Assumption Parish Sheriff Leland Falcon advised the public Monday not to enter flooded parts of the parish by car or boat unless "it's absolutely necessary."

Backwater flooding from the cresting Atchafalaya River continued Monday to push high water into the Lake Verret Basin and Assumption Parish, federal river forecasters said.

Forecast hydrologist Jeff Graschel said heavy rain in late April and early May in Arkansas, Missouri, Oklahoma and parts of Illinois have caused high water conditions on the Mississippi River that have finally made their way down to the lower Atchafalaya.

The river has been cresting at about a foot above flood stage since May 30, but Graschel said that while the water is high, it's nothing too different than what happens on the river every so often.

"We do get those levels here every few years or so," said Graschel, who works at the National Weather Service's Lower Mississippi River Forecast Center in Slidell.

In the years where there was even more severe flooding along the Atchafalaya, particularly in 2011 and 2016, a sunken barge and temporary levees and sheet piles were installed in Bayou Chene southeast of Morgan City to prevent the same kind of backwater flooding in Assumption and parts of St. Martin, St. Mary and Terrebonne parishes.

But those steps weren't taken this year primarily due to the high cost of the sunken barge along with the other remedies and the relatively moderate flooding this year, a key levee district official said.  

Still, Assumption Police Jury President Martin "Marty" Triche declared a state of emergency Friday due to the high water. Several roads in low-lying parts of Pierre Part, Bayou Pigeon, Bayou L'Ourse and other areas remained closed. A "no wake" order also remained in effect for boaters in the Lake Verret area of Assumption.

John Boudreaux, the parish homeland security director, said no homes have flooded and major thoroughfares, including La. 70, remain open. Sandbagging has been ongoing for several days.

He said the major concern at this point is if the parish should get a heavy downpour of 8 to 10 inches.

"Because everything is so saturated with the water being up, that would really hurt many folks," Boudreaux said.

Assumption and other areas around lakes Verret and Palourde, including parts of St. Martin and Terrebonne parishes, are being affected by the backwater. It flows from the Atchafalaya northeast through Bayou Chene and to the north through the lakes Palourde and Verret. 

In 2011, the St. Mary Levee District constructed temporary control structures, sunk a large barge and made temporary levee upgrades to block the flow of water coming from the Atchafalaya after the Morganza Spillway was opened during historic flooding on the Mississippi.

Tim Matte, levee district executive director, said the Atchafalaya was projected to be much higher in 2011 and 2016, between 10.5 and 12 feet at Morgan City, than this year. River levels appear to be cresting at 7.2 feet.

Matte called that river level "borderline" to employ the sunken barge and other measures. He said the district's permit with the U.S. Army Corps of Engineers doesn't authorize the use of those measures until the river reaches 7 feet at Morgan City.

But the past events, he added, included presidential disaster declarations that allowed the district to get a 75 percent match for the cost of the work through the Federal Emergency Management Agency.

Matte doubted this flooding would get the same declaration, meaning the district would have to bear all the cost.

The barge, the related structures along Bayou Chene and temporary levee improvements cost $11 million to install and remove under the terms of the Corps' temporary permit in 2011, Matte said.

Some of the shoreline structures along Bayou Chene were allowed to remain, but in January 2016, when the barge and other temporary improvements were installed and removed again, the cost was still $7.5 million, Matte said.

The district is seeking Corps approval for a permanent structure now estimated to cost $80 million.

A portion of Louisiana's increased share of offshore oil and gas royalties were earmarked for the project, but President Donald Trump's budget recently proposed repealing the law that would have directed those increased royalty revenues toward Louisiana and other Gulf Coast states.   

Follow David J. Mitchell on Twitter, @NewsieDave.