Air pollution

First Order Acidity Balance Model (FAB)

With critical loads for sulphur (S) it was assumed that the SO42- anion is mobile in catchments, and therefore S deposition would quickly reach steady-state with leaching into surface waters (Seip 1980), taking anything from weeks to decades in soils with the greatest adsorption capacity (Reuss & Johnson 1986). In theory, non-marine SO42- in lake or stream water could be linked directly to S deposition. For S deposition, therefore, the response of SO42- leaching to surface waters is relatively fast. This does not mean that damage occurs immediately, because cation exchange processes in soils generally provide a degree of buffering against surface water acidification.

If we consider only sulphur-based acid deposition, there are two responses as a steady-state between deposition and leaching is achieved:

  • SO42- may be partially adsorbed on to the soil complex, but this is usually considered a small and short-term response, so that SO42- leaching flux quickly reaches the value of the deposition flux,
  • Exchange of protons from acid deposition with base cations from the soil exchange complex leads to a reduction in the leaching flux of protons, but an increase in the leaching flux of base cations. This process occurs over a finite timescale which is largely independent of the steady-state between S inputs and outputs.

Schematic representation of the FAB model mass balance for nitrogen For nitrogen (N), as a major nutrient, the situation is much more complex, since deposition inputs enter the terrestrial N cycle. Terrestrial processes can remove or immobilise N deposition over very long timescales or even permanently. For example, denitrification returns N to the atmosphere as N2O, NO or N2 and permanently neutralises the associated acid inputs.

Catchment input-output budgets generally indicate that only a small proportion of N deposition is leached into surface waters with its associated protons (e.g. Curtis et al. 1998). The SSWC model was adapted to take account of NO3- leaching by using measured NO3-, converted into a flux using runoff, as a measure of the contribution of N deposition to critical load exceedance (Kämäri et al. 1992). This method makes no reference to actual N deposition, and hence cannot take account of possible changes in NO3- leaching under a different N deposition scenario.

A steady-state critical loads model for total acidity that can be used for scenario testing therefore requires the quantification of N retention processes over the very long term. If the sustainable (as opposed to short-term) rates of N retention or removal can be quantified, then the critical load can be determined.

General description of the FAB model

With the FAB model, a charge balance incorporating the major processes affecting the acid anion budget for the lake and catchment is invoked (Posch et al. 1997):

Ndep + Sdep = { f Nupt + (1-r) . (Nimm + Nden) + r(Nret + Sret) } + ANleach

All units are in equivalents (moles of charge) per unit area and time (See Notes). Braces enclose "internal" catchment processes, i.e. those terrestrial and in-lake processes which operate on acid anion inputs to control the net export in catchment runoff.

The charge balance equates the deposition inputs of acid anoins with the sum of processes that control their long-term storage, removal and leaching exports. Several major assumptions are made in this formulation:

  • Long-term sinks of S in the terrestrial part of the catchment (soils and vegetation) are negligible,
  • There are no significant N inputs from sources other than atmospheric deposition, i.e. no fertiliser application in the catchment,
  • NH4+ leaching is negligible because any inputs are either taken up by the biota, adsorbed on to soils, or nitrified to NO3-.

The FAB model mass balance for N is shown schematically in Figure 1.


Definitions used in the formulae
  • Ndep = total N deposition
  • Sdep = total S deposition
  • Nupt = net growth uptake of N by forest vegetation (removed by harvesting)
  • Nimm = long-term immobilisation of N in catchment soils
  • Nden = N lost through denitrification in catchment soils
  • Nret = in-lake retention of N
  • Sret = in-lake retention of S
  • ANleach = acid anion leaching from the catchment
  • f = the fraction of forested land in the catchment
  • r = lake:catchment area ratio


  • Curtis, C.J., Allott, T.E.H., Reynolds, B. and Harriman, R. (1988) The prediction of nitrate leaching with the first-order acidity balance (FAB) model for upland catchments in Great Britain. Water, Air and Soil Pollution 105: 205-215.
  • Kämäri, J., Jeffries, D.S., Hessen, D.O., Henriksen, A., Posch, M. and Forsius, M. (1997) Nitrogen critical loads and their exceedance for surface waters. In: P. Grennfelt and E. Thörnelöf (Eds.), Critical Loads for Nitrogen - a workshop report. Nord 1992:41, Nordic Council of Ministers, Copenhagen, pp 163-200.
  • Reuss, J.O. and Johnson, D.W. (1986) Acid deposition and the acidification of soils and waters. Ecological Studies 59, Springer-Verlag, New York, 119pp.
  • Seip, H.M. (1980) Acidification of freshwater - sources and mechanisms. In D. Drabløs and A. Tollan (Eds.) Ecological impact of acid precipitation. Proceedings of an international conference, Sandefjord, Norway, March 11-14, 1980. SNSF Project, Oslo, Norway, pp. 358-365.