An evaluation of critical loads of soil acidity in areas of high sea salt deposition

An evaluation of critical loads of soil acidity in areas of high sea salt deposition

The Science of the Total Environment 253 Ž2000. 169]176 An evaluation of critical loads of soil acidity in areas of high sea salt deposition B. Reyno...

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The Science of the Total Environment 253 Ž2000. 169]176

An evaluation of critical loads of soil acidity in areas of high sea salt deposition B. ReynoldsU Institute of Terrestrial Ecology, Bangor Research Unit, UWB, Deiniol Road, Bangor, Gwynedd LL57 2UP, Wales, UK Received 15 June 1999; accepted 1 February 2000

Abstract The empirical and mass balance approaches to setting critical loads of acidity for mineral soils have been evaluated using field data from forest sites in Wales. Using the Simple Mass Balance Equation ŽSMBE. with Sitka spruce as the biological target, critical loads ranged between 2.3 and 9.8 keq Hq hay1 yeary1 compared to mapped empirical critical loads which ranged between 0.2 and 0.5 keq Hq hay1 yeary1 . At all sites the empirical critical load was exceeded with respect to deposited sulfur acidity. There were no exceeded sites for the SMBE critical loads. The big differences between the two methods arise from the large ANC leaching term in the SMBE model which is determined by the relatively low ŽCa q Mgq K.rAl crit ratio for Sitka spruce, compared to other conifers, and the influence of the large deposition of sea salt base cations. The low value of the ŽCa q Mgq K.rAl crit ratio for Sitka spruce implies that it is tolerant of very acidic soil conditions, however, the ratio is based on the results of only one solution culture study and may thus be uncertain under field conditions. Large sea salt base cation deposition directly influences SMBE critical loads because the predicted soil water base cation concentrations permit large concentrations of hydrogen ions and aluminium Žlow ANC values. before the critical chemical limit is transgressed. Where weathering rates are low, critical ANC leaching ŽANC lecrit . becomes the dominant term in the SMBE, with the counter intuitive result that the critical load becomes a linear function of sea salt base cation deposition. Thus the current formulation of the SMBE may not be appropriate for low weathering rate areas receiving large amounts of sea salt base cation deposition. Q 2000 Elsevier Science B.V. All rights reserved. Keywords: Acidification; Critical loads; Soils; Acid deposition

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Tel.: q44-1248-370045; fax: q44-1248-355365. E-mail address: [email protected] ŽB. Reynolds. 0048-9697r00r$ - see front matter Q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 8 - 9 6 9 7 Ž 0 0 . 0 0 4 3 5 - 6

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1. Introduction Two approaches have been used to set critical loads of acidity for mineral soils within the UK ŽDOE, 1994.. The simplest method effectively sets the critical load so that inputs of acidity from atmospheric deposition do not exceed the annual production of base cations by weathering Žthe so called empirical or level zero approach; Hornung et al., 1995.. The second Žor level 1. approach uses a simple mass balance equation of sources and sinks of acid neutralising capacity ŽANC. within the ecosystem to set the critical load with respect to a critical chemical limit within the rooting zone for a chosen biological indicator, generally fine roots ŽSverdrup and de Vries, 1994.. Whilst the two approaches are complimentary, they generally yield different critical load values. In particular, there has been debate concerning the simple mass balance approach as to the appropriate quantification of atmospheric base cation inputs and the role of sea salts Žsee, e.g. Sverdrup et al., 1995.. The purpose of this paper is to explore this issue with respect to the application of the critical loads approach to mineral soils in the UK by discussing the underlying principles of the two methods in relation to field data from Welsh sites. The detailed methodology of the approaches will not be discussed as this has been published extensively elsewhere Žsee Sverdrup and de Vries, 1994; Hornung et al., 1995; Løkke et al., 1996.. Critical loads for peat soils in the UK are addressed separately by Smith et al. Ž1993..

2. Background 2.1. The empirical approach The empirical soil acidification critical load map for the UK was based on principles and proposals developed at two workshops held in 1986 and 1988 ŽNilsson, 1986; Nilsson and Grennfelt, 1988.. Effectively, the critical load was set to prevent chemical changes in the soil resulting from acid deposition which might lead to long-term damage to the soil]plant system. This was interpreted as preventing atmospheric acid inputs to the soil

from exceeding internal alkalinity production which in turn was equated with the production of base cations by weathering. The main factor determining the rate of weathering in soils is the mineralogy. At the 1988 workshop, soil materials were divided into five classes on the basis of the dominant weatherable minerals ŽNilsson and Grennfelt, 1988.. Critical loads were then assigned to these classes according to the amount of acidity which would be neutralised by the weathering release of base cations. Modifying factors were applied to the critical load derived for a given soil to allow for the effects of soil texture, depth, local topography, rainfall etc. For application in the UK, the original classification was further modified to include a range of secondary minerals ŽHornung et al., 1995.. 2.2. The Simple Mass Balance Equation The mass balance approach used in the UK and most widely applied in Europe ŽHall et al., submitted. is that developed by Sverdrup and de Vries Ž1994. and utilises the Simple Mass Balance Equation ŽSMBE.. The full derivation and final form of the equation is given by a number of authors ŽSverdrup and de Vries, 1994; Løkke et al., 1996; Werner and Spranger, 1996. and will not be repeated here. Rather, this discussion will be confined to the implications of its use for mapping critical loads in areas receiving large atmospheric inputs of sea salts. The steady-state critical load of acidity for terrestrial systems is generally set with respect to a critical value of the Acid Neutralisation Capacity of the soil solution ŽwANCx crit ., where wx denote concentrations in meq ly1 . For acid forest soils ŽpH- 5.0., it is assumed that the concentrations of bicarbonate and anions of weak organic acids are negligible so that wANCx crit can be defined in relation to critical concentrations of hydrogen ions ŽwHqx crit . and inorganic aluminium wAlxcrit at which a deleterious effect on the ecosystem is observed. Thus: w ANCx crit s y w Hq x crit y w Alx crit

Ž1.

B. Reynolds r The Science of the Total En¨ ironment 253 (2000) 169]176

In flux terms: ANC lecrit s y Žw Hq x crit q w Alx crit . ? Q

Ž2.

where Q is the precipitation surplus Ži.e. the flux of water leaving the rooting zone. and ANC lecrit is the critical ANC leaching and all fluxes are measured in keq hay1 yeary1 . The critical load of acidity can then be defined by the available sources of alkalinity in the soil]plant system, independent of land use as: CL Ž Ac. s BCwy ANC lecrit

Ž3.

where BCw is the weathering rate of base cations ŽNa q Ca q Mgq K. in the soil. In the SMBE, ANC lecrit and hence the critical load for terrestrial systems links the chemical status of the soil to plant response via a critical base cation to aluminium ratio ŽCa q Mg q KrAl crit . for a chosen biological indicator within the rooting zone. The biological indicator is usually tree roots and sodium is excluded from the ratio because it is believed to offer no ‘protection’ to the plant against the toxic effects of aluminium in the soil solution. Within the model, wAlx crit is determined from the ŽCa q Mgq K.rAl crit ratio and the concentration of available base cations ŽCa q Mgq K. in the soil solution of the rooting zone. The latter is determined by a mass balance of all base cations Žsea salt q excess. from atmospheric deposition and weathering vs. those removed from the site by harvesting of vegetation. Total sea salt q excess base cations are used in the model because vegetation does not discriminate between base cations from different origins Ži.e. sea salt vs. non-sea salt.; they all contribute to the flux in the rooting zone. As will be demonstrated, for sites receiving large quantities of sea salts, this approach has direct consequences for critical loads set using ŽCa q Mgq K.rAl crit ratios, as Ca, Mg and K of sea salt origin will have an important role in determining whether ratios of ŽCa q Mgq K.rAl in the soil solution of the rooting zone fall below critical values. The critical hydrogen ion concentration is calculated using a gibbsite relationship and wAlx crit . To convert to fluxes, the values of wAlx crit and

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wHqx crit are multiplied by the precipitation surplus Ž Q .. The full derivation of the equation used to calculate ANC lecrit is given by Sverdrup and de Vries Ž1994.. In final form: Bc w q Bcd tot y Bc u ANC lecrit s 1.5= R = K gibb

ž

= Q 2r3 q 1.5=

1r3

/

ž Bc q BcdR w

tot y Bc u

Ž4. where: Bc w Bcd tot Q

R K gibb

s weathering of Ca q Mgq K Žkeq hay1 yeary1 .. s total excess q sea salt deposition of Ca q Mgq K Žkeq hay1 yeary1 .. s precipitation surplus, i.e. the volume of water leaving the rooting zone Žm3 hay1 yeary1 .. s ŽCa q Mgq K.rAl crit. s gibbsite equilibrium constant.

For physiological reasons base cations will not be taken up below a certain minimum concentration Žw Bc min x. even though they are present in the rooting zone ŽSverdrup and de Vries, 1994.. Therefore, calculations based on Eq. Ž4. are restricted so that Ži. base cation uptake cannot exceed the quantity of available base cations in the soil solution; and Žii. w Bc min x.Q does not exceed the quantity of base cations available from weathering and deposition. This introduces a mathematical discontinuity into the equation as shown by Thomas and Reynolds Ž1998..

3. Application of the SMBE to sites in Wales Field data for testing the critical loads methods were taken from 20 stands of first rotation Sitka spruce w Picea sitchensis ŽBong.. Carr.x plantation forest ranging in age between 10 and 55 years, growing on ferric stagnopodzol soils ŽAvery, 1980. developed from lower Palaeozoic greywackes; the sites are described in detail by Stevens et al. Ž1994.. At all sites samples of bulk precipitation,

/

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canopy throughfall and soil water from the Bs horizon were collected every 4 weeks between November 1990 and October 1991. Details of the sampling and analytical methods are given in Stevens et al. Ž1994.. The main input variables for the SMBE are: weathering rate, base cation deposition, runoff volume, base cation leaching below the rooting zone, net base cation uptake by the vegetation, a Gibbsite coefficient and a critical base cation to aluminium ratio. These were assigned using a combination of site measurements and information from national data sets. The flux of percolating water for each forest site was calculated from an evaporation model published by Calder Ž1990. in which total evaporation was predicted from the sum of interception loss plus transpiration. The transpiration term was calculated from daily Penman evapotranspiration estimates based on climatological data collected in each forest area ŽEmmett et al., 1993., multiplied by the transpiration fraction Žb; Calder, 1990. and the fraction of time for which the canopy was dry ŽCalder and Newson, 1979.. Interception loss was calculated as the difference between rainfall and throughfall measured at each site. Net base cation uptake for the forest sites was set equal to the net removal in harvested forest products determined from an empirical relationship between published tree biomass nutrient content and yield class ŽITE unpublished.. The minimum base cation leaching concentration Žw Bc min x. was set to the default value of 15 meq ly1 suggested by Sverdrup and de Vries Ž1994.. The base cation weathering rate at each site was

estimated using the empirical critical load for the 1-km square in which each site was located ŽHall et al., 1998.. Atmospheric deposition of base cations Ž Bcd s Ca q Mgq K in keq hay1 yeary1 . was estimated from the annual bulk precipitation inputs measured at each site modified for dry deposition using the method suggested by Sverdrup et al. Ž1990.. This method assumes that foliar leaching of sodium is negligible so that a scaling factor for dry deposition ŽFNa. can be defined as: FNas TFNarWDNa

Ž5.

where TFNa is the throughfall deposition and WDNa is the wet or bulk deposition of sodium. Total base cation inputs wsea salt q excess Žwet q dry.x are therefore: Bcd tot s FNa. Ž WDCaq WDMgq WDK.

Ž6.

A value of y8.5 was used for p K Gibbsite ŽSverdrup and de Vries, 1994; Werner and Spranger, 1996. and the ŽCa q Mgq K.rAl crit was set to 0.4; the published figure for Sitka spruce ŽSverdrup and Warfvinge, 1993..

4. Results and discussion Solving Eqs. Ž3. and Ž4. for each site gives critical loads which vary between a minimum of 2.3 and a maximum of 9.8 keq hay1 yeary1 ŽTable 1.. This compares with empirical critical loads of between 0.2 and 0.5 keq hay1 yeary1 . Ex-

Table 1 Summary of: Ži. empirical and SMBE critical loads for Sitka and Norway spruce; and Žii. ANC lecrit and observed ANC le in the Bs horizon of 20 forest sites in Wales Modelrparameter

Mean

Min keq hay1 yeary1

Max

Empirical CL Empirical ANClecrit SMBE CLŽAc. Sitka spruce SMBE ANClecrit Sitka spruce SMBE CLŽAc. Norway spruce SMBE ANClecrit Norway spruce Observed ANCle

0.41 0.00 5.24 y4.83 2.32 y1.91 y1.87

0.20 0.00 2.33 y9.61 1.11 y3.67 y3.26

0.50 0.00 9.81 y2.13 3.87 y0.91 y0.86

B. Reynolds r The Science of the Total En¨ ironment 253 (2000) 169]176 Table 2 Summary of exceedance values for the empirical and SMBE critical loads calculated for Sitka spruce and Norway spruce a Modelrparameter

Mean keq hay1 yeary1

Min

Max

Empirical CL SMBE CLŽAc. Sitka spruce SMBE CLŽAc. Norway spruce

0.91 y3.87 y0.94

0.36 y8.97 y2.85

1.31 y0.83 0.39

a

Negative values denote non-exceeded sites.

ceedance of the critical load at each site was calculated with respect to deposited sulfur acidity Ž1989]1992 values. for the 20 km squares containing the sites. At all sites the empirical critical load was exceeded but there were no exceeded sites for critical loads calculated using the SMBE ŽTable 2.. The large differences between the critical loads and exceedances calculated using the two methods can be understood in relation to the theory and assumptions underlying the SMBE model. One underlying assumption of the SMBE is that the critical chemical limit wŽCa q Mgq K.rAl crit x must have a value which will result in ANC lecrit remaining negative. A consequence of this and of the definition of the critical load for acidity given in Eq. Ž3., is that the SMBE critical load will always be numerically greater than the weathering rate. The empirical classification for mineral soils allows no ANC leaching and the empirical critical load closely approximates to the weathering rate. By implication therefore, the SMBE critical load will almost always be greater than the empirical critical load. This outcome reflects the conceptual difference between the two approaches and needs to be recognised by those using critical loads information to formulate policy. The empirical approach sets the critical load with reference to selected inherent chemical and physical properties of the soil to prevent chemical changes occurring within the soil in response to pollutant deposition. As such it represents a ‘precautionary approach’. The SMBE adopts an ‘ecosystem approach’ by setting the critical load with respect to a critical chemical limit or threshold for a chosen target organism. Depending on

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the sensitivity of this target organism, chemical changes in the soil andror damage to other ecosystem components may occur before the critical chemical limit is transgressed. This can be illustrated by comparison of currently observed Bs horizon ANC leaching fluxes at the forest sites with predicted values at critical load ŽTable 1. which show that quite severe acidification of the soil solution can be tolerated before the critical load is transgressed. This could have important implications for acidification of freshwaters receiving drainage from these forest sites. The size of the difference between the empirical and SMBE critical load depends on two factors. Firstly, the value of the critical base cation to aluminium ratio for Sitka spruce Ž0.4. is relatively low compared to many tree species used in commercial forestry. Norway spruce, for example, has a value of 1.2 and larch a value of 2.0 ŽSverdrup and Warfvinge, 1993.. The implication is that Sitka spruce can tolerate very acidic, aluminium-rich soil conditions before adverse effects on tree health are observed ŽRyan et al., 1986.. It follows, therefore that the critical load for Sitka spruce will be relatively large. The effect of different tree species on the critical load can be illustrated by solving the SMBE as above, only using a ŽCa q Mgq K.rAl crit value of 1.2 for Norway spruce Žassuming that Bc u for Norway is the same as for Sitka spruce.. The resulting critical loads have a mean value of 2.32 keq hay1 yeary1 and are approximately 50% of those for Sitka spruce ŽTable 1.. Accordingly, the mean permitted ANC leaching at critical load for Norway spruce would be y1.91 keq hay1 yeary1 which is close to observed values, and compares to y4.83 keq hay1 yeary1 for Sitka spruce. For Norway spruce, the SMBE CLŽAc. is exceeded by a small amount Ž0.17 and 0.39 keq hay1 yeary1 . at two sites. The second factor which has a direct bearing on the magnitude of SMBE critical loads is the large flux of sea salt base cations deposited on forests in western Britain. The SMBE relies on a good estimate of the base cation flux through the soil profile in order to calculate wAl 3q x crit in the rooting zone via the specified ŽCa q Mg q K.rAl crit ratio. For the 20 forest sites, the flux

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Table 3 Sea salt base cation fluxes as a proportion of total ŽCa q Mgq K. deposition and the Bs horizon ŽCa q Mgq K. leaching flux a

Total ŽCa q Mgq K. deposition ŽCa q Mgq K. Bs horizon leaching flux a

Sea salt Ca deposition Ž%.

Sea salt Mg deposition Ž%.

Sea salt ŽCa q Mgq K. deposition Ž%.

12

63

81

10

52

66

Values are averages across the 20 forest sites.

Fig. 1. Comparison of Bs horizon base cation fluxes predicted from the SMBE with those calculated from modelled soil water fluxes and observed base cation concentrations.

Fig. 2. Plot of SMBE critical load of acidity against sea salt base cation deposition for 20 forest stands in Wales.

B. Reynolds r The Science of the Total En¨ ironment 253 (2000) 169]176

estimated using the simple mass balance: Bc le s Bcd tot q Bc w y Bc u compares well with an estimate based on the arithmetic mean of observed soil]water base cation concentrations multiplied by the modelled soil]water percolation flux ŽFig. 1. despite the assumptions and errors inherent in both estimates. For forest sites in western Britain, where weathering rates are generally low, atmospheric inputs are sufficient to explain the majority of the flux of base cations through the soil profile ŽStevens et al., 1989.. Assuming that weathering and atmospheric inputs are the main sources of base cations in the Bs horizon for the 20 survey sites, a simple comparison ŽTable 3. shows that the major proportion Žaverage 66%. of this flux is derived from atmospheric deposition of sea salts with an average 52% from the deposition of sea salt magnesium alone. As a consequence of this and of the dependence in the model of ANC lecrit on the soil]water base cation flux via the ŽCa q Mgq K.rAl crit ratio, ANC lecrit becomes the dominant term in Eq. Ž3. defining the critical load for acidity ŽTable 1.. This leads to the apparently counter intuitive result that the critical load becomes a direct, linear function of sea salt base cation deposition ŽFig. 2.. The case of commercially grown Sitka spruce plantations in western Britain might be considered an atypical situation for evaluating the SMBE critical loads model. Sitka spruce is uncommon in the rest of Europe and the combination of a wet maritime climate and low weathering rates is not geographically extensive. However, the example focuses attention on the need to be certain that the correct mechanisms are represented in environmental impact and assessment models and that the models themselves are applied in an appropriate manner. As far as the mechanisms are concerned, a key factor in the prediction of large critical loads for these systems is the use of the ŽCa q Mgq K.rAl crit ratio as the critical chemical limit. The concept of the ŽCa q Mgq K.rAl crit ratio arose from the need to generate a quantitative link between forest vitality and soil acidification and was a development of the CarAl ratio originally proposed by Ulrich Ž1983.. It was formulated by Sverdrup and Warfvinge Ž1993. following a synthesis of a large

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body of mainly laboratory experimental data on plant responses to aluminium, from which they concluded that the most consistent correlations with growth effect parameters were observed using the ŽCa q Mgq K.rAl ratio. Several authors have subsequently been critical of the concept Že.g. Hogberg and Jensen ¨ ´ 1994; Cronan and Grigal, 1995; Løkke et al., 1996; Skeffington, 1999.. The base cation to aluminium ratio for Sitka spruce quoted by Sverdrup and Warfvinge Ž1993. is based on the results of only one solution culture study ŽRyan et al., 1986.. The main effect of aluminium treatment was a reduction in root length which became apparent at total aluminium concentrations exceeding 25 mg ly1 . These concentrations are much higher than generally observed in the field. Total aluminium concentrations in soil waters extracted by suction lysimeters from the Bs horizons of the forest sites in this study ranged between 0.06 and 3.70 mg ly1 with an average of 1.15 mg ly1 although rhizosphere and fine pore water, extracted by centrifugation may have larger concentrations ŽAlexander, 1997.. There is a clear need for more experimental work using realistic aluminium concentrations in soils to confirm experimental results in artificial media.

5. Conclusions Critical loads calculated using the SMBE with Sitka spruce as the biological target will be large compared to both empirical values and SMBE values for other tree species. This arises because the low ŽCa q Mgq K.rAl crit ratio for Sitka spruce implies that it is tolerant of very acid soil conditions. However, this ratio is based on only one solution culture study in which effects were observed at relatively large total aluminium concentrations. Further work is required to confirm these data under field conditions. Large sea salt deposition to areas with low weathering rates in western parts of the UK has a direct influence on SMBE critical loads. The large predicted soil]water base cation concentrations derived from sea salts permit high concentrations of hydrogen ions and aluminium Žlow ANC values. before the critical chemical limit is trans-

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gressed. Whilst this may be acceptable for the target organism, it could have deleterious consequences for other more sensitive ecosystem components and for linked ecosystems such as freshwaters.

Acknowledgements This work was undertaken with funding from NERC-DETR contract PECD 7r12r4 as part of the UK Critical Loads Mapping Programme. References Alexander S. Hydrochemical relationships between soils and streamwater } an experimental investigation. Unpublished Phil M. Thesis. University of London, 1997;172. Avery BW. Soil classification for England and Wales. Soil Survey Technical Monograph No. 14. Soil Survey. Harpenden, 1980. Calder IR. Evaporation in the uplands. Chichester: Wiley, 1990. Calder IR, Newson MD. Land use and upland water resources in Britain. Water Resour Bull 1979;16:1628]1639. Cronan CS, Grigal DF. Use of calciumraluminium ratios as indicators of stress in forest ecosystems. J Environ Qual 1995;24:209]226. DOE. Critical loads of acidity in the United Kingdom. Critical Loads Advisory Group Summary Report. Institute of Terrestrial Ecology. Edinburgh, 1994:61. Emmett BA, Reynolds B, Stevens PA et al. Nitrate leaching from afforested Welsh catchments } interactions between stand age and nitrogen deposition. Ambio 1993;22:386]394. Hall J, Reynolds B, Aherne J, Hornung M. The importance of selecting appropriate criteria for calculating acidity critical loads for terrestrial ecosystems using the Simple Mass Balance equation. Water Air and Soil Pollut, submitted. Hall J, Bull K, Bradley I, et al. Status of UK critical loads and exceedances January 1998. Part 1 } Critical loads and critical loads maps. Report to the Department of the Environment Transport and the Regions. Institute of Terrestrial Ecology Monks Wood, 1998:26. Hogberg P, Jensen ¨ ´ P. Aluminium and uptake of base cations by tree roots: a critique of the model proposed by Sverdrup et al. Water Air Soil Pollut 1994;75:121]125. Hornung M, Bull KR, Cresser M et al. Mapping critical loads for the soils of Great Britain. In: Battarbee RW, editor. Acid rain and its impact the critical loads debate. London: Ensis Publishing, 1995:43]51. Løkke H, Bak J, Falkengren-Grerup U et al. Critical loads of acidic deposition for forest soils: is the current approach

adequate? Ambio 1996;25:510]516. Nilsson J, editor. Critical loads for sulphur and nitrogen. Report 11. Nordic Council of Ministers. Copenhagen, 1986. Nilsson J, Grennfelt P, editors. Critical loads for sulphur and nitrogen. Miljorapport 15. Nordic Council of Ministers. Copenhagen, 1988. Ryan PJ, Gessel SP, Zasoski RJ. Acid tolerance of Pacific Northwest conifers in solution culture. II. Effect of varying aluminium concentration at constant pH. Plant Soil 1986;96:259]272. Skeffington RA. The use of critical loads in environmental policy making: a critical appraisal. Environ Sci Technol June 1st, 1999;245A]252A. Smith CMS, Cresser MS, Mitchell RDJ. Sensitivity to acid deposition of dystrophic peat in Great Britain. Ambio 1993;22:22]26. Stevens PA, Hornung M, Hughes S. Solute concentrations, fluxes and major nutrient cycles in a mature Sitka spruce plantation in Beddgelert forest North Wales. For Ecol Manage 1989;27:1]20. Stevens PA, Norris DA, Sparks TH, Hodgson AL. The impacts of atmospheric N inputs on throughfall, soil and stream water interactions for different aged forest and moorland catchments in Wales. Water Air Soil Pollut 1994;73: 297]317. Sverdrup H, de Vries W. Calculating critical loads for acidity with the simple mass balance method. Water Air Soil Pollut 1994;72:143]162. Sverdrup H, Warfvinge P. The effect of soil acidification on the growth of trees, grass and herbs as expressed by the ŽCa q Mgq K.rAl ratio. Reports in Ecology and Environmental Engineering 2. Department of Chemical Engineering II. Lund University. Sweden, 1993;177. Sverdrup H, de Vries W, Henriksen A. Mapping critical loads. Report 98. Nordic Council of Ministers. Copenhagen, 1990:124. Sverdrup H, de Vries W, Hornung M, et al. Modification of the Simple Mass Balance Equation for calculation of critical loads of acidity. In: Hornung M, Sutton MA, Wilson RB, editors. Mapping and modelling of critical loads for nitrogen: a workshop report. Institute of Terrestrial Ecology. Edinburgh, 1995;87]92. Thomas AH, Reynolds B. Numerical stability considerations in the simple mass balance calculation of critical loads of acidity. Sci Total Environ 1998;217:257]264. Ulrich B. Interaction of forest canopies with atmospheric constituents SO 2 alkali and earth alkali cations and chloride. In: Ulrich B, Pankrath J, editors. Effects of accumulation of air pollutants in forest ecosystems. The Netherlands: Reidel Dordrecht, 1983:33]45. Werner B, Spranger T. Manual on methodologies and criteria for mapping critical levelsrloads and geographical areas where they are exceeded. UNECE Convention on Longrange Transboundary Air Pollution. Federal Environmental Agency. Berlin, 1996:142.