DRAFT DOCUMENT (February 2015) Prepared by M. Posch (CCE) To be reviewed by ICP M&M NFCs
VII. EXCEEDANCE CALCULATIONS
Updated by Max Posch, CCE, from the initial text of the Mapping Manual 2004
Updated: 16 February 2015
Please refer to this document as: CLRTAP, 2015. Exceedance calculations, Chapter VII of Manual on methodologies and criteria for modelling and mapping critical loads and levels and air pollution effects, risks and trends. UNECE Convention on Long-range Transboundary Air Pollution; accessed on [date of consultation] on Web at www.icpmapping.org .”
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TABLE OF CONTENT
VII. EXCEEDANCE CALCULATIONS ...... 1 VII.1 INTRODUCTION ...... 5 VII.2 BASIC DEFINITIONS ...... 5 VII.3 CONDITIONAL CRITICAL LOADS OF N AND S ...... 6 VII.4 TWO POLLUTANTS ...... 7 VII.5 THE AVERAGE ACCUMULATED EXCEEDANCE (AAE) ...... 10 VII.6 SURFACE WATERS ...... 11 VII.6.1 The SSWC model ...... 11 VII.6.2 The empirical diatom model ...... 11 VII.6.3 The FAB model ...... 11 VII.7 REFERENCES ...... 11
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Chapter VII – Exceedance calculations Page VII - 5
VII.1 INTRODUCTION In this Chapter the calculation of In Section VII.4 the exceedance of critical exceedances, i.e. the comparison of critical loads is defined that involves two pollutants loads/levels with depositions/ simultaneously, in Section VII.5 concentrations, is described. In Section exceedances are regionalised by defining VII.2 the basic definition of an exceedance the Average Accumulated Exceedance is given, including some historical remarks (AAE), and in Section VII.6 the on the origin and use of the word exceedances of surface water critical loads ‘exceedance’. In Section VII.3 the concept are considered. Most of the material of a conditional critical load of S and N is presented here is based on Posch et al. introduced, which allows treating these two (1997, 1999, 2001). acidifying pollutants separately, and thus also makes exceedance calculations straightforward.
VII.2 BASIC DEFINITIONS
The word 'exceedance' is defined as "the where Xdep is the deposition of pollutant X. amount by which something, especially a In the case of the critical level, the pollutant, exceeds a standard or comparison is with the respective permissible measurement" (The American concentration quantity. If the critical load is Heritage Dictionary of the English greater than or equal to the deposition, one Language, Fourth Edition 2000) and is a says that it is not exceeded or there is non- generally accepted term within the air exceedance of the critical load. pollution discipline. Interestingly, the Oxford An exceedance defined by eq. VII.1 can English Dictionary (OED) database has an obtain positive, negative or zero value. example of 'exceedance' from 1836 Since it is in most cases sufficient to know (Quinion 2004) – 36 years before Robert that there is non-exceedance, without Angus Smith is credited with coining the being interested in the magnitude of non- term 'acid rain' (Smith 1872). However, the exceedance, the exceedance can be also term 'acid rain' (in French) had already defined as: been used in 1845 by Ducros in a scientific (VII.2) journal article (Ducros 1845).
Critical loads and levels are derived to Ex (X ) = max { ,0 X − CL (X )} characterise the vulnerability of ecosystem dep dep X − CL (X ) X > CL (X ) (parts, components) in terms of a = dep dep ≤ deposition or concentration. If the critical 0 X dep CL (X ) load of pollutant X at a given location is smaller than the deposition of X at that An example of the application of this basic location, the critical load is said to be equation is the exceedance of the critical exceeded, and the difference is called load of nutrient N (see Chapter V), which is exceedance 1. In mathematical terms, the given by: = − exceedance Ex of the critical load CL (X) is (VII.3) Ex nut (N dep ) N dep CL nut (N) given as:
= − (VII.1) Ex (X dep ) X dep CL (X )
1 When comparing deposition(s) to target load (functions), one does not talk about the exceedance, but the ‘non-achievement’ of a target load.
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It should be noted that exceedances differ The exceedance of a critical load is often fundamentally from critical loads, as misinterpreted as the amount of excess exceedances are time-dependent. One can leaching, i.e. the amount leached above speak of the critical load of X for an the critical/acceptable leaching. This is in ecosystem, but not of the exceedance of it. general not the case as exemplified by the For exceedances the time (or the exceedance of the critical load of nutrient deposition) for which they have been N. The excess leaching due to the calculated has to be reported, since – deposition Ndep , Exle , is given as: especially in integrated assessment – it is (VII.4) Ex (N ) = N − N exceedances due to (past or future) le dep le ,accle anthropogenic depositions that are of Inserting the mass balance of N and the interest. deposition-dependent denitrification one Of course, the time-invariance of critical obtains for the excess leaching (eqs.V.2– loads and levels has its limitations, V.5): certainly when considering a geological Ex (N ) = 1( − f )⋅(N − CL N)( ) (VII.5) le dep de dep nut time frame. But also during shorter time = 1( − f )⋅ Ex (N ) periods, such as decades or centuries, one de nut dep can anticipate changes in the magnitude of which shows that a deposition reduction of critical loads due to global (climate) 1 eq/ha/yr reduces the leaching of N by change, which influences the processes only 1–fde eq/ha/yr. Only in the simplest from which critical loads are derived. An case, in which all terms of the mass early example of a study of the (first-order) balances are independent of depositions, influence of temperature and precipitation does the change in leaching equal the changes on critical loads of acidity and change in deposition. nutrient N in Europe can be found in Posch (2002).
VII.3 CONDITIONAL CRITICAL LOADS OF N AND S
The non-uniqueness of the critical loads of sulphur deposition Sdep can be derived from S and N acidity makes both their imple- the critical load function. We call it the mentation into integrated assessment conditional critical load of nitrogen , models and their communication to CL (N|S dep ), and it is computed as: decision makers more difficult. However, if (VII.6) one is interested in reductions of only one of the two pollutants, a unique critical load CL N)( if S ≥ CL S)( CL N |( S ) = min dep max can be derived, and thus also a unique dep − α ⋅ < CL max N)( S dep if S dep CL max S)( exceedance according to eq. VII.1 can be calculated. with CL N)( − CL N )( If emission reductions deal with nitrogen (VII.7) α = max min only, a unique critical load of N for a fixed CL max s)(
In Figure VII.1a the procedure for calculating CL (N|S dep ) is depicted graphically.
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(a) (b) dep dep S S
S1
CL(S|N1)
CL(S|N2) S2
Ndep Ndep CL(N|S1) CL(N|S2) N1 N2 Figure VII.1: Examples of computing (a) conditional critical loads of N for different S deposition values S1 and S2, and (b) conditional critical loads of S for different N deposition values N1 and N2. In an analogous manner a conditional When using conditional critical loads, the critical load of sulphur , CL (S|N dep ), for a following caveats should be kept in mind: fixed nitrogen deposition Ndep can be (a) A conditional critical load can be computed as: considered a true critical load only when the (VII.8) chosen deposition of the other pollutant is kept constant. 0 if N ≥ CL N)( dep max (b) If the conditional critical loads of CL N)( − N = max dep < < CL |( NS dep ) if CL min N)( N dep CL max N)( both pollutants are considered α CL S)( if N ≤ CL N)( max dep min simultaneously, care has to be exercised. It is not necessary to reduce the exceedances of both, but only one of them to reach non- α where is given by eq. VII.7. The exceedance for both pollutants; procedure for calculating CL (S|N dep ) is recalculating the conditional critical load of depicted graphically in Figure VII.1b. Setting the other pollutant results (in general) in Ndep = CL nut (N), the resulting conditional non-exceedance. However, if S > critical load has been termed minimum dep CL max (S) or Ndep > CL max (N), depositions critical load of sulphur : C Lmin (S) = have to be reduced at least to their CL (S|CL nut (N)). respective maximum critical load values, irrespective of the conditional critical loads.
VII.4 TWO POLLUTANTS
As shown in Chapter V, there is no unique (current) deposition of N and S. By critical load of N and S in the case of reducing Ndep substantially, one reaches acidity or in the case of a critical load the point Z 1 and thus non-exceedance function derived from multiple criteria without reducing Sdep ; on the other hand related to N and S. Consequently, there is one can reach non-exceedance by only no unique exceedance, although non- reducing Sdep (by a smaller amount) until exceedance is easily defined (as long as its reaching Z 3; finally, with a reduction of both amount is not important). This is illustrated Ndep and Sdep , one can reach non- in Figure VII.2: Let the point E denote the exceedance as well (e.g. point Z 2).
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dep S
CLSmax E Z1
Z2 Z3 CLSmin
N CLNmin CLNmax dep
Figure VII.2 : The N-S critical load function defined by two points (four values): (CLN min ,CLS max ) and (CLN max ,CLS min ). (thick line). The grey-shaded area below the critical load function defines deposition pairs (N dep ,S dep ) for which there is non-exceedance. The points E and Z1–Z3 demonstrate that non-exceedance can be attained in different ways, i.e. there is no unique exceedance.
Intuitively, the reduction required in N and (c) … Region 2 (e.g. point E 2): the S deposition to reach point Z 2 (see Figure exceedance in this region is defined as the VII.2), i.e. the shortest distance to the sum of N and S deposition reduction critical load function, seems a good needed to reach the corner-point point Z 2; measure for exceedance. Thus we define (d) … Region 3 (e.g. point E 3): the the exceedance for a given pair of exceedance is given by the sum of N and S depositions ( Ndep ,Sdep ) as the sum of the N deposition reduction, ExN +ExS , required to and S deposition reductions required to reach the point Z 3, with the line E 3–Z3 reach the critical load function by the perpendicular to the CLF; ‘shortest’ path. Figure 7.3 depicts the cases (e) … Region 4 (e.g. point E ): the that can arise, if the deposition falls … 4 exceedance is defined as the sum of N and (a) … on or below the critical load S deposition reduction needed to reach the function (Region 0). In this case the corner-point Z 4; exceedance is defined as zero (non- (f) … Region 5 (e.g. point E ): an N exceedance); 5 deposition reduction does not help; an S (b) … Region 1 (e.g. point E 1): An S deposition reduction is needed: the deposition reduction does not help; an N exceedance is defined as Sdep –CL max S. deposition reduction is needed: the exceedance is defined as Ndep –CL max N; Region 5 Region 4 dep
S E5 Region 3 E4
E3 Region 2
ExS Z5 Z4 E2 Z3 ExN
Region 0 Z2 Region 1 Z1 E1
Ndep Figure VII.3 : Illustration of the different cases for calculating the exceedance for a given critical load function.
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The exceedance function can be described by the following equation (the coordinates of the point Z 3 are denoted by ( N0,S0); see also Figure VII.2): (VII.9)
if , ∈ Region 0 0 − if , ∈ Region 1 − + − if , ∈ Region 2 , = − + − if , ∈ Region 3 − + − if , ∈ Region 4 − if , ∈ Region 5 The function thus defined fulfils the criteria The final difficulty in computing the of a meaningful exceedance function: it is Ex (Ndep ,Sdep ) is to determine into which of zero, if there is non-exceedance, positive the regions (Region 0 through Region 5 in when there is exceedance, and increases Figure VII.3) a given pair of deposition in value when the point ( Ndep ,Sdep ) moves (Ndep ,Sdep ) falls. Without going into the away from the critical load function. details of the geometrical considerations, a The computation of the exceedance FORTRAN subroutine is listed below, function requires the estimation of the which returns the number of the region as well as ExN and ExS . The coordinates of the point ( N0,S0) on the correspondences of the 4 quantities – critical load function. If ( x1,y1) and ( x2,y2) are two arbitrary points of a straight line g CLN min , CLS max , CLN max and CLS min – with the classical critical load function for and ( xe,ye) another point (not on that line), acidity, defined by CL S, CL N and then the coordinates ( x0,y0)=( N0,S0) of the max min point obtained by intersecting the line CL max N, intersected with the nutrient N critical load CL N (or CL N) are: passing through ( xe,ye) and perpendicular nut emp to g (called the ‘foot’ or ‘foot of the perpendicular’) are given by: = (VII.10a) and, if CL=nut N < CL max N: = + 2 = − 2 x0 ( 1sd 2vd ) d and y0 ( 2sd 1vd ) d with = (VII.10b) − = × = − = − 2 = 2 + 2 otherwise − d1 x2 x1 , d2 y2 y1 , d d1 d2 and = (VII.10c) (see also Posch= 0 et al. 2014). s = dx + dy , e 1 e 2 = − = − v dx 21 dy 11 yx 21 1xy 2
subroutine exceedNS (CLNmin,CLSmax,CLNmax,CLSmin,depN,depS,ExN,ExS,ireg) ! ! Returns the exceedances ExN and ExS (Ex=ExN+ExS) for N and S depositions ! depN and depS and the CLF defined by (CLNmin,CLSmax) and (CLNmax,CLSmin). ! The "region" in which (depN,depS) lies, is returned in ireg. ! implicit none ! real, intent(in) :: CLNmin, CLSmax, CLNmax, CLSmin, depN, depS real, intent(out) :: ExN, ExS integer, intent(out) :: ireg ! real :: dN, dS, dd, s, v, xf, yf
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! ExN = -1; ExS = -1; ireg = -1 if (CLNmin < 0 .or. CLSmax < 0 .or. CLNmax < 0 .or. CLSmin < 0) return ExN = depN; ExS = depS; ireg = 9 ! CLN = CLNmax if (CLSmax == 0 .and. CLNmax == 0) return ! CLS = CLSmin dN = CLNmin-CLNmax dS = CLSmax-CLSmin if (depS <= CLSmax .and. depN <= CLNmax .and. & & (depN-CLNmax)*dS <= (depS-CLSmin)*dN) then ! non-exceedance: ireg = 0 ExN = 0; ExS = 0 else if (depS <= CLSmin) then ireg = 1 ExN = depN-CLNmax; ExS = 0 else if (depN <= CLNmin) then ireg = 5 ExN = 0; ExS = depS-CLSmax else if (-(depN-CLNmax)*dN >=(depS-CLSmin)*dS) then ireg = 2 ExN = depN-CLNmax; ExS = depS-CLSmin else if (-(depN-CLNmin)*dN <= (depS-CLSmax)*dS) then ireg = 4 ExN = depN-CLNmin; ExS = depS-CLSmax else ireg = 3 dd = dN*dN+dS*dS s = depN*dN+depS*dS v = CLNmax*dS-CLSmin*dN xf = (dN*s+dS*v)/dd yf = (dS*s-dN*v)/dd ExN = depN-xf; ExS = depS-yf end if return end subroutine exceedNS
VII.5 THE AVERAGE ACCUMULATED EXCEEDANCE (AAE) To summarise exceedances in a grid cell This function is thus strongly determined by (e.g. for mapping) or country/region (for the total ecosystem area in a grid cell. In tabulation) one could resort to standard order to minimise this dependence and to statistical quantities such as mean or any obtain a quantity which is directly percentile of the distribution of individual comparable to depositions (in eq/ha/yr), we exceedance values (see Chapter VIII). define the average accumulated Alternatively, the so-called Average exceedance (AAE) by dividing the AE Accumulated Exceedance (Posch et al. function by the total ecosystem area: 2001) has been used, especially in n = integrated assessment, which is defined as (VII.12) AAE AE / ∑ Ai follows. i=1
Let Ex i be the exceedance for ecosystem i Instead of the total ecosystem area, one with area Ai, then we define the could also think of dividing by another area, accumulated exceedance (AE) of n e.g. the area exceeded for a given (fixed) ecosystems on a region (grid cell) as: deposition scenario. However, re- n calculating the AAE with new areas when = (VII.11) AE ∑ Ai Ex i depositions change can lead to i=1 inconsistencies: the new AAE could be For a given deposition, AE is total amount larger, despite declining deposition – as (in eq/yr) deposited in excess over the can be shown with simple examples. critical loads in the region in a given year.
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VII.6 SURFACE WATERS
Since exceedance calculations for the are treated here separately. The three critical loads for surface waters require critical load models mentioned are special considerations due to the described in Chapter V. peculiarities of (some of) the models, they
VII.6.1 THE SSWC MODEL In the SSWC model, sulphate is assumed the exceedance at present rates of to be a mobile anion (i.e. leaching equals retention of N in the catchment. Nitrogen deposition), whereas N is assumed to a processes are modelled explicitly in the large extent to be retained in the catchment FAB model (see below), and thus it is the by various processes. Therefore, only the only surface water model that can be used so-called present-day exceedance can be for comparing the effects of different N calculated from the leaching of N, Nle , deposition scenarios. In the above which is determined from the sum of the derivation we assumed that base cation measured concentrations of nitrate and deposition and net uptake did not change ammonia in the runoff. This present over time. exceedance of the critical load of acidity is If there is increased base cation deposition defined as (Henriksen and Posch 2001): due to human activities or a change in the = + − net uptake due to changes in management (VII.13) Ex (A) Sdep Nle CL (A) practices, this has to be taken into account where CL (A) is the critical load of acidity as in the exceedance calculations by computed with eq.V.50. No N deposition subtracting that anthropogenic BC* dep –Bc u data are required for this exceedance from Sdep +Nle . calculation; however, Ex (A) quantifies only
VII.6.2 THE EMPIRICAL DIATOM MODEL
For the diatom model the exceedance of where fN is the fraction of the N deposition the critical load of acidity is given by: contributing to acidification (see eq.V.66). = + ⋅ − (VII.14) Ex (A) Sdep f N Ndep CL (A) VII.6.3 THE FAB MODEL In the FAB model a critical load function for Again there is no unique exceedance for a surface waters is derived in the same way given pair of depositions ( Ndep ,Sdep ), but an as in the SMB model for soils, and the exceedance can be defined in an same considerations hold as given in analogous manner as above (see also Section VII.4. Henriksen and Posch 2001).
VII.7 REFERENCES
Ducros M (1845) Observation d’une pluie Posch M, Hettelingh J-P, De Smet PAM, acide. Journal de Pharmacie et de Downing RJ (eds) (1997) Calculation Chimie 3(7): 273-277 and mapping of critical thresholds in Henriksen A, Posch M (2001) Steady- Europe. Status Report 1997, state models for calculating critical Coordination Centre for Effects, RIVM loads of acidity for surface waters. Report 259101007, Bilthoven, Water, Air and Soil Pollution: Focus 1: Netherlands, iv+163 pp. www.wge- 375-398 cce.org
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Posch M, De Smet PAM, Hettelingh J-P, Quinion M (2004) “The example I quoted Downing RJ (eds) (1999) Calculation [on www.worldwidewords.org ] is and mapping of critical thresholds in known to the compilers of the OED Europe. Status Report 1999, (who will be writing an entry for Coordination Centre for Effects, RIVM ‘exceedance’ at some point) from their Report 259101009, Bilthoven, in-house database of unpublished Netherlands, iv+165 pp. www.wge- citations. They didn’t provide me with cce.org a full citation, only with the date” Posch M, Hettelingh J-P, De Smet PAM (personal communication to Julian (2001) Characterization of critical load Aherne in July 2004). – As of January exceedances in Europe. Water, Air 2014, no entry for ‘exceedance’ had and Soil Pollution 130: 1139-1144 yet been prepared for the OED (email by David Simpson from 25 Jan 2014). Posch M (2002) Impacts of climate change on critical loads and their Smith RA (1872) Air and Rain: The exceedances in Europe. Beginnings of a Chemical Environmental Science and Policy Climatology. Longmans, Green & Co., 5(4): 307-317 London, 600 pp. Posch M, Hettelingh J-P, Slootweg J, Reinds GJ (2014) Deriving critical loads based on plant diversity targets. Chapter 3 in: Slootweg J, Posch M, Hettelingh J-P, Mathijssen L (eds), Modelling and mapping the impacts of atmospheric deposition on plant species diversity in Europe: CCE Status Report 2014. RIVM Report 2014-0075, Coordination Centre for Effects, Bilthoven, Netherlands, pp. 41-46; www.wge-cce.org
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