At NASA headquarters, part of a map of Kenyan waterways blinks repeatedly in blue-gray, indicating where stream flow is heaviest and likely to cause flooding over the next 72 hours.

Halfway around the world, officials at Kenya’s Ministry of Water and Irrigation can see the same data, which they use to try to reduce the loss of life and property from increasingly frequent floods linked to global warming.

The mapping technology is part of a collaboration by the space agency and the U.S. Agency for International Development that helps cash-strapped nations deal with the challenges of a changing climate. Over the past three years, the United States has ratcheted up support for foreign countries to cope with global warming, spending nearly $1.4 billion. A small slice of the total, $18 million, has transformed the satellite-based mapping program, called SERVIR, from a modest effort targeting seven countries in Central America to one serving 32 countries worldwide.

But even as spending rises, a central question remains: Are rich countries, which bear the historic responsibility for putting carbon dioxide into the air, doing enough to help the poorest nations prepare themselves for the negative effects of greenhouse gas emissions?

In 2009, the world’s leaders — including President Obama — promised to give $30 billion between 2010 and 2012 to a “fast-track finance” program to help cut the emissions worldwide and make the most vulnerable nations more resilient in the face of global warming, a process called adaptation. That same year, they pledged that by 2020, they would mobilize $100 billion for the two goals.

The United States has provided $7.5 billion in international climate aid over the past three years, nearly $1.4 billion of which has been spent on adaptation.

David Waskow, who directs Oxfam America’s climate-change program, praised the United States for ramping up the assistance, but he noted that while leaders agreed to a balanced division between cutting emissions and helping poor countries adapt to climate change, only 19 percent of the funding has gone toward adaptation.

“The percentage of what’s going to adaptation is not adequate,” Waskow said, noting that it is often hard to tell how much of the climate assistance is money that the United States and other countries would have given as foreign aid anyway.

Of the industrialized nations, according to Oxfam America, Japan has given roughly $2.1 billion, Britain has donated about $800 million and Canada has provided $121 million. The region that has benefited the most from multilateral adaptation funds is sub-Saharan Africa, according to Germany’s Heinrich Boll Foundation.

But many representatives from the developing world remain critical of rich nations. At the U.N. Framework Convention on Climate Change talks, the latest round of which is now underway in Doha, Qatar, one South African delegate spoke of the need for “restorative justice” because her country has experienced co­lo­ni­al­ism, apartheid and now, global warming. Farah Kabir, country director at ActionAid Bangladesh, said industrialized countries are obligated to pay for the effects of climate change because “those that are suffering the most have done the least to cause it.”

The U.N. Framework Convention on Climate Change has created an adaptation committee that will help oversee rich countries’ contributions to the world’s most vulnerable nations.

But marshaling a global approach to what is often a local problem can be difficult. Rockefeller Foundation president Judith Rodin, whose group has spent more than $90 million on such projects in 10 Asian cities, said one concern is that the money won’t filter down quickly enough to local leaders who “know what they need” when it comes to coping with such problems as rising sea levels and more frequent heat waves.

The debate over how much public money will be available and how it will flow is critical. Unlike a renewable energy project, which can attract private capital, almost all the funding that poor countries need for building more climate-resilient societies must come from governments — either their own or foreign ones.

“We need a lot of public resources,” said Keya Chatterjee, who directs international climate policy for the World Wildlife Fund in the United States. “It’s very, very hard to believe you’re going to get private money to go into the communities that will be the most devastated” by global warming.

Kit Batten, USAID’s global climate change coordinator, said the agency is doing all it can “in this tough budget cycle and budget time.” She said it has focused its aid on three types of countries — the least developed, small islands and those dependent on glaciers for fresh water supplies — to “make sure our investments are getting the biggest bang for the buck.”

Still, these countries have very different needs, even within their own regions. “If you’re a farmer trying to figure out what crops to plant, you’re going to need different information than if you’re a policymaker trying to design infrastructure along the coast,” Batten said.

USAID’s climate programs, which now make up a third of the agency’s budget, vary widely. One involves sending a Peruvian engineer with expertise in glacial lake outbursts to Nepal to advise officials on managing the same phenomenon there. Another involves advising Jamaica on a national climate-adaptation plan. The agency has funded research for a new program in Kenya and Ethiopia: Herders insure their livestock and are compensated when a certain percentage of local vegetation dries up.

Christopher B. Barrett, an economics and international agriculture professor at Cornell University who helped develop the herders’ insurance, said this financial backup is crucial as higher temperatures take their toll on African livestock. “If the intervals between droughts are shorter, it means you can still rebuild herds and remain viable,” he said.

One of USAID’s most successful programs is the SERVIR satellite-mapping program it has spearheaded with NASA. As precipitation patterns shift, glaciers melt and fires become more intense, the program allows policymakers in Central America, eastern and southern Africa and the Hindu Kush Himalaya region to predict these changes with better accuracy.

Dan Irwin, who directs the program from his base at NASA’s Marshall Space Flight Center in Huntsville, Ala., describes the initiative as a “space to village” collaboration of the United States and developing nations. In the flood-prediction mapping, “We’re providing the data, and our African colleagues are doing all the work,” he said.

In many ways, poor countries have more robust policies than affluent ones on coping with global warming, because they recognized their vulnerability several years ago. For example, Bangladesh has developed an early-warning system for cyclones and built more shelters to reduce the loss of life that accompanies such extreme weather, noted Saleemul Huq, director of the International Center for Climate Change and Development.

“It’s about being a society that’s getting its act together,” Huq said. “We are doing that, and the rest of the world needs to do it, too.”

Princeton University geosciences and international affairs professor Michael Oppenheimer said that while adaptation can never be completely effective, storms such as Sandy have underscored the need for immediate action. “At least there’s a realization that climate change is not tomorrow’s problem, it’s today’s problem, and we need to deal with it now,” he said.

Geoff Dabelko, Ohio University’s program director for environmental studies, said the task of coping with the impact of future climate changes is far from complete.

“There’s a recognition that we’re not going to solve this problem quickly or easily,” he said. “On a large scale, you could say no one is well prepared to deal with it.”