The Nobel Prize for physics has been awarded to scientists from Japan, Germany and Italy for work that included expanding our understanding of climate change.

Syukuro Manabe, 90, and Klaus Hasselmann, 89, were cited for their work in "the physical modelling of Earth's climate, quantifying variability and reliably predicting global warming".

The second half of the prize was awarded to Giorgio Parisi, 73, for "the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales".

All three work on what are known as "complex systems", of which climate is one example.

The judges said Mr Manabe, 90, and Mr Hasselmann, 89, "laid the foundation of our knowledge of the Earth's climate and how human actions influence it".

Starting in the 1960s, Mr Manabe, now based at Princeton University in the US, demonstrated how increases in the amount of carbon dioxide in the atmosphere would raise global surface temperatures, laying the foundations for current climate models.

About a decade later, Mr Hasselmann, of the Max Planck Institute for Meteorology in Hamburg, created a model that helped explain why climate models can be reliable despite the seemingly chaotic nature of the weather. He also developed ways to look for specific signs of human influence on the climate.

Mr Parisi, of Sapienza University of Rome, "built a deep physical and mathematical model" that made it possible to understand complex systems in fields as different as mathematics, biology, neuroscience and machine learning.

His work originally focused on so-called spin glass, a type of metal alloy in which atoms are arranged in a way that changes the material's magnetic properties in apparently random ways that baffled scientists.

Mr Parisi, 73, discovered hidden patterns that explained this behaviour, theories that could be applied to other fields of research.

The physicists used complex mathematics to explain and predict what seemed like chaotic forces of nature in computer simulations, called modelling. That has given scientists such a solid understanding of those forces that they can accurately predict weather a week in advance and warn about the climate decades in advance.

Some non-scientists have attacked modelling, but it has been key to the way the world tackles one of its biggest problems: climate change.

German climate scientist Stefan Rahmstorf said: "Physics-based climate models made it possible to predict the amount and pace of global warming, including some of the consequences like risings seas, increased extreme rainfall events and stronger hurricanes, decades before they could be observed. Klaus Hasselmann and Suki Manabe were pioneers in this area and personal role models for me.

"We now witnessing how their early predictions are coming true one after the other."

While Mr Parisi's work was not focused on climate, he spoke about the pressing problems facing the Earth after the announcement.

"It's very urgent that we take very strong decisions and move at a very strong pace" in tackling global warming, he said. "It's clear for future generations that we have to act now."

Asked whether he expected to get the prize, he added: "I knew there was a non-negligible possibility."

It is common for several scientists who work in related fields to share the prize.

The prestigious award comes with a gold medal and 10 million Swedish kronor (£840,000). The money comes from a bequest left by the prize's creator, Swedish inventor Alfred Nobel, who died in 1895.

On Monday, the Nobel Committee awarded the prize in physiology or medicine to Americans David Julius and Ardem Patapoutian for their discoveries into how the human body perceives temperature and touch.

Over the coming days prizes will also be awarded for outstanding work in the fields of chemistry, literature, peace and economics.