The 4.6 is more interesting than any of the headline percentages. Goyal, Bhatia and Kumar report that the water saved by optimizing for nitrogen surplus is roughly 4.6 times the nitrogen saved by optimizing for water [7], which read on the same relative scale means a water-first plan collects about a fifth of the cross-benefit a nitrogen-first plan does [3]. The mechanism they give is physical rather than statistical: paddy rice tops three lists at once, water use, fertilizer application and methane, so an objective that pushes nitrogen surplus down has to contract paddy in stressed districts, and the water comes off with it [9]. It is also why farm greenhouse gases fall 8.7% in the same run, with paddy methane and nitrous oxide leaving together [16]. Water saved in a district that was never a heavy fertilizer user, by contrast, buys nothing on nitrogen. That is the asymmetry.
Scale is worth checking before anyone builds policy on it. A cut of 18.6% amounting to 86.8 billion cubic meters a year [6] implies a modelled baseline near 467 billion cubic meters of water in Indian cereal cultivation [1]. That is the denominator any rival proposal has to work against.
The monetized part is thinner than it reads. About $1.19 billion of avoided damage a year [8], spread across the 664 districts in the optimization [10], averages roughly $1.8 million per district [4], and it is damage not incurred rather than money arriving anywhere. The constraint set holds the cereal sector's net returns at 2017 levels and keeps every state at or above its 2017 calorie production [11]. Both are aggregates. Which districts inside a state give up paddy area, and who carries the adjustment, is not a question the objective function is asked.
The narrative is about rice, but the arithmetic points at wheat too: rice area contracts 8.8% and wheat 12.1% [12], so wheat's proportional cut is about 1.4 times rice's [2]. The paper as summarized does not give absolute areas, so which crop surrenders more hectares is not something a reader can settle. The authors are explicit that this is reallocation at the margin, not replacement of rice or wheat [14].
One thing the model cannot reach is the reason the surplus exists. Nitrogen is overapplied partly because it is cheap [4], and nitrogen surplus is whatever the crop does not take up, ending in wells, rivers and the air as nitrous oxide [3]. Reallocating land changes the crop mix, not the price of a bag of urea, so the 13.4% fall in fertilizer pollution [17] holds only if application rates track crop choice rather than habit. Bhatia's line that "when we optimize for nitrogen surplus, water savings follow on their own" [19] is a statement about an objective function; whether the surplus follows the plan is decided in the field.
