The specks on ice are explorers Lonnie Dupre and Eric Larsen, setting off on the first ever unsupported summer crossing of the Arctic Ocean in order to draw attention to global warming.
It was realised by the mid-18th century that some gases in the Earth's atmosphere, such as carbon dioxide, trap heat and keep the Earth warm. At the start of the 20th century, a Swedish scientist named Svante Arrhenius put forward the idea that human emissions of carbon dioxide would eventually raise temperatures. He didn't see this as a particularly bad thing, and most scientists at the time were sceptical that humans could burn fossil fuels fast enough to have a noticeable impact at all.
So, although the idea that mankind could influence Earth's global temperature was proposed over a century ago, it wasn't until relatively recently that scientists were able to confirm this with confidence. Data had to be gathered from around the world, technology had to develop to allow us to analyse that data, and basic advances in physics and other disciplines had to come about before we could understand it. What we now know about the climate is thanks to literally generations of dedicated researchers.
However, it is also easier to observe human caused climate change today because we've put so much more carbon dioxide into the climate system over the past century that the impacts of climate change are now clearly visible, affecting people and ecosystems all over the world. More cars, more factories, and more power plants - all are changing the climate faster than was previously possible - and causing more obvious changes.
Taking the planet's temperature
To get an accurate picture of how warm the Earth is, you need measurements from all over because the whole planet does not heat up at the same rate. In fact, some parts might even cool down while the world as a whole heats up. Also, many temperature readings are needed over time to develop an accurate long-term picture. In order to develop a global temperature history, researchers have had to travel to the farthest corners of the Earth, and come up with ways to "go back in time".
Methods of measuring past temperatures:
Historical records: This includes sources like ship's logs, farmer's diaries and newspaper articles. When carefully evaluated these can provide both quantitative and qualitative data.
Personal accounts and oral histories: Useful information can be gathered especially from the older generations of indigenous people who have always relied on nature for their survival, and so are particularly observant of changes over the past decades.
Direct (e.g. thermometer) measurements: These only go back around 300 years, and are very sparse until about 150 years ago. Also, differences in thermometer types and other variables have to be taken into account.
Data collected by balloon and satellite: This kind of data is very useful, but has only been available since 1979.
Tree ring thickness: This indicates temperature because the width and density of tree rings varies depending on growing conditions.
Ocean and lake sediments: Billions of tons of sediments accumulate each year in lakes and the ocean. The tiny preserved fossils and chemicals in the layers of sediment can be used understand past climate conditions.
Coral skeletons: The water temperature that the coral grew in can be determined from trace metals, oxygen and the isotopes of oxygen contained in its skeleton.
Fossil pollen: Each plant has uniquely shaped pollen. Knowing what plants were growing at a particular time in the fossil record enables scientists to make inferences about what the climate was like at the time.
Ice cores: Over the centuries snow falling on high mountains and the polar ice caps packs down and becomes solid ice. Dust and air bubbles trapped in this ice provide valuable climate data. For example, the air trapped in the ice serves as a record of carbon dioxide concentrations across the millennia.
Observed melting: Rates of glacial retreat, permafrost thaw, shrinking polar ice caps and reduction in Arctic sea ice are indicators of both short and long term climate change.
The important thing is not to look at any one source of data independently, but instead to take them together. This produces a scientifically compelling picture of a warming world that matches with the corresponding increase in greenhouse gases.
Predicting the climate future
Global climate models are mathematical representations of the real world's climate. Some models are attempts by scientists to boil the complex behaviour of the climate down to (comparatively!) simple formulas in an attempt to understand the forces at work. However, when people talk about specific predictions of long term climate behaviour they are usually talking about general circulation models.
In these models, the equations are tweaked (within reason) until the model is able to predict past and present conditions, as accurately as possible, when tested against actual observations of past and present conditions.
Since it's impossible to know every last variable in such a complex system, and because the model will never match the real world perfectly, scientists compensate by running each model over and over, while making tiny changes to the starting conditions (increasing the wind speed over Detroit by one percent, for example) and other factors. This way they can get an idea of the different possible outcomes. If one result occurs more frequently than another, then it is the more likely outcome.
In the end, each model predicts a range of possible outcomes. For example, the Intergovernmental Panel on Climate Change (IPCC) - taking into account all of the different available models - agreed on a projected global temperature rise of 1.4 - 5.8 degrees Celsius (about 3 to 8 degrees Fahrenheit). No one can say exactly how much the temperature will increase over the next hundred years, but with a couple of caveats it's a safe bet that it will be within this range.
One thing climate models cannot predict are all the possible effects of feedback mechanisms, which might help stabilise the climate or cause the climate to change much faster and in unpredictable ways. Of course, it would be irresponsible to ignore the climate models and hope for the best because of these uncertainties.
Another thing these models cannot really predict is human behaviour, and ingenuity. We might burn more fossil fuels than expected, and end up with a hotter planet then even the worst case scenario. Or we might deploy renewable energy and energy efficiency solutions faster then thought possible - eliminating the likelihood of the higher temperature ranges.