A rendering shows what a light-rail Purple Line train would look like running through the University of Maryland campus in College Park. (Maryland Transit Administration)

Even though Maryland Gov. Larry Hogan has committed to build a $2 billion light-rail Purple Line in the Washington suburbs, there remains a looming question: How many people will ride it?

The state’s predictions have grown over the years — at one point, the number jumped by 45 percent — as Maryland transit planners refined regional computer models in the quest for nearly $1 billion in highly competitive federal construction funds.

But how those numbers were calculated, and how realistic they are, remains a mystery to the taxpayers who will pay for the 16-mile line linking Prince George’s and Montgomery counties. The predictions stem from highly technical and complex computer models that few transit experts say they truly understand.

Some of the only scrutiny of the ridership models beyond state and federal transit agencies came from the town of Chevy Chase, which has long fought the rail project because trains would run along its border and a popular wooded recreation trail. The town hired an engineering firm to review the state’s forecasts. However, the data files that the Maryland Transit Administration provided were indecipherable without software that the town said it couldn’t afford.

“We looked at it and couldn’t figure out what was changing to make the numbers go up,” said Harris Schechtman, a New York-based transit planner for the town’s consulting firm, Sam Schwartz Engineering. “It was a mystery to us. . . . But we had no access to the model. It raised a lot of questions that we couldn’t find answers to.”

In its most recent forecasts, the MTA predicted that the Purple Line will draw an average of 58,800 trips daily — not including University of Maryland students and special events — in its opening year, now scheduled for 2021. That would be almost 75 percent more daily trips than Metro’s Silver Line extension in Northern Virginia averaged in its first year. It also would make the Purple Line one of the busiest light-rail systems in the country, rivaling established lines in Phoenix, Houston and St. Louis. By 2040, Maryland planners say, the Purple Line’s daily ridership is expected to reach 74,000.

Purple Line supporters chalk up questions about the line’s ridership to opponents seeking to kill the project. They note that it would provide a missing east-west link in suburban Maryland’s rail network and would connect neighborhoods, major job centers and U-Md.’s flagship College Park campus with Metro, Amtrak and MARC commuter rail lines.

Even so, the Washington area has had its share of large transportation projects promising more than they delivered.

Ridership on the year-old Silver Line fell 30 percent below its opening year projections, according to Metro officials. An internal Metro report attributed that to a lack of sidewalks, crosswalks and bike lanes that would help more people reach stations, according to WAMU (88.5 FM).

Traffic projections for new roads haven’t fared much better. Toll revenue on the four-year-old Intercounty Connector in suburban Maryland aligns with forecasts, but only because the state significantly downgraded projections as construction neared.

Early usage of the 495 Express Lanes in Northern Virginia was “well below” initial projections, which hadn’t anticipated the recession, according to Transurban, the lanes’ operator. Transurban revised those estimates shortly after the lanes opened in late 2012, in part to reflect the recession’s lasting economic impact. Traffic now meets the revised projections, Transurban said.

Maryland transit officials say they stand behind their Purple Line predictions and that the numbers passed muster with the Federal Transit Administration before it recommended the project last year for $900 million in federal grants. Maryland Transportation Secretary Pete K. Rahn said he, too, recently reviewed the estimates as part of a financial analysis that Hogan (R) requested amid skepticism about the project’s cost.

Rahn said he didn’t take “a super-deep dive” on the calculations but that he was “comfortable” with the explanation he received about why the daily ridership projection jumped by 21,000 trips — or 45 percent — in 2008. The higher numbers emerged after transportation officials for then-Gov. Martin O’Malley (D) said estimates made under his predecessor, Gov. Robert L. Ehrlich Jr. (R), were “flawed” and “clearly too low.” Ehrlich had prioritized building the Intercounty Connector, while O’Malley championed the Purple Line.

Rahn said he was told that the increase stemmed from changes made to the regional computer model and state planners’ discovery that people will ride a Purple Line for more non-work trips, such as midday errands, than the model had accounted for. He also said it’s not unusual for forecasts to change as project planning becomes more detailed.

“Nothing I saw made me uncomfortable with the changes in projections,” Rahn said. “The fact that gave me the most comfort is that the FTA was involved, and they were acceptable to them. That satisfied my questions regarding the numbers.”

How many people ride the Purple Line is important to the state’s ability to pay its construction debt as well as ongoing costs to run the line. All transit systems require long-term government subsidies because fares don’t cover all of their operating and maintenance costs. How much taxpayers will have to subsidize the Purple Line — and how much money the system could take from other transportation projects across the state — depends on how much fare revenue the line collects.

Although less common, a significant undercounting of potential riders also could pose problems, leaving the Purple Line with crowded trains and platforms. Ridership also can affect the pace of development around stations, experts say.

Studies of travel forecasts show that inaccurate predictions most often result from unexpected economic slumps, changes in train frequency and “optimism bias” — when planners become so focused on getting a project built that they use the most optimistic “inputs” in the model. Those can include the rosiest predictions for gas prices, the amount of planned development that is likely to actually occur and other factors that help predict how many people will choose transit over driving.

A 2008 FTA study concluded that ridership estimates had generally improved. But the agency also found that only half of 18 recently built U.S. transit projects had reached their projections or stood a “good chance” of getting close.

A more recent MTA review found that seven U.S. light-rail systems that opened in the past decade averaged 8 percent higher ridership than predicted. But when not averaged out, the review showed that most projects were far off the mark. Three systems’ riderships were as much as 45 percent below forecasts while four exceeded projections — one by as much as 79 percent.

Schechtman, who reviewed the Purple Line projections for the town of Chevy Chase, said he was particularly curious about the daily ridership forecast that jumped by 21,000 boardings — or 45 percent — in 2008.

Under the Ehrlich administration, daily ridership was said to be about 47,000 by 2030. That prompted the O’Malley administration to postpone the release of the project’s draft environmental-impact study by a year to redo the estimates. One top MTA official was quoted as saying, “We know that we can make this a better model and a more competitive model.”

A year later, the official number was up to 68,000 trips daily by 2030. A top Purple Line planner said the higher number took into account potential trips made by Metro and MARC riders — an explanation that several travel modeling experts now question as being too simplistic because such transfers are built into regional models.

Maryland Del. Robert L. Flanagan (R-Howard), the transportation secretary under Ehrlich, said he questioned the jump.

“They claimed that somehow our administration had deliberately kept the forecasts down, which simply wasn’t true,” Flanagan said. “I don’t know why they redid the numbers, other than for political reasons or for getting the results they wanted.”

Schechtman said he, too, suspects that state officials wanted higher numbers to help the project win federal money.

“In the competition for federal funding,” Schechtman said, “ridership counts.”

MTA officials now say that the 21,000-boardings increase stemmed from a more “geographically refined analysis” the state did to help the Metropolitan Washington Council of Governments’ regional model better reflect the Purple Line area. That included incorporating a new survey finding that Washington-area transit riders will use a Purple Line for significantly more trips during non-rush hours than the model previously accounted for. The previous model, they now say, also undercounted — but did not omit — the Metro and MARC riders who also will use the Purple Line.

The lower ridership numbers in 2007 stemmed from “pretty crude” modeling intended to compare different Purple Line proposals — rail vs. buses and different routes — against each other, said Henry Kay, the MTA’s former head of project development. Kay left the agency in August, saying he wanted to pursue work in the private sector.

“We’re as confident as we can be, given that it’s a model and we’re trying to predict the future,” Kay said. “To suggest somehow the numbers are changing to serve a political purpose really misrepresents the whole process and level of accountability, both to the public and the FTA. . . . There’s a lot of competition for this money, so [FTA officials] have a lot of vested interest to make sure it’s right.”

The FTA declined to provide a representative to be interviewed about how the agency scrutinizes ridership forecasts. In response to e-mailed questions, a spokesman wrote, “FTA reviews ridership estimates carefully to ensure they are developed properly and are reasonable.” The agency uses the ridership forecasts to evaluate fare revenues assumed in a project’s financial plan as well as its cost-effectiveness, environmental benefits and mobility improvements, the spokesman said.

John D. Porcari, who was Maryland’s transportation secretary when the forecasts jumped by 45 percent, said he thinks that even the higher numbers are conservative. Porcari, also a former deputy U.S. transportation secretary, is now a senior vice president at Parsons Brinckerhoff, the state’s consultant on the ridership forecasts. Porcari said he does no Purple Line work for Parsons and was speaking as a former Maryland official.

“There’s a high degree of confidence in the numbers,” Porcari said. “I’m confident the ridership will at least meet, and probably exceed, those numbers.”

The state didn’t seek to boost ridership estimates to clinch federal money, he said.

“It was always a competitive project at the federal level,” Porcari said. “It was even more competitive after more-accurate ridership numbers were developed.”

There’s no way to know how many people will ride the Purple Line until trains are running, and the focus now is on financial details. State officials are waiting on construction bids, due in November, to determine the project’s final cost and who will pay how much.

“The sad thing is, with the project moving forward, it all becomes moot,” Schechtman, the consultant for Chevy Chase, said of the ridership forecasts. “It’s in the past. The snowball is so far down the hill, the focus now is just on finding a [funding] mechanism that works.”

Magda Jean-Louis contributed to this report.