Mayor Todd Gloria’s proposed cuts to San Diego library branches and neighborhood recreation centers would require sharp reductions in hours at some facilities and possible full closures at others, a new analysis shows.

The mayor’s new 40-page analysis doesn’t recommend specific cuts but ranks each facility based on its importance to the nearby community and uses those rankings to provide the City Council with possible scenarios.

Aides to Gloria said Monday that the goal is giving councilmembers the tools and information to make thoughtful decisions and surgical cuts that do the least damage possible to city residents and neighborhoods.

The rankings of the city’s 37 library branches and 56 rec centers are based on a variety of factors, including the average income nearby, the variety of programs offered at the site, the crime rate and the site’s proximity to similar city facilities.

Other factors include proximity to child care options, education level of nearby residents and what percentage of their income nearby households spend on transportation.

For libraries, branches that experienced the deepest cuts last spring are mostly spared in the mayor’s proposed scenarios. The only branch facing possible closure in any of the scenarios is North Clairemont.

For rec centers, the mayor’s scenarios prioritize preserving hours at facilities that have gyms, also have a senior center on site and host events in the city’s Parks After Dark program for low-income neighborhoods.

The rec centers facing possible closures in at least one of the mayor’s scenarios are: La Jolla, Santa Clara, South Clairemont, Cadman, Cabrillo, Tecolote, Adams, San Carlos, Irving Salomon, Morley Field Gym, Mid-City Gym, Lopez Ridge, Penn Athletic Field, Robb Field, Nobel Athletic Fields and Hourglass Fieldhouse.

For both libraries and rec centers, the mayor lays out three separate scenarios. Generally, two options strongly consider socioeconomic factors and the new rankings, while a third proposes cuts more evenly across the city.

In a memo sent to the council Monday afternoon, Gloria’s aides say the mayor has no preference for any of the proposed scenarios over any of the others.

Each scenario would save the $7.8 million from libraries and rec centers that the mayor says is needed to close a $146 million budget deficit the city is facing for the new fiscal year that begins July 1.

When he released his budget April 15, Gloria said libraries and rec centers must suffer cuts so the city can avoid severe cuts to higher priorities such as public safety, infrastructure, transportation and homelessness programs.

The mayor’s memo suggests that the council, which is scheduled to begin its budget deliberations Monday with a week of department-by-department public hearings, use the library and rec center scenarios as a menu of options.

“None of the options are preferred and all three for each have adverse impacts on our communities,” the memo says. “As the budget process moves forward, the council may want to explore additional options, and we are ready to support that work.”

The memo was signed by Rania Amen, the city engineer and the mayor’s chief community officer, and Bethany Bezak, the mayor’s chief performance and logistics officer.

One of the options for libraries would make traditional citywide cuts based more on usage than socioeconomics and other factors.

Under this scenario, which is known as Option 2, 18 branches would maintain their current hours and four — Allied Gardens, North Park, University Heights and Carmel Valley — would lose Monday service.

The remaining 13 locations would still operate Monday through Saturday, but Saturday hours would shrink from a full day to service only from 11 a.m. to 4 p.m.

Option 1 would focus on helping low-income areas by fully preserving existing hours at three branches: Malcolm X in Council District 4, San Ysidro in District 8 and City Heights in District 9.

The money to preserve those hours would come from closing the La Jolla branch completely on Saturdays and the Linda Vista branch completely on Mondays.

Option 3 would focus even more on socioeconomics and keep every branch in low-income Districts 4, 8 and 9 open a full day on Saturdays.

The money to preserve those hours would come from fully closing the North Clairemont branch, which Gloria’s aides stress is in poor condition and within 3 miles of two other branches: Balboa and Clairemont.

All of the library scenarios anticipate extended closures of the Ocean Beach and Rancho Peñasquitos branches for scheduled renovations.

On rec centers, each of the options recommends that some sites get fully closed.

Option 3 would be the more traditional citywide style of cuts, with the presence of a gym mattering more than socioeconomics.

Option 1 prioritizes socioeconomics the most, while Option 3 focuses more on the new rankings, which were compiled by the city’s Performance and Analytics Department.

Another factor considered for rec centers was whether similar programs are offered nearby by nonprofit organizations or commercial facilities.

For libraries, the rankings say the 10 branches most needed by their communities are, in order, Oak Park, Malcolm X, City Heights, Mira Mesa, downtown, Otay Mesa, San Ysidro, Logan Heights, Rancho Peñasquitos and University Heights.

The 10 branches least needed, in order, are La Jolla, Allied Gardens, University City, Carmel Valley, Pacific Highlands Ranch, Rancho Bernardo, Carmel Mountain Ranch, San Carlos, Tierrasanta and Hillcrest-Mission Hills.

For rec centers, the rankings say the 10 sites most needed by their communities are, in order, Colina del Sol, Stockton, South Bay, Presidio, Larsen Field, Memorial-King, Lopez Ridge, Municipal Gym, Balboa Park Activity Center and Scripps Ranch.

The 10 rec centers least needed, in order, are Adams, Nobel, La Jolla, Pacific Highlands Ranch, Ocean Air, Standley, Carmel Valley, Santa Clara, Montgomery-Waller and South Clairemont.

Gloria’s aides stressed that the rankings are simply a tool for the council.

“The objective of the analysis is to provide key budget decision-makers with a tool to help analyze potential community impacts of reductions to library and recreation facilities, helping to support equitable decision making and minimize disproportionate impacts across communities,” the memo says.

The council’s Budget Review Committee is scheduled to discuss proposed cuts to libraries and rec centers on Tuesday, May 3.

The city’s independent budget analyst is scheduled to release a full analysis of the mayor’s proposed budget Wednesday.