State officials need to come up with some cash as the Massachusetts Department of Transportation has already depleted its snow-removal budget this winter.

MassDOT this year budgeted $45.5 million for snow and ice removal, but had already spent $84 million as of March 11. The agency is authorized to spend $30 million in addition to its budget without seeking supplemental funding from the state legislature.

MassDOT spokeswoman Sara Lavoie said wishful thinking was behind the grossly underestimated budget.

“Last year for example, we spent $35 million on snow and ice removal,” she said. “This year we thought, ‘OK, let’s budget at $45 million and see how we go.’ Obviously, at $84 million now, we will be in need of some supplemental funding.”

It costs $1.2 million to remove an inch of snow in the state, and LaVoie says that number has been falling in recent years.

“We are using different techniques and different materials and better equipment in order to drive that number down,” she said.

The agency, for example, makes its own salt brine and hires contractors with equipment that controls the amount of salt dispensed.

At the end of the season, MassDOT will review practices and other ways it can curb more snow-clearing costs in preparation of next winter.