The mother of all climate reports is so scary that one of its authors resigned from the Intergovernmental Panel on Climate Change (IPCC) in protest. "Farmers are not stupid," the Sussex University economist Richard Tol said this past week, as hundreds of researchers cloistered away in Yokohama, Japan, hammering out the final wording of a document that he called "alarmist" when it comes to the many threats of global warming. The people who grow our food will find ways to adapt, said the rogue climate scientist at the most important climate science meeting in seven years.

But change isn't easy – especially not tectonic changes to the Earth. The final wording arrived today, and the IPCC report's most alarming projections make clear what many other studies have warned: the future of agriculture – of global hunger, of your grocery bill – is screwed. Or as UN secretary general Ban-Ki Moon put it rather more politely when he inaugurated the first rounds of the IPCC report last September: "The heat is on. We must act."

Glaciers will continue to shrink in the Himalayas, according to the IPCC, severely impacting the availability of water for farming in vast areas of south Asia and China. Climate change will damage heat-sensitive crops like wheat and corn, and have a smaller impact on rice and soy production. Prices for essential staples will rise on the global market. Hunger will increase in large parts of Asia and Africa. "Nobody on this planet is going to be untouched by the impacts of climate change," predicted the IPCC chief Rajendra Pachauri at a morning news conference.

The new report says that all of these very bad things will happen in future decades, as climate change picks up steam. But as I found out in east Africa last month, the future is already here for too many of the world's farmers. In Tanzania, the twice yearly seasonal rains upon which so many growers depend no longer come on time – and they're sporadic, drenching downpours at that, alternating with prolonged dry spells. Heat spikes have also been withering maize crop, and wells and streams are increasingly drying up.

The area where Dephath Omondi farms in southern Kenya looks lush, with emerald maize fields bordered by towering acacias. But he tells me that appearances are deceptive.

Twenty-five years ago the weather here was predictable – the long rains started mid-March to mid-May, then the short rains started in late August, early September. In the last decade, these rains never come on time. We have had floods and week upon week, with no rain at all. Farmers are confused about when and what to plant. It is all very worrying.

Similar disruptions are already challenging farmers worldwide. In Vietnam's Mekong Delta, rural people are losing ground as higher sea levels turn rivers too salty to grow rice. In Nicaragua, rising temperatures are spreading "coffee rust fungus", a disease which is killing thousands of trees and may render 80% of its the nation's coffee-growing areas unusable by 2050. And in the central Philippines, coconut farmers are struggling to recover from November's Typhoon Haiyan, which badly damaged or tore out an estimated 33m trees.

Just as there are no atheists in foxholes, there are few climate-change skeptics amongst those who grow the world's food – if any. Farmers don't have to read UN reports to know how radically their weather is changing. And consumers don't need academic studies or bullet points to know that food prices are steadily rising.

But you might need to know this: one such report published by the Institute of Development Studies in the UK predicts a whopping 20% to 60% rise in food prices by 2050, depending on the type of food, largely due to declining yields brought upon us by climate change. And if you think that's going to be painful, the entire world is in for some serious sticker shock: the IPCC predicts that a 2.5°C rise in global temperatures will cost the world economy up to 2% of its output, an estimated $1.4tn annually.

And you might want to know this: a report issued last week by the development group Oxfam warns that global warming may delay the fight against world hunger by decades and put an extra 50m people at risk. The world "is woefully unprepared" for the impacts on food, says Oxfam. Over 75% of global seed varieties have vanished over the last century, and spending on critical agricultural research and development is at an all-time low.

Lester Brown, the controversial founder of the Earth Policy Institute, warns that we face a looming "food crisis" not just from climate change – there are also escalating water shortages and the conversion of farmland to non-food uses. The vast amounts of land being used to produce biofuels and grain to feed livestock are also cutting down on the staple grains that people need to survive.

But make no mistake: the greatest single strain on our food supply will be our changing weather. "The agricultural system that we have today is designed to maximize production within a climate system that has existed over the past several thousand years," Brown told the Harvard Crimson. "Now suddenly, we don't know exactly what's going to happen in the future. We do know that we need to get the brakes on as quickly as possible."

Tol, the researcher who quit the IPCC in protest, says the farmers "will adapt". But that's like expecting squirrels to adapt to a forest fire. How will Amani Peter, a young farmer I met in Tanzania, adapt to his well going dry? How will he adapt to his corn withering when the rains stop a month early, as they did last year? And what will the nine out of 10 growers in western China who lack crop insurance do when the wheat harvests begin to fail? Even the smartest farmers may be unable to cope.

That is the bad news, and there is a lot of it. The good news? There will be some global winners in this climate-change roulette. Yields for some warmth-loving crops are rising in the US and Canada, even as agriculture suffers from dry-out in the American Southwest and extreme drought in California.

And the IPCC has called on policymakers to prepare – right now: "Climate-change adaptation is not an exotic agenda that has never been tried," says Chris Field, co-chair of one of the working groups. Remember the $1.4 trillion a year that climate change will cost? If a small fraction of the $1.4tn in overall climate spending recommendations went to ramping up regionally-based agricultural research, it would go a long way. Farmers need new drought- and heat-tolerant seed varieties. They need outreach programs to train them in the latest farming techniques. And of course, we need to stop spewing ever more CO2 into the air. While the alarm is sounding.