Classification

The principle underlying diagnostic use of modelling of tracer transport is that the space–time distributions of trace-gas concentrations in the atmosphere reflect the space–time distributions of their sources and sinks. Observations of these distributions can in turn provide information about the processes involved. Tracer-inversion calculations use the relation between fluxes and concentrations in order to make specific estimates of fluxes. The possibility of using atmospheric-concentration data to make more direct inferences about processes is addressed in Chapter 12.

In this chapter, we review the general characteristics of sources that will influence the effectiveness of such inversions. In practice, the question of which source characteristics are important depends on the objectives of the inversion.

In considering the sources, there are two questions that we need to ask.

• What do we wish to learn about the sources and sinks?

• What prior information is available for Bayesian estimation?

The first question is addressed in very broad terms in the following section. To put the discussion in context, we consider some of the generic ways of classifying sources and sinks of greenhouse gases.

Location. This is the primary information required by forward modelling of atmospheric transport of trace constituents. Conversely, information about source strengths at specific locations is the most direct output from inverse modelling.

Principles

This chapter considers a range of non-linear estimation techniques. In reality, the majority of real-world estimation problemswould be expected to be non-linear, with linear problems as a minor special case. This book's emphasis on linear problems reflects current practice – most progress has been made on these more tractable problems. This reflects the simplicity of the linear problems and their suitability for illustrating principles of indirect estimation. Most of the cases for which there are results with explicit mathematical expressions are linear problems.

Non-linear problems are defined by what they lack, rather than by any common type of behaviour. Furthermore, there have been relatively few applications of non-linear techniques in tracer studies. Consequently, this chapter is rather more exploratory than most of the rest of this book. Simple cases are used to illustrate the techniques so that analytical solutions can illustrate the key features. Analysing the corresponding cases with real-world complexity will almost always require numerical techniques.

Taking the case of linear estimation as a starting point, there are a number of approaches of varying degrees of generality.

1. ▪ Cases in which linear estimation is used because it is optimal. The requisite conditions are described below.

2. ▪ Cases in which linear estimation is used for convenience, even though it is not optimal.

3. […]

General issues

The previous chapters of this book have described the progress in tracer inversions applied to global-scale problems. In parallel with these developments, there has been increasing interest in problems on smaller scales. Motivations for such work include applications such as monitoring of emissions and also improving our understanding of the observational data used in global inversions.

In this section we consider problems defined with a spatial resolution of order 100 km defined over continental-scale regions. This is a rapidly developing field, with, as yet, relatively little sign of any consolidation of techniques.

Some of the new features that can be expected in going from the global to regional scale are the following.

1. ▪ Data will be needed on synoptic time-scales, rather than monthly means: at Cape Grim, the operational conditions defined as ‘baseline’ apply for less than 50% of the time (see Section 5.2 above). For the remainder of the time, the concentrations of CO2 reflect more local influences. Model studies indicate that, for as much as 70% of the time, air at Cape Grim has been influenced by Tasmania, south-eastern Australia (as illustrated in Figure 9.1), or more westerly parts of the Australian continent). This raises the possibility of using these ‘non-baseline’ data to interpret the local sources and sinks. Similar possibilities arise for other sites on the coasts of continents or on nearby islands.

2. ▪ The nature of the inverse problem is likely to change since the transport characteristics are dominated by advection rather than appearing diffusive.

3. […]

Issues

Methane (CH4) is the second most important of the anthropogenic greenhouse gases in terms of its current contribution to radiative forcing. Mole for mole, the radiative forcing is 21 times that of CO2, but the climatic impact from methane is smaller than that from CO2 due to the lower concentrations which result from smaller sources and faster removal from the atmosphere.

Over the period of direct observations, the atmospheric concentration of CH4 increased for several decades, but during the late 1980s and the 1990s the rate of growth dropped considerably. On longer time-scales, ice-core records show that the atmospheric concentration has more than doubled over the last 400 years. On still longer time-scales, concentrations of CH4 are closely coupled to glacial/interglacial cycles. However, the current budget of atmospheric CH4 remains rather uncertain (see Section 15.2 and Table 15.1 below).

Analysis of the behaviour of CH4 is in many ways more complicated than that for CO2 because the main process by which CH4 is lost from the atmosphere is by oxidation through the OH radical in the free atmosphere, rather than by gas exchange at the earth's surface.

Background

CO2 is the most important of the anthropogenic greenhouse gases. Its concentration in the atmosphere has increased by about 30% during the industrial period and is almost certain to reach double pre-industrial concentrations in the second half of the twenty-first century.

On time-scales of millions of years, geological processes dominate the carbon cycle. Atmospheric concentrations of CO2 are determined by the balance among erosion, sedimentation and volcanic emissions. Sundquist has described a hierarchical classification of geological exchanges of carbon on the basis of time-scale. On any particular time-scale, any faster processes make the reservoirs involved appear to be in a well-mixed equilibrium state whereas any slower processes appear as almost-fixed boundary conditions. Geological processes act too slowly to cause significant changes to atmospheric concentrations of CO2 on time-scales less than millennia. On timescales of centuries or less, the dominant fluxes of CO2 to and from the atmosphere come from the oceans and the terrestrial biosphere, i.e. living biota, dead and decaying biota and active carbon reservoirs in soil. It is these ‘active’ reservoirs that we need to consider when we are analysing anthropogenic changes in the carbon cycle. Figure 14.1 gives a schematic representation of the exchanges between these reservoirs, showing the large natural cycle in approximate balance and a comparatively small anthropogenic perturbation.

Issues

The halocarbons are a group of compounds with halogen atoms (and possibly hydrogen) attached to a carbon skeleton. Most of the halocarbons are purely synthetic. However, there are significant natural sources of the methyl halides (CH3Cl, CH3Br and CH3I), chloroform (CHCl3) and, to a lesser extent, dichloromethane (CH2Cl2). The halocarbons can be regarded as derived from the alkane CnH2n+2 structure by substituting hydrogen atoms with halogens. An outline of the relevant chemical nomenclature is given in Box 16.1.

As polyatomic species, all these compounds will be likely to affect the infra-red radiative balance of the earth. However, the main concern about these gases has arisen from their role in the depletion of stratospheric ozone (see Box 16.2). The extent of depletion of ozone depends on the amount of chlorine and bromine released when halocarbon compounds are photolysed in the stratosphere and on the altitude at which the photolysis occurs. Chlorine and bromine participate in catalytic cycles that destroy ozone while leaving the halogens free to participate in further cycles of destruction of ozone.

Most of the compounds that are not fully halogenated, i.e. those with one or more hydrogen atoms remaining, react primarily with tropospheric OH. The products are removed by rainout and so relatively little of the chlorine or bromine reaches the stratosphere.

The main classes of compounds of concern are the following.

Our immediate environment – the atmosphere, soils, surface water and groundwater – is host to a vast number of chemical reactions, even leaving aside the biochemical reactions of living organisms. Environmental chemists aim to define and quantify these reactions, make analytical determinations of reactants and products, construct predictive models, and relate their findings to the functioning of ecosystems. A major part of the research effort is to take account of natural organic matter and mineral particulates, because these abundant, poorly defined, components exert a powerful and ubiquitous chemical influence on the environment. This book focuses on the most chemically significant fraction of natural organic matter, humic substances.

Humic substances are complex, acidic organic molecules formed by the decomposition of plant, animal and microbial material. They are abundant and persistent in the biosphere and immediate subsurface, being present in particulate and dissolved forms in soils, waters and sediments. They interact with a variety of solutes, adsorb at surfaces, and are photochemically active. Humic substances first came to prominence in agriculture, because of their positive influence on the structure, water retention properties, and nutrient status of soils. More negatively, they pose problems to the water supply industry, requiring removal to minimise water colour, and giving rise to potentially mutagenic by-products as a result of chlorination. There is interest in using humic substances to recover metals from wastewaters and from seawater. Schnitzer (1991) lists a variety of uses of humic matter, in agriculture, industry, environmental engineering, and medicine.

Humic substances undergo a number of physico-chemical interactions other than cation binding. They include aggregation, adsorption, the binding of hydrophobic organic compounds, photochemical reactions, and involvement in mineral precipitation and dissolution. In laboratory studies, conditions will usually be arranged to keep ‘background’ conditions simple, to focus on the interaction of interest. In the natural environment, however, some or all of the processes, including cation binding, proceed in parallel, and must influence one another. The purpose of the present chapter is to consider how cation binding influences these other interactions, and how they in turn may influence cation binding.

The conformation of humic matter

When cations are bound by humic substances, changes may occur in the conformation of the humic molecules. For example, it can be envisaged that the formation of multidentate complexes involving separate parts of the molecule may lead to a more compact structure. Another possibility is that, by reducing the net humic charge, cation binding leads to the reduction of repulsive interactions, again leading to compaction. The sensitivity of humic acid size and shape to cation binding has been emphasised by Swift (1989a), as discussed in Chapter 2. The more flexible and ‘diffuse’ is the conformation of the material before cation binding, the greater will be the changes in conformation on binding. Being smaller, fulvic acids have fewer opportunities to undergo conformational change.

Evidence for conformational change induced by proton binding comes from viscosity measurements (Ghosh & Schnitzer, 1980; Avena et al., 1999).

The comprehensive models described in Chapter 9, and evaluated in Chapter 10, depend upon fitting data to equations. In Model VI, assumptions are made about molecular size and shape in the electrostatic sub-model, and in the calculation of proximity factors (defining multidentate sites). These aspects of Model VI can therefore be regarded as predictive, i.e. not dependent upon data fitting. The purpose of this chapter is to discuss how predictive modelling can be taken further, the ultimate aim being to describe cation binding from knowledge about humic molecular properties, structures and sizes, without the need to extract parameters from binding data.

Electrostatic interactions

As has already been discussed in Section 9.5, electrostatic interactions can be simulated given information or assumptions about molecular size, shape, solvent permeability and net charge. Some work has been done to explore the influence of molecular size heterogeneity, which may influence the overall binding characteristics of a humic sample. Thus, a physically more realistic model is obtained by the strategy of Bartschat et al. (1992), i.e. postulating the humic matter to consist of molecules with a range of electrostatic characteristics, dependent upon molecular size. Implementation requires knowledge or assumptions about the size distribution of the sample.

As well as size, Coulombic effects depend upon the conformations of the humic molecules, the extent to which the structures are penetrated by water, and the degree to which conformations change as a function of molecular charge and solution conditions.

An appreciation of the formation and properties of humic substances is needed to understand their interactions with cations, and the influence of those interactions within the natural environment. This chapter presents a summary of current knowledge, emphasising those aspects of most relevance to cation binding. More detailed, wider-ranging, information can be found in the books of Aiken et al. (1985a), Hayes et al. (1989), Averett et al. (1989), Beck et al. (1993), Stevenson (1994), Piccolo (1995) and Gaffney et al. (1996). Jones & Bryan (1998) reviewed the colloidal properties of humic substances. Thurman (1985) is an essential text on the organic matter of natural waters, and includes much information on humic substances.

Natural organic matter and humic substances

Most (99.95%) of the Earth's carbon is held in sedimentary rocks, to and from which it cycles on geological time scales. The remaining carbon (about 4 × 1019g) is in the biosphere or shallow subsurface, 90% of it in the form of carbonate dissolved in seawater, and about 9% in organic forms (Table 2.1). In soils, natural waters and their sediments, the majority of the organic carbon is present in humic matter.

Stevenson (1994) considers natural organic matter in soils to consist principally of litter (macroorganic material lying on the soil surface), the light fraction (plant residues within the soil proper), soil biomass (predominantly microorganisms living in the soil), and stable humus. Of these pools, the last predominates in most agricultural, forest and moorland soils.

The aims here are (a) to examine whether or not parameterised models can fit experimental data from laboratory experiments with isolated humic substances, (b) to discuss the meanings of the parameter values, and (c) to explore some of the predictions that the models can make. There is little point in considering applications of all the models discussed in Chapter 9. The simpler ones can fit data over small concentration ranges, or at a single pH, but their applicability is restricted. Therefore we shall confine our discussion to the models that might be able to fit most or all of the available data, and which can therefore be termed comprehensive models. Thus we shall just be examining the performances of Models V and VI and the NIC(C)A models.

Interactions with protons

Simulation of the dissociation of protons from humic substances is the first task for any model that purports to describe cation binding comprehensively. Figures 10.1 and 10.2 illustrate applications of Model V/VI and the NICCA–Donnan model to proton-binding data at different ionic strengths. Note that Models V and VI are identical in their descriptions of proton binding, and the same applies to the NICA and NICCA models. It can be seen that the models work well, reproducing the shapes of the curves and the ionic strength dependence. Generally, the NIC(C)A model provides superior fits, with smaller and more random residuals.

This chapter summarises information about the chemical groupings responsible for the binding of protons and metal cations by humic substances. The bonding atoms themselves are considered, together with structural arrangements at the molecular level (conformation). Such information complements the quantitative binding data reviewed in Chapter 7, and can help in the formulation of mechanistic models of cation binding by humic matter (Chapters 9–11).

Proton-dissociating groups

The proton dissociation properties of humic substances (Section 7.1) point very strongly to the presence of carboxylic acid groups in their structures. Direct evidence for the chemical nature of groups dissociating in the acid-to-neutral pH range was provided by Cabaniss (1991), who used Fourier-transform infra-red (FTIR) spectroscopy to show that the groups were nearly all carboxylic acids (Fig. 8.1).

Leenheer et al. (1995a, b) carried out detailed studies to investigate the chemical natures of carboxylic acid groups in Suwannee River fulvic acid. They used chemical modifications specific to individual groupings, titration data, model compound studies, NMR, and theoretical arguments, to estimate the contributions of different groups. They pointed out that a significant number of the groups are quite strongly acidic. For the fulvic acid sample in question, they estimated that one-third of the carboxyl groups had pK values of 3.0 or less. The main aim of their work was to account for such acidity. Table 8.1 summarises their findings. It was deduced that the strong carboxyl acidity is associated with polycarboxylic α-ether and α-ester structures.

We now consider the results of experimental studies in which extents of interaction of protons and metal ions with humic substances have been determined. The emphasis is on amounts of binding, rather than the qualitative nature of the complexes, which is dealt with in Chapter 8. The review material is not exhaustive, but key examples are given to cover the present state of knowledge. Some simple interpretations are offered, to prepare the ground for Chapters 9–11, which deal with modelling. The ‘isolated’ appears in the chapter title because only results with isolated materials are considered; results from field samples are discussed in Chapters 13 and 14.

Proton dissociation

Titration curves for humic substances

Some results have already been presented in Chapter 4, including comparisons with simple ligands and polyacids. More data are plotted in Fig. 7.1. As has been noted before, the plots of Z vs. pH are rather featureless, with only suggestions of an end-point around neutral pH. Also, there is an appreciable effect of ionic strength, which is greater for humic acid than for fulvic acid, but in both cases less than for high molecular weight polyprotic acids. As mentioned in Chapter 4, the results can be interpreted in terms of a combination of (a) Coulombic effects, which give the ionic-strength dependence and cause some of the ‘smearing’ of the titration curves, and (b) site heterogeneity. The exact contributions of the two factors are difficult to extract from the experimental data.