1
Introduction and the Purpose of this Book

An aerosol particle is defined a solid or liquid particle suspended in a carrier gas. The term "aerosol" technically includes both the particle and carrier gas, though it is common to often hear this used when referring to just the particle. In this book, we will retain the use of the term "aerosol particle". Whilst we often treat scientific challenges in a siloed way, aerosol particles are of interest across many disciplines. For example, atmospheric aerosol particles are key determinants of air quality [1-3] and climate change [4-6]. Improving our understanding of sources, processes and sinks is important as we develop strategies to lesson the impacts we have on human health and environmental systems. Knowledge of aerosol physics and generation mechanisms is key to all factors of fuel delivery [7] and drug delivery to the lungs [8]. Likewise, various manufacturing processes require optimal generation, delivery and removal of aerosol particles in a range of conditions [9].

The purpose of this book is to provide you, the reader, with the tools to translate theory on which numerical aerosol models are based into working code. In following the content provided in this book, you will be able to reproduce models of key processes that can either be used in isolation or brought together to construct a demonstrator 0D box-model of a coupled gaseous-particulate system.

You may be reading this book as an undergraduate, postgraduate, seasoned researcher in the private/public sector or as someone who wishes to better understand the pathways to aerosol model development. Wherever you position yourself, the coupling between experimental and modeling infrastructure is important in any discipline. Whilst the driving factors that influence both can vary, Figure 1.1 presents an idealized workflow of model development and model scales both in response to and as a driving force behind aerosol experiments. Particular emphasis is given to atmospheric aerosol particles in this workflow where, as we move from left to right, we move from aerosol models at the molecular and single particle scale to aerosol models acting as an import component in regional and global scale models. The purpose of this figure is to represent a workflow that migrates our understanding of aerosol processes to a framework that may be used to predict impacts. In a perhaps controversial approach, we can imagine a scale at the bottom of the figure that assumes as we move from left to right we reduce the physical and chemical complexity of our aerosol models. This sets the scene for understanding the research landscape of much of the developments you will find in this book.

Figure 1.1 Ideal workflow of aerosol model development in environmental science.

If we start at the left-hand side of the figure, we use the term mechanistic model. In aerosol modeling parlance, a mechanistic model is one that is built around a numerical representation of an underlying physical theory. For example, this might include a set of coupled differential equations that describe the movement of mass between a gaseous and condensed phase, or between different compartments of a condensed phase. Parameters in these mechanistic models may describe chemical and physical properties that are included in these differential equations and have been derived from a series of experiments or provided through separate models. In a mechanistic model, our mathematical framework provides a clear numerical narrative and separation of the processes we wish to include. We can then choose an appropriate numerical method to provide, for example, a time-varying solution to a set of initial conditions or predict a point of equilibrium. Once we have constructed our mechanistic model, we can consider uncertainties associated with the model architecture itself and/or errors associated with the parameters we use in our simulation. Indeed, the next phase in our workflow in Figure 1.1 is to compare with targeted laboratory experiments that serve to quantify the accuracy of our model or identify uncertainties that need further reduction. You may find mechanistic frameworks used at the single particle level, or indeed in models that are designed to capture the evolution of a population of particles. Where mechanistic models cannot replicate observed behavior within a specific level of accuracy, or simply do not have an appropriate theoretical basis to build on, parameterizations can be developed. This can be used in combination with, or as an alternative to, the mechanistic model. We often state that a parameterization has a higher computational efficiency than an equivalent mechanistic model. Specifically, the time to solution is reduced. As we move further right in Figure 1.1, and typically start to consider populations of particles and multiple processes, we might refer to hybrid models that combine both mechanistic and parameterizations. We may also start to consider the computational resource available to conduct more complex simulations. At the global scale, an aerosol model is one of many components in a framework that attempts to capture the dynamics of multiple components of the earth system (e.g., ocean, biosphere, land-air interactions etc.). The level of physical and chemical complexity retained in our aerosol model is dictated by a number of factors. These include the computational resource available, the associated detail carried in components that drive and respond to aerosol processes (e.g., how many emissions that lead to aerosol formation are captured) and ongoing efforts to resolve how much detail is needed to resolve potential impacts on, for example, human health. Of course, this narrative is an ideal one but at least provides an insight into factors that dictate the methods we use to construct our aerosol models. In this manner, we start to appreciate the ecosystem of aerosols models and why they exist. The aerosol scientist may come across a range of "simple" and "complex" models that have been designed to provide benchmark simulations in isolation. You will find a description of these benchmark models in the chapters of this book. Once we begin to capture processes across multiple scales, an aerosol model developer starts to consider any approximations that may be needed according to the numerical methods and compute resource available.

Whilst we focus on atmospheric aerosol to define our composition space in this book, the theory and tools developed are based on core aerosol physics that translate across multiple disciplines. Likewise, demonstrating a programming solution to common numerical operations is valuable to a large number of scientific disciplines.

Research developments often move at a rapid pace and, as the global aerosol community develop new observational and modeling platforms, we continually hypothesize and verify new species and/or processes deemed important to improve our understanding. We do not provide a comprehensive coupling of all known and emerging chemical and process complexity in this book. Indeed, there are remaining challenges on how we actually do that from a programming and real-world validation perspective. The landscape of computing hardware and software also moves at a rapid pace. The choice of programming language to solve a particular problem, or provide a particular service, is influenced by a number of factors ranging from required time-to-solution and ability to share across multiple platforms. As with numerical representations of aerosol processes, we do not provide a comprehensive multilanguage demonstration in this book. It is anticipated that readers of this book will have a wide range of programming experience; from those who have no prior experience to those who regularly develop their own applications. We expect therefore that you will take away different lessons from working through the material provided, whether it be the solution to a set of common operations or learning how to develop your first numerical model in your first programming language. You will find there are often multiple ways to write a piece of code that performs a particular task. You will also find that as we often have our own style in writing, so too can we develop our own style of developing code. In this book, we provide complete demonstrations of how to develop working code around key concepts (highlighted in figure 1.2), but we do not force a particular style beyond requirements of the language syntax. We also however provide examples of how we can optimize the code we develop. By looking at a range of examples, this will help you start to more broadly consider how efficient your code is and perhaps embed these considerations as you start to develop mode applications. We also discuss best practice in sharing any code in the public domain and ensuring reproducibility.

Figure 1.2 The topics covered in each chapter, summarized in the main body of text in this chapter, as a visual schematic that connects processes across the aerosol size spectrum. In this hypothetical example, the aerosol size distribution has three peaks represented as multiple log-normal contributions. We start to discuss log-normal distributions in Sections 1.3.2 and 1.3.3.

Seminal publications [e.g., [10, 11]] provide an extensive overview on the history and basis of core theoretical frameworks that aerosol models are based on. We do not repeat that content in this book; rather we present the theoretical basis used in constructing a model and then focus on how we map this to code...