By Shaun WatermanA call by al Qaeda American spokesman Adam Gadahn for Muslim extremists living in the West to launch attacks highlights the way U.S. officials are struggling to define and meet the growing threat of homegrown terrorism and domestic radicalization.

“My brothers: Know that Jihad is your duty as well,” the 32-year old California-raised Muslim convert said in a 40-minute English-language video released over the weekend. Gadahn, who is on the FBI’s most wanted list, said he was addressing militants “on the margins of [Western] society in the miserable suburbs of Paris, London and Detroit.”

“You have an opportunity to strike the leaders of unbelief and retaliate against them on their own soil,” he told them, according to a transcript prepared by the private-sector SITE Intelligence Group. (SITE stands for Search for International Terrorist Entities.)

Officials continue to warn publicly about the danger from homegrown Muslim extremists, including those who “self-radicalize” using websites and Internet chat rooms, and who are drawn from a variety of ethnic and social backgrounds.

On Monday, Homeland Security Secretary Janet Napolitano told police chiefs that the threat from such individuals “prepared to carry out terrorist acts … with little or no warning” meant that “a real turning point in how we approach our nation’s security” had been reached.

“More and more,” she told the International Association of Chiefs of Police annual conference in Orlando, Fla., “we’re seeing the increased role of Westerners, including U.S. citizens,” many of whom “are unknown to the intelligence community and unknown to federal authorities.”

A study last month by congressional researchers identified 19 arrests in U.S. homegrown Islamic extremist terrorist plots between May 2009 and August 2010 — more than three times the number in any single year since 2001.

Ms. Napolitano warned that such lone-wolf attackers could strike without having had any contact with terrorist groups abroad that might be detected by travel analysis or other traditional means. Federal authorities and local agencies had to gain “a better understanding of the behaviors, and other indicators, that could point to terrorist activity,” she said.

But a slew of reports from think tanks and other scholars, including one to be published Tuesday, shows the daunting scale of that task.

“There is no profile,” said James M. Ludes, executive director of the bipartisan American Security Project. “No silver-bullet solution.”

The project’s study, “Enemies Among Us,” states that there is no clear demographic profile for homegrown Muslim extremists and that it is hardly possible to generalize meaningfully about the process of radicalization.

“The paths to radicalism are as numerous and varied as the cases themselves,” the study reads. So, they offer “little in the way of clear implications on which law enforcement or intelligence agencies can build workable profiles, templates, or models.”

“If we rely on a tactical approach, on intelligence or law enforcement to stop these guys … it’s not going to work,” said Mr. Ludes.

Ms. Napolitano laid out a series of initiatives her department has adopted over the summer following the recommendations of an advisory panel. These include an emphasis on community policing, training for local law enforcement and more information-sharing about threats and suspicious activities.

She pledged to expand the Suspicious Activity Reporting initiative — which creates a standard process for state and local law enforcement to identify and report suspicious activity — to fusion centers and transit police forces nationwide.

A report published by the Institute for Homeland Security Solutions, which is independent but partly funded by the Homeland Security Department, found that more than 80 percent of foiled domestic terrorist plots between 1999 and 2009 were discovered “via observations from law enforcement or the general public.” The tips included “reports of suspicious activity, such as pre-operational surveillance, para-military training, [or] smuggling activities.”