So much of modeling with differential equations is concerned with long-time behavior of solutions that taking time in the reverse direction is almost never seen or discussed in a Diff Eq class.Yet climate and weather modelers need to do just that - they need to model and understand the conditions of the earth's climate in Deep Time - a time in earth's past well beyond the current state of knowledge of earth's climate states.
They need to go 'way back' in time, effectively to - ? This has been pointed out with great urgency by geologist G.S. Soreghan of Univ. of Oklahoma, who writes in Lessons From Earth's Deep Time that much is known about Earth's climate over the last 100,000 years. This time is miniscule when compared to earth's age of 4.5 billion years.
Going back so far in time is essential in order to understand the nature and causes of the extreme climate states that existed over that vast expanse of time, climate states that, according to Soreghan, "would seem very alien" to us today.
And why is this a pressing need? The answer is extremely chilling, and almost too obvious: our current path of global warming could well be a harbinger of a future earth climate that mimics some deep-time regime.
Soreghan and a significant number of other concerned scientists have banded together to form GeoSystems, described as
an interdisciplinary, community-based initiative stemming from the growing recognition that a full understanding of Earth's climate system --and our climate future-- lies in examining the wealth of "alternative-Earth" climatic extremes archived in the pre-Quaternary geologic record.
Visit the GeoSystems, site for resources on deep time climate issues, including reports on extreme climate states such as the Snowball Earth scenario that is claimed to have existed over 600 million years ago. The site also lists the ongoing efforts of the concerned scientists to seek research funding (GeoScience is NSF-supported).To read more about the "alien" climates of deep-time, visit the Paleomap Project of C. R. Scotese of the Univ. of Guelph (Ontario). Here you'll find a climate history of the earth from the Pre-Cambrian period to the present day, some fascinating animations, and a description of the methodology used to determine the deep-time climate.
And you'll also find the image of the Snowball Earth/ Mitten at the top of this post.
Given the rate of increase of atmospheric greenhouse gases since the Industrial Revolution, the more appropriate image would consist of kitchen mit...and a different color earth.