THE DYNAMIC INTER-RELATIONSHIP BETWEEN

THE DYNAMIC INTER-RELATIONSHIP BETWEEN ACID RAIN AND EUTROPHICATION IN THE SOIL DOMAIN T. OXLEY∗ and P. M. ALLEN International Ecotechnology Research Centre, Cranfield University, Bedford, MK43 0AL, England (∗ author for correspondence, e-mail: [email protected])

(Received 5 September 1997; accepted 17 February 1999)

Abstract. This work recognises the widespread deterioration of the natural environment, and the continual emergence of sudden environmental changes resulting from complex non-linear interactions of apparently disparate phenomena. Incorporating contemporary views of complexity and evolution, this paper presents a dynamic complex systems model which displays the discontinuous and non-linear characteristics which emerge from the inter-relationships of two such phenomena – acid rain and eutrophication – within the soil domain. A description is given of the chemical and hydrological sub-modules which provide the basis of this spatio-temporal model, and the interrelationships between the buffering of acid and the adsorption of phosphates by the soil. Various representations of soil acidification, phosphate adsorption and hydrology drawn from existing models and literature are used to address both the chemical interactions and the spatial hydrological flows within the context of a river catchment. The resulting model can be easily applied to any chosen catchment due to the minimal data requirements and its generic representation. It may be utilised to describe non-point sources of phosphates as part of assessments of potential eutrophication, overcoming some of the limitations found in existing models, and provides the basis for the examination of Chemical Time Bomb (CTB) phenomena whereby the soil changes from being a phosphate sink to being a phosphate source. Keywords: atmospheric acid deposition, chemical time bombs, complex systems modelling, eutrophication, phosphate adsorption

1. Introduction This paper is based upon research which recognises the widespread deterioration of the natural environment and the continual emergence of sudden environmental changes resulting from complex interactions of apparently disparate phenomena. The work reflects contemporary views of complexity and evolution (Allen, 1988, 1990), and presents a dynamic complex systems model which displays emergent spatial and temporal characteristics which can be directly related to the modelled phenomena. Contamination and accumulation of chemicals in the environment have occurred partly due to the ability of the natural environment (particularly soils and sediments) to adsorb and immobilise chemicals in what are termed as chemical sinks and which are traditionally perceived as limitless, and partly due to the shortterm socio-economic benefits of industrial developments prevailing over long-term Water, Air, and Soil Pollution 117: 371–400, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.

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environmental disbenefits; contemporary economic analyses tend to overlook the problems caused by the legacy of chemicals accumulated in the environment over time (Bonazountas, 1987; Stigliani, 1988, 1991). It is because of the limited capacity of these sinks that Chemical Time Bomb (CTB) phenomena emerge; once a sink reaches its capacity, or the capacity is reduced through other influences (eg. acidification), a sudden release of previously inert chemicals may occur. This suggests how a change in the environmental conditions may suddenly transform a sink into a chemical source. Whilst considering such Chemical Time-Bomb phenomena and discontinuous and non-linear environmental change (Stigliani, 1988, 1991; Stigliani et al., 1991, 1993a; Hesterberg et al., 1992; Ter Meulen et al., 1992; Salomons and Stigliani, 1995), a relationship between acid rain and eutrophication was perceived – specifically through soil acidification and soil phosphate retention – whereby the effects of acidification upon the soil may promote discontinuous changes in nonpoint sources of nutrients affecting eutrophic phenomena (Oxley, 1994). Owing to the disparate spatial and temporal scales involved, a complex systems model was developed to confirm the nature of this relationship – presented in this paper – from which a complex and dynamic indicator of its characteristic discontinuity emerged (Oxley, 2000, this issue). The model was applied to the Rutland Water catchment where an eutrophication problem has already been highlighted (Ball, 1990; Trow, 1990), with a spatial examination of the qualitative nature of this discontinuity within the catchment, particularly noting the paradoxical effects of liming when agricultural land changes towards a natural ecosystem (Oxley, 2000, this issue). The model was developed in order to observe the characteristic complexities of this discontinuous relationship, with inevitable simplifications to some processes, and thus great care should be taken if it is to be used as a tool for predicting environmental change. This paper describes the chemical and hydrological sub-modules at the heart of this spatio-temporal complex systems model. These sub-modules themselves use various simplified representations of soil acidification, phosphate adsorption and hydrology drawn from existing models and the literature summarised below. These representations have necessarily been simplified specifically to facilitate the linking of these disparate phenomena. This process of model development reflects the inevitable trade-offs between reality, generality and precision which will always occur (Levins, 1966). Thus, through simplification of the processes of acid buffering and phosphate adsorption, the conceptual linkages can be formalised, with the consequence in the model presented here that, for example, the chemistry of adsorption is based upon Ca2+ acting as the major base cation in the process, omitting other base cations such as Na+ , Mg2+ and K + ; given the simplifications required to link the disparate phenomena in this CTB, it is assumed that these cations would have minimal influence on the emergent dynamics of the model (Ernami, 1996). Likewise, aluminium (Al3+ ) is assumed to be the major acid cation involved, omitting others such as iron (Fe); a consequence of the simplifications

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made in the model, the need for cations which are directly involved in both the adsorption and buffering processes, and the specific non-linearity being observed (Oxley, 2000, this issue). Similarly, the model concentrates upon phosphates only as the significant nutrient involved, and assumes that acidification is predominately through sulphate deposition, ignoring the effects of nitrate fertilisers and ammonia. In the case of nitrates, it is assumed that the acidifying effects of ammonia based fertilisers is compensated by nitrate based fertilisers, and that production of acid through nitrification is compensated by denitrification and mineralization. Although this assumption is theoretically sound, it does not entirely account for the effects of residual nitrates in the soil due to the high level of fertiliser applications; acidification due to ammonia is then likely (and may be compensated for by liming), but since the lifetime of ammonia in the soil is very short the impact of ammonia acidification may be ignored. Furthermore, the model is addressing a CTB phenomenon involving nutrient adsorption in the soil, and since nitrates are not strongly adsorbed in the soil they play little or no part in this CTB. A number of acidification models were examined, of which two were immediately discounted. At the time of the original work the MAGIC model (Cosby et al., 1985), used by Whitehead (1990), was limited to a maximum of two soil types, precluding its use in catchments containing a diversity of soils. Since that time, however, the MAGIC model has been further developed, as an aggregated catchment scale model of acidification addressing volume-weighted annual average concentrations of all major ions, and successfully applied to sites in Norway (Wright et al., 1990; Cosby et al., 1995). The SESOIL model (Bonazountas and Wagner, 1984) overcame the limitation of soil types and was able to address the fate of both acid and phosphate, but it could not address two ‘pollutants’ simultaneously, nor their interactions which are central to the acid/phosphate relationship, and the ILWAS model, compared with MAGIC by Rose and others (1991), includes both acidification and phosphorus, but is limited to natural ecosystems only. Another model, RAINS (Regional Acidification INformation System) (Alcamo et al., 1990), was limited to the dynamics of acid emissions, transport, deposition and subsequent soil, water or forest acidification, but it provided definitions of soil acidification which were not dependent upon soil types. The phosphate adsorption models examined (Barrow, 1978; Enfield et al., 1976; Jones et al., 1984) were all based upon variations of a limited number of adsorption ‘isotherms’. They invariably required large volumes of data, were focused at the micro level, and ignored the spatial context and the possibility of changing environmental conditions such as soil pH. Such descriptions address the complexity of phosphate compounds and the diversity of compounds’ stability and reaction rates (Enfield et al., 1976), the specific dynamics of phosphate adsorption in calcareous or acidic soils (Barrow, 1980a, b), the influence of microbial activity and organic matter levels upon adsorption (Cosgrove, 1977), and the effects of temperature,

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plant uptake and diffusion of phosphates through the soil solution (Barrow, 1974; Barrow and Shaw, 1975a, b). The soil hydrology models examined (Mein and Larsen, 1971; Chen and Waganet, 1992; Workman and Skaggs, 1990) were found to be unsuitable for the representation of flows across a catchment, operating at the micro level and being excessively data heavy. However, the latter two did recognise that the soil is not an homogenous medium, addressing macropores and preferential flows (in the PREFLO model), respectively. The MAGIC model, as presented by Whitehead (1990) – aside from being antithetical to notions of complexity – was location specific, addressed flows of nitrates as opposed to phosphates, and was limited to two soil types. Billen’s (1992) PHISON model, although generic in form and employing the concept of stream orders, addresses the adsorption of phosphate in the context of eutrophication, but only in the aquatic continuum. The hydrological processes as implemented in this work are therefore based upon the Hydrology Of Soil Types (HOST) classification system developed by SSLRC and the Institute of Hydrology (Boorman et al., 1995); being based upon the dominant flow pathways through soils, use of the HOST classification system overcomes the limitations of the micro-level soil hydrology models (Mein and Larsen, 1971; Chen and Waganet, 1992) and accounts for the effects of soil flows omitted from the catchment models. Finally, the structure of the model is summarised schematically in Figure 1. The Chemical Sub-Module addresses the chemical phenomena being modelled, maintains a set of state variables defining the soil composition, and operates on a daily basis with a timestep, dt, of 0.1. The chemical phenomena modelled are acid buffering and phosphate adsorption, and the state variables are calcium (Ca), aluminium (Al), phosphorus (P), acid (H) and the soil pH. The Hydrological SubModule, which provides the spatial context for the chemical sub-model, addresses the soil hydrological flows and maintains the current volumes of soil water and surface water, also operating on a daily basis.

2. Model Conceptualisation and Specification Eutrophication is a naturally occurring phenomenon which, under ‘normal’ conditions, is controlled by one or more limiting nutrients, and it is when such limiting nutrients, particularly phosphates, become abundant that eutrophic algal growth represents a potential problem, such as in the case of Rutland Water (Trow, 1990; Ball, 1990). Sources of Acid Rain are many and diverse, but the major sources can be identified as from fossil fuel combustion arising from power stations (Gillham et al., 1992). All such airborne acidic emissions will be dispersed spatially through atmospheric transportation, and, depending upon the climatic conditions, will be


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Figure 1. Schematic representation of the hierarchical structure of the model.

deposited over a wide area (Alcamo et al., 1990) with effects as diverse as building corrosion, watershed acidification, tree loss and soil acidification. The common element linking these two phenomena involves the effect of acidification on the ability of the soil to act as a source or a sink for phosphates determining, in part, the rate of release of agricultural phosphates into the river systems. Thus, we are interested in the effects upon and the movement through the soil of both acid and phosphates. What remains unclear are the interdependencies between soil acidification and phosphate adsorption. With a given acid loading, soil has been found to buffer acidity depending upon the soil composition and soil pH (Ulrich, 1983; Alcamo et al., 1990; Kaupi et al., 1990); this buffering has a non-linear effect upon the soil pH as a result of changes to the soil composition

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Figure 2. Acid buffering and phosphate adsorption feedbacks.

creating a feedback which may represent an important influence upon the qualitative characteristics of the soil. Conceptually, this effect of acid buffering by the soil is presented in Figure 2a, highlighting the feedback. The processes of phosphate adsorption are highly complex, resulting in diverse rates and permanence of adsorption involving the emergence of many similar and dissimilar phosphate compounds of varying chemical stability within the soil (Cosgrove, 1977; Barrow, 1978; Jones et al., 1984). Furthermore, these processes represent an inherent part of a specific Chemical Time-Bomb (CTB) phenomenon, triggered upon reaching the adsorptive capacity of the soil (Breeuwsma and Reijerink, 1992). The CTB characteristics suggest that these adsorptive pro-


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cesses are highly significant regarding future unexpected eutrophic releases of phosphate. Adsorption is dependent upon redox potential and the soil composition, with rates varying significantly between calcareous and acidic, or sandy, soils (Barrow, 1980a, b), and also displays feedback characteristics involving soil pH which are not addressed by the studies cited above. The feedbacks associated with adsorption are presented in Figure 2b. Thus, it is essential to address this influence of changing soil pH since it represents the key linkage between the two phenomena being examined. Stevenson (1986) identifies the varying affinity for adsorption depending upon the soil pH, and thus provides a basis upon which these conflicting processes of acid buffering and phosphate adsorption within the soil domain may be related. A potential conflict between these processes is apparent through their dependency and influence upon the soil composition and pH, suggesting a perturbatory and discontinuous influence of acid buffering upon the capacity of the soil to retain phosphates. The chemical sub-module addresses the key processes of Acid Buffering and Phosphate Adsorption, and the key variables as Soil Composition (discussed below) and Soil pH, with acid and phosphate loading representing external influences. Spatially, this sub-module must be located within the perspective of a catchment module within which eutrophic phenomena may be observable and which is naturally bounded. Since acidic emissions are subject to atmospheric transportation over a wider area, this model can only address acid rain as an external perturbatory influence upon the catchment. This also allows additional acidifying influences to be incorporated into this external influence, whether the source is atmospheric or terrestrial. Since the focus of the model involves the capacity of the soil to retain phosphates, once phosphates have been lost from the soil and entered the river system, they are assumed to have no further influence upon the capacity. The hydrological dynamics of the catchment are implemented in a hydrological sub-module controlled by the catchment module, recognising that the appropriate spatial scale for meaningful observation of accumulations of phosphate within the river system may be different to that required for observation of capacity variations within the soil. With the scope of the model spatially bounded by the definition of a catchment, the spatial scale of the individual cells – each containing chemical and hydrological sub-modules – requires definition. The model is based upon an 8 × 8 spatial grid (Oxley, 1994) where spatial demarcation of the cells reflects the availability of spatial data to define the soil composition and soil pH. In the present case the data available for definition of soil composition and pH reflects measurements at 5 km intervals across England and Wales (Loveland, 1990). Thus, each individual cell in the model necessarily reflects an area of 25 km2 . The mechanisms of acid buffering, as defined by Alcamo et al. (1990), represent an abstraction of the actual chemical processes – based upon the cation composition of the soil – which is compatible with the spatial scaling of this model due to the broad spatial perspective required of RAINS. This representation is based en-

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tirely on sulphate based acidification, excluding the effects of nitrates, and provides a non-linear definition of the soil pH as a consequence of acidification. Definition of phosphate adsorption requires additional spatial abstraction since, although many perceptions of this process have been described (Olsen and Watanabe, 1957; Russell and Prescott, 1916; Hayward and Trapnell, 1964; Barrow, 1978; Jones et al., 1984), they tend to describe the changes at the ‘micro’ scale, incompatible spatio-temporally with the perspective required of this model. The current model employs a variant of the multi-term Langmuir ‘isotherm’ making it possible to link the processes of acidification and adsorption so that the dynamics of their interaction become observable from a catchment perspective with minimal data requirements. This will result in the omission of some of these micro-level influences to the benefit of a representation which can accommodate the key inter-relationships with acid buffering. However, such simplifications are essential for the purposes of integrating disparate processes, at least until the connections have been made at which time additional complexity can be incorporated (Levins, 1966). The hydrological processes are primarily related to the spatial flows through the catchment; flow directions being controlled at the catchment level. These hydrological representations define the boundary conditions relating to the spatial flow of acid and phosphates between individual cells. The HOST classification provides the basis for definition of these hydrological dynamics (Boorman et al., 1995). Since the fundamental difference in this model to existing representations of phosphate adsorption is the changing pH resulting from acidification, it is necessary to define the soil composition to reflect the definition of acidification. Thus, Soil Composition, for acidification purposes, may be represented by Base Cations and Acid Cations, with adsorption reflecting a similar cation split, where base and acid cations are represented by Calcium and Aluminium respectively. Soil pH is determined by the base/acid cation levels and the soil pH itself in the fashion employed by RAINS (Alcamo et al., 1990). Variables in the hydrological submodule will be required to define the volumes of water maintained both on the surface and within the soil, reflecting saturation levels for each of the individual cells. Finally, it is important to highlight the assumptions and omissions inherent in the model. The major assumptions may be summarised as:

– Only acid buffering and phosphate adsorption have any influence upon the soil composition and soil pH. – The soil is composed of only base and acid cation reserves (calcium and aluminium, respectively). – The soil pH is determined from soil composition and the soil pH itself (Ulrich, 1983; Alcamo et al., 1990; Kaupi et al., 1990).


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– The hydrological characteristics of the soil are adequately represented by the HOST classification system and related Standard Percentage Runoff and Volumetric Moisture Content (Boorman et al., 1995). – Acid rain and phosphate loadings may be treated as external influences, thus facilitating modification of the acid load due to other atmospheric or terrestrial acidifying influences. – A 5 km spatial resolution is adequate for observation of the emergent characteristics. And the major omissions are: – The effects of alternative base cation sites, other than Ca2+ , for buffering and adsorption (Na+ , Mg2+ , K + ). – The effects of alternative acid cation sites, other than Al3+ , such as Fe2+ . – The variability and complexity of phosphate compounds and their solubility or permanence, such as adsorption with iron hydroxides, for the purposes of simplicity (Levins, 1966). – The effects of natural acidification (in sandy soils, for example) which can be addressed by modifications to the extraneous acid loading applied to the model. – The influence of organic matter and microbial activity on the processes of buffering and adsorption, and of these and weathering on the soil composition. – The effects of groundwater flows. – The effects of temperature.

3. Chemical Sub-Module A schematic representation of the inter-relationships of the processes of Acid Buffering and Phosphate Adsorption is provided in Figure 3. A distinction is made between cation reserves which are free of phosphates and thus available for subsequent adsorption of phosphates (Ca, Al) and the reserves accounting for previously adsorbed phosphates (QCa , QAl ). The inputs of acid rain, phosphates and lime increase the pools of acid (H), phosphate (P) and ‘free’ calcium (Ca), respectively. The variables define the current state of the sub-module and are necessary inputs to the buffering and adsorption processes. The pools of acid and phosphate represent the loadings applied to the buffering and adsorption processes, respectively. The pools of ‘free’ calcium and aluminium define the remaining adsorptive capacity by base (RCa ) and acid (RAl ) reserves, respectively. The processes of acid buffering and phosphate adsorption directly affect the pools of acid, phosphate, calcium and aluminium, but only indirectly affect the soil pH. Acid buffering decreases the pool of acid and the pools of calcium and aluminium. Phosphate adsorption decreases the pool of

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Figure 3. Acid buffering and phosphate adsorption interactions.

phosphate, but it also has the effect of reducing the pools of ‘free’ cations (Ca, Al) and increasing proportionately the pools of adsorbed phosphates (QCa , QAl ). The CTB phenomenon, whereby sudden release of phosphates may occur due to changing conditions in the soil, becomes evident when the ‘free’ base cation reserves (Ca) are depleted and acid buffering is still predominately by base cations; since there are no remaining reserves of ‘free’ base cations, further acid buffering by base cations leads to the release of the phosphates associated with these sites (Ghani and Aleem, 1943). Acid buffering now reduces the remaining base cation pool, QCa , which increases the dissolved phosphate pool proportionately. Thus, if flushing of phosphate from the soil is to be avoided when the ‘free’ calcium reserves are depleted, the rate of adsorption of phosphates at acid cation (aluminium) sites must be great enough to counteract the release of phosphates due to acid buffering by base cations (calcium). Spatially, all quantities are normalised to reflect quantities per hectare, enabling easy use of input data such as phosphorus (approx. 31 kg ha−1 yr−1 in fertiliser (CAS, 1978; ADAS, 1982; MAFF, 1983; Archer, 1988)), and correlation with generally derived acid buffering capacities of soils (Ulrich, 1983). A single cell will represent 5 km × 5 km thus correlating with the resolution of the National Soil Inventory (NSI) data and HOST classification data obtained from SSLRC.


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Vertical demarcation of the model is implemented to reflect a soil depth of 10 cm; the depth of samples taken for the NSI data. Vertical flows which exceed this soil depth will be categorised into leaching flows. It is accepted that this soil depth may be unrealistic, but, since the NSI data are point measurements taken to represent an area of 25 km2 and no data are available to define different soil profiles, the degree of aggregation reflected in the available data would mean that the effect of increasing the soil depth in this model would be purely quantitative. Using spatial dimensions of a hectare and soil depth of 10 cm, it is possible to convert the various percentages, or mg g−1 (soil), of soil constituents, as specified by the NSI data, into equivalent units of kmoles ha−1 . It has also been helpful to further modify these figures to reflect kEq(H+ ) ha−1 to avoid the potential confusion of dealing with varying ionic charges (Al3+ , Ca2+ , H+ , PO3− 4 ). Finally, change is addressed on a daily basis, thus reflecting the definition of Standard Percentage Runoff (SPR), the daily rainfall data, and the phosphate adsorption rates identified by Olsen and Watanabe (1957). The acid buffering rates identified by RAINS reflect a yearly rate, so these have been modified to provide an average (continuous) daily rate. With processes normalised to daily rates, the model utilises a further timestep, dt, of 0.1; the model thus implements partial changes to key state variables 10 times a day. The complexity of the processes of phosphate adsorption has resulted in a number of empirical and mechanistic equations to represent adsorption depending upon the precision or generality required (Enfield et al., 1976; Barrow, 1978). These each attempt to account for influences on adsorption such as increases in negative charges at or near adsorption sites due to adsorption, concentrations of phosphate in the soil solution, maximum adsorptive capacity and various affinity constants addressing the relative rates of adsorption and desorption. It was concluded that a multiple surface Langmuir form of adsorption equation would be the most suitable for use in the current model since it facilitates integration with the processes of acid buffering through the common elements of calcium, aluminium and soil pH. Accounting for two discrete surfaces, the generic adsorption equation may be written thus: X = A1 Xm1 C/(1 + A1 C) + A2 Xm2 C/(1 + A2 C)

(1)

where A1 and A2 are affinity terms describing the relative rates of adsorption and desorption by the two surfaces, and Xm1 and Xm2 are the adsorption maxima. Using this 2-surface form of the Langmuir equation, the model deals with the changing affinity for adsorption by treating the ‘surfaces’ as distinct and addressing adsorption by Base Cation (Ca) sites separately to Acid Cation (Al) sites. Thus

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Figure 4. Adsorption affinity and cation dissolution curves.

Xm1 and Xm2 will change with the base and acid cation composition of the soil at any one time. The affinity terms, A1 and A2 , will be dependent upon the pH of the soil at any one time, thus addressing the solubility of calcium and aluminium phosphates at a given pH and consequently the ability to adsorb phosphate at these sites. Additional terms could be incorporated into this representation of adsorption (for example, addressing the effects of iron (Fe)), but only a single acid and a single base cation has been included for the simplicity of representation necessary to integrate the processes (Levins, 1966) and in order to observe specific non-linearities in their interactions (Oxley, 2000, this issue).


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The affinity terms controlling adsorption at either base or acid cation sites will thus reflect the changing total capacity for adsorption due to both changes in pH (affected by additional acid loading) and through previous adsorption of phosphates. The affinity terms, A1 and A2 , are derived (see below) to reflect the relative ability of the soil to adsorb phosphates as identified by Stevenson (1986) where adsorption tends to be at a minimum at around pH 6.5, and increases both above pH 6.5, due to base cation reserves, and below, due to acid cation reserves. Graphical representation of these adsorption affinities is reproduced in Figure 4a. To incorporate these varying adsorption affinities, use is made of cosine functions – see θ and φ, below – to describe the curves with reference to the soil pH. Thus, using the 2-Surface Langmuir equation as a basis we have: Total P adsorbed (Adstot ) = adsorption by Ca (AdsCa ) + adsorption by Al (AdsAl )

(2)

where AdsCa = ACa MCa C/(1 + ACa C) and similarly AdsAl = AAl MAl C/(1 + AAl C) with the remaining capacities (at a given pH) for adsorption at base and acid cation sites given by: RCa = β (1 − Cos θ)

(3)

and RAl = α (1 − Cos φ) where

α and β are proportional to Al and Ca, respectively. The influences of the components of these adsorption equations are presented graphically in Figure 5 reflecting the affinity and capacity functions derived from Stevenson (1986). The surface is unrealistic in that adsorption will reduce the cation reserves, and thus dynamically move the surface. However, it provides a

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Figure 5. Adsorption affinity surface.

temporally static representation of the qualitative characteristics of the adsorption equations. Similar relationships with pH and phosphate concentration were found for the capacity equations (Oxley, 1994). The processes of acid buffering in the soil have been derived from the RAINS model developed by IIASA (Alcamo et al., 1990). The soil acidification processes implemented in the RAINS model are based upon the two fundamental concepts of Acid Loading and Acid Buffering, where the acid loading is driven by the wet and dry deposition rates of sulphur. Acid buffering is dependent upon the soil type and the soil pH, and determines the effect of additional acid loading on the soil with regards a change in soil pH. To estimate the level of acid buffering, it is first necessary to determine the rate of dissolution of base and acid cations (Ca2+ and Al3+ , respectively) so that the buffer capacity can be determined. The dissolution rates will reflect a relationship


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with the soil pH, and the total buffer capacity will reflect both the dissolution rates and the soil composition with respect to calcium and aluminium (Dalal, 1975; Manahan, 1991) (see Figure 4). The rate of dissolution of calcium is related to the level of CO2 present in the soil solution, and follows the reaction: CaCO3 (s) + CO2 (aq) + H2 O ↔ Ca2+ + 2HCO− 3 2− The fraction of carbon dioxide species present in solution (CO2 , HCO− 3 , and CO3 ) 2+ changes with changing pH, and thus the dissolution rate of Ca can be derived as shown in Figure 4b. Similarly, the dissolution rate of Al3+ can be derived (Figure 4c) from the fraction of aluminium species present in solution due to hydrolysis in relation to the pH. Thus, the Buffer Rates with respect to calcium (BRCa ) and aluminium (BRAl) can be given by:

BRCa = BCCa Cadiss kt

(4)

and BRAl = BCAl Aldiss kt where BCCa = 2 kCa (Ca + QCa ) BCAl = 3 kAl (Al + QAl ) kt , kAl and kCa are constants. To calculate the level of acid buffering and to determine the change in soil pH in the Cation Exchange, two further relationships are required – the total Cation Exchange Capacity (CEC) and the Base Saturation (βsat ). These can be represented by: CECt = BRCa + BRAl

(5)

and βsat = BRCa /CECt .

(6)

The Cation Exchange Capacity changes over time in response to the processes of adsorption and buffering implemented in the model. Thus, both CEC and BR are implemented in units of kEq ha−1 with the temporal dimensions implicit. The predominate buffering mechanisms depend upon the soil pH and the base saturation level, which together identify the appropriate Buffer Range in the following way

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Calcium Carbonate Buffer Range – pH>6.2 and βsat >85% Cation Exchange Buffer Range – pH>4.2 and βsat >5% Aluminium Buffer Range – pH