{width=\linewidth} |
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\includegraphics[width=0.8\linewidth]{"./figures/sequence-diagram.pdf"} |
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\caption{ |
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\label{fig:coupling_cycle} |
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Sequence diagram for one coupling time step. |
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} |
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\end{figure} |
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\subsubsection{Flux formulas} |
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\label{sec:flux_formulas} |
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In the current implementation of the \esm, flux formulas are used, as they are implemented in the \cclm~\citesqr{cclmManualII2011}. |
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% |
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The formulas are based on the work in~\citesqr{louis1979} and will be briefly presented in the following. |
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Using the surface's air pressure $p_s(x,y,t)$ and the specific water vapor content $q^v_{s}(x,y,t)$ can be calculated via |
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% |
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\begin{align} |
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q^v_{s}(x,y,t) =\frac{R_d/R_v p_{\mathrm{sat}}(x,y,t)}{p_s(x,y,t) - (1-R_d/R_v) p_{\mathrm{sat}}(x,y,t)}, |
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\end{align} |
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% |
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with the gas constants $R_d$ for dry air and $R_v$ for water vapor. |
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% |
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The sea-surface temperature $T_s(x,y,t)$ determines the saturation pressure $p_{\mathrm{sat}}(x,y,t)$ that is calculated according to the Tetens approximation~\citesqr{tetens1930}. |
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%, i.e. |
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% |
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%\begin{align} |
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% p_{\mathrm{sat}}(x,y,t) = 0.61078 \cdot \exp \left( \frac{17.27 \cdot T_s(x,y,t)}%{T_s(x,y,t) + 237.3} \right). |
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%\end{align} |
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|
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Having the water vapor content $q^s_{v}(x,y,t)$ at hand, one may then calculate the temperature $\tilde{T}$ at which dry air at the surface would show the same energy $p\cdot V$ as the moist air which is there now. |
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% |
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\begin{align} |
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\tilde{T}(x,y,t) = T_s(x,y,t) \left( 1 + (R_v/R_d - 1) q^v_{s}(x,y,t) \right) |
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\end{align} |
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% |
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This temperature is related to the air's density by the ideal gas law (valid for dry air) |
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\begin{align} |
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\rho(x,y,t) = \frac{p_s(x,y,t)}{R_d\tilde{T}(x,y,t)} |
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\end{align} |
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% |
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With the density and the coefficients $c_h(x,y,t)$ for turbulent moisture and heat transfer as well as $c_m(x,y,t)$ for the turbulent momentum transfer, one can compute the underlying fluxes according to the following formulas. |
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% |
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All fluxes scale with the magnitude of the horizontal wind velocity $\vec{u}(x,y,t)$ present at the water surface. |
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|
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The evaporation mass flux is calculated assuming that the air adjusts its water vapor content $q_a^v(x,y,t)$ to the one present at the sea surface $q_s^v(x,y,t)$, i.e. |
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% |
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\begin{align} |
||||
\phi_{\mathrm{evap}}(x,y,t) = c_h \rho | \vec{u} | (q_s^v - q_a^v), |
||||
\end{align} |
||||
% |
||||
where all quantities are meant to be functions of $(x,y,t)$, i.e. the horizontal location on the sea surface and time, however, for the sake of brevity we skip these arguments. |
||||
|
||||
The \lh\ flux is then directly proportional to the evaporation |
||||
% |
||||
\begin{align} |
||||
\phi_{\mathrm{LH}}(x,y,t) = \Delta H \phi_{\mathrm{evap}}, |
||||
\end{align} |
||||
% |
||||
where $\Delta H$ is the constant for the latent heat of either evaporation, freezing or sublimation, depending on the type of phase transition. |
||||
|
||||
The \sh\ flux is determined by the difference between the temperatures of the lowest (discretized) atmospheric layer $T_a(x,y,t)$ and the ocean's surface $T_s(x,y,t)$, i.e. |
||||
\begin{align} |
||||
\phi_{\mathrm{SH}}(x,y,t) = c_h C_p \rho | \vec{u} | (T_s - \theta_s). |
||||
\end{align} |
||||
% |
||||
The appearing $\theta_s(x,y,t)=(p_s/p_a)^{R_d/C_p} T_a$ is the atmospheric potential directly at the surface. |
||||
|
||||
The momentum fluxes (i.e. the shear stress at the components interface) depend non-linearly on the wind velocity $\vec{u}(x,y,t)$ at the lowest atmospheric layer and are calculated as |
||||
% |
||||
\begin{align} |
||||
\phi_{\mathrm{mom}_\xi}(x,y,t) = -c_m \rho | \vec{u} | u_\xi, |
||||
\end{align} |
||||
% |
||||
where $\xi$ and $u_\xi$ account either for the $x$ or $y$ direction of the velocity field. |
||||
% |
||||
It is noteworthy, that the horizontal velocity components of the ocean's water body are negligible compared to atmospheric ones. |
||||
|
||||
The thermal radiation that is emitted in upward direction by the ocean is described by the radiation of a black body having the ocean's surface temperature. |
||||
% |
||||
Thus the thermal flux can be calculated via the Stephan-Boltzmann law suitable for \bbr |
||||
% |
||||
\begin{align} |
||||
\phi_{\mathrm{BBR}}(x,y,t) = \sigma T_s^4, |
||||
\end{align} |
||||
% |
||||
where $\sigma$ is the Stephan-Boltzmann constant. |
||||
% |
||||
Importantly, since the \bbr\ depends strongly non-linear on the temperature, this flux exemplifies the importance of the local consistency within the coupling. |
||||
|
||||
The downward radiation fluxes (i.e. \sw\ and \lw radiation) as computed by the atmospheric \cclm\ do not only simply depend on surface fields. |
||||
% |
||||
Thus, these fluxes are still calculated by the atmospheric model and then passed through the flux calculator to the ocean model. |
||||
|
||||
\section{Simulation setup for the validation} |
||||
|
||||
In order to validate the quality of the developed coupled \esm, a setup is used as described in the following section and is illustrated in \Fig{fig:simulation-setup}. |
||||
|
||||
\begin{figure} |
||||
\centering |
||||
\includegraphics[width=0.8\textwidth]{"./figures/coupled_vs_uncoupled.pdf"} |
||||
\captionsetup{width=\linewidth} |
||||
\caption{\label{fig:simulation-setup}\textbf{Model setup for coupled and uncoupled runs.} Atmospheric grid has a resolution of 0.22 by 0.22$^\circ$ whereas the ocean model's grid has the size 3 by 3 \nm.} |
||||
\end{figure} |
||||
|
||||
\subsection{Uncoupled atmospheric model} |
||||
First, ERA5~\citesqr{era5} reanalysis data is prepared as forcing/boundary data for the \cclm\ atmospheric model for the time range \FullTime. |
||||
% |
||||
With these forcing files an \text{uncoupled} \cclm\ run is performed over the \EC~\citesqr{jacob2014eurocordex} domain using a resolution of 0.22$^\circ$ by 0.22$^\circ$. |
||||
|
||||
\subsection{Uncoupled ocean model} |
||||
From the resulting atmospheric model output, a meteorological forcing for the \mom\ stand-alone ocean model for the Batlic Sea is generated. |
||||
% |
||||
The uncoupled \mom\ run is then performed with a horizontal resolution of 3$ \times $3 \nm. |
||||
% |
||||
\open{The Baltic Sea's \obcs\ at the Skagerrak stems from ...} |
||||
% |
||||
\open{The river runoff ... } |
||||
% |
||||
The marine bio-geochemistry is modeled by the latest version of the internally coupled \ergom~\citesqr{neumann2021}. |
||||
|
||||
\subsection{Coupled \esm} |
||||
For the coupled \esm\ run the same atmospheric (ERA5) forcings is used as for the uncoupled \cclm run. |
||||
% |
||||
Likewise, for the ocean model the same \obcs\ and river runoff data has been used as for the uncoupled \mom\ run. |
||||
% |
||||
The other input parameters of the model components are also kept the same as in both, atmospheric and ocean model, uncoupled runs. |
||||
% |
||||
However, the interaction between ocean and atmosphere over the Baltic Sea region is now realized as a two-way coupling via the \textit{exchange grid} and the \textit{flux calculator}. |
||||
% |
||||
(Thus, the forcings generated from the uncoupled \cclm\ run are not needed for the coupled run.)\\ |
||||
|
||||
The data of all three kinds of runs, i.e. uncoupled \cclm, uncoupled \mom\ and the coupled \esm, is analyzed in the following for a time span of 60 years, i.e. \ValidationTime. |
||||
% |
||||
The employed analysis is described in detail in the following and the resulting figures are shown and discussed in \Secs{\ref{sec:CCLM} and \ref{sec:MOM5}}. |
||||
|
||||
|
||||
\section{Validation procedure} |
||||
|
||||
In order to judge the quality of the individual model runs the data has been compared to ERA5 reanalysis data. |
||||
% |
||||
To examine the quality of the model the following quantities are examined. |
||||
|
||||
\subsection{Two-dimensional climatologies/anomalies} |
||||
|
||||
As a first indicator for the model's accuracy, temporal means of two-dimensional surface variables $\langle \phi \rangle_S(x,y)$ are considered for different seasons $S$, i.e. |
||||
% |
||||
\begin{align} |
||||
\langle \phi \rangle_S(x,y) = \frac{1}{N_S} \sum_{t\in S} \phi(x,y,t), |
||||
\end{align} |
||||
% |
||||
where $t$ are all time steps that are contained in season $S$. The number of these time steps is given by $N_S$, where the considered time period is \ValidationTime. |
||||
|
||||
The corresponding two-dimensional seasonal anomaly $\langle \Delta \phi \rangle_S(x,y)$ with respect to a reference field $\phi_{\mathrm{ref}}(x,y,t)$ is then consequently |
||||
% |
||||
\begin{align} |
||||
\langle \Delta \phi \rangle_S(x,y) & = \frac{1}{N_S} \sum_{t\in S} \phi(x,y,t) - \phi_{\mathrm{ref}}(x,y,t) \\ |
||||
& = \langle \phi \rangle_S(x,y) - \langle \phi_{\mathrm{ref}} \rangle_S(x,y) |
||||
\end{align} |
||||
% |
||||
The smaller the magnitude of these anomalies are the better is the performance. |
||||
|
||||
|
||||
\subsection{Time series} |
||||
|
||||
In addition to the two-dimensional data also time series of model and reference data are compared. |
||||
% |
||||
The time series are considered at various coordinates where measurement stations are located as well as spatial means over certain regions. |
||||
|
||||
The stations and regions may be naturally different for the atmospheric and the ocean model, as it is depicted in \Fig{fig:stations-and-regions}. |
||||
% |
||||
\begin{figure} |
||||
\centering |
||||
\begin{subfigure}[t]{0.45\textwidth} |
||||
\centering |
||||
\includegraphics[width=\linewidth]{"./data_figures/MOM5/latest/figures/draw_stations_and_regions/SST.png"} |
||||
\caption{\label{fig:stations-and-regions-MOM5} Stations and regions that are used for validation of the ocean component (\mom) of the \esm.} |
||||
\end{subfigure} |
||||
\hfill |
||||
\begin{subfigure}[t]{0.45\textwidth} |
||||
\centering |
||||
\includegraphics[width=\linewidth]{"./data_figures/CCLM/latest/figures/draw_stations_and_regions/T_2M_AV.png"} |
||||
\caption{\label{fig:stations-and-regions-CCLM} Stations and regions that are used for validation of the atmospheric component (\cclm) of the \esm.} |
||||
\end{subfigure} |
||||
\captionsetup{width=\linewidth} |
||||
\caption{\label{fig:stations-and-regions} |
||||
\textbf{Particularly analyzed domains of the ocean and atmospheric models.} |
||||
} |
||||
\end{figure} |
||||
|
||||
|
||||
\subsection{Taylor Diagrams} |
||||
|
||||
Since comparing time series by eye will only allow qualitative judgment of the model results, Taylor diagrams~\citesqr{taylor2001} are created for each of the above mentioned time series. |
||||
% |
||||
Taylor diagrams graphically indicate which of several model data represents best a given reference data. |
||||
% |
||||
In order to quantify the degree of correspondence between the modeled and observed behavior, three statistical measures determine the diagram, i.e. the Pearson correlation coefficient, the \rmse, and the standard deviation. |
||||
% |
||||
Here both data, model and reference, consist of the same number of samples that correspond to a time series starting from \ValidationTime\ post-processed with different temporal means. |
||||
|
||||
|
||||
\subsection{Cost functions} |
||||
|
||||
The cost function $c$ as it is defined here, further summarizes the information given in a Taylor diagram. |
||||
% |
||||
It measures the \rmse |
||||
% |
||||
\begin{align} |
||||
\epsilon = \sqrt{\frac{1}{N}\sum_{t=t_1}^{t_{N}} (\phi(t)-\phi_{\mathrm{ref}}(t))^2} |
||||
\end{align} |
||||
% |
||||
of the model data $\phi(t)$in units of the standard deviation $\sigma_{\mathrm{ref}}$ of reference data $\phi_{\mathrm{ref}}(t)$, i.e. |
||||
\begin{align} |
||||
c = \epsilon / \sigma_{\mathrm{ref}}. |
||||
\end{align} |
||||
Both data consist of $N$ samples corresponding to a time series starting from $t_1$ and ending at $t_N$, i.e. spanning a time of \ValidationTime. |
||||
|
||||
|
||||
\subsection{Vertical profiles} |
||||
|
||||
In order to go beyond the analysis of surface fields, vertical profiles of important ocean state variables are compared against observation data at particular stations. |
||||
% |
||||
The vertical profiles are generated from a four-dimensional field $\phi(x, y, z, t)$ at the chosen stations $\zeta$ (i.e. fixing $x = x_\zeta$ and $y = y_\zeta$ and using remapping to nearest neighbors) accompanied by performing the configured seasonal means for the aforementioned seasons $S$. |
||||
% |
||||
In other words, the vertical profile for a station $\zeta$ and seasons $S$ is given by |
||||
% |
||||
\begin{align} |
||||
\langle \phi_{\zeta} \rangle_S (z) = \frac{1}{N_S} \sum_{t\in S} \phi(x_\zeta, y_\zeta, z, t). |
||||
\end{align} |
||||
\\ |
||||
The described analysis is automatically done within developed framework that is driving the coupled \esm, as it will be published elsewhere with technical details. |
||||
|
||||
\section{Results of the uncorrected model} |
||||
|
||||
\subsection{Atmospheric model output from \cclm} |
||||
\label{sec:CCLM} |
||||
|
||||
|
||||
\subsubsection{Two-meter air temperature} |
||||
|
||||
\paragraph{Seasonal anomalies} |
||||
|
||||
See \Fig{fig:T_2M_AV_anomalies}. |
||||
|
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=\textwidth]{"./data_figures/CCLM/latest/figures/compare_2D_anomalies/T_2M_AV.png"} |
||||
\captionsetup{width=\linewidth} |
||||
\caption{\label{fig:T_2M_AV_anomalies}\textbf{Seasonal anomalies for the two-meter air temperature.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
|
||||
\paragraph{Time series} |
||||
|
||||
See \Fig{fig:T_2M_AV_time_series_stations} and \Fig{fig:T_2M_AV_time_series_regions}. |
||||
|
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=0.7\linewidth]{"./data_figures/CCLM/latest/figures/compare_time_series/T_2M_AV-stations.png"} |
||||
\caption{\label{fig:T_2M_AV_time_series_stations}\textbf{Time series for the two-meter air temperature at chosen stations.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
% |
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=0.7\linewidth]{"./data_figures/CCLM/latest/figures/compare_time_series/T_2M_AV-regions.png"} |
||||
\caption{\label{fig:T_2M_AV_time_series_regions}\textbf{Time series for the two-meter air temperature at chosen regions.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
|
||||
\paragraph{Taylor diagrams} |
||||
|
||||
See \Fig{fig:T_2M_AV_taylor_diagrams_stations} and \Fig{fig:T_2M_AV_taylor_diagrams_regions}. |
||||
|
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=0.7\linewidth]{"./data_figures/CCLM/latest/figures/create_taylor_diagrams/T_2M_AV-stations.png"} |
||||
\caption{\label{fig:T_2M_AV_taylor_diagrams_stations}\textbf{Taylor diagrams for the two-meter air temperature at chosen stations.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
% |
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=0.7\linewidth]{"./data_figures/CCLM/latest/figures/create_taylor_diagrams/T_2M_AV-regions.png"} |
||||
\caption{\label{fig:T_2M_AV_taylor_diagrams_regions}\textbf{Taylor diagrams for the two-meter air temperature at chosen regions.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
|
||||
\paragraph{Cost functions} |
||||
|
||||
See \Fig{fig:T_2M_AV_cost_functions_stations} and \Fig{fig:T_2M_AV_cost_functions_regions}. |
||||
|
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=0.5\linewidth]{"./data_figures/CCLM/latest/figures/get_cost_function/T_2M_AV-stations.png"} |
||||
\caption{\label{fig:T_2M_AV_cost_functions_stations}\textbf{Cost functions for the two-meter air temperature at chosen stations.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
% |
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=0.5\linewidth]{"./data_figures/CCLM/latest/figures/get_cost_function/T_2M_AV-regions.png"} |
||||
\caption{\label{fig:T_2M_AV_cost_functions_regions}\textbf{Cost functions for the two-meter air temperature at chosen regions.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
|
||||
|
||||
\subsubsection{Wind speed} |
||||
|
||||
\paragraph{Seasonal anomalies} |
||||
|
||||
See \Fig{fig:SPEED_10M_AV_anomalies}. |
||||
|
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=\textwidth]{"./data_figures/CCLM/latest/figures/compare_2D_anomalies/SPEED_10M_AV.png"} |
||||
\captionsetup{width=\linewidth} |
||||
\caption{\label{fig:SPEED_10M_AV_anomalies}\textbf{Seasonal anomalies for the ten-meter wind speed.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
|
||||
\subsection{Precipitation} |
||||
|
||||
\paragraph{Seasonal anomalies} |
||||
|
||||
See \Fig{fig:DAY_PREC_anomalies}. |
||||
|
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=\textwidth]{"./data_figures/CCLM/latest/figures/compare_2D_anomalies/DAY_PREC.png"} |
||||
\captionsetup{width=\linewidth} |
||||
\caption{\label{fig:DAY_PREC_anomalies}\textbf{Seasonal anomalies for the precipitation.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
|
||||
\open{ |
||||
\paragraph{Further plan} |
||||
|
||||
\begin{itemize} |
||||
\item now only results from coupled model are shown, next step is to compare to uncoupled (data is available) |
||||
\end{itemize} |
||||
} |
||||
|
||||
\subsection{Ocean model output from \mom} |
||||
\label{sec:MOM5} |
||||
|
||||
|
||||
\subsubsection{Sea-surface temperature} |
||||
|
||||
\paragraph{Seasonal anomalies} |
||||
|
||||
See \Fig{fig:SST_anomalies}. |
||||
|
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=\textwidth]{"./data_figures/MOM5/latest/figures/compare_2D_anomalies/SST.png"} |
||||
\captionsetup{width=\linewidth} |
||||
\caption{\label{fig:SST_anomalies}\textbf{Seasonal anomalies for the sea-surface temperature.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
|
||||
|
||||
\paragraph{Time series} |
||||
|
||||
\paragraph{Taylor diagrams} |
||||
|
||||
\paragraph{Cost functions} |
||||
|
||||
\subsubsection{Vertical temperature profiles} |
||||
|
||||
See \Fig{fig:temp_profiles_stations}. |
||||
|
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=0.7\textwidth]{"./data_figures/MOM5/latest/figures/compare_vertical_profiles/temp-stations.png"} |
||||
\captionsetup{width=\linewidth} |
||||
\caption{\label{fig:temp_profiles_stations}\textbf{Vertical temperature profiles at chosen stations in the Baltic Sea.} The reference is the BED data set\open{~\citesqr{???}}. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
|
||||
\subsubsection{Sea-ice coverage} |
||||
|
||||
\paragraph{Seasonal anomalies} |
||||
|
||||
See \Fig{fig:FI_anomalies}. |
||||
|
||||
\begin{figure*} |
||||
\centering |
||||
\includegraphics[width=\textwidth]{"./data_figures/MOM5/latest/figures/compare_2D_anomalies/FI.png"} |
||||
\captionsetup{width=\linewidth} |
||||
\caption{\label{fig:FI_anomalies}\textbf{Seasonal anomalies for the sea-ice coverage.} The anomaly is with respect to the ERA5 reanalysis data. The temporal averages are performed over a time range \ValidationTime.} |
||||
\end{figure*} |
||||
|
||||
\open{ |
||||
\paragraph{Further plan} |
||||
|
||||
\begin{itemize} |
||||
\item now only results from coupled model are shown, next step is to compare to uncoupled (data is available) |
||||
\end{itemize} |
||||
} |
||||
|
||||
\section{Results of the bias corrected models} |
||||
|
||||
\section{Conclusions} |
||||
|
||||
{\color{red} |
||||
\lipsum[1-3] |
||||
} |
||||
|
||||
\bibliography{all} |
||||
%\bibliography{test} |
||||
|
||||
\end{document} |
||||
@ -0,0 +1,22 @@
|
||||
\newcommand{\Fig}[1]{Fig.\,\ref{#1}} |
||||
\newcommand{\Figs}[1]{Figs.\,#1} |
||||
|
||||
\newcommand{\Sec}[1]{Sect.\,\ref{#1}} |
||||
|
||||
\newcommand{\Secs}[1]{Sects.\,#1} |
||||
|
||||
\newcommand{\open}[1]{{\color{red}#1}} |
||||
|
||||
\newcommand{\FullTime}{1959-01-01 - 2021-12-31} |
||||
|
||||
\newcommand{\ValidationTime}{1960-01-01 - 2019-12-31} |
||||
|
||||
\newcommand{\EC}{EURO-CORDEX } |
||||
|
||||
\renewcommand{\vec}[1]{\mathbf{#1}} |
||||
|
||||
\usepackage[square,numbers]{natbib} |
||||
\bibliographystyle{unsrtnat} |
||||
\newcommand{\citesqr}[1]{\cite{#1}} |
||||
|
||||
|
||||
Loading…
Reference in new issue