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If only one pollutant contributes to an effect, e.g. nitrogen to eutrophication or sulphur to acidification (as assumed before 1994), a unique critical load (CL) can be calculated and compared with deposition (Dep), and the difference has been termed the exceedance of the critical load (Ex = DepCL)
In the case of two pollutants no unique exceedance exists as is illustrated in Figure 2. But for a given deposition of N and S an exceedance has been defined as the sum of the N and S deposition reductions required to achieve nonexceedance by taking the shortest path to the critical load function (see figure below). Within a grid cell, these exceedances are multiplied by the respective ecosystem area and summed to yield the socalled accumulated exceedance (AE) for that grid cell. In addition, the average accumulated exceedance (AAE) is defined by dividing the AE by the total ecosystem area of the grid cell, and which has thus the dimension of a deposition.
Critical load function for S and acidifying N (see Figure 1 ). It shows that no unique exceedance exists: Let the point E denote the current deposition of N and S. Reducing Ndep substantially one reaches point Z1 and thus nonexceedance without reducing Sdep; but nonexceedance can also be achieved by reducing Sdep only (by a smaller amount) until reaching Z3. However, an exceedance has been defined as the sum of Ndep and Sdep reductions (delta N+ delta S) which are needed to reach the critical load function on the shortest path (point Z2).
When comparing present or feasible future deposition scenarios with European critical loads it appeared that nonexceedance could not be reached everywhere. Thus it was decided by integrated assessment modelers to use uniform percentage reductions of the excess depositions, socalled gap closures, for the definition of reduction scenarios. In the following we summarize the different gap closure methods used and illustrate them for the case of a single pollutant. In the 1994 Oslo Protocol only sulphur was
considered as acidifying pollutant (N deposition was fixed; it determined, together with N uptake and immobilization, the sulfur fraction). Furthermore, taking into account the uncertainties in the CL calculations, it was decided to use the 5th percentile of the critical load CDF in a grid cell as the only value representing the ecosystem sensitivity of that cell. And the exceedance was simply the difference between the (current) S deposition and that 5th percentile critical load. This is illustrated in Figure 3a: Critical loads and deposition are plotted along the horizontal axis and the (relative) ecosystem area along the vertical axis. The thick solid and the thick broken lines are two examples of critical load CDFs (which have the same 5th percentile critical load, indicated by `CL'). `D0' indicates the (present) deposition, which is higher than the CLs for 85% of the ecosystem area. The difference between `D0' and `CL' is the exceedance in that grid cell. It was decided to reduce the exceedance everywhere by a fixed percentage, i.e. to "close the gap" between (present) deposition and (5th percentile) critical load.
In order to take into account all critical loads within a grid cell (and not only the 5th percentile), it was suggested to use an ecosystem area gap closure instead of the deposition gap closure. This is illustrated in the figure above: for a given deposition `D0' to a grid cell the ecosystem area unprotected, i.e. with deposition exceeding the critical loads, can be read from the vertical axis. After agreeing to a certain (percent) reduction of the unprotected area (e.g. 60%), it is easy to compute for a given CDF the required deposition reduction (`D1' and `D2' in the figure above). Another important reason to use the ecosystem area gap closure is that it can be easily generalized to two (or more) pollutants, which is not the case for a depositionbased exceedance. This generalization became necessary in the preparation for the "multipollutant, multieffect" protocol in the case of acidity critical loads, since both N and S are contributing to acidification. Critical load values have been replaced by critical load functions and percentiles are replaced by ecosystem protection isolines. However the use of the area gap closure becomes problematic, if only a few critical load values or functions are given for a grid cell. In such a case the CDF becomes discontinuous and (small) changes in deposition may result in either no increase in the protected area at all or large jumps in the area protected.
To remedy the problem with the area gap closure caused by discontinuous CDFs, the accumulated exceedance (AE) concept has been introduced. In the case of one pollutant, the AE is given as the area under the CDF of the critical loads. Deposition reductions are quantified in terms of an AE (or AAE) gap closure, also illustrated in Figure 3c: A 60% AE gap closure is achieved by a deposition `D1' which reduces the total grey area by 60%, resulting in the dark grey area; also the corresponding protection percentage (67%) can easily be derived. The greatest advantage of the AE and AAE is that it varies smoothly when deposition is varied, thus facilitating optimization calculations in integrated assessments.
The advantages and disadvantages of the three gap closure methods described above are summarized in the following table: Gap closure methods and their advantages and disadvantages

Advantages 
Disadvantages/Shortcomings 

Deposition gap closure: (used for the 1994 Sulphur Protocol) 
 Easy to use even for discontinuous CDFs (e.g. grid cells withonly one CL) 
 Takes only one CL value (percentile) into account  May result in no increase in protected area  Difficult to define for 2 pollutants 

Ecosystem area gap closure 
 In line with CL definition  Easy to apply to any number of pollutants 
 Difficult (or even impossible) to define a gap closure for discontinuous CDFs (e.g. grid cells with only one ecosystem) 

Accumulated Exceedance (AE) gap closure: (used for the 1999 Gothenburg Protocol) 
 AE (and AAE) is a smooth and convex function of depositions even for discontinuous CDFs 
 AE stretches the limits of the critical load definition (linear damage function!)  Definition not unique for more than 2 pollutants 
last update 5 Jun 2013