Mosul, Iraq ? Gen. David Petraeus is flying in a C-130 transport plane back to the place he once made into a model of U.S.-Iraqi cooperation.

Iraq’s third-largest city warmed to Petraeus because he reached out to Sunni Arab leaders during a yearlong assignment as commander of the 101st Airborne.

But Mosul fell apart when U.S. troops in the city were cut by two-thirds after Petraeus departed early in 2004 and Iraqi security was too weak to fill the vacuum. Insurgents flooded into the city, and the Iraqi police force collapsed. Politicians and intellectuals have been assassinated by the dozens, and most Sunnis are too scared, or too angry, to vote.

So Petraeus’ visit to Mosul is bittersweet.

President Bush sent him back to Iraq in June to rebuild Iraq’s security forces, a job U.S. officials botched because they lacked a clear strategy for the postwar period. A newly elected Iraqi government won’t be able to function without adequate security forces. And American troops can’t go home until Iraqis are able to keep order.

Petraeus has come to Mosul to check out what progress is being made.

First stop as he blitzes the city: a briefing on the security outlook for elections — dicey.

U.S. forces were beefed up in Mosul after the police fled, and several battalions of Iraqi troops also have been moved in. A couple of these are composed of Kurds, who are good fighters, but their presence fuels Sunni fears that Kurds want to take over the city.

Next, we travel through Mosul inside heavily armored Stryker vehicles where the only view of city streets is on the TV monitor below the gunner’s turret.

We visit one of the Interior Ministry’s enthusiastic new police commando units composed of former Iraqi army special forces. They may be best suited to fighting the insurgents, but they can’t do it alone.

The Stryker speeds us to the al-Kindi base, where a new Iraqi division headquarters was set up three months ago. Fighters from one of the Kurdish battalions tell me, with graphic motions: “Kurds good, Arabs not good.”

Then to provincial headquarters, where the governor embraces Petraeus warmly over a table laden with grilled fish and lamb. The governor’s son and his predecessor were assassinated. Here’s proof that moderate Sunni leaders can be wooed into a new political system. But few will risk it under current conditions.

Then by helicopter to al-Kisik division headquarters outside Mosul, a huge, isolated complex built under Saddam Hussein, looted after the U.S. invasion, then rebuilt with U.S. funds. The challenge here is keeping new recruits. With no bank system in place, soldiers return home monthly to take money to their families, and many never return. The depleted ranks are now being refilled with former Iraqi soldiers.

How to assess all this?

Back in Baghdad, Petraeus tells me: “We are trying to gather momentum.”

When he arrived in June, there was one operational army battalion of the New Iraqi Army (around 700 men). Now, he says, there are 69 operational Iraqi battalions (around 50,000 men) and around 55,000 trained and equipped police.

“Many Iraqi security forces just have come online in the last two months,” he says. “The amount of equipment delivered has been staggering.” In addition, his operation has built $1.7 billion worth of infrastructure for the Iraqi military, including barracks, police stations, and border guard posts.

“The herd is getting bigger,” he says, using his favorite metaphor about the need to continually add to the force. “We have to keep it going.”

The problem with these numbers is that it’s hard to judge what they mean.

Building a security force from scratch under current conditions is a mind-boggling venture. Before Petraeus arrived, the Pentagon claimed the Iraqi security force numbered 200,000, a bogus figure it has since dropped.

The bulk of the current 50,000 soldiers are poorly trained national guard battalions that have been subsumed into the army this month. Even regular army soldiers get only an eight-week course. Their fighting abilities are only beginning to be tested.

Petraeus has made the best of a very bad hand. Counterterrorism and special commando units show promise.

Training of army and police is being improved. An overall command structure is being shaped. More U.S. trainers are arriving.

Still, Petraeus doesn’t see Iraqi forces being able to take over full responsibility for internal security in 2005. Success or failure also will depend on political factors beyond Petraeus’ control.

If the next Iraqi government reaches out to Sunnis, it may undermine the insurgents’ strength and make the security job easier. If the government favors Shiites and Kurds, the security forces could splinter and commando units disband.

Petraeus doesn’t have time to wait on these factors. He is charging ahead, trying to add to the herd and keep the training and equipment moving. His may be mission almost-impossible — but he is determined to get it done.

— Trudy Rubin is a columnist and editorial-board member for the Philadelphia Inquirer.