Much has been made of two photographs that define George Bush’s presidency. After Sept. 11, he stood in the smoldering ruins of Ground Zero and rallied the nation’s resolve. After Katrina, he flew over the storm’s wreckage in Air Force One, days late, distracted and detached.

The contrast between those images helps explain the president’s plunging popularity. In the latest New York Times/CBS poll, only 36 percent approve of the job he’s doing, and barely 1-in-4 express great confidence in his ability to handle a crisis. Only 29 percent say the country is headed in the right direction.

A year later it’s worth asking exactly why Katrina caused such devastating political fallout. The answer goes far beyond those two photos to the very nature of the presidency itself.

Any American president really holds two jobs at once. One is chief executive, or head of government, the provider of federal goods and services. The second role, chief chaplain or head of state, is charged with embodying and elevating the nation’s spirit.

After Katrina, Bush failed to fulfill both responsibilities.

Start with the head of government role. Natural disasters are always high-stakes events for any executive — mayors and governors, as well as presidents. Ordinary citizens who seldom intersect with government suddenly need help. And that help must be delivered quickly and efficiently, under difficult circumstances, in the full glare of media attention.

The mayor who clears the streets after a blizzard is a hero, the one who doesn’t is a bum. Everybody knows the difference, the signs of incompetence are unavoidable, and the streets that Bush walked through this week in Mississippi and New Orleans (to stretch the metaphor) still haven’t been plowed.

Even Republicans agree that the president’s post-Katrina performance left him severely wounded. Rep. Patrick McHenry of North Carolina told The Washington Post that Bush’s “ability to lead” has always been his greatest asset, “and Katrina undermined it badly.”

Andrew Kohut of the Pew Research Center said: “This is an event that calcified the criticism people were having about Bush, made it more personal and had a big impact on how people look at him.” Added presidential historian Robert Dallek: “It triggered Bush’s downturn.”

Of course, the demoralizing news from Iraq contributed heavily to that downturn, but now the two issues are starting to overlap. Congress has appropriated a lot of money for storm relief, $110 billion. But the exploding costs of the Iraqi mission, and the expanding budget deficit, place limits on Washington’s generosity, and a lot of voters now believe that for every bridge rebuilt in Baghdad, one is not getting repaired in Biloxi.

The more important question is safety. George Bush won a second term by convincing Americans he would protect them from harm. But when Katrina hit, his promises of security proved hollow. Then he compounded the damage with the same kind of misleading statements that have blemished his record on Iraq.

No one could have predicted that the levees would burst, the president said, when in fact many experts had raised that precise possibility. The pattern is all too familiar. Many experts had issued warnings — also ignored by the administration — that the invasion of Iraq would trigger anti-American resentment and inter-tribal warfare.

As a result, Katrina damaged more than the president’s reputation for competence, it damaged his reputation for integrity. It led voters to ask: Can we really trust this guy?

The trust issue connects to the president’s second role, as head of state. Bush triumphed at Ground Zero because he was authentic and spontaneous. He spoke for all Americans, including his opponents, who sensed his sincerity and united behind him.

But the president’s performance in New York set a very high standard, one that he’s never been able to duplicate. Many of his subsequent efforts to speak for and to his countrymen seem false and phony by comparison.

Remember the flight suit and the aircraft carrier and “Mission Accomplished” banner? Or the floodlight speech in New Orleans’ Jackson Square promising “bold action” to rebuild the city? Or the unfortunate praise for his emergency management chief, “Brownie, you’re doing a heckuva job”? (The Brownie in question, Michael Brown, admitted this week, “There was no plan. … I let the American public down.”)

No wonder the president’s poll numbers are so low. No wonder his credibility is shot. Since Katrina, he has not been doing a “heckuva job” as either chief executive or chief chaplain.

Like Brownie, he “let the American public down.”

(Steve Roberts’ latest book is “My Fathers’ Houses: Memoir of a Family” (William Morrow, 2005). Steve and Cokie Roberts can be contacted by e-mail at stevecokie@gmail.com.)