Ecosystems impacts

Within the European domain and East Asia domains, GAINS quantifies the deposition of total nitrogen (N) as the sum of oxidized (\(NO_x\)) and reduced (\(NH_y\)) nitrogen compounds, as well as deposition of sulfur, using linear transfer coefficients from the EMEP CTM For quantifying ecosystems risks from acidification and eutrophication, the GAINS models employs the critical loads approach, with Critical Loads (CL) being defined to characterise the vulnerability of (parts of) an ecosystem in terms of deposition. If the CL of pollutant X at a given location is smaller than the deposition of X at that location, it is said that the CL is exceeded and the difference is called exceedance.

Eutrophication

For a critical load of eutrophication \(CL_{eut}N\) (also called CL of nutrient N), the exceedance \(Ex_{eut}N\) for a deposition \(N_{dep}\) is calculated as:

\begin{equation} Ex_{eut}(N_{dep}) = \max\{0, N_{dep} - CL_{eut}N\} = \begin{cases} N_{dep} - CL_{eut}N & \text{if } N_{dep} > CL_{eut}N \\ 0 & \text{if } N_{dep} \leq CL_{eut}N \tag{1} \end{cases} \end{equation}

where:

\(N_{dep}, CL_{eut}N\)	N deposition and Critical Load of N for eutrophication respectively
\(Ex_{eut}(N_{dep})\)	Exceedance of N eutrophication Critical Load for a given N deposition \(N_{dep}\)

In case exceedances are negative, they are simply set to zero.

Acidification

For acidification impacts, there is no unique critical load of S and N acidity. Instead, acidity CL are defined by a trapezoidal-shaped critical load function (CLF), defined by the quantities \(CL_{max}S\), \(CL_{min}N\), and \(CL_{max}N\). Thus, the exceedance is defined as the sum of the N- and S-deposition reductions needed to reach the closest point on the CLF, with zero exceedance for deposition pairs (\(N_{dep}\), \(S_{dep}\)) lying below the CLF (see below Figure 1).

Figure 1 Critical Load Function (CLF) for acidifying Sulfur and Nitrogen defined by \(CL_{max}S\), \(CL_{min}N\), and \(CL_{max}N\) (thick black line). The grey-shaded area below the CLF (region 0) defines deposition pairs (\(N_{dep}\), \(S_{dep}\)) for which there is non-exceedance. The points E1 to E4 refer to deposition pairs in four different regions and the way the exceedance (\(N_{ex}\), \(S_{ex}\)) is computed for a point in Region 2.

Given the above Figure 1, the exceedance of N and S acidity CLs is obtained as follows:

\begin{equation} Ex_{ac}(N_{dep},S_{dep}) = \begin{cases} 0 & \text{if } (N_{dep},S_{dep}) \in \text{Region } 0 \\ N_{dep} - CL_{max}N + S_{dep} & \text{if } (N_{dep},S_{dep}) \in \text{Region } 1 \\ N_{dep} - N_0 + S_{dep} - S_0 = (N_{ex},S_{ex}) & \text{if } (N_{dep},S_{dep}) \in \text{Region } 2 \\ N_{dep} - CL_{min}N + S_{dep} - CL_{max}S & \text{if } (N_{dep},S_{dep}) \in \text{Region } 3 \\ S_{dep} - CL_{max}S & \text{if } (N_{dep},S_{dep}) \in \text{Region } 4 \tag{2} \end{cases} \end{equation}

where:

\(N_0, S_0, N_{dep},S_{dep},CL_{max}S,CL_{min}N,CL_{max}N\)	N and S deposition for point Z2, N and S deposition, maximum Critical Load of S, and minimum and maximum Critical Load of N respectively
\(Ex_{ac}(N_{dep},S_{dep})\)	Exceedance of N and S acidity Critical Load for a given deposition pair (\(N_{dep}\), \(S_{dep}\))

To obtain a single exceedance value for a given grid cell or an entire region, GAINS computes the Average Accumulated Exceedance (AAE), defined as follows:

\begin{align} AAE = \frac {\sum_{j=1}^n A_j Ex_j} {\sum_{j=1}^n A_j} \tag{3} \end{align}

where:

j, n	Ecosystem, number of ecosystems respectively
\(A_j\)	Area of ecosystem j
\(Ex_j\)	Exceedance of N or S Critical Load for ecosystem A_j
AAE	Average Accumulated Exceedance of N or S Critical Load

The AAE is thus expressed as the area-weighted exceedance of the CLs for the individual ecosystems. To remain consistent with the latter definition, \(Ex_j\) needs to be set to zero if the CL is not exceeded.