Interesting question . here is an abstract of work..
Review of measured crop water productivity values for irrigated wheat, rice, cotton and maize by Sander J. Zwart∗, Wim G.M. Bastiaanssen
Abstract : The great challenge of the agricultural sector is to produce more food from less water, which can be achieved by increasing Crop Water Productivity (CWP). Based on a review of 84 literature sources with results of experiments not older than 25 years, it was found that the ranges of CWP of wheat, rice, cotton and maize exceed in all cases those reported by FAO earlier. Globally measured average CWP values per unit water depletion are 1.09, 1.09, 0.65, 0.23 and 1.80 kg m−3 for wheat, rice, cottonseed, cottonlint and maize, respectively. The range of CWP is very large (wheat, 0.6–1.7 kg m−3; rice, 0.6–1.6 kg m−3; cottonseed, 0.41–0.95 kg m−3; cottonlint, 0.14–0.33 kg m−3 and maize, 1.1–2.7 kg m−3) and thus offers tremendous opportunities for maintaining or increasing agricultural production with 20–40% less water resources. The variability of CWP can be ascribed to: (i) climate; (ii) irrigation water management and (iii) soil (nutrient) management, among others. The vapour pressure deficit is inversely related to CWP. Vapour pressure deficit decreases with latitude, and thus favourable areas for water wise irrigated agriculture are located at the higher latitudes. The most outstanding conclusion
is that CWP can be increased significantly if irrigation is reduced and crop water deficit is intendently induced. source ; Agricultural Water Management 69 (2004) 115–133...PDF enclosed for further reading...
The simplest method is to just record the amount of water used at each irrigation, excluding leakage water by collecting and measuring it to derive the actual amount of water absorbed into the soil. You can also include the leakage water if you want to see the efficiency of say different irrigation methods. Then at the end of experiment, simply divide yield to the accumulated amount of water used.
In case of water productivity, all the possible water use and loss mechanism to be documented like evapo transpiration, leakage from the pot etc. addition of water must be based on the water uptake and loss from the pot, which will be known from weighing the pot on daily basis.
Kato and Okami 2011 studied root system development, stomatal conductance (gs) and leaf water potential (Ψleaf) were monitored in a high-yielding rice cultivar (‘Takanari’) under flooded and aerobic conditions at two soil moisture levels [nearly saturated (> –10 kPa) and mildly dry (> –30 kPa)] over 2 years. In an ancillary pot experiment, whole-plant hydraulic conductivity (soil-leaf hydraulic conductance; Kpa) was measured under flooded and aerobic conditions.