Solution Exercise 2 – Recharge Altitude
1. The mean stable isotope composition for the Kirstenbosch spring is:
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[latex]\bar{\delta}=\frac{\sum_i^n \delta_i}{n}[/latex] |
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where:
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δi |
= |
value for a given sample |
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n |
= |
total number of samples |
the means are -11.45‰ and -3.11‰ for δ2H and d18O respectively.
2. The weighted means for the precipitation stations are:
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[latex]\bar{\delta}=\sum_i^n \delta_i \times r f_i[/latex] |
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where:
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δ |
= |
denotes a year |
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δi |
= |
value for a given month |
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rfi |
= |
fraction of the total precipitation |
(over 3 years) for that month, calculated as:
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[latex]r f_i=\frac{r_i}{r_t}[/latex] |
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where:
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ri |
= |
rain amount for a month |
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rt |
= |
total rain for the period of the study |
For months with missing data, the total precipitation amount must exclude those months. Final answers of -9.15‰ and -2.90‰ for δ2H and δ18O at University of Cape Town and -14.34‰ and -3.73‰ similarly for the Table Mountain Cableway.
3. The altitude effect per isotope pair is calculated as:
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[latex]\frac{\Delta \delta}{m}=\frac{\bar{\delta}_{T M C}-\bar{\delta}_{U C T}}{h_{T M C}-h_{U C T}}[/latex] |
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where:
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Δ𝛿⁄𝑚
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= |
change in values per meter of altitude |
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𝛿x |
= |
mean stable isotope composition for a station |
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hx |
= |
elevation of that station |
giving answers of -0.0055‰/m for δ2H and -0.00089‰/m for δ18O. These answers are more reasonably displayed for δ2H and δ18O as -0.55‰/100 m and -0.089‰/100 m.
4. The recharge elevation for Kirstenbosch can be calculated by addition of the isotopic altitude effect to the starting elevation at UCT, as follows:
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[latex]h_{K b}=h_{U C T}+\frac{\left(\bar{\delta}_{K b}-\bar{\delta}_{U C T}\right)}{(\Delta \delta / m)}[/latex] |
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or by using the same formula with the hTMC and TMC values, which will produce a subtraction, both of which should give the same answer. Using δ2H gives 591 m and δ18O gives 368 m, the average of which is 479 m. This means the recharge area is 319 m above the spring at 160 m. This is obviously an average elevation as recharge occurs over an area and not at one point.