RASHAYIDA, West Bank, July 28 (Reuters) - Hewn from rock, the cavernous cisterns which dot the desert beyond Bethlehem have for centuries harvested winter rain to provide shepherds and their flocks with water through summer.

Under a baking sun, an elderly Bedouin explains how cisterns he remembers from childhood, many of them restored to full working order in the last few years, are once again helping his goat-herding community to survive.

That, he concludes, is why the Israeli authorities who control the West Bank have demolished at least three in the area since November.

"Maybe they are doing this to make us leave. We will not leave," said Falah Hedawa, 64, sitting on cushions in his tent home pitched in the hills that slope down to the Dead Sea.

Out into the desert, a stagnant pool marked the spot where one of the cisterns, chiselled out of a hillside, had stood until its recent demolition. A mud trail on the otherwise dry ground indicated where the water inside had drained away towards a wadi, a valley which becomes a river when the rain falls.

Israel has demolished 20 rainwater collection cisterns in the West Bank in the first half of this year, according to the U.N. Office for the Coordination of Humanitarian Affairs (OCHA), which monitors conditions in the Palestinian territories.

Their razing is part of a marked acceleration in demolitions of Palestinian structures in "Area C" -- the 60 percent of the West Bank where Israel exercises total control.

Defined by interim peace agreements concluded between Israel and the Palestinians in the 1990s, Area C is where all of Israel's West Bank settlements are located.

In the first half of 2011, more Palestinians lost their homes in Area C than in the whole of 2009 or 2010, OCHA says. Many of them were Bedouin. A total of 342 Palestinian-owned structures have been demolished in the area so far this year.

Typically, demolitions are carried out on the grounds that the structures, some of them as simple as tents, have been put up without Israeli permission -- something Palestinians say is almost impossible to obtain.

As for the cisterns, the Israeli civil administration for the West Bank says that in at least two cases, probably more, it took action because they were located in military training zones where live fire could pose a danger to people using them.

"LICENSED BY HISTORY"

That, Palestinians say, is just an excuse, part of a system of Israeli restrictions designed to curb their development while allowing the settlements to grow.

The non-governmental organisations (NGOs) behind the cistern rehabilitation project are deeply concerned: the Bedouin, who number around 27,500 in Area C, are some of the poorest of all Palestinians.

Rehabilitated, the cisterns have been providing them with a free water resource, easing their reliance on expensive tankered water that they have to tow to their encampments by tractor.

By reviving old cisterns, the project leaders hoped they could sidestep tight restrictions on the construction of new water infrastructure -- a factor which the Palestinian Authority says has exacerbated water shortages across the West Bank.

"These cisterns are licensed by history," said Nadi Farraj, a Palestinian agricultural expert who has helped to rehabilitate around 140 old cisterns in the last four years.

The Bedouin talk of cisterns dating back to the Nabatean era, some 2,000 years ago. During their rehabilitation, workers drawn from the Bedouin communities have uncovered artifacts including Ottoman-era military helmets.

At one remote desert site, amid stone structures believed to be the remnants of an early Christian church, workers found parts of ancient mosaic floors while rehabilitating two cisterns where goats are today taken to drink.

"It's clear they have been here a long time -- from the days of our ancestors at least," said Ibrahim Moussa, sitting in the shade underneath a rock outcrop as he watched over his herd.

Photographs taken during restoration work reveal cavernous spaces, buttressed by supporting columns and archways. Not all the cisterns are underground. Some consist of pools dug at the end of wadis to trap the rainwater flows.

Reaching the remote sites is often the hardest part of the work, Farraj says. Once there, workers must remove sediment, waterproof the walls with plaster and then rebuild collection channels that funnel the rainwater into the cistern.

"WATER CRISIS EVERYWHERE"

In the desert outside the town of Zaatara, one cistern bears a Christian symbol which shows that it predates the 7th century spread of Islam from the Arabian peninsula, said Ahmad Abou Rabada, a local notable.

The cistern is one of two where Israel ordered a halt to restoration work in June on the grounds the area was within a firing zone. Abou Rabada said firing had not been heard there for years.

"They have presented many excuses," he said.

He fears it is now only a matter of time before the civil administration demolishes the cistern.

The demolitions have drawn U.N. condemnation. DanChurchAid, a Danish NGO that has financed the project, says five of the cisterns it has worked on have been demolished this year, three by Israeli forces and two by Jewish settlers.

"I find it extremely concerning. The whole Horn of Africa and the Middle East are facing major droughts this year," said Mads Lindegarde, regional representative of DanChurchAid, part of an NGO coalition that has formed The Emergency Water Sanitation and Hygiene group in the Palestinian territories.

"To destroy ancient water cisterns and water resources in general is madness, but particularly in a situation where people are suffering from an extreme lack of water," he said.

The demolitions are compounding a water crisis across the West Bank, said Shadad Attili, head of the Palestinian Water Authority.

"I have a water crisis everywhere, especially in the area classified as Area C," he said. "I fail in providing water to those people. Supposing I have a water source, I have to get approval to lay a pipe, but I don't, so these people are relying on the cisterns," he said.

"What message are they sending? 'Leave this land' -- this is the only message they are sending," he said.

Though Israel denies seeking to displace the Bedouin by such methods, it does have a plan for resettling them in built communities.

"They will get land for free, electricity, water, which will probably improve their situation," a spokesman for the Israeli civil administration said. "They can't keep moving from place to place and land is limited."

"This is the only solution with the Bedouin."