# 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 (HCO_{3}^{- }) 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):

_{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:

_{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 NO_{3}^{-} are close to zero in near-pristine Scottish lochs and
*background* SO_{4}^{2-} (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
NO_{3}^{-} leaching:

^{*}

_{dep}+ ( [NO

_{3}

^{- }]. Q ) ) - critical load

where S^{*}_{dep} is non-marine sulphur deposition.
NO_{3}^{-} 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).
NO_{3}^{-} is therefore converted to an exceedance flux using runoff (Q).

#### Notes

##### Base cations

For the purposes of critical load calculations base cations are the ions of calcium (Ca^{2+}), magnesium
(Mg^{2+}), potassium (K^{+}) and sodium (Na^{+}). All have a positive charge (denoted by the +
symbols). Minor components, such ammonium ions (NH_{4}^{+}) are ignored.

##### Acid anions

For the purposes of critical load calculations, acid anions are the sulphate ion
(SO_{4}^{2-}), and the nitrate ion (NO_{3}^{-}).
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*.

#### References

- 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. (1986)
- Critical loads of acidity: Nordic surface waters. Ambio 21(5), 356-363. (1992)