In general, water-use efficiency is defined as the ratio of carbon assimilation to water consumption. But according to different research scales and purposes, it can be calculated in different ways.

• At the leaf scale, the Intrinsic Water-use Efficiency is defined as the amount of carbon assimilated per unit leaf area per unit time at per unit cost of water [1].

iWUE = leaf-level photosynthesis rate (A) / stomatal conductance (g) 

                               = (Ca-Ci)/(1.6)

                               = (ca(1-ci/ca))/(1.6)

(where Ca is the atmospheric CO2 concentration, and Ci is the leaf intercellular CO2 concentration).

 

• In an individual tree scale, the Instantaneous Water-use Efficiency is the ratio of carbon assimilation (A) to transpiration of the plant [2]. If productivity is the major concern, then at the same scale, water-use efficiency for productivity can also be calculated as the ratio of tree biomass to tree transpiration [3].

 

• At the watershed or even larger spatial scale, the Ecosystem Water-use Efficiency (eWUE) is calculated as the ratio of gross primary production (GPP, the amount of carbon assimilated by plant through photosynthesis) to watershed evapotranspiration (ET) [4]. Evapotranspiration is the total of transpiration and evaporation of that concerned ecosystem. If the non-productive carbon exchange and water consumption processes are excluded, the eWUE can also be calculated as the ratio of net primary production (NPP, the net amount of carbon assimilated by plant by taking photosynthesis and respiration into account) to total transpiration (T).  NPP is the difference between GPP and respiration, and T is the productive water consumption of the studied ecosystem.

the eWUE has its limitation under drought conditions, for several studies found that the variability of that ratio in different regions is largely due to variability in the vapor pressure difference between leaf and air[6-9], thus the effect of Vapor Pressure Defict (VPD) on canopy conductance under water stress complicates the response of eWUE to drought conditions. Lloyd et al. (2002) uses canopy conductance (GS), instead of evapotranspiration, to modify eWUE [10]. The corrected eWUE is denoted as Ecosystem Intrinsic Water-Use Efficiency (eiWUE), which is the ratio of GPP or NPP to GS). However, eiWUE requires mono-layer canopy and similar underground vegetation [11], and GS needs to be inferred from inverted Penman–Monteith equation [10], which, as a consequence, increases the difficulty of research.

Beer et al. (2009) proposed a different method to calculate eWUE under drought condition, and named the new metrics as Inherent Water-use Efficiency (iWUE*) [12]. the new method approximated the vapor pressure difference between plant and air by VPD, and approximated carbon assimilation A and transpiration E by GPP and ET. All data can be inferred from flux tower observations, thus reducing the complication of the research.

iWUE* = GPP x VPD / ET

Different definitions of water-use efficiency origin from different research scales and purposes. They are useful metrics in forest hydrological research. If you are interested in these metrics or if you know more definitions, feel free to share your thoughts with me by leaving your comments!

Thank you for reading!

April, 5, 2016

References:

[1] Ehleringer, J.R.  1993.  Carbon and water relations in desert plants: an isotopic perspective, p. 155-172.  In J.R. Ehleringer, A.E. Hall, and G.D. Farquhar (eds.),  Stable Isotopes and Plant Carbon/Water Relations.  Academic Press, San Diego.

[2] Hipólito Medrano, Magdalena Tomás, Sebastià Martorell, Jaume Flexas, Esther Hernández, Joan Rosselló, Alicia Pou, José-Mariano Escalona, Josefina Bota, From leaf to whole-plant water use efficiency (WUE) in complex canopies: Limitations of leaf WUE as a selection target, The Crop Journal, Volume 3, Issue 3, June 2015, Pages 220-228.

[3] Peñuelas, J., J.G. Canadell, and R. Ogaya, Increased water-use efficiency during the 20th century did not translate into enhanced tree growth. Global Ecology and Biogeography, 2011. 20(4): p. 597-608.

[4] Clark, K.L., Skowronski, N.S., Gallagher, M.R., Renninger, H. and Schäfer, K.V.R., 2014. Contrasting effects of invasive insects and fire on ecosystem water use efficiency. Biogeosciences, 11(23): 6509-6523

[5] Sun, Y., Piao, S., Huang, M., Ciais, P., Zeng, Z., Cheng, L., Li, X., Zhang, X., Mao, J., Peng, S., Poulter, B., Shi, X., Wang, X., Wang, Y.-P. and Zeng, H. (2016), Global patterns and climate drivers of water-use efficiency in terrestrial ecosystems deduced from satellite-based datasets and carbon cycle models. Global Ecology and Biogeography, 25: 311–323.

[6] Bierhuizen, J., and R. Slatyer (1965), Effect of atmospheric concentration of water vapor and CO2 in determining transpiration-photosynthesis relationships of cotton leaves, Agric. Meteorol., 2, 259–270.

[7] Baldocchi, D. D., S. B. Verma, and N. J. Rosenberg (1985), Water use efficiency in a soybean field: Influence of plant water stress, Agric. For. Meteorol., 34, 53–65.

[8] Monteith, J. L. (1986), How do crops manipulate water supply and demand? Philos. Trans. R. Soc. London Ser. A, 316, 245–259.

[9] Irvine, J., B. E. Law, M. R. Kurpius, P. M. Anthoni, D. Moore, and P. A. Schwarz (2004), Age-related changes in ecosystem structure and function and effects on water and carbon exchange in ponderosa pine, Tree Physiol., 24, 753–763.

[10] LLOYD, J., SHIBISTOVA, O., ZOLOTOUKHINE, D., KOLLE, O., ARNETH, A., WIRTH, C., STYLES, J. M., TCHEBAKOVA, N. M. and SCHULZE, E.-D. (2002), Seasonal and annual variations in the photosynthetic productivity and carbon balance of a central Siberian pine forest. Tellus B, 54: 590–610.

[11] Arneth, A., E. M. Veenendaal, C. Best, W. Timmermans, O. Kolle, L. Montagnani, and O. Shibistova (2006), Water use strategies and ecosystem-atmosphere exchange of CO2 in two highly seasonal environments, Biogeosciences, 3, 421–437.

[12] Beer, C., et al. (2009), Temporal and among-site variability of inherent water use efficiency at the ecosystem level, Global Biogeochem. Cycles, 23, GB2018,

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