The idea that loads on the Earth’s surface may be regionally rather than locally supported can be traced back to Gilbert and Barrell’s work at the turn of the twentieth century. Their work was carried out at a time when the U.S. Coast and Geodetic Survey promoted the use of local, rather than regional, models of isostasy. The geodesists, with the exception of Putnam, showed that regional models of isostasy were not required to explain geodetic data.

While Gilbert perhaps was influenced by the geodesists, Barrell was not. Barrell challenged the geodesists’ conclusions concerning local models of isostasy, invoking instead the idea that topography was supported regionally by the lateral strength of the lithosphere. Following Barrell’s death, there was a vacuum, and the new ideas of regional isostasy gradually gave way again to local models of isostasy, which continued to be championed by the geodesists, notably Hayford, Bowie and Heiskanen

The history thereafter is a punctuated one with “bursts” of activity followed by long periods of quiet. The work centred on the activities of a few individuals: Vening Meinesz, Gunn and Walcott. Vening Meinesz and Gunn were contemporaries but there is little evidence of any contact between them.

In this chapter we provide an overview of data modeling and describe the formulation of probabilistic models. We introduce random variables, their probability distributions, associated probability densities, examples of common densities, and the fundamental theorem of simulation to draw samples from discrete or continuous probability distributions. We then present the mathematical machinery required in describing and handling probabilistic models, including models with complex variable dependencies. In doing so, we introduce the concepts of joint, conditional, and marginal probability distributions, marginalization, and ancestral sampling.

How certain can we be about projections of future climate change from computer models? In 1979, President Jimmy Carter asked the US National Academy of Science to address this question, and the quest for an answer laid the foundation for a new way of comparing and assessing computational models of climate change. My own work on climate models began with a similar question, and led me to investigate how climate scientists build and test their models. My research took me to climate modelling labs in five different countries, where I interviewed dozens of scientists. In this chapter, we will examine the motivating questions for that work, and explore the original benchmark experiment for climate models – known as Charney sensitivity – developed in response to President Carter’s question.

We assault the living world from every angle, and all at the same time. As we remember this onslaught, we grieve. Reminiscing is a powerful act. In grieving, we consider the state of our natural environment and take the necessary actions to rectify our abuse of the living planet.

Discovery of the significance of fluvial megafans came about in the mid to late twentieth century. We suggest reasons why appreciation of their existence came late in the history of Earth science, even after the advent of space-based observation of planetary landscapes. The reasons are partly cultural: megafans are uncommon in the historic cradles of modern geology (Europe, North America). Reasons are also partly theoretical: rivers have been conceptualised chiefly as sediment bypass systems terminating in deltas, rather than as aggradational systems in their own right. Reasons are also perceptual: just as the megaflood origin of channeled scablands was held in disbelief, the inordinate size of megafans has stood in the way of accepting (i) the sheer magnitude of their unit-size and also (ii) their existence as active systems in modern landscapes, rather than just as stratigraphic features in the rock record. Post-1990, scientific activity around megafans accelerated and involved global mapping, classification, and regional investigations into patterns and processes. An overview of this take-off period is provided as a partial introduction to the remaining 17 chapters of this book, which are briefly outlined.

People often assume that to give ourselves a fighting chance of avoiding catastrophic climate change, we need either inspired political leadership, or a moral revolution in society. Both would be nice to have, but there are more plausible ways to make faster progress. They involve thinking differently. We need science that gives us risk assessment instead of prediction; economics that understands change instead of assuming stability; and diplomacy that focusses on international collaboration instead of unilateral national action.

The historical development of statistics and artificial intelligence (AI) is outlined, with machine learning (ML) emerging as the dominant branch of AI. Data science is viewed as being composed of a yin part (ML) and a yang part (statistics), and environmental data science is the intersection between data science and environmental science. Supervised learning and unsupervised learning are compared. Basic concepts of underfitting/overfitting and the curse of dimensionality are introduced.

Desert sand dunes form part of self-organized complex systems of aeolian bedforms that comprise sand seas and dune fields. They form part of local to regional-scale sand transport systems in which sand is moved by the wind from source zones to depositional sinks via transport pathways. The state of these systems can be evaluated in terms of sediment supply, availability, and mobility, which in turn are controlled by changes in climate and sea level on a range of spatial and temporal scales.

Transport barriers offer a simplified global template for the redistribution ofsubstances without the need to simulate or observe numerous different initial distributions in detail. Because of their simplifying role, transport barriers are broadly invoked as explanations for observations in several physical disciplines, including geophysical flows,fluid dynamics,plasma fusion, reactive flowsand molecular dynamics. Despite their frequent conceptual use, however, transport barriers are rarely defined precisely or extracted systematically from data. The purpose of this book is to survey effective and mathematically grounded methods for defining, locating and leveraging transport barriers in numerical simulations, laboratory experiments, technological processes and nature. In the rest of this Introduction, we briefly survey the main topics that we will be covering in later chapters.

The integrated aspects of volcanic and plutonic magmatic systems are rarely exposed, yet this connection is fundamentally important to understand the evolution of magma, which is important, in and of itself, to understanding planetary evolution itself. Magmatic systems beneath major volcanic centers, including the ocean ridges, are an interconnected plexus of sills and conduits. Beneath Hawaii the underlying mush column extends through the entire lithosphere, whereas beneath ocean ridges the mush column is much less vertically extensive, yet they function in very similar ways in spawning a steady flux of basaltic magma. The Ferrar magmatic system exposed in the McMurdo Dry Valleys reveals critical connections at a high level in the crust, demonstrating the operation of a magmatic mush column.

Forests regulate climate through exchanges of energy and materials with the atmosphere. The idea that forests affect climate is not new. A vigorous debate about deforestation, reforestation, and climate change began during European settlement of the Americas, spreading to all regions of the world before collapsing in the early 1900s. The story of forests and climate change is told as being scientifically wrong and advanced for political, economic, or cultural reasons, but it has not been told from a modern scientific perspective. In fact, it represents the foundation for the interdisciplinary study of Earth as a system. Many of the questions posed in today’s study of climate change and climate solutions have their origins in the forest-climate question. The multicentury controversy over forests and climate change is a narrative in which purposeful modification of climate is longstanding, but by felling or planting trees. Earth system science is a centuries old idea, conceived in the long-held belief that forests influence climate and doomed to fail by the disciplinary specialization of the sciences. Narrow-mindedness prevented a vision of the world as an interconnected system.

This chapter first reviews the linear first-order non-homogeneous ordinary differential equation. Introduction to statistics and stochastic processes follows. Afterward, it explains the stochastic fluid continuum concept, associated control volume, and spatial- and ensemble-representative control volume concepts. It then uses the well-known solute concentration definition as an example to elucidate the volume- and spatial-, ensemble-average, and ergodicity concepts. This chapter is to provide basic mathematics and statistics knowledge necessary to comprehend the themes of this book. Besides, this chapter’s home works demonstrate the power of the widely available Microsoft Excel for scientific investigations.

Why do we want to transition all of our energy to clean, renewable energy? Why don’t we just continue burning fossil fuels until they run out, which may be in 50 to 150 years? For three major reasons. Namely, fossil fuels today cause massive air pollution health damage, climate damage, and risks to our energy security. These three problems require immediate and drastic solutions. The longer we wait to solve these problems, the more the accumulated damage. This chapter examines each problem, in turn.

Our food systems have performed well in the past, but they are failing us in the face of climate change and other challenges. There is a broad consensus that transformation of food systems is required to make them sustainable and equitable for all. Transformation occurs via agents of change: individual behaviour, policies and institutions, research and innovation, and partnerships and alliances. Outcome-oriented agricultural research for development can help bring about directed transformation that maximises benefits and minimises trade-offs.

This chapter examines the ten mega-threats, how they link and why they must be solved together; why the solutions must occur at both global and personal levels; and the importance of the individual in saving humankind.

Chapter 1 offers a historical examination of the causes and discovery of global heating and the development of the scientific consensus that it is human-caused and can be curtailed only by cutting greenhouse gas emissions and describes how those developments nonetheless failed to lead to extensive action.

This chapter introduces the aims, scope, framing, intended readership, and organisation of the book. We explain why a book offering a critical assessment of the IPCC is necessary and we situate this justification in the context of other global environmental assessments. We point out the intended readership of the book and why it is of importance and relevance for these readers. We conclude by explaining how the book is structured around five parts.