{"id":125,"date":"2023-08-23T20:46:48","date_gmt":"2023-08-23T20:46:48","guid":{"rendered":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/chapter\/solution-exercise-1-meteoric-water-lines\/"},"modified":"2024-01-15T14:44:43","modified_gmt":"2024-01-15T14:44:43","slug":"solution-exercise-1-meteoric-water-lines","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/chapter\/solution-exercise-1-meteoric-water-lines\/","title":{"raw":"Solution Exercise\u00a01\u00a0-\u00a0Meteoric Water Lines","rendered":"Solution Exercise\u00a01\u00a0–\u00a0Meteoric Water Lines"},"content":{"raw":"
\r\n

Step-by-step calculation is shown in the tables and calculations that follow.<\/p>\r\n \r\n

Calculation of a meteoric water line<\/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
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Location<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

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

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

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

\r\n
\r\n

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

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

\r\n
\r\n\r\n(\u03b418<\/sup>Oi<\/sub>- \u03b4\ud835\udfcf\ud835\udfd6<\/sup>\ud835\udc0e\u0305\u0305\u0305\u0305\u0305)2<\/sup><\/strong>\r\n\r\n<\/div><\/td>\r\n
\r\n
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(\u03b4Di \u2212 \u03b4\ud835\udc03\u0305\u0305\u0305\u0305)2<\/sup><\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

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(\u03b418<\/sup><\/strong>Oi<\/sub> \u2212 \u03b4\ud835\udfcf\ud835\udfd6\u0305\u0305\u0305\u0305\ud835\udc0e\u0305)<\/strong>\r\n(\u03b4Di \u2212 \u03b4\ud835\udc03\u0305\u0305)<\/strong><\/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

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

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

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

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

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

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54.36<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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

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

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4.96<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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

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

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12.50<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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

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

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0.21<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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

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

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-0.25<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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

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

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9.20<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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

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

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9.30<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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

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

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1.75<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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

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

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-0.30<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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

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

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0.20<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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

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

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-0.53<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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-39.9<\/p>\r\n\r\n<\/div><\/td>\r\n

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

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

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89.34<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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SS-\u03b418<\/sup>O<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

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SS-\u03b4D<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

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SP-\u03b418<\/sup>O-\u03b4D<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

\r\n
\r\n

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

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

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1150<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
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-2.19<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

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-8.82<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

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

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1602.30<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

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180.74<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

SS = sum of squares; SP = sum of products.<\/p>\r\n

For the best fit line by RMA (reduced major axis) regression:<\/p>\r\n

[latex] \\begin{aligned}\r\n& \\text { the gradient }=\\sqrt{\\frac{S S \\delta D}{S S \\delta^{18} O}}=\\sqrt{\\frac{1602.30}{25.56}}=7.92 \\\\\r\n& \\text { the intercept }=\\overline{\\delta D}-\\left(7.92 \\overline{\\delta^{18} O}\\right)=-8.8-(7.92(-2.19))=8.49\r\n\\end{aligned} [\/latex]<\/p>\r\n

therefore, the LMWL<\/strong>UCT<\/sub>-<\/sub>2010<\/sub> is D<\/em>\u00a0=\u00a07.9218<\/em><\/sup>O<\/em>\u00a0+\u00a08.49<\/p>\r\n

Pearson\u2019s r<\/em>, the sample correlation coefficient<\/p>\r\n

[latex]{=r}_{^{18}OD}=\\frac{{SP}^{18}OD}{\\sqrt{{SS}^{18}O}\\sqrt{SSD}}=\\frac{180.74}{\\sqrt{25.56}\\sqrt{1602.30}}=0.893[\/latex]<\/span><\/p>\r\n \r\n

Calculation of a <\/strong>precipitation<\/strong>-<\/strong>weighted meteoric water line<\/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
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Location<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

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

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

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

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

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

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

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

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Rain-fraction<\/strong>
(rf)<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

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

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

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

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

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

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

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

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

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

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0.0078<\/p>\r\n\r\n<\/div><\/td>\r\n

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0.0059<\/p>\r\n\r\n<\/div><\/td>\r\n

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0.0759<\/p>\r\n\r\n<\/div><\/td>\r\n

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

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

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0.43<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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0.0104<\/p>\r\n\r\n<\/div><\/td>\r\n

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-0.0056<\/p>\r\n\r\n<\/div><\/td>\r\n

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-0.0605<\/p>\r\n\r\n<\/div><\/td>\r\n

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

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

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0.05<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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0.0061<\/p>\r\n\r\n<\/div><\/td>\r\n

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-0.0051<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
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0.0024<\/p>\r\n\r\n<\/div><\/td>\r\n

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

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

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0.08<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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

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

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

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0.0383<\/p>\r\n\r\n<\/div><\/td>\r\n

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-0.0861<\/p>\r\n\r\n<\/div><\/td>\r\n

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-0.4630<\/p>\r\n\r\n<\/div><\/td>\r\n

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

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

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0.01<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

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

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

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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

\r\n
\r\n

0.2409<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.6696<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-2.0233<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

-0.06<\/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

\r\n
\r\n

0.1930<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.6390<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-3.2817<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

1.78<\/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

\r\n
\r\n

0.1443<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.5326<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-2.1652<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

1.34<\/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

\r\n
\r\n

0.1052<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.1831<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.5156<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

0.18<\/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

\r\n
\r\n

0.0870<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.1948<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.2870<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

-0.03<\/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

\r\n
\r\n

0.0887<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.1907<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.2927<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

0.02<\/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

\r\n
\r\n

0.0635<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.1517<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.3936<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

-0.03<\/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

\r\n
\r\n

0.0148<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.0748<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-0.5898<\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

1.32<\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

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

\"\"<\/strong><\/td>\r\n<\/tr>\r\n
\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

1150<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-2.19<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-8.82<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

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

\r\n
\r\n

-2.73<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

-9.99<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n

\r\n
\r\n

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

\r\n
\r\n

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

\r\n
\r\n

5.08<\/strong><\/p>\r\n\r\n<\/div><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

SS = sum of squares; SP = sum of products; rf = rain fraction (i.e., weighted by precipitation).<\/p>\r\n

For the best fit line by RMA (reduced major axis) regression:<\/p>\r\n

[latex]\\begin{aligned}\r\n& \\text { the gradient }=\\sqrt{\\frac{S S \\times r f \\delta D}{S S \\times r f \\delta^{18} O}}=\\sqrt{\\frac{43.98}{0.909}}=6.95 \\\\\r\n& \\text { the intercept }=\\sum r f . \\delta D-6.95 \\sum r f . \\delta^{18} O=-9.99-(6.95(-2.73))=8.96\r\n\\end{aligned}[\/latex]<\/p>\r\n

the precipitation<\/strong> weighted LMWL<\/strong>UCT<\/sub>-<\/sub>2010<\/sub> is \u03b4D<\/em>\u00a0=\u00a06.95\u03b418<\/em><\/sup>O<\/em>\u00a0+\u00a08.96<\/p>\r\n

Pearson\u2019s r<\/em>, the sample correlation coefficient<\/p>\r\n

[latex]r_{r f \\delta^{18} O \\delta D}=\\frac{\\operatorname{SPrf} \\delta^{18} O \\delta D}{\\sqrt{\\operatorname{SSrf} \\delta^{18} O} \\sqrt{\\operatorname{SSrf} \\delta D}}=\\frac{5.08}{\\sqrt{0.909} \\sqrt{43.87}}=0.805[\/latex]<\/span><\/p>\r\n

Return to Exercise\u00a0<\/span>1<\/span><\/a><\/strong><\/p>\r\n\r\n<\/div>","rendered":"

\n

Step-by-step calculation is shown in the tables and calculations that follow.<\/p>\n

 <\/p>\n

Calculation of a meteoric water line<\/strong><\/p>\n\n\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 mm<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

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

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

\n
\n

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

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

\n
\n

(\u03b418<\/sup>Oi<\/sub>– \u03b4\ud835\udfcf\ud835\udfd6<\/sup>\ud835\udc0e\u0305\u0305\u0305\u0305\u0305)2<\/sup><\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

(\u03b4Di \u2212 \u03b4\ud835\udc03\u0305\u0305\u0305\u0305)2<\/sup><\/strong><\/p>\n<\/div>\n<\/td>\n

\n
(\u03b418<\/sup><\/strong>Oi<\/sub> \u2212 \u03b4\ud835\udfcf\ud835\udfd6\u0305\u0305\u0305\u0305\ud835\udc0e\u0305)<\/strong>
\n(\u03b4Di \u2212 \u03b4\ud835\udc03\u0305\u0305)<\/strong><\/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

\n
\n

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

\n
\n

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

\n
\n

54.36<\/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

\n
\n

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

\n
\n

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

\n
\n

4.96<\/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

\n
\n

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

\n
\n

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

\n
\n

12.50<\/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

\n
\n

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

\n
\n

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

\n
\n

0.21<\/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

\n
\n

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

\n
\n

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

\n
\n

-0.25<\/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

\n
\n

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

\n
\n

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

\n
\n

9.20<\/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

\n
\n

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

\n
\n

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

\n
\n

9.30<\/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

\n
\n

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

\n
\n

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

\n
\n

1.75<\/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

\n
\n

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

\n
\n

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

\n
\n

-0.30<\/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

\n
\n

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

\n
\n

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

\n
\n

0.20<\/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

\n
\n

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

\n
\n

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

\n
\n

-0.53<\/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

\n
\n

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

\n
\n

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

\n
\n

89.34<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

\n
\n

\n<\/div>\n<\/td>\n

\n
\n

\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

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

\n
\n

SS-\u03b418<\/sup>O<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

SS-\u03b4D<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

SP-\u03b418<\/sup>O-\u03b4D<\/strong><\/p>\n<\/div>\n<\/td>\n<\/tr>\n

\n
\n

\n<\/div>\n<\/td>\n

\n
\n

\n<\/div>\n<\/td>\n

\n
\n

1150<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

-2.19<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

-8.82<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

1602.30<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

180.74<\/strong><\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

SS = sum of squares; SP = sum of products.<\/p>\n

For the best fit line by RMA (reduced major axis) regression:<\/p>\n

[latex]\\begin{aligned} & \\text { the gradient }=\\sqrt{\\frac{S S \\delta D}{S S \\delta^{18} O}}=\\sqrt{\\frac{1602.30}{25.56}}=7.92 \\\\ & \\text { the intercept }=\\overline{\\delta D}-\\left(7.92 \\overline{\\delta^{18} O}\\right)=-8.8-(7.92(-2.19))=8.49 \\end{aligned}[\/latex]<\/p>\n

therefore, the LMWL<\/strong>UCT<\/sub>–<\/sub>2010<\/sub> is D<\/em>\u00a0=\u00a07.9218<\/em><\/sup>O<\/em>\u00a0+\u00a08.49<\/p>\n

Pearson\u2019s r<\/em>, the sample correlation coefficient<\/p>\n

[latex]{=r}_{^{18}OD}=\\frac{{SP}^{18}OD}{\\sqrt{{SS}^{18}O}\\sqrt{SSD}}=\\frac{180.74}{\\sqrt{25.56}\\sqrt{1602.30}}=0.893[\/latex]<\/span><\/p>\n

 <\/p>\n

Calculation of a <\/strong>precipitation<\/strong>–<\/strong>weighted meteoric water line<\/strong><\/p>\n\n\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 mm<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

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

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

\n
\n

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

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

\n
\n

Rain-fraction<\/strong>
(rf)<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

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

\n
\n

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

\"\"<\/td>\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

\n
\n

0.0078<\/p>\n<\/div>\n<\/td>\n

\n
\n

0.0059<\/p>\n<\/div>\n<\/td>\n

\n
\n

0.0759<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

0.43<\/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

\n
\n

0.0104<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.0056<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.0605<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

0.05<\/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

\n
\n

0.0061<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.0051<\/p>\n<\/div>\n<\/td>\n

\n
\n

0.0024<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

0.08<\/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

\n
\n

0.0383<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.0861<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.4630<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

0.01<\/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

\n
\n

0.2409<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.6696<\/p>\n<\/div>\n<\/td>\n

\n
\n

-2.0233<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

-0.06<\/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

\n
\n

0.1930<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.6390<\/p>\n<\/div>\n<\/td>\n

\n
\n

-3.2817<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

1.78<\/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

\n
\n

0.1443<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.5326<\/p>\n<\/div>\n<\/td>\n

\n
\n

-2.1652<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

1.34<\/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

\n
\n

0.1052<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.1831<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.5156<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

0.18<\/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

\n
\n

0.0870<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.1948<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.2870<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

-0.03<\/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

\n
\n

0.0887<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.1907<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.2927<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

0.02<\/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

\n
\n

0.0635<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.1517<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.3936<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

-0.03<\/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

\n
\n

0.0148<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.0748<\/p>\n<\/div>\n<\/td>\n

\n
\n

-0.5898<\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

1.32<\/p>\n<\/div>\n<\/td>\n<\/tr>\n

\n
\n

\n<\/div>\n<\/td>\n

\n
\n

\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

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

\n
\n

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

\n
\n

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

\n
\n

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

\n
\n

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

\n
\n

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

\"\"<\/strong><\/td>\n<\/tr>\n
\n
\n

\n<\/div>\n<\/td>\n

\n
\n

\n<\/div>\n<\/td>\n

\n
\n

1150<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

-2.19<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

-8.82<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

-2.73<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

-9.99<\/strong><\/p>\n<\/div>\n<\/td>\n

\n
\n

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

\n
\n

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

\n
\n

5.08<\/strong><\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

SS = sum of squares; SP = sum of products; rf = rain fraction (i.e., weighted by precipitation).<\/p>\n

For the best fit line by RMA (reduced major axis) regression:<\/p>\n

[latex]\\begin{aligned} & \\text { the gradient }=\\sqrt{\\frac{S S \\times r f \\delta D}{S S \\times r f \\delta^{18} O}}=\\sqrt{\\frac{43.98}{0.909}}=6.95 \\\\ & \\text { the intercept }=\\sum r f . \\delta D-6.95 \\sum r f . \\delta^{18} O=-9.99-(6.95(-2.73))=8.96 \\end{aligned}[\/latex]<\/p>\n

the precipitation<\/strong> weighted LMWL<\/strong>UCT<\/sub>–<\/sub>2010<\/sub> is \u03b4D<\/em>\u00a0=\u00a06.95\u03b418<\/em><\/sup>O<\/em>\u00a0+\u00a08.96<\/p>\n

Pearson\u2019s r<\/em>, the sample correlation coefficient<\/p>\n

[latex]r_{r f \\delta^{18} O \\delta D}=\\frac{\\operatorname{SPrf} \\delta^{18} O \\delta D}{\\sqrt{\\operatorname{SSrf} \\delta^{18} O} \\sqrt{\\operatorname{SSrf} \\delta D}}=\\frac{5.08}{\\sqrt{0.909} \\sqrt{43.87}}=0.805[\/latex]<\/span><\/p>\n

Return to Exercise\u00a0<\/span>1<\/span><\/a><\/strong><\/p>\n<\/div>\n","protected":false},"author":4,"menu_order":35,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-125","chapter","type-chapter","status-publish","hentry"],"part":198,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapters\/125","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":82,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapters\/125\/revisions"}],"predecessor-version":[{"id":631,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapters\/125\/revisions\/631"}],"part":[{"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/parts\/198"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapters\/125\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/wp\/v2\/media?parent=125"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/pressbooks\/v2\/chapter-type?post=125"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/wp\/v2\/contributor?post=125"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/wp-json\/wp\/v2\/license?post=125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}