BBC science correspondent David Shukman travels to the Pacific island state of Tuvalu, where the highest point on land is just five metres (16 ft). This puts the collection of atolls that make up the country at high risk of flooding - particularly if sea levels continue to rise as expected.
BIG WAVES, BIG GRINS - FRIDAY, 25 JANUARY
You might think that living on the equivalent of a leaking ship - stranded amid thousands of miles of forbidding ocean, sending out plaintive mayday signals that waft through the ether unanswered - would have a rather dampening effect on morale.
For now, the waves are a playground for Tuvalu's children
Certainly I've met people here who are scared by the rising waves and want to get out. And there is nervousness as the surf overwhelms the roads.
But I can say without doubt that the population of Tuvalu still has to be one of the most cheerful on Earth.
There's a ridiculously heavy downpour right now and I've just watched two children playing in the middle of it - grinning from ear to ear.
A girl riding on the back of a motorbike while carrying a huge tuna breaks into a beautiful smile.
And as I walk past the police post or people resting in their hammocks or the dockers returning from the jetty, they all say hello with bright faces.
Even the prime minister, describing what he calls "the life or death" situation facing his diminutive country, makes time to crack jokes about the weather - blaming us for the very English rain.
We visit Teimana again, the woman we had interviewed a few days earlier and who'd shown us how her vegetable plot was flooded with seawater, and carry on laughing.
In her kitchen, we eat a cake she's made using coconut syrup. Tony asks for the recipe and she cracks up. Everything we say or do makes her laugh - it's infectious. We all sit around giggling.
But the heartiest laughter of all came when we abandoned all our European reserve and sampled the South Pacific way of life by joining in a dance.
Yes, I really did wear a garland of flowers on my head. Yes, I did feel an utter idiot when, while clapping in time to the music, I noticed too late that it had suddenly stopped, leaving one solitary mistaken clap to echo through the hall.
Then the rows of Polynesian heads were thrown back in unrestrained mirth.
If they really do have to abandon these islands, the people of Tuvalu will be desperately sad - but somehow they'll find something to be jolly about.
Maybe it'll be another TV crew, perplexed but pleasantly surprised, at seeing such big grins amid such big waves.
A TOUR OF TUVALU - THURSDAY, 24 JANUARY
Tuvalu is a tiny, remote nation, and while I have been staying here one question that has frequently crossed my mind is how on Earth can it sustain itself?
It is a poor place and depends on money coming in from other countries such as Taiwan, Australia and Japan.
In this video,
I'll show you how some of the donations provided by the outside world have made a difference to this endangered state.
KING TIDE - WEDNESDAY, 23 JANUARY
Night after night, I watch the Moon getting fuller. And as it rises over the lagoon, I picture it tugging at the waters, lifting them inch by inch towards a dreaded King Tide.
I've read a lot about how Tuvalu is scarcely above sea level and it's all true. We drive up and down the island stunned at how high the waves get, how low the land is.
This is a country without any hills - a collection of coral pancakes. The only high ground is the odd very slight bump. We've yet to detect a feature marked on the map as Mount Funafuti.
There's a curious paradox. The fate of the islands could hardly look more precarious. Waves crash over the main road and seawater bubbles up through the coral to poison the soil.
Yet life goes on. We watch a rugby contest. The players are from Tuvalu's different islands and, though the sea may yet engulf them all and the floodwaters lie beside the pitch, they show no restraint at all in the tackling.
Parents perch their youngsters on motorbikes and steer through the puddles. A woman lugs a freshly caught tuna home from a roadside stall. A meeting hall, the venue for a funeral, is surrounded by floodwater, forcing the priest to gingerly pick his way in open sandals through murky pools.
I chat to Teimana Avanitele whose garden is flooded - which means that none of her vegetables will grow. She's worried about the rising tides but remains, like so many here, a cheerful soul. At least her coconuts survive and she keeps a fire burning under a pot of palm syrup, promising us a bottle of "toddy" when it's ready.
She's curious about us, and why we've come from half-way around the world. People are also fascinated by how we see them.
The children are fascinated to see a David Attenborough film
A group of children is glued to a video we've brought of a documentary by David Attenborough which includes some scenes from Tuvalu.
And when our first news report is aired on BBC World, a small crowd in the hotel lobby erupts with pleasure when friends and relatives are spotted.
Never mind that the report contains dire scientific warnings about their future. I mention this to the presenter of Radio Tuvalu and she smiles, as if to say that's simply the Tuvaluan way.
Tonight, the wind is hammering the windows. We wonder if tomorrow's waves will be even larger.
REACHING TUVALU - SATURDAY, 19 JANUARY
We're a small band of people on the bumpy, two-hour, twice-weekly flight over the turbulent waters from Fiji to the coral atolls of Tuvalu.
There's a family dressed in black, returning for the funeral of a son.
A father clutches his young boy, recovering from medical treatment, to his arm. Tuvalu has a hospital but some operations can only be done in Fiji.
A senior official, with distinguished grey hair and a garish flowery shirt, has been studying civil service management - Tuvalu may only have 11,000 citizens but it has the full apparatus of government.
A woman teacher worries that she will be late for the start of term at a boarding school on one of Tuvalu's outer islands - our plane, already 24 hours late, may not land in time to catch the weekly boat.
A former sailor is heading home after a short break - the remittances from Tuvaluans working the world's cargo ships are a major source of national income.
Below us is nothing but ocean - until the engines of our sturdy old propeller plane start to slow.
Then, suddenly, improbably, we spot the few delicate, slender scraps of land that make up Tuvalu.
Barely wider than the runway, I see a narrow stripe of green and white, a huddle of roofs amid the palms.
Beside it, amid the reefs and shallows, are colours so vivid they look artificial. There are patches of incandescent cobalt and deep blue and lurid green.
When the King Tide comes, Tuvalu is awash with floodwater
When the aircraft door opens, the heat and humidity hit like a steam train. We scurry across the runway to the shade of the tiny airport building.
I notice a woman customs officer looking at me intently. Naturally, I wonder if I've done something wrong. But she roars with laughter.
"Did I see you on TV?" she asks. "In the ice? All dressed up for the cold?"
She watches the BBC on satellite and saw our journey through the unimaginably chillier climate of the Northwest Passage in the Arctic last year. My presence in the tropics is obviously hilarious.
Pasty-faced from a European winter, bathed in sweat in the stifling temperatures, I'm obviously out of place in a land that never sees snow.
With another giggle, she stamps my form and waves me through, chuckling. Welcome to Tuvalu.
TRANSIT THROUGH FIJI - THURSDAY, 17 JANUARY
Somewhere in the infinite black of the Pacific night, I cross the International Date Line and lose not only the entire 24 hours of Wednesday but also my luggage and some, if not all, of my marbles.
Our eventual destination: The small island nation of Tuvalu
Few quicker roads to insanity have been devised than combining sleep deprivation with a 12-hour time difference and then having to wait on hold for various airline and airport offices to tell me my suitcase never existed.
I sit in the drenching torpor of Fiji wishing I could fast forward to my eventual destination, the tiny island nation of Tuvalu, preferably accompanied by a few of my belongings.
The particular problem is that because Tuvalu barely pokes above an ocean whose level is rising, I had wanted to be prepared with a Scoop-like array of possessions - everything from rubber boots for the flooding, sandals for the heat and a snorkel in case things get really bad. The so-called King Tide - the year's highest - is due soon.
Instead, I find my brain developing its own International Incomprehension Line as I struggle to understand how a missing bag on a flight booked with Air New Zealand seems to also involve Pacific Air, United Airlines, Qantas, and the luggage black hole of Los Angeles airport.
So I resign myself to having to find replacements which means enduring a personal double horror - shopping in intense heat.
The streets of the Fijian capital Suva, alternately soaked and steaming, are the scene for this quest. I stumble from one bemused Indian trader to another trying to avoid shirts that would look appropriate on the set of Borat or might be useful in livening up a damp barbecue in south London.
Eventually, producer Mark Georgiou and cameraman Tony Fallshaw agree I'm ready for the final leg of this Pacific journey. And then I get a message. My suitcase has been found and will be with me tonight. It's like finding a lost child, pure joy.
But I hardly sleep. My mobile keeps ringing. On the one occasion I manage to find it in time, I answer to a surreal cold call from an estate agent. But better that than sleeping too much - my dreams, fuelled by too many airline meals, are uncomfortably repetitive on the twin themes of waiting on hold and watching the vast Pacific Ocean rising in the dark.