Winter storms that have disrupted travel patterns for MBTA riders should cost the transit authority $36.5 million in lost revenues and additional costs this year, MBTA Chief Financial Officer Jonathan Davis told transportation officials Tuesday.

The T had to shut down some lines and halt service during the historic levels of snow this winter, and state officials are seeking funding options to cover the costs of the winter storms while simultaneously weighing whether to offer riders rebates or discounts to account for their troubles.

Lost revenues accounted for about $6 million, though ridership is now back up above what it was before the storms, Davis told the Massachusetts Department of Transportation Board of Directors Finance and Audit Committee. The $36.5 million estimate also includes about $5 million in contingency and $3 million in projected costs.

Davis said insurance will cover damages to buildings and equipment, and federal emergency funding could cover 75 percent of costs associated with storms, though not the foregone fares. Davis said the Federal Transit Administration has no funding for an emergency relief program. In-house, funding could be drawn from the T's $19.5 million rainy day fund, a $30.7 million maintenance fund or from projected $13.2 million in savings by the end of the fiscal year.

Snow and ice removal has been highlighted as a major cost-driver for the state's transportation system, and the unusually cold and snowy weather took a toll on MBTA equipment. The MBTA has never had a specific line item in its budget for snow and ice removal, according to MBTA spokesman Joe Pesaturo.

Davis said the T has gone through roughly 200 traction motors, compared to 40 or 50 in a typical winter, and he credited organized labor with cooperating with the MBTA's efforts to dig out of historic snowfalls. No one was injured during the snowstorms, he said.

"Safety was their number one priority," Davis said.

MassDOT Chief Financial Officer Dana Levenson said the average storm costs the state's transportation department $4.9 million and there have been 25 storm events so far in fiscal year 2015. He said the blizzard dubbed Juno cost $21 million.

In fiscal 2015, which began July 1, 2014, the state has so far used 555,000 tons of salt, 1.4 million gallons of liquid de-icer, and equipment has worked 712,000 hours, Levenson said.

He said the five-year average of snow and ice removal costs is $103.4 million and snow and ice has cost $129 million so far this fiscal year.

Transportation Secretary Stephanie Pollack said she hopes to "gradually" change how snow-and-ice is budgeted, moving the budget closer to the actual average. She said $48.6 million was budgeted this year while the state was authorized to deficit-spend an additional $50 million.