from my own understanding, and in simple terms, the difference is in the denominator. WUE is yield/ET where ET is often estimated using reference evapotranspiration, while water productivity is yield/T where T is the actual water used by the plant.

http://www.ceps.eu/files/ABattilani_water_good1.pdf

http://plantsinaction.science.uq.edu.au/edition1/?q=content/15-3-1-water-use-ef-ciency-crops

for further reading

Your question does not give the exact definition of water productivity (W) vs. WUE. It is all a matter of what is in the numerator, and what is in the denominator. If you normalize transpiration for biomass production, you have not taken care of effects of water deficit on harvest index, the proportion of biomass that ends up in yield. Please see the attached paper Hsiao et al. (2007) for the complexity of how to improve WUE or WP. Also attached is the paper by Pasquale et al (2007)

Sorry, I pushed the wrong button before finishing. The paper by Pasquale Steduto et al. (2007), also attached, presents evidence and conceptual basis that normalization for evaporative demand as measured by reference ET and air carbon dioxide concentration makes it possible for WP for biomass to remain virtually constant.

Thanks Mr Hsiao,

As I know, this theories applied in AquaCrop model and for WP is constant in each specific crop. But for more information about differences and application of Efficiency, Water Productivity and Water Use Efficiency, I suggest you this article:

Efficiency and productivity terms for water management: A matter of contextual relativism versus general absolutism

Gerardo E. van Halsema, , Linden Vincent

http://www.sciencedirect.com/science/article/pii/S0378377411001430

Dear Dr. Rahimi:

Thanks for the reference by van Halsema & Vincent. I think you might not have looked at the first paper I sent, Hsiao, Steduto, and Fereres (2007), which covers much of the same ground as van Halsems & V., but more quantitatively and with more fundamental underpinning. I am attaching that paper here.

With best wishes,

Ted Hsiao

Dear,

@Theodore C Hsiao explanation is very clear. I would only add that water productivity is a broader and more complex concept than the efficiency of water use. Water productivity can have different time scales (eg. phenological states of a crop, growing season of a crop or crop sequences) and spatial (eg. plants, lot, region, district). At each scale, the way of measuring water productivity can change. In the attached I send a poster of a work done in Argentina evaluating the WP of agricultural crops.  It can also be used to evaluate the efficiency of rainfall, in addition to transpiration and / or evapotranspiration.

Greetings.

Conference Paper PRODUCTIVIDAD DEL AGUA DE LLUVIA EN SISTEMAS AGRÍCOLAS DE LA...