Air pollution

Steady-state Water Chemistry model

The steady-state water chemistry model (SSWC) derived by Henriksen et al (1986) has been adopted by the Nordic countries for national mapping exercises. The method assumes a steady-state situation where outputs balance inputs. This has the advantage of allowing the use of mean chemistry values in the calculations of critical loads. The key to the SSWC model is the calculation of the sustainable supply of ANC (acid neutralising capacity), or the inherent buffering capacity of the system.

Empirical relationships are used to determine the pre-industrial concentration of base cations ( [BC]0) from weathering. [BC]0* is the long-term critical load because the value represents the sole source of base cations over such a time-scale. Base cations produced by weathering are numerically equivalent to the bicarbonate (HCO3) that is produced, and indicates the sustainable rate of production of ANC that defines the critical load.

A pre-selected value for ANC[crit] is used in the critical load calculation. This allows the critical load to be targeted towards sensitive or indicative organisms. In the case of the UK, ANC[crit] = 0 µeq ANC L-1 = ANC[0] and represents the 50% probability of the occurrence of damaged Brown trout (Salmo trutta) populations.

Calculating the critical load

Given this value of ANC[crit], the fresh water critical load is simply the input of acid anions from acid deposition that gives the critical ANC when subtracted from the pre-industrial flux of base cations (Henriksen et al, 1992):

Critical load = ([BC]0* - ANC[crit]) . Q

where Q = runoff from the site, which has the effect of converting the concentrations to fluxes.

[BC]0* is not known and so must be calculated using another equation and the F-factor. The F-factor (F) is an index of the exchangeability of base cations in the soil exchange complex of a catchment, and is used in the following equation:

[BC]0* = [BC]t * - F([AA]t * - [AA]0*)

where [AA]0* is the pre-acidification concentration of non-marine acid anions from weathering and natural sources, [AA]t *, and [BC]t * is the leaching rate of non-marine base cations.

[AA]0* is derived from data from near-pristine lakes. Background levels of NO3- are close to zero in near-pristine Scottish lochs and background SO42- (sulphate) levels are derived from empirical equations using data from near-pristine lakes.

Critical load exceedance is calculated using the following formula, which takes into account both S deposition and NO3- leaching:

Exceedance = ( S*dep + ( [NO3]. Q ) ) - critical load

where S*dep is non-marine sulphur deposition. NO3- is treated differently as only a small fraction of the deposition is leached into surface waters (the remainder is bound to the terrestrial part of the catchment). NO3- is therefore converted to an exceedance flux using runoff (Q).


Base cations

For the purposes of critical load calculations base cations are the ions of calcium (Ca2+), magnesium (Mg2+), potassium (K+) and sodium (Na+). All have a positive charge (denoted by the + symbols). Minor components, such ammonium ions (NH4+) are ignored.

Acid anions

For the purposes of critical load calculations, acid anions are the sulphate ion (SO42-), and the nitrate ion (NO3-). These have negative charge. Again, this definition ignores ions that play a minor role in acid surface waters, such a fluoride (F-). Chloride (Cl-) is not considered in the calculations as it is assumed to be derived soley from marine sources (it is used however to provide seasalt corrected values for the other ions used in the calculations).

Non-marine measurements

Critical loads relate only to inputs by acid deposition, the proportion of ions derived from neutral sea-spray inputs is removed from the sums of base cations and acid anions. Items noted by a * in the main text denote non-marine values.

It is assumed that all chloride is derived from marine sources. Therefore, it is simple to remove the non-marine fractions by subtracting them as a proportion of the measured chloride concentrations based on the known ratios of these ions in seawater. These ratios are known as sea salt correction factors.


  • Henriksen, A., Dickson, W. and Brakke, D.F. (1986) Estimates of critical loads to surface waters. In: Critical loads for sulphur and nitrogen (Ed. J. Nilsson). Nordic Council of Ministers, Copenhagen, pp. 87-120.
  • Henriksen, A., Kämäri, J., Posch, M. and Wilander, A. (1992) Critical loads of acidity: Nordic surface waters. Ambio 21(5), 356-363.