Saudi Arabia and their allies need to think again about the bombing campaign in Yemen. They are nowhere close to breaking the will of the Houthis, their main target.

The Houthis started as insurgents from north Yemen. Last September, with the co-operation of the former President Ali Abdullah Saleh and his considerable forces, they took the capital, Sanaa.

King Salman, Saudi Arabia's new monarch, put together a coalition to attack the Houthis when in March they looked close to capturing Aden, the main city in the south.

Since then Yemen, the poorest Arab country, has been bombed daily by a coalition that includes the richest Arab countries.

Common enemy

During a raid in Sanaa a few days ago, Mohammed Ali al-Houthi strolled across the compound that houses the presidential palace, looking unconcerned about the sound of hostile jet engines and anti-aircraft fire.

He laughed. "We are not worried. The Yemeni people can fight their battles and they know that."

As president of the rebel revolutionary council, Mr Houthi is the de facto - though internationally unrecognised - president of Yemen.

When I asked if he was prepared to allow the restoration of Abdrabbuh Mansour Hadi, the president the Houthis, and Saleh loyalists, forced to resign, he laughed again.

A UN Security Council resolution has reinforced Saudi demands for Mr Hadi to get his job back.

To Mohammed Ali al-Houthi that notion was preposterous. Others here in Sanaa, not just Houthi supporters, feel the same.

President Hadi is seen by many as a traitor who fled the country, who sits now in luxury in Saudi Arabia while his allies bomb Yemenis.

After our meeting he went walkabout outside the palace. Mohammed Ali al-Houthi is a thick-set man in his early 40s, dressed in a white robe, with a traditional curved dagger stuck into an embroidered, golden belt.

He strolled down a shopping street, stopping to shake hands, wave at supporters and to hand wads of cash to children.

Plenty of Yemenis dislike and distrust the Houthis. But the bombing means that at least they can agree on a common enemy.

I asked him about the Saudi statements that the Houthis are tools of Iran. He denied it.

"This is not true. We have our own weapons, we have our own country and our own military… We told them if you have a feud with Iran, then attack them, not Yemen."

Cold war

But for Saudi Arabia, sending a message to Iran is at least as important as trying to bend the Houthis to their will.

Senior Saudis I spoke to when the bombing campaign started talked about the threat they perceived from Iran, not about the Houthis.

The most significant conflict in the Middle East these days is the cold war between Iran and Saudi Arabia.

It is not the only reason for the chaos in the region. But it is an important factor driving instability and violence in Lebanon, and outright war in Syria and Iraq.

Western diplomats with experience of Yemen say that Iran has given the Houthis training and a certain amount of weapons.

The Houthis had plenty already. Yemen is among the most heavily armed countries in the world. But the Western diplomatic consensus is that the Houthis may share some goals with Iran, as well as Shia Islam. But they do not follow Tehran's orders if it doesn't suit them.

Whatever the degree of co-operation with Iran, what matters is the Saudis and their allies have chosen Yemen as the place to send a firm message to Tehran that they will not accept any meddling in what they see as their back yard.

And as usual in modern warfare, civilians are in the firing line.

Right across the Middle East these days you can find schools that are no longer used for education, because they house families who have lost their homes because of the violent upheaval that is convulsing the region.

'Everything is wiped out'

I visited one of 11 schools in Sanaa that is being used for internal refugees.

A man in his 30s called Mahmoud Khaled al-Haddah sat with his wife, Wardah, and Imam, their one-year-old daughter.

They fled their town after 24 of their neighbours were killed in an air strike. Mahmoud told the family's story.

"It was not a military town. We are on Yemen's border with Saudi. Everything has gone, houses, schools, mosques, everything was destroyed, even the main street has gone.

"It was very scary, no-one can live there anymore, it is like a ghost town. Everything is wiped out, mosques, hospitals, houses and schools, everything was destroyed."

I asked him why the war was happening.

"Only God knows. America is behind the attack that is a clear assault by Saudi Arabia, with no just cause.

"Why kill our women and children, destroy our houses, our belongings? Everything we worked for all these years has been destroyed by a missile strike. Our shops have been destroyed and we have abandoned our homes."

Insurgencies, separatism and bouts of civil war have become endemic in Yemen. But they have mainly been home-grown contests for power.

What is different now is that Yemen is being drawn, whether it wants to or not, into a much bigger confrontation.

Yemenis often say that, left to themselves, they can make deals with each other to stop fights before they become too destructive.

The problem is that they rarely get the chance to try. Big powers, over generations, have the habit of trying to direct events here, and it is happening again.

BBC