Research

Temperature fluctuations - The Code

The tempFGN github repository contains all the material related to the paper: How does temperature vary over time? Evidence on the stationary and fractal nature of temperature by John Dagsvik, Mariachiara Fortuna, Sigmund H. Moen All the materials are stored in the form of an R package. You can download or clone the repository and install the package: then all the functions will be available for usage. The same repository contains the online resources published as paper supplementary materials.

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Temperature fluctuations - The Idea Behind

Usually, looking at the time series of observed temperatures, we see graphs as the one below. These graphs show the temperature fluctuations over the past 150 years, where temperatures show a systematic increase. The length of the time series is a crucial feature for understanding temperature fluctuations, because temperatures show cycles that seem to persist for several decades: so, if we want to understand the amplitude of the climate fluctuations, the limited length of the time series may compromise our understanding of the phenomena.

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Temperature fluctuation paper - Main Results

Affiliations: John K. Dagsvik, Statistics Norway, Research Department; Mariachiara Fortuna, freelance statistician, Turin; Sigmund Hov Moen, Westerdals Oslo School of Arts, Communication and Technology. Corresponding author: John K. Dagsvik, E-mail: john.dagsvik@ssb.no Mariachiara Fortuna, E-mail: mariachiara.fortuna@vanlog.it (reference for code and analysis) TABLES Table 1. Parameter estimation for the selected time series Estimation results for selected cities based on characteristic function regression and Whittle MLE method. Monthly data. City H_c SE(H_c) H_w SE(H_w) Ann.

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Appendix B - Summary data information

Affiliations: John K. Dagsvik, Statistics Norway, Research Department; Mariachiara Fortuna, freelance statistician, Turin; Sigmund Hov Moen, Westerdals Oslo School of Arts, Communication and Technology. Corresponding author: John K. Dagsvik, E-mail: john.dagsvik@ssb.no Mariachiara Fortuna, E-mail: mariachiara.fortuna@vanlog.it (reference for code and analysis) Figure B1. Plots of temperature series for 9 selected cities Table B1. Summary information about data Weather station First year Last year Years Nonmissing months Missing months Argentina, Buenos Aires 1856 2006 151 1781 36 Australia, Adelaide 1881 2012 132 1567 27 Australia, Alice Springs 1881 2012 132 1564 30 Australia, Cap Otway 1865 2012 148 1731 56 Austria, Kremsmunster 1876 2009 134 1601 15 Austria, Vienna 1855 2009 155 1829 38 Belgium, Uccle 1833 2008 176 2108 11 Canada, Winnipeg 1881 2012 132 1575 19 Croatia, Zagreb 1861 2008 148 1765 11 Czech Republic, Prague 1775 2005 231 2764 11 Denmark, Copenhagen 1798 2011 214 2568 11 Denmark, Vestervig 1875 2012 138 1648 11 Egypt, Alexandria 1870 1990 121 1395 66 France, Nantes 1851 2009 159 1893 20 France, Paris 1757 2009 253 3030 11 Germany, Berlin 1756 2012 257 3083 12 Germany, Hohenpeissenberg 1781 2012 232 2782 13 Germany, Karlsruhe 1876 2008 133 1586 20 Greece, Athens 1858 2009 152 1814 14 Greenland, Illulisat 1873 2012 140 1674 16 Greenland, Ivittuut 1873 1960 88 1056 11 Hungary, Budapest 1780 2009 230 2753 13 Iceland, Djupivogur 1873 2009 137 1635 14 Iceland, Reykjavik 1870 2012 143 1711 11 India, Agra 1881 1987 107 1269 21 India, Allahabad 1881 2012 132 1517 70 India, Bombay 1881 2012 132 1569 18 India, Indore 1881 2012 132 1569 18 India, Madras 1881 2012 132 1569 18 India, Nagpur 1881 2011 131 1565 16 Israel, Jerusalem 1861 2004 144 1660 79 Italy, Bologna 1814 2009 196 2334 27 Italy, Milan 1763 2009 247 2943 30 Japan, Hiroshima 1881 2005 125 1489 22 Japan, Nagasaki 1881 2012 132 1582 11 Japan, Tokyo 1876 2012 137 1642 11 Kazakhstan, Kazalinsk 1881 1990 110 1307 16 Luxembourg, Luxembourg 1838 2008 171 2036 27 New Zealand, Wellington 1864 1989 126 1503 13 Norway, Andoya 1868 2012 145 1739 12 Norway, Bergen 1858 2012 155 1860 11 Norway, Bodo 1868 2012 145 1740 11 Norway, Dombas 1865 2012 148 1773 14 Norway, Karasjok 1876 2012 137 1644 11 Norway, Mandal 1861 2007 147 1760 11 Norway, Oksoy Lighthouse 1870 2012 143 1716 11 Norway, Ona 1868 2012 145 1717 34 Norway, Oslo 1816 2012 197 2364 11 Norway, Roros 1871 2012 142 1704 11 Norway, Tromso 1868 2012 145 1740 11 Norway, Utsira 1868 2012 145 1740 11 Norway, Vardo 1858 2008 151 1809 11 Pakistan, Lahore 1876 2012 137 1631 16 Portugal, Lisbon 1881 2009 129 1539 20 Romania, Sulina 1881 2009 129 1530 24 Russia, Archangelsk 1881 2012 132 1580 14 Russia, Sort 1881 1990 110 1294 29 Russia, St Petersburg 1881 2009 129 1543 12 Spain, Gibraltar 1852 2010 159 1850 65 Sweden, Bromma 1756 2011 256 3067 12 Sweden, Stockholm 1756 2004 249 2988 11 Sweden, Tullinge 1756 2011 256 3049 30 Sweden, Uppsala 1722 2012 291 3334 169 Switzerland, Basel 1755 2009 255 3014 52 Switzerland, Geneva 1753 2009 257 3077 13 UK, Aberdeen 1881 2012 132 1582 11 UK, Belfast 1881 2012 132 1576 12 UK, Cambridge 1871 2012 142 1702 11 UK, Durham 1847 2012 166 1989 12 UK, Edinbourg 1785 1993 209 2507 12 UK, London 1841 2004 164 1944 31 UK, Plymouth 1865 1993 129 1543 16 USA, Atlanta 1881 2012 132 1582 12 USA, Bismarck 1881 2012 132 1582 12 USA, Boise 1881 2012 132 1583 11 USA, Boston 1881 2012 132 1583 11 USA, Chattanooga 1881 2012 132 1583 11 USA, Cincinatti 1881 2012 132 1581 13 USA, Columbus 1881 2012 132 1583 11 USA, Concord 1881 2012 132 1583 11 USA, Des Moines 1881 2012 132 1583 11 USA, Detroit 1881 2012 132 1583 11 USA, Dodge City 1881 2012 132 1582 12 USA, Fargo 1881 2012 132 1583 11 USA, Galveston 1881 2012 132 1574 20 USA, Indianapolis 1881 2012 132 1583 11 USA, Jacksonville 1881 2012 132 1581 13 USA, Knoxville 1881 2012 132 1582 12 USA, Las Vegas 1875 1993 119 1428 11 USA, Madison 1881 2012 132 1583 11 USA, Marquette 1881 2012 132 1552 42 USA, Milwaukee 1881 2012 132 1583 11 USA, Mobile 1881 2012 132 1583 11 USA, Nashville 1881 2012 132 1582 12 USA, New Orleans 1874 2005 132 1580 11 USA, New York 1822 2007 186 2225 11

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Appendix C - Estimation and test results

Affiliations: John K. Dagsvik, Statistics Norway, Research Department; Mariachiara Fortuna, freelance statistician, Turin; Sigmund Hov Moen, Westerdals Oslo School of Arts, Communication and Technology. Corresponding author: John K. Dagsvik, E-mail: john.dagsvik@ssb.no Mariachiara Fortuna, E-mail: mariachiara.fortuna@vanlog.it (reference for code and analysis) Table C1. Estimation results when using the characteristic function estimator and the Whittle method. Monthly data. Weather station \(H_c\) \(H_w\) \(SE(H_w)\) Argentina, Buenos Aires 0.

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Appendix D - Properties of the estimators

Affiliations: John K. Dagsvik, Statistics Norway, Research Department; Mariachiara Fortuna, freelance statistician, Turin; Sigmund Hov Moen, Westerdals Oslo School of Arts, Communication and Technology. Corresponding author: John K. Dagsvik, E-mail: john.dagsvik@ssb.no Mariachiara Fortuna, E-mail: mariachiara.fortuna@vanlog.it (reference for code and analysis) Table D1, D2, D3. Properties of different estimators of the FGN model. Bootstrap simulations The following tables show the results of the bootstrap simultations for different estimators of \(\mu\), \(\sigma\), \(H\) and \(\alpha\), given the FGN model with H equal to 0.

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Appendix F - Selection procedure

Affiliations: John K. Dagsvik, Statistics Norway, Research Department; Mariachiara Fortuna, freelance statistician, Turin; Sigmund Hov Moen, Westerdals Oslo School of Arts, Communication and Technology. Corresponding author: John K. Dagsvik, E-mail: john.dagsvik@ssb.no Mariachiara Fortuna, E-mail: mariachiara.fortuna@vanlog.it (reference for code and analysis) Raw data organization The data used in this project were collected by Sigmund Hov Moen, and are available in the Rimfrost system, www.rimfrost.no. All the data are available in the tempFgn repository, see the temperature data section for more.

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Temperature Data

The goal of this section is to describe the data used in the Temperature Fluctuation paper and how these data are organized. All the data are available in the tempFGN repository, and their organization strongly depend from the aim of the analysis that we have carried out. Since the goal of our work was to study the historical variations of temperature fluctuations, we needed long temperatures time series, possibly for several weather station.

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