{"id":120,"date":"2023-08-23T20:46:48","date_gmt":"2023-08-23T20:46:48","guid":{"rendered":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/chapter\/exercise-1-meteoric-water-line-calculations\/"},"modified":"2024-01-15T01:03:00","modified_gmt":"2024-01-15T01:03:00","slug":"exercise-1-meteoric-water-line-calculations","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/chapter\/exercise-1-meteoric-water-line-calculations\/","title":{"raw":"Exercise\u00a01\u00a0-\u00a0Meteoric Water Line Calculations","rendered":"Exercise\u00a01\u00a0–\u00a0Meteoric Water Line Calculations"},"content":{"raw":"
\r\n

Meteoric water lines are not essential for every stable isotope study, but they are needed frequently, particularly when comparing surface water or groundwater to precipitation. The calculation of a meteoric water line was covered theoretically in this book, but this exercise provides readers with the opportunity to develop a MWL.<\/p>\r\n

Precipitation and stable isotope data for the University of Cape Town for 2010 are given in the table below. Using the data:<\/p>\r\n\r\n

    \r\n \t
  1. Calculate the local meteoric water line using the RMA (reduced major axis) regression method and calculate the Pearson's r correlation coefficient; and,<\/li>\r\n \t
  2. Calculate the precipitation-weighted RMA regression line and its Pearson's r<\/em>.<\/span><\/li>\r\n<\/ol>\r\n

    Stable isotope data for UCT <\/strong>precipitation<\/strong><\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \r\n
    \r\n

    Location<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Date<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Precipitation<\/strong><\/p>\r\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 mm<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    \u03b418<\/sup>O<\/strong><\/p>\r\n

    \u2030<\/span><\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    \u03b4D<\/strong><\/p>\r\n

    \u2030<\/span><\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Jan 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    9<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    +0.75<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    +9.7<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Feb 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    12<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -0.54<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -5.8<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Mar 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    7<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -0.83<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    +0.4<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Apr 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    44<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -2.25<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -12.1<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    May 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    277<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -2.78<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -8.4<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Jun 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    222<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -3.31<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -17.0<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Jul 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    166<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -3.69<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -15.0<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Aug 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    121<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -1.74<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -4.9<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Sep 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    100<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -2.24<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -3.3<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Oct 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    102<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -2.15<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -3.3<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Nov 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    73<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -2.39<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -6.2<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

    \r\n
    \r\n

    UCT<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    Dec 2010<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    17<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -5.06<\/p>\r\n\r\n<\/div><\/td>\r\n

    		\r\n
    \r\n

    -39.9<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    Click for solutio<\/span>n to<\/span> Exercise\u00a01<\/span><\/a><\/strong><\/p>\r\n

    <\/p>\r\n\r\n<\/div>","rendered":"

    \n

    Meteoric water lines are not essential for every stable isotope study, but they are needed frequently, particularly when comparing surface water or groundwater to precipitation. The calculation of a meteoric water line was covered theoretically in this book, but this exercise provides readers with the opportunity to develop a MWL.<\/p>\n

    Precipitation and stable isotope data for the University of Cape Town for 2010 are given in the table below. Using the data:<\/p>\n

      \n
    1. Calculate the local meteoric water line using the RMA (reduced major axis) regression method and calculate the Pearson’s r correlation coefficient; and,<\/li>\n
    2. Calculate the precipitation-weighted RMA regression line and its Pearson’s r<\/em>.<\/span><\/li>\n<\/ol>\n

      Stable isotope data for UCT <\/strong>precipitation<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
      \n
      \n

      Location<\/strong><\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Date<\/strong><\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Precipitation<\/strong><\/p>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 mm<\/strong><\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      \u03b418<\/sup>O<\/strong><\/p>\n

      \u2030<\/span><\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      \u03b4D<\/strong><\/p>\n

      \u2030<\/span><\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Jan 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      9<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      +0.75<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      +9.7<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Feb 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      12<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -0.54<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -5.8<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Mar 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      7<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -0.83<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      +0.4<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Apr 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      44<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -2.25<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -12.1<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      May 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      277<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -2.78<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -8.4<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Jun 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      222<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -3.31<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -17.0<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Jul 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      166<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -3.69<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -15.0<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Aug 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      121<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -1.74<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -4.9<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Sep 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      100<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -2.24<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -3.3<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Oct 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      102<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -2.15<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -3.3<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Nov 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      73<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -2.39<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -6.2<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

      \n
      \n

      UCT<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      Dec 2010<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      17<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -5.06<\/p>\n<\/div>\n<\/td>\n

      		\n
      \n

      -39.9<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      Click for solutio<\/span>n to<\/span> Exercise\u00a01<\/span><\/a><\/strong><\/p>\n

      \n<\/div>\n","protected":false},"author":4,"menu_order":32,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-120","chapter","type-chapter","status-publish","hentry"],"part":190,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapters\/120","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/wp\/v2\/users\/4"}],"version-history":[{"count":13,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapters\/120\/revisions"}],"predecessor-version":[{"id":507,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapters\/120\/revisions\/507"}],"part":[{"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/parts\/190"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapters\/120\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/wp\/v2\/media?parent=120"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapter-type?post=120"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/wp\/v2\/contributor?post=120"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/wp\/v2\/license?post=120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}