The methods for calculating critical loads are based on internationally agreed approaches and have been adapted to make use of national data sets that are available for producing UK maps. The methods currently used in the UK to calculate acidity and nutrient nitrogen critical loads are summarised below:

- Critical Loads of acidity
- Critical Loads of nutrient nitrogen
- Empirical critical load for nutrient nitrogen
- Mass balance critical loads for nutrient nitrogen
- Calculation and mapping of critical load exceedances
- Dynamic Modelling

## Critical loads of acidity: Simple Mass Balance (SMB) equation

The critical loads for acidity are designed to protect the soil. The SMB equation is used for calculating acidity critical loads for woodland ecosystems. The SMB method provides critical loads for systems at steady-state. This model is based on balancing the acidic inputs to and outputs from a system, to derive a critical load that ensures a critical chemical limit (related to effects on the ecosystem) is not exceeded. The equation has been derived from a charge balance of ions in leaching fluxes from the soil compartment, combined with mass balance equations for the inputs, sinks, sources and outputs of sulphur and nitrogen. The simplified equation between the sources and sinks of sulphur and nitrogen is:

**S _{dep} + N_{dep} = BC_{dep} – Cl_{dep} + BC_{w} – BC_{u} + N_{I} + N_{u} + N_{de} - ANC_{le}**

Where:

**BC** = the sum of base cations (Ca+Mg+K+Na).

Subscripts _{dep, le, w, u, i} and _{de} represent deposition, leaching, weathering, uptake, immobilisation and denitrification processes.

**ANC _{le}** = the leaching of Acid Neutralising Capacity.

The simplified mass balance equation is converted to a critical load equation by the addition of the ‘biological limit’:

**CL (S + N) = CL(S) + CL(N) = BC _{dep} – Cl_{dep} + BC_{w} – BC_{u} + N_{I} + N_{u} + N_{de} - ANC_{le(crit)}**

Where:

**CL(S)**, **CL(N)** and **CL(S+N)** represent the critical loads of sulphur, nitrogen and sulphur plus nitrogen, respectively.

**ANC _{le(crit)}** = the leaching of Acid Neutralising Capacity with the addition of the biological limit denoted as

**. Further details of how this is calculated are given by the United Kingdom National Focal Centre (UK NFC).**

_{crit}If sulphur deposition is zero, then the equation above becomes the maximum critical load of acidifying nitrogen **CL _{max} (N)**. However, if nitrogen deposition is zero, then the equation above is not the maximum critical load of sulphur because nitrogen acidity sinks cannot compensate for incoming sulphur acidity. Therefore, the

**CL**is defined as:

_{max}(S)The SMB equation is parameterised according to the appropriate critical chemical criteria and critical limits that will protect the receptor (soils) from the adverse effects of acidification. A critical molar ratio of calcium to aluminium of one in soil solution is a common criterion applied in the SMB to protect the fine roots of trees. This criterion is used for mineral and organo-mineral soils. In the case of peat soils, critical loads of acidity use a critical soil solution pH value of 4.4.

Most tree species grow well in soils of considerable lower pH. However, a critical soil solution pH of 4.4 was set to protect soils to enable future non-woodland land use and possible reversion to semi-natural vegetation. Further investigation of pH values of pristine peat soils is currently in progress.

In the UK, the SMB equation is applied to all woodland ecosystems including both managed and unmanaged woodlands.

## Critical Loads of nutrient nitrogen

Enhanced nitrogen deposition to forest ecosystems can lead to acidification or eutrophication. The latter can have major impacts on plant communities leading to changes in species composition and the sensitivity of vegetation to environmental stresses such as drought, frost or insect predation. Therefore, methods have been developed to set critical loads to protect against these adverse effects. Two approaches are currently in use: empirical and mass balance; both methods are described, briefly, below.

**Empirical critical load for nutrient nitrogen**

Empirical nutrient nitrogen critical loads are based on the results of experimental studies and field observations, or on 'expert judgement'.

Ranges of critical load values are given to take account of:

- Inter-ecosystem variability due to factors such as climate and management practice
- The range of experimental treatments where an effect was observed or not observed
- Uncertainties in deposition values where critical loads are based on field observations.

The ranges of critical load values recommended are also accompanied by one of the following 'reliability' scores:

- 'Reliable' - where a number of published papers of various studies show comparable results
- 'Quite reliable' when the results of some studies are comparable
- 'Expert judgement' or 'informed estimate' where no data are available for a particular ecosystem type.

Empirical critical loads for unmanaged woodland ecosystems are set to protect the woodland ground flora from adverse effects, rather than to protect the trees themselves. Atlantic oakwoods are a special case, with a lower empirical critical load set to protect the epiphytic lichen community.

## Mass balance critical loads for nutrient nitrogen

The steady state mass balance for nutrient nitrogen is calculated as:

**CL _{nut}N = N_{u} + N_{i} + N_{le(acc)} + N_{de}**

Where:

**N _{u}** = nitrogen uptake

**N**= nitrogen immobilisation

_{i}**N**= acceptable level of nitrogen leaching

_{le(acc)}**N**= denitrification

_{de}This method is based on the above equation, which balances all significant long-term inputs and outputs of nitrogen for terrestrial ecosystems, assuming that the system is at equilibrium. In this context, long-term is defined as at least one forest rotation or 100 years. Critical loads calculated using this method are set to:

- Prevent an increase in leaching of nitrogenous compounds, particularly nitrate, which may result in damage to the terrestrial or, linked, aquatic systems
- Ensure sustainable production by limiting nitrogen uptake and removal to a level which will not result in deficiencies of other nutrients.

In the UK, the mass balance equation has been used to calculate nutrient nitrogen critical loads for managed coniferous and deciduous woodland ecosystems. The national maps are currently based on the minimum of the empirical or mass balance critical load values.

## Calculation and mapping of critical load exceedances

Critical loads are compared with acidifying or eutrophying deposition to determine the excess deposition above the critical load; ie the exceedance.

**Exceedance = Deposition – Critical Load**

For eutrophication, the exceedance is calculated using total nitrogen deposition (derived from nitrogen oxides and ammonia).

For acidification, the contribution of both sulphur and nitrogen compounds must be taken into account as explained in the methods for calculating the critical loads of acidity above. It is these 'minimum' and 'maximum' critical loads that are used in the calculation of critical loads exceedance for acidity.

In addition, the “accumulated exceedance” (**AE**) can be calculated, where exceedance is summed over the whole habitat area:

**AE = exceedance * exceeded habitat area**

Therefore, the AE is a measure of exceedance that takes into account **both the magnitude of exceedance and the habitat area exceeded**.

## Dynamic Modelling

The current empirical and steady state mass balance critical load methodologies define receptor tolerance to a given pollutant. However, they do not provide information on the response of the receptor to temporal variations in the pollutant, including the periods prior to damage being observed in response to exceedance, and during recovery to reduced pollutant input. There are two factors that can give rise to delays in the cause-effects relationships:

- Biogeochemical processes can delay the chemical response of soils
- Biological processes can further delay the response of indicator organisms, eg damage to trees in forest ecosystems.

Pressure to evaluate the impact of planned reductions in S and N emissions now requires the application of methodologies capable of representing the dynamics of ecosystem change in the above processes. Thus, process-based dynamic models have been developed such as:

- SAFE
- MAGIC
- VSD (Very Simple Dynamic Model).

The evaluation and testing of these models is reliant on the availability of site specific data-sets, including both input parameters required for running the models and, also, output data-sets on which an assessment of the performance of the models can be based. The evaluation and testing of these models can be found on the Terrestrial Umbrella website.