Every year, like a giant frozen reservoir, snow that falls across the Sierra Nevada mountain range slowly melts in spring and summer months, providing roughly one-third of the water supply for California’s cities and farms, from the Bay Area to Los Angeles.

But at the current rate at which the climate is warming, the amount of runoff from Sierra snow into California’s largest reservoirs is heading for a dramatic decline — a 54 percent drop in the next 20 to 40 years and 79 percent in the next 60 to 80 years, according to a new study from scientists at Lawrence Berkeley National Laboratory.

The fading role of the Sierra snow pack as a central feature in California’s water supply already is underway. As it continues, much less water from melting snow will be available to fill huge reservoirs such as Shasta, Oroville and Folsom. The ominous trend is occurring as the state’s population and farm economy continue to grow, establishing a new reality that will require fundamental changes in the way California and the federal government have operated the state’s water system for nearly 100 years.

“It’s a dramatic loss of snow. It has huge implications for water management,” said Alan Rhoades, a postdoctoral fellow at Berkeley Lab and lead author of the study, which was published this month in the journal Geophysical Research Letters.

What’s happening is fairly simple.

The burning of fossil fuels traps heat in the atmosphere. As a result, the earth’s temperature already has risen 1.8 degrees Fahrenheit over the last century and is on track to rise another 4 degrees Fahrenheit by 2050 and 9 degrees or more by 2100. The 10 hottest years since modern temperature records began in 1880 all have occurred since 1998, according to NASA and NOAA, the agency that oversees the National Weather Service.

As that warming continues — and much of it is guaranteed, based on the amount of carbon dioxide humans already have emitted — more of the precipitation falling on California’s vast Sierra Nevada range is coming in the form of rain, rather than snow. The warmer temperatures also will continue to melt the Sierra snow pack earlier in the winter season than in decades past.

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That has major implications for the years ahead. It means more flood risk, because more winter precipitation will be coming down as rain during major storms instead of being held in the mountains as snow, Rhoades noted.

That, in turn, will require dam operators to keep less water in reservoirs at the beginning of each winter, so they have more room to catch the water from big rainfall events and reduce flood risk to cities downstream as rivers rise. But in dry years, if reservoirs are kept low and not much rain falls in the winter, that could mean severe water shortages in the summer.

The shrinking snow pack also increases wildfire risk. It affects the amount and timing of hydro-electric power that can be generated. And it has implications for endangered salmon and other species that depend on steady flows in rivers.

The state has several options to avert disaster, said Ellen Hanak, director of the Water Policy Center at the Public Policy Institute of California, a nonprofit research organization in San Francisco.

One, she noted, is to build more off-stream reservoirs or raise the height of existing reservoirs to capture more water for use later in the year. Second is to store billions of gallons more than is now being stored underground, in groundwater aquifers, so it can be pumped out later by farmers and cities.

“If we don’t want to lose the water,” Hanak said, “we have to put it somewhere else.”

The Sierra Nevada snowpack already has been shrinking.

Previous studies have shown that since 1906, the amount of snowmelt runoff reaching the Sacramento River between April and July has decreased by about 9 percent.

The new research, from Berkeley Lab, a part of the U.S. Department of Energy, used supercomputers to analyze current warming trends, carbon emissions and other information. It analyzed the most likely scenarios for snowpack upstream of 10 major reservoirs — three in Northern California, three in Central California, and four in Southern California. The reservoirs are Shasta, Oroville, Folsom, New Melones, Don Pedro, Exchequer, Pine Flat, Terminus, Success and Isabella.

By 2039 to 2059, the average snowpack runoff will fall 54 percent, the study found, and then 79 percent from 2079 to 2099. Of note: the three northernmost reservoirs, Shasta, Oroville and Folsom, will see an even larger drop in runoff, 83 percent, by the end of the century.

Rhoades and his co-authors — Berkeley Lab climate scientist Andrew Jones and UC Davis Assistant Professor of Regional Climate Modeling Paul Ullrich — also found that peak runoff will come one month earlier by the end of the century, at the beginning of March rather than April 1.

Hanak noted that the state already has begun to address the issue. Voters passed Proposition 1 in 2014, a water bond with $2.7 billion for new storage projects. This summer, state officials earmarked that money for eight projects, including raising the dam at Los Vaqueros Reservoir in Contra Costa County, building a new reservoir at Pacheco Pass in Southern Santa Clara County, building the massive Sites Reservoir in Colusa County, and several large groundwater storage projects in Southern California.

Gov. Jerry Brown also signed a landmark groundwater law that requires farmers and cities to better track and sustainably manage their groundwater. Hanak said far more projects are needed, such as efforts to pay farmers to flood their fields and orchards in wet years, recharging groundwater tables, along with far more recycled water projects, conservation efforts and other initiatives.

“We have surface reservoirs, groundwater basins, and we have rivers and canals and aqueducts to connect them,” she said. “We’re going to have to manage them together more consistently.”

The statewide Sierra snow pack on Saturday was 86 percent of the historic average for Dec. 15.