Δ15N

In geochemistry, hydrology, paleoclimatology and paleoceanography, δ15N  (pronounced "delta fifteen n") or delta-N-15 is a measure of the ratio of the two stable isotopes of nitrogen, 15N:14N.

Formulas
Two very similar expressions for are in wide use in hydrology. Both have the form $$1000\cdot\frac{s-a}a$$ ‰ (‰ = permil or parts per thousand) where s and a are the relative abundances of 15N in respectively the sample and the atmosphere. The difference is whether the relative abundance is with respect to all the nitrogen, i.e. 14N plus 15N, or just to 14N. Since the atmosphere is 99.6337% 14N and 0.3663% 15N, a is 0.003663 in the former case and 0.003663/0.996337 = 0.003676 in the latter. However s varies similarly; for example if in the sample 15N is 0.385% and 14N is 99.615%, s is 0.003850 in the former case and 0.00385/0.99615 = 0.003865 in the latter. The value of $$1000\cdot\frac{s-a}a$$ is then 51.05‰ in the former case and 51.38‰ in the latter, an insignificant difference in practice given the typical range of $-20$ for.

Applications
The ratio of 15N to 14N is of relevance because in most biological contexts, 14N is preferentially uptaken as the lighter isotope. As a result, samples enriched in 15N can often be introduced through a non-biological context.

One use of 15N is as a tracer to determine the path taken by fertilizers applied to anything from pots to landscapes. Fertilizer enriched in 15N to an extent significantly different from that prevailing in the soil (which may be different from the atmospheric standard a) is applied at a point and other points are then monitored for variations in.

Another application is the assessment of human waste water discharge into bodies of water. The abundance of 15N is greater in human waste water than in natural water sources. Hence in benthic sediment gives an indication of the contribution of human waste to the total nitrogen in the sediment. Sediment cores analyzed for yield an historical record of such waste, with older samples at greater depths.

is also used to measure food chain length and the trophic level of a given organism; high values are positively correlated with higher trophic levels; likewise, organisms low on the food chain generally exhibit lower  values. Higher values in apex predators generally indicate longer food chains.