Last year a judge known as a special master and appointed by the Supreme Court recommended the $5.5 million penalty. That represented $3.7 million for Kansas’ loss, plus $1.8 million representing a portion of the amount by which Nebraska farmers’ gain exceeded Kansas farmers’ loss.

Kansas beseeched the court to adopt “meaningful and robust remedies to put an end to a long and sad history’’ of Nebraska’s overuse of the river.

Nebraska Chief Deputy Attorney General David Cookson will argue that the state never knowingly violated the compact. He will say that strict pumping limits, imposed on the state’s irrigators in the basin in recent years, and new pipelines to pump underground water into the river as needed are more than adequate to protect the river flows that Kansas needs, even in dry years.

He also will say the judge correctly determined that Nebraska had been wrongly charged with consuming Republican River water that it naturally imports from outside the basin. The imported water originates as leakage from Platte River irrigation canals and from farmers watering cropland near the northern edge of the Republican basin. Over time, the water migrates south from the Platte basin into the Republican basin, where wells withdraw some of it for irrigation use again.