And finally we talk about isotope concentration

 If I understand correctly, colleagues arre measuring the concentration of an isotope in stream or some other catchment outlet.  This is quite not a measure of the age of water but the latter has to be inferred from  a hypothesis the system behavior, and possibly the knowledge of the distribution of water ages within the control volume, obtained iteratively from an initial data (derived from the isotopic data of precipitation).

Therefore, assume you have measured in the outflow a concentration of 5 of solute X in appropriate units. You mai have  the knowledge of the concentration of the same solute in the water of a given age resident in the control volume. It would be a tuple like (7,3,6,2) where the number of concentration is the number of precipitation happened before the present instant. The 5 units out of the tuple can be taken all from the oldest (7) concentration, from the youngest (3,2) where the 3 are out of the 6 of the penultimate concentration.

Therefore a concentration of 5 can be fitted with a water age of 4 in the first case or (3*2+2*1)/5=1.8 in the second case.

In fact, the concentration doesn't identify  the exact age of the water but rather a range of ages spanning from the "first in first out" age to the "last in first out" age illustrated in the simple example.

Potentially the old water is infinitely old and, therefore, the lower bound could be very large, while the upper bound for the ages is, clearly, related to the last rainfall age.

So, the division between young water and old water is reasonable. Instead of trying to guess the distribution, you're trying to guess parts of its integral.

Then SAS (StorAge Selection functions, see this previous post for understanding what they are) are summarizing the mechanics of mixing inside the control volume. If the waters mix a lot the travel time and the residence time should coincides  because of the uniform selection of isotopes (or tracers) among the various populations. SAS have a non trivial form if the mixing of waters is incomplete.

Due to the localized nature of water physics, the actual travel times are intricately linked to the specific location from which water emerges or is extracted from the soil. Within the unsaturated zone, it's logical to posit that newly introduced water is the first to flow out for two primary reasons: it occupies the empty pores, and these pores are typically where water is loosely retained. However, when young water mixes with old water in the saturated zone, the aquifer's pressure rises, causing a pressure wave that pushes out the oldest water near the streams.

Consequently, in a typical zeroth-order catchment, runoff tends to adhere to a "last in, first out" (LIFO) logic, while subsurface stormwater tends to expel old water first, following a "first in, first out" (FIFO) logic. Consequently, the recession of the flood wave is expected to contain a higher proportion of old water than young water. In this hypothetical simplified model delineating two distinct dynamics, and drawing from the aforementioned insights, it becomes feasible to estimate the global effect of the system, as proposed by Rigon and Bancheri in 2022 and applying the recent methods of TT probability determination.

Vegetation withdrawal we can think to extract water from the places where active roots are, according to root density. Plants with shallow roots should mostly sample young water, while plants with deeper roots wold sample older water but maybe also being effective in mixing water of different ages because of exudation and because of preferential water infiltration close to the roots.

The presentation (under construction) is exemplifying these concepts.

Isotopes, Tracers and Hydrology

I asked to Daniele Penna (GS, RG), who I know to work on tracers, some bibliography. He answered to me throughly, and I share is notable contribution.

He said:

" - I cited recent or relatively recent papers, leaving out pioneering works, even if they were important historically^1.

- I included almost exclusively experimental papers, and therefore neglecting the integration model-tracers.

-Also, I included essentially only papers that talk about the two most diffuse families of tracers, i.e. stable water isotopes  (no tritium included) and hydrochemical tracers, included electric conductivity.  I did not included: traditional tracers, and recent tracers (other elements, optic fibres for temperature, dyers, DOC, CFC, thermal infrared imagery, dyatomee, synthetic DNA)

- For what regards water isotopes, there is plenty of literature. I left out: all what regards isotopes in precipitation (this has grown almost to be a discipline by itself); all what regards groundwater-surface water interaction at large spatial scales; various methods for the isotopic measure (recent developments connected to laser spectroscopy) and methods for the extraction of water from plants and soil;isotope studies in landslide hydrology (actually there is not very much, but there are groups that started to work on this topics); isotopes in irrigation and through fall; and I also not included works on residence time and travel time that represent another world^2.

- Essentially, I concentrated my attention on the use of isotopic tracers and hydrochemical  which are used for the analysis of the hydrological cycle functioning at catchment scale and of the partition of water fluxes among vegetation and the other parts of the cycle.  Please do not pretend completeness. "

"I subdivided my literature review in three parts^3:

isotopes: general info and reviews

isotopes about ecohydrology

isotopes plus hydrochemistry for catchment hydrology

In the third group there is a fourth group (here presented separately) dedicated to snow-dominated basins. ^4

Finally a good reading would be the book by Leibundgut et al, 2009.  "

Notes

^1 [If someone wants to fill this gap, he can refer to literature cited in Benchmark paper ….]

^2 [Thank you Daniele, also know what you neglected is very informative]  

^3 [They actually became four]
^4 [I added at the bottom the papers included in the IAHR book]

References

0 - Books

Christian Leibundgut, Piotr Maloszewski, Christor.ph Külls, Tracers in Hydrology, 2009

Aggarwal P. K., FrÃhlich K. O. , Gat J. R. and Gonfiantini (eds.), Benchmark papers in Isotope Hydrology,  IAHR, 2012

1 - General info and reviews

Burns, D. A. (2002). Stormflow-hydrograph separation based on isotopes: the thrill is gone ? what's next? Hydrological Processes, 16(7), 1515–1517. http://doi.org/10.1002/hyp.5008

Buttle, J. (2005). 116: Isotope Hydrograph Separation of Runoff Sources, In: Anderson MG, McDonnell JJ, eds., Encyclopaedia of Hydrological Sciences. Chichester: Wiley 1763-1174, ch. 116.

Gat, J. R. (1996). OXYGEN AND HYDROGEN ISOTOPES IN THE HYDROLOGIC CYCLE. Annual Review of Earth and Planetary Sciences, 24, 225–262.

Klaus, J., & McDonnell, J. J. (2013). Hydrograph separation using stable isotopes: Review and evaluation. Journal of Hydrology, 505(C), 47–64. http://doi.org/10.1016/j.jhydrol.2013.09.006

Leibundgut, C., & Seibert, J. (2014). 2.09 Tracer Hydrology (pp. 215–236).

McDonnel, J., Bonnell, B., Stewart, M. K., & Pearce, J. (1990). Deuterium Variations in Storm Rainfall: Implications for Stream Hydrograph Separation. Water Resources Research, 26(3), 455–458.

McGuire, K. J., & McDonnell, J. J. (2015). Tracer advances in catchment hydrology. Hydrological Processes, 29(25), 5135–5138. http://doi.org/10.1002/hyp.10740

McGuire, K., & McDonnell, J. (2008). Stable isotope tracers in watershed hydrology (pp. 1–21).

Ogunkoya, O. O., & Jenkins, A. (1993). Analysis of storm hydrograph and flow pathways using a three-component hydrograph separation model. Journal of Hydrology, 142, 71–88.

Tetzlaff, D., Buttle, J., Carey, S. K., McGuire, K., Laudon, H., & Soulsby, C. (2014). Tracer-based assessment of flow paths, storage and runoff generation in northern catchments: a review. Hydrological Processes, 29(16), 3475–3490. http://doi.org/10.1002/hyp.10412

Vitvar, T., Aggarval, P. K., & McDonnel, J. (2016). 12. A review of isotope applications in catchmen hydrology, 1–19.

Wels, C., Cornett, R. J., & Lazerte, B. D. (1991). Hydrograph separation: a comparison of geochemical and isotopic tracers. Journal of Hydrology, 122, 253–274.

2 - Ecohydrology

Asbjornsen, H., Goldsmith, G. R., Alvarado-Barrientos, M. S., Rebel, K., Van Osch, F. P., Rietkerk, M., et al. (2011). Ecohydrological advances and applications in plant-water relations research: a review. Journal of Plant Ecology, 4(1-2), 3–22. http://doi.org/10.1093/jpe/rtr005

Beyer, M., Koeniger, P., Gaj, M., Hamutoko, J. T., Wanke, H., & Himmelsbach, T. (2016). A deuterium-based labeling technique for the investigation of rooting depths, water uptake dynamics and unsaturated zone water transport in semiarid environments. Journal of Hydrology, 533(C), 627–643. http://doi.org/10.1016/j.jhydrol.2015.12.037

Bowen, G. (2015). The diversified economics of soil water. Nature, 525, 43–44.

Brooks, J. R., Barnard, H. R., Coulombe, R., & McDonnell, J. J. (2009). Ecohydrologic separation of water between trees and streams in a Mediterranean climate. Nature Geoscience, 3(2), 1–5. http://doi.org/10.1038/ngeo722

Evaristo, J., Jasechko, S., & McDonnell, J. J. (2015). Global separation of plant transpiration from groundwater and streamflow. Nature, 525(7567), 91–94. http://doi.org/10.1038/nature14983

Evaristo, J., McDonnell, J. J., Scholl, M. A., Bruijnzeel, L. A., & Chun, K. P. (2016). Insights into plant water uptake from xylem-water isotope measurements in two tropical catchments with contrasting moisture conditions. Hydrological Processes, n/a–n/a. http://doi.org/10.1002/hyp.10841

Geris, J., Tetzlaff, D., McDonnell, J., Anderson, J., Paton, G., & Soulsby, C. (2015). Ecohydrological separation in wet, low energy northern environments? A preliminary assessment using different soil water extraction techniques. Hydrological Processes, 29(25), 5139–5152. http://doi.org/10.1002/hyp.10603

Goldsmith, G. R., Muñoz-Villers, L. E., Holwerda, F., McDonnell, J. J., Asbjornsen, H., & Dawson, T. E. (2011). Stable isotopes reveal linkages among ecohydrological processes in a seasonally dry tropical montane cloud forest. Ecohydrology, 5(6), 779–790. http://doi.org/10.1002/eco.268

Good, P. G., Noone, D., & Bowen, G. (2015). Hydrologic connectivity constrains partitioning of global terrestrial water fluxes. Science, 349(6244), 175–178.

Hsueh, Y.-H., Chambers, J. L., Krauss, K. W., Allen, S. T., & Keim, R. F. (2016). Hydrologic exchanges and baldcypress water use on deltaic hummocks, Louisiana USA. Ecohydrology, n/a–n/a. http://doi.org/10.1002/eco.1738

McDonnell, J. J. (2014). The two water worlds hypothesis: ecohydrological separation of water between streams and trees? Wiley Interdisciplinary Reviews: Water, n/a–n/a. http://doi.org/10.1002/wat2.1027

McGuire, K., & McDonnell, J. J. (2008). Stable isotope tracers in watershed hydrology (pp. 335–346).

Rong, L., Chen, X., Chen, X., Wang, S., & Du, X. (2011). Isotopic analysis of water sources of mountainous plant uptake in a karst plateau of southwest China. Hydrological Processes, 25(23), 3666–3675. http://doi.org/10.1002/hyp.8093

Singer, M. B., Sargeant, C. I., Piégay, H., Riquier, J., Wilson, R. J. S., & Evans, C. M. (2014). Floodplain ecohydrology: Climatic, anthropogenic, and local physical controls on partitioning of water sources to riparian trees. Water Resources Research, 50(5), 4490–4513. http://doi.org/10.1002/2014WR015581

Tetzlaff, D., Buttle, J., Carey, S. K., van Huijgevoort, M. H. J., Laudon, H., McNamara, J. P., et al. (2015). A preliminary assessment of water partitioning and ecohydrological coupling in northern headwaters using stable isotopes and conceptual runoff models. Hydrological Processes, 29(25), 5153–5173. http://doi.org/10.1002/hyp.10515

Treydte, K., Boda, S., Graf Pannatier, E., Fonti, P., Frank, D., Ullrich, B., et al. (2014). Seasonal transfer of oxygen isotopes from precipitation and soil to the tree ring: source water versus needle water enrichment. New Phytologist, 202(3), 772–783. http://doi.org/10.1111/nph.12741

Wang, L., Liu, J., Sun, G., Wei, X., Liu, S., & Dong, Q. (2012). Preface “Water, climate, and vegetation: ecohydrology in a changing world.” Hydrology and Earth System Sciences, 16(12), 4633–4636. http://doi.org/10.5194/hess-16-4633-2012

3 - Hydrochemistry for catchment hydrology

Barthold, F. K., Wu, J., Vaché, K. B., Schneider, K., Frede, H.-G., & Breuer, L. (2010). Identification of geographic runoff sources in a data sparse region: hydrological processes and the limitations of tracer-based approaches. Hydrological Processes, 24(16), 2313–2327. http://doi.org/10.1002/hyp.7678

Burns, D. A., McDonnell, J. J., Hooper, R. P., Peters, N. E., Freer, J. E., Kendall, C., & Beven, K. (2001). Quantifying contributions to storm runoff through end-member mixing analysis and hydrologic measurements at the Panola Mountain Research Watershed (Georgia, USA). Hydrological Processes, 15(10), 1903–1924. http://doi.org/10.1002/hyp.246

Camacho Suarez, V. V., Saraiva Okello, A. M. L., Wenninger, J. W., & Uhlenbrook, S. (2015). Understanding runoff processes in a semi-arid environment through isotope and hydrochemical hydrograph separations. Hydrology and Earth System Sciences, 19(10), 4183–4199. http://doi.org/10.5194/hess-19-4183-2015

Farrick, K. K., & Branfireun, B. A. (2015). Flowpaths, source water contributions and water residence times in a Mexican tropical dry forest catchment. Journal of Hydrology, 529(P3), 854–865. http://doi.org/10.1016/j.jhydrol.2015.08.059

Fischer, B. M. C., Rinderer, M., Schneider, P., Ewen, T., & Seibert, J. (2015). Contributing sources to baseflow in pre-alpine headwaters using spatial snapshot sampling. Hydrological Processes, 29(26), 5321–5336. http://doi.org/10.1002/hyp.10529

Genereux, D. (1998). Quantifying uncertainty in tracer-based hydrograph separations. Water Resources Research, 34(4), 915–919.

Hooper, R. P. (2001). Applying the scientific method to small catchment studies: a review of the Panola Mountain experience. Hydrological Processes, 15(10), 2039–2050. http://doi.org/10.1002/hyp.255

Hrachowitz, M., Bohte, R., Mul, M. L., Bogaard, T. A., Savenije, H. H. G., & Uhlenbrook, S. (2011). On the value of combined event runoff and tracer analysis to improve understanding of catchment functioning in a data-scarce semi-arid area. Hydrology and Earth System Sciences, 15(6), 2007–2024. http://doi.org/10.5194/hess-15-2007-2011

Katsuyama, M., Ohte, N., & Kobashi, S. (2001). A three-component end-member analysis of streamwater hydrochemistry in a small Japanese forested headwater catchment. Hydrol. Proc., 15, 249–260.

Inamdar, S., Dhillon, G., Singh, S., Dutta, S., Levia, D., Scott, D., et al. (2013). Temporal variation in end-member chemistry and its influence on runoff mixing patterns in a forested, Piedmont catchment. Water Resources Research, 49(4), 1828–1844. http://doi.org/10.1002/wrcr.20158

James, A. L., & Roulet, N. T. (2006). Investigating the applicability of end-member mixing analysis (EMMA) across scale: A study of eight small, nested catchments in a temperate forested watershed. Water Resources Research, 42(8), n/a–n/a. http://doi.org/10.1029/2005WR004419

Klaus, J., McDonnell, J. J., Jackson, C. R., Du, E., & Griffiths, N. A. (2015). Where does streamwater come from in low-relief forested watersheds? A dual-isotope approach. Hydrology and Earth System Sciences, 19(1), 125–135. http://doi.org/10.5194/hess-19-125-2015

Lee, J., Feng, X., Faiia, A. M., Posmentier, E. S., Kirchner, J. W., Osterhuber, R., & Taylor, S. (2010). Isotopic evolution of a seasonal snowcover and its melt by isotopic exchange between liquid water and ice. Chemical Geology, 270(1-4), 126–134. http://doi.org/10.1016/j.chemgeo.2009.11.011

Lu, H.-Y. (2014). Application of water chemistry as a hydrological tracer in a volcano catchment area: A case study of the Tatun Volcano Group, North Taiwan. Journal of Hydrology, 511(C), 825–837. http://doi.org/10.1016/j.jhydrol.2014.02.036

Machavaram, M. V., Whittemore, D. O., Conrad, M. E., & Miller, N. L. (2006). Precipitation induced stream flow: An event based chemical and isotopic study of a small stream in the Great Plains region of the USA. Journal of Hydrology, 330(3-4), 470–480. http://doi.org/10.1016/j.jhydrol.2006.04.004

Marc, V., Didon-Lescot, J., & Michael, C. (2001). Investigation of the hydrological processes using chemical and isotopic tracers in a small Mediterranean forested catchment during autumn recharge. Journal of Hydrology, (247), 2215–2229.

McGlynn, B. L., & McDonnell, J. J. (2003). Quantifying the relative contributions of riparian and hillslope zones to catchment runoff. Water Resources Research, 39(11), n/a–n/a. http://doi.org/10.1029/2003WR002091

Meriano, M., Howard, K. W. F., & Eyles, N. (2011). The role of midsummer urban aquifer recharge in stormflow generation using isotopic and chemical hydrograph separation techniques. Journal of Hydrology, 396(1-2), 82–93. http://doi.org/10.1016/j.jhydrol.2010.10.041

Muñoz-Villers, L. E., & McDonnell, J. J. (2012). Runoff generation in a steep, tropical montane cloud forest catchment on permeable volcanic substrate. Water Resources Research, 48(9), n/a–n/a. http://doi.org/10.1029/2011WR011316

Muñoz-Villers, L. E., & McDonnell, J. J. (2013). Land use change effects on runoff generation in a humid tropical montane cloud forest region. Hydrology and Earth System Sciences, 17(9), 3543–3560. http://doi.org/10.5194/hess-17-3543-2013

Neal, C., Reynolds, B., Kirchner, J. W., Rowland, P., Norris, D., Sleep, D., et al. (2013). High-frequency precipitation and stream water quality time series from Plynlimon, Wales: an openly accessible data resource spanning the periodic table. Hydrological Processes, 27(17), 2531–2539. http://doi.org/10.1002/hyp.9814

Pellerin, B. A., Wollheim, W. M., Feng, X., & Vörösmarty, C. J. (2008). The application of electrical conductivity as a tracer for hydrograph separation in urban catchments. Hydrological Processes, 22(12), 1810–1818. http://doi.org/10.1002/hyp.6786

Penna, D., van Meerveld, H. J., Oliviero, O., Zuecco, G., Assendelft, R. S., Dalla Fontana, G., & Borga, M. (2014). Seasonal changes in runoff generation in a small forested mountain catchment. Hydrological Processes, 29(8), 2027–2042. http://doi.org/10.1002/hyp.10347

Šanda, M., Vitvar, T., Kulasová, A., Jankovec, J., & Císlerová, M. (2013). Run-off formation in a humid, temperate headwater catchment using a combined hydrological, hydrochemical and isotopic approach (Jizera Mountains, Czech Republic). Hydrological Processes, 28(8), 3217–3229. http://doi.org/10.1002/hyp.9847

Tetzlaff, D., & Soulsby, C. (2008). Sources of baseflow in larger catchments – Using tracers to develop a holistic understanding of runoff generation. Journal of Hydrology, 359(3-4), 287–302. http://doi.org/10.1016/j.jhydrol.2008.07.008

Tetzlaff, D., Waldron, S., Brewer, M. J., & Soulsby, C. (2007). Assessing nested hydrological and hydrochemical behaviour of a mesoscale catchment using continuous tracer data. Journal of Hydrology, 336(3-4), 430–443. http://doi.org/10.1016/j.jhydrol.2007.01.020

4 - Snow dominated catchments

Carey, S. K., & Quinton, W. L. (2004). Evaluating snowmelt runoff generation in a discontinuous permafrost catchment using stable isotope, hydrochemical and hydrometric data. Nordic Hydrology, 309–324.

Chiogna, G., Santoni, E., Camin, F., Tonon, A., Majone, B., Trenti, A., & Bellin, A. (2014). Stable isotope characterization of the Vermigliana catchment. Journal of Hydrology, 509(C), 1–11. http://doi.org/10.1016/j.jhydrol.2013.11.052

Dahlke, H. E., Lyon, S. W., Jansson, P., Karlin, T., & Rosqvist, G. (2013). Isotopic investigation of runoff generation in a glacierized catchment in northern Sweden. Hydrological Processes, 28(3), 1383–1398. http://doi.org/10.1002/hyp.9668

Earman, S., Campbell, A. R., Phillips, F. M., & Newman, B. D. (2006). Isotopic exchange between snow and atmospheric water vapor: Estimation of the snowmelt component of groundwater recharge in the southwestern United States. Journal of Geophysical Research, 111(D9), D09302–18. http://doi.org/10.1029/2005JD006470

Engel, M., Penna, D., Bertoldi, G., Dell'Agnese, A., Soulsby, C., & Comiti, F. (2015). Identifying run-off contributions during melt-induced run-off events in a glacierized alpine catchment. Hydrological Processes, 30(3), 343–364. http://doi.org/10.1002/hyp.10577

Jeelani, G., Bhat, N. A., & Shivanna, K. (2010). Use of d18 O tracer to identify stream and spring origins of a mountainous catchment: A case study from Liddar watershed, Western Himalaya, India. Journal of Hydrology, 393(3-4), 257–264. http://doi.org/10.1016/j.jhydrol.2010.08.021

Maurya, A. S., Shah, M., Deshpande, R. D., Bhardwaj, R. M., Prasad, A., & Gupta, S. K. (2010). Hydrograph separation and precipitation source identification using stable water isotopes and conductivity: River Ganga at Himalayan foothills. Hydrological Processes, 25(10), 1521–1530. http://doi.org/10.1002/hyp.7912

Ohlanders, N., Rodriguez, M., & McPhee, J. (2013). Stable water isotope variation in a Central Andean watershed dominated by glacier and snowmelt. Hydrology and Earth System Sciences, 17(3), 1035–1050. http://doi.org/10.5194/hess-17-1035-2013

Peng, T.-R., Chen, K.-Y., Zhan, W.-J., Lu, W.-C., & Tong, L.-T. J. (2015). Use of stable water isotopes to identify hydrological processes of meteoric water in montane catchments. Hydrological Processes, 29(23), 4957–4967. http://doi.org/10.1002/hyp.10557

Penna, D., Ahmad, M., Birks, S. J., Bouchaou, L., Brenčič, M., Butt, S., et al. (2014a). A new method of snowmelt sampling for water stable isotopes. Hydrological Processes, 28(22), 5637–5644. http://doi.org/10.1002/hyp.10273

Penna, D., Engel, M., Mao, L., Dell'Agnese, A., Bertoldi, G., & Comiti, F. (2014b). Tracer-based analysis of spatial and temporal variations of water sources in a glacierized catchment. Hydrology and Earth System Sciences, 18(12), 5271–5288. http://doi.org/10.5194/hess-18-5271-2014

Penna, D., van Meerveld, H. J., Zuecco, G., Dalla Fontana, G., & Borga, M. (2016). Hydrological response of an Alpine catchment to rainfall and snowmelt events. Journal of Hydrology, 537, 382–397. http://doi.org/10.1016/j.jhydrol.2016.03.040

Shanley, J. B., Kendall, C., Smith, T. E., Wolock, D. M., & McDonnell, J. J. (2002). Controls on old and new water contributions to stream flow at some nested catchments in Vermont, USA. Hydrological Processes, 16(3), 589–609. http://doi.org/10.1002/hyp.312

Shanley, J. B., Sebestyen, S. D., McDonnell, J. J., McGlynn, B. L., & Dunne, T. (2014). Water's Way at Sleepers River watershed - revisiting flow generation in a post-glacial landscape, Vermont USA. Hydrological Processes, 29(16), 3447–3459. http://doi.org/10.1002/hyp.10377

Sueker, J. K., Ryan, J. A., Kendall, C., & Jarret, R. D. (2000). Determination of hydrologic pathways during snowmelt for alpine/subalpine basins, Rocky Mountain National Park, Colorado. Water Resources Res., 36(1), 63–75.

Taylor, S., FEng, X., Kirchner, J. W., Osterhuber, R., Klaue, B., & Renshaw, C. E. (2001). Isotopic evolution of a seasonal snowpack and its melt. Water Resources Res., 37(3), 759–769.

Taylor, S., Feng, X., Williams, M., & McNamara, J. (2002). How isotopic fractionation of snowmelt affects hydrograph separation. Hydrological Processes, 16(18), 3683–3690. http://doi.org/10.1002/hyp.1232

Unnikrishna, P. V., Mcdonnell, J. J., & Kendall, C. (2002). Isotope variations in a Sierra Nevada snowpack and their relation to meltwater. Journal of Hydrology, 260, 38–57.

Yde, J. C., Knudsen, N. T., Steffensen, J. P., Carrivick, J. L., Hasholt, B., Ingeman-Nielsen, T., et al. (2016). Stable oxygen isotope variability in two contrasting glacier river catchments in Greenland. Hydrology and Earth System Sciences, 20(3), 1197–1210. http://doi.org/10.5194/hess-20-1197-2016

Zhang, Y. H., Song, X. F., & Wu, Y. Q. (2008). Use of oxygen-18 isotope to quantify flows in the upriver and middle reaches of the Heihe River, Northwestern China. Environmental Geology, 58(3), 645–653. http://doi.org/10.1007/s00254-008-1539-y