en:hydro:isotopes
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| en:hydro:isotopes [2022/06/28 09:32] – ckuells | en:hydro:isotopes [2024/04/10 10:02] (current) – external edit 127.0.0.1 | ||
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| - | # Environmental Isotopes | + | ====== |
| - | ## Equilibrium fractionation | + | ===== Equilibrium fractionation |
| Equilibrium fractionation occurs in closed systems. Equilibrium fractionation of water during phase changes is mainly controlled by temperature. The initial isotopic ratio | Equilibrium fractionation occurs in closed systems. Equilibrium fractionation of water during phase changes is mainly controlled by temperature. The initial isotopic ratio | ||
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| $$1000 \cdot ln(\alpha)$$ | $$1000 \cdot ln(\alpha)$$ | ||
| - | |||
| is chosen, to produce values that can be read and interpreted more easily and as $ln(\alpha)$ is quite close (within the error margin of the measurement) to $(alpha-1)\cdot(1000)$ for small deviations of the fractionation factor $\alpha$ from 1.0 (or for small fractionations -- which is very often the case in hydrology). Once the term $1000 \cdot ln(\alpha)$ has been calculated for a given phase change, it can be converted to $\alpha$. Finally, the isotope ratio of the resulting phase B can be calculated using the relationship $\alpha=R_A/ | is chosen, to produce values that can be read and interpreted more easily and as $ln(\alpha)$ is quite close (within the error margin of the measurement) to $(alpha-1)\cdot(1000)$ for small deviations of the fractionation factor $\alpha$ from 1.0 (or for small fractionations -- which is very often the case in hydrology). Once the term $1000 \cdot ln(\alpha)$ has been calculated for a given phase change, it can be converted to $\alpha$. Finally, the isotope ratio of the resulting phase B can be calculated using the relationship $\alpha=R_A/ | ||
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| $$\delta { }^{18}O = \frac{R_{Standard}-R_{Probe}}{R_{Standard}} \cdot 1000 $$ | $$\delta { }^{18}O = \frac{R_{Standard}-R_{Probe}}{R_{Standard}} \cdot 1000 $$ | ||
| - | Hence, once the isotope ratio $R_{Probe}$ has been calculated, it can be converted to a $\delta$ value using that relationship. | + | Hence, once the isotope ratio $R_{Probe}$ has been calculated, it can be converted to a $\delta$ value using that relationship. |
| - | < | + | < |
| library(ggplot2) | library(ggplot2) | ||
| library(latex2exp) | library(latex2exp) | ||
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| </ | </ | ||
| - | ## Non-equilibrium fractionation | + | If you do not have R or your computer or do not want to install it now, you can use the window below to run the code online. Just copy the R code in the (grey) block and insert it into the window. The example code can be deleted. |
| - | ### Diffuse fractionation | + | {{url> |
| + | |||
| + | ===== Non-equilibrium fractionation ===== | ||
| + | |||
| + | ==== Diffuse fractionation | ||
| Diffuse fractionation occurs, if a gas is moving through a vaccum or through another gas. A simpler case is given, if the gase travels through another inert gas. A more complex fractionation occurs, if the gas moves through another gase that contains the moving gas and that gets enriched with the moving gas during the process. This is the case, for example, when evaporation occurs over a water surface and changes the vapour content of the boundary layer during the process as a result of evaporation. | Diffuse fractionation occurs, if a gas is moving through a vaccum or through another gas. A simpler case is given, if the gase travels through another inert gas. A more complex fractionation occurs, if the gas moves through another gase that contains the moving gas and that gets enriched with the moving gas during the process. This is the case, for example, when evaporation occurs over a water surface and changes the vapour content of the boundary layer during the process as a result of evaporation. | ||
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| $$\epsilon_{{}^{2} H}=12.5 \cdot (1-h) $$ | $$\epsilon_{{}^{2} H}=12.5 \cdot (1-h) $$ | ||
| + | |||
| In the case of evaporation from an open water surface, both effects combine and add up. The total fractionation at a temperature $T$ and at a humidity $h$ can be calculated as: | In the case of evaporation from an open water surface, both effects combine and add up. The total fractionation at a temperature $T$ and at a humidity $h$ can be calculated as: | ||
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| An application of this stepwise calculation indicates that the evaporation slope approaches the theoretical value for equilibration with increasing humidity. At the lowest possible humidity, the slope of the evaporation line is between 4.4 at lower temperatures and 3.4 at high temperatures in dry ambient air. | An application of this stepwise calculation indicates that the evaporation slope approaches the theoretical value for equilibration with increasing humidity. At the lowest possible humidity, the slope of the evaporation line is between 4.4 at lower temperatures and 3.4 at high temperatures in dry ambient air. | ||
| - | ```{r diffuse, include=TRUE, | + | <code S| Diffuse.R> |
| hum = 0.8 | hum = 0.8 | ||
| diffusefrac <- function(humidity = 0.8){ | diffusefrac <- function(humidity = 0.8){ | ||
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| } | } | ||
| epsdf <- diffusefrac(hum) | epsdf <- diffusefrac(hum) | ||
| - | ``` | + | </ |
| Both processes can be combined to obtain the isotopic fractionation during evaporation. At a given temperature a phase equilibrium between water and vapour will develop according to the equilibrium fractionation process. In addition, diffuse fractionation will conctribute additional fractionation by diffusion. The result of both processes results in isotope ratios of heavy and light oxygen and hydrogen isotopes in water that define the slope of the evaporation curve. For a given temperature and humidity, the combined effect of equilibrium and diffuse fractionation can now be calculated (still provided that sufficient water is available to prevent any fractionation effects due to enrichment in the reservoir of evaporating water). | Both processes can be combined to obtain the isotopic fractionation during evaporation. At a given temperature a phase equilibrium between water and vapour will develop according to the equilibrium fractionation process. In addition, diffuse fractionation will conctribute additional fractionation by diffusion. The result of both processes results in isotope ratios of heavy and light oxygen and hydrogen isotopes in water that define the slope of the evaporation curve. For a given temperature and humidity, the combined effect of equilibrium and diffuse fractionation can now be calculated (still provided that sufficient water is available to prevent any fractionation effects due to enrichment in the reservoir of evaporating water). | ||
| - | ### The Craig-Gordon Modell | + | ==== The Craig-Gordon Modell |
| - | ### Rayleigh Fractionation | + | ==== Rayleigh Fractionation |
| Rayleigh fractionation occurs, if a reservoir is depleted significantly. The initial istopic ratio $R_0$ changes towards the actual ratio $R$ at a certain degree of depletion $f$ if the fractionation factor for the depleting process is $\alpha$: | Rayleigh fractionation occurs, if a reservoir is depleted significantly. The initial istopic ratio $R_0$ changes towards the actual ratio $R$ at a certain degree of depletion $f$ if the fractionation factor for the depleting process is $\alpha$: | ||
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| $$R = R_0 \cdot f^{\left(\alpha-1\right)}$$ | $$R = R_0 \cdot f^{\left(\alpha-1\right)}$$ | ||
| - | ```{r rayleigh, include=TRUE, | + | Code for Rayleigh fractionation. Please not that it requires the function equilibrium that is provided above. To run this code, you can add it to the first block of code at the bottom and execute the entire block - the function is then available. |
| + | |||
| + | <code S| Rayleigh.R> | ||
| alpha18O <- equilibrium(10)$alpha18O | alpha18O <- equilibrium(10)$alpha18O | ||
| fR <- seq(0.9, | fR <- seq(0.9, | ||
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| R < | R < | ||
| plot(fR,R, type=" | plot(fR,R, type=" | ||
| - | ``` | + | </ |
/usr/www/users/uhydro/doku/data/attic/en/hydro/isotopes.1656401560.txt.gz · Last modified: 2024/04/10 10:14 (external edit)