To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Endemic infectious diseases constantly circulate in human populations, with prevalence fluctuating about a (theoretical and unobserved) time-independent equilibrium. For diseases for which acquired immunity is not lifelong, the classic susceptible–infectious–recovered–susceptible (SIRS) model provides a framework within which to consider temporal trends in the observed epidemiology. However, in some cases (notably pertussis), sustained multiannual fluctuations are observed, whereas the SIRS model is characterized by damped oscillatory dynamics for all biologically meaningful choices of model parameters. We show that a model that allows for “boosting” of immunity may naturally give rise to undamped oscillatory behaviour for biologically realistic parameter choices. The life expectancy of the population is critical in determining the characteristic dynamics of the system. For life expectancies up to approximately $50$ years, we find that, even with boosting, damped oscillatory dynamics persist. For increasing life expectancy, the system may sustain oscillatory dynamics, or even exhibit bistable behaviour, in which both stable point attractor and limit cycle dynamics may coexist. Our results suggest that rising life expectancy may induce changes in the characteristic dynamics of infections for which immunity is not lifelong, with potential implications for disease control strategies.
It is fitting to begin this exploration of mesoscale-convective processes with a definition of the atmospheric mesoscale. Likely, the reader has at least a vague idea of atmospheric phenomena that are normally categorized as mesoscale. Thunderstorms and the dryline are common examples. What the reader might not yet appreciate, however, is that devising an objective and quantitative basis for such categorization is nontrivial. Indeed, even the more basic practice of separating the atmosphere into discrete intervals can be difficult to rationalize universally, because the atmosphere is, in fact, continuous in time and space in its properties.
Consider the atmospheric measurements represented in Figure 1.1. These have been analyzed to reveal a frequency spectrum of zonal atmospheric kinetic energy. Although the spectrum is continuous, it does exhibit a number of distinct peaks. Conceivably (and arguably), the intervals centered about the peaks represent atmospheric scales. The relatively narrow peak at a frequency of 100 (/day) is compelling here, because it indicates the existence of energetic eddies with a diurnal cycle. Dry and moist convective motions that grow and decay with the daily cycle of solar insolation are the presumed manifestations of such eddies, and would fall generally within the atmospheric mesoscale.
Synopsis: Chapter 3introduces the different instrumentation for in-situ and remotely sensed observations, for operational/routine uses as well as special field collection. The placement of such instruments in observation networks is justified using sampling theory, and then is illustrated by example networks from past field programs. Finally, the spatial analysis of the data is motivated and described.
Introduction
This chapter provides an introduction to the data collection and analysis that underlie much of the discussion in subsequent chapters. For example, in Chapter 4 we will describe how observational data are used to provide the initial and boundary conditions for numerical weather prediction and simulation models. The characteristics of phenomena such as thunderstorm gust fronts (Chapters 5–6), supercells (Chapter 7), squall lines (Chapter 8), and mesoscale convective vortices (Chapter 9) are revealed by analysis techniques that extract the scale-relevant information obtained from appropriately configured observing systems.
Synopsis: A mesoscale convective system (MCS) is composed of precipitating convective clouds that interact to produce a nearly contiguous, extensive area of precipitation. Chapter 8describes MCS structure and organization, and then explains the dynamical links among structure, longevity, and intensity. The quasilinear MCSs, especially those that have leading edges that “bow” outward, can produce swaths of damaging “straight-line” surface winds. Proposed mechanisms for this wind production are described, including one that involves vertical vortices at low levels. The chapter also includes discussions of mesoscale convective complexes, another common organizational mode, as well as of the remnant vortices that these and other MCSs often generate.
Overview of MCS Characteristics and Morphology
A mesoscale convective system (MCS) is an organized collection of two or more cumulonimubus clouds that interact to form an extensive region of precipitation. As observed in weather radar scans at low elevation angles, the precipitation is nearly contiguous, especially at the leading edge of the system (Figure 8.1a). Indeed, this characteristic is one that allows for an observational distinction between an MCS and a group (or line) of discrete cells; it additionally has consequences on the MCS dynamics, as will be explained shortly. Another characteristic is the time scale, which typically is much longer than the ~1 h life cycle of the individual cumulonimbi comprising the system (see Chapter 6).
Synopsis: Upon initiation, deep convective clouds may evolve into precipitating convective storms. The elemental storm processes are updrafts and downdrafts. Their dynamical structure is described in this chapter, as is that of the storm outflow, to which the updrafts and downdrafts are intimately linked. Consideration is then given to storm evolution, in the context of the single- and multicelled storms of lowest hierarchical rank.
Overview of the Convective Storm Spectrum
Once initiated, convective clouds may evolve into deep convective storms that produce precipitation at the ground, gusty surface winds, and sometimes hail, lightning, and tornadoes. The duration, intensity, and types of phenomena attendant to the storm are related largely to the storm morphology or convective mode. Observable structural characteristics can be used to classify storms as:
Discrete, unicellular storms, including supercell storms
Multicellular storms
Mesoscale-convective systems (MCSs)
This classification – which is well supported by weather radar and satellite observations – borrows from the biological sciences, with convective cells regarded as the basic building blocks of convective storms. A convective cell has a definite, yet porous, boundary (visible cloud edge) like a biological cell wall. A convective cell may also divide and split into two cells (a splitting supercell), encounter and merge with other cells to become a larger cell (an MCS), have more than one “nucleus” (a multicell), and decay or grow depending on the availability of “nutrients” such as atmospheric moisture in its environment.
Synopsis: This chapter addresses ways in which convective storms affect and are affected by external processes. Perhaps the most familiar of such interactions involve convective-storm “remnants” like outflow boundaries and mesoscale-convective vortices. Chapter 9also explores convective influences on the synoptic-scale dynamics, especially through the diabatic heating due to the convective storms. Finally, the roles of mesoscale-convective processes over longer time scales are considered. This includes feedbacks involving the land surface type, and global radiative forcing, and the formation of precipitating convective clouds.
Introduction
Taken in order of increasing length scale, time scale, and complexity across these scales, some of the ways in which convective storms affect and are affected by processes external to the storms are explored in this chapter. Frequently implicated in such interactions on the mesoscale are storm “remnants” introduced in Chapters 6 and 8, namely, outflow boundaries and mesoscale convective vortices (MCVs). Both are convectively generated, persist long after the demise of the generating storms, and thereafter help initiate new convective storms. The diabatic heating due to convective storms influences the synoptic-scale dynamics, particularly in terms of surface cyclone development and intensification. This interaction is two-way, because an effect of a deepening cyclone is to enhance transports of heat and water vapor. Locally, this helps to sustain ongoing, and support subsequent, convective activity.
The primary resource for students enrolled in my early mesoscale meteorology courses at Purdue University was Mesoscale Meteorology and Forecasting, the edited collection of review articles published by the American Meteorological Society in 1986. Though still valuable, it was conspicuously missing a number of important developments that had taken place since its publication, including: (1) major field programs such as IHOP (International H2O Project), BAMEX (Bow Echo and Mesoscale Convective Vortex Experiment), and VORTEX (Verification of the Origins of Rotation in Tornadoes Experiment) and its successor VORTEX2; (2) the maturation and implementation of operational Doppler weather radar, and an equivalent advancement of airborne and ground-based mobile radar systems; and (3) the relative proliferation of open-source community models and a concurrent ability to run such models using accessible computing resources, including desktop systems.
In short, these and other developments have led to significant evolution in the understanding of the atmospheric mesoscale since 1986, and motivated my effort to produce an updated resource. The realization of this effort is Mesoscale-Convective Processes in the Atmosphere.
As a perusal of the book shows, a major difference between Mesoscale-Convective Processes in the Atmosphere and other newly available mesoscale books is its focus on deep moist convection. This limited focus was driven partly by my perception of student interest, and partly by a philosophical choice to provide a concentrated treatment of a few topics, rather than a diluted treatment of all things mesoscale. Of course, it also follows my own interests, which most certainly biased the directions of some explanations (as in my considerable use of numerical modeling results, for example), although I did strive for balance as much as possible.
Synopsis: This chapter considers the basic problem of how moist air becomes positively buoyant and thereafter rises freely in the form of a deep convective cloud. Following a review of parcel theory, much of the discussion in this chapter regards the means by which air parcels are “lifted” some vertical distance so that they become positively buoyant. Synoptic-scale processes provide weak lifting, but mostly serve to precondition the thermodynamic environment. Orographic lifting is the canonical example, whereby air parcels are forced to rise as they encounter sloped terrain. Other lifting mechanisms include horizontal convective rolls, gravity waves, horizontal outflow due to other convective storms, and relatively larger-scale fronts, drylines, and sea-breeze fronts. As shown, these mechanisms may operate individually or in tandem.
Parcel Theory
Paramount to studies of convective processes is the origin of the deep cumuli that subsequently organize into convective storms. Such convection initiation (CI) is a topic that is treated separately here, even though some of the concepts will be used in later chapters to explain the sustenance and longevity of storms.
Synopsis: This chapter provides information on the design and implementation of mesoscale numerical models. The governing equations of typical mesoscale models are given, as are their numerical approximations. Physical processes such as those involving cloud and precipitation microphysics are represented as simplified functions of model variables. Schemes for the parameterization of these and other relatively complex processes are provided to show basic formulations. Design and implementation issues, such as the size of the model domain, the use of nested grids, and model initialization, are also discussed.
Introduction
The objective of this chapter is to introduce the reader to the basic design and implementation of mesoscale numerical models. As will be demonstrated in the remaining chapters – and perhaps as the reader has already experienced – such models play dual roles as experimental and weather prediction tools. Indeed, some community models, such as the Weather Research and Forecasting (WRF) model, have a built-in functionality that allows for (1) idealized modeling, which employs simplified initial and boundary conditions (ICs, BCs), and for (2) real-data modeling, which employs observationally derived ICs and BCs such that real events can be simulated or predicted. Our treatment herein assumes a fairly generous definition of a mesoscale model so that both approaches can be discussed.
Synopsis: This chapter is devoted to an in-depth discussion of the class of thunderstorms known as supercells. A hallmark of a supercell is a long-lived rotating updraft. Such mesocyclonic rotation influences the supercell dynamics, and in turn the supercell intensity, longevity, motion, and structure. Rotation generated near the ground and then become concentrated to form a tornado. A description of the sequence of processes leading to tornadogenesis is included in this chapter, as is a summary of parameters that help quantify the supercell environment. Some concluding remarks are made regarding tropical convective phenomena that share some of the same characteristics as supercells.
Characteristics of Supercell Thunderstorms: An Overview
Observations with weather radar from the 1950s through the 1970s revealed the existence of single large thunderstorms that persisted for periods of several hours, a time much longer than thought typical. These intense storms also were observed to have an atypical movement – in directions to the right and/or left of, rather than parallel to, the cloud-bearing environmental winds. Finally, the storms were distinguished on radar by a persistent, internal circulation that coupled a primary updraft with downdrafts and rotation about a vertical axis.
Synopsis: The general focus of this final chapter is on numerical weather prediction (NWP) at the mesoscale. NWP models have theoretical limits imposed by the nonlinear governing equations and approximations, as well as by errors in the initial and boundary conditions. These theoretical limits are viewed in the context of actual applications of mesoscale forecast models. Consideration is given to deterministic forecasts, and then to the use of model ensembles to produce probabilistic forecasts. Measures needed to evaluate the accuracy and skill of these forecasts, especially on the scale of convective precipitating storms, are also considered. The chapter concludes with a section devoted to possible approaches to – and the feasibility of – longer-range prediction of mesoscale-convective processes.
Introduction
This chapter focuses on the limits and uses of numerical weather prediction (NWP) on the mesoscale. Because of an intrinsic link to digital computing technology, mesoscale predictability and prediction comprise rapidly advancing areas of basic and applied research. An attempt is made herein to introduce the reader to enough material to appreciate the directions of these advances.
A nation-wide vaccination campaign began in New Zealand in 2004 with the aim of stopping the epidemic of meningococcal B disease. Approximately 80% of those under 20 years of age when the campaign was launched were vaccinated with three doses of a tailor-made vaccine. We propose a framework for a mathematical model based on the susceptible–carrier–infectious–removed (SCIR) structure. We show how the model could be used to calculate the predicted yearly incidence of infection in the absence of vaccination, and compare this to the effect that vaccination had on the course of the epidemic. Our model shows that vaccination led to a considerable decrease in the incidence of infection compared to what would have been seen otherwise. We then use our model to explore the potential effect of alternative vaccination schemes, and show that the one that was implemented was the best of all the possibilities we consider.
A susceptible–exposed–infectious theoretical model describing Tasmanian devil population and disease dynamics is presented and mathematically analysed using a dynamical systems approach to determine its behaviour under a range of scenarios. The steady states of the system are calculated and their stability analysed. Closed forms for the bifurcation points between these steady states are found using the rate of removal of infected individuals as a bifurcation parameter. A small-amplitude Hopf region, in which the populations oscillate in time, is shown to be present and subjected to numerical analysis. The model is then studied in detail in relation to an unfolding parameter which describes the disease latent period. The model’s behaviour is found to be biologically reasonable for Tasmanian devils and potentially applicable to other species.