Water that enters an ecosystem through rain can leave through several mechanisms. It can runoff the surface, flow through the soil and enter groundwater, or it can evaporate. Soil evaporation is generally confined to the first few centimeters of soil; however, plant roots can reach depths of many meters to remove water from far below the surface. This water evaporates out of leaves and returns to the atmosphere in the process of transpiration.  The combination of evaporation from the soil surface and transpiration from plant leaves is called evapotranspiration.

Water may contain isotopes of both hydrogen and oxygen - the light isotope of hydrogen is 1H (usually abbreviated as H) and the heavy stable isotope is 2H (abbreviated as D for deuterium).  The light isotope of oxygen is 16O, while the most common heavy stable isotope is 18O.  Recall that lighter isotopes evaporate more quickly than heavier ones, so that there is more of heavy isotope in the liquid phase and more of the lighter isotope in the gas phase.  This is called an equilibrium effect.  It can be described by an equilibrium fractionation factor, or a*:

 a* = RL/Rv   

where R is the ratio of the amount heavy isotope/light isotope, L refers to the liquid phase, and v refers to the vapor phase.

As we discussed in the section on photosynthesis, light isotopes also diffuse more quickly than heavy isotopes.  This is called a kinetic effect, and it can be described by a kinetic fractionation factor, ak:

 ak = D/D' = g/g'  

where D is the diffusion coefficient of the light isotope and D' is the diffusion coefficient of the heavy isotope (ak = 1.025 for H/D and 1.0285 for 16O/18O).

A diffusion coefficient is a constant that quantifies differences in diffusion rates among various molecules.  We can describe differences in diffusion rates through any substance, including the stomates of plants, so we can also express ak as the ratio of the stomatal conductance of a light isotope (g)/stomatal conductance of a heavy isotope (g').  This will be useful later in our calculations.

Both equilibrium and kinetic effects are involved in transpiration.  Water molecules evaporate into the leaf pore space from xylem, the conduits that transport water from the soil to the leaves, and then diffuse into the atmosphere. The rate of plant transpiration depends on the stomatal conductance and the dryness of the air relative to the leaf pore space, as expressed by the difference between vapor pressure inside the leaf (ei) and outside the leaf (ea):

 E = g(ei - ea)      

where E is transpiration and g is stomatal conductance.   Let us define E as the transpiration rate of water containing light isotopes only.  We can also describe the transpiration rate of water containing heavy isotopes:

 E' = g'(Rvei-Raea)    

 where Rv is the ratio of the heavy and light isotopes of water vapor in the leaf pore space, and Ra is the ratio of heavy and light isotopes of water vapor in the air outside the leaf.

By combining these two equations, we can describe the ratio of heavy to light isotopes in transpired water (recall that ak = g/g' and a* = RL/Rv):

 E'/E = RT = (1/ak) * (RLei/a* - Raea)/(ei - ea)  

 There is no fractionation during transport of the water from the soil to the leaves.  Therefore RT is the isotopic composition of the plant's source of water.  It can be measured by sampling the water in stem xylem.  If RT is known, we can rearrange the equation to predict the enrichment of 18O and D that occurs in leaves:

RL = a*[akRT(ei-ea/ei) + Ra(ea/ei)]   

 This leaf water is used in photosynthesis to build plant tissues; therefore all plant material carries the isotopic signature of the water source in addition to the evaporative enrichment influenced by the vapor pressure in the air.


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